diff --git a/.gitignore b/.gitignore index b6f12bf..2af7f81 100644 --- a/.gitignore +++ b/.gitignore @@ -4,9 +4,10 @@ *.mat # dropbox *.dropbox -# winows files +# windows files *.ini # windows thumb *.db # Sandboxing -/scratch \ No newline at end of file +/scratch +/logs \ No newline at end of file diff --git a/.gitmodules b/.gitmodules index 198ca6e..d8b1b5c 100644 --- a/.gitmodules +++ b/.gitmodules @@ -22,3 +22,9 @@ [submodule "bin/ciecam02"] path = bin/ciecam02 url = https://github.com/brycehenson/CIECAM02.git +[submodule "bin/MBeautifier"] + path = bin/MBeautifier + url = https://github.com/davidvarga/MBeautifier.git +[submodule "bin/dependency_matlab-master/dependency_matlab"] + path = bin/dependency_matlab-master/dependency_matlab + url = https://github.com/dohyun-cse/dependency_matlab diff --git a/README.md b/README.md index 9beb53d..dc118d2 100644 --- a/README.md +++ b/README.md @@ -1,13 +1,21 @@ # Core_BEC_Analysis -**Bryce M. Henson, [Jacob A. Ross](https://github.com/GroundhogState)** -A reasonably comprehensive library analysis of data generated in the He* BEC group. +**Bryce M. Henson, [Jacob A. Ross](https://github.com/GroundhogState),[Kieran F. Thomas](https://github.com/KF-Thomas),[David Shin](https://github.com/spicydonkey)** +A reasonably comprehensive toolset for analysis of data generated in the He* BEC group. **Status:** This Code is **ready for use in other projects**. Unit Testing is implemented for **most** functions. Integration/system testing is **not** implemented. -## Install +## Install + +As a submodule (most common usage) +``` +git submodule add -b dev https://github.com/brycehenson/Core_BEC_Analysis.git lib/Core_BEC_Analysis +``` + +Solo (not recomended) ``` git clone --recursive https://github.com/brycehenson/Core_BEC_Analysis.git ``` -then to update + +to update and initalize all the sub-sub-modules ``` git submodule update --init --recursive --remote --merge ``` diff --git a/bin/DERIVESTsuite/ReadMe.rtf b/bin/DERIVESTsuite/ReadMe.rtf new file mode 100644 index 0000000..f53051b --- /dev/null +++ b/bin/DERIVESTsuite/ReadMe.rtf @@ -0,0 +1,38 @@ +{\rtf1\mac\ansicpg10000\cocoartf102 +{\fonttbl\f0\fswiss\fcharset77 Helvetica;} +{\colortbl;\red255\green255\blue255;\red0\green0\blue0;} +\margl1440\margr1440\vieww9000\viewh9000\viewkind0 +\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\ql\qnatural + +\f0\fs24 \cf2 Numerical differentiation \ +\ +\pard\pardeftab720\ql\qnatural +\cf2 Author: John D'Errico\ +e-mail: woodchips@rochester.rr.com\ +Release: 1.0\ +Release date: 3/7/2007\ +\ +This is a suite of tools to solve automatic numerical differentiation problems in one or more variables. All of these methods also produce error estimates on the result.\ +A pdf file is also provided to explain the theory behind these tools.\ +\ +\ +DERIVEST.m\ +A flexible tool for the computation of derivatives of order 1 through 4 on any scalar function. Finite differences are used in an adaptive manner, coupled with a Romberg extrapolation methodology to provide a maximally accurate result. The user can configure many of the options, changing the order of the method or the extrapolation, even allowing the user to specify whether central, forward or backward differences are used.\ +\ +GRADEST.m\ +Computes the gradient vector of a scalar function of one or more variables at any location.\ +\ +JACOBIANEST.m\ +Computes the Jacobian matrix of a vector (or array) valued function of one or more variables.\ +\ +DIRECTIONALDIFF.m\ +Computes the directional derivative (along some line) of a scalar function of one or more variables.\ +\ +HESSIAN.m\ +Computes the Hessian matrix of all 2nd partial derivatives of a scalar function of one or more variables.\ +\ +HESSDIAG.m\ +The diagonal elements of the Hessian matrix are the pure second order partial derivatives. This function is called by HESSIAN.m, but since some users may need only the diagonal elements, I've provided HESSDIAG.\ +\ +\ +} \ No newline at end of file diff --git a/bin/DERIVESTsuite/demo/derivest_demo.m b/bin/DERIVESTsuite/demo/derivest_demo.m new file mode 100644 index 0000000..de703df --- /dev/null +++ b/bin/DERIVESTsuite/demo/derivest_demo.m @@ -0,0 +1,95 @@ +% DERIVEST demo script + +% This script file is designed to be used in cell mode +% from the matlab editor, or best of all, use the publish +% to HTML feature from the matlab editor. Older versions +% of matlab can copy and paste entire blocks of code into +% the Matlab command window. + +% DERIVEST is property/value is driven for its arguments. +% Properties can be shortened to the + +%% derivative of exp(x), at x == 0 +[deriv,err] = derivest(@(x) exp(x),0) + +%% DERIVEST can also use an inline function +[deriv,err] = derivest(inline('exp(x)'),0) + +%% Higher order derivatives (second derivative) +% Truth: 0 +[deriv,err] = derivest(@(x) sin(x),pi,'deriv',2) + +%% Higher order derivatives (third derivative) +% Truth: 1 +[deriv,err] = derivest(@(x) cos(x),pi/2,'der',3) + +%% Higher order derivatives (up to the fourth derivative) +% Truth: sqrt(2)/2 = 0.707106781186548 +[deriv,err] = derivest(@(x) sin(x),pi/4,'d',4) + +%% Evaluate the indicated (default = first) derivative at multiple points +[deriv,err] = derivest(@(x) sin(x),linspace(0,2*pi,13)) + +%% Specify the step size (default stepsize = 0.1) +deriv = derivest(@(x) polyval(1:5,x),1,'deriv',4,'FixedStep',1) + +%% Provide other parameters via an anonymous function +% At a minimizer of a function, its derivative should be +% essentially zero. So, first, find a local minima of a +% first kind bessel function of order nu. +nu = 0; +fun = @(t) besselj(nu,t); +fplot(fun,[0,10]) +x0 = fminbnd(fun,0,10,optimset('TolX',1.e-15)) +hold on +plot(x0,fun(x0),'ro') +hold off + +deriv = derivest(fun,x0,'d',1) + +%% The second derivative should be positive at a minimizer. +deriv = derivest(fun,x0,'d',2) + +%% Compute the numerical gradient vector of a 2-d function +% Note: the gradient at this point should be [4 6] +fun = @(x,y) x.^2 + y.^2; +xy = [2 3]; +gradvec = [derivest(@(x) fun(x,xy(2)),xy(1),'d',1), ... + derivest(@(y) fun(xy(1),y),xy(2),'d',1)] + +%% Compute the numerical Laplacian function of a 2-d function +% Note: The Laplacian of this function should be everywhere == 4 +fun = @(x,y) x.^2 + y.^2; +xy = [2 3]; +lapval = derivest(@(x) fun(x,xy(2)),xy(1),'d',2) + ... + derivest(@(y) fun(xy(1),y),xy(2),'d',2) + +%% Compute the derivative of a function using a central difference scheme +% Sometimes you may not want your function to be evaluated +% above or below a given point. A 'central' difference scheme will +% look in both directions equally. +[deriv,err] = derivest(@(x) sinh(x),0,'Style','central') + +%% Compute the derivative of a function using a forward difference scheme +% But a forward scheme will only look above x0. +[deriv,err] = derivest(@(x) sinh(x),0,'Style','forward') + +%% Compute the derivative of a function using a backward difference scheme +% And a backward scheme will only look below x0. +[deriv,err] = derivest(@(x) sinh(x),0,'Style','backward') + +%% Although a central rule may put some samples in the wrong places, it may still succeed +[d,e,del]=derivest(@(x) log(x),.001,'style','central') + +%% But forcing the use of a one-sided rule may be smart anyway +[d,e,del]=derivest(@(x) log(x),.001,'style','forward') + +%% Control the behavior of DERIVEST - forward 2nd order method, with only 1 Romberg term +% Compute the first derivative, also return the final stepsize chosen +[deriv,err,fdelta] = derivest(@(x) tan(x),pi,'deriv',1,'Style','for','MethodOrder',2,'RombergTerms',1) + +%% Functions should be vectorized for speed, but its not always easy to do. +[deriv,err] = derivest(@(x) x.^2,0:5,'deriv',1) +[deriv,err] = derivest(@(x) x^2,0:5,'deriv',1,'vectorized','no') + + diff --git a/bin/DERIVESTsuite/demo/html/derivest_demo.html b/bin/DERIVESTsuite/demo/html/derivest_demo.html new file mode 100644 index 0000000..83f1222 --- /dev/null +++ b/bin/DERIVESTsuite/demo/html/derivest_demo.html @@ -0,0 +1,337 @@ + + + + + + + + derivest_demo + + + + +
+

Contents

+
+ + 
% DERIVEST demo script
+
+% This script file is designed to be used in cell mode
+% from the matlab editor, or best of all, use the publish
+% to HTML feature from the matlab editor. Older versions
+% of matlab can copy and paste entire blocks of code into
+% the Matlab command window.
+
+% DERIVEST is property/value is driven for its arguments.
+% Properties can be shortened to the
+

derivative of exp(x), at x == 0

[deriv,err] = derivest(@(x) exp(x),0)
+
deriv =
+            1
+err =
+   1.4046e-14
+

DERIVEST can also use an inline function

[deriv,err] = derivest(inline('exp(x)'),0)
+
deriv =
+            1
+err =
+   1.4046e-14
+

Higher order derivatives (second derivative)

+

Truth: 0

[deriv,err] = derivest(@(x) sin(x),pi,'deriv',2)
+
deriv =
+  -5.5372e-19
+err =
+    1.865e-18
+

Higher order derivatives (third derivative)

+

Truth: 1

[deriv,err] = derivest(@(x) cos(x),pi/2,'der',3)
+
deriv =
+            1
+err =
+   4.3657e-12
+

Higher order derivatives (up to the fourth derivative)

+

Truth: sqrt(2)/2 = 0.707106781186548

[deriv,err] = derivest(@(x) sin(x),pi/4,'d',4)
+
deriv =
+      0.70711
+err =
+   1.9122e-05
+

Evaluate the indicated (default = first) derivative at multiple points

[deriv,err] = derivest(@(x) sin(x),linspace(0,2*pi,13))
+
deriv =
+  Columns 1 through 7
+            1      0.86603          0.5            0         -0.5     -0.86603           -1
+  Columns 8 through 13
+     -0.86603         -0.5            0          0.5      0.86603            1
+err =
+  Columns 1 through 7
+   1.0412e-15   1.4725e-15   2.5102e-14            0   1.3754e-14   2.7429e-14   1.8034e-15
+  Columns 8 through 13
+   3.0284e-14   4.9044e-14            0   3.2092e-15   1.2987e-13   2.5504e-15
+

Specify the step size (default stepsize = 0.1)

deriv = derivest(@(x) polyval(1:5,x),1,'deriv',4,'FixedStep',1)
+
deriv =
+           24
+

Provide other parameters via an anonymous function

+

At a minimizer of a function, its derivative should be essentially zero. So, first, find a local minima of a first kind bessel + function of order nu. + 

nu = 0;
+fun = @(t) besselj(nu,t);
+fplot(fun,[0,10])
+x0 = fminbnd(fun,0,10,optimset('TolX',1.e-15))
+hold on
+plot(x0,fun(x0),'ro')
+hold off
+
+deriv = derivest(fun,x0,'d',1)
+
x0 =
+       3.8317
+deriv =
+  -2.3285e-09
+

The second derivative should be positive at a minimizer.

deriv = derivest(fun,x0,'d',2)
+
deriv =
+      0.40276
+

Compute the numerical gradient vector of a 2-d function

+

Note: the gradient at this point should be [4 6]

fun = @(x,y) x.^2 + y.^2;
+xy = [2 3];
+gradvec = [derivest(@(x) fun(x,xy(2)),xy(1),'d',1), ...
+           derivest(@(y) fun(xy(1),y),xy(2),'d',1)]
+
gradvec =
+            4            6
+

Compute the numerical Laplacian function of a 2-d function

+

Note: The Laplacian of this function should be everywhere == 4

fun = @(x,y) x.^2 + y.^2;
+xy = [2 3];
+lapval = derivest(@(x) fun(x,xy(2)),xy(1),'d',2) + ...
+           derivest(@(y) fun(xy(1),y),xy(2),'d',2)
+
lapval =
+     4
+

Compute the derivative of a function using a central difference scheme

+

Sometimes you may not want your function to be evaluated above or below a given point. A 'central' difference scheme will + look in both directions equally. + 

[deriv,err] = derivest(@(x) sinh(x),0,'Style','central')
+
deriv =
+     1
+err =
+   1.0412e-15
+

Compute the derivative of a function using a forward difference scheme

+

But a forward scheme will only look above x0.

[deriv,err] = derivest(@(x) sinh(x),0,'Style','forward')
+
deriv =
+     1
+err =
+   3.1516e-15
+

Compute the derivative of a function using a backward difference scheme

+

And a backward scheme will only look below x0.

[deriv,err] = derivest(@(x) sinh(x),0,'Style','backward')
+
deriv =
+     1
+err =
+   3.1516e-15
+

Although a central rule may put some samples in the wrong places, it may still succeed

[d,e,del]=derivest(@(x) log(x),.001,'style','central')
+
d =
+         1000
+e =
+   1.7072e-10
+del =
+   3.0518e-05
+

But forcing the use of a one-sided rule may be smart anyway

[d,e,del]=derivest(@(x) log(x),.001,'style','forward')
+
d =
+         1000
+e =
+   6.5547e-08
+del =
+   0.00012207
+

Control the behavior of DERIVEST - forward 2nd order method, with only 1 Romberg term

+

Compute the first derivative, also return the final stepsize chosen

[deriv,err,fdelta] = derivest(@(x) tan(x),pi,'deriv',1,'Style','for','MethodOrder',2,'RombergTerms',1)
+
deriv =
+            1
+err =
+   2.8399e-13
+fdelta =
+    0.0011984
+

Functions should be vectorized for speed, but its not always easy to do.

[deriv,err] = derivest(@(x) x.^2,0:5,'deriv',1)
+[deriv,err] = derivest(@(x) x^2,0:5,'deriv',1,'vectorized','no')
+
deriv =
+            0            2            4            6            8           10
+err =
+            0   4.6563e-15   9.3127e-15    1.178e-14   1.8625e-14   2.3559e-14
+deriv =
+            0            2            4            6            8           10
+err =
+            0   4.6563e-15   9.3127e-15    1.178e-14   1.8625e-14   2.3559e-14
+


+ Published with MATLAB® 7.4

+
+ + + \ No newline at end of file diff --git a/bin/DERIVESTsuite/demo/html/derivest_demo.png b/bin/DERIVESTsuite/demo/html/derivest_demo.png new file mode 100644 index 0000000..593c1e9 Binary files /dev/null and b/bin/DERIVESTsuite/demo/html/derivest_demo.png differ diff --git a/bin/DERIVESTsuite/demo/html/derivest_demo_01.png b/bin/DERIVESTsuite/demo/html/derivest_demo_01.png new file mode 100644 index 0000000..b4b875d Binary files /dev/null and b/bin/DERIVESTsuite/demo/html/derivest_demo_01.png differ diff --git a/bin/DERIVESTsuite/demo/html/multivariable_calc_demo.html b/bin/DERIVESTsuite/demo/html/multivariable_calc_demo.html new file mode 100644 index 0000000..e29ad59 --- /dev/null +++ b/bin/DERIVESTsuite/demo/html/multivariable_calc_demo.html @@ -0,0 +1,290 @@ + + + + + + + + multivariable_calc_demo + + + + +
+

Contents

+
+ + 
% Multivariate calculus demo script
+
+% This script file is designed to be used in cell mode
+% from the matlab editor, or best of all, use the publish
+% to HTML feature from the matlab editor. Older versions
+% of matlab can copy and paste entire blocks of code into
+% the Matlab command window.
+
+% Typical usage of the gradient and Hessian might be in
+% optimization problems, where one might compare an analytically
+% derived gradient for correctness, or use the Hessian matrix
+% to compute confidence interval estimates on parameters in a
+% maximum likelihood estimation.
+

Gradient of the Rosenbrock function at [1,1], the global minimizer

rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;
+% The gradient should be zero (within floating point noise)
+[grad,err] = gradest(rosen,[1 1])
+
grad =
+   3.6989e-20            0
+err =
+   1.4545e-18            0
+

The Hessian matrix at the minimizer should be positive definite

H = hessian(rosen,[1 1])
+% The eigenvalues of h should be positive
+eig(H)
+
H =
+          842         -420
+         -420          210
+ans =
+      0.39939
+       1051.6
+

Gradient estimation using gradest - a function of 5 variables

[grad,err] = gradest(@(x) sum(x.^2),[1 2 3 4 5])
+
grad =
+            2            4            6            8           10
+err =
+   1.2533e-14   2.5067e-14   3.4734e-14   5.0134e-14    2.836e-14
+

Simple Hessian matrix of a problem with 3 independent variables

[H,err] = hessian(@(x) x(1) + x(2)^2 + x(3)^3,[1 2 3])
+
H =
+     0     0     0
+     0     2     0
+     0     0    18
+err =
+            0            0            0
+            0   4.6563e-15            0
+            0            0   3.3318e-14
+

A semi-definite Hessian matrix

H = hessian(@(xy) cos(xy(1) - xy(2)),[0 0])
+% one of these eigenvalues will be zero (approximately)
+eig(H)
+
H =
+           -1            1
+            1           -1
+ans =
+           -2
+  -3.8795e-07
+

Directional derivative of the Rosenbrock function at the solution

+

This should be zero. Ok, its a trivial test case.

[dd,err] = directionaldiff(rosen,[1 1],[1 2])
+
dd =
+     0
+err =
+     0
+

Directional derivative at other locations

[dd,err] = directionaldiff(rosen,[2 3],[1 -1])
+
+% We can test this example
+v = [1 -1];
+v = v/norm(v);
+g = gradest(rosen,[2 3]);
+
+% The directional derivative will be the dot product of the gradient with
+% the (unit normalized) vector. So this difference will be (approx) zero.
+dot(g,v) - dd
+
dd =
+       743.88
+err =
+   1.5078e-12
+ans =
+   1.5916e-12
+

Jacobian matrix of a scalar function is just the gradient

[jac,err] = jacobianest(rosen,[2 3])
+
+grad = gradest(rosen,[2 3])
+
jac =
+          842         -210
+err =
+   2.8698e-12   1.0642e-12
+grad =
+          842         -210
+

Jacobian matrix of a linear system will reduce to the design matrix

A = rand(5,3);
+b = rand(5,1);
+fun = @(x) (A*x-b);
+
+x = rand(3,1);
+[jac,err] = jacobianest(fun,x)
+
+disp 'This should be essentially zero at any location x'
+jac - A
+
jac =
+      0.81472      0.09754      0.15761
+      0.90579       0.2785      0.97059
+      0.12699      0.54688      0.95717
+      0.91338      0.95751      0.48538
+      0.63236      0.96489      0.80028
+err =
+   3.9634e-15   3.8376e-16   5.4271e-16
+   3.9634e-15   8.8625e-16   5.0134e-15
+   7.0064e-16   3.0701e-15   5.3175e-15
+     3.76e-15   4.8542e-15   2.4271e-15
+   3.0701e-15   4.3417e-15   3.9634e-15
+This should be essentially zero at any location x
+ans =
+            0  -3.1919e-16            0
+   1.1102e-16  -1.6653e-16            0
+   2.7756e-17            0  -1.1102e-16
+  -1.1102e-16  -3.3307e-16   1.6653e-16
+            0   2.2204e-16   1.1102e-16
+

The jacobian matrix of a nonlinear transformation of variables

+

evaluated at some arbitrary location [-2, -3]

fun = @(xy) [xy(1).^2, cos(xy(1) - xy(2))];
+[jac,err] = jacobianest(fun,[-2 -3])
+
jac =
+           -4            0
+     -0.84147      0.84147
+err =
+   2.5067e-14            0
+   6.1478e-14   1.9658e-14
+


+ Published with MATLAB® 7.4

+
+ + + \ No newline at end of file diff --git a/bin/DERIVESTsuite/demo/multivariable_calc_demo.m b/bin/DERIVESTsuite/demo/multivariable_calc_demo.m new file mode 100644 index 0000000..f0f1c5b --- /dev/null +++ b/bin/DERIVESTsuite/demo/multivariable_calc_demo.m @@ -0,0 +1,73 @@ +% Multivariate calculus demo script + +% This script file is designed to be used in cell mode +% from the matlab editor, or best of all, use the publish +% to HTML feature from the matlab editor. Older versions +% of matlab can copy and paste entire blocks of code into +% the Matlab command window. + +% Typical usage of the gradient and Hessian might be in +% optimization problems, where one might compare an analytically +% derived gradient for correctness, or use the Hessian matrix +% to compute confidence interval estimates on parameters in a +% maximum likelihood estimation. + +%% Gradient of the Rosenbrock function at [1,1], the global minimizer +rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2; +% The gradient should be zero (within floating point noise) +[grad,err] = gradest(rosen,[1 1]) + +%% The Hessian matrix at the minimizer should be positive definite +H = hessian(rosen,[1 1]) +% The eigenvalues of h should be positive +eig(H) + +%% Gradient estimation using gradest - a function of 5 variables +[grad,err] = gradest(@(x) sum(x.^2),[1 2 3 4 5]) + +%% Simple Hessian matrix of a problem with 3 independent variables +[H,err] = hessian(@(x) x(1) + x(2)^2 + x(3)^3,[1 2 3]) + +%% A semi-definite Hessian matrix +H = hessian(@(xy) cos(xy(1) - xy(2)),[0 0]) +% one of these eigenvalues will be zero (approximately) +eig(H) + +%% Directional derivative of the Rosenbrock function at the solution +% This should be zero. Ok, its a trivial test case. +[dd,err] = directionaldiff(rosen,[1 1],[1 2]) + +%% Directional derivative at other locations +[dd,err] = directionaldiff(rosen,[2 3],[1 -1]) + +% We can test this example +v = [1 -1]; +v = v/norm(v); +g = gradest(rosen,[2 3]); + +% The directional derivative will be the dot product of the gradient with +% the (unit normalized) vector. So this difference will be (approx) zero. +dot(g,v) - dd + +%% Jacobian matrix of a scalar function is just the gradient +[jac,err] = jacobianest(rosen,[2 3]) + +grad = gradest(rosen,[2 3]) + +%% Jacobian matrix of a linear system will reduce to the design matrix +A = rand(5,3); +b = rand(5,1); +fun = @(x) (A*x-b); + +x = rand(3,1); +[jac,err] = jacobianest(fun,x) + +disp 'This should be essentially zero at any location x' +jac - A + +%% The jacobian matrix of a nonlinear transformation of variables +% evaluated at some arbitrary location [-2, -3] +fun = @(xy) [xy(1).^2, cos(xy(1) - xy(2))]; +[jac,err] = jacobianest(fun,[-2 -3]) + + diff --git a/bin/DERIVESTsuite/derivest.m b/bin/DERIVESTsuite/derivest.m new file mode 100644 index 0000000..4cd6fb8 --- /dev/null +++ b/bin/DERIVESTsuite/derivest.m @@ -0,0 +1,772 @@ +function [der,errest,finaldelta] = derivest(fun,x0,varargin) +% DERIVEST: estimate the n'th derivative of fun at x0, provide an error estimate +% usage: [der,errest] = DERIVEST(fun,x0) % first derivative +% usage: [der,errest] = DERIVEST(fun,x0,prop1,val1,prop2,val2,...) +% +% Derivest will perform numerical differentiation of an +% analytical function provided in fun. It will not +% differentiate a function provided as data. Use gradient +% for that purpose, or differentiate a spline model. +% +% The methods used by DERIVEST are finite difference +% approximations of various orders, coupled with a generalized +% (multiple term) Romberg extrapolation. This also yields +% the error estimate provided. DERIVEST uses a semi-adaptive +% scheme to provide the best estimate that it can by its +% automatic choice of a differencing interval. +% +% Finally, While I have not written this function for the +% absolute maximum speed, speed was a major consideration +% in the algorithmic design. Maximum accuracy was my main goal. +% +% +% Arguments (input) +% fun - function to differentiate. May be an inline function, +% anonymous, or an m-file. fun will be sampled at a set +% of distinct points for each element of x0. If there are +% additional parameters to be passed into fun, then use of +% an anonymous function is recommended. +% +% fun should be vectorized to allow evaluation at multiple +% locations at once. This will provide the best possible +% speed. IF fun is not so vectorized, then you MUST set +% 'vectorized' property to 'no', so that derivest will +% then call your function sequentially instead. +% +% Fun is assumed to return a result of the same +% shape as its input x0. +% +% x0 - scalar, vector, or array of points at which to +% differentiate fun. +% +% Additional inputs must be in the form of property/value pairs. +% Properties are character strings. They may be shortened +% to the extent that they are unambiguous. Properties are +% not case sensitive. Valid property names are: +% +% 'DerivativeOrder', 'MethodOrder', 'Style', 'RombergTerms' +% 'FixedStep', 'MaxStep' +% +% All properties have default values, chosen as intelligently +% as I could manage. Values that are character strings may +% also be unambiguously shortened. The legal values for each +% property are: +% +% 'DerivativeOrder' - specifies the derivative order estimated. +% Must be a positive integer from the set [1,2,3,4]. +% +% DEFAULT: 1 (first derivative of fun) +% +% 'MethodOrder' - specifies the order of the basic method +% used for the estimation. +% +% For 'central' methods, must be a positive integer +% from the set [2,4]. +% +% For 'forward' or 'backward' difference methods, +% must be a positive integer from the set [1,2,3,4]. +% +% DEFAULT: 4 (a second order method) +% +% Note: higher order methods will generally be more +% accurate, but may also suffere more from numerical +% problems. +% +% Note: First order methods would usually not be +% recommended. +% +% 'Style' - specifies the style of the basic method +% used for the estimation. 'central', 'forward', +% or 'backwards' difference methods are used. +% +% Must be one of 'Central', 'forward', 'backward'. +% +% DEFAULT: 'Central' +% +% Note: Central difference methods are usually the +% most accurate, but sometiems one must not allow +% evaluation in one direction or the other. +% +% 'RombergTerms' - Allows the user to specify the generalized +% Romberg extrapolation method used, or turn it off +% completely. +% +% Must be a positive integer from the set [0,1,2,3]. +% +% DEFAULT: 2 (Two Romberg terms) +% +% Note: 0 disables the Romberg step completely. +% +% 'FixedStep' - Allows the specification of a fixed step +% size, preventing the adaptive logic from working. +% This will be considerably faster, but not necessarily +% as accurate as allowing the adaptive logic to run. +% +% DEFAULT: [] +% +% Note: If specified, 'FixedStep' will define the +% maximum excursion from x0 that will be used. +% +% 'Vectorized' - Derivest will normally assume that your +% function can be safely evaluated at multiple locations +% in a single call. This would minimize the overhead of +% a loop and additional function call overhead. Some +% functions are not easily vectorizable, but you may +% (if your matlab release is new enough) be able to use +% arrayfun to accomplish the vectorization. +% +% When all else fails, set the 'vectorized' property +% to 'no'. This will cause derivest to loop over the +% successive function calls. +% +% DEFAULT: 'yes' +% +% +% 'MaxStep' - Specifies the maximum excursion from x0 that +% will be allowed, as a multiple of x0. +% +% DEFAULT: 100 +% +% 'StepRatio' - Derivest uses a proportionally cascaded +% series of function evaluations, moving away from your +% point of evaluation. The StepRatio is the ratio used +% between sequential steps. +% +% DEFAULT: 2.0000001 +% +% Note: use of a non-integer stepratio is intentional, +% to avoid integer multiples of the period of a periodic +% function under some circumstances. +% +% +% See the document DERIVEST.pdf for more explanation of the +% algorithms behind the parameters of DERIVEST. In most cases, +% I have chosen good values for these parameters, so the user +% should never need to specify anything other than possibly +% the DerivativeOrder. I've also tried to make my code robust +% enough that it will not need much. But complete flexibility +% is in there for your use. +% +% +% Arguments: (output) +% der - derivative estimate for each element of x0 +% der will have the same shape as x0. +% +% errest - 95% uncertainty estimate of the derivative, such that +% +% abs(der(j) - f'(x0(j))) < erest(j) +% +% finaldelta - The final overall stepsize chosen by DERIVEST +% +% +% Example usage: +% First derivative of exp(x), at x == 1 +% [d,e]=derivest(@(x) exp(x),1) +% d = +% 2.71828182845904 +% +% e = +% 1.02015503167879e-14 +% +% True derivative +% exp(1) +% ans = +% 2.71828182845905 +% +% Example usage: +% Third derivative of x.^3+x.^4, at x = [0,1] +% derivest(@(x) x.^3 + x.^4,[0 1],'deriv',3) +% ans = +% 6 30 +% +% True derivatives: [6,30] +% +% +% See also: gradient +% +% +% Author: John D'Errico +% e-mail: woodchips@rochester.rr.com +% Release: 1.0 +% Release date: 12/27/2006 + +par.DerivativeOrder = 1; +par.MethodOrder = 4; +par.Style = 'central'; +par.RombergTerms = 2; +par.FixedStep = []; +par.MaxStep = 100; +% setting a default stepratio as a non-integer prevents +% integer multiples of the initial point from being used. +% In turn that avoids some problems for periodic functions. +par.StepRatio = 2.0000001; +par.NominalStep = []; +par.Vectorized = 'yes'; + +na = length(varargin); +if (rem(na,2)==1) + error 'Property/value pairs must come as PAIRS of arguments.' +elseif na>0 + par = parse_pv_pairs(par,varargin); +end +par = check_params(par); + +% Was fun a string, or an inline/anonymous function? +if (nargin<1) + help derivest + return +elseif isempty(fun) + error 'fun was not supplied.' +elseif ischar(fun) + % a character function name + fun = str2func(fun); +end + +% no default for x0 +if (nargin<2) || isempty(x0) + error 'x0 was not supplied' +end +par.NominalStep = max(x0,0.02); + +% was a single point supplied? +nx0 = size(x0); +n = prod(nx0); + +% Set the steps to use. +if isempty(par.FixedStep) + % Basic sequence of steps, relative to a stepsize of 1. + delta = par.MaxStep*par.StepRatio .^(0:-1:-25)'; + ndel = length(delta); +else + % Fixed, user supplied absolute sequence of steps. + ndel = 3 + ceil(par.DerivativeOrder/2) + ... + par.MethodOrder + par.RombergTerms; + if par.Style(1) == 'c' + ndel = ndel - 2; + end + delta = par.FixedStep*par.StepRatio .^(-(0:(ndel-1)))'; +end + +% generate finite differencing rule in advance. +% The rule is for a nominal unit step size, and will +% be scaled later to reflect the local step size. +fdarule = 1; +switch par.Style + case 'central' + % for central rules, we will reduce the load by an + % even or odd transformation as appropriate. + if par.MethodOrder==2 + switch par.DerivativeOrder + case 1 + % the odd transformation did all the work + fdarule = 1; + case 2 + % the even transformation did all the work + fdarule = 2; + case 3 + % the odd transformation did most of the work, but + % we need to kill off the linear term + fdarule = [0 1]/fdamat(par.StepRatio,1,2); + case 4 + % the even transformation did most of the work, but + % we need to kill off the quadratic term + fdarule = [0 1]/fdamat(par.StepRatio,2,2); + end + else + % a 4th order method. We've already ruled out the 1st + % order methods since these are central rules. + switch par.DerivativeOrder + case 1 + % the odd transformation did most of the work, but + % we need to kill off the cubic term + fdarule = [1 0]/fdamat(par.StepRatio,1,2); + case 2 + % the even transformation did most of the work, but + % we need to kill off the quartic term + fdarule = [1 0]/fdamat(par.StepRatio,2,2); + case 3 + % the odd transformation did much of the work, but + % we need to kill off the linear & quintic terms + fdarule = [0 1 0]/fdamat(par.StepRatio,1,3); + case 4 + % the even transformation did much of the work, but + % we need to kill off the quadratic and 6th order terms + fdarule = [0 1 0]/fdamat(par.StepRatio,2,3); + end + end + case {'forward' 'backward'} + % These two cases are identical, except at the very end, + % where a sign will be introduced. + + % No odd/even trans, but we already dropped + % off the constant term + if par.MethodOrder==1 + if par.DerivativeOrder==1 + % an easy one + fdarule = 1; + else + % 2:4 + v = zeros(1,par.DerivativeOrder); + v(par.DerivativeOrder) = 1; + fdarule = v/fdamat(par.StepRatio,0,par.DerivativeOrder); + end + else + % par.MethodOrder methods drop off the lower order terms, + % plus terms directly above DerivativeOrder + v = zeros(1,par.DerivativeOrder + par.MethodOrder - 1); + v(par.DerivativeOrder) = 1; + fdarule = v/fdamat(par.StepRatio,0,par.DerivativeOrder+par.MethodOrder-1); + end + + % correct sign for the 'backward' rule + if par.Style(1) == 'b' + fdarule = -fdarule; + end + +end % switch on par.style (generating fdarule) +nfda = length(fdarule); + +% will we need fun(x0)? +if (rem(par.DerivativeOrder,2) == 0) || ~strncmpi(par.Style,'central',7) + if strcmpi(par.Vectorized,'yes') + f_x0 = fun(x0); + else + % not vectorized, so loop + f_x0 = zeros(size(x0)); + for j = 1:numel(x0) + f_x0(j) = fun(x0(j)); + end + end +else + f_x0 = []; +end + +% Loop over the elements of x0, reducing it to +% a scalar problem. Sorry, vectorization is not +% complete here, but this IS only a single loop. +der = zeros(nx0); +errest = der; +finaldelta = der; +for i = 1:n + x0i = x0(i); + h = par.NominalStep(i); + + % a central, forward or backwards differencing rule? + % f_del is the set of all the function evaluations we + % will generate. For a central rule, it will have the + % even or odd transformation built in. + if par.Style(1) == 'c' + % A central rule, so we will need to evaluate + % symmetrically around x0i. + if strcmpi(par.Vectorized,'yes') + f_plusdel = fun(x0i+h*delta); + f_minusdel = fun(x0i-h*delta); + else + % not vectorized, so loop + f_minusdel = zeros(size(delta)); + f_plusdel = zeros(size(delta)); + for j = 1:numel(delta) + f_plusdel(j) = fun(x0i+h*delta(j)); + f_minusdel(j) = fun(x0i-h*delta(j)); + end + end + + if ismember(par.DerivativeOrder,[1 3]) + % odd transformation + f_del = (f_plusdel - f_minusdel)/2; + else + f_del = (f_plusdel + f_minusdel)/2 - f_x0(i); + end + elseif par.Style(1) == 'f' + % forward rule + % drop off the constant only + if strcmpi(par.Vectorized,'yes') + f_del = fun(x0i+h*delta) - f_x0(i); + else + % not vectorized, so loop + f_del = zeros(size(delta)); + for j = 1:numel(delta) + f_del(j) = fun(x0i+h*delta(j)) - f_x0(i); + end + end + else + % backward rule + % drop off the constant only + if strcmpi(par.Vectorized,'yes') + f_del = fun(x0i-h*delta) - f_x0(i); + else + % not vectorized, so loop + f_del = zeros(size(delta)); + for j = 1:numel(delta) + f_del(j) = fun(x0i-h*delta(j)) - f_x0(i); + end + end + end + + % check the size of f_del to ensure it was properly vectorized. + f_del = f_del(:); + if length(f_del)~=ndel + error 'fun did not return the correct size result (fun must be vectorized)' + end + + % Apply the finite difference rule at each delta, scaling + % as appropriate for delta and the requested DerivativeOrder. + % First, decide how many of these estimates we will end up with. + ne = ndel + 1 - nfda - par.RombergTerms; + + % Form the initial derivative estimates from the chosen + % finite difference method. + der_init = vec2mat(f_del,ne,nfda)*fdarule.'; + + % scale to reflect the local delta + der_init = der_init(:)./(h*delta(1:ne)).^par.DerivativeOrder; + + % Each approximation that results is an approximation + % of order par.DerivativeOrder to the desired derivative. + % Additional (higher order, even or odd) terms in the + % Taylor series also remain. Use a generalized (multi-term) + % Romberg extrapolation to improve these estimates. + switch par.Style + case 'central' + rombexpon = 2*(1:par.RombergTerms) + par.MethodOrder - 2; + otherwise + rombexpon = (1:par.RombergTerms) + par.MethodOrder - 1; + end + [der_romb,errors] = rombextrap(par.StepRatio,der_init,rombexpon); + + % Choose which result to return + + % first, trim off the + if isempty(par.FixedStep) + % trim off the estimates at each end of the scale + nest = length(der_romb); + switch par.DerivativeOrder + case {1 2} + trim = [1 2 nest-1 nest]; + case 3 + trim = [1:4 nest+(-3:0)]; + case 4 + trim = [1:6 nest+(-5:0)]; + end + + [der_romb,tags] = sort(der_romb); + + der_romb(trim) = []; + tags(trim) = []; + errors = errors(tags); + trimdelta = delta(tags); + + [errest(i),ind] = min(errors); + + finaldelta(i) = h*trimdelta(ind); + der(i) = der_romb(ind); + else + [errest(i),ind] = min(errors); + finaldelta(i) = h*delta(ind); + der(i) = der_romb(ind); + end +end + +end % mainline end + +% ============================================ +% subfunction - romberg extrapolation +% ============================================ +function [der_romb,errest] = rombextrap(StepRatio,der_init,rombexpon) +% do romberg extrapolation for each estimate +% +% StepRatio - Ratio decrease in step +% der_init - initial derivative estimates +% rombexpon - higher order terms to cancel using the romberg step +% +% der_romb - derivative estimates returned +% errest - error estimates +% amp - noise amplification factor due to the romberg step + +srinv = 1/StepRatio; + +% do nothing if no romberg terms +nexpon = length(rombexpon); +rmat = ones(nexpon+2,nexpon+1); +switch nexpon + case 0 + % rmat is simple: ones(2,1) + case 1 + % only one romberg term + rmat(2,2) = srinv^rombexpon; + rmat(3,2) = srinv^(2*rombexpon); + case 2 + % two romberg terms + rmat(2,2:3) = srinv.^rombexpon; + rmat(3,2:3) = srinv.^(2*rombexpon); + rmat(4,2:3) = srinv.^(3*rombexpon); + case 3 + % three romberg terms + rmat(2,2:4) = srinv.^rombexpon; + rmat(3,2:4) = srinv.^(2*rombexpon); + rmat(4,2:4) = srinv.^(3*rombexpon); + rmat(5,2:4) = srinv.^(4*rombexpon); +end + +% qr factorization used for the extrapolation as well +% as the uncertainty estimates +[qromb,rromb] = qr(rmat,0); + +% the noise amplification is further amplified by the Romberg step. +% amp = cond(rromb); + +% this does the extrapolation to a zero step size. +ne = length(der_init); +rhs = vec2mat(der_init,nexpon+2,max(1,ne - (nexpon+2))); +rombcoefs = rromb\(qromb.'*rhs); +der_romb = rombcoefs(1,:).'; + +% uncertainty estimate of derivative prediction +s = sqrt(sum((rhs - rmat*rombcoefs).^2,1)); +rinv = rromb\eye(nexpon+1); +cov1 = sum(rinv.^2,2); % 1 spare dof +errest = s.'*12.7062047361747*sqrt(cov1(1)); + +end % rombextrap + + +% ============================================ +% subfunction - vec2mat +% ============================================ +function mat = vec2mat(vec,n,m) +% forms the matrix M, such that M(i,j) = vec(i+j-1) +[i,j] = ndgrid(1:n,0:m-1); +ind = i+j; +mat = vec(ind); +if n==1 + mat = mat.'; +end + +end % vec2mat + + +% ============================================ +% subfunction - fdamat +% ============================================ +function mat = fdamat(sr,parity,nterms) +% Compute matrix for fda derivation. +% parity can be +% 0 (one sided, all terms included but zeroth order) +% 1 (only odd terms included) +% 2 (only even terms included) +% nterms - number of terms + +% sr is the ratio between successive steps +srinv = 1./sr; + +switch parity + case 0 + % single sided rule + [i,j] = ndgrid(1:nterms); + c = 1./factorial(1:nterms); + mat = c(j).*srinv.^((i-1).*j); + case 1 + % odd order derivative + [i,j] = ndgrid(1:nterms); + c = 1./factorial(1:2:(2*nterms)); + mat = c(j).*srinv.^((i-1).*(2*j-1)); + case 2 + % even order derivative + [i,j] = ndgrid(1:nterms); + c = 1./factorial(2:2:(2*nterms)); + mat = c(j).*srinv.^((i-1).*(2*j)); +end + +end % fdamat + + + +% ============================================ +% subfunction - check_params +% ============================================ +function par = check_params(par) +% check the parameters for acceptability +% +% Defaults +% par.DerivativeOrder = 1; +% par.MethodOrder = 2; +% par.Style = 'central'; +% par.RombergTerms = 2; +% par.FixedStep = []; + +% DerivativeOrder == 1 by default +if isempty(par.DerivativeOrder) + par.DerivativeOrder = 1; +else + if (length(par.DerivativeOrder)>1) || ~ismember(par.DerivativeOrder,1:4) + error 'DerivativeOrder must be scalar, one of [1 2 3 4].' + end +end + +% MethodOrder == 2 by default +if isempty(par.MethodOrder) + par.MethodOrder = 2; +else + if (length(par.MethodOrder)>1) || ~ismember(par.MethodOrder,[1 2 3 4]) + error 'MethodOrder must be scalar, one of [1 2 3 4].' + elseif ismember(par.MethodOrder,[1 3]) && (par.Style(1)=='c') + error 'MethodOrder==1 or 3 is not possible with central difference methods' + end +end + +% style is char +valid = {'central', 'forward', 'backward'}; +if isempty(par.Style) + par.Style = 'central'; +elseif ~ischar(par.Style) + error 'Invalid Style: Must be character' +end +ind = find(strncmpi(par.Style,valid,length(par.Style))); +if (length(ind)==1) + par.Style = valid{ind}; +else + error(['Invalid Style: ',par.Style]) +end + +% vectorized is char +valid = {'yes', 'no'}; +if isempty(par.Vectorized) + par.Vectorized = 'yes'; +elseif ~ischar(par.Vectorized) + error 'Invalid Vectorized: Must be character' +end +ind = find(strncmpi(par.Vectorized,valid,length(par.Vectorized))); +if (length(ind)==1) + par.Vectorized = valid{ind}; +else + error(['Invalid Vectorized: ',par.Vectorized]) +end + +% RombergTerms == 2 by default +if isempty(par.RombergTerms) + par.RombergTerms = 2; +else + if (length(par.RombergTerms)>1) || ~ismember(par.RombergTerms,0:3) + error 'RombergTerms must be scalar, one of [0 1 2 3].' + end +end + +% FixedStep == [] by default +if (length(par.FixedStep)>1) || (~isempty(par.FixedStep) && (par.FixedStep<=0)) + error 'FixedStep must be empty or a scalar, >0.' +end + +% MaxStep == 10 by default +if isempty(par.MaxStep) + par.MaxStep = 10; +elseif (length(par.MaxStep)>1) || (par.MaxStep<=0) + error 'MaxStep must be empty or a scalar, >0.' +end + +end % check_params + + +% ============================================ +% Included subfunction - parse_pv_pairs +% ============================================ +function params=parse_pv_pairs(params,pv_pairs) +% parse_pv_pairs: parses sets of property value pairs, allows defaults +% usage: params=parse_pv_pairs(default_params,pv_pairs) +% +% arguments: (input) +% default_params - structure, with one field for every potential +% property/value pair. Each field will contain the default +% value for that property. If no default is supplied for a +% given property, then that field must be empty. +% +% pv_array - cell array of property/value pairs. +% Case is ignored when comparing properties to the list +% of field names. Also, any unambiguous shortening of a +% field/property name is allowed. +% +% arguments: (output) +% params - parameter struct that reflects any updated property/value +% pairs in the pv_array. +% +% Example usage: +% First, set default values for the parameters. Assume we +% have four parameters that we wish to use optionally in +% the function examplefun. +% +% - 'viscosity', which will have a default value of 1 +% - 'volume', which will default to 1 +% - 'pie' - which will have default value 3.141592653589793 +% - 'description' - a text field, left empty by default +% +% The first argument to examplefun is one which will always be +% supplied. +% +% function examplefun(dummyarg1,varargin) +% params.Viscosity = 1; +% params.Volume = 1; +% params.Pie = 3.141592653589793 +% +% params.Description = ''; +% params=parse_pv_pairs(params,varargin); +% params +% +% Use examplefun, overriding the defaults for 'pie', 'viscosity' +% and 'description'. The 'volume' parameter is left at its default. +% +% examplefun(rand(10),'vis',10,'pie',3,'Description','Hello world') +% +% params = +% Viscosity: 10 +% Volume: 1 +% Pie: 3 +% Description: 'Hello world' +% +% Note that capitalization was ignored, and the property 'viscosity' +% was truncated as supplied. Also note that the order the pairs were +% supplied was arbitrary. + +npv = length(pv_pairs); +n = npv/2; + +if n~=floor(n) + error 'Property/value pairs must come in PAIRS.' +end +if n<=0 + % just return the defaults + return +end + +if ~isstruct(params) + error 'No structure for defaults was supplied' +end + +% there was at least one pv pair. process any supplied +propnames = fieldnames(params); +lpropnames = lower(propnames); +for i=1:n + p_i = lower(pv_pairs{2*i-1}); + v_i = pv_pairs{2*i}; + + ind = strmatch(p_i,lpropnames,'exact'); + if isempty(ind) + ind = find(strncmp(p_i,lpropnames,length(p_i))); + if isempty(ind) + error(['No matching property found for: ',pv_pairs{2*i-1}]) + elseif length(ind)>1 + error(['Ambiguous property name: ',pv_pairs{2*i-1}]) + end + end + p_i = propnames{ind}; + + % override the corresponding default in params + params = setfield(params,p_i,v_i); %#ok + +end + +end % parse_pv_pairs + + + + + + diff --git a/bin/DERIVESTsuite/directionaldiff.m b/bin/DERIVESTsuite/directionaldiff.m new file mode 100644 index 0000000..9d6d0f4 --- /dev/null +++ b/bin/DERIVESTsuite/directionaldiff.m @@ -0,0 +1,68 @@ +function [dd,err,finaldelta] = directionaldiff(fun,x0,vec) +% directionaldiff: estimate of the directional derivative of a function of n variables +% usage: [grad,err,finaldelta] = directionaldiff(fun,x0,vec) +% +% Uses derivest to provide both a directional derivative +% estimates plus an error estimates. fun needs not be vectorized. +% +% arguments: (input) +% fun - analytical function to differentiate. fun must +% be a function of the vector or array x0. Fun needs +% not be vectorized. +% +% x0 - vector location at which to differentiate fun +% If x0 is an nxm array, then fun is assumed to be +% a function of n*m variables. +% +% vec - vector defining the line along which to take the +% derivative. Vec should be the same size as x0. It +% need not be a vector of unit length. +% +% arguments: (output) +% dd - scalar estimate of the first derivative of fun +% in the SPECIFIED direction. +% +% err - error estimate of the directional derivative +% +% finaldelta - vector of final step sizes chosen for +% each partial derivative. +% +% +% Example: +% At the global minimizer (1,1) of the Rosenbrock function, +% compute the directional derivative in the direction [1 2] +% It should be 0. +% +% rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2; +% [dd,err] = directionaldiff(rosen,[1 1]) +% +% dd = +% 0 +% err = +% 0 +% +% +% See also: derivest, gradest, gradient +% +% +% Author: John D'Errico +% e-mail: woodchips@rochester.rr.com +% Release: 1.0 +% Release date: 3/5/2007 + +% get the size of x0 so we can make sure vec is +% the same shape. +sx = size(x0); +if numel(x0)~=numel(vec) + error 'vec and x0 must be the same sizes' +end +vec = vec(:); +vec = vec/norm(vec); +vec = reshape(vec,sx); + +[dd,err,finaldelta] = derivest(@(t) fun(x0+t*vec), ... + 0,'deriv',1,'vectorized','no'); + +end % mainline function end + + diff --git a/bin/DERIVESTsuite/doc/DERIVEST.pdf b/bin/DERIVESTsuite/doc/DERIVEST.pdf new file mode 100644 index 0000000..596299c Binary files /dev/null and b/bin/DERIVESTsuite/doc/DERIVEST.pdf differ diff --git a/bin/DERIVESTsuite/doc/DERIVEST.tex b/bin/DERIVESTsuite/doc/DERIVEST.tex new file mode 100644 index 0000000..663edaf --- /dev/null +++ b/bin/DERIVESTsuite/doc/DERIVEST.tex @@ -0,0 +1,396 @@ + \documentclass[a4paper,11pt]{article} + +\usepackage{fancyhdr} +\usepackage[dvips]{graphicx} % for eps and MatLab Diagrams +\usepackage{amsmath} +\usepackage{psfrag,color} +\usepackage[framed]{/Applications/TeX/mcode} + +\pagestyle{fancy} + +\begin{document} % Begin Document + +% Title +\title{\textsc{DERIVEST}} + +% Authors and Contact Information +\author{\textbf{John R. D'Errico}\\ +Email: woodchips@rochester.rr.com} + +\maketitle + +\section{Introduction - Derivative Estimation} + +The general problem of differentiation of a function typically pops up in +three ways in Matlab. + +\begin{itemize} + \item The symbolic derivative of a function. + \item Compute numerical derivatives of a function defined only by a sequence of data points. + \item Compute numerical derivatives of a analytically supplied function. +\end{itemize} + +Clearly the first member of this list is the domain of the symbolic toolbox, or some +set of symbolic tools. Numerical differentiation of a function defined by data points +can be achieved with the function gradient, or perhaps by differentiation of a curve fit +to the data, perhaps to an interpolating spline or a least squares spline fit. + +The third class of differentiation problems is where \mcode{DERIVEST} is valuable. This +document will describe the methods used in \mcode{DERIVEST}. + +\bigskip + +\section{Numerical differentiation of a general function of one variable} + +Surely you recall the traditional definition of a derivative, in terms of a limit. + +\begin{equation} \tag{1} + f'(x) = \lim_{\delta \to 0}{\frac{f(x+\delta) - f(x)}{\delta}} +\end{equation} + +For small $\delta$, the limit approaches $f'(x)$. This is a one-sided approximation for +the derivative. For a fixed value of $\delta$, this is also known as a finite difference +approximation (a forward difference.) Other approximations for the derivative are also +available. We will see the origin of these approximations in the Taylor series expansion +of a function $f(x)$ around some point $x_0$. + +\begin{multline} \tag{2} + f(x) = f(x_0) + (x - x_0)f'(x_0) + \frac{(x - x_0)^2}{2} f''(x_0) + \\ + \frac{(x - x_0)^3}{6} f^{(3)}(x_0) + \frac{(x - x_0)^4}{24} f^{(4)}(x_0) + \\ + \frac{(x - x_0)^5}{120} f^{(5)}(x_0) + \frac{(x - x_0)^6}{720} f^{(6)}(x_0) +... +\end{multline} + +Truncate the series in (2) to the first three terms, then form the forward difference +approximation (1), where $x = x_0 + \delta$. + +\begin{equation} \tag{3} + f'(x_0) = \frac{f(x_0+\delta) - f(x_0)}{\delta} - \frac{\delta}{2} f''(x_0) - \frac{\delta^2}{6} f'''(x_0) + ... +\end{equation} + +When $\delta$ is small, $\delta^2$ and any higher powers are vanishingly small. So we tend +to ignore those higher powers, and describe the approximation in (3) as a "first" order +approximation since the error in this approximation approaches zero at the same rate as the first power of $\delta$. \footnote{We would normally write these additional terms using O() notation, where all that matters is that the error term is $O(\delta)$ or perhaps $O(\delta^2)$, but explicit understanding of these error terms will be useful in the Romberg extrapolation step later on.} The values of $f''(x_0)$ and $f'''(x_0)$, while unknown to us, are fixed constants as $\delta$ varies. + +Higher order approximations arise in the same fashion. The central difference (4) is a second +order approximation. + +\begin{equation} \tag{4} + f'(x_0) = \frac{f(x_0+\delta) - f(x_0-\delta)}{2\delta} - \frac{\delta^2}{3} f'''(x_0) + ... +\end{equation} + + +\bigskip + +\section{Unequally spaced finite difference rules} + +While most finite difference rules used to differentiate a function will use equally spaced points, +this fails to be appropriate when one does not know the final spacing. Adaptive quadrature +rules can succeed by subdividing each sub-interval as necessary. But an adaptive +differentiation scheme must work differently, since differentiation is a point estimate. +\mcode{DERIVEST} generates a sequence of sample points that follow a log spacing away +from the point in question, then it uses a single rule (generated on the fly) to estimate the +desired derivative. Because the points are log spaced, the same rule applies at any scale, +with only a scale factor applied. + + +\bigskip + +\section{Odd and even transformations of a function} + +Returning to the Taylor series expansion of $f(x)$ around some point $x_0$, an even function \footnote{An even function is one which expresses an even symmetry around a given point. An even symmetry has the property that $f(x) = f(-x)$. Likewise, an odd function expresses an odd symmetry, wherein $f(x) = -f(-x)$.} around $x_0$ must have all the odd order derivatives vanish at $x_0$. An odd function has all its even derivatives vanish from its expansion. Consider the derived functions $f_{odd}(x)$ and $f_{even}(x)$. + +\begin{equation} \tag{5} +f_{odd}(x) = \frac{f(x - x_0) - f(-x - x_0)}{2} +\end{equation} + +The Taylor series expansion of $f_{odd}(x)$ has the useful property that we have killed off any even order terms, but the odd order terms are identical to $f(x)$, as expanded around $x_0$. + +\begin{multline} \tag{6} +f_{odd}(x) = (x - x_0)f'(x_0) + \frac{(x - x_0)^3}{6} f^{(3)}(x_0) + \\ +\frac{(x - x_0)^5}{120} f^{(5)}(x_0) + \frac{(x - x_0)^7}{5040} f^{(7)}(x_0) +... +\end{multline} + +Likewise, $f_{even}(x)$ has no odd order terms or a constant term, but other even order terms that are +identical to $f(x)$. + +\begin{equation} \tag{7} +f_{even}(x) = \frac{f(-x-x_0) - 2f(x_0) + f(x-x_0)}{2} +\end{equation} + +\begin{multline} \tag{8} +f_{even}(x) = \frac{(x - x_0)^2}{2} f^{(2)}(x_0) + \frac{(x - x_0)^4}{24} f^{(4)}(x_0) + \\ + \frac{(x - x_0)^6}{720} f^{(6)}(x_0) + \frac{(x - x_0)^8}{40320} f^{(8)}(x_0) + ... +\end{multline} + +The point of these transformations is we can rather simply generate a higher order approximation +for any odd order derivatives of $f(x)$ by working with $f_{odd}(x)$. Even order derivatives of $f(x)$ are similarly generated from $f_{even}(x)$. For example, a second order approximation for $f'(x_0)$ is trivially written in (9) as a function of $\delta$. + +\begin{equation} \tag{9} + f'(x_0; \delta) = \frac{f_{odd}(x_0 + \delta)}{\delta} - \frac{\delta^2}{6} f^{(3)}(x_0) +\end{equation} + +We can do better rather simply, so why not? (10) shows a fourth order approximation for $f'(x_0)$. + +\begin{equation} \tag{10} + f'(x_0; \delta) = \frac{8 f_{odd}(x_0+\delta)-f_{odd}(x_0+2\delta)}{6\delta} + \frac{\delta^4}{30} f^{(5)}(x_0) +\end{equation} + +Again, the next non-zero term (11) in that expansion has a higher power of $\delta$ on it, so we +would normally ignore it since the lowest order neglected term should dominate the behavior +for small $\delta$. + +\begin{equation} \tag{11} + \frac{\delta^6}{252} f^{(7)}(x_0) +\end{equation} + +\mcode{DERIVEST} uses similar approximations for all derivatives of $f$ up to the fourth order. +Of course, its not always possible for evaluation of a function on both sides of a point, as central difference rules will require. In these cases, you can specify forward or backward difference rules +as appropriate. + + +\bigskip + +\section{Romberg extrapolation methodology applied to derivative estimation} + +Some individuals might suggest that the above set of approximations are entirely adequate for +any sane person. Can we do better? + +Suppose we were to generate several different estimates of the approximation in (3) for +different values of $\delta$ at a fixed $x_0$. Thus, choose a single $\delta$, estimate a +corresponding resulting approximation to $f'(x_0)$, then do the same for $\delta/2$. +If we assume that the error drops off linearly as $\delta \to 0$, then it is a simple matter +to extrapolate this process to a zero step size. Our lack of knowledge of $f''(x_0)$ is +irrelevant. All that matters is $\delta$ is small enough that the linear term dominates so we +can ignore the quadratic term, therefore the error is purely linear. + +\begin{equation} \tag{12} + f'(x_0) = \frac{f(x_0+\delta) - f(x_0)}{\delta} - \frac{\delta}{2} f''(x_0) +\end{equation} + +The linear extrapolant for this interval halving scheme as $\delta \to 0$ is given by (13). + +\begin{equation} \tag{13} + f'_0 = 2f'_\delta - f'_{\delta/2} +\end{equation} + +Since I've always been a big fan of convincing myself that something will work before I +proceed too far, lets try this out in Matlab. Consider the function $e^x$. Generate a pair of +approximations to $f'(0)$, once at $\delta$ of 0.1, and the second approximation at $1/2$ +that value. Recall that $\frac{d(e^x)}{dx} = e^x$, so at x = 0, the derivative should be +exactly 1. How well will we do? + +\begin{lstlisting} +>> format long g + +>> f = @(x) exp(x); +>> del = 0.1; + +>> df1 = (f(del) - f(0))/del +df1 = + 1.05170918075648 + +>> df2 = (f(del/2) - f(0))/(del/2) +df2 = + 1.02542192752048 + +>> 2*df2 - df1 +ans = + 0.999134674284488 +\end{lstlisting} + +In fact, this worked very nicely, reducing the error to roughly 1 percent of our initial estimates. +Should we be surprised at this reduction? Not if we recall that last term in (3). We saw there that +the next term in the expansion was $O(\delta^2)$. Since $\delta$ was 0.1 in our experiment, that +1 percent number makes perfect sense. + +The Romberg extrapolant in (13) assumed a linear process, with a specific reduction in $\delta$ +by a factor of 2. Assume the two term (linear + quadratic) residual term in (3), evaluating our approximation there with a third value of $\delta$. Again, assume the step size is cut in half again. +The three term Romberg extrapolant is given by (14). + +\begin{equation} \tag{14} + f'_0 = \frac{1}{3}f'_\delta - 2f'_{\delta/2} + \frac{8}{3}f'_{\delta/4} +\end{equation} + +A quick test in matlab yields much better results yet. + +\begin{lstlisting} +>> format long g +>> f = @(x) exp(x); +>> del = 0.1; + +>> df1 = (f(del) - f(0))/del +df1 = + 1.05170918075648 + +>> df2 = (f(del/2) - f(0))/(del/2) +df2 = + 1.02542192752048 + +>> df3 = (f(del/4) - f(0))/(del/4) +df3 = + 1.01260482097715 + +>> 1/3*df1 - 2*df2 + 8/3*df3 +ans = + 1.00000539448361 +\end{lstlisting} + +Again, \mcode{DERIVEST} uses the appropriate multiple term Romberg extrapolants for all derivatives +of $f$ up to the fourth order. This, combined with the use of high order approximations for the derivatives, allows the use of quite large step sizes. + +\bigskip + +\section{Uncertainty estimates for DERIVEST} + +We can view the Romberg extrapolation step as a polynomial curve fit in the step size parameter +$\delta$. Our desired extrapolated value is seen as simply the constant term coefficient in that polynomial model. Remember though, this polynomial model (see (10) and (11)) has only a few +terms in it with known non-zero coefficients. That is, we will expect a constant term $a_0$, a term +of the form $a_1 \delta^4$, and a third term $a_2 \delta^6$. + +A neat trick to compute the "statistical" uncertainty in the estimate of our desired derivative is to +use statistical methodology for that error estimate. While I do appreciate that there is nothing +truly statistical or stochastic in this estimate, the approach still works nicely, providing a very reasonable estimate in practice. A three term Romberg-like extrapolant, then evaluated at four distinct values for $\delta$, will yield an estimate of the standard error of the constant term, with one spare degree of freedom. The uncertainty is then derived by multiplying that standard error by the appropriate percentile from the Students-t distribution. + +\begin{lstlisting} +>> tcdf(12.7062047361747,1) +ans = + 0.975 +\end{lstlisting} + +This critical level will yield a two-sided confidence interval of 95 percent. + +These error estimates are also of value in a difference sense. Since they are efficiently generated +at all the different scales, the particular spacing which yields the minimum predicted error is chosen +as the best derivative estimate. This has been shown to work consistently well. A spacing too large +tends to have large errors of approximation due to the finite difference schemes used. But a too +small spacing is bad also, in that we see a significant amplification of least significant fit errors +in the approximation. A middle value generally seems to yield quite good results. For example, +\mcode{DERIVEST} will estimate the derivative of $e^x$ automatically. As we see, the final overall +spacing used was 0.1953125. + +\begin{lstlisting} +>> [d,e,del]=derivest(@(x) exp(x),1) +d = + 2.71828182845904 +e = + 1.02015503167879e-14 +del = + 0.1953125 +\end{lstlisting} + +However, if we force the step size to be artificially large, then approximation error takes over. + +\begin{lstlisting} +>> [d,e,del]=derivest(@(x) exp(x),1,'FixedStep',10) +d = + 2.3854987890005 +e = + 3.90016042034995 +del = + 10 +\end{lstlisting} + +And if the step size is forced to be too small, then we see noise dominate the problem. + +\begin{lstlisting} +>> [d,e,del]=derivest(@(x) exp(x),1,'FixedStep',.0000000001) +d = + 2.71826406220403 +e = + 0.000327191484277048 +del = + 1e-10 +\end{lstlisting} + +\mcode{DERIVEST}, like Goldilocks in the fairy tale bearing her name, stays comfortably in +the middle ground. + + +\bigskip + +\section{DERIVEST in action} + +How does \mcode{DERIVEST} work in action? A simple nonlinear function with a well +known derivative is $e^x$. At $x = 0$, the derivative should be 1. + +\begin{lstlisting} +>> [d,err] = derivest(@(x) exp(x),0) +d = + 0.999999999999997 + +err = + 2.22066469352214e-14 +\end{lstlisting} + +A second simple example comes from trig functions. The first four derivatives of the sine +function, evaluated at $x = 0$, should be respectively $[cos(0), -sin(0), -cos(0), sin(0)]$, +or $[1,0,-1,0]$. + +\begin{lstlisting} +>> d = derivest(@(x) sin(x),0,1) +d = + 0.999999999999999 + +>> d = derivest(@(x) sin(x),0,2) +d = + 0 + +>> d = derivest(@(x) sin(x),0,3) +d = + -1.00000000000046 + +>> d = derivest(@(x) sin(x),0,4) +d = + 0 +\end{lstlisting} + + +\bigskip + +\section{Gradient (\mcode{GRADEST}) and Hessian (\mcode{HESSIAN}) estimation} + +Estimation of the gradient vector (\mcode{GRADEST}) of a function of multiple variables is a +simple task, requiring merely repeated calls to \mcode{DERIVEST}. Likewise, the diagonal +elements of the hessian matrix are merely pure second partial derivatives of a function. +\mcode{HESSDIAG} accomplishes this task, again calling \mcode{DERIVEST} multiple +times. Efficient computation of the off-diagonal (mixed partial derivative) elements of the +Hessian matrix uses a scheme much like that of \mcode{DERIVEST}, wherein +\mcode{DERIVEST} is called to determine an initial step size, then Romberg extrapolation +is used to improve a set of second order finite difference estimates of those mixed partials. + +\bigskip + +\section{Conclusion} + +\mcode{DERIVEST} is an a adaptive scheme that can compute the derivative of arbitrary +(well behaved) functions. It is reasonably fast as an adaptive method. Many options have +been provided for the user who wishes the ultimate amount of control over the estimation. + + +\bigskip + +\section{Acknowledgments} + +My thanks are due to Shaun Simmons for convincing me to learn enough +LaTeX to write this document. + +\bigskip + + +\begin{thebibliography}{3} + +\bibitem{LM66} Lyness, J. M., Moler, C. B. (1966). +\newblock Vandermonde Systems and Numerical Differentiation. +\newblock \emph{Numerische Mathematik}. + +\bibitem{LM69} Lyness, J. M., Moler, C. B. (1969). +\newblock Generalized Romberg Methods for Integrals of Derivatives. +\newblock \emph{Numerische Mathematik}. + +\bibitem{LM66} \emph{NAG Library}. +\newblock NAG Fortran Library Document: D04AAF + +\end{thebibliography} + + +\end{document} diff --git a/bin/DERIVESTsuite/gradest.m b/bin/DERIVESTsuite/gradest.m new file mode 100644 index 0000000..e82ccf3 --- /dev/null +++ b/bin/DERIVESTsuite/gradest.m @@ -0,0 +1,96 @@ +function [grad,err,finaldelta] = gradest(fun,x0) +% gradest: estimate of the gradient vector of an analytical function of n variables +% usage: [grad,err,finaldelta] = gradest(fun,x0) +% +% Uses derivest to provide both derivative estimates +% and error estimates. fun needs not be vectorized. +% +% arguments: (input) +% fun - analytical function to differentiate. fun must +% be a function of the vector or array x0. +% +% x0 - vector location at which to differentiate fun +% If x0 is an nxm array, then fun is assumed to be +% a function of n*m variables. +% +% arguments: (output) +% grad - vector of first partial derivatives of fun. +% grad will be a row vector of length numel(x0). +% +% err - vector of error estimates corresponding to +% each partial derivative in grad. +% +% finaldelta - vector of final step sizes chosen for +% each partial derivative. +% +% +% Example: +% [grad,err] = gradest(@(x) sum(x.^2),[1 2 3]) +% grad = +% 2 4 6 +% err = +% 5.8899e-15 1.178e-14 0 +% +% +% Example: +% At [x,y] = [1,1], compute the numerical gradient +% of the function sin(x-y) + y*exp(x) +% +% z = @(xy) sin(diff(xy)) + xy(2)*exp(xy(1)) +% +% [grad,err ] = gradest(z,[1 1]) +% grad = +% 1.7183 3.7183 +% err = +% 7.537e-14 1.1846e-13 +% +% +% Example: +% At the global minimizer (1,1) of the Rosenbrock function, +% compute the gradient. It should be essentially zero. +% +% rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2; +% [g,err] = gradest(rosen,[1 1]) +% g = +% 1.0843e-20 0 +% err = +% 1.9075e-18 0 +% +% +% See also: derivest, gradient +% +% +% Author: John D'Errico +% e-mail: woodchips@rochester.rr.com +% Release: 1.0 +% Release date: 2/9/2007 + +% get the size of x0 so we can reshape +% later. +sx = size(x0); + +% total number of derivatives we will need to take +nx = numel(x0); + +grad = zeros(1,nx); +err = grad; +finaldelta = grad; +for ind = 1:nx + [grad(ind),err(ind),finaldelta(ind)] = derivest( ... + @(xi) fun(swapelement(x0,ind,xi)), ... + x0(ind),'deriv',1,'vectorized','no', ... + 'methodorder',2); +end + +end % mainline function end + +% ======================================= +% sub-functions +% ======================================= +function vec = swapelement(vec,ind,val) +% swaps val as element ind, into the vector vec +vec(ind) = val; + +end % sub-function end + + diff --git a/bin/DERIVESTsuite/hessdiag.m b/bin/DERIVESTsuite/hessdiag.m new file mode 100644 index 0000000..6082093 --- /dev/null +++ b/bin/DERIVESTsuite/hessdiag.m @@ -0,0 +1,76 @@ +function [HD,err,finaldelta] = hessdiag(fun,x0) +% HESSDIAG: diagonal elements of the Hessian matrix (vector of second partials) +% usage: [HD,err,finaldelta] = hessdiag(fun,x0) +% +% When all that you want are the diagonal elements of the hessian +% matrix, it will be more efficient to call HESSDIAG than HESSIAN. +% HESSDIAG uses DERIVEST to provide both second derivative estimates +% and error estimates. fun needs not be vectorized. +% +% arguments: (input) +% fun - SCALAR analytical function to differentiate. +% fun must be a function of the vector or array x0. +% +% x0 - vector location at which to differentiate fun +% If x0 is an nxm array, then fun is assumed to be +% a function of n*m variables. +% +% arguments: (output) +% HD - vector of second partial derivatives of fun. +% These are the diagonal elements of the Hessian +% matrix, evaluated at x0. +% HD will be a row vector of length numel(x0). +% +% err - vector of error estimates corresponding to +% each second partial derivative in HD. +% +% finaldelta - vector of final step sizes chosen for +% each second partial derivative. +% +% +% Example usage: +% [HD,err] = hessdiag(@(x) x(1) + x(2)^2 + x(3)^3,[1 2 3]) +% HD = +% 0 2 18 +% +% err = +% 0 0 0 +% +% +% See also: derivest, gradient, gradest +% +% +% Author: John D'Errico +% e-mail: woodchips@rochester.rr.com +% Release: 1.0 +% Release date: 2/9/2007 + +% get the size of x0 so we can reshape +% later. +sx = size(x0); + +% total number of derivatives we will need to take +nx = numel(x0); + +HD = zeros(1,nx); +err = HD; +finaldelta = HD; +for ind = 1:nx + [HD(ind),err(ind),finaldelta(ind)] = derivest( ... + @(xi) fun(swapelement(x0,ind,xi)), ... + x0(ind),'deriv',2,'vectorized','no'); +end + +end % mainline function end + +% ======================================= +% sub-functions +% ======================================= +function vec = swapelement(vec,ind,val) +% swaps val as element ind, into the vector vec +vec(ind) = val; + +end % sub-function end + + + diff --git a/bin/DERIVESTsuite/hessian.m b/bin/DERIVESTsuite/hessian.m new file mode 100644 index 0000000..df06743 --- /dev/null +++ b/bin/DERIVESTsuite/hessian.m @@ -0,0 +1,189 @@ +function [hess,err] = hessian(fun,x0) +% hessian: estimate elements of the Hessian matrix (array of 2nd partials) +% usage: [hess,err] = hessian(fun,x0) +% +% Hessian is NOT a tool for frequent use on an expensive +% to evaluate objective function, especially in a large +% number of dimensions. Its computation will use roughly +% O(6*n^2) function evaluations for n parameters. +% +% arguments: (input) +% fun - SCALAR analytical function to differentiate. +% fun must be a function of the vector or array x0. +% fun does not need to be vectorized. +% +% x0 - vector location at which to compute the Hessian. +% +% arguments: (output) +% hess - nxn symmetric array of second partial derivatives +% of fun, evaluated at x0. +% +% err - nxn array of error estimates corresponding to +% each second partial derivative in hess. +% +% +% Example usage: +% Rosenbrock function, minimized at [1,1] +% rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2; +% +% [h,err] = hessian(rosen,[1 1]) +% h = +% 842 -420 +% -420 210 +% err = +% 1.0662e-12 4.0061e-10 +% 4.0061e-10 2.6654e-13 +% +% +% Example usage: +% cos(x-y), at (0,0) +% Note: this hessian matrix will be positive semi-definite +% +% hessian(@(xy) cos(xy(1)-xy(2)),[0 0]) +% ans = +% -1 1 +% 1 -1 +% +% +% See also: derivest, gradient, gradest, hessdiag +% +% +% Author: John D'Errico +% e-mail: woodchips@rochester.rr.com +% Release: 1.0 +% Release date: 2/10/2007 + +% parameters that we might allow to change +params.StepRatio = 2.0000001; +params.RombergTerms = 3; + +% get the size of x0 so we can reshape +% later. +sx = size(x0); + +% was a string supplied? +if ischar(fun) + fun = str2func(fun); +end + +% total number of derivatives we will need to take +nx = length(x0); + +% get the diagonal elements of the hessian (2nd partial +% derivatives wrt each variable.) +[hess,err] = hessdiag(fun,x0); + +% form the eventual hessian matrix, stuffing only +% the diagonals for now. +hess = diag(hess); +err = diag(err); +if nx<2 + % the hessian matrix is 1x1. all done + return +end + +% get the gradient vector. This is done only to decide +% on intelligent step sizes for the mixed partials +[grad,graderr,stepsize] = gradest(fun,x0); + +% Get params.RombergTerms+1 estimates of the upper +% triangle of the hessian matrix +dfac = params.StepRatio.^(-(0:params.RombergTerms)'); +for i = 2:nx + for j = 1:(i-1) + dij = zeros(params.RombergTerms+1,1); + for k = 1:(params.RombergTerms+1) + dij(k) = fun(x0 + swap2(zeros(sx),i, ... + dfac(k)*stepsize(i),j,dfac(k)*stepsize(j))) + ... + fun(x0 + swap2(zeros(sx),i, ... + -dfac(k)*stepsize(i),j,-dfac(k)*stepsize(j))) - ... + fun(x0 + swap2(zeros(sx),i, ... + dfac(k)*stepsize(i),j,-dfac(k)*stepsize(j))) - ... + fun(x0 + swap2(zeros(sx),i, ... + -dfac(k)*stepsize(i),j,dfac(k)*stepsize(j))); + + end + dij = dij/4/prod(stepsize([i,j])); + dij = dij./(dfac.^2); + + % Romberg extrapolation step + [hess(i,j),err(i,j)] = rombextrap(params.StepRatio,dij,[2 4]); + hess(j,i) = hess(i,j); + err(j,i) = err(i,j); + end +end + + +end % mainline function end + +% ======================================= +% sub-functions +% ======================================= +function vec = swap2(vec,ind1,val1,ind2,val2) +% swaps val as element ind, into the vector vec +vec(ind1) = val1; +vec(ind2) = val2; + +end % sub-function end + + +% ============================================ +% subfunction - romberg extrapolation +% ============================================ +function [der_romb,errest] = rombextrap(StepRatio,der_init,rombexpon) +% do romberg extrapolation for each estimate +% +% StepRatio - Ratio decrease in step +% der_init - initial derivative estimates +% rombexpon - higher order terms to cancel using the romberg step +% +% der_romb - derivative estimates returned +% errest - error estimates +% amp - noise amplification factor due to the romberg step + +srinv = 1/StepRatio; + +% do nothing if no romberg terms +nexpon = length(rombexpon); +rmat = ones(nexpon+2,nexpon+1); +switch nexpon + case 0 + % rmat is simple: ones(2,1) + case 1 + % only one romberg term + rmat(2,2) = srinv^rombexpon; + rmat(3,2) = srinv^(2*rombexpon); + case 2 + % two romberg terms + rmat(2,2:3) = srinv.^rombexpon; + rmat(3,2:3) = srinv.^(2*rombexpon); + rmat(4,2:3) = srinv.^(3*rombexpon); + case 3 + % three romberg terms + rmat(2,2:4) = srinv.^rombexpon; + rmat(3,2:4) = srinv.^(2*rombexpon); + rmat(4,2:4) = srinv.^(3*rombexpon); + rmat(5,2:4) = srinv.^(4*rombexpon); +end + +% qr factorization used for the extrapolation as well +% as the uncertainty estimates +[qromb,rromb] = qr(rmat,0); + +% the noise amplification is further amplified by the Romberg step. +% amp = cond(rromb); + +% this does the extrapolation to a zero step size. +ne = length(der_init); +rombcoefs = rromb\(qromb'*der_init); +der_romb = rombcoefs(1,:)'; + +% uncertainty estimate of derivative prediction +s = sqrt(sum((der_init - rmat*rombcoefs).^2,1)); +rinv = rromb\eye(nexpon+1); +cov1 = sum(rinv.^2,2); % 1 spare dof +errest = s'*12.7062047361747*sqrt(cov1(1)); + +end % rombextrap + + diff --git a/bin/DERIVESTsuite/jacobianest.m b/bin/DERIVESTsuite/jacobianest.m new file mode 100644 index 0000000..10afa28 --- /dev/null +++ b/bin/DERIVESTsuite/jacobianest.m @@ -0,0 +1,216 @@ +function [jac,err] = jacobianest(fun,x0) +% gradest: estimate of the Jacobian matrix of a vector valued function of n variables +% usage: [jac,err] = jacobianest(fun,x0) +% +% +% arguments: (input) +% fun - (vector valued) analytical function to differentiate. +% fun must be a function of the vector or array x0. +% +% x0 - vector location at which to differentiate fun +% If x0 is an nxm array, then fun is assumed to be +% a function of n*m variables. +% +% +% arguments: (output) +% jac - array of first partial derivatives of fun. +% Assuming that x0 is a vector of length p +% and fun returns a vector of length n, then +% jac will be an array of size (n,p) +% +% err - vector of error estimates corresponding to +% each partial derivative in jac. +% +% +% Example: (nonlinear least squares) +% xdata = (0:.1:1)'; +% ydata = 1+2*exp(0.75*xdata); +% fun = @(c) ((c(1)+c(2)*exp(c(3)*xdata)) - ydata).^2; +% +% [jac,err] = jacobianest(fun,[1 1 1]) +% +% jac = +% -2 -2 0 +% -2.1012 -2.3222 -0.23222 +% -2.2045 -2.6926 -0.53852 +% -2.3096 -3.1176 -0.93528 +% -2.4158 -3.6039 -1.4416 +% -2.5225 -4.1589 -2.0795 +% -2.629 -4.7904 -2.8742 +% -2.7343 -5.5063 -3.8544 +% -2.8374 -6.3147 -5.0518 +% -2.9369 -7.2237 -6.5013 +% -3.0314 -8.2403 -8.2403 +% +% err = +% 5.0134e-15 5.0134e-15 0 +% 5.0134e-15 0 2.8211e-14 +% 5.0134e-15 8.6834e-15 1.5804e-14 +% 0 7.09e-15 3.8227e-13 +% 5.0134e-15 5.0134e-15 7.5201e-15 +% 5.0134e-15 1.0027e-14 2.9233e-14 +% 5.0134e-15 0 6.0585e-13 +% 5.0134e-15 1.0027e-14 7.2673e-13 +% 5.0134e-15 1.0027e-14 3.0495e-13 +% 5.0134e-15 1.0027e-14 3.1707e-14 +% 5.0134e-15 2.0053e-14 1.4013e-12 +% +% (At [1 2 0.75], jac should be numerically zero) +% +% +% See also: derivest, gradient, gradest +% +% +% Author: John D'Errico +% e-mail: woodchips@rochester.rr.com +% Release: 1.0 +% Release date: 3/6/2007 + +% get the length of x0 for the size of jac +nx = numel(x0); + +MaxStep = 100; +StepRatio = 2.0000001; + +% was a string supplied? +if ischar(fun) + fun = str2func(fun); +end + +% get fun at the center point +f0 = fun(x0); +f0 = f0(:); +n = length(f0); +if n==0 + % empty begets empty + jac = zeros(0,nx); + err = jac; + return +end + +relativedelta = MaxStep*StepRatio .^(0:-1:-25); +nsteps = length(relativedelta); + +% total number of derivatives we will need to take +jac = zeros(n,nx); +err = jac; +for i = 1:nx + x0_i = x0(i); + if x0_i ~= 0 + delta = x0_i*relativedelta; + else + delta = relativedelta; + end + + % evaluate at each step, centered around x0_i + % difference to give a second order estimate + fdel = zeros(n,nsteps); + for j = 1:nsteps + fdif = fun(swapelement(x0,i,x0_i + delta(j))) - ... + fun(swapelement(x0,i,x0_i - delta(j))); + + fdel(:,j) = fdif(:); + end + + % these are pure second order estimates of the + % first derivative, for each trial delta. + derest = fdel.*repmat(0.5 ./ delta,n,1); + + % The error term on these estimates has a second order + % component, but also some 4th and 6th order terms in it. + % Use Romberg exrapolation to improve the estimates to + % 6th order, as well as to provide the error estimate. + + % loop here, as rombextrap coupled with the trimming + % will get complicated otherwise. + for j = 1:n + [der_romb,errest] = rombextrap(StepRatio,derest(j,:),[2 4]); + + % trim off 3 estimates at each end of the scale + nest = length(der_romb); + trim = [1:3, nest+(-2:0)]; + [der_romb,tags] = sort(der_romb); + der_romb(trim) = []; + tags(trim) = []; + + errest = errest(tags); + + % now pick the estimate with the lowest predicted error + [err(j,i),ind] = min(errest); + jac(j,i) = der_romb(ind); + end +end + +end % mainline function end + +% ======================================= +% sub-functions +% ======================================= +function vec = swapelement(vec,ind,val) +% swaps val as element ind, into the vector vec +vec(ind) = val; + +end % sub-function end + +% ============================================ +% subfunction - romberg extrapolation +% ============================================ +function [der_romb,errest] = rombextrap(StepRatio,der_init,rombexpon) +% do romberg extrapolation for each estimate +% +% StepRatio - Ratio decrease in step +% der_init - initial derivative estimates +% rombexpon - higher order terms to cancel using the romberg step +% +% der_romb - derivative estimates returned +% errest - error estimates +% amp - noise amplification factor due to the romberg step + +srinv = 1/StepRatio; + +% do nothing if no romberg terms +nexpon = length(rombexpon); +rmat = ones(nexpon+2,nexpon+1); +% two romberg terms +rmat(2,2:3) = srinv.^rombexpon; +rmat(3,2:3) = srinv.^(2*rombexpon); +rmat(4,2:3) = srinv.^(3*rombexpon); + +% qr factorization used for the extrapolation as well +% as the uncertainty estimates +[qromb,rromb] = qr(rmat,0); + +% the noise amplification is further amplified by the Romberg step. +% amp = cond(rromb); + +% this does the extrapolation to a zero step size. +ne = length(der_init); +rhs = vec2mat(der_init,nexpon+2,ne - (nexpon+2)); +rombcoefs = rromb\(qromb'*rhs); +der_romb = rombcoefs(1,:)'; + +% uncertainty estimate of derivative prediction +s = sqrt(sum((rhs - rmat*rombcoefs).^2,1)); +rinv = rromb\eye(nexpon+1); +cov1 = sum(rinv.^2,2); % 1 spare dof +errest = s'*12.7062047361747*sqrt(cov1(1)); + +end % rombextrap + + +% ============================================ +% subfunction - vec2mat +% ============================================ +function mat = vec2mat(vec,n,m) +% forms the matrix M, such that M(i,j) = vec(i+j-1) +[i,j] = ndgrid(1:n,0:m-1); +ind = i+j; +mat = vec(ind); +if n==1 + mat = mat'; +end + +end % vec2mat + + + diff --git a/bin/DERIVESTsuite/~$ReadMe.rtf b/bin/DERIVESTsuite/~$ReadMe.rtf new file mode 100644 index 0000000..4d39df4 Binary files /dev/null and b/bin/DERIVESTsuite/~$ReadMe.rtf differ diff --git a/bin/MBeautifier b/bin/MBeautifier deleted file mode 160000 index 9a30089..0000000 --- a/bin/MBeautifier +++ /dev/null @@ -1 +0,0 @@ -Subproject commit 9a300892a3e6378ed46ed226dff3f78e3000c0f4 diff --git a/bin/OuterProduct.m b/bin/OuterProduct.m new file mode 100644 index 0000000..e8340ed --- /dev/null +++ b/bin/OuterProduct.m @@ -0,0 +1,10 @@ +% A = magic(3); +% B = [1,2,3]'; +% C = OuterProduct(A,B) + +function C = OuterProduct(A, B) % version 4 +% https://au.mathworks.com/matlabcentral/answers/445798-outer-product-of-two-rectangular-matrices +C = A .* reshape(B, [ones(1, ndims(A)), size(B)]); +% Matlab < R2016b: +% C = bsxfun(@times, A, reshape(B, [ones(1, ndims(A)), size(B)])) +end \ No newline at end of file diff --git a/bin/distinguishable_colors.zip b/bin/distinguishable_colors.zip new file mode 100644 index 0000000..15cb0ec Binary files /dev/null and b/bin/distinguishable_colors.zip differ diff --git a/bin/distinguishable_colors/distinguishable_colors.m b/bin/distinguishable_colors/distinguishable_colors.m new file mode 100644 index 0000000..f9e9e25 --- /dev/null +++ b/bin/distinguishable_colors/distinguishable_colors.m @@ -0,0 +1,152 @@ +function colors = distinguishable_colors(n_colors,bg,func) +% DISTINGUISHABLE_COLORS: pick colors that are maximally perceptually distinct +% +% When plotting a set of lines, you may want to distinguish them by color. +% By default, Matlab chooses a small set of colors and cycles among them, +% and so if you have more than a few lines there will be confusion about +% which line is which. To fix this problem, one would want to be able to +% pick a much larger set of distinct colors, where the number of colors +% equals or exceeds the number of lines you want to plot. Because our +% ability to distinguish among colors has limits, one should choose these +% colors to be "maximally perceptually distinguishable." +% +% This function generates a set of colors which are distinguishable +% by reference to the "Lab" color space, which more closely matches +% human color perception than RGB. Given an initial large list of possible +% colors, it iteratively chooses the entry in the list that is farthest (in +% Lab space) from all previously-chosen entries. While this "greedy" +% algorithm does not yield a global maximum, it is simple and efficient. +% Moreover, the sequence of colors is consistent no matter how many you +% request, which facilitates the users' ability to learn the color order +% and avoids major changes in the appearance of plots when adding or +% removing lines. +% +% Syntax: +% colors = distinguishable_colors(n_colors) +% Specify the number of colors you want as a scalar, n_colors. This will +% generate an n_colors-by-3 matrix, each row representing an RGB +% color triple. If you don't precisely know how many you will need in +% advance, there is no harm (other than execution time) in specifying +% slightly more than you think you will need. +% +% colors = distinguishable_colors(n_colors,bg) +% This syntax allows you to specify the background color, to make sure that +% your colors are also distinguishable from the background. Default value +% is white. bg may be specified as an RGB triple or as one of the standard +% "ColorSpec" strings. You can even specify multiple colors: +% bg = {'w','k'} +% or +% bg = [1 1 1; 0 0 0] +% will only produce colors that are distinguishable from both white and +% black. +% +% colors = distinguishable_colors(n_colors,bg,rgb2labfunc) +% By default, distinguishable_colors uses the image processing toolbox's +% color conversion functions makecform and applycform. Alternatively, you +% can supply your own color conversion function. +% +% Example: +% c = distinguishable_colors(25); +% figure +% image(reshape(c,[1 size(c)])) +% +% Example using the file exchange's 'colorspace': +% func = @(x) colorspace('RGB->Lab',x); +% c = distinguishable_colors(25,'w',func); + +% Copyright 2010-2011 by Timothy E. Holy + + % Parse the inputs + if (nargin < 2) + bg = [1 1 1]; % default white background + else + if iscell(bg) + % User specified a list of colors as a cell aray + bgc = bg; + for i = 1:length(bgc) + bgc{i} = parsecolor(bgc{i}); + end + bg = cat(1,bgc{:}); + else + % User specified a numeric array of colors (n-by-3) + bg = parsecolor(bg); + end + end + + % Generate a sizable number of RGB triples. This represents our space of + % possible choices. By starting in RGB space, we ensure that all of the + % colors can be generated by the monitor. + n_grid = 30; % number of grid divisions along each axis in RGB space + x = linspace(0,1,n_grid); + [R,G,B] = ndgrid(x,x,x); + rgb = [R(:) G(:) B(:)]; + if (n_colors > size(rgb,1)/3) + error('You can''t readily distinguish that many colors'); + end + + % Convert to Lab color space, which more closely represents human + % perception + if (nargin > 2) + lab = func(rgb); + bglab = func(bg); + else + C = makecform('srgb2lab'); + lab = applycform(rgb,C); + bglab = applycform(bg,C); + end + + % If the user specified multiple background colors, compute distances + % from the candidate colors to the background colors + mindist2 = inf(size(rgb,1),1); + for i = 1:size(bglab,1)-1 + dX = bsxfun(@minus,lab,bglab(i,:)); % displacement all colors from bg + dist2 = sum(dX.^2,2); % square distance + mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color + end + + % Iteratively pick the color that maximizes the distance to the nearest + % already-picked color + colors = zeros(n_colors,3); + lastlab = bglab(end,:); % initialize by making the "previous" color equal to background + for i = 1:n_colors + dX = bsxfun(@minus,lab,lastlab); % displacement of last from all colors on list + dist2 = sum(dX.^2,2); % square distance + mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color + [~,index] = max(mindist2); % find the entry farthest from all previously-chosen colors + colors(i,:) = rgb(index,:); % save for output + lastlab = lab(index,:); % prepare for next iteration + end +end + +function c = parsecolor(s) + if ischar(s) + c = colorstr2rgb(s); + elseif isnumeric(s) && size(s,2) == 3 + c = s; + else + error('MATLAB:InvalidColorSpec','Color specification cannot be parsed.'); + end +end + +function c = colorstr2rgb(c) + % Convert a color string to an RGB value. + % This is cribbed from Matlab's whitebg function. + % Why don't they make this a stand-alone function? + rgbspec = [1 0 0;0 1 0;0 0 1;1 1 1;0 1 1;1 0 1;1 1 0;0 0 0]; + cspec = 'rgbwcmyk'; + k = find(cspec==c(1)); + if isempty(k) + error('MATLAB:InvalidColorString','Unknown color string.'); + end + if k~=3 || length(c)==1, + c = rgbspec(k,:); + elseif length(c)>2, + if strcmpi(c(1:3),'bla') + c = [0 0 0]; + elseif strcmpi(c(1:3),'blu') + c = [0 0 1]; + else + error('MATLAB:UnknownColorString', 'Unknown color string.'); + end + end +end diff --git a/bin/distinguishable_colors/license.txt b/bin/distinguishable_colors/license.txt new file mode 100644 index 0000000..63168b1 --- /dev/null +++ b/bin/distinguishable_colors/license.txt @@ -0,0 +1,24 @@ +Copyright (c) 2010-2011, Tim Holy +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in + the documentation and/or other materials provided with the distribution + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +POSSIBILITY OF SUCH DAMAGE. diff --git a/bin/export_fig b/bin/export_fig index b1a7288..8b0ba13 160000 --- a/bin/export_fig +++ b/bin/export_fig @@ -1 +1 @@ -Subproject commit b1a72880758c073ff5a44cc02e1e1cdeb9b6c089 +Subproject commit 8b0ba1314514d2ff47cef4b8d4701605e42e6312 diff --git a/bin/histcn/histcn.m b/bin/histcn/histcn.m index 6f693d1..90465bc 100644 --- a/bin/histcn/histcn.m +++ b/bin/histcn/histcn.m @@ -1,4 +1,4 @@ -function [count edges mid loc] = histcn(X, varargin) +function [count,edges,mid,loc] = histcn(X, varargin) % function [count edges mid loc] = histcn(X, edge1, edge2, ..., edgeN) % % Purpose: compute n-dimensional histogram @@ -59,7 +59,7 @@ % Bruno Luong: % Last update: 25/August/2011 -if ndims(X)>2 +if ~ismatrix(X) error('histcn: X requires to be an (M x N) array of M points in R^N'); end DEFAULT_NBINS = 32; @@ -105,20 +105,19 @@ end edges{d} = ed; % Call histc on this dimension - [dummy loc(:,d)] = histc(Xd, ed, 1); + [~, loc(:,d)] = histc(Xd, ed, 1); %bryce change dummy to ~ % Use sz(d) = length(ed); to create consistent number of bins sz(d) = length(ed)-1; end % for-loop -% Clean -clear dummy + % This is need for seldome points that hit the right border sz = max([sz; max(loc,[],1)]); % Compute the mid points mid = cellfun(@(e) 0.5*(e(1:end-1)+e(2:end)), edges, ... - 'UniformOutput', false); + 'UniformOutput', false); %%very slow part of the code, would be better to vector % Count for points where all coordinates are falling in a corresponding % bins @@ -133,6 +132,7 @@ count = accumarray(loc(hasdata,:), 1, sz); end -return +%count=loc; %speed diagnosing + end % histcn diff --git a/bin/level_data/drake_triplet_singlet_transitions.txt b/bin/level_data/drake_triplet_singlet_transitions.txt new file mode 100644 index 0000000..55d00d3 --- /dev/null +++ b/bin/level_data/drake_triplet_singlet_transitions.txt @@ -0,0 +1,355 @@ +Title: A Multiplet Table for Neutral Helium (^4^He I) with Transition Rates +Authors: Drake, G.W.F., Morton D.C. +Table: Multiplet Table for ^4^He Triplet - Singlet Transitions +================================================================================ +Byte-by-byte Description of file: datafile7.txt +-------------------------------------------------------------------------------- + Bytes Format Units Label Explanations +-------------------------------------------------------------------------------- + 1- 3 I3 --- N Sequential multiplet number + 5- 16 A12 --- Trans Level designations n ^2S+1^L (Lower-Upper) + 18- 21 A4 --- J-J Lower and Upper J-values + 23- 32 F10.4 0.1nm AWave Air wavelength (1) + 34- 45 F12.6 --- VWave Vacuum wavelength/wavenumber (2) + 47- 50 A4 --- Units Units for VWave (3) + 52- 64 F13.6 cm-1 Elow Lower level energy from Drake & Morton (2006) + 66- 78 F13.6 cm-1 Eup Upper level energy from Drake & Morton (2006) + 80- 89 E10.4 s-1 Aul Spontaneous transition rate (4) + 91-100 E10.4 s-1 SAul Sum of all A_ul_ to lower levels (5) + 102-111 E10.4 --- flu Absorption oscillator strength or f-value (4) +-------------------------------------------------------------------------------- +Note (1): For {lambda} > 2000 Angstroms following Peck & Reeder (1972). +Note (2): Calculated from the energy levels of Paper I according to equation 1. + If the vacuum wavelength exceeds 1e4 Angstroms, the value is the more + useful vacuum wavenumber as indicated by the Units column. +Note (3): cm-1 = Inverse cm; wavenumber if {lambda} > 1e4 Angstroms. +Note (4): Including singlet-triplet mixing and spin-orbit coupling. +Note (5): Which is the reciprocal of the lifetime of the upper level. +-------------------------------------------------------------------------------- +742 2 3S - 2 1P 1-1 8863.6613 8866.095052 159855.974330 171134.896946 1.4423E+00 1.8009E+09 1.7000E-08 +743 2 3P - 3 1D 1-2 5874.4603 5876.088412 169086.842898 186104.966689 1.2324E+04 6.3721E+07 1.0632E-04 +743 2 3P - 3 1D 2-2 5874.4339 5876.062023 169086.766473 186104.966689 4.3097E+03 6.3721E+07 2.2307E-05 +744 2 3P - 4 1D 1-2 4471.0947 4472.349352 169086.842898 191446.455741 2.2565E+03 2.6983E+07 1.1276E-05 +744 2 3P - 4 1D 2-2 4471.0794 4472.334065 169086.766473 191446.455741 7.9822E+02 2.6983E+07 2.3933E-06 +745 2 3P - 5 1D 1-2 4026.0138 4027.151538 169086.842898 193918.289901 8.3444E+02 1.3929E+07 3.3809E-06 +746 3 3S - 3 1P 1-1 2972.573239 cm-1 183236.791701 186209.364940 1.4612E-01 5.7996E+08 2.4796E-08 +747 3 3P - 3 1D 1-2 540.382794 cm-1 185564.583895 186104.966689 2.3169E+00 6.3721E+07 1.9854E-05 +747 3 3P - 3 1D 2-2 540.404769 cm-1 185564.561920 186104.966689 8.0194E-01 6.3721E+07 4.1232E-06 +748 3 3P - 4 1D 1-2 5881.871845 cm-1 185564.583895 191446.455741 6.0382E+02 2.6983E+07 4.3605E-05 +748 3 3P - 4 1D 2-2 5881.893821 cm-1 185564.561920 191446.455741 2.1479E+02 2.6983E+07 9.3067E-06 +749 3 3P - 5 1D 1-2 8353.706006 cm-1 185564.583895 193918.289901 2.4997E+02 1.3929E+07 8.9489E-06 +749 3 3P - 5 1D 2-2 8353.727981 cm-1 185564.561920 193918.289901 8.8991E+01 1.3929E+07 1.9115E-06 +750 3 3P - 6 1D 1-2 9696.186613 cm-1 185564.583895 195260.770508 1.2703E+02 8.1234E+06 3.3755E-06 +751 3 3P - 7 1D 1-2 9516.1727 9518.783164 185564.583895 196070.128383 7.3873E+01 5.1495E+06 1.6722E-06 +752 3 3D - 3 1P 1-1 107.772050 cm-1 186101.592890 186209.364940 2.8333E-06 5.7996E+08 3.6735E-10 +752 3 3D - 3 1P 2-1 107.816251 cm-1 186101.548689 186209.364940 3.9860E-02 5.7996E+08 3.1008E-06 +753 3 3D - 4 1P 2-1 5391.163220 cm-1 186101.548689 191492.711909 6.9189E+01 2.5227E+08 2.1408E-06 +754 3 3D - 4 1F 2-3 5350.348772 cm-1 186101.548689 191451.897461 4.2938E+06 1.3833E+07 3.1474E-01 +754 3 3D - 4 1F 3-3 5350.351284 cm-1 186101.546177 191451.897461 5.6112E+05 1.3833E+07 2.9379E-02 +755 3 3D - 5 1F 2-3 7819.582192 cm-1 186101.548689 193921.130881 1.1684E+06 7.1556E+06 4.0095E-02 +755 3 3D - 5 1F 3-3 7819.584704 cm-1 186101.546177 193921.130881 1.5372E+05 7.1556E+06 3.7680E-03 +756 3 3D - 6 1F 2-3 9160.883095 cm-1 186101.548689 195262.431784 4.8843E+05 4.1865E+06 1.2212E-02 +756 3 3D - 6 1F 3-3 9160.885608 cm-1 186101.546177 195262.431784 6.4549E+04 4.1865E+06 1.1528E-03 +757 3 3D - 7 1F 2-3 9969.632376 cm-1 186101.548689 196071.181065 2.5370E+05 2.6620E+06 5.3559E-03 +757 3 3D - 7 1F 3-3 9969.634888 cm-1 186101.546177 196071.181065 3.3628E+04 2.6620E+06 5.0709E-04 +758 3 3D - 8 1F 2-3 9526.1573 9528.770471 186101.548689 196596.082093 1.5015E+05 1.7979E+06 2.8607E-03 +758 3 3D - 8 1F 3-3 9526.1551 9528.768190 186101.546177 196596.082093 1.9944E+04 1.7979E+06 2.7141E-04 +759 3 3D - 9 1F 2-3 9210.3273 9212.854879 186101.548689 196955.947387 9.6907E+04 1.2714E+06 1.7259E-03 +759 3 3D - 9 1F 3-3 9210.3252 9212.852746 186101.546177 196955.947387 1.2891E+04 1.2714E+06 1.6399E-04 +760 3 3D -10 1F 2-3 8996.9681 8999.437941 186101.548689 197213.353743 6.6513E+04 9.3212E+05 1.1303E-03 +760 3 3D -10 1F 3-3 8996.9661 8999.435907 186101.546177 197213.353743 8.8574E+03 9.3212E+05 1.0752E-04 +761 4 3S - 4 1P 1-1 1194.598649 cm-1 190298.113260 191492.711909 3.1254E-02 2.5227E+08 3.2840E-08 +762 4 3P - 4 1D 1-2 229.405777 cm-1 191217.049963 191446.455741 3.9467E-01 2.6983E+07 1.8765E-05 +762 4 3P - 4 1D 2-2 229.414773 cm-1 191217.040967 191446.455741 1.3841E-01 2.6983E+07 3.9485E-06 +763 4 3P - 5 1D 1-2 2701.239938 cm-1 191217.049963 193918.289901 9.1222E+01 1.3929E+07 3.1234E-05 +763 4 3P - 5 1D 2-2 2701.248934 cm-1 191217.040967 193918.289901 3.2759E+01 1.3929E+07 6.7299E-06 +764 4 3P - 6 1D 1-2 4043.720545 cm-1 191217.049963 195260.770508 5.1475E+01 8.1234E+06 7.8644E-06 +764 4 3P - 6 1D 2-2 4043.729541 cm-1 191217.040967 195260.770508 1.8418E+01 8.1234E+06 1.6884E-06 +765 4 3P - 7 1D 1-2 4853.078420 cm-1 191217.049963 196070.128383 3.0856E+01 5.1495E+06 3.2729E-06 +766 4 3P - 8 1D 1-2 5378.324089 cm-1 191217.049963 196595.374052 1.9893E+01 3.4685E+06 1.7180E-06 +767 4 3D - 4 1P 1-1 48.211258 cm-1 191444.500651 191492.711909 1.0241E-06 2.5227E+08 6.6338E-10 +767 4 3D - 4 1P 2-1 48.229779 cm-1 191444.482131 191492.711909 8.0579E-03 2.5227E+08 3.1318E-06 +768 4 3D - 4 1F 2-3 7.415330 cm-1 191444.482131 191451.897461 2.7852E-02 1.3833E+07 1.0684E-03 +768 4 3D - 4 1F 3-3 7.416532 cm-1 191444.480929 191451.897461 3.5957E-03 1.3833E+07 9.8523E-05 +769 4 3D - 5 1P 2-1 2497.980163 cm-1 191444.482131 193942.462294 2.0046E+01 1.3115E+08 2.8891E-06 +770 4 3D - 5 1F 2-3 2476.648750 cm-1 191444.482131 193921.130881 6.6970E+05 7.1556E+06 2.2910E-01 +770 4 3D - 5 1F 3-3 2476.649952 cm-1 191444.480929 193921.130881 8.6889E+04 7.1556E+06 2.1232E-02 +771 4 3D - 6 1P 2-1 3830.426335 cm-1 191444.482131 195274.908466 1.0088E+01 7.6575E+07 6.1832E-07 +772 4 3D - 6 1F 2-3 3817.949654 cm-1 191444.482131 195262.431784 2.9609E+05 4.1865E+06 4.2622E-02 +772 4 3D - 6 1F 3-3 3817.950855 cm-1 191444.480929 195262.431784 3.8539E+04 4.1865E+06 3.9626E-03 +773 4 3D - 7 1F 2-3 4626.698934 cm-1 191444.482131 196071.181065 1.5620E+05 2.6620E+06 1.5311E-02 +773 4 3D - 7 1F 3-3 4626.700136 cm-1 191444.480929 196071.181065 2.0375E+04 2.6620E+06 1.4266E-03 +774 4 3D - 8 1F 2-3 5151.599962 cm-1 191444.482131 196596.082093 9.3069E+04 1.7979E+06 7.3585E-03 +774 4 3D - 8 1F 3-3 5151.601163 cm-1 191444.480929 196596.082093 1.2158E+04 1.7979E+06 6.8663E-04 +775 4 3D - 9 1F 2-3 5511.465256 cm-1 191444.482131 196955.947387 6.0284E+04 1.2714E+06 4.1643E-03 +775 4 3D - 9 1F 3-3 5511.466458 cm-1 191444.480929 196955.947387 7.8839E+03 1.2714E+06 3.8900E-04 +776 4 3D -10 1F 2-3 5768.871612 cm-1 191444.482131 197213.353743 4.1467E+04 9.3212E+05 2.6145E-03 +776 4 3D -10 1F 3-3 5768.872814 cm-1 191444.480929 197213.353743 5.4273E+03 9.3212E+05 2.4442E-04 +777 4 3F - 5 1D 3-2 2466.415952 cm-1 191451.873949 193918.289901 1.8332E+04 1.3929E+07 3.2262E-03 +778 4 3F - 5 1G 4-4 2469.740845 cm-1 191451.881089 193921.621933 1.2799E+05 4.2583E+06 3.1450E-02 +778 4 3F - 5 1G 3-4 2469.747984 cm-1 191451.873949 193921.621933 4.2449E+04 4.2583E+06 1.3411E-02 +779 4 3F - 6 1D 3-2 3808.896559 cm-1 191451.873949 195260.770508 7.8046E+03 8.1234E+06 5.7592E-04 +780 4 3F - 6 1G 4-4 3810.846036 cm-1 191451.881089 195262.727124 4.1289E+04 2.4812E+06 4.2612E-03 +780 4 3F - 6 1G 3-4 3810.853176 cm-1 191451.873949 195262.727124 1.3603E+04 2.4812E+06 1.8050E-03 +781 4 3F - 7 1D 3-2 4618.254435 cm-1 191451.873949 196070.128383 4.0948E+03 5.1495E+06 2.0554E-04 +782 4 3F - 7 1G 4-4 4619.490195 cm-1 191451.881089 196071.371284 1.9417E+04 1.5756E+06 1.3638E-03 +782 4 3F - 7 1G 3-4 4619.497335 cm-1 191451.873949 196071.371284 6.3643E+03 1.5756E+06 5.7471E-04 +783 4 3F - 8 1D 3-2 5143.500104 cm-1 191451.873949 196595.374052 2.4454E+03 3.4685E+06 9.8957E-05 +784 4 3F - 8 1G 4-4 5144.330273 cm-1 191451.881089 196596.211362 1.0949E+04 1.0641E+06 6.2009E-04 +784 4 3F - 8 1G 3-4 5144.337413 cm-1 191451.873949 196596.211362 3.5753E+03 1.0641E+06 2.6034E-04 +785 4 3F - 9 1D 3-2 5503.574801 cm-1 191451.873949 196955.448750 1.5903E+03 2.4468E+06 5.6209E-05 +786 4 3F - 9 1G 4-4 5504.157972 cm-1 191451.881089 196956.039061 6.8772E+03 7.5279E+05 3.4023E-04 +786 4 3F - 9 1G 3-4 5504.165112 cm-1 191451.873949 196956.039061 2.2394E+03 7.5279E+05 1.4244E-04 +787 4 3F -10 1D 3-2 5761.115582 cm-1 191451.873949 197212.989530 1.0983E+03 1.7903E+06 3.5426E-05 +788 4 3F -10 1G 4-4 5761.539945 cm-1 191451.881089 197213.421034 4.6421E+03 5.5231E+05 2.0959E-04 +788 4 3F -10 1G 3-4 5761.547085 cm-1 191451.873949 197213.421034 1.5084E+03 5.5231E+05 8.7564E-05 +789 5 3S - 5 1P 1-1 595.470949 cm-1 193346.991344 193942.462294 9.6778E-03 1.3115E+08 4.0926E-08 +790 5 3P - 5 1D 1-2 117.577783 cm-1 193800.712118 193918.289901 1.1325E-01 1.3929E+07 2.0497E-05 +790 5 3P - 5 1D 2-2 117.582306 cm-1 193800.707595 193918.289901 3.9960E-02 1.3929E+07 4.3395E-06 +791 5 3P - 6 1D 1-2 1460.058390 cm-1 193800.712118 195260.770508 2.3039E+01 8.1234E+06 2.7000E-05 +791 5 3P - 6 1D 2-2 1460.062913 cm-1 193800.707595 195260.770508 8.3221E+00 8.1234E+06 5.8518E-06 +792 5 3P - 7 1D 1-2 2269.416265 cm-1 193800.712118 196070.128383 1.5240E+01 5.1495E+06 7.3924E-06 +792 5 3P - 7 1D 2-2 2269.420789 cm-1 193800.707595 196070.128383 5.4724E+00 5.1495E+06 1.5927E-06 +793 5 3P - 8 1D 1-2 2794.661934 cm-1 193800.712118 196595.374052 1.0095E+01 3.4685E+06 3.2290E-06 +794 5 3P - 9 1D 1-2 3154.736632 cm-1 193800.712118 196955.448750 6.9729E+00 2.4468E+06 1.7503E-06 +795 5 3D - 5 1P 1-1 25.300907 cm-1 193917.161387 193942.462294 3.9493E-07 1.3115E+08 9.2881E-10 +795 5 3D - 5 1P 2-1 25.310365 cm-1 193917.151929 193942.462294 2.5013E-03 1.3115E+08 3.5296E-06 +796 5 3D - 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9 1D 1-2 928.132109 cm-1 196027.316641 196955.448750 2.4855E+00 2.4468E+06 7.2080E-06 +865 7 3P - 9 1D 2-2 928.133724 cm-1 196027.315027 196955.448750 8.9661E-01 2.4468E+06 1.5601E-06 +866 7 3P -10 1D 1-2 1185.672890 cm-1 196027.316641 197212.989530 1.8443E+00 1.7903E+06 3.2773E-06 +867 7 3D - 7 1P 1-1 9.411080 cm-1 196069.676490 196079.087570 8.3562E-08 4.8499E+07 1.4203E-09 +867 7 3D - 7 1P 2-1 9.414520 cm-1 196069.673050 196079.087570 4.4706E-04 4.8499E+07 4.5593E-06 +868 7 3D - 7 1F 2-3 1.508015 cm-1 196069.673050 196071.181065 2.7881E-03 2.6620E+06 2.5830E-03 +868 7 3D - 7 1F 3-3 1.508256 cm-1 196069.672809 196071.181065 3.6068E-04 2.6620E+06 2.3868E-04 +869 7 3D - 8 1P 2-1 531.727197 cm-1 196069.673050 196601.400247 2.0200E+00 3.2619E+07 6.4253E-06 +870 7 3D - 8 1F 2-3 526.409043 cm-1 196069.673050 196596.082093 2.2160E+04 1.7979E+06 1.6780E-01 +870 7 3D - 8 1F 3-3 526.409284 cm-1 196069.672809 196596.082093 2.8705E+03 1.7979E+06 1.5526E-02 +871 7 3D - 9 1P 2-1 890.019766 cm-1 196069.673050 196959.692816 1.2876E+00 2.2974E+07 1.4618E-06 +872 7 3D - 9 1F 2-3 886.274337 cm-1 196069.673050 196955.947387 1.5246E+04 1.2714E+06 4.0728E-02 +872 7 3D - 9 1F 3-3 886.274578 cm-1 196069.672809 196955.947387 1.9766E+03 1.2714E+06 3.7716E-03 +873 7 3D -10 1F 2-3 1143.680693 cm-1 196069.673050 197213.353743 1.0656E+04 9.3212E+05 1.7094E-02 +873 7 3D -10 1F 3-3 1143.680934 cm-1 196069.672809 197213.353743 1.3824E+03 9.3212E+05 1.5840E-03 +874 7 3F - 8 1D 3-2 524.197874 cm-1 196071.176178 196595.374052 3.9043E+03 3.4685E+06 1.5211E-02 +875 7 3F - 8 1G 4-4 525.034238 cm-1 196071.177123 196596.211362 4.6090E+03 1.0641E+06 2.5060E-02 +875 7 3F - 8 1G 3-4 525.035184 cm-1 196071.176178 196596.211362 7.5823E+03 1.0641E+06 5.3005E-02 +876 7 3F - 9 1D 3-2 884.272572 cm-1 196071.176178 196955.448750 2.2652E+03 2.4468E+06 3.1013E-03 +877 7 3F - 9 1G 4-4 884.861937 cm-1 196071.177123 196956.039061 3.0919E+03 7.5279E+05 5.9186E-03 +877 7 3F - 9 1G 3-4 884.862883 cm-1 196071.176178 196956.039061 5.0813E+03 7.5279E+05 1.2506E-02 +878 7 3F -10 1D 3-2 1141.813352 cm-1 196071.176178 197212.989530 1.4401E+03 1.7903E+06 1.1825E-03 +879 7 3F -10 1G 4-4 1142.243910 cm-1 196071.177123 197213.421034 2.1274E+03 5.5231E+05 2.4438E-03 +879 7 3F -10 1G 3-4 1142.244856 cm-1 196071.176178 197213.421034 3.4935E+03 5.5231E+05 5.1597E-03 +880 7 3G - 8 1F 3-3 524.711429 cm-1 196071.370664 196596.082093 1.2529E+02 1.7979E+06 6.8205E-04 +880 7 3G - 8 1F 4-3 524.713354 cm-1 196071.368738 196596.082093 6.0534E+02 1.7979E+06 2.5630E-03 +881 7 3G - 8 1H 5-5 524.872459 cm-1 196071.369746 196596.242205 4.0583E+03 7.0248E+05 2.2079E-02 +881 7 3G - 8 1H 4-5 524.873467 cm-1 196071.368738 196596.242205 6.6250E+00 7.0248E+05 4.4052E-05 +882 7 3G - 9 1F 3-3 884.576723 cm-1 196071.370664 196955.947387 6.2941E+01 1.2714E+06 1.2056E-04 +882 7 3G - 9 1F 4-3 884.578649 cm-1 196071.368738 196955.947387 3.3832E+02 1.2714E+06 5.0402E-04 +883 7 3G - 9 1H 5-5 884.691335 cm-1 196071.369746 196956.061082 2.4101E+03 4.9674E+05 4.6152E-03 +883 7 3G - 9 1H 4-5 884.692343 cm-1 196071.368738 196956.061082 3.9339E+00 4.9674E+05 9.2073E-06 +884 7 3G -10 1F 3-3 1141.983079 cm-1 196071.370664 197213.353743 3.6404E+01 9.3212E+05 4.1838E-05 +884 7 3G -10 1F 4-3 1141.985005 cm-1 196071.368738 197213.353743 2.1089E+02 9.3212E+05 1.8851E-04 +885 7 3G -10 1H 5-5 1142.067528 cm-1 196071.369746 197213.437274 1.5322E+03 3.6446E+05 1.7606E-03 +885 7 3G -10 1H 4-5 1142.068536 cm-1 196071.368738 197213.437274 2.5035E+00 3.6446E+05 3.5160E-06 +886 7 3H - 8 1G 4-4 524.795595 cm-1 196071.415767 196596.211362 7.4139E+01 1.0641E+06 4.0346E-04 +886 7 3H - 8 1G 5-4 524.796849 cm-1 196071.414513 196596.211362 8.4310E-01 1.0641E+06 3.7539E-06 +887 7 3H - 8 1I 6-6 524.836696 cm-1 196071.415170 196596.251866 3.7990E+03 4.9846E+05 2.0671E-02 +887 7 3H - 8 1I 5-6 524.837354 cm-1 196071.414513 196596.251866 6.0574E+00 4.9846E+05 3.8952E-05 +888 7 3H - 9 1G 4-4 884.623294 cm-1 196071.415767 196956.039061 3.3462E+01 7.5279E+05 6.4088E-05 +889 7 3H - 9 1I 6-6 884.652867 cm-1 196071.415170 196956.068037 1.7797E+03 3.5197E+05 3.4083E-03 +889 7 3H - 9 1I 5-6 884.653524 cm-1 196071.414513 196956.068037 2.8375E+00 3.5197E+05 6.4222E-06 +890 7 3H -10 1G 4-4 1142.005267 cm-1 196071.415767 197213.421034 1.8160E+01 5.5231E+05 2.0870E-05 +891 7 3H -10 1I 6-6 1142.027263 cm-1 196071.415170 197213.442433 9.8297E+02 2.5807E+05 1.1296E-03 +891 7 3H -10 1I 5-6 1142.027920 cm-1 196071.414513 197213.442433 1.5672E+00 2.5807E+05 2.1284E-06 +892 7 3I - 8 1H 5-5 524.812432 cm-1 196071.429773 196596.242205 1.6037E+01 7.0248E+05 8.7268E-05 +893 7 3I - 9 1H 5-5 884.631309 cm-1 196071.429773 196956.061082 5.9162E+00 4.9674E+05 1.1331E-05 +894 7 3I -10 1H 5-5 1142.007501 cm-1 196071.429773 197213.437274 2.8365E+00 3.6446E+05 3.2597E-06 +895 8 3S - 8 1P 1-1 140.038437 cm-1 196461.361811 196601.400247 8.5285E-04 3.2619E+07 6.5212E-08 +896 8 3P - 8 1D 1-2 28.661155 cm-1 196566.712897 196595.374052 9.3957E-03 3.4685E+06 2.8618E-05 +896 8 3P - 8 1D 2-2 28.662230 cm-1 196566.711822 196595.374052 3.3376E-03 3.4685E+06 6.0995E-06 +897 8 3P - 9 1D 1-2 388.735853 cm-1 196566.712897 196955.448750 1.5072E+00 2.4468E+06 2.4917E-05 +897 8 3P - 9 1D 2-2 388.736928 cm-1 196566.711822 196955.448750 5.4913E-01 2.4468E+06 5.4470E-06 +898 8 3P -10 1D 1-2 646.276633 cm-1 196566.712897 197212.989530 1.2196E+00 1.7903E+06 7.2946E-06 +898 8 3P -10 1D 2-2 646.277708 cm-1 196566.711822 197212.989530 4.4063E-01 1.7903E+06 1.5813E-06 +899 8 3D - 8 1P 1-1 6.335579 cm-1 196595.064668 196601.400247 4.4162E-08 3.2619E+07 1.6562E-09 +899 8 3D - 8 1P 2-1 6.337882 cm-1 196595.062365 196601.400247 2.2734E-04 3.2619E+07 5.1155E-06 +900 8 3D - 8 1F 2-3 1.019728 cm-1 196595.062365 196596.082093 1.4689E-03 1.7979E+06 2.9754E-03 +900 8 3D - 8 1F 3-3 1.019890 cm-1 196595.062202 196596.082093 1.9011E-04 1.7979E+06 2.7506E-04 +901 8 3D - 9 1P 2-1 364.630451 cm-1 196595.062365 196959.692816 1.1505E+00 2.2974E+07 7.7822E-06 +902 8 3D - 9 1F 2-3 360.885022 cm-1 196595.062365 196955.947387 1.0228E+04 1.2714E+06 1.6479E-01 +902 8 3D - 9 1F 3-3 360.885185 cm-1 196595.062202 196955.947387 1.3250E+03 1.2714E+06 1.5248E-02 +903 8 3D -10 1P 2-1 621.027197 cm-1 196595.062365 197216.089562 7.6693E-01 1.6784E+07 1.7883E-06 +904 8 3D -10 1F 2-3 618.291378 cm-1 196595.062365 197213.353743 7.4521E+03 9.3212E+05 4.0904E-02 +904 8 3D -10 1F 3-3 618.291541 cm-1 196595.062202 197213.353743 9.6594E+02 9.3212E+05 3.7871E-03 +905 8 3F - 9 1D 2-2 359.368308 cm-1 196596.080442 196955.448750 9.1502E-02 2.4468E+06 1.0619E-06 +905 8 3F - 9 1D 3-2 359.369990 cm-1 196596.078760 196955.448750 2.3695E+03 2.4468E+06 1.9642E-02 +906 8 3F - 9 1G 4-4 359.959695 cm-1 196596.079366 196956.039061 2.1414E+03 7.5279E+05 2.4770E-02 +906 8 3F - 9 1G 3-4 359.960301 cm-1 196596.078760 196956.039061 3.9813E+03 7.5279E+05 5.9211E-02 +907 8 3F -10 1D 3-2 616.910770 cm-1 196596.078760 197212.989530 1.4532E+03 1.7903E+06 4.0878E-03 +908 8 3F -10 1G 4-4 617.341668 cm-1 196596.079366 197213.421034 1.5413E+03 5.5231E+05 6.0615E-03 +908 8 3F -10 1G 3-4 617.342274 cm-1 196596.078760 197213.421034 2.8636E+03 5.5231E+05 1.4479E-02 +909 8 3G - 9 1F 3-3 359.736441 cm-1 196596.210946 196955.947387 8.6438E+01 1.2714E+06 1.0011E-03 +909 8 3G - 9 1F 4-3 359.737731 cm-1 196596.209656 196955.947387 4.6394E+02 1.2714E+06 4.1791E-03 +910 8 3G - 9 1H 5-5 359.850750 cm-1 196596.210331 196956.061082 1.8317E+03 4.9674E+05 2.1201E-02 +910 8 3G - 9 1H 4-5 359.851425 cm-1 196596.209656 196956.061082 2.7703E+00 4.9674E+05 3.9190E-05 +911 8 3G -10 1F 3-3 617.142797 cm-1 196596.210946 197213.353743 4.7231E+01 9.3212E+05 1.8586E-04 +911 8 3G -10 1F 4-3 617.144087 cm-1 196596.209656 197213.353743 2.7322E+02 9.3212E+05 8.3625E-04 +912 8 3G -10 1H 5-5 617.226942 cm-1 196596.210331 197213.437274 1.2223E+03 3.6446E+05 4.8087E-03 +912 8 3G -10 1H 4-5 617.227617 cm-1 196596.209656 197213.437274 1.8507E+00 3.6446E+05 8.8989E-06 +913 8 3H - 9 1G 4-4 359.797154 cm-1 196596.241907 196956.039061 6.3947E+01 7.5279E+05 7.4036E-04 +913 8 3H - 9 1G 5-4 359.797995 cm-1 196596.241066 196956.039061 7.4314E-01 7.5279E+05 7.0395E-06 +914 8 3H - 9 1I 6-6 359.826530 cm-1 196596.241507 196956.068037 1.6665E+03 3.5197E+05 1.9291E-02 +914 8 3H - 9 1I 5-6 359.826971 cm-1 196596.241066 196956.068037 2.6561E+00 3.5197E+05 3.6337E-05 +915 8 3H -10 1G 4-4 617.179127 cm-1 196596.241907 197213.421034 3.2012E+01 5.5231E+05 1.2596E-04 +915 8 3H -10 1G 5-4 617.179967 cm-1 196596.241066 197213.421034 3.7806E-01 5.5231E+05 1.2171E-06 +916 8 3H -10 1I 6-6 617.200926 cm-1 196596.241507 197213.442433 9.6844E+02 2.5807E+05 3.8103E-03 +916 8 3H -10 1I 5-6 617.201367 cm-1 196596.241066 197213.442433 1.5435E+00 2.5807E+05 7.1770E-06 +917 8 3I - 9 1H 5-5 359.809439 cm-1 196596.251643 196956.061082 2.0818E+01 4.9674E+05 2.4101E-04 +917 8 3I - 9 1H 6-5 359.810030 cm-1 196596.251052 196956.061082 1.3478E-01 4.9674E+05 1.3203E-06 +918 8 3I -10 1H 5-5 617.185631 cm-1 196596.251643 197213.437274 8.9677E+00 3.6446E+05 3.5285E-05 +919 8 3K - 9 1I 6-6 359.812701 cm-1 196596.255336 196956.068037 4.8086E+00 3.5197E+05 5.5668E-05 +920 8 3K -10 1I 6-6 617.187097 cm-1 196596.255336 197213.442433 1.6790E+00 2.5807E+05 6.6063E-06 +921 9 3S - 9 1P 1-1 97.705476 cm-1 196861.987340 196959.692816 4.6670E-04 2.2974E+07 7.3308E-08 +922 9 3P - 9 1D 1-2 20.116580 cm-1 196935.332170 196955.448750 5.1138E-03 2.4468E+06 3.1618E-05 +922 9 3P - 9 1D 2-2 20.117332 cm-1 196935.331418 196955.448750 1.8182E-03 2.4468E+06 6.7449E-06 +923 9 3P -10 1D 1-2 277.657360 cm-1 196935.332170 197212.989530 7.8140E-01 1.7903E+06 2.5322E-05 +923 9 3P -10 1D 2-2 277.658112 cm-1 196935.331418 197212.989530 2.8513E-01 1.7903E+06 5.5439E-06 +924 9 3D - 9 1P 1-1 4.464558 cm-1 196955.228258 196959.692816 2.5006E-08 2.2974E+07 1.8886E-09 +924 9 3D - 9 1P 2-1 4.466175 cm-1 196955.226641 196959.692816 1.2545E-04 2.2974E+07 5.6848E-06 +925 9 3D -10 1P 2-1 260.862921 cm-1 196955.226641 197216.089562 6.9534E-01 1.6784E+07 9.1895E-06 +926 9 3D -10 1F 2-3 258.127102 cm-1 196955.226641 197213.353743 5.2280E+03 9.3212E+05 1.6464E-01 +926 9 3D -10 1F 3-3 258.127216 cm-1 196955.226527 197213.353743 6.7732E+02 9.3212E+05 1.5236E-02 +927 9 3F -10 1D 2-2 257.043346 cm-1 196955.946185 197212.989530 5.8742E-02 1.7903E+06 1.3325E-06 +927 9 3F -10 1D 3-2 257.044514 cm-1 196955.945017 197212.989530 1.4967E+03 1.7903E+06 2.4251E-02 +928 9 3F -10 1G 4-4 257.475605 cm-1 196955.945429 197213.421034 1.0972E+03 5.5231E+05 2.4806E-02 +928 9 3F -10 1G 3-4 257.476017 cm-1 196955.945017 197213.421034 2.2077E+03 5.5231E+05 6.4173E-02 +929 9 3G -10 1F 3-3 257.314974 cm-1 196956.038769 197213.353743 5.9453E+01 9.3212E+05 1.3458E-03 +929 9 3G -10 1F 4-3 257.315880 cm-1 196956.037863 197213.353743 3.4356E+02 9.3212E+05 6.0488E-03 +930 9 3G -10 1H 5-5 257.398937 cm-1 196956.038337 197213.437274 9.1691E+02 3.6446E+05 2.0742E-02 +930 9 3G -10 1H 4-5 257.399410 cm-1 196956.037863 197213.437274 1.3078E+00 3.6446E+05 3.6159E-05 +931 9 3H -10 1G 4-4 257.360162 cm-1 196956.060872 197213.421034 5.0394E+01 5.5231E+05 1.1403E-03 +931 9 3H -10 1G 5-4 257.360752 cm-1 196956.060282 197213.421034 5.9517E-01 5.5231E+05 1.1019E-05 +932 9 3H -10 1I 6-6 257.381842 cm-1 196956.060591 197213.442433 8.1536E+02 2.5807E+05 1.8447E-02 +932 9 3H -10 1I 5-6 257.382151 cm-1 196956.060282 197213.442433 1.2997E+00 2.5807E+05 3.4752E-05 +933 9 3I -10 1H 5-5 257.369394 cm-1 196956.067880 197213.437274 1.9754E+01 3.6446E+05 4.4697E-04 +933 9 3I -10 1H 6-5 257.369808 cm-1 196956.067465 197213.437274 1.2798E-01 3.6446E+05 2.4503E-06 +934 9 3K -10 1I 6-6 257.371868 cm-1 196956.070564 197213.442433 6.8580E+00 2.5807E+05 1.5517E-04 +935 10 3S -10 1P 1-1 70.856304 cm-1 197145.233258 197216.089562 2.7254E-04 1.6784E+07 8.1400E-08 +936 10 3P -10 1D 1-2 14.656262 cm-1 197198.333268 197212.989530 2.9770E-03 1.7903E+06 3.4675E-05 +936 10 3P -10 1D 2-2 14.656808 cm-1 197198.332722 197212.989530 1.0592E-03 1.7903E+06 7.4024E-06 +937 10 3D -10 1P 1-1 3.262439 cm-1 197212.827123 197216.089562 1.4977E-08 1.6784E+07 2.1183E-09 +937 10 3D -10 1P 2-1 3.263617 cm-1 197212.825945 197216.089562 7.3794E-05 1.6784E+07 6.2625E-06 \ No newline at end of file diff --git a/bin/level_data/drake_triplet_triplet_transitions.txt b/bin/level_data/drake_triplet_triplet_transitions.txt new file mode 100644 index 0000000..1d8db11 --- /dev/null +++ b/bin/level_data/drake_triplet_triplet_transitions.txt @@ -0,0 +1,1622 @@ +Title: A Multiplet Table for Neutral Helium (^4^He I) with Transition Rates +Authors: Drake, G.W.F., Morton D.C. +Table: Multiplet Table for ^4^He Triplet - Triplet Transitions +================================================================================ +Byte-by-byte Description of file: datafile5.txt +-------------------------------------------------------------------------------- + Bytes Format Units Label Explanations +-------------------------------------------------------------------------------- + 1- 3 I3 --- N Sequential multiplet number + 5- 16 A12 --- Trans Level designations n ^2S+1^L (Lower-Upper) + 18- 21 A4 --- J-J Lower and Upper J-values + 23- 32 F10.4 0.1nm AWave Air wavelength (1) + 34- 45 F12.6 --- VWave Vacuum wavelength/wavenumber (2) + 47- 50 A4 --- Units Units for VWave (3) + 52- 64 F13.6 cm-1 Elow Lower level energy from Drake & Morton (2006) + 66- 78 F13.6 cm-1 Eup Upper level energy from Drake & Morton (2006) + 80- 89 E10.4 s-1 Aul Spontaneous transition rate (4) + 91-100 E10.4 s-1 SAul Sum of all A_ul_ to lower levels (5) + 102-111 E10.4 --- flu Absorption oscillator strength or f-value (4) + 113-118 F6.4 --- Rat Ratio of flu to one from pure LS-coupled states + with no singlet-triplet mixing +-------------------------------------------------------------------------------- +Note (1): For {lambda} > 2000 Angstroms following Peck & Reeder (1972). +Note (2): Calculated from the energy levels of Paper I according to equation 1. + If the vacuum wavelength exceeds 1e4 Angstroms, the value is the more + useful vacuum wavenumber as indicated by the Units column. The + important 2 3S - 2 3P transition at 10833 Angstroms or 9231 cm-1 + is tabulated both ways +Note (3): cm-1 = Inverse cm; wavenumber if {lambda} > 1e4 Angstroms. +Note (4): Including singlet-triplet mixing and spin-orbit coupling. +Note (5): Which is the reciprocal of the lifetime of the upper level. The + numbers are nearly identical for all three J-values of each upper + triplet term. +-------------------------------------------------------------------------------- +296 2 3S - 2 3P Mean 10830.1711 10833.137758 159855.974330 169086.910208 1.0216E+07 1.0216E+07 5.3907E-01 1.0000 +296 2 3S - 2 3P 1-2 10830.3398 10833.306444 159855.974330 169086.766473 1.0216E+07 1.0216E+07 2.9948E-01 1.0000 +296 2 3S - 2 3P 1-1 10830.2501 10833.216751 159855.974330 169086.842898 1.0216E+07 1.0216E+07 1.7969E-01 1.0000 +296 2 3S - 2 3P 1-0 10829.0911 10832.057472 159855.974330 169087.830813 1.0216E+07 1.0216E+07 5.9897E-02 1.0000 +296 2 3S - 2 3P Mean 9230.935878 cm-1 159855.974330 169086.910208 1.0216E+07 1.0216E+07 5.3907E-01 1.0000 +296 2 3S - 2 3P 1-2 9230.792143 cm-1 159855.974330 169086.766473 1.0216E+07 1.0216E+07 2.9948E-01 1.0000 +296 2 3S - 2 3P 1-1 9230.868568 cm-1 159855.974330 169086.842898 1.0216E+07 1.0216E+07 1.7969E-01 1.0000 +296 2 3S - 2 3P 1-0 9231.856483 cm-1 159855.974330 169087.830813 1.0216E+07 1.0216E+07 5.9897E-02 1.0000 +297 2 3S - 3 3P Mean 3888.6429 3889.744806 159855.974330 185564.601758 9.4746E+06 1.0548E+07 6.4461E-02 1.0000 +297 2 3S - 3 3P 1-2 3888.6489 3889.750833 159855.974330 185564.561920 9.4746E+06 1.0548E+07 3.5812E-02 1.0000 +297 2 3S - 3 3P 1-1 3888.6456 3889.747508 159855.974330 185564.583895 9.4746E+06 1.0548E+07 2.1487E-02 1.0000 +297 2 3S - 3 3P 1-0 3888.6046 3889.706560 159855.974330 185564.854540 9.4746E+06 1.0548E+07 7.1624E-03 1.0000 +298 2 3S - 4 3P Mean 3187.7437 3188.665402 159855.974330 191217.057224 5.6361E+06 7.2190E+06 2.5769E-02 1.0000 +298 2 3S - 4 3P 1-2 3187.7453 3188.667055 159855.974330 191217.040967 5.6361E+06 7.2190E+06 1.4316E-02 1.0000 +298 2 3S - 4 3P 1-1 3187.7444 3188.666140 159855.974330 191217.049963 5.6361E+06 7.2190E+06 8.5896E-03 1.0000 +298 2 3S - 4 3P 1-0 3187.7332 3188.654923 159855.974330 191217.160290 5.6361E+06 7.2190E+06 2.8632E-03 1.0000 +299 2 3S - 5 3P Mean 2945.1034 2945.964405 159855.974330 193800.715766 3.2006E+06 4.5601E+06 1.2491E-02 1.0000 +299 2 3S - 5 3P 1-2 2945.1041 2945.965114 159855.974330 193800.707595 3.2006E+06 4.5601E+06 6.9392E-03 1.0000 +299 2 3S - 5 3P 1-1 2945.1037 2945.964721 159855.974330 193800.712118 3.2006E+06 4.5601E+06 4.1635E-03 1.0000 +299 2 3S - 5 3P 1-0 2945.0989 2945.959909 159855.974330 193800.767563 3.2006E+06 4.5601E+06 1.3878E-03 1.0000 +300 2 3S - 6 3P Mean 2829.0808 2829.913164 159855.974330 195192.747648 1.9389E+06 2.9557E+06 6.9823E-03 1.0000 +300 2 3S - 6 3P 1-2 2829.0812 2829.913539 159855.974330 195192.742974 1.9389E+06 2.9557E+06 3.8791E-03 1.0000 +300 2 3S - 6 3P 1-1 2829.0809 2829.913332 159855.974330 195192.745559 1.9389E+06 2.9557E+06 2.3274E-03 1.0000 +300 2 3S - 6 3P 1-0 2829.0784 2829.910791 159855.974330 195192.777281 1.9389E+06 2.9557E+06 7.7581E-04 1.0000 +301 2 3S - 7 3P Mean 2763.8030 2764.619447 159855.974330 196027.317947 1.2508E+06 1.9947E+06 4.2989E-03 1.0000 +301 2 3S - 7 3P 1-2 2763.8032 2764.619671 159855.974330 196027.315027 1.2508E+06 1.9947E+06 2.3883E-03 1.0000 +301 2 3S - 7 3P 1-1 2763.8031 2764.619547 159855.974330 196027.316641 1.2508E+06 1.9947E+06 1.4330E-03 1.0000 +301 2 3S - 7 3P 1-0 2763.8016 2764.618032 159855.974330 196027.336465 1.2508E+06 1.9947E+06 4.7765E-04 1.0000 +302 2 3S - 8 3P Mean 2723.1919 2723.998523 159855.974330 196566.713767 8.4996E+05 1.3990E+06 2.8360E-03 1.0000 +302 2 3S - 8 3P 1-2 2723.1921 2723.998667 159855.974330 196566.711822 8.4996E+05 1.3990E+06 1.5756E-03 1.0000 +302 2 3S - 8 3P 1-1 2723.1920 2723.998587 159855.974330 196566.712897 8.4996E+05 1.3990E+06 9.4534E-04 1.0000 +302 2 3S - 8 3P 1-0 2723.1910 2723.997607 159855.974330 196566.726105 8.4996E+05 1.3990E+06 3.1511E-04 1.0000 +303 2 3S - 9 3P Mean 2696.1182 2696.918290 159855.974330 196935.332779 6.0234E+05 1.0146E+06 1.9700E-03 1.0000 +303 2 3S - 9 3P 1-2 2696.1183 2696.918389 159855.974330 196935.331418 6.0234E+05 1.0146E+06 1.0945E-03 1.0000 +303 2 3S - 9 3P 1-1 2696.1183 2696.918335 159855.974330 196935.332170 6.0234E+05 1.0146E+06 6.5668E-04 1.0000 +303 2 3S - 9 3P 1-0 2696.1176 2696.917663 159855.974330 196935.341408 6.0234E+05 1.0146E+06 2.1889E-04 1.0000 +304 2 3S -10 3P Mean 2677.1285 2677.923989 159855.974330 197198.333711 4.4174E+05 7.5715E+05 1.4245E-03 1.0001 +304 2 3S -10 3P 1-2 2677.1286 2677.924060 159855.974330 197198.332722 4.4174E+05 7.5715E+05 7.9138E-04 1.0000 +304 2 3S -10 3P 1-1 2677.1285 2677.924021 159855.974330 197198.333268 4.4174E+05 7.5715E+05 4.7483E-04 1.0000 +304 2 3S -10 3P 1-0 2677.1280 2677.923540 159855.974330 197198.339982 4.4174E+05 7.5716E+05 1.5828E-04 1.0000 +305 2 3P - 3 3S Mean 7065.2489 7067.196997 169086.910208 183236.791701 2.7853E+07 2.7853E+07 6.9512E-02 1.0000 +305 2 3P - 3 3S 0-1 7065.7086 7067.656826 169087.830813 183236.791701 3.0948E+06 2.7853E+07 6.9512E-02 1.0000 +305 2 3P - 3 3S 1-1 7065.2153 7067.163379 169086.842898 183236.791701 9.2844E+06 2.7853E+07 6.9512E-02 1.0000 +305 2 3P - 3 3S 2-1 7065.1771 7067.125209 169086.766473 183236.791701 1.5474E+07 2.7853E+07 6.9512E-02 1.0000 +306 2 3P - 3 3D Mean 5875.6609 5877.289432 169086.910208 186101.556357 7.0703E+07 7.0720E+07 6.1018E-01 0.9999 +306 2 3P - 3 3D 0-1 5875.9663 5877.594829 169087.830813 186101.592890 3.9282E+07 7.0721E+07 6.1022E-01 1.0000 +306 2 3P - 3 3D 1-2 5875.6404 5877.268830 169086.842898 186101.548689 5.3019E+07 7.0719E+07 4.5757E-01 0.9998 +306 2 3P - 3 3D 1-1 5875.6251 5877.253562 169086.842898 186101.592890 2.9462E+07 7.0721E+07 1.5256E-01 1.0000 +306 2 3P - 3 3D 2-3 5875.6148 5877.243299 169086.766473 186101.546177 7.0708E+07 7.0721E+07 5.1259E-01 1.0000 +306 2 3P - 3 3D 2-2 5875.6140 5877.242431 169086.766473 186101.548689 1.7673E+07 7.0719E+07 9.1513E-02 0.9998 +306 2 3P - 3 3D 2-1 5875.5987 5877.227163 169086.766473 186101.592890 1.9641E+06 7.0721E+07 6.1022E-03 1.0000 +307 2 3P - 4 3S Mean 4713.1711 4714.489779 169086.910208 190298.113260 9.5209E+06 1.6033E+07 1.0574E-02 1.0000 +307 2 3P - 4 3S 0-1 4713.3757 4714.694406 169087.830813 190298.113260 1.0579E+06 1.6033E+07 1.0574E-02 1.0000 +307 2 3P - 4 3S 1-1 4713.1561 4714.474819 169086.842898 190298.113260 3.1736E+06 1.6033E+07 1.0573E-02 1.0000 +307 2 3P - 4 3S 2-1 4713.1392 4714.457832 169086.766473 190298.113260 5.2894E+06 1.6033E+07 1.0574E-02 1.0000 +308 2 3P - 4 3D Mean 4471.5022 4472.756983 169086.910208 191444.485274 2.4578E+07 3.1192E+07 1.2284E-01 1.0000 +308 2 3P - 4 3D 0-1 4471.6832 4472.938086 169087.830813 191444.500651 1.3655E+07 3.1192E+07 1.2285E-01 1.0000 +308 2 3P - 4 3D 1-2 4471.4894 4472.744146 169086.842898 191444.482131 1.8432E+07 3.1192E+07 9.2124E-02 0.9999 +308 2 3P - 4 3D 1-1 4471.4857 4472.740441 169086.842898 191444.500651 1.0241E+07 3.1192E+07 3.0711E-02 1.0000 +308 2 3P - 4 3D 2-3 4471.4743 4472.729097 169086.766473 191444.480929 2.4579E+07 3.1192E+07 1.0319E-01 1.0000 +308 2 3P - 4 3D 2-2 4471.4741 4472.728857 169086.766473 191444.482131 6.1440E+06 3.1192E+07 1.8425E-02 0.9999 +308 2 3P - 4 3D 2-1 4471.4704 4472.725152 169086.766473 191444.500651 6.8275E+05 3.1192E+07 1.2285E-03 1.0000 +309 2 3P - 5 3S Mean 4120.8352 4121.997756 169086.910208 193346.991344 4.4529E+06 9.2072E+06 3.7803E-03 1.0000 +309 2 3P - 5 3S 0-1 4120.9916 4122.154181 169087.830813 193346.991344 4.9476E+05 9.2072E+06 3.7803E-03 1.0000 +309 2 3P - 5 3S 1-1 4120.8237 4121.986319 169086.842898 193346.991344 1.4843E+06 9.2072E+06 3.7803E-03 1.0000 +309 2 3P - 5 3S 2-1 4120.8108 4121.973334 169086.766473 193346.991344 2.4738E+06 9.2072E+06 3.7803E-03 1.0000 +310 2 3P - 5 3D Mean 4026.2089 4027.346762 169086.910208 193917.153521 1.1600E+07 1.6412E+07 4.7006E-02 1.0000 +310 2 3P - 5 3D 0-1 4026.3570 4027.494809 169087.830813 193917.161387 6.4448E+06 1.6412E+07 4.7007E-02 1.0000 +310 2 3P - 5 3D 1-2 4026.1983 4027.336103 169086.842898 193917.151929 8.6997E+06 1.6411E+07 3.5252E-02 0.9999 +310 2 3P - 5 3D 1-1 4026.1968 4027.334569 169086.842898 193917.161387 4.8336E+06 1.6412E+07 1.1752E-02 1.0000 +310 2 3P - 5 3D 2-3 4026.1860 4027.323811 169086.766473 193917.151287 1.1601E+07 1.6412E+07 3.9487E-02 1.0000 +310 2 3P - 5 3D 2-2 4026.1859 4027.323707 169086.766473 193917.151929 2.8999E+06 1.6411E+07 7.0504E-03 0.9999 +310 2 3P - 5 3D 2-1 4026.1844 4027.322173 169086.766473 193917.161387 3.2224E+05 1.6412E+07 4.7007E-04 1.0000 +311 2 3P - 6 3S Mean 3867.4938 3868.590258 169086.910208 194936.119697 2.4465E+06 5.6296E+06 1.8295E-03 1.0000 +311 2 3P - 6 3S 0-1 3867.6316 3868.728040 169087.830813 194936.119697 2.7184E+05 5.6296E+06 1.8295E-03 1.0000 +311 2 3P - 6 3S 1-1 3867.4838 3868.580184 169086.842898 194936.119697 8.1551E+05 5.6296E+06 1.8295E-03 1.0000 +311 2 3P - 6 3S 2-1 3867.4723 3868.568746 169086.766473 194936.119697 1.3592E+06 5.6296E+06 1.8295E-03 1.0000 +312 2 3P - 6 3D Mean 3819.6236 3820.707574 169086.910208 195260.072653 6.4351E+06 9.6698E+06 2.3469E-02 1.0000 +312 2 3P - 6 3D 0-1 3819.7573 3820.841303 169087.830813 195260.077203 3.5752E+06 9.6698E+06 2.3469E-02 1.0000 +312 2 3P - 6 3D 1-2 3819.6139 3820.697882 169086.842898 195260.071736 4.8261E+06 9.6697E+06 1.7600E-02 0.9999 +312 2 3P - 6 3D 1-1 3819.6131 3820.697084 169086.842898 195260.077203 2.6814E+06 9.6698E+06 5.8673E-03 1.0000 +312 2 3P - 6 3D 2-3 3819.6028 3820.686781 169086.766473 195260.071358 6.4353E+06 9.6698E+06 1.9714E-02 1.0000 +312 2 3P - 6 3D 2-2 3819.6028 3820.686726 169086.766473 195260.071736 1.6087E+06 9.6697E+06 3.5201E-03 0.9999 +312 2 3P - 6 3D 2-1 3819.6020 3820.685928 169086.766473 195260.077203 1.7876E+05 9.6698E+06 2.3469E-04 1.0000 +313 2 3P - 7 3S Mean 3732.8835 3733.944956 169086.910208 195868.236975 1.4895E+06 3.6533E+06 1.0376E-03 1.0000 +313 2 3P - 7 3S 0-1 3733.0118 3734.073314 169087.830813 195868.236975 1.6550E+05 3.6533E+06 1.0376E-03 1.0000 +313 2 3P - 7 3S 1-1 3732.8741 3733.935571 169086.842898 195868.236975 4.9650E+05 3.6533E+06 1.0376E-03 1.0000 +313 2 3P - 7 3S 2-1 3732.8635 3733.924916 169086.766473 195868.236975 8.2750E+05 3.6533E+06 1.0376E-03 1.0000 +314 2 3P - 7 3D Mean 3705.0154 3706.069629 169086.910208 196069.673625 3.9528E+06 6.1663E+06 1.3563E-02 1.0000 +314 2 3P - 7 3D 0-1 3705.1414 3706.195684 169087.830813 196069.676490 2.1961E+06 6.1664E+06 1.3564E-02 1.0000 +314 2 3P - 7 3D 1-2 3705.0062 3706.060463 169086.842898 196069.673050 2.9644E+06 6.1661E+06 1.0172E-02 0.9999 +314 2 3P - 7 3D 1-1 3705.0058 3706.059990 169086.842898 196069.676490 1.6470E+06 6.1664E+06 3.3909E-03 1.0000 +314 2 3P - 7 3D 2-3 3704.9958 3706.049999 169086.766473 196069.672809 3.9529E+06 6.1664E+06 1.1394E-02 1.0000 +314 2 3P - 7 3D 2-2 3704.9957 3706.049966 169086.766473 196069.673050 9.8814E+05 6.1661E+06 2.0344E-03 0.9999 +314 2 3P - 7 3D 2-1 3704.9953 3706.049493 169086.766473 196069.676490 1.0980E+05 6.1664E+06 1.3563E-04 1.0000 +315 2 3P - 8 3S Mean 3652.0007 3653.041217 169086.910208 196461.361811 9.7444E+05 2.4913E+06 6.4973E-04 1.0000 +315 2 3P - 8 3S 0-1 3652.1235 3653.164073 169087.830813 196461.361811 1.0827E+05 2.4913E+06 6.4972E-04 1.0000 +315 2 3P - 8 3S 1-1 3651.9917 3653.032235 169086.842898 196461.361811 3.2481E+05 2.4913E+06 6.4972E-04 1.0000 +315 2 3P - 8 3S 2-1 3651.9815 3653.022036 169086.766473 196461.361811 5.4136E+05 2.4913E+06 6.4973E-04 1.0000 +316 2 3P - 8 3D Mean 3634.2500 3635.285934 169086.910208 196595.062750 2.6062E+06 4.1689E+06 8.6045E-03 1.0000 +316 2 3P - 8 3D 0-1 3634.3714 3635.407345 169087.830813 196595.064668 1.4479E+06 4.1690E+06 8.6045E-03 1.0000 +316 2 3P - 8 3D 1-2 3634.2412 3635.277089 169086.842898 196595.062365 1.9546E+06 4.1688E+06 6.4532E-03 0.9999 +316 2 3P - 8 3D 1-1 3634.2409 3635.276785 169086.842898 196595.064668 1.0859E+06 4.1690E+06 2.1511E-03 1.0000 +316 2 3P - 8 3D 2-3 3634.2311 3635.267011 169086.766473 196595.062202 2.6063E+06 4.1690E+06 7.2280E-03 1.0000 +316 2 3P - 8 3D 2-2 3634.2311 3635.266990 169086.766473 196595.062365 6.5151E+05 4.1688E+06 1.2906E-03 0.9999 +316 2 3P - 8 3D 2-1 3634.2308 3635.266685 169086.766473 196595.064668 7.2396E+04 4.1690E+06 8.6046E-05 1.0000 +317 2 3P - 9 3S Mean 3599.3231 3600.350038 169086.910208 196861.987340 6.7245E+05 1.7692E+06 4.3553E-04 1.0000 +317 2 3P - 9 3S 0-1 3599.4424 3600.469375 169087.830813 196861.987340 7.4716E+04 1.7692E+06 4.3552E-04 1.0000 +317 2 3P - 9 3S 1-1 3599.3144 3600.341313 169086.842898 196861.987340 2.2415E+05 1.7692E+06 4.3553E-04 1.0000 +317 2 3P - 9 3S 2-1 3599.3045 3600.331406 169086.766473 196861.987340 3.7358E+05 1.7692E+06 4.3552E-04 1.0000 +318 2 3P - 9 3D Mean 3587.2805 3588.304276 169086.910208 196955.226911 1.8107E+06 2.9483E+06 5.8245E-03 1.0000 +318 2 3P - 9 3D 0-1 3587.3988 3588.422643 169087.830813 196955.228258 1.0060E+06 2.9484E+06 5.8249E-03 1.0000 +318 2 3P - 9 3D 1-2 3587.2718 3588.295644 169086.842898 196955.226641 1.3580E+06 2.9482E+06 4.3683E-03 0.9999 +318 2 3P - 9 3D 1-1 3587.2716 3588.295436 169086.842898 196955.228258 7.5448E+05 2.9484E+06 1.4562E-03 1.0000 +318 2 3P - 9 3D 2-3 3587.2620 3588.285819 169086.766473 196955.226527 1.8107E+06 2.9483E+06 4.8926E-03 1.0000 +318 2 3P - 9 3D 2-2 3587.2620 3588.285804 169086.766473 196955.226641 4.5265E+05 2.9482E+06 8.7363E-04 0.9999 +318 2 3P - 9 3D 2-1 3587.2618 3588.285596 169086.766473 196955.228258 5.0298E+04 2.9484E+06 5.8246E-05 1.0000 +319 2 3P -10 3S Mean 3562.9873 3564.004870 169086.910208 197145.233258 4.8362E+05 1.2990E+06 3.0694E-04 1.0000 +319 2 3P -10 3S 0-1 3563.1042 3564.121811 169087.830813 197145.233258 5.3735E+04 1.2990E+06 3.0693E-04 1.0000 +319 2 3P -10 3S 1-1 3562.9788 3563.996320 169086.842898 197145.233258 1.6121E+05 1.2990E+06 3.0694E-04 1.0000 +319 2 3P -10 3S 2-1 3562.9691 3563.986613 169086.766473 197145.233258 2.6868E+05 1.2990E+06 3.0694E-04 1.0000 +320 2 3P -10 3D Mean 3554.4244 3555.439767 169086.910208 197212.826141 1.3099E+06 2.1609E+06 4.1367E-03 1.0000 +320 2 3P -10 3D 0-1 3554.5406 3555.556022 169087.830813 197212.827123 7.2772E+05 2.1609E+06 4.1368E-03 1.0000 +320 2 3P -10 3D 1-2 3554.4159 3555.431283 169086.842898 197212.825945 9.8235E+05 2.1608E+06 3.1023E-03 0.9999 +320 2 3P -10 3D 1-1 3554.4158 3555.431134 169086.842898 197212.827123 5.4579E+05 2.1609E+06 1.0342E-03 1.0000 +320 2 3P -10 3D 2-3 3554.4063 3555.421633 169086.766473 197212.825861 1.3099E+06 2.1609E+06 3.4749E-03 1.0000 +320 2 3P -10 3D 2-2 3554.4063 3555.421622 169086.766473 197212.825945 3.2745E+05 2.1608E+06 6.2047E-04 1.0000 +320 2 3P -10 3D 2-1 3554.4061 3555.421473 169086.766473 197212.827123 3.6386E+04 2.1609E+06 4.1368E-05 1.0000 +321 3 3S - 3 3P Mean 2327.810058 cm-1 183236.791701 185564.601758 1.0736E+06 1.0548E+07 8.9081E-01 1.0000 +321 3 3S - 3 3P 1-2 2327.770219 cm-1 183236.791701 185564.561920 1.0736E+06 1.0548E+07 4.9490E-01 1.0000 +321 3 3S - 3 3P 1-1 2327.792195 cm-1 183236.791701 185564.583895 1.0736E+06 1.0548E+07 2.9694E-01 1.0000 +321 3 3S - 3 3P 1-0 2328.062839 cm-1 183236.791701 185564.854540 1.0736E+06 1.0548E+07 9.8979E-02 1.0000 +322 3 3S - 4 3P Mean 7980.265523 cm-1 183236.791701 191217.057224 7.0932E+05 7.2190E+06 5.0083E-02 1.0000 +322 3 3S - 4 3P 1-2 7980.249266 cm-1 183236.791701 191217.040967 7.0932E+05 7.2190E+06 2.7824E-02 1.0000 +322 3 3S - 4 3P 1-1 7980.258263 cm-1 183236.791701 191217.049963 7.0932E+05 7.2190E+06 1.6694E-02 1.0000 +322 3 3S - 4 3P 1-0 7980.368589 cm-1 183236.791701 191217.160290 7.0932E+05 7.2190E+06 5.5648E-03 1.0000 +323 3 3S - 5 3P Mean 9463.5832 9466.179365 183236.791701 193800.715766 5.6868E+05 4.5601E+06 2.2914E-02 1.0000 +323 3 3S - 5 3P 1-2 9463.5905 9466.186687 183236.791701 193800.707595 5.6868E+05 4.5601E+06 1.2730E-02 1.0000 +323 3 3S - 5 3P 1-1 9463.5865 9466.182634 183236.791701 193800.712118 5.6868E+05 4.5601E+06 7.6381E-03 1.0000 +323 3 3S - 5 3P 1-0 9463.5368 9466.132951 183236.791701 193800.767563 5.6868E+05 4.5601E+06 2.5460E-03 1.0000 +324 3 3S - 6 3P Mean 8361.7341 8364.032156 183236.791701 195192.747648 3.8126E+05 2.9557E+06 1.1993E-02 1.0000 +324 3 3S - 6 3P 1-2 8361.7374 8364.035426 183236.791701 195192.742974 3.8126E+05 2.9557E+06 6.6630E-03 1.0000 +324 3 3S - 6 3P 1-1 8361.7356 8364.033618 183236.791701 195192.745559 3.8126E+05 2.9557E+06 3.9978E-03 1.0000 +324 3 3S - 6 3P 1-0 8361.7134 8364.011426 183236.791701 195192.777281 3.8126E+05 2.9557E+06 1.3326E-03 1.0000 +325 3 3S - 7 3P Mean 7816.1360 7818.286603 183236.791701 196027.317947 2.5748E+05 1.9947E+06 7.0771E-03 1.0000 +325 3 3S - 7 3P 1-2 7816.1378 7818.288388 183236.791701 196027.315027 2.5748E+05 1.9947E+06 3.9317E-03 1.0000 +325 3 3S - 7 3P 1-1 7816.1368 7818.287402 183236.791701 196027.316641 2.5748E+05 1.9947E+06 2.3590E-03 1.0000 +325 3 3S - 7 3P 1-0 7816.1247 7818.275284 183236.791701 196027.336465 2.5748E+05 1.9947E+06 7.8634E-04 1.0000 +326 3 3S - 8 3P Mean 7499.8541 7501.919329 183236.791701 196566.713767 1.7942E+05 1.3990E+06 4.5405E-03 1.0000 +326 3 3S - 8 3P 1-2 7499.8552 7501.920423 183236.791701 196566.711822 1.7942E+05 1.3990E+06 2.5225E-03 1.0000 +326 3 3S - 8 3P 1-1 7499.8546 7501.919818 183236.791701 196566.712897 1.7942E+05 1.3990E+06 1.5135E-03 1.0000 +326 3 3S - 8 3P 1-0 7499.8471 7501.912385 183236.791701 196566.726105 1.7942E+05 1.3990E+06 5.0450E-04 1.0000 +327 3 3S - 9 3P Mean 7298.0366 7300.047460 183236.791701 196935.332779 1.2913E+05 1.0146E+06 3.0943E-03 0.9999 +327 3 3S - 9 3P 1-2 7298.0374 7300.048185 183236.791701 196935.331418 1.2913E+05 1.0146E+06 1.7191E-03 1.0000 +327 3 3S - 9 3P 1-1 7298.0370 7300.047784 183236.791701 196935.332170 1.2913E+05 1.0146E+06 1.0314E-03 1.0000 +327 3 3S - 9 3P 1-0 7298.0320 7300.042861 183236.791701 196935.341408 1.2913E+05 1.0146E+06 3.4381E-04 1.0000 +328 3 3S -10 3P Mean 7160.5588 7162.532615 183236.791701 197198.333711 9.5686E+04 7.5715E+05 2.2073E-03 1.0000 +328 3 3S -10 3P 1-2 7160.5594 7162.533122 183236.791701 197198.332722 9.5686E+04 7.5715E+05 1.2263E-03 1.0000 +328 3 3S -10 3P 1-1 7160.5591 7162.532842 183236.791701 197198.333268 9.5686E+04 7.5715E+05 7.3578E-04 1.0000 +328 3 3S -10 3P 1-0 7160.5556 7162.529398 183236.791701 197198.339982 9.5686E+04 7.5716E+05 2.4526E-04 1.0000 +329 3 3P - 3 3D Mean 536.954599 cm-1 185564.601758 186101.556357 1.2916E+04 7.0720E+07 1.1209E-01 0.9999 +329 3 3P - 3 3D 0-1 536.738351 cm-1 185564.854540 186101.592890 7.1759E+03 7.0721E+07 1.1210E-01 1.0000 +329 3 3P - 3 3D 1-2 536.964794 cm-1 185564.583895 186101.548689 9.6851E+03 7.0719E+07 8.4055E-02 0.9998 +329 3 3P - 3 3D 2-3 536.984257 cm-1 185564.561920 186101.546177 1.2917E+04 7.0721E+07 9.4168E-02 1.0000 +329 3 3P - 3 3D 2-2 536.986769 cm-1 185564.561920 186101.548689 3.2284E+03 7.0719E+07 1.6811E-02 0.9998 +329 3 3P - 3 3D 1-1 537.008995 cm-1 185564.583895 186101.592890 5.3819E+03 7.0721E+07 2.8025E-02 1.0000 +329 3 3P - 3 3D 2-1 537.030970 cm-1 185564.561920 186101.592890 3.5879E+02 7.0721E+07 1.1210E-03 1.0000 +330 3 3P - 4 3S Mean 4733.511502 cm-1 185564.601758 190298.113260 6.5122E+06 1.6033E+07 1.4522E-01 1.0000 +330 3 3P - 4 3S 0-1 4733.258720 cm-1 185564.854540 190298.113260 7.2358E+05 1.6033E+07 1.4522E-01 1.0000 +330 3 3P - 4 3S 1-1 4733.529365 cm-1 185564.583895 190298.113260 2.1707E+06 1.6033E+07 1.4522E-01 1.0000 +330 3 3P - 4 3S 2-1 4733.551340 cm-1 185564.561920 190298.113260 3.6179E+06 1.6033E+07 1.4522E-01 1.0000 +331 3 3P - 4 3D Mean 5879.883516 cm-1 185564.601758 191444.485274 6.6087E+06 3.1192E+07 4.7757E-01 1.0000 +331 3 3P - 4 3D 0-1 5879.646111 cm-1 185564.854540 191444.500651 3.6717E+06 3.1192E+07 4.7759E-01 1.0000 +331 3 3P - 4 3D 1-2 5879.898235 cm-1 185564.583895 191444.482131 4.9562E+06 3.1192E+07 3.5815E-01 0.9999 +331 3 3P - 4 3D 1-1 5879.916756 cm-1 185564.583895 191444.500651 2.7538E+06 3.1192E+07 1.1940E-01 1.0000 +331 3 3P - 4 3D 2-3 5879.919009 cm-1 185564.561920 191444.480929 6.6090E+06 3.1192E+07 4.0118E-01 1.0000 +331 3 3P - 4 3D 2-2 5879.920211 cm-1 185564.561920 191444.482131 1.6520E+06 3.1192E+07 7.1628E-02 0.9999 +331 3 3P - 4 3D 2-1 5879.938731 cm-1 185564.561920 191444.500651 1.8358E+05 3.1192E+07 4.7758E-03 1.0000 +332 3 3P - 5 3S Mean 7782.389586 cm-1 185564.601758 193346.991344 2.7317E+06 9.2072E+06 2.2536E-02 1.0000 +332 3 3P - 5 3S 0-1 7782.136805 cm-1 185564.854540 193346.991344 3.0352E+05 9.2072E+06 2.2535E-02 1.0000 +332 3 3P - 5 3S 1-1 7782.407449 cm-1 185564.583895 193346.991344 9.1057E+05 9.2072E+06 2.2536E-02 1.0000 +332 3 3P - 5 3S 2-1 7782.429424 cm-1 185564.561920 193346.991344 1.5176E+06 9.2072E+06 2.2535E-02 1.0000 +333 3 3P - 5 3D Mean 8352.551763 cm-1 185564.601758 193917.153521 3.4781E+06 1.6412E+07 1.2455E-01 1.0000 +333 3 3P - 5 3D 0-1 8352.306847 cm-1 185564.854540 193917.161387 1.9323E+06 1.6412E+07 1.2455E-01 1.0000 +333 3 3P - 5 3D 1-2 8352.568033 cm-1 185564.583895 193917.151929 2.6084E+06 1.6411E+07 9.3406E-02 0.9999 +333 3 3P - 5 3D 1-1 8352.577492 cm-1 185564.583895 193917.161387 1.4493E+06 1.6412E+07 3.1139E-02 1.0000 +333 3 3P - 5 3D 2-3 8352.589368 cm-1 185564.561920 193917.151287 3.4782E+06 1.6412E+07 1.0462E-01 1.0000 +333 3 3P - 5 3D 2-2 8352.590009 cm-1 185564.561920 193917.151929 8.6946E+05 1.6411E+07 1.8681E-02 0.9999 +333 3 3P - 5 3D 2-1 8352.599467 cm-1 185564.561920 193917.161387 9.6617E+04 1.6412E+07 1.2455E-03 1.0000 +334 3 3P - 6 3S Mean 9371.517939 cm-1 185564.601758 194936.119697 1.4471E+06 5.6296E+06 8.2325E-03 1.0000 +334 3 3P - 6 3S 0-1 9371.265157 cm-1 185564.854540 194936.119697 1.6079E+05 5.6296E+06 8.2327E-03 1.0000 +334 3 3P - 6 3S 1-1 9371.535802 cm-1 185564.583895 194936.119697 4.8236E+05 5.6296E+06 8.2325E-03 1.0000 +334 3 3P - 6 3S 2-1 9371.557777 cm-1 185564.561920 194936.119697 8.0394E+05 5.6296E+06 8.2326E-03 1.0000 +335 3 3P - 6 3D Mean 9695.470895 cm-1 185564.601758 195260.072653 1.9945E+06 9.6698E+06 5.3007E-02 1.0000 +335 3 3P - 6 3D 0-1 9695.222663 cm-1 185564.854540 195260.077203 1.1081E+06 9.6698E+06 5.3008E-02 1.0000 +335 3 3P - 6 3D 1-2 9695.487841 cm-1 185564.583895 195260.071736 1.4958E+06 9.6697E+06 3.9753E-02 0.9999 +335 3 3P - 6 3D 1-1 9695.493308 cm-1 185564.583895 195260.077203 8.3108E+05 9.6698E+06 1.3252E-02 1.0000 +335 3 3P - 6 3D 2-3 9695.509438 cm-1 185564.561920 195260.071358 1.9946E+06 9.6698E+06 4.4527E-02 1.0000 +335 3 3P - 6 3D 2-2 9695.509817 cm-1 185564.561920 195260.071736 4.9860E+05 9.6697E+06 7.9505E-03 0.9999 +335 3 3P - 6 3D 2-1 9695.515283 cm-1 185564.561920 195260.077203 5.5405E+04 9.6698E+06 5.3008E-04 1.0000 +336 3 3P - 7 3S Mean 9702.6516 9705.312532 185564.601758 195868.236975 8.6511E+05 3.6533E+06 4.0714E-03 1.0000 +336 3 3P - 7 3S 0-1 9702.8896 9705.550641 185564.854540 195868.236975 9.6124E+04 3.6533E+06 4.0715E-03 1.0000 +336 3 3P - 7 3S 1-1 9702.6348 9705.295707 185564.583895 195868.236975 2.8837E+05 3.6533E+06 4.0714E-03 1.0000 +336 3 3P - 7 3S 2-1 9702.6141 9705.275007 185564.561920 195868.236975 4.8062E+05 3.6533E+06 4.0715E-03 1.0000 +337 3 3P - 7 3D Mean 9516.6009 9519.211412 185564.601758 196069.673625 1.2439E+06 6.1663E+06 2.8158E-02 1.0000 +337 3 3P - 7 3D 0-1 9516.8273 9519.437881 185564.854540 196069.676490 6.9105E+05 6.1664E+06 2.8159E-02 1.0000 +337 3 3P - 7 3D 1-2 9516.5852 9519.195747 185564.583895 196069.673050 9.3285E+05 6.1661E+06 2.1117E-02 0.9999 +337 3 3P - 7 3D 1-1 9516.5821 9519.192630 185564.583895 196069.676490 5.1829E+05 6.1664E+06 7.0397E-03 1.0000 +337 3 3P - 7 3D 2-3 9516.5655 9519.176052 185564.561920 196069.672809 1.2439E+06 6.1664E+06 2.3653E-02 1.0000 +337 3 3P - 7 3D 2-2 9516.5653 9519.175834 185564.561920 196069.673050 3.1095E+05 6.1661E+06 4.2235E-03 0.9999 +337 3 3P - 7 3D 2-1 9516.5622 9519.172717 185564.561920 196069.676490 3.4553E+04 6.1664E+06 2.8159E-04 1.0000 +338 3 3P - 8 3S Mean 9174.5218 9177.039737 185564.601758 196461.361811 5.5996E+05 2.4913E+06 2.3562E-03 1.0000 +338 3 3P - 8 3S 0-1 9174.7347 9177.252629 185564.854540 196461.361811 6.2217E+04 2.4913E+06 2.3562E-03 1.0000 +338 3 3P - 8 3S 1-1 9174.5068 9177.024693 185564.583895 196461.361811 1.8665E+05 2.4913E+06 2.3562E-03 1.0000 +338 3 3P - 8 3S 2-1 9174.4883 9177.006186 185564.561920 196461.361811 3.1109E+05 2.4913E+06 2.3562E-03 1.0000 +339 3 3P - 8 3D Mean 9063.3164 9065.804238 185564.601758 196595.062750 8.2702E+05 4.1689E+06 1.6981E-02 1.0000 +339 3 3P - 8 3D 0-1 9063.5226 9066.010424 185564.854540 196595.064668 4.5947E+05 4.1690E+06 1.6981E-02 1.0000 +339 3 3P - 8 3D 1-2 9063.3021 9065.789873 185564.583895 196595.062365 6.2023E+05 4.1688E+06 1.2735E-02 0.9999 +339 3 3P - 8 3D 1-1 9063.3002 9065.787980 185564.583895 196595.064668 3.4460E+05 4.1690E+06 4.2453E-03 1.0000 +339 3 3P - 8 3D 2-3 9063.2842 9065.771945 185564.561920 196595.062202 8.2704E+05 4.1690E+06 1.4264E-02 1.0000 +339 3 3P - 8 3D 2-2 9063.2840 9065.771811 185564.561920 196595.062365 2.0674E+05 4.1688E+06 2.5469E-03 0.9999 +339 3 3P - 8 3D 2-1 9063.2821 9065.769918 185564.561920 196595.064668 2.2973E+04 4.1690E+06 1.6981E-04 1.0000 +340 3 3P - 9 3S Mean 8849.1756 8851.605469 185564.601758 196861.987340 3.8377E+05 1.7692E+06 1.5023E-03 1.0000 +340 3 3P - 9 3S 0-1 8849.3736 8851.803530 185564.854540 196861.987340 4.2641E+04 1.7692E+06 1.5023E-03 1.0000 +340 3 3P - 9 3S 1-1 8849.1616 8851.591474 185564.583895 196861.987340 1.2792E+05 1.7692E+06 1.5023E-03 1.0000 +340 3 3P - 9 3S 2-1 8849.1444 8851.574256 185564.561920 196861.987340 2.1321E+05 1.7692E+06 1.5024E-03 1.0000 +341 3 3P - 9 3D Mean 8776.7392 8779.149402 185564.601758 196955.226911 5.7758E+05 2.9483E+06 1.1121E-02 1.0000 +341 3 3P - 9 3D 0-1 8776.9329 8779.343195 185564.854540 196955.228258 3.2088E+05 2.9484E+06 1.1121E-02 1.0000 +341 3 3P - 9 3D 1-2 8776.7256 8779.135842 185564.583895 196955.226641 4.3316E+05 2.9482E+06 8.3402E-03 0.9999 +341 3 3P - 9 3D 1-1 8776.7244 8779.134596 185564.583895 196955.228258 2.4066E+05 2.9484E+06 2.7803E-03 1.0000 +341 3 3P - 9 3D 2-3 8776.7088 8779.118994 185564.561920 196955.226527 5.7759E+05 2.9483E+06 9.3418E-03 1.0000 +341 3 3P - 9 3D 2-2 8776.7087 8779.118905 185564.561920 196955.226641 1.4439E+05 2.9482E+06 1.6681E-03 0.9999 +341 3 3P - 9 3D 2-1 8776.7074 8779.117659 185564.561920 196955.228258 1.6044E+04 2.9484E+06 1.1121E-04 1.0000 +342 3 3P -10 3S Mean 8632.7364 8635.107680 185564.601758 197145.233258 2.7471E+05 1.2990E+06 1.0235E-03 1.0001 +342 3 3P -10 3S 0-1 8632.9248 8635.296171 185564.854540 197145.233258 3.0523E+04 1.2990E+06 1.0234E-03 1.0000 +342 3 3P -10 3S 1-1 8632.7231 8635.094360 185564.583895 197145.233258 9.1570E+04 1.2990E+06 1.0234E-03 1.0000 +342 3 3P -10 3S 2-1 8632.7067 8635.077974 185564.561920 197145.233258 1.5262E+05 1.2990E+06 1.0235E-03 1.0000 +343 3 3P -10 3D Mean 8582.6417 8584.999457 185564.601758 197212.826141 4.1927E+05 2.1609E+06 7.7196E-03 1.0000 +343 3 3P -10 3D 0-1 8582.8273 8585.185042 185564.854540 197212.827123 2.3293E+05 2.1609E+06 7.7197E-03 1.0000 +343 3 3P -10 3D 1-2 8582.6287 8584.986436 185564.583895 197212.825945 3.1444E+05 2.1608E+06 5.7895E-03 0.9999 +343 3 3P -10 3D 1-1 8582.6278 8584.985568 185564.583895 197212.827123 1.7470E+05 2.1609E+06 1.9300E-03 1.0000 +343 3 3P -10 3D 2-3 8582.6126 8584.970302 185564.561920 197212.825861 4.1928E+05 2.1609E+06 6.4847E-03 1.0000 +343 3 3P -10 3D 2-2 8582.6125 8584.970240 185564.561920 197212.825945 1.0481E+05 2.1608E+06 1.1579E-03 0.9999 +343 3 3P -10 3D 2-1 8582.6116 8584.969371 185564.561920 197212.827123 1.1647E+04 2.1609E+06 7.7201E-05 1.0000 +344 3 3D - 4 3P Mean 5115.500867 cm-1 186101.556357 191217.057224 6.4529E+05 7.2190E+06 2.2174E-02 0.9999 +344 3 3D - 4 3P 1-2 5115.448077 cm-1 186101.592890 191217.040967 6.4534E+03 7.2190E+06 6.1598E-04 1.0000 +344 3 3D - 4 3P 1-1 5115.457073 cm-1 186101.592890 191217.049963 1.6134E+05 7.2190E+06 9.2400E-03 1.0000 +344 3 3D - 4 3P 2-2 5115.492278 cm-1 186101.548689 191217.040967 9.6778E+04 7.2190E+06 5.5425E-03 0.9997 +344 3 3D - 4 3P 3-2 5115.494790 cm-1 186101.546177 191217.040967 5.4209E+05 7.2190E+06 2.2176E-02 1.0000 +344 3 3D - 4 3P 2-1 5115.501274 cm-1 186101.548689 191217.049963 4.8389E+05 7.2190E+06 1.6628E-02 0.9998 +344 3 3D - 4 3P 1-0 5115.567399 cm-1 186101.592890 191217.160290 6.4534E+05 7.2190E+06 1.2320E-02 1.0000 +345 3 3D - 4 3F Mean 5350.324404 cm-1 186101.556357 191451.880761 1.2220E+07 1.3837E+07 8.9572E-01 0.8831 +345 3 3D - 4 3F 1-2 5350.296817 cm-1 186101.592890 191451.889707 1.1624E+07 1.3838E+07 1.0143E+00 1.0000 +345 3 3D - 4 3F 2-3 5350.325260 cm-1 186101.548689 191451.873949 8.0071E+06 1.3836E+07 5.8693E-01 0.6510 +345 3 3D - 4 3F 3-3 5350.327772 cm-1 186101.546177 191451.873949 9.7644E+05 1.3836E+07 5.1124E-02 0.6351 +345 3 3D - 4 3F 3-4 5350.334912 cm-1 186101.546177 191451.881089 1.3838E+07 1.3838E+07 9.3153E-01 1.0000 +345 3 3D - 4 3F 2-2 5350.341018 cm-1 186101.548689 191451.889707 2.1521E+06 1.3838E+07 1.1268E-01 0.9998 +345 3 3D - 4 3F 3-2 5350.343530 cm-1 186101.546177 191451.889707 6.1502E+04 1.3838E+07 2.3001E-03 1.0000 +346 3 3D - 5 3P Mean 7699.159409 cm-1 186101.556357 193800.715766 2.7292E+05 4.5601E+06 4.1403E-03 0.9999 +346 3 3D - 5 3P 1-2 7699.114705 cm-1 186101.592890 193800.707595 2.7294E+03 4.5601E+06 1.1502E-04 1.0000 +346 3 3D - 5 3P 1-1 7699.119228 cm-1 186101.592890 193800.712118 6.8235E+04 4.5601E+06 1.7252E-03 1.0000 +346 3 3D - 5 3P 2-2 7699.158906 cm-1 186101.548689 193800.707595 4.0931E+04 4.5601E+06 1.0349E-03 0.9998 +346 3 3D - 5 3P 3-2 7699.161418 cm-1 186101.546177 193800.707595 2.2927E+05 4.5601E+06 4.1406E-03 1.0000 +346 3 3D - 5 3P 2-1 7699.163429 cm-1 186101.548689 193800.712118 2.0466E+05 4.5601E+06 3.1048E-03 0.9998 +346 3 3D - 5 3P 1-0 7699.174673 cm-1 186101.592890 193800.767563 2.7294E+05 4.5601E+06 2.3003E-03 1.0000 +347 3 3D - 5 3F Mean 7819.565010 cm-1 186101.556357 193921.121367 4.1339E+06 7.1597E+06 1.4186E-01 0.9037 +347 3 3D - 5 3F 1-2 7819.532863 cm-1 186101.592890 193921.125753 3.8426E+06 7.1603E+06 1.5698E-01 1.0000 +347 3 3D - 5 3F 2-3 7819.569575 cm-1 186101.548689 193921.118264 2.8980E+06 7.1585E+06 9.9449E-02 0.7127 +347 3 3D - 5 3F 3-3 7819.572088 cm-1 186101.546177 193921.118264 3.5457E+05 7.1585E+06 8.6912E-03 0.6976 +347 3 3D - 5 3F 3-4 7819.575166 cm-1 186101.546177 193921.121343 4.5746E+06 7.1603E+06 1.4417E-01 1.0000 +347 3 3D - 5 3F 2-2 7819.577064 cm-1 186101.548689 193921.125753 7.1142E+05 7.1603E+06 1.7438E-02 0.9998 +347 3 3D - 5 3F 3-2 7819.579576 cm-1 186101.546177 193921.125753 2.0331E+04 7.1603E+06 3.5596E-04 1.0000 +348 3 3D - 6 3P Mean 9091.191291 cm-1 186101.556357 195192.747648 1.4253E+05 2.9557E+06 1.5507E-03 0.9999 +348 3 3D - 6 3P 1-2 9091.150084 cm-1 186101.592890 195192.742974 1.4254E+03 2.9557E+06 4.3080E-05 1.0000 +348 3 3D - 6 3P 1-1 9091.152669 cm-1 186101.592890 195192.745559 3.5634E+04 2.9557E+06 6.4619E-04 1.0000 +348 3 3D - 6 3P 1-0 9091.184391 cm-1 186101.592890 195192.777281 1.4254E+05 2.9557E+06 8.6161E-04 1.0000 +348 3 3D - 6 3P 2-2 9091.194285 cm-1 186101.548689 195192.742974 2.1375E+04 2.9557E+06 3.8761E-04 0.9997 +348 3 3D - 6 3P 3-2 9091.196798 cm-1 186101.546177 195192.742974 1.1973E+05 2.9557E+06 1.5508E-03 1.0000 +348 3 3D - 6 3P 2-1 9091.196870 cm-1 186101.548689 195192.745559 1.0688E+05 2.9557E+06 1.1629E-03 0.9997 +349 3 3D - 6 3F Mean 9160.869537 cm-1 186101.556357 195262.425894 1.9801E+06 4.1897E+06 4.9509E-02 0.9148 +349 3 3D - 6 3F 1-2 9160.835483 cm-1 186101.592890 195262.428373 1.8181E+06 4.1901E+06 5.4117E-02 1.0000 +349 3 3D - 6 3F 2-3 9160.875528 cm-1 186101.548689 195262.424217 1.4356E+06 4.1889E+06 3.5895E-02 0.7462 +349 3 3D - 6 3F 3-3 9160.878040 cm-1 186101.546177 195262.424217 1.7594E+05 4.1889E+06 3.1422E-03 0.7316 +349 3 3D - 6 3F 3-4 9160.879645 cm-1 186101.546177 195262.425821 2.1644E+06 4.1901E+06 4.9699E-02 1.0000 +349 3 3D - 6 3F 2-2 9160.879684 cm-1 186101.548689 195262.428373 3.3661E+05 4.1901E+06 6.0117E-03 0.9998 +349 3 3D - 6 3F 3-2 9160.882196 cm-1 186101.546177 195262.428373 9.6197E+03 4.1901E+06 1.2272E-04 1.0000 +350 3 3D - 7 3P Mean 9925.761590 cm-1 186101.556357 196027.317947 8.4430E+04 1.9947E+06 7.7065E-04 0.9999 +350 3 3D - 7 3P 1-2 9925.722136 cm-1 186101.592890 196027.315027 8.4437E+02 1.9947E+06 2.1409E-05 1.0000 +350 3 3D - 7 3P 1-1 9925.723751 cm-1 186101.592890 196027.316641 2.1109E+04 1.9947E+06 3.2113E-04 1.0000 +350 3 3D - 7 3P 1-0 9925.743575 cm-1 186101.592890 196027.336465 8.4437E+04 1.9947E+06 4.2818E-04 1.0000 +350 3 3D - 7 3P 2-2 9925.766338 cm-1 186101.548689 196027.315027 1.2662E+04 1.9947E+06 1.9262E-04 0.9995 +350 3 3D - 7 3P 2-1 9925.767952 cm-1 186101.548689 196027.316641 6.3312E+04 1.9947E+06 5.7789E-04 0.9998 +350 3 3D - 7 3P 3-2 9925.768850 cm-1 186101.546177 196027.315027 7.0927E+04 1.9947E+06 7.7071E-04 1.0000 +351 3 3D - 7 3F Mean 9969.620834 cm-1 186101.556357 196071.177191 1.1225E+06 2.6643E+06 2.3698E-02 0.9214 +351 3 3D - 7 3F 1-2 9969.585840 cm-1 186101.592890 196071.178730 1.0234E+06 2.6646E+06 2.5720E-02 1.0000 +351 3 3D - 7 3F 2-3 9969.627489 cm-1 186101.548689 196071.176178 8.2928E+05 2.6638E+06 1.7507E-02 0.7658 +351 3 3D - 7 3F 3-3 9969.630001 cm-1 186101.546177 196071.176178 1.0174E+05 2.6638E+06 1.5342E-03 0.7516 +351 3 3D - 7 3F 2-2 9969.630041 cm-1 186101.548689 196071.178730 1.8947E+05 2.6646E+06 2.8571E-03 0.9998 +351 3 3D - 7 3F 3-4 9969.630947 cm-1 186101.546177 196071.177123 1.2183E+06 2.6646E+06 2.3620E-02 1.0000 +351 3 3D - 7 3F 3-2 9969.632553 cm-1 186101.546177 196071.178730 5.4147E+03 2.6646E+06 5.8322E-05 1.0000 +352 3 3D - 8 3P Mean 9552.8976 9555.517999 186101.556357 196566.713767 5.4372E+04 1.3990E+06 4.4645E-04 1.0000 +352 3 3D - 8 3P 1-2 9552.9328 9555.553133 186101.592890 196566.711822 5.4376E+02 1.3990E+06 1.2402E-05 1.0000 +352 3 3D - 8 3P 1-1 9552.9318 9555.552152 186101.592890 196566.712897 1.3594E+04 1.3990E+06 1.8603E-04 1.0000 +352 3 3D - 8 3P 1-0 9552.9197 9555.540092 186101.592890 196566.726105 5.4376E+04 1.3990E+06 2.4805E-04 1.0000 +352 3 3D - 8 3P 2-2 9552.8924 9555.512774 186101.548689 196566.711822 8.1544E+03 1.3990E+06 1.1159E-04 1.0000 +352 3 3D - 8 3P 2-1 9552.8914 9555.511792 186101.548689 196566.712897 4.0772E+04 1.3990E+06 3.3478E-04 0.9998 +352 3 3D - 8 3P 3-2 9552.8901 9555.510480 186101.546177 196566.711822 4.5676E+04 1.3990E+06 4.4649E-04 1.0000 +353 3 3D - 8 3F Mean 9526.1667 9528.779859 186101.556357 196596.079420 7.0457E+05 1.7997E+06 1.3424E-02 0.9255 +353 3 3D - 8 3F 1-2 9526.1990 9528.812103 186101.592890 196596.080442 6.3946E+05 1.7998E+06 1.4504E-02 1.0000 +353 3 3D - 8 3F 2-3 9526.1604 9528.773497 186101.548689 196596.078760 5.2655E+05 1.7993E+06 1.0032E-02 0.7781 +353 3 3D - 8 3F 2-2 9526.1588 9528.771969 186101.548689 196596.080442 1.1839E+05 1.7998E+06 1.6111E-03 0.9998 +353 3 3D - 8 3F 3-3 9526.1581 9528.771215 186101.546177 196596.078760 6.4641E+04 1.7993E+06 8.7968E-04 0.7642 +353 3 3D - 8 3F 3-4 9526.1575 9528.770665 186101.546177 196596.079366 7.6127E+05 1.7999E+06 1.3320E-02 1.0000 +353 3 3D - 8 3F 3-2 9526.1566 9528.769688 186101.546177 196596.080442 3.3834E+03 1.7998E+06 3.2888E-05 1.0000 +354 3 3D - 9 3P Mean 9227.8594 9230.391703 186101.556357 196935.332779 3.7167E+04 1.0146E+06 2.8477E-04 1.0000 +354 3 3D - 9 3P 1-2 9227.8916 9230.423989 186101.592890 196935.331418 3.7170E+02 1.0146E+06 7.9108E-06 1.0000 +354 3 3D - 9 3P 1-1 9227.8910 9230.423349 186101.592890 196935.332170 9.2925E+03 1.0146E+06 1.1866E-04 1.0000 +354 3 3D - 9 3P 1-0 9227.8831 9230.415478 186101.592890 196935.341408 3.7170E+04 1.0146E+06 1.5822E-04 1.0000 +354 3 3D - 9 3P 2-2 9227.8540 9230.386330 186101.548689 196935.331418 5.5742E+03 1.0146E+06 7.1181E-05 1.0000 +354 3 3D - 9 3P 2-1 9227.8533 9230.385689 186101.548689 196935.332170 2.7871E+04 1.0146E+06 2.1354E-04 0.9997 +354 3 3D - 9 3P 3-2 9227.8518 9230.384189 186101.546177 196935.331418 3.1223E+04 1.0146E+06 2.8479E-04 1.0000 +355 3 3D - 9 3F Mean 9210.3354 9212.863013 186101.556357 196955.945471 4.7381E+05 1.2727E+06 8.4385E-03 0.9283 +355 3 3D - 9 3F 1-2 9210.3658 9212.893416 186101.592890 196955.946185 4.2875E+05 1.2728E+06 9.0904E-03 1.0000 +355 3 3D - 9 3F 2-3 9210.3293 9212.856891 186101.548689 196955.945017 3.5681E+05 1.2724E+06 6.3547E-03 0.7864 +355 3 3D - 9 3F 2-2 9210.3283 9212.855899 186101.548689 196955.946185 7.9378E+04 1.2728E+06 1.0098E-03 0.9998 +355 3 3D - 9 3F 3-3 9210.3272 9212.854758 186101.546177 196955.945017 4.3822E+04 1.2724E+06 5.5747E-04 0.7727 +355 3 3D - 9 3F 3-4 9210.3268 9212.854408 186101.546177 196955.945429 5.1041E+05 1.2728E+06 8.3482E-03 1.0000 +355 3 3D - 9 3F 3-2 9210.3262 9212.853767 186101.546177 196955.946185 2.2685E+03 1.2728E+06 2.0613E-05 1.0000 +356 3 3D -10 3P Mean 9009.1522 9011.625340 186101.556357 197198.333711 2.6573E+04 7.5715E+05 1.9406E-04 1.0000 +356 3 3D -10 3P 1-2 9009.1827 9011.655812 186101.592890 197198.332722 2.6575E+02 7.5715E+05 5.3910E-06 1.0000 +356 3 3D -10 3P 1-1 9009.1822 9011.655369 186101.592890 197198.333268 6.6439E+03 7.5715E+05 8.0867E-05 1.0000 +356 3 3D -10 3P 1-0 9009.1768 9011.649917 186101.592890 197198.339982 2.6575E+04 7.5716E+05 1.0782E-04 1.0000 +356 3 3D -10 3P 2-2 9009.1468 9011.619916 186101.548689 197198.332722 3.9853E+03 7.5715E+05 4.8507E-05 1.0000 +356 3 3D -10 3P 2-1 9009.1463 9011.619473 186101.548689 197198.333268 1.9927E+04 7.5715E+05 1.4553E-04 0.9996 +356 3 3D -10 3P 3-2 9009.1447 9011.617876 186101.546177 197198.332722 2.2323E+04 7.5715E+05 1.9408E-04 1.0000 +357 3 3D -10 3F Mean 8996.9755 8999.445299 186101.556357 197213.352326 3.3504E+05 9.3313E+05 5.6938E-03 0.9302 +357 3 3D -10 3F 1-2 8997.0046 8999.474469 186101.592890 197213.352843 3.0254E+05 9.3321E+05 6.1207E-03 1.0000 +357 3 3D -10 3F 2-3 8996.9695 8999.439354 186101.548689 197213.351998 2.5364E+05 9.3293E+05 4.3104E-03 0.7923 +357 3 3D -10 3F 2-2 8996.9688 8999.438670 186101.548689 197213.352843 5.6012E+04 9.3321E+05 6.7991E-04 0.9997 +357 3 3D -10 3F 3-3 8996.9675 8999.437320 186101.546177 197213.351998 3.1161E+04 9.3293E+05 3.7825E-04 0.7787 +357 3 3D -10 3F 3-4 8996.9672 8999.437081 186101.546177 197213.352292 3.6017E+05 9.3323E+05 5.6211E-03 1.0000 +357 3 3D -10 3F 3-2 8996.9668 8999.436635 186101.546177 197213.352843 1.6007E+03 9.3321E+05 1.3879E-05 1.0000 +358 4 3S - 4 3P Mean 918.943964 cm-1 190298.113260 191217.057224 2.2825E+05 7.2190E+06 1.2152E+00 1.0000 +358 4 3S - 4 3P 1-2 918.927707 cm-1 190298.113260 191217.040967 2.2825E+05 7.2190E+06 6.7514E-01 1.0000 +358 4 3S - 4 3P 1-1 918.936703 cm-1 190298.113260 191217.049963 2.2825E+05 7.2190E+06 4.0508E-01 1.0000 +358 4 3S - 4 3P 1-0 919.047030 cm-1 190298.113260 191217.160290 2.2825E+05 7.2190E+06 1.3503E-01 1.0000 +359 4 3S - 5 3P Mean 3502.602506 cm-1 190298.113260 193800.715766 1.2068E+05 4.5601E+06 4.4231E-02 1.0000 +359 4 3S - 5 3P 1-2 3502.594335 cm-1 190298.113260 193800.707595 1.2068E+05 4.5601E+06 2.4573E-02 1.0000 +359 4 3S - 5 3P 1-1 3502.598858 cm-1 190298.113260 193800.712118 1.2068E+05 4.5601E+06 1.4744E-02 1.0000 +359 4 3S - 5 3P 1-0 3502.654303 cm-1 190298.113260 193800.767563 1.2068E+05 4.5601E+06 4.9146E-03 1.0000 +360 4 3S - 6 3P Mean 4894.634388 cm-1 190298.113260 195192.747648 1.1524E+05 2.9557E+06 2.1629E-02 1.0000 +360 4 3S - 6 3P 1-2 4894.629714 cm-1 190298.113260 195192.742974 1.1524E+05 2.9557E+06 1.2016E-02 1.0000 +360 4 3S - 6 3P 1-1 4894.632299 cm-1 190298.113260 195192.745559 1.1524E+05 2.9557E+06 7.2098E-03 1.0000 +360 4 3S - 6 3P 1-0 4894.664021 cm-1 190298.113260 195192.777281 1.1524E+05 2.9557E+06 2.4033E-03 1.0000 +361 4 3S - 7 3P Mean 5729.204687 cm-1 190298.113260 196027.317947 8.5957E+04 1.9947E+06 1.1775E-02 1.0000 +361 4 3S - 7 3P 1-2 5729.201767 cm-1 190298.113260 196027.315027 8.5957E+04 1.9947E+06 6.5419E-03 1.0000 +361 4 3S - 7 3P 1-1 5729.203381 cm-1 190298.113260 196027.316641 8.5957E+04 1.9947E+06 3.9251E-03 1.0000 +361 4 3S - 7 3P 1-0 5729.223205 cm-1 190298.113260 196027.336465 8.5957E+04 1.9947E+06 1.3084E-03 1.0000 +362 4 3S - 8 3P Mean 6268.600507 cm-1 190298.113260 196566.713767 6.2580E+04 1.3990E+06 7.1610E-03 1.0000 +362 4 3S - 8 3P 1-2 6268.598562 cm-1 190298.113260 196566.711822 6.2580E+04 1.3990E+06 3.9783E-03 1.0000 +362 4 3S - 8 3P 1-1 6268.599637 cm-1 190298.113260 196566.712897 6.2580E+04 1.3990E+06 2.3870E-03 1.0000 +362 4 3S - 8 3P 1-0 6268.612844 cm-1 190298.113260 196566.726105 6.2580E+04 1.3990E+06 7.9567E-04 1.0000 +363 4 3S - 9 3P Mean 6637.219519 cm-1 190298.113260 196935.332779 4.6126E+04 1.0146E+06 4.7082E-03 1.0000 +363 4 3S - 9 3P 1-2 6637.218158 cm-1 190298.113260 196935.331418 4.6126E+04 1.0146E+06 2.6157E-03 1.0000 +363 4 3S - 9 3P 1-1 6637.218910 cm-1 190298.113260 196935.332170 4.6126E+04 1.0146E+06 1.5694E-03 1.0000 +363 4 3S - 9 3P 1-0 6637.228148 cm-1 190298.113260 196935.341408 4.6126E+04 1.0146E+06 5.2313E-04 1.0000 +364 4 3S -10 3P Mean 6900.220451 cm-1 190298.113260 197198.333711 3.4680E+04 7.5715E+05 3.2752E-03 1.0000 +364 4 3S -10 3P 1-2 6900.219462 cm-1 190298.113260 197198.332722 3.4680E+04 7.5715E+05 1.8195E-03 1.0000 +364 4 3S -10 3P 1-1 6900.220008 cm-1 190298.113260 197198.333268 3.4680E+04 7.5715E+05 1.0917E-03 1.0000 +364 4 3S -10 3P 1-0 6900.226722 cm-1 190298.113260 197198.339982 3.4680E+04 7.5716E+05 3.6391E-04 1.0000 +365 4 3P - 4 3D Mean 227.428050 cm-1 191217.057224 191444.485274 4.1537E+03 3.1192E+07 2.0094E-01 1.0000 +365 4 3P - 4 3D 0-1 227.340362 cm-1 191217.160290 191444.500651 2.3077E+03 3.1192E+07 2.0095E-01 1.0000 +365 4 3P - 4 3D 1-2 227.432167 cm-1 191217.049963 191444.482131 3.1150E+03 3.1192E+07 1.5069E-01 0.9999 +365 4 3P - 4 3D 2-3 227.439962 cm-1 191217.040967 191444.480929 4.1539E+03 3.1192E+07 1.6880E-01 1.0000 +365 4 3P - 4 3D 2-2 227.441164 cm-1 191217.040967 191444.482131 1.0383E+03 3.1192E+07 3.0137E-02 0.9999 +365 4 3P - 4 3D 1-1 227.450688 cm-1 191217.049963 191444.500651 1.7308E+03 3.1192E+07 5.0238E-02 1.0000 +365 4 3P - 4 3D 2-1 227.459684 cm-1 191217.040967 191444.500651 1.1539E+02 3.1192E+07 2.0096E-03 1.0000 +366 4 3P - 5 3S Mean 2129.934120 cm-1 191217.057224 193346.991344 2.0227E+06 9.2072E+06 2.2277E-01 1.0000 +366 4 3P - 5 3S 0-1 2129.831055 cm-1 191217.160290 193346.991344 2.2474E+05 9.2072E+06 2.2277E-01 1.0000 +366 4 3P - 5 3S 1-1 2129.941381 cm-1 191217.049963 193346.991344 6.7421E+05 9.2072E+06 2.2277E-01 1.0000 +366 4 3P - 5 3S 2-1 2129.950377 cm-1 191217.040967 193346.991344 1.1237E+06 9.2072E+06 2.2277E-01 1.0000 +367 4 3P - 5 3D Mean 2700.096297 cm-1 191217.057224 193917.153521 1.2792E+06 1.6412E+07 4.3838E-01 1.0000 +367 4 3P - 5 3D 0-1 2700.001097 cm-1 191217.160290 193917.161387 7.1071E+05 1.6412E+07 4.3839E-01 1.0000 +367 4 3P - 5 3D 1-2 2700.101965 cm-1 191217.049963 193917.151929 9.5937E+05 1.6411E+07 3.2876E-01 0.9999 +367 4 3P - 5 3D 2-3 2700.110320 cm-1 191217.040967 193917.151287 1.2793E+06 1.6412E+07 3.6825E-01 1.0000 +367 4 3P - 5 3D 2-2 2700.110961 cm-1 191217.040967 193917.151929 3.1979E+05 1.6411E+07 6.5752E-02 0.9999 +367 4 3P - 5 3D 1-1 2700.111424 cm-1 191217.049963 193917.161387 5.3303E+05 1.6412E+07 1.0960E-01 1.0000 +367 4 3P - 5 3D 2-1 2700.120420 cm-1 191217.040967 193917.161387 3.5536E+04 1.6412E+07 4.3839E-03 1.0000 +368 4 3P - 6 3S Mean 3719.062473 cm-1 191217.057224 194936.119697 9.5913E+05 5.6296E+06 3.4647E-02 1.0000 +368 4 3P - 6 3S 0-1 3718.959408 cm-1 191217.160290 194936.119697 1.0657E+05 5.6296E+06 3.4647E-02 1.0000 +368 4 3P - 6 3S 1-1 3719.069734 cm-1 191217.049963 194936.119697 3.1971E+05 5.6296E+06 3.4647E-02 1.0000 +368 4 3P - 6 3S 2-1 3719.078730 cm-1 191217.040967 194936.119697 5.3285E+05 5.6296E+06 3.4647E-02 1.0000 +369 4 3P - 6 3D Mean 4043.015429 cm-1 191217.057224 195260.072653 8.1093E+05 9.6698E+06 1.2394E-01 1.0000 +369 4 3P - 6 3D 0-1 4042.916913 cm-1 191217.160290 195260.077203 4.5053E+05 9.6698E+06 1.2394E-01 1.0000 +369 4 3P - 6 3D 1-2 4043.021773 cm-1 191217.049963 195260.071736 6.0816E+05 9.6697E+06 9.2948E-02 0.9999 +369 4 3P - 6 3D 1-1 4043.027240 cm-1 191217.049963 195260.077203 3.3790E+05 9.6698E+06 3.0986E-02 1.0000 +369 4 3P - 6 3D 2-3 4043.030391 cm-1 191217.040967 195260.071358 8.1095E+05 9.6698E+06 1.0411E-01 1.0000 +369 4 3P - 6 3D 2-2 4043.030769 cm-1 191217.040967 195260.071736 2.0272E+05 9.6697E+06 1.8590E-02 0.9999 +369 4 3P - 6 3D 2-1 4043.036236 cm-1 191217.040967 195260.077203 2.2527E+04 9.6698E+06 1.2394E-03 1.0000 +370 4 3P - 7 3S Mean 4651.179752 cm-1 191217.057224 195868.236975 5.5212E+05 3.6533E+06 1.2751E-02 1.0000 +370 4 3P - 7 3S 0-1 4651.076686 cm-1 191217.160290 195868.236975 6.1346E+04 3.6533E+06 1.2751E-02 1.0000 +370 4 3P - 7 3S 1-1 4651.187012 cm-1 191217.049963 195868.236975 1.8404E+05 3.6533E+06 1.2751E-02 1.0000 +370 4 3P - 7 3S 2-1 4651.196008 cm-1 191217.040967 195868.236975 3.0673E+05 3.6533E+06 1.2751E-02 1.0000 +371 4 3P - 7 3D Mean 4852.616402 cm-1 191217.057224 196069.673625 5.2062E+05 6.1663E+06 5.5232E-02 1.0000 +371 4 3P - 7 3D 0-1 4852.516200 cm-1 191217.160290 196069.676490 2.8924E+05 6.1664E+06 5.5234E-02 1.0000 +371 4 3P - 7 3D 1-2 4852.623087 cm-1 191217.049963 196069.673050 3.9044E+05 6.1661E+06 4.1422E-02 0.9999 +371 4 3P - 7 3D 1-1 4852.626526 cm-1 191217.049963 196069.676490 2.1693E+05 6.1664E+06 1.3808E-02 1.0000 +371 4 3P - 7 3D 2-3 4852.631842 cm-1 191217.040967 196069.672809 5.2063E+05 6.1664E+06 4.6396E-02 1.0000 +371 4 3P - 7 3D 2-2 4852.632083 cm-1 191217.040967 196069.673050 1.3015E+05 6.1661E+06 8.2845E-03 0.9999 +371 4 3P - 7 3D 2-1 4852.635523 cm-1 191217.040967 196069.676490 1.4462E+04 6.1664E+06 5.5234E-04 1.0000 +372 4 3P - 8 3S Mean 5244.304587 cm-1 191217.057224 196461.361811 3.5053E+05 2.4913E+06 6.3679E-03 1.0000 +372 4 3P - 8 3S 0-1 5244.201521 cm-1 191217.160290 196461.361811 3.8948E+04 2.4913E+06 6.3680E-03 1.0000 +372 4 3P - 8 3S 1-1 5244.311847 cm-1 191217.049963 196461.361811 1.1684E+05 2.4913E+06 6.3677E-03 1.0000 +372 4 3P - 8 3S 2-1 5244.320843 cm-1 191217.040967 196461.361811 1.9474E+05 2.4913E+06 6.3680E-03 1.0000 +373 4 3P - 8 3D Mean 5378.005526 cm-1 191217.057224 196595.062750 3.5063E+05 4.1689E+06 3.0285E-02 1.0000 +373 4 3P - 8 3D 0-1 5377.904379 cm-1 191217.160290 196595.064668 1.9480E+05 4.1690E+06 3.0286E-02 1.0000 +373 4 3P - 8 3D 1-2 5378.012402 cm-1 191217.049963 196595.062365 2.6296E+05 4.1688E+06 2.2713E-02 0.9999 +373 4 3P - 8 3D 1-1 5378.014705 cm-1 191217.049963 196595.064668 1.4610E+05 4.1690E+06 7.5715E-03 1.0000 +373 4 3P - 8 3D 2-3 5378.021235 cm-1 191217.040967 196595.062202 3.5063E+05 4.1690E+06 2.5439E-02 1.0000 +373 4 3P - 8 3D 2-2 5378.021398 cm-1 191217.040967 196595.062365 8.7651E+04 4.1688E+06 4.5424E-03 0.9999 +373 4 3P - 8 3D 2-1 5378.023701 cm-1 191217.040967 196595.064668 9.7398E+03 4.1690E+06 3.0285E-04 1.0000 +374 4 3P - 9 3S Mean 5644.930116 cm-1 191217.057224 196861.987340 2.3748E+05 1.7692E+06 3.7235E-03 1.0000 +374 4 3P - 9 3S 0-1 5644.827050 cm-1 191217.160290 196861.987340 2.6387E+04 1.7692E+06 3.7236E-03 1.0000 +374 4 3P - 9 3S 1-1 5644.937376 cm-1 191217.049963 196861.987340 7.9160E+04 1.7692E+06 3.7235E-03 1.0000 +374 4 3P - 9 3S 2-1 5644.946373 cm-1 191217.040967 196861.987340 1.3193E+05 1.7692E+06 3.7235E-03 1.0000 +375 4 3P - 9 3D Mean 5738.169687 cm-1 191217.057224 196955.226911 2.4658E+05 2.9483E+06 1.8708E-02 1.0000 +375 4 3P - 9 3D 0-1 5738.067969 cm-1 191217.160290 196955.228258 1.3699E+05 2.9484E+06 1.8708E-02 1.0000 +375 4 3P - 9 3D 1-2 5738.176678 cm-1 191217.049963 196955.226641 1.8493E+05 2.9482E+06 1.4031E-02 0.9999 +375 4 3P - 9 3D 1-1 5738.178295 cm-1 191217.049963 196955.228258 1.0275E+05 2.9484E+06 4.6774E-03 1.0000 +375 4 3P - 9 3D 2-3 5738.185560 cm-1 191217.040967 196955.226527 2.4659E+05 2.9483E+06 1.5715E-02 1.0000 +375 4 3P - 9 3D 2-2 5738.185674 cm-1 191217.040967 196955.226641 6.1643E+04 2.9482E+06 2.8061E-03 0.9999 +375 4 3P - 9 3D 2-1 5738.187291 cm-1 191217.040967 196955.228258 6.8497E+03 2.9484E+06 1.8709E-04 1.0000 +376 4 3P -10 3S Mean 5928.176034 cm-1 191217.057224 197145.233258 1.6871E+05 1.2990E+06 2.3985E-03 1.0000 +376 4 3P -10 3S 0-1 5928.072968 cm-1 191217.160290 197145.233258 1.8745E+04 1.2990E+06 2.3985E-03 1.0000 +376 4 3P -10 3S 1-1 5928.183295 cm-1 191217.049963 197145.233258 5.6236E+04 1.2990E+06 2.3985E-03 1.0000 +376 4 3P -10 3S 2-1 5928.192291 cm-1 191217.040967 197145.233258 9.3727E+04 1.2990E+06 2.3985E-03 1.0000 +377 4 3P -10 3D Mean 5995.768918 cm-1 191217.057224 197212.826141 1.7977E+05 2.1609E+06 1.2492E-02 1.0000 +377 4 3P -10 3D 0-1 5995.666834 cm-1 191217.160290 197212.827123 9.9872E+04 2.1609E+06 1.2492E-02 1.0000 +377 4 3P -10 3D 1-2 5995.775982 cm-1 191217.049963 197212.825945 1.3482E+05 2.1608E+06 9.3688E-03 0.9999 +377 4 3P -10 3D 1-1 5995.777160 cm-1 191217.049963 197212.827123 7.4904E+04 2.1609E+06 3.1231E-03 1.0000 +377 4 3P -10 3D 2-3 5995.784894 cm-1 191217.040967 197212.825861 1.7977E+05 2.1609E+06 1.0494E-02 1.0000 +377 4 3P -10 3D 2-2 5995.784978 cm-1 191217.040967 197212.825945 4.4939E+04 2.1608E+06 1.8737E-03 0.9999 +377 4 3P -10 3D 2-1 5995.786156 cm-1 191217.040967 197212.827123 4.9936E+03 2.1609E+06 1.2492E-04 1.0000 +378 4 3D - 4 3F Mean 7.395487 cm-1 191444.485274 191451.880761 7.8012E-02 1.3837E+07 2.9972E-03 0.8817 +378 4 3D - 4 3F 1-2 7.389056 cm-1 191444.500651 191451.889707 7.4329E-02 1.3838E+07 3.3992E-03 1.0000 +378 4 3D - 4 3F 2-3 7.391818 cm-1 191444.482131 191451.873949 5.0864E-02 1.3836E+07 1.9539E-03 0.6466 +378 4 3D - 4 3F 3-3 7.393020 cm-1 191444.480929 191451.873949 6.2438E-03 1.3836E+07 1.7132E-04 0.6349 +378 4 3D - 4 3F 3-4 7.400159 cm-1 191444.480929 191451.881089 8.8487E-02 1.3838E+07 3.1217E-03 1.0000 +378 4 3D - 4 3F 2-2 7.407576 cm-1 191444.482131 191451.889707 1.3763E-02 1.3838E+07 3.7765E-04 0.9997 +378 4 3D - 4 3F 3-2 7.408778 cm-1 191444.480929 191451.889707 3.9328E-04 1.3838E+07 7.7081E-06 1.0000 +379 4 3D - 5 3P Mean 2356.230492 cm-1 191444.485274 193800.715766 3.2710E+05 4.5601E+06 5.2979E-02 1.0000 +379 4 3D - 5 3P 1-2 2356.206944 cm-1 191444.500651 193800.707595 3.2711E+03 4.5601E+06 1.4717E-03 1.0000 +379 4 3D - 5 3P 1-1 2356.211467 cm-1 191444.500651 193800.712118 8.1779E+04 4.5601E+06 2.2076E-02 1.0000 +379 4 3D - 5 3P 2-2 2356.225464 cm-1 191444.482131 193800.707595 4.9061E+04 4.5601E+06 1.3244E-02 0.9999 +379 4 3D - 5 3P 3-2 2356.226666 cm-1 191444.480929 193800.707595 2.7478E+05 4.5601E+06 5.2982E-02 1.0000 +379 4 3D - 5 3P 2-1 2356.229987 cm-1 191444.482131 193800.712118 2.4530E+05 4.5601E+06 3.9730E-02 0.9999 +379 4 3D - 5 3P 1-0 2356.266912 cm-1 191444.500651 193800.767563 3.2711E+05 4.5601E+06 2.9434E-02 1.0000 +380 4 3D - 5 3F Mean 2476.636093 cm-1 191444.485274 193921.121367 2.3336E+06 7.1597E+06 7.9830E-01 0.9025 +380 4 3D - 5 3F 1-2 2476.625102 cm-1 191444.500651 193921.125753 2.1720E+06 7.1603E+06 8.8456E-01 1.0000 +380 4 3D - 5 3F 2-3 2476.636134 cm-1 191444.482131 193921.118264 1.6288E+06 7.1585E+06 5.5720E-01 0.7086 +380 4 3D - 5 3F 3-3 2476.637335 cm-1 191444.480929 193921.118264 2.0042E+05 7.1585E+06 4.8973E-02 0.6976 +380 4 3D - 5 3F 3-4 2476.640414 cm-1 191444.480929 193921.121343 2.5858E+06 7.1603E+06 8.1238E-01 1.0000 +380 4 3D - 5 3F 2-2 2476.643622 cm-1 191444.482131 193921.125753 4.0218E+05 7.1603E+06 9.8274E-02 0.9999 +380 4 3D - 5 3F 3-2 2476.644824 cm-1 191444.480929 193921.125753 1.1492E+04 7.1603E+06 2.0058E-03 1.0000 +381 4 3D - 6 3P Mean 3748.262374 cm-1 191444.485274 195192.747648 1.5975E+05 2.9557E+06 1.0225E-02 1.0000 +381 4 3D - 6 3P 1-2 3748.242323 cm-1 191444.500651 195192.742974 1.5976E+03 2.9557E+06 2.8404E-04 1.0000 +381 4 3D - 6 3P 1-1 3748.244908 cm-1 191444.500651 195192.745559 3.9939E+04 2.9557E+06 4.2605E-03 1.0000 +381 4 3D - 6 3P 2-2 3748.260844 cm-1 191444.482131 195192.742974 2.3961E+04 2.9557E+06 2.5561E-03 0.9998 +381 4 3D - 6 3P 3-2 3748.262045 cm-1 191444.480929 195192.742974 1.3420E+05 2.9557E+06 1.0226E-02 1.0000 +381 4 3D - 6 3P 2-1 3748.263428 cm-1 191444.482131 195192.745559 1.1980E+05 2.9557E+06 7.6679E-03 0.9999 +381 4 3D - 6 3P 1-0 3748.276630 cm-1 191444.500651 195192.777281 1.5976E+05 2.9557E+06 5.6809E-03 1.0000 +382 4 3D - 6 3F Mean 3817.940620 cm-1 191444.485274 195262.425894 1.1807E+06 4.1897E+06 1.6997E-01 0.9137 +382 4 3D - 6 3F 1-2 3817.927722 cm-1 191444.500651 195262.428373 1.0855E+06 4.1901E+06 1.8602E-01 1.0000 +382 4 3D - 6 3F 2-3 3817.942086 cm-1 191444.482131 195262.424217 8.5264E+05 4.1889E+06 1.2274E-01 0.7423 +382 4 3D - 6 3F 3-3 3817.943288 cm-1 191444.480929 195262.424217 1.0505E+05 4.1889E+06 1.0801E-02 0.7316 +382 4 3D - 6 3F 3-4 3817.944892 cm-1 191444.480929 195262.425821 1.2923E+06 4.1901E+06 1.7084E-01 1.0000 +382 4 3D - 6 3F 2-2 3817.946242 cm-1 191444.482131 195262.428373 2.0100E+05 4.1901E+06 2.0667E-02 0.9999 +382 4 3D - 6 3F 3-2 3817.947444 cm-1 191444.480929 195262.428373 5.7436E+03 4.1901E+06 4.2183E-04 1.0000 +383 4 3D - 7 3P Mean 4582.832673 cm-1 191444.485274 196027.317947 9.1121E+04 1.9947E+06 3.9015E-03 1.0000 +383 4 3D - 7 3P 1-2 4582.814376 cm-1 191444.500651 196027.315027 9.1125E+02 1.9947E+06 1.0838E-04 1.0000 +383 4 3D - 7 3P 1-1 4582.815990 cm-1 191444.500651 196027.316641 2.2781E+04 1.9947E+06 1.6257E-03 1.0000 +383 4 3D - 7 3P 2-2 4582.832896 cm-1 191444.482131 196027.315027 1.3667E+04 1.9947E+06 9.7530E-04 0.9999 +383 4 3D - 7 3P 3-2 4582.834098 cm-1 191444.480929 196027.315027 7.6545E+04 1.9947E+06 3.9017E-03 1.0000 +383 4 3D - 7 3P 2-1 4582.834510 cm-1 191444.482131 196027.316641 6.8335E+04 1.9947E+06 2.9259E-03 0.9999 +383 4 3D - 7 3P 1-0 4582.835814 cm-1 191444.500651 196027.336465 9.1125E+04 1.9947E+06 2.1676E-03 1.0000 +384 4 3D - 7 3F Mean 4626.691917 cm-1 191444.485274 196071.177191 6.7931E+05 2.6643E+06 6.6588E-02 0.9203 +384 4 3D - 7 3F 1-2 4626.678079 cm-1 191444.500651 196071.178730 6.2007E+05 2.6646E+06 7.2358E-02 1.0000 +384 4 3D - 7 3F 2-3 4626.694047 cm-1 191444.482131 196071.176178 4.9996E+05 2.6638E+06 4.9008E-02 0.7620 +384 4 3D - 7 3F 3-3 4626.695249 cm-1 191444.480929 196071.176178 6.1644E+04 2.6638E+06 4.3161E-03 0.7516 +384 4 3D - 7 3F 3-4 4626.696194 cm-1 191444.480929 196071.177123 7.3817E+05 2.6646E+06 6.6451E-02 1.0000 +384 4 3D - 7 3F 2-2 4626.696599 cm-1 191444.482131 196071.178730 1.1481E+05 2.6646E+06 8.0386E-03 0.9999 +384 4 3D - 7 3F 3-2 4626.697801 cm-1 191444.480929 196071.178730 3.2808E+03 2.6646E+06 1.6408E-04 1.0000 +385 4 3D - 8 3P Mean 5122.228493 cm-1 191444.485274 196566.713767 5.7358E+04 1.3990E+06 1.9659E-03 0.9999 +385 4 3D - 8 3P 1-2 5122.211171 cm-1 191444.500651 196566.711822 5.7360E+02 1.3990E+06 5.4611E-05 1.0000 +385 4 3D - 8 3P 1-1 5122.212246 cm-1 191444.500651 196566.712897 1.4340E+04 1.3990E+06 8.1916E-04 1.0000 +385 4 3D - 8 3P 1-0 5122.225453 cm-1 191444.500651 196566.726105 5.7360E+04 1.3990E+06 1.0922E-03 1.0000 +385 4 3D - 8 3P 2-2 5122.229691 cm-1 191444.482131 196566.711822 8.6030E+03 1.3990E+06 4.9144E-04 0.9998 +385 4 3D - 8 3P 2-1 5122.230766 cm-1 191444.482131 196566.712897 4.3015E+04 1.3990E+06 1.4743E-03 0.9999 +385 4 3D - 8 3P 3-2 5122.230893 cm-1 191444.480929 196566.711822 4.8183E+04 1.3990E+06 1.9660E-03 1.0000 +386 4 3D - 8 3F Mean 5151.594146 cm-1 191444.485274 196596.079420 4.2901E+05 1.7997E+06 3.3920E-02 0.9244 +386 4 3D - 8 3F 1-2 5151.579791 cm-1 191444.500651 196596.080442 3.8984E+05 1.7998E+06 3.6694E-02 1.0000 +386 4 3D - 8 3F 2-3 5151.596629 cm-1 191444.482131 196596.078760 3.1946E+05 1.7993E+06 2.5258E-02 0.7744 +386 4 3D - 8 3F 3-3 5151.597831 cm-1 191444.480929 196596.078760 3.9407E+04 1.7993E+06 2.2255E-03 0.7642 +386 4 3D - 8 3F 2-2 5151.598311 cm-1 191444.482131 196596.080442 7.2183E+04 1.7998E+06 4.0766E-03 0.9999 +386 4 3D - 8 3F 3-4 5151.598437 cm-1 191444.480929 196596.079366 4.6409E+05 1.7999E+06 3.3698E-02 1.0000 +386 4 3D - 8 3F 3-2 5151.599513 cm-1 191444.480929 196596.080442 2.0626E+03 1.7998E+06 8.3204E-05 1.0000 +387 4 3D - 9 3P Mean 5490.847505 cm-1 191444.485274 196935.332779 3.8633E+04 1.0146E+06 1.1523E-03 1.0000 +387 4 3D - 9 3P 1-2 5490.830767 cm-1 191444.500651 196935.331418 3.8634E+02 1.0146E+06 3.2009E-05 1.0000 +387 4 3D - 9 3P 1-1 5490.831519 cm-1 191444.500651 196935.332170 9.6585E+03 1.0146E+06 4.8014E-04 1.0000 +387 4 3D - 9 3P 1-0 5490.840757 cm-1 191444.500651 196935.341408 3.8634E+04 1.0146E+06 6.4019E-04 1.0000 +387 4 3D - 9 3P 2-2 5490.849287 cm-1 191444.482131 196935.331418 5.7943E+03 1.0146E+06 2.8805E-04 0.9997 +387 4 3D - 9 3P 2-1 5490.850039 cm-1 191444.482131 196935.332170 2.8972E+04 1.0146E+06 8.6415E-04 0.9999 +387 4 3D - 9 3P 3-2 5490.850489 cm-1 191444.480929 196935.331418 3.2453E+04 1.0146E+06 1.1524E-03 1.0000 +388 4 3D - 9 3F Mean 5511.460197 cm-1 191444.485274 196955.945471 2.8944E+05 1.2727E+06 1.9994E-02 0.9272 +388 4 3D - 9 3F 1-2 5511.445534 cm-1 191444.500651 196955.946185 2.6221E+05 1.2728E+06 2.1563E-02 1.0000 +388 4 3D - 9 3F 2-3 5511.462886 cm-1 191444.482131 196955.945017 2.1720E+05 1.2724E+06 1.5004E-02 0.7828 +388 4 3D - 9 3F 2-2 5511.464054 cm-1 191444.482131 196955.946185 4.8552E+04 1.2728E+06 2.3956E-03 0.9999 +388 4 3D - 9 3F 3-3 5511.464087 cm-1 191444.480929 196955.945017 2.6801E+04 1.2724E+06 1.3224E-03 0.7727 +388 4 3D - 9 3F 3-4 5511.464500 cm-1 191444.480929 196955.945429 3.1216E+05 1.2728E+06 1.9803E-02 1.0000 +388 4 3D - 9 3F 3-2 5511.465256 cm-1 191444.480929 196955.946185 1.3874E+03 1.2728E+06 4.8897E-05 1.0000 +389 4 3D -10 3P Mean 5753.848437 cm-1 191444.485274 197198.333711 2.7341E+04 7.5715E+05 7.4267E-04 0.9999 +389 4 3D -10 3P 1-2 5753.832071 cm-1 191444.500651 197198.332722 2.7342E+02 7.5715E+05 2.0630E-05 1.0000 +389 4 3D -10 3P 1-1 5753.832617 cm-1 191444.500651 197198.333268 6.8356E+03 7.5715E+05 3.0946E-04 1.0000 +389 4 3D -10 3P 1-0 5753.839330 cm-1 191444.500651 197198.339982 2.7342E+04 7.5716E+05 4.1260E-04 1.0000 +389 4 3D -10 3P 2-2 5753.850592 cm-1 191444.482131 197198.332722 4.1008E+03 7.5715E+05 1.8565E-04 0.9995 +389 4 3D -10 3P 2-1 5753.851138 cm-1 191444.482131 197198.333268 2.0504E+04 7.5715E+05 5.5694E-04 0.9999 +389 4 3D -10 3P 3-2 5753.851793 cm-1 191444.480929 197198.332722 2.2968E+04 7.5715E+05 7.4271E-04 1.0000 +390 4 3D -10 3F Mean 5768.867052 cm-1 191444.485274 197213.352326 2.0506E+05 9.3313E+05 1.2929E-02 0.9292 +390 4 3D -10 3F 1-2 5768.852192 cm-1 191444.500651 197213.352843 1.8538E+05 9.3321E+05 1.3915E-02 1.0000 +390 4 3D -10 3F 2-3 5768.869868 cm-1 191444.482131 197213.351998 1.5470E+05 9.3293E+05 9.7539E-03 0.7886 +390 4 3D -10 3F 2-2 5768.870713 cm-1 191444.482131 197213.352843 3.4325E+04 9.3321E+05 1.5459E-03 0.9999 +390 4 3D -10 3F 3-3 5768.871069 cm-1 191444.480929 197213.351998 1.9094E+04 9.3293E+05 8.5992E-04 0.7787 +390 4 3D -10 3F 3-4 5768.871363 cm-1 191444.480929 197213.352292 2.2069E+05 9.3323E+05 1.2779E-02 1.0000 +390 4 3D -10 3F 3-2 5768.871914 cm-1 191444.480929 197213.352843 9.8084E+02 9.3321E+05 3.1552E-05 1.0000 +391 4 3F - 5 3D Mean 2465.272760 cm-1 191451.880761 193917.153521 4.5778E+04 1.6412E+07 8.0637E-03 0.8814 +391 4 3F - 5 3D 2-3 2465.261580 cm-1 191451.889707 193917.151287 1.1777E+02 1.6412E+07 4.0660E-05 1.0000 +391 4 3F - 5 3D 2-2 2465.262222 cm-1 191451.889707 193917.151929 5.7703E+03 1.6411E+07 1.4230E-03 0.9999 +391 4 3F - 5 3D 4-3 2465.270199 cm-1 191451.881089 193917.151287 4.7698E+04 1.6412E+07 9.1488E-03 1.0000 +391 4 3F - 5 3D 2-1 2465.271680 cm-1 191451.889707 193917.161387 5.1938E+04 1.6412E+07 7.6850E-03 1.0000 +391 4 3F - 5 3D 3-3 2465.277339 cm-1 191451.873949 193917.151287 2.6178E+03 1.6412E+07 6.4557E-04 0.6351 +391 4 3F - 5 3D 3-2 2465.277980 cm-1 191451.873949 193917.151929 2.9793E+04 1.6411E+07 5.2480E-03 0.6453 +392 4 3F - 5 3G Mean 2469.736688 cm-1 191451.880761 193921.617449 4.2016E+06 4.2584E+06 1.3274E+00 0.9867 +392 4 3F - 5 3G 2-3 2469.730531 cm-1 191451.889707 193921.620238 3.9107E+06 4.2584E+06 1.3453E+00 1.0000 +392 4 3F - 5 3G 4-4 2469.733860 cm-1 191451.881089 193921.614949 1.3816E+05 4.2584E+06 3.3949E-02 0.5191 +392 4 3F - 5 3G 4-5 2469.736631 cm-1 191451.881089 193921.617719 4.2584E+06 4.2584E+06 1.2789E+00 1.0000 +392 4 3F - 5 3G 4-3 2469.739150 cm-1 191451.881089 193921.620238 5.4316E+03 4.2584E+06 1.0381E-03 1.0000 +392 4 3F - 5 3G 3-4 2469.741000 cm-1 191451.873949 193921.614949 4.0469E+06 4.2584E+06 1.2785E+00 1.0137 +392 4 3F - 5 3G 3-3 2469.746289 cm-1 191451.873949 193921.620238 2.1731E+05 4.2584E+06 5.3397E-02 0.6351 +393 4 3F - 6 3D Mean 3808.191893 cm-1 191451.880761 195260.072653 1.9466E+04 9.6698E+06 1.4370E-03 0.8812 +393 4 3F - 6 3D 2-3 3808.181651 cm-1 191451.889707 195260.071358 5.0091E+01 9.6698E+06 7.2475E-06 1.0000 +393 4 3F - 6 3D 2-2 3808.182030 cm-1 191451.889707 195260.071736 2.4542E+03 9.6697E+06 2.5364E-04 0.9996 +393 4 3F - 6 3D 2-1 3808.187496 cm-1 191451.889707 195260.077203 2.2090E+04 9.6698E+06 1.3698E-03 1.0000 +393 4 3F - 6 3D 4-3 3808.190269 cm-1 191451.881089 195260.071358 2.0287E+04 9.6698E+06 1.6307E-03 1.0000 +393 4 3F - 6 3D 3-3 3808.197409 cm-1 191451.873949 195260.071358 1.1134E+03 9.6698E+06 1.1507E-04 0.6352 +393 4 3F - 6 3D 3-2 3808.197788 cm-1 191451.873949 195260.071736 1.2660E+04 9.6697E+06 9.3456E-04 0.6447 +394 4 3F - 6 3G Mean 3810.843768 cm-1 191451.880761 195262.724528 1.3565E+06 2.4812E+06 1.8000E-01 0.9867 +394 4 3F - 6 3G 2-3 3810.836435 cm-1 191451.889707 195262.726142 1.2626E+06 2.4812E+06 1.8243E-01 1.0000 +394 4 3F - 6 3G 4-4 3810.841994 cm-1 191451.881089 195262.723082 4.4636E+04 2.4812E+06 4.6066E-03 0.5195 +394 4 3F - 6 3G 4-5 3810.843596 cm-1 191451.881089 195262.724684 1.3748E+06 2.4812E+06 1.7342E-01 1.0000 +394 4 3F - 6 3G 4-3 3810.845053 cm-1 191451.881089 195262.726142 1.7536E+03 2.4812E+06 1.4076E-04 1.0000 +394 4 3F - 6 3G 3-4 3810.849134 cm-1 191451.873949 195262.723082 1.3066E+06 2.4812E+06 1.7337E-01 1.0138 +394 4 3F - 6 3G 3-3 3810.852193 cm-1 191451.873949 195262.726142 7.0158E+04 2.4812E+06 7.2406E-03 0.6351 +395 4 3F - 7 3D Mean 4617.792865 cm-1 191451.880761 196069.673625 1.0208E+04 6.1663E+06 5.1250E-04 0.8812 +395 4 3F - 7 3D 2-3 4617.783102 cm-1 191451.889707 196069.672809 2.6271E+01 6.1664E+06 2.5851E-06 1.0000 +395 4 3F - 7 3D 2-2 4617.783343 cm-1 191451.889707 196069.673050 1.2872E+03 6.1661E+06 9.0473E-05 1.0000 +395 4 3F - 7 3D 2-1 4617.786783 cm-1 191451.889707 196069.676490 1.1585E+04 6.1664E+06 4.8856E-04 1.0000 +395 4 3F - 7 3D 4-3 4617.791720 cm-1 191451.881089 196069.672809 1.0640E+04 6.1664E+06 5.8166E-04 1.0000 +395 4 3F - 7 3D 3-3 4617.798860 cm-1 191451.873949 196069.672809 5.8392E+02 6.1664E+06 4.1042E-05 0.6347 +395 4 3F - 7 3D 3-2 4617.799101 cm-1 191451.873949 196069.673050 6.6361E+03 6.1661E+06 3.3316E-04 0.6444 +396 4 3F - 7 3G Mean 4619.488887 cm-1 191451.880761 196071.369648 6.3833E+05 1.5756E+06 5.7642E-02 0.9867 +396 4 3F - 7 3G 2-3 4619.480957 cm-1 191451.889707 196071.370664 5.9411E+05 1.5756E+06 5.8418E-02 1.0000 +396 4 3F - 7 3G 4-4 4619.487650 cm-1 191451.881089 196071.368738 2.1016E+04 1.5756E+06 1.4761E-03 0.5198 +396 4 3F - 7 3G 4-5 4619.488658 cm-1 191451.881089 196071.369746 6.4692E+05 1.5756E+06 5.5533E-02 1.0000 +396 4 3F - 7 3G 4-3 4619.489575 cm-1 191451.881089 196071.370664 8.2516E+02 1.5756E+06 4.5076E-05 1.0000 +396 4 3F - 7 3G 3-4 4619.494789 cm-1 191451.873949 196071.368738 6.1488E+05 1.5756E+06 5.5525E-02 1.0138 +396 4 3F - 7 3G 3-3 4619.496715 cm-1 191451.873949 196071.370664 3.3014E+04 1.5756E+06 2.3187E-03 0.6351 +397 4 3F - 8 3G Mean 5144.329505 cm-1 191451.880761 196596.210266 3.6010E+05 1.0641E+06 2.6221E-02 0.9867 +397 4 3F - 8 3G 2-3 5144.321239 cm-1 191451.889707 196596.210946 3.3515E+05 1.0641E+06 2.6574E-02 1.0000 +397 4 3F - 8 3G 4-4 5144.328568 cm-1 191451.881089 196596.209656 1.1860E+04 1.0641E+06 6.7169E-04 0.5200 +397 4 3F - 8 3G 4-5 5144.329243 cm-1 191451.881089 196596.210331 3.6494E+05 1.0641E+06 2.5261E-02 1.0000 +397 4 3F - 8 3G 4-3 5144.329858 cm-1 191451.881089 196596.210946 4.6549E+02 1.0641E+06 2.0504E-05 1.0000 +397 4 3F - 8 3G 3-4 5144.335708 cm-1 191451.873949 196596.209656 3.4688E+05 1.0641E+06 2.5258E-02 1.0139 +397 4 3F - 8 3G 3-3 5144.336997 cm-1 191451.873949 196596.210946 1.8624E+04 1.0641E+06 1.0548E-03 0.6350 +398 4 3F - 9 3G Mean 5504.157530 cm-1 191451.880761 196956.038291 2.2627E+05 7.5280E+05 1.4392E-02 0.9868 +398 4 3F - 9 3G 2-3 5504.149062 cm-1 191451.889707 196956.038769 2.1059E+05 7.5280E+05 1.4586E-02 1.0000 +398 4 3F - 9 3G 4-4 5504.156775 cm-1 191451.881089 196956.037863 7.4545E+03 7.5280E+05 3.6879E-04 0.5202 +398 4 3F - 9 3G 4-5 5504.157249 cm-1 191451.881089 196956.038337 2.2931E+05 7.5280E+05 1.3865E-02 1.0000 +398 4 3F - 9 3G 4-3 5504.157680 cm-1 191451.881089 196956.038769 2.9248E+02 7.5280E+05 1.1254E-05 1.0000 +398 4 3F - 9 3G 3-4 5504.163914 cm-1 191451.873949 196956.037863 2.1797E+05 7.5280E+05 1.3864E-02 1.0139 +398 4 3F - 9 3G 3-3 5504.164820 cm-1 191451.873949 196956.038769 1.1702E+04 7.5280E+05 5.7892E-04 0.6350 +399 4 3F -10 3G Mean 5761.539712 cm-1 191451.880761 197213.420472 1.5277E+05 5.5231E+05 8.8684E-03 0.9868 +399 4 3F -10 3G 2-3 5761.531114 cm-1 191451.889707 197213.420821 1.4218E+05 5.5231E+05 8.9873E-03 1.0000 +399 4 3F -10 3G 4-4 5761.539072 cm-1 191451.881089 197213.420161 5.0342E+03 5.5231E+05 2.2730E-04 0.5203 +399 4 3F -10 3G 4-5 5761.539417 cm-1 191451.881089 197213.420506 1.5482E+05 5.5231E+05 8.5436E-03 1.0000 +399 4 3F -10 3G 4-3 5761.539732 cm-1 191451.881089 197213.420821 1.9748E+02 5.5231E+05 6.9349E-06 1.0000 +399 4 3F -10 3G 3-4 5761.546212 cm-1 191451.873949 197213.420161 1.4717E+05 5.5231E+05 8.5433E-03 1.0139 +399 4 3F -10 3G 3-3 5761.546872 cm-1 191451.873949 197213.420821 7.9008E+03 5.5231E+05 3.5673E-04 0.6350 +400 5 3S - 5 3P Mean 453.724421 cm-1 193346.991344 193800.715766 7.0086E+04 4.5601E+06 1.5306E+00 1.0000 +400 5 3S - 5 3P 1-2 453.716251 cm-1 193346.991344 193800.707595 7.0086E+04 4.5601E+06 8.5036E-01 1.0000 +400 5 3S - 5 3P 1-1 453.720774 cm-1 193346.991344 193800.712118 7.0086E+04 4.5601E+06 5.1021E-01 1.0000 +400 5 3S - 5 3P 1-0 453.776219 cm-1 193346.991344 193800.767563 7.0086E+04 4.5601E+06 1.7007E-01 1.0000 +401 5 3S - 6 3P Mean 1845.756303 cm-1 193346.991344 195192.747648 3.1456E+04 2.9557E+06 4.1517E-02 1.0000 +401 5 3S - 6 3P 1-2 1845.751630 cm-1 193346.991344 195192.742974 3.1456E+04 2.9557E+06 2.3065E-02 1.0000 +401 5 3S - 6 3P 1-1 1845.754215 cm-1 193346.991344 195192.745559 3.1456E+04 2.9557E+06 1.3839E-02 1.0000 +401 5 3S - 6 3P 1-0 1845.785937 cm-1 193346.991344 195192.777281 3.1456E+04 2.9557E+06 4.6130E-03 1.0000 +402 5 3S - 7 3P Mean 2680.326603 cm-1 193346.991344 196027.317947 3.3712E+04 1.9947E+06 2.1100E-02 1.0000 +402 5 3S - 7 3P 1-2 2680.323682 cm-1 193346.991344 196027.315027 3.3712E+04 1.9947E+06 1.1722E-02 1.0000 +402 5 3S - 7 3P 1-1 2680.325297 cm-1 193346.991344 196027.316641 3.3712E+04 1.9947E+06 7.0334E-03 1.0000 +402 5 3S - 7 3P 1-0 2680.345121 cm-1 193346.991344 196027.336465 3.3712E+04 1.9947E+06 2.3445E-03 1.0000 +403 5 3S - 8 3P Mean 3219.722423 cm-1 193346.991344 196566.713767 2.7073E+04 1.3990E+06 1.1743E-02 1.0000 +403 5 3S - 8 3P 1-2 3219.720478 cm-1 193346.991344 196566.711822 2.7073E+04 1.3990E+06 6.5239E-03 1.0000 +403 5 3S - 8 3P 1-1 3219.721553 cm-1 193346.991344 196566.712897 2.7073E+04 1.3990E+06 3.9143E-03 1.0000 +403 5 3S - 8 3P 1-0 3219.734760 cm-1 193346.991344 196566.726105 2.7073E+04 1.3990E+06 1.3048E-03 1.0000 +404 5 3S - 9 3P Mean 3588.341435 cm-1 193346.991344 196935.332779 2.0818E+04 1.0146E+06 7.2699E-03 1.0000 +404 5 3S - 9 3P 1-2 3588.340074 cm-1 193346.991344 196935.331418 2.0818E+04 1.0146E+06 4.0388E-03 1.0000 +404 5 3S - 9 3P 1-1 3588.340826 cm-1 193346.991344 196935.332170 2.0818E+04 1.0146E+06 2.4233E-03 1.0000 +404 5 3S - 9 3P 1-0 3588.350064 cm-1 193346.991344 196935.341408 2.0818E+04 1.0146E+06 8.0777E-04 1.0000 +405 5 3S -10 3P Mean 3851.342367 cm-1 193346.991344 197198.333711 1.6011E+04 7.5715E+05 4.8537E-03 1.0000 +405 5 3S -10 3P 1-2 3851.341378 cm-1 193346.991344 197198.332722 1.6011E+04 7.5715E+05 2.6965E-03 1.0000 +405 5 3S -10 3P 1-1 3851.341924 cm-1 193346.991344 197198.333268 1.6011E+04 7.5715E+05 1.6179E-03 1.0000 +405 5 3S -10 3P 1-0 3851.348637 cm-1 193346.991344 197198.339982 1.6011E+04 7.5716E+05 5.3930E-04 1.0000 +406 5 3P - 5 3D Mean 116.437755 cm-1 193800.715766 193917.153521 1.5174E+03 1.6412E+07 2.8005E-01 1.0000 +406 5 3P - 5 3D 0-1 116.393824 cm-1 193800.767563 193917.161387 8.4304E+02 1.6412E+07 2.8006E-01 1.0000 +406 5 3P - 5 3D 1-2 116.439811 cm-1 193800.712118 193917.151929 1.1380E+03 1.6411E+07 2.1002E-01 0.9999 +406 5 3P - 5 3D 2-3 116.443693 cm-1 193800.707595 193917.151287 1.5175E+03 1.6412E+07 2.3525E-01 1.0000 +406 5 3P - 5 3D 2-2 116.444334 cm-1 193800.707595 193917.151929 3.7933E+02 1.6411E+07 4.2004E-02 0.9999 +406 5 3P - 5 3D 1-1 116.449269 cm-1 193800.712118 193917.161387 6.3228E+02 1.6412E+07 7.0014E-02 1.0000 +406 5 3P - 5 3D 2-1 116.453792 cm-1 193800.707595 193917.161387 4.2152E+01 1.6412E+07 2.8006E-03 1.0000 +407 5 3P - 6 3S Mean 1135.403931 cm-1 193800.715766 194936.119697 7.7681E+05 5.6296E+06 3.0108E-01 1.0000 +407 5 3P - 6 3S 0-1 1135.352134 cm-1 193800.767563 194936.119697 8.6312E+04 5.6296E+06 3.0107E-01 1.0000 +407 5 3P - 6 3S 1-1 1135.407579 cm-1 193800.712118 194936.119697 2.5894E+05 5.6296E+06 3.0108E-01 1.0000 +407 5 3P - 6 3S 2-1 1135.412102 cm-1 193800.707595 194936.119697 4.3156E+05 5.6296E+06 3.0107E-01 1.0000 +408 5 3P - 6 3D Mean 1459.356887 cm-1 193800.715766 195260.072653 3.6607E+05 9.6698E+06 4.2943E-01 1.0000 +408 5 3P - 6 3D 0-1 1459.309640 cm-1 193800.767563 195260.077203 2.0338E+05 9.6698E+06 4.2944E-01 1.0000 +408 5 3P - 6 3D 1-2 1459.359619 cm-1 193800.712118 195260.071736 2.7454E+05 9.6697E+06 3.2205E-01 0.9999 +408 5 3P - 6 3D 2-3 1459.363763 cm-1 193800.707595 195260.071358 3.6608E+05 9.6698E+06 3.6073E-01 1.0000 +408 5 3P - 6 3D 2-2 1459.364142 cm-1 193800.707595 195260.071736 9.1512E+04 9.6697E+06 6.4410E-02 0.9999 +408 5 3P - 6 3D 1-1 1459.365085 cm-1 193800.712118 195260.077203 1.5253E+05 9.6698E+06 1.0736E-01 1.0000 +408 5 3P - 6 3D 2-1 1459.369608 cm-1 193800.707595 195260.077203 1.0169E+04 9.6698E+06 4.2944E-03 1.0000 +409 5 3P - 7 3S Mean 2067.521210 cm-1 193800.715766 195868.236975 3.9977E+05 3.6533E+06 4.6726E-02 1.0000 +409 5 3P - 7 3S 0-1 2067.469412 cm-1 193800.767563 195868.236975 4.4419E+04 3.6533E+06 4.6726E-02 1.0000 +409 5 3P - 7 3S 1-1 2067.524857 cm-1 193800.712118 195868.236975 1.3326E+05 3.6533E+06 4.6727E-02 1.0000 +409 5 3P - 7 3S 2-1 2067.529381 cm-1 193800.707595 195868.236975 2.2209E+05 3.6533E+06 4.6725E-02 1.0000 +410 5 3P - 7 3D Mean 2268.957860 cm-1 193800.715766 196069.673625 2.5808E+05 6.1663E+06 1.2524E-01 1.0000 +410 5 3P - 7 3D 0-1 2268.908927 cm-1 193800.767563 196069.676490 1.4338E+05 6.1664E+06 1.2524E-01 1.0000 +410 5 3P - 7 3D 1-2 2268.960932 cm-1 193800.712118 196069.673050 1.9355E+05 6.1661E+06 9.3922E-02 0.9999 +410 5 3P - 7 3D 1-1 2268.964372 cm-1 193800.712118 196069.676490 1.0754E+05 6.1664E+06 3.1311E-02 1.0000 +410 5 3P - 7 3D 2-3 2268.965214 cm-1 193800.707595 196069.672809 2.5809E+05 6.1664E+06 1.0520E-01 1.0000 +410 5 3P - 7 3D 2-2 2268.965455 cm-1 193800.707595 196069.673050 6.4516E+04 6.1661E+06 1.8784E-02 0.9999 +410 5 3P - 7 3D 2-1 2268.968895 cm-1 193800.707595 196069.676490 7.1691E+03 6.1664E+06 1.2524E-03 1.0000 +411 5 3P - 8 3S Mean 2660.646045 cm-1 193800.715766 196461.361811 2.4421E+05 2.4913E+06 1.7236E-02 1.0000 +411 5 3P - 8 3S 0-1 2660.594248 cm-1 193800.767563 196461.361811 2.7135E+04 2.4913E+06 1.7236E-02 1.0000 +411 5 3P - 8 3S 1-1 2660.649693 cm-1 193800.712118 196461.361811 8.1405E+04 2.4913E+06 1.7236E-02 1.0000 +411 5 3P - 8 3S 2-1 2660.654216 cm-1 193800.707595 196461.361811 1.3567E+05 2.4913E+06 1.7236E-02 1.0000 +412 5 3P - 8 3D Mean 2794.346984 cm-1 193800.715766 196595.062750 1.7834E+05 4.1689E+06 5.7058E-02 1.0000 +412 5 3P - 8 3D 0-1 2794.297105 cm-1 193800.767563 196595.064668 9.9081E+04 4.1690E+06 5.7059E-02 1.0000 +412 5 3P - 8 3D 1-2 2794.350247 cm-1 193800.712118 196595.062365 1.3375E+05 4.1688E+06 4.2791E-02 0.9999 +412 5 3P - 8 3D 1-1 2794.352550 cm-1 193800.712118 196595.064668 7.4311E+04 4.1690E+06 1.4265E-02 1.0000 +412 5 3P - 8 3D 2-3 2794.354608 cm-1 193800.707595 196595.062202 1.7835E+05 4.1690E+06 4.7930E-02 1.0000 +412 5 3P - 8 3D 2-2 2794.354770 cm-1 193800.707595 196595.062365 4.4583E+04 4.1688E+06 8.5581E-03 0.9999 +412 5 3P - 8 3D 2-1 2794.357073 cm-1 193800.707595 196595.064668 4.9541E+03 4.1690E+06 5.7059E-04 1.0000 +413 5 3P - 9 3S Mean 3061.271574 cm-1 193800.715766 196861.987340 1.6219E+05 1.7692E+06 8.6471E-03 1.0000 +413 5 3P - 9 3S 0-1 3061.219777 cm-1 193800.767563 196861.987340 1.8021E+04 1.7692E+06 8.6469E-03 1.0000 +413 5 3P - 9 3S 1-1 3061.275222 cm-1 193800.712118 196861.987340 5.4064E+04 1.7692E+06 8.6471E-03 1.0000 +413 5 3P - 9 3S 2-1 3061.279745 cm-1 193800.707595 196861.987340 9.0107E+04 1.7692E+06 8.6471E-03 1.0000 +414 5 3P - 9 3D Mean 3154.511146 cm-1 193800.715766 196955.226911 1.2681E+05 2.9483E+06 3.1834E-02 1.0000 +414 5 3P - 9 3D 0-1 3154.460695 cm-1 193800.767563 196955.228258 7.0449E+04 2.9484E+06 3.1835E-02 1.0000 +414 5 3P - 9 3D 1-2 3154.514523 cm-1 193800.712118 196955.226641 9.5099E+04 2.9482E+06 2.3874E-02 0.9999 +414 5 3P - 9 3D 1-1 3154.516140 cm-1 193800.712118 196955.228258 5.2836E+04 2.9484E+06 7.9585E-03 1.0000 +414 5 3P - 9 3D 2-3 3154.518932 cm-1 193800.707595 196955.226527 1.2681E+05 2.9483E+06 2.6741E-02 1.0000 +414 5 3P - 9 3D 2-2 3154.519047 cm-1 193800.707595 196955.226641 3.1699E+04 2.9482E+06 4.7747E-03 0.9999 +414 5 3P - 9 3D 2-1 3154.520664 cm-1 193800.707595 196955.228258 3.5224E+03 2.9484E+06 3.1834E-04 1.0000 +415 5 3P -10 3S Mean 3344.517492 cm-1 193800.715766 197145.233258 1.1384E+05 1.2990E+06 5.0849E-03 1.0000 +415 5 3P -10 3S 0-1 3344.465695 cm-1 193800.767563 197145.233258 1.2649E+04 1.2990E+06 5.0848E-03 1.0000 +415 5 3P -10 3S 1-1 3344.521140 cm-1 193800.712118 197145.233258 3.7948E+04 1.2990E+06 5.0849E-03 1.0000 +415 5 3P -10 3S 2-1 3344.525663 cm-1 193800.707595 197145.233258 6.3246E+04 1.2990E+06 5.0849E-03 1.0000 +416 5 3P -10 3D Mean 3412.110376 cm-1 193800.715766 197212.826141 9.2978E+04 2.1609E+06 1.9950E-02 1.0000 +416 5 3P -10 3D 0-1 3412.059560 cm-1 193800.767563 197212.827123 5.1656E+04 2.1609E+06 1.9951E-02 1.0000 +416 5 3P -10 3D 1-2 3412.113827 cm-1 193800.712118 197212.825945 6.9730E+04 2.1608E+06 1.4962E-02 0.9999 +416 5 3P -10 3D 1-1 3412.115005 cm-1 193800.712118 197212.827123 3.8742E+04 2.1609E+06 4.9877E-03 1.0000 +416 5 3P -10 3D 2-3 3412.118266 cm-1 193800.707595 197212.825861 9.2980E+04 2.1609E+06 1.6759E-02 1.0000 +416 5 3P -10 3D 2-2 3412.118350 cm-1 193800.707595 197212.825945 2.3243E+04 2.1608E+06 2.9923E-03 0.9999 +416 5 3P -10 3D 2-1 3412.119529 cm-1 193800.707595 197212.827123 2.5828E+03 2.1609E+06 1.9951E-04 1.0000 +417 5 3D - 5 3F Mean 3.967846 cm-1 193917.153521 193921.121367 4.4017E-02 7.1597E+06 5.8743E-03 0.9021 +417 5 3D - 5 3F 1-2 3.964366 cm-1 193917.161387 193921.125753 4.0992E-02 7.1603E+06 6.5121E-03 1.0000 +417 5 3D - 5 3F 2-3 3.966336 cm-1 193917.151929 193921.118264 3.0685E-02 7.1585E+06 4.0947E-03 0.7074 +417 5 3D - 5 3F 3-3 3.966977 cm-1 193917.151287 193921.118264 3.7824E-03 7.1585E+06 3.6053E-04 0.6976 +417 5 3D - 5 3F 3-4 3.970055 cm-1 193917.151287 193921.121343 4.8800E-02 7.1603E+06 5.9805E-03 1.0000 +417 5 3D - 5 3F 2-2 3.973825 cm-1 193917.151929 193921.125753 7.5903E-03 7.1603E+06 7.2349E-04 0.9999 +417 5 3D - 5 3F 3-2 3.974466 cm-1 193917.151287 193921.125753 2.1689E-04 7.1603E+06 1.4767E-05 1.0000 +418 5 3D - 6 3P Mean 1275.594127 cm-1 193917.153521 195192.747648 1.5958E+05 2.9557E+06 8.8188E-02 1.0000 +418 5 3D - 6 3P 1-2 1275.581587 cm-1 193917.161387 195192.742974 1.5959E+03 2.9557E+06 2.4498E-03 1.0000 +418 5 3D - 6 3P 1-1 1275.584172 cm-1 193917.161387 195192.745559 3.9897E+04 2.9557E+06 3.6747E-02 1.0000 +418 5 3D - 6 3P 2-2 1275.591046 cm-1 193917.151929 195192.742974 2.3936E+04 2.9557E+06 2.2046E-02 0.9999 +418 5 3D - 6 3P 3-2 1275.591687 cm-1 193917.151287 195192.742974 1.3405E+05 2.9557E+06 8.8190E-02 1.0000 +418 5 3D - 6 3P 2-1 1275.593630 cm-1 193917.151929 195192.745559 1.1968E+05 2.9557E+06 6.6138E-02 0.9999 +418 5 3D - 6 3P 1-0 1275.615894 cm-1 193917.161387 195192.777281 1.5959E+05 2.9557E+06 4.8996E-02 1.0000 +419 5 3D - 6 3F Mean 1345.272373 cm-1 193917.153521 195262.425894 6.5936E+05 4.1897E+06 7.6449E-01 0.9133 +419 5 3D - 6 3F 1-2 1345.266986 cm-1 193917.161387 195262.428373 6.0641E+05 4.1901E+06 8.3702E-01 1.0000 +419 5 3D - 6 3F 2-3 1345.272288 cm-1 193917.151929 195262.424217 4.7555E+05 4.1889E+06 5.5137E-01 0.7411 +419 5 3D - 6 3F 3-3 1345.272929 cm-1 193917.151287 195262.424217 5.8684E+04 4.1889E+06 4.8601E-02 0.7316 +419 5 3D - 6 3F 3-4 1345.274534 cm-1 193917.151287 195262.425821 7.2192E+05 4.1901E+06 7.6870E-01 1.0000 +419 5 3D - 6 3F 2-2 1345.276444 cm-1 193917.151929 195262.428373 1.1229E+05 4.1901E+06 9.2996E-02 0.9999 +419 5 3D - 6 3F 3-2 1345.277086 cm-1 193917.151287 195262.428373 3.2085E+03 4.1901E+06 1.8980E-03 1.0000 +420 5 3D - 7 3P Mean 2110.164426 cm-1 193917.153521 196027.317947 8.5944E+04 1.9947E+06 1.7356E-02 1.0000 +420 5 3D - 7 3P 1-2 2110.153640 cm-1 193917.161387 196027.315027 8.5946E+02 1.9947E+06 4.8213E-04 1.0000 +420 5 3D - 7 3P 1-1 2110.155254 cm-1 193917.161387 196027.316641 2.1487E+04 1.9947E+06 7.2322E-03 1.0000 +420 5 3D - 7 3P 2-2 2110.163098 cm-1 193917.151929 196027.315027 1.2891E+04 1.9947E+06 4.3389E-03 0.9999 +420 5 3D - 7 3P 3-2 2110.163739 cm-1 193917.151287 196027.315027 7.2195E+04 1.9947E+06 1.7357E-02 1.0000 +420 5 3D - 7 3P 2-1 2110.164712 cm-1 193917.151929 196027.316641 6.4453E+04 1.9947E+06 1.3016E-02 0.9999 +420 5 3D - 7 3P 1-0 2110.175078 cm-1 193917.161387 196027.336465 8.5946E+04 1.9947E+06 9.6427E-03 1.0000 +421 5 3D - 7 3F Mean 2154.023670 cm-1 193917.153521 196071.177191 3.9911E+05 2.6643E+06 1.8049E-01 0.9199 +421 5 3D - 7 3F 1-2 2154.017343 cm-1 193917.161387 196071.178730 3.6443E+05 2.6646E+06 1.9620E-01 1.0000 +421 5 3D - 7 3F 2-3 2154.024249 cm-1 193917.151929 196071.176178 2.9340E+05 2.6638E+06 1.3269E-01 0.7608 +421 5 3D - 7 3F 3-3 2154.024891 cm-1 193917.151287 196071.176178 3.6230E+04 2.6638E+06 1.1703E-02 0.7516 +421 5 3D - 7 3F 3-4 2154.025836 cm-1 193917.151287 196071.177123 4.3385E+05 2.6646E+06 1.8019E-01 1.0000 +421 5 3D - 7 3F 2-2 2154.026801 cm-1 193917.151929 196071.178730 6.7481E+04 2.6646E+06 2.1798E-02 0.9999 +421 5 3D - 7 3F 3-2 2154.027443 cm-1 193917.151287 196071.178730 1.9282E+03 2.6646E+06 4.4490E-04 1.0000 +422 5 3D - 8 3P Mean 2649.560246 cm-1 193917.153521 196566.713767 5.2292E+04 1.3990E+06 6.6985E-03 1.0000 +422 5 3D - 8 3P 1-2 2649.550435 cm-1 193917.161387 196566.711822 5.2294E+02 1.3990E+06 1.8607E-04 1.0000 +422 5 3D - 8 3P 1-1 2649.551510 cm-1 193917.161387 196566.712897 1.3073E+04 1.3990E+06 2.7910E-03 1.0000 +422 5 3D - 8 3P 2-2 2649.559893 cm-1 193917.151929 196566.711822 7.8433E+03 1.3990E+06 1.6745E-03 0.9999 +422 5 3D - 8 3P 3-2 2649.560535 cm-1 193917.151287 196566.711822 4.3927E+04 1.3990E+06 6.6987E-03 1.0000 +422 5 3D - 8 3P 2-1 2649.560969 cm-1 193917.151929 196566.712897 3.9217E+04 1.3990E+06 5.0236E-03 0.9999 +422 5 3D - 8 3P 1-0 2649.564717 cm-1 193917.161387 196566.726105 5.2294E+04 1.3990E+06 3.7215E-03 1.0000 +423 5 3D - 8 3F Mean 2678.925899 cm-1 193917.153521 196596.079420 2.5528E+05 1.7997E+06 7.4638E-02 0.9241 +423 5 3D - 8 3F 1-2 2678.919055 cm-1 193917.161387 196596.080442 2.3205E+05 1.7998E+06 8.0770E-02 1.0000 +423 5 3D - 8 3F 2-3 2678.926832 cm-1 193917.151929 196596.078760 1.8988E+05 1.7993E+06 5.5517E-02 0.7733 +423 5 3D - 8 3F 3-3 2678.927473 cm-1 193917.151287 196596.078760 2.3458E+04 1.7993E+06 4.8990E-03 0.7642 +423 5 3D - 8 3F 3-4 2678.928079 cm-1 193917.151287 196596.079366 2.7625E+05 1.7999E+06 7.4177E-02 1.0000 +423 5 3D - 8 3F 2-2 2678.928514 cm-1 193917.151929 196596.080442 4.2968E+04 1.7998E+06 8.9736E-03 0.9999 +423 5 3D - 8 3F 3-2 2678.929155 cm-1 193917.151287 196596.080442 1.2278E+03 1.7998E+06 1.8316E-04 1.0000 +424 5 3D - 9 3P Mean 3018.179258 cm-1 193917.153521 196935.332779 3.4487E+04 1.0146E+06 3.4045E-03 1.0000 +424 5 3D - 9 3P 1-2 3018.170031 cm-1 193917.161387 196935.331418 3.4488E+02 1.0146E+06 9.4572E-05 1.0000 +424 5 3D - 9 3P 1-1 3018.170783 cm-1 193917.161387 196935.332170 8.6220E+03 1.0146E+06 1.4186E-03 1.0000 +424 5 3D - 9 3P 2-2 3018.179490 cm-1 193917.151929 196935.331418 5.1727E+03 1.0146E+06 8.5107E-04 1.0000 +424 5 3D - 9 3P 1-0 3018.180021 cm-1 193917.161387 196935.341408 3.4488E+04 1.0146E+06 1.8914E-03 1.0000 +424 5 3D - 9 3P 3-2 3018.180131 cm-1 193917.151287 196935.331418 2.8970E+04 1.0146E+06 3.4046E-03 1.0000 +424 5 3D - 9 3P 2-1 3018.180241 cm-1 193917.151929 196935.332170 2.5863E+04 1.0146E+06 2.5532E-03 0.9999 +425 5 3D - 9 3F Mean 3038.791950 cm-1 193917.153521 196955.945471 1.7309E+05 1.2727E+06 3.9332E-02 0.9269 +425 5 3D - 9 3F 1-2 3038.784798 cm-1 193917.161387 196955.946185 1.5687E+05 1.2728E+06 4.2435E-02 1.0000 +425 5 3D - 9 3F 2-3 3038.793088 cm-1 193917.151929 196955.945017 1.2975E+05 1.2724E+06 2.9483E-02 0.7816 +425 5 3D - 9 3F 3-3 3038.793729 cm-1 193917.151287 196955.945017 1.6033E+04 1.2724E+06 2.6023E-03 0.7727 +425 5 3D - 9 3F 3-4 3038.794142 cm-1 193917.151287 196955.945429 1.8675E+05 1.2728E+06 3.8971E-02 1.0000 +425 5 3D - 9 3F 2-2 3038.794256 cm-1 193917.151929 196955.946185 2.9046E+04 1.2728E+06 4.7144E-03 0.9999 +425 5 3D - 9 3F 3-2 3038.794897 cm-1 193917.151287 196955.946185 8.2998E+02 1.2728E+06 9.6223E-05 1.0000 +426 5 3D -10 3P Mean 3281.180190 cm-1 193917.153521 197198.333711 2.4069E+04 7.5715E+05 2.0105E-03 1.0000 +426 5 3D -10 3P 1-2 3281.171335 cm-1 193917.161387 197198.332722 2.4070E+02 7.5715E+05 5.5847E-05 1.0000 +426 5 3D -10 3P 1-1 3281.171881 cm-1 193917.161387 197198.333268 6.0174E+03 7.5715E+05 8.3770E-04 1.0000 +426 5 3D -10 3P 1-0 3281.178594 cm-1 193917.161387 197198.339982 2.4070E+04 7.5716E+05 1.1169E-03 1.0000 +426 5 3D -10 3P 2-2 3281.180794 cm-1 193917.151929 197198.332722 3.6101E+03 7.5715E+05 5.0257E-04 1.0000 +426 5 3D -10 3P 2-1 3281.181340 cm-1 193917.151929 197198.333268 1.8051E+04 7.5715E+05 1.5078E-03 0.9999 +426 5 3D -10 3P 3-2 3281.181435 cm-1 193917.151287 197198.332722 2.0219E+04 7.5715E+05 2.0105E-03 1.0000 +427 5 3D -10 3F Mean 3296.198805 cm-1 193917.153521 197213.352326 1.2293E+05 9.3313E+05 2.3741E-02 0.9288 +427 5 3D -10 3F 1-2 3296.191456 cm-1 193917.161387 197213.352843 1.1117E+05 9.3321E+05 2.5559E-02 1.0000 +427 5 3D -10 3F 2-3 3296.200070 cm-1 193917.151929 197213.351998 9.2647E+04 9.3293E+05 1.7893E-02 0.7875 +427 5 3D -10 3F 3-3 3296.200711 cm-1 193917.151287 197213.351998 1.1451E+04 9.3293E+05 1.5796E-03 0.7787 +427 5 3D -10 3F 2-2 3296.200915 cm-1 193917.151929 197213.352843 2.0586E+04 9.3321E+05 2.8398E-03 0.9999 +427 5 3D -10 3F 3-4 3296.201005 cm-1 193917.151287 197213.352292 1.3235E+05 9.3323E+05 2.3474E-02 1.0000 +427 5 3D -10 3F 3-2 3296.201556 cm-1 193917.151287 197213.352843 5.8822E+02 9.3321E+05 5.7960E-05 1.0000 +428 5 3F - 6 3D Mean 1338.951286 cm-1 193921.121367 195260.072653 3.6181E+04 9.6698E+06 2.1606E-02 0.9019 +428 5 3F - 6 3D 2-3 1338.945605 cm-1 193921.125753 195260.071358 9.0965E+01 9.6698E+06 1.0647E-04 1.0000 +428 5 3F - 6 3D 2-2 1338.945983 cm-1 193921.125753 195260.071736 4.4569E+03 9.6697E+06 3.7260E-03 0.9999 +428 5 3F - 6 3D 4-3 1338.950015 cm-1 193921.121343 195260.071358 3.6841E+04 9.6698E+06 2.3955E-02 1.0000 +428 5 3F - 6 3D 2-1 1338.951450 cm-1 193921.125753 195260.077203 4.0116E+04 9.6698E+06 2.0122E-02 1.0000 +428 5 3F - 6 3D 3-3 1338.953094 cm-1 193921.118264 195260.071358 2.2209E+03 9.6698E+06 1.8567E-03 0.6976 +428 5 3F - 6 3D 3-2 1338.953472 cm-1 193921.118264 195260.071736 2.5203E+04 9.6697E+06 1.5050E-02 0.7068 +429 5 3F - 6 3G Mean 1341.603161 cm-1 193921.121367 195262.724528 1.0854E+06 2.4812E+06 1.1621E+00 0.9810 +429 5 3F - 6 3G 2-3 1341.600389 cm-1 193921.125753 195262.726142 1.0161E+06 2.4812E+06 1.1846E+00 1.0000 +429 5 3F - 6 3G 4-4 1341.601740 cm-1 193921.121343 195262.723082 3.5923E+04 2.4812E+06 2.9913E-02 0.5195 +429 5 3F - 6 3G 4-5 1341.603341 cm-1 193921.121343 195262.724684 1.1064E+06 2.4812E+06 1.1260E+00 1.0000 +429 5 3F - 6 3G 4-3 1341.604799 cm-1 193921.121343 195262.726142 1.4113E+03 2.4812E+06 9.1405E-04 1.0000 +429 5 3F - 6 3G 3-4 1341.604818 cm-1 193921.118264 195262.723082 1.0284E+06 2.4812E+06 1.1010E+00 0.9914 +429 5 3F - 6 3G 3-3 1341.607877 cm-1 193921.118264 195262.726142 6.2021E+04 2.4812E+06 5.1645E-02 0.6976 +430 5 3F - 7 3D Mean 2148.552259 cm-1 193921.121367 196069.673625 1.7703E+04 6.1663E+06 4.1056E-03 0.9018 +430 5 3F - 7 3D 2-3 2148.547056 cm-1 193921.125753 196069.672809 4.4513E+01 6.1664E+06 2.0233E-05 1.0000 +430 5 3F - 7 3D 2-2 2148.547297 cm-1 193921.125753 196069.673050 2.1810E+03 6.1661E+06 7.0812E-04 0.9999 +430 5 3F - 7 3D 2-1 2148.550737 cm-1 193921.125753 196069.676490 1.9630E+04 6.1664E+06 3.8240E-03 1.0000 +430 5 3F - 7 3D 4-3 2148.551466 cm-1 193921.121343 196069.672809 1.8028E+04 6.1664E+06 4.5525E-03 1.0000 +430 5 3F - 7 3D 3-3 2148.554545 cm-1 193921.118264 196069.672809 1.0868E+03 6.1664E+06 3.5286E-04 0.6977 +430 5 3F - 7 3D 3-2 2148.554786 cm-1 193921.118264 196069.673050 1.2328E+04 6.1661E+06 2.8590E-03 0.7065 +431 5 3F - 7 3G Mean 2150.248281 cm-1 193921.121367 196071.369648 5.3839E+05 1.5756E+06 2.2439E-01 0.9810 +431 5 3F - 7 3G 2-3 2150.244911 cm-1 193921.125753 196071.370664 5.0400E+05 1.5756E+06 2.2873E-01 1.0000 +431 5 3F - 7 3G 4-4 2150.247395 cm-1 193921.121343 196071.368738 1.7828E+04 1.5756E+06 5.7792E-03 0.5198 +431 5 3F - 7 3G 4-5 2150.248403 cm-1 193921.121343 196071.369746 5.4880E+05 1.5756E+06 2.1743E-01 1.0000 +431 5 3F - 7 3G 4-3 2150.249321 cm-1 193921.121343 196071.370664 7.0000E+02 1.5756E+06 1.7649E-04 1.0000 +431 5 3F - 7 3G 3-4 2150.250474 cm-1 193921.118264 196071.368738 5.1013E+05 1.5756E+06 2.1261E-01 0.9915 +431 5 3F - 7 3G 3-3 2150.252400 cm-1 193921.118264 196071.370664 3.0763E+04 1.5756E+06 9.9722E-03 0.6976 +432 5 3F - 8 3D Mean 2673.941383 cm-1 193921.121367 196595.062750 1.0083E+04 4.1689E+06 1.5097E-03 0.9018 +432 5 3F - 8 3D 2-3 2673.936449 cm-1 193921.125753 196595.062202 2.5353E+01 4.1690E+06 7.4404E-06 1.0000 +432 5 3F - 8 3D 2-2 2673.936612 cm-1 193921.125753 196595.062365 1.2422E+03 4.1688E+06 2.6039E-04 1.0000 +432 5 3F - 8 3D 2-1 2673.938915 cm-1 193921.125753 196595.064668 1.1181E+04 4.1690E+06 1.4063E-03 1.0000 +432 5 3F - 8 3D 4-3 2673.940860 cm-1 193921.121343 196595.062202 1.0268E+04 4.1690E+06 1.6741E-03 1.0000 +432 5 3F - 8 3D 3-3 2673.943938 cm-1 193921.118264 196595.062202 6.1901E+02 4.1690E+06 1.2976E-04 0.6978 +432 5 3F - 8 3D 3-2 2673.944101 cm-1 193921.118264 196595.062365 7.0195E+03 4.1688E+06 1.0510E-03 0.7063 +433 5 3F - 8 3G Mean 2675.088899 cm-1 193921.121367 196596.210266 3.0797E+05 1.0641E+06 8.2930E-02 0.9811 +433 5 3F - 8 3G 2-3 2675.085193 cm-1 193921.125753 196596.210946 2.8829E+05 1.0641E+06 8.4532E-02 1.0000 +433 5 3F - 8 3G 4-4 2675.088314 cm-1 193921.121343 196596.209656 1.0202E+04 1.0641E+06 2.1367E-03 0.5200 +433 5 3F - 8 3G 4-5 2675.088989 cm-1 193921.121343 196596.210331 3.1391E+05 1.0641E+06 8.0356E-02 1.0000 +433 5 3F - 8 3G 4-3 2675.089604 cm-1 193921.121343 196596.210946 4.0040E+02 1.0641E+06 6.5225E-05 1.0000 +433 5 3F - 8 3G 3-4 2675.091392 cm-1 193921.118264 196596.209656 2.9181E+05 1.0641E+06 7.8579E-02 0.9916 +433 5 3F - 8 3G 3-3 2675.092682 cm-1 193921.118264 196596.210946 1.7597E+04 1.0641E+06 3.6856E-03 0.6976 +434 5 3F - 9 3D Mean 3034.105545 cm-1 193921.121367 196955.226911 6.3607E+03 2.9483E+06 7.3970E-04 0.9018 +434 5 3F - 9 3D 2-3 3034.100774 cm-1 193921.125753 196955.226527 1.5995E+01 2.9483E+06 3.6458E-06 1.0000 +434 5 3F - 9 3D 2-2 3034.100888 cm-1 193921.125753 196955.226641 7.8370E+02 2.9482E+06 1.2759E-04 1.0000 +434 5 3F - 9 3D 2-1 3034.102505 cm-1 193921.125753 196955.228258 7.0538E+03 2.9484E+06 6.8905E-04 1.0000 +434 5 3F - 9 3D 4-3 3034.105184 cm-1 193921.121343 196955.226527 6.4780E+03 2.9483E+06 8.2031E-04 1.0000 +434 5 3F - 9 3D 3-3 3034.108262 cm-1 193921.118264 196955.226527 3.9052E+02 2.9483E+06 6.3580E-05 0.6981 +434 5 3F - 9 3D 3-2 3034.108377 cm-1 193921.118264 196955.226641 4.4277E+03 2.9482E+06 5.1491E-04 0.7062 +435 5 3F - 9 3G Mean 3034.916924 cm-1 193921.121367 196956.038291 1.9462E+05 7.5280E+05 4.0717E-02 0.9811 +435 5 3F - 9 3G 2-3 3034.913016 cm-1 193921.125753 196956.038769 1.8218E+05 7.5280E+05 4.1503E-02 1.0000 +435 5 3F - 9 3G 4-4 3034.916520 cm-1 193921.121343 196956.037863 6.4489E+03 7.5280E+05 1.0494E-03 0.5201 +435 5 3F - 9 3G 4-5 3034.916994 cm-1 193921.121343 196956.038337 1.9837E+05 7.5280E+05 3.9452E-02 1.0000 +435 5 3F - 9 3G 4-3 3034.917426 cm-1 193921.121343 196956.038769 2.5303E+02 7.5280E+05 3.2024E-05 1.0000 +435 5 3F - 9 3G 3-4 3034.919599 cm-1 193921.118264 196956.037863 1.8442E+05 7.5280E+05 3.8583E-02 0.9916 +435 5 3F - 9 3G 3-3 3034.920505 cm-1 193921.118264 196956.038769 1.1120E+04 7.5280E+05 1.8095E-03 0.6976 +436 5 3F -10 3G Mean 3292.299106 cm-1 193921.121367 197213.420472 1.3179E+05 5.5231E+05 2.3430E-02 0.9811 +436 5 3F -10 3G 2-3 3292.295068 cm-1 193921.125753 197213.420821 1.2336E+05 5.5231E+05 2.3881E-02 1.0000 +436 5 3F -10 3G 4-4 3292.298818 cm-1 193921.121343 197213.420161 4.3678E+03 5.5231E+05 6.0396E-04 0.5203 +436 5 3F -10 3G 4-5 3292.299163 cm-1 193921.121343 197213.420506 1.3433E+05 5.5231E+05 2.2702E-02 1.0000 +436 5 3F -10 3G 4-3 3292.299478 cm-1 193921.121343 197213.420821 1.7134E+02 5.5231E+05 1.8427E-05 1.0000 +436 5 3F -10 3G 3-4 3292.301896 cm-1 193921.118264 197213.420161 1.2488E+05 5.5231E+05 2.2201E-02 0.9917 +436 5 3F -10 3G 3-3 3292.302556 cm-1 193921.118264 197213.420821 7.5297E+03 5.5231E+05 1.0412E-03 0.6976 +437 5 3G - 6 3F Mean 1340.808445 cm-1 193921.617449 195262.425894 1.1155E+04 4.1897E+06 7.2330E-03 0.9765 +437 5 3G - 6 3F 3-3 1340.803979 cm-1 193921.620238 195262.424217 5.2232E+02 4.1889E+06 4.3545E-04 0.7317 +437 5 3G - 6 3F 3-4 1340.805583 cm-1 193921.620238 195262.425821 8.8141E+00 4.1901E+06 9.4477E-06 1.0000 +437 5 3G - 6 3F 5-4 1340.808102 cm-1 193921.617719 195262.425821 1.0859E+04 4.1901E+06 7.4070E-03 1.0000 +437 5 3G - 6 3F 3-2 1340.808135 cm-1 193921.620238 195262.428373 1.1423E+04 4.1901E+06 6.8023E-03 1.0000 +437 5 3G - 6 3F 4-3 1340.809268 cm-1 193921.614949 195262.424217 1.0439E+04 4.1889E+06 6.7689E-03 0.9748 +437 5 3G - 6 3F 4-4 1340.810873 cm-1 193921.614949 195262.425821 2.8825E+02 4.1901E+06 2.4031E-04 0.5191 +438 5 3G - 6 3H Mean 1341.176557 cm-1 193921.617449 195262.794006 1.6352E+06 1.6459E+06 1.6653E+00 0.9935 +438 5 3G - 6 3H 3-4 1341.174805 cm-1 193921.620238 195262.795043 1.5646E+06 1.6459E+06 1.6762E+00 1.0000 +438 5 3G - 6 3H 5-5 1341.175332 cm-1 193921.617719 195262.793051 3.3922E+04 1.6459E+06 2.8265E-02 0.5153 +438 5 3G - 6 3H 5-6 1341.176376 cm-1 193921.617719 195262.794095 1.6459E+06 1.6459E+06 1.6208E+00 1.0000 +438 5 3G - 6 3H 5-4 1341.177324 cm-1 193921.617719 195262.795043 8.1279E+02 1.6459E+06 5.5411E-04 1.0000 +438 5 3G - 6 3H 4-5 1341.178102 cm-1 193921.614949 195262.793051 1.6117E+06 1.6459E+06 1.6414E+00 1.0200 +438 5 3G - 6 3H 4-4 1341.180094 cm-1 193921.614949 195262.795043 4.1770E+04 1.6459E+06 3.4804E-02 0.5191 +439 5 3G - 7 3F Mean 2149.559742 cm-1 193921.617449 196071.177191 4.5482E+03 2.6643E+06 1.1475E-03 0.9734 +439 5 3G - 7 3F 3-3 2149.555940 cm-1 193921.620238 196071.176178 2.1949E+02 2.6638E+06 7.1196E-05 0.7518 +439 5 3G - 7 3F 3-4 2149.556885 cm-1 193921.620238 196071.177123 3.6054E+00 2.6646E+06 1.5036E-06 1.0000 +439 5 3G - 7 3F 3-2 2149.558492 cm-1 193921.620238 196071.178730 4.6725E+03 2.6646E+06 1.0826E-03 1.0000 +439 5 3G - 7 3F 5-4 2149.559404 cm-1 193921.617719 196071.177123 4.4418E+03 2.6646E+06 1.1788E-03 1.0000 +439 5 3G - 7 3F 4-3 2149.561229 cm-1 193921.614949 196071.176178 4.2206E+03 2.6638E+06 1.0648E-03 0.9635 +439 5 3G - 7 3F 4-4 2149.562175 cm-1 193921.614949 196071.177123 1.1791E+02 2.6646E+06 3.8246E-05 0.5183 +440 5 3G - 7 3H Mean 2149.797665 cm-1 193921.617449 196071.415114 5.0580E+05 1.0417E+06 2.0048E-01 0.9935 +440 5 3G - 7 3H 3-4 2149.795529 cm-1 193921.620238 196071.415767 4.8396E+05 1.0417E+06 2.0179E-01 1.0000 +440 5 3G - 7 3H 5-5 2149.796793 cm-1 193921.617719 196071.414513 1.0493E+04 1.0417E+06 3.4029E-03 0.5152 +440 5 3G - 7 3H 5-6 2149.797451 cm-1 193921.617719 196071.415170 5.0910E+05 1.0417E+06 1.9512E-01 1.0000 +440 5 3G - 7 3H 5-4 2149.798048 cm-1 193921.617719 196071.415767 2.5141E+02 1.0417E+06 6.6708E-05 1.0000 +440 5 3G - 7 3H 4-5 2149.799564 cm-1 193921.614949 196071.414513 4.9851E+05 1.0417E+06 1.9759E-01 1.0200 +440 5 3G - 7 3H 4-4 2149.800818 cm-1 193921.614949 196071.415767 1.2920E+04 1.0417E+06 4.1899E-03 0.5191 +441 5 3G - 8 3H Mean 2674.624020 cm-1 193921.617449 196596.241469 2.3250E+05 7.0248E+05 5.9538E-02 0.9935 +441 5 3G - 8 3H 3-4 2674.621669 cm-1 193921.620238 196596.241907 2.2246E+05 7.0248E+05 5.9925E-02 1.0000 +441 5 3G - 8 3H 5-5 2674.623347 cm-1 193921.617719 196596.241066 4.8232E+03 7.0248E+05 1.0105E-03 0.5152 +441 5 3G - 8 3H 5-6 2674.623788 cm-1 193921.617719 196596.241507 2.3402E+05 7.0248E+05 5.7945E-02 1.0000 +441 5 3G - 8 3H 5-4 2674.624187 cm-1 193921.617719 196596.241907 1.1556E+02 7.0248E+05 1.9809E-05 1.0000 +441 5 3G - 8 3H 4-5 2674.626118 cm-1 193921.614949 196596.241066 2.2915E+05 7.0248E+05 5.8679E-02 1.0200 +441 5 3G - 8 3H 4-4 2674.626958 cm-1 193921.614949 196596.241907 5.9389E+03 7.0248E+05 1.2443E-03 0.5191 +442 5 3G - 9 3H Mean 3034.443116 cm-1 193921.617449 196956.060565 1.2949E+05 4.9674E+05 2.5761E-02 0.9935 +442 5 3G - 9 3H 3-4 3034.440634 cm-1 193921.620238 196956.060872 1.2390E+05 4.9674E+05 2.5930E-02 1.0000 +442 5 3G - 9 3H 5-5 3034.442563 cm-1 193921.617719 196956.060282 2.6862E+03 4.9674E+05 4.3724E-04 0.5152 +442 5 3G - 9 3H 5-6 3034.442872 cm-1 193921.617719 196956.060591 1.3033E+05 4.9674E+05 2.5071E-02 1.0000 +442 5 3G - 9 3H 5-4 3034.443153 cm-1 193921.617719 196956.060872 6.4363E+01 4.9674E+05 8.5717E-06 1.0000 +442 5 3G - 9 3H 4-5 3034.445333 cm-1 193921.614949 196956.060282 1.2762E+05 4.9674E+05 2.5389E-02 1.0200 +442 5 3G - 9 3H 4-4 3034.445923 cm-1 193921.614949 196956.060872 3.3076E+03 4.9674E+05 5.3839E-04 0.5191 +443 5 3G -10 3H Mean 3291.819448 cm-1 193921.617449 197213.436897 8.0822E+04 3.6446E+05 1.3663E-02 0.9935 +443 5 3G -10 3H 3-4 3291.816883 cm-1 193921.620238 197213.437121 7.7331E+04 3.6446E+05 1.3752E-02 1.0000 +443 5 3G -10 3H 5-5 3291.818971 cm-1 193921.617719 197213.436691 1.6766E+03 3.6446E+05 2.3190E-04 0.5152 +443 5 3G -10 3H 5-6 3291.819197 cm-1 193921.617719 197213.436916 8.1349E+04 3.6446E+05 1.3298E-02 1.0000 +443 5 3G -10 3H 5-4 3291.819402 cm-1 193921.617719 197213.437121 4.0172E+01 3.6446E+05 4.5461E-06 1.0000 +443 5 3G -10 3H 4-5 3291.821742 cm-1 193921.614949 197213.436691 7.9656E+04 3.6446E+05 1.3466E-02 1.0200 +443 5 3G -10 3H 4-4 3291.822172 cm-1 193921.614949 197213.437121 2.0644E+03 3.6446E+05 2.8554E-04 0.5190 +444 6 3S - 6 3P Mean 256.627951 cm-1 194936.119697 195192.747648 2.6979E+04 2.9557E+06 1.8418E+00 1.0000 +444 6 3S - 6 3P 1-2 256.623277 cm-1 194936.119697 195192.742974 2.6979E+04 2.9557E+06 1.0232E+00 1.0000 +444 6 3S - 6 3P 1-1 256.625862 cm-1 194936.119697 195192.745559 2.6979E+04 2.9557E+06 6.1393E-01 1.0000 +444 6 3S - 6 3P 1-0 256.657584 cm-1 194936.119697 195192.777281 2.6979E+04 2.9557E+06 2.0464E-01 1.0000 +445 6 3S - 7 3P Mean 1091.198250 cm-1 194936.119697 196027.317947 1.0673E+04 1.9947E+06 4.0304E-02 1.0000 +445 6 3S - 7 3P 1-2 1091.195330 cm-1 194936.119697 196027.315027 1.0673E+04 1.9947E+06 2.2391E-02 1.0000 +445 6 3S - 7 3P 1-1 1091.196944 cm-1 194936.119697 196027.316641 1.0673E+04 1.9947E+06 1.3435E-02 1.0000 +445 6 3S - 7 3P 1-0 1091.216768 cm-1 194936.119697 196027.336465 1.0673E+04 1.9947E+06 4.4782E-03 1.0000 +446 6 3S - 8 3P Mean 1630.594070 cm-1 194936.119697 196566.713767 1.2413E+04 1.3990E+06 2.0992E-02 1.0000 +446 6 3S - 8 3P 1-2 1630.592125 cm-1 194936.119697 196566.711822 1.2413E+04 1.3990E+06 1.1662E-02 1.0000 +446 6 3S - 8 3P 1-1 1630.593200 cm-1 194936.119697 196566.712897 1.2413E+04 1.3990E+06 6.9974E-03 1.0000 +446 6 3S - 8 3P 1-0 1630.606407 cm-1 194936.119697 196566.726105 1.2413E+04 1.3990E+06 2.3325E-03 1.0000 +447 6 3S - 9 3P Mean 1999.213082 cm-1 194936.119697 196935.332779 1.0521E+04 1.0146E+06 1.1836E-02 1.0000 +447 6 3S - 9 3P 1-2 1999.211721 cm-1 194936.119697 196935.331418 1.0521E+04 1.0146E+06 6.5757E-03 1.0000 +447 6 3S - 9 3P 1-1 1999.212473 cm-1 194936.119697 196935.332170 1.0521E+04 1.0146E+06 3.9454E-03 1.0000 +447 6 3S - 9 3P 1-0 1999.221711 cm-1 194936.119697 196935.341408 1.0521E+04 1.0146E+06 1.3151E-03 1.0000 +448 6 3S -10 3P Mean 2262.214014 cm-1 194936.119697 197198.333711 8.4323E+03 7.5715E+05 7.4089E-03 1.0000 +448 6 3S -10 3P 1-2 2262.213025 cm-1 194936.119697 197198.332722 8.4323E+03 7.5715E+05 4.1160E-03 1.0000 +448 6 3S -10 3P 1-1 2262.213571 cm-1 194936.119697 197198.333268 8.4323E+03 7.5715E+05 2.4696E-03 1.0000 +448 6 3S -10 3P 1-0 2262.220284 cm-1 194936.119697 197198.339982 8.4323E+03 7.5716E+05 8.2321E-04 1.0000 +449 6 3P - 6 3D Mean 67.325005 cm-1 195192.747648 195260.072653 6.4181E+02 9.6698E+06 3.5429E-01 1.0000 +449 6 3P - 6 3D 0-1 67.299922 cm-1 195192.777281 195260.077203 3.5657E+02 9.6698E+06 3.5430E-01 1.0000 +449 6 3P - 6 3D 1-2 67.326177 cm-1 195192.745559 195260.071736 4.8134E+02 9.6697E+06 2.6571E-01 0.9999 +449 6 3P - 6 3D 2-3 67.328384 cm-1 195192.742974 195260.071358 6.4183E+02 9.6698E+06 2.9761E-01 1.0000 +449 6 3P - 6 3D 2-2 67.328762 cm-1 195192.742974 195260.071736 1.6044E+02 9.6697E+06 5.3140E-02 0.9999 +449 6 3P - 6 3D 1-1 67.331644 cm-1 195192.745559 195260.077203 2.6743E+02 9.6698E+06 8.8576E-02 1.0000 +449 6 3P - 6 3D 2-1 67.334229 cm-1 195192.742974 195260.077203 1.7829E+01 9.6698E+06 3.5431E-03 1.0000 +450 6 3P - 7 3S Mean 675.489328 cm-1 195192.747648 195868.236975 3.4683E+05 3.6533E+06 3.7978E-01 1.0000 +450 6 3P - 7 3S 0-1 675.459694 cm-1 195192.777281 195868.236975 3.8536E+04 3.6533E+06 3.7978E-01 1.0000 +450 6 3P - 7 3S 1-1 675.491416 cm-1 195192.745559 195868.236975 1.1561E+05 3.6533E+06 3.7978E-01 1.0000 +450 6 3P - 7 3S 2-1 675.494001 cm-1 195192.742974 195868.236975 1.9268E+05 3.6533E+06 3.7978E-01 1.0000 +451 6 3P - 7 3D Mean 876.925978 cm-1 195192.747648 196069.673625 1.3352E+05 6.1663E+06 4.3377E-01 1.0000 +451 6 3P - 7 3D 0-1 876.899208 cm-1 195192.777281 196069.676490 7.4180E+04 6.1664E+06 4.3379E-01 1.0000 +451 6 3P - 7 3D 1-2 876.927491 cm-1 195192.745559 196069.673050 1.0013E+05 6.1661E+06 3.2530E-01 0.9999 +451 6 3P - 7 3D 2-3 876.929835 cm-1 195192.742974 196069.672809 1.3352E+05 6.1664E+06 3.6437E-01 1.0000 +451 6 3P - 7 3D 2-2 876.930076 cm-1 195192.742974 196069.673050 3.3378E+04 6.1661E+06 6.5062E-02 0.9999 +451 6 3P - 7 3D 1-1 876.930931 cm-1 195192.745559 196069.676490 5.5635E+04 6.1664E+06 1.0845E-01 1.0000 +451 6 3P - 7 3D 2-1 876.933515 cm-1 195192.742974 196069.676490 3.7090E+03 6.1664E+06 4.3379E-03 1.0000 +452 6 3P - 8 3S Mean 1268.614163 cm-1 195192.747648 196461.361811 1.8923E+05 2.4913E+06 5.8747E-02 1.0000 +452 6 3P - 8 3S 0-1 1268.584529 cm-1 195192.777281 196461.361811 2.1026E+04 2.4913E+06 5.8747E-02 1.0000 +452 6 3P - 8 3S 1-1 1268.616252 cm-1 195192.745559 196461.361811 6.3079E+04 2.4913E+06 5.8748E-02 1.0000 +452 6 3P - 8 3S 2-1 1268.618836 cm-1 195192.742974 196461.361811 1.0513E+05 2.4913E+06 5.8747E-02 1.0000 +453 6 3P - 8 3D Mean 1402.315102 cm-1 195192.747648 196595.062750 1.0081E+05 4.1689E+06 1.2806E-01 1.0000 +453 6 3P - 8 3D 0-1 1402.287387 cm-1 195192.777281 196595.064668 5.6005E+04 4.1690E+06 1.2807E-01 1.0000 +453 6 3P - 8 3D 1-2 1402.316806 cm-1 195192.745559 196595.062365 7.5601E+04 4.1688E+06 9.6042E-02 0.9999 +453 6 3P - 8 3D 1-1 1402.319109 cm-1 195192.745559 196595.064668 4.2004E+04 4.1690E+06 3.2017E-02 1.0000 +453 6 3P - 8 3D 2-3 1402.319228 cm-1 195192.742974 196595.062202 1.0081E+05 4.1690E+06 1.0758E-01 1.0000 +453 6 3P - 8 3D 2-2 1402.319391 cm-1 195192.742974 196595.062365 2.5200E+04 4.1688E+06 1.9208E-02 0.9999 +453 6 3P - 8 3D 2-1 1402.321694 cm-1 195192.742974 196595.064668 2.8002E+03 4.1690E+06 1.2806E-03 1.0000 +454 6 3P - 9 3S Mean 1669.239692 cm-1 195192.747648 196861.987340 1.2088E+05 1.7692E+06 2.1675E-02 1.0000 +454 6 3P - 9 3S 0-1 1669.210058 cm-1 195192.777281 196861.987340 1.3431E+04 1.7692E+06 2.1675E-02 1.0000 +454 6 3P - 9 3S 1-1 1669.241781 cm-1 195192.745559 196861.987340 4.0293E+04 1.7692E+06 2.1675E-02 1.0000 +454 6 3P - 9 3S 2-1 1669.244365 cm-1 195192.742974 196861.987340 6.7155E+04 1.7692E+06 2.1675E-02 1.0000 +455 6 3P - 9 3D Mean 1762.479264 cm-1 195192.747648 196955.226911 7.3352E+04 2.9483E+06 5.8991E-02 1.0000 +455 6 3P - 9 3D 0-1 1762.450977 cm-1 195192.777281 196955.228258 4.0752E+04 2.9484E+06 5.8992E-02 1.0000 +455 6 3P - 9 3D 1-2 1762.481082 cm-1 195192.745559 196955.226641 5.5012E+04 2.9482E+06 4.4241E-02 0.9999 +455 6 3P - 9 3D 1-1 1762.482699 cm-1 195192.745559 196955.228258 3.0564E+04 2.9484E+06 1.4748E-02 1.0000 +455 6 3P - 9 3D 2-3 1762.483553 cm-1 195192.742974 196955.226527 7.3354E+04 2.9483E+06 4.9553E-02 1.0000 +455 6 3P - 9 3D 2-2 1762.483667 cm-1 195192.742974 196955.226641 1.8337E+04 2.9482E+06 8.8481E-03 0.9999 +455 6 3P - 9 3D 2-1 1762.485284 cm-1 195192.742974 196955.228258 2.0376E+03 2.9484E+06 5.8992E-04 1.0000 +456 6 3P -10 3S Mean 1952.485610 cm-1 195192.747648 197145.233258 8.3144E+04 1.2990E+06 1.0897E-02 1.0000 +456 6 3P -10 3S 0-1 1952.455977 cm-1 195192.777281 197145.233258 9.2383E+03 1.2990E+06 1.0897E-02 1.0000 +456 6 3P -10 3S 1-1 1952.487699 cm-1 195192.745559 197145.233258 2.7715E+04 1.2990E+06 1.0897E-02 1.0000 +456 6 3P -10 3S 2-1 1952.490284 cm-1 195192.742974 197145.233258 4.6191E+04 1.2990E+06 1.0897E-02 1.0000 +457 6 3D - 6 3F Mean 2.353241 cm-1 195260.072653 195262.425894 2.2585E-02 4.1897E+06 8.5688E-03 0.9132 +457 6 3D - 6 3F 1-2 2.351170 cm-1 195260.077203 195262.428373 2.0777E-02 4.1901E+06 9.3837E-03 1.0000 +457 6 3D - 6 3F 2-3 2.352480 cm-1 195260.071736 195262.424217 1.6281E-02 4.1889E+06 6.1766E-03 0.7405 +457 6 3D - 6 3F 3-3 2.352859 cm-1 195260.071358 195262.424217 2.0107E-03 4.1889E+06 5.4487E-04 0.7316 +457 6 3D - 6 3F 3-4 2.354463 cm-1 195260.071358 195262.425821 2.4735E-02 4.1901E+06 8.6179E-03 1.0000 +457 6 3D - 6 3F 2-2 2.356637 cm-1 195260.071736 195262.428373 3.8473E-03 4.1901E+06 1.0426E-03 0.9999 +457 6 3D - 6 3F 3-2 2.357015 cm-1 195260.071358 195262.428373 1.0993E-04 4.1901E+06 2.1278E-05 1.0000 +458 6 3D - 7 3P Mean 767.245294 cm-1 195260.072653 196027.317947 8.2460E+04 1.9947E+06 1.2596E-01 1.0000 +458 6 3D - 7 3P 1-2 767.237824 cm-1 195260.077203 196027.315027 8.2462E+02 1.9947E+06 3.4989E-03 1.0000 +458 6 3D - 7 3P 1-1 767.239438 cm-1 195260.077203 196027.316641 2.0616E+04 1.9947E+06 5.2485E-02 1.0000 +458 6 3D - 7 3P 2-2 767.243290 cm-1 195260.071736 196027.315027 1.2368E+04 1.9947E+06 3.1487E-02 0.9999 +458 6 3D - 7 3P 3-2 767.243669 cm-1 195260.071358 196027.315027 6.9268E+04 1.9947E+06 1.2596E-01 1.0000 +458 6 3D - 7 3P 2-1 767.244904 cm-1 195260.071736 196027.316641 6.1841E+04 1.9947E+06 9.4463E-02 0.9999 +458 6 3D - 7 3P 1-0 767.259262 cm-1 195260.077203 196027.336465 8.2462E+04 1.9947E+06 6.9979E-02 1.0000 +459 6 3D - 7 3F Mean 811.104538 cm-1 195260.072653 196071.177191 2.3774E+05 2.6643E+06 7.5826E-01 0.9198 +459 6 3D - 7 3F 1-2 811.101527 cm-1 195260.077203 196071.178730 2.1712E+05 2.6646E+06 8.2440E-01 1.0000 +459 6 3D - 7 3F 2-3 811.104441 cm-1 195260.071736 196071.176178 1.7468E+05 2.6638E+06 5.5713E-01 0.7603 +459 6 3D - 7 3F 3-3 811.104820 cm-1 195260.071358 196071.176178 2.1585E+04 2.6638E+06 4.9175E-02 0.7516 +459 6 3D - 7 3F 3-4 811.105765 cm-1 195260.071358 196071.177123 2.5848E+05 2.6646E+06 7.5711E-01 1.0000 +459 6 3D - 7 3F 2-2 811.106993 cm-1 195260.071736 196071.178730 4.0204E+04 2.6646E+06 9.1592E-02 0.9999 +459 6 3D - 7 3F 3-2 811.107372 cm-1 195260.071358 196071.178730 1.1488E+03 2.6646E+06 1.8694E-03 1.0000 +460 6 3D - 8 3P Mean 1306.641114 cm-1 195260.072653 196566.713767 4.7665E+04 1.3990E+06 2.5105E-02 1.0000 +460 6 3D - 8 3P 1-2 1306.634619 cm-1 195260.077203 196566.711822 4.7666E+02 1.3990E+06 6.9738E-04 1.0000 +460 6 3D - 8 3P 1-1 1306.635694 cm-1 195260.077203 196566.712897 1.1917E+04 1.3990E+06 1.0461E-02 1.0000 +460 6 3D - 8 3P 2-2 1306.640086 cm-1 195260.071736 196566.711822 7.1493E+03 1.3990E+06 6.2759E-03 0.9999 +460 6 3D - 8 3P 3-2 1306.640464 cm-1 195260.071358 196566.711822 4.0040E+04 1.3990E+06 2.5106E-02 1.0000 +460 6 3D - 8 3P 2-1 1306.641161 cm-1 195260.071736 196566.712897 3.5747E+04 1.3990E+06 1.8828E-02 0.9999 +460 6 3D - 8 3P 1-0 1306.648902 cm-1 195260.077203 196566.726105 4.7666E+04 1.3990E+06 1.3948E-02 1.0000 +461 6 3D - 8 3F Mean 1336.006767 cm-1 195260.072653 196596.079420 1.5942E+05 1.7997E+06 1.8741E-01 0.9239 +461 6 3D - 8 3F 1-2 1336.003239 cm-1 195260.077203 196596.080442 1.4494E+05 1.7998E+06 2.0284E-01 1.0000 +461 6 3D - 8 3F 2-3 1336.007024 cm-1 195260.071736 196596.078760 1.1852E+05 1.7993E+06 1.3933E-01 0.7728 +461 6 3D - 8 3F 3-3 1336.007402 cm-1 195260.071358 196596.078760 1.4651E+04 1.7993E+06 1.2302E-02 0.7642 +461 6 3D - 8 3F 3-4 1336.008008 cm-1 195260.071358 196596.079366 1.7255E+05 1.7999E+06 1.8629E-01 1.0000 +461 6 3D - 8 3F 2-2 1336.008706 cm-1 195260.071736 196596.080442 2.6838E+04 1.7998E+06 2.2536E-02 0.9999 +461 6 3D - 8 3F 3-2 1336.009084 cm-1 195260.071358 196596.080442 7.6687E+02 1.7998E+06 4.5996E-04 1.0000 +462 6 3D - 9 3P Mean 1675.260126 cm-1 195260.072653 196935.332779 3.0467E+04 1.0146E+06 9.7622E-03 1.0000 +462 6 3D - 9 3P 1-2 1675.254215 cm-1 195260.077203 196935.331418 3.0467E+02 1.0146E+06 2.7117E-04 1.0000 +462 6 3D - 9 3P 1-1 1675.254967 cm-1 195260.077203 196935.332170 7.6169E+03 1.0146E+06 4.0677E-03 1.0000 +462 6 3D - 9 3P 2-2 1675.259682 cm-1 195260.071736 196935.331418 4.5697E+03 1.0146E+06 2.4404E-03 0.9999 +462 6 3D - 9 3P 3-2 1675.260060 cm-1 195260.071358 196935.331418 2.5593E+04 1.0146E+06 9.7625E-03 1.0000 +462 6 3D - 9 3P 2-1 1675.260434 cm-1 195260.071736 196935.332170 2.2849E+04 1.0146E+06 7.3213E-03 0.9999 +462 6 3D - 9 3P 1-0 1675.264205 cm-1 195260.077203 196935.341408 3.0467E+04 1.0146E+06 5.4235E-03 1.0000 +463 6 3D - 9 3F Mean 1695.872818 cm-1 195260.072653 196955.945471 1.0928E+05 1.2727E+06 7.9732E-02 0.9267 +463 6 3D - 9 3F 1-2 1695.868982 cm-1 195260.077203 196955.946185 9.9057E+04 1.2728E+06 8.6038E-02 1.0000 +463 6 3D - 9 3F 2-3 1695.873280 cm-1 195260.071736 196955.945017 8.1879E+04 1.2724E+06 5.9739E-02 0.7811 +463 6 3D - 9 3F 3-3 1695.873659 cm-1 195260.071358 196955.945017 1.0124E+04 1.2724E+06 5.2760E-03 0.7727 +463 6 3D - 9 3F 3-4 1695.874071 cm-1 195260.071358 196955.945429 1.1792E+05 1.2728E+06 7.9011E-02 1.0000 +463 6 3D - 9 3F 2-2 1695.874448 cm-1 195260.071736 196955.946185 1.8342E+04 1.2728E+06 9.5588E-03 0.9999 +463 6 3D - 9 3F 3-2 1695.874827 cm-1 195260.071358 196955.946185 5.2411E+02 1.2728E+06 1.9510E-04 1.0000 +464 6 3D -10 3P Mean 1938.261058 cm-1 195260.072653 197198.333711 2.0847E+04 7.5715E+05 4.9901E-03 1.0000 +464 6 3D -10 3P 1-2 1938.255519 cm-1 195260.077203 197198.332722 2.0848E+02 7.5715E+05 1.3862E-04 1.0000 +464 6 3D -10 3P 1-1 1938.256065 cm-1 195260.077203 197198.333268 5.2119E+03 7.5715E+05 2.0793E-03 1.0000 +464 6 3D -10 3P 2-2 1938.260986 cm-1 195260.071736 197198.332722 3.1269E+03 7.5715E+05 1.2475E-03 0.9998 +464 6 3D -10 3P 3-2 1938.261364 cm-1 195260.071358 197198.332722 1.7512E+04 7.5715E+05 4.9902E-03 1.0000 +464 6 3D -10 3P 2-1 1938.261532 cm-1 195260.071736 197198.333268 1.5634E+04 7.5715E+05 3.7422E-03 0.9999 +464 6 3D -10 3P 1-0 1938.262779 cm-1 195260.077203 197198.339982 2.0848E+04 7.5716E+05 2.7724E-03 1.0000 +465 6 3D -10 3F Mean 1953.279672 cm-1 195260.072653 197213.352326 7.7923E+04 9.3313E+05 4.2855E-02 0.9287 +465 6 3D -10 3F 1-2 1953.275640 cm-1 195260.077203 197213.352843 7.0481E+04 9.3321E+05 4.6146E-02 1.0000 +465 6 3D -10 3F 2-3 1953.280262 cm-1 195260.071736 197213.351998 5.8698E+04 9.3293E+05 3.2282E-02 0.7870 +465 6 3D -10 3F 3-3 1953.280640 cm-1 195260.071358 197213.351998 7.2594E+03 9.3293E+05 2.8518E-03 0.7787 +465 6 3D -10 3F 3-4 1953.280934 cm-1 195260.071358 197213.352292 8.3906E+04 9.3323E+05 4.2379E-02 1.0000 +465 6 3D -10 3F 2-2 1953.281107 cm-1 195260.071736 197213.352843 1.3051E+04 9.3321E+05 5.1269E-03 0.9999 +465 6 3D -10 3F 3-2 1953.281485 cm-1 195260.071358 197213.352843 3.7291E+02 9.3321E+05 1.0464E-04 1.0000 +466 6 3F - 7 3D Mean 807.247731 cm-1 195262.425894 196069.673625 2.3615E+04 6.1663E+06 3.8797E-02 0.9131 +466 6 3F - 7 3D 2-3 807.244436 cm-1 195262.428373 196069.672809 5.8648E+01 6.1664E+06 1.8885E-04 1.0000 +466 6 3F - 7 3D 2-2 807.244677 cm-1 195262.428373 196069.673050 2.8735E+03 6.1661E+06 6.6090E-03 0.9999 +466 6 3F - 7 3D 4-3 807.246988 cm-1 195262.425821 196069.672809 2.3752E+04 6.1664E+06 4.2489E-02 1.0000 +466 6 3F - 7 3D 2-1 807.248117 cm-1 195262.428373 196069.676490 2.5864E+04 6.1664E+06 3.5692E-02 1.0000 +466 6 3F - 7 3D 3-3 807.248592 cm-1 195262.424217 196069.672809 1.5017E+03 6.1664E+06 3.4539E-03 0.7316 +466 6 3F - 7 3D 3-2 807.248833 cm-1 195262.424217 196069.673050 1.7017E+04 6.1661E+06 2.7956E-02 0.7402 +467 6 3F - 7 3G Mean 808.943754 cm-1 195262.425894 196071.369648 3.6771E+05 1.5756E+06 1.0828E+00 0.9766 +467 6 3F - 7 3G 2-3 808.942291 cm-1 195262.428373 196071.370664 3.4578E+05 1.5756E+06 1.1087E+00 1.0000 +467 6 3F - 7 3G 4-4 808.942917 cm-1 195262.425821 196071.368738 1.2231E+04 1.5756E+06 2.8013E-02 0.5198 +467 6 3F - 7 3G 4-5 808.943925 cm-1 195262.425821 196071.369746 3.7651E+05 1.5756E+06 1.0540E+00 1.0000 +467 6 3F - 7 3G 3-4 808.944521 cm-1 195262.424217 196071.368738 3.4418E+05 1.5756E+06 1.0135E+00 0.9751 +467 6 3F - 7 3G 4-3 808.944843 cm-1 195262.425821 196071.370664 4.8025E+02 1.5756E+06 8.5552E-04 1.0000 +467 6 3F - 7 3G 3-3 808.946447 cm-1 195262.424217 196071.370664 2.2135E+04 1.5756E+06 5.0697E-02 0.7316 +468 6 3F - 8 3D Mean 1332.636856 cm-1 195262.425894 196595.062750 1.2739E+04 4.1689E+06 7.6796E-03 0.9130 +468 6 3F - 8 3D 2-3 1332.633829 cm-1 195262.428373 196595.062202 3.1640E+01 4.1690E+06 3.7384E-05 1.0000 +468 6 3F - 8 3D 2-2 1332.633992 cm-1 195262.428373 196595.062365 1.5502E+03 4.1688E+06 1.3083E-03 0.9999 +468 6 3F - 8 3D 2-1 1332.636295 cm-1 195262.428373 196595.064668 1.3953E+04 4.1690E+06 7.0654E-03 1.0000 +468 6 3F - 8 3D 4-3 1332.636381 cm-1 195262.425821 196595.062202 1.2814E+04 4.1690E+06 8.4112E-03 1.0000 +468 6 3F - 8 3D 3-3 1332.637986 cm-1 195262.424217 196595.062202 8.1017E+02 4.1690E+06 6.8374E-04 0.7315 +468 6 3F - 8 3D 3-2 1332.638148 cm-1 195262.424217 196595.062365 9.1781E+03 4.1688E+06 5.5328E-03 0.7400 +469 6 3F - 8 3G Mean 1333.784372 cm-1 195262.425894 196596.210266 2.2114E+05 1.0641E+06 2.3954E-01 0.9766 +469 6 3F - 8 3G 2-3 1333.782573 cm-1 195262.428373 196596.210946 2.0794E+05 1.0641E+06 2.4527E-01 1.0000 +469 6 3F - 8 3G 4-4 1333.783835 cm-1 195262.425821 196596.209656 7.3585E+03 1.0641E+06 6.1995E-03 0.5200 +469 6 3F - 8 3G 4-5 1333.784510 cm-1 195262.425821 196596.210331 2.2643E+05 1.0641E+06 2.3316E-01 1.0000 +469 6 3F - 8 3G 4-3 1333.785125 cm-1 195262.425821 196596.210946 2.8881E+02 1.0641E+06 1.8925E-04 1.0000 +469 6 3F - 8 3G 3-4 1333.785440 cm-1 195262.424217 196596.209656 2.0700E+05 1.0641E+06 2.2423E-01 0.9751 +469 6 3F - 8 3G 3-3 1333.786729 cm-1 195262.424217 196596.210946 1.3311E+04 1.0641E+06 1.1215E-02 0.7316 +470 6 3F - 9 3D Mean 1692.801017 cm-1 195262.425894 196955.226911 7.7178E+03 2.9483E+06 2.8833E-03 0.9130 +470 6 3F - 9 3D 2-3 1692.798154 cm-1 195262.428373 196955.226527 1.9169E+01 2.9483E+06 1.4036E-05 1.0000 +470 6 3F - 9 3D 2-2 1692.798268 cm-1 195262.428373 196955.226641 9.3919E+02 2.9482E+06 4.9123E-04 0.9998 +470 6 3F - 9 3D 2-1 1692.799885 cm-1 195262.428373 196955.228258 8.4534E+03 2.9484E+06 2.6528E-03 1.0000 +470 6 3F - 9 3D 4-3 1692.800705 cm-1 195262.425821 196955.226527 7.7633E+03 2.9483E+06 3.1581E-03 1.0000 +470 6 3F - 9 3D 3-3 1692.802310 cm-1 195262.424217 196955.226527 4.9083E+02 2.9483E+06 2.5672E-04 0.7315 +470 6 3F - 9 3D 3-2 1692.802425 cm-1 195262.424217 196955.226641 5.5595E+03 2.9482E+06 2.0770E-03 0.7399 +471 6 3F - 9 3G Mean 1693.612397 cm-1 195262.425894 196956.038291 1.4152E+05 7.5280E+05 9.5074E-02 0.9767 +471 6 3F - 9 3G 2-3 1693.610396 cm-1 195262.428373 196956.038769 1.3307E+05 7.5280E+05 9.7347E-02 1.0000 +471 6 3F - 9 3G 4-4 1693.612042 cm-1 195262.425821 196956.037863 4.7104E+03 7.5280E+05 2.4613E-03 0.5201 +471 6 3F - 9 3G 4-5 1693.612516 cm-1 195262.425821 196956.038337 1.4490E+05 7.5280E+05 9.2540E-02 1.0000 +471 6 3F - 9 3G 4-3 1693.612947 cm-1 195262.425821 196956.038769 1.8482E+02 7.5280E+05 7.5113E-05 1.0000 +471 6 3F - 9 3G 3-4 1693.613646 cm-1 195262.424217 196956.037863 1.3247E+05 7.5280E+05 8.8997E-02 0.9752 +471 6 3F - 9 3G 3-3 1693.614552 cm-1 195262.424217 196956.038769 8.5184E+03 7.5280E+05 4.4511E-03 0.7316 +472 6 3F -10 3G Mean 1950.994578 cm-1 195262.425894 197213.420472 9.6303E+04 5.5231E+05 4.8754E-02 0.9767 +472 6 3F -10 3G 2-3 1950.992448 cm-1 195262.428373 197213.420821 9.0553E+04 5.5231E+05 4.9918E-02 1.0000 +472 6 3F -10 3G 4-4 1950.994339 cm-1 195262.425821 197213.420161 3.2062E+03 5.5231E+05 1.2625E-03 0.5203 +472 6 3F -10 3G 4-5 1950.994685 cm-1 195262.425821 197213.420506 9.8602E+04 5.5231E+05 4.7453E-02 1.0000 +472 6 3F -10 3G 4-3 1950.994999 cm-1 195262.425821 197213.420821 1.2577E+02 5.5231E+05 3.8518E-05 1.0000 +472 6 3F -10 3G 3-4 1950.995944 cm-1 195262.424217 197213.420161 9.0152E+04 5.5231E+05 4.5640E-02 0.9752 +472 6 3F -10 3G 3-3 1950.996604 cm-1 195262.424217 197213.420821 5.7967E+03 5.5231E+05 2.2825E-03 0.7316 +473 6 3G - 7 3F Mean 808.452663 cm-1 195262.724528 196071.177191 1.0853E+04 2.6643E+06 1.9356E-02 0.9735 +473 6 3G - 7 3F 3-3 808.450036 cm-1 195262.726142 196071.176178 5.2366E+02 2.6638E+06 1.2008E-03 0.7516 +473 6 3G - 7 3F 3-4 808.450982 cm-1 195262.726142 196071.177123 8.6019E+00 2.6646E+06 2.5361E-05 1.0000 +473 6 3G - 7 3F 5-4 808.452439 cm-1 195262.724684 196071.177123 1.0598E+04 2.6646E+06 1.9884E-02 1.0000 +473 6 3G - 7 3F 3-2 808.452588 cm-1 195262.726142 196071.178730 1.1148E+04 2.6646E+06 1.8260E-02 1.0000 +473 6 3G - 7 3F 4-3 808.453096 cm-1 195262.723082 196071.176178 1.0072E+04 2.6638E+06 1.7964E-02 0.9637 +473 6 3G - 7 3F 4-4 808.454041 cm-1 195262.723082 196071.177123 2.8151E+02 2.6646E+06 6.4554E-04 0.5194 +474 6 3G - 7 3H Mean 808.690586 cm-1 195262.724528 196071.415114 5.2914E+05 1.0417E+06 1.4822E+00 0.9935 +474 6 3G - 7 3H 3-4 808.689625 cm-1 195262.726142 196071.415767 5.0629E+05 1.0417E+06 1.4918E+00 1.0000 +474 6 3G - 7 3H 5-5 808.689828 cm-1 195262.724684 196071.414513 1.0977E+04 1.0417E+06 2.5157E-02 0.5153 +474 6 3G - 7 3H 5-6 808.690486 cm-1 195262.724684 196071.415170 5.3259E+05 1.0417E+06 1.4425E+00 1.0000 +474 6 3G - 7 3H 5-4 808.691083 cm-1 195262.724684 196071.415767 2.6301E+02 1.0417E+06 4.9317E-04 1.0000 +474 6 3G - 7 3H 4-5 808.691430 cm-1 195262.723082 196071.414513 5.2151E+05 1.0417E+06 1.4608E+00 1.0200 +474 6 3G - 7 3H 4-4 808.692685 cm-1 195262.723082 196071.415767 1.3526E+04 1.0417E+06 3.0999E-02 0.5195 +475 6 3G - 8 3F Mean 1333.354892 cm-1 195262.724528 196596.079420 5.1081E+03 1.7997E+06 3.3493E-03 0.9713 +475 6 3G - 8 3F 3-3 1333.352618 cm-1 195262.726142 196596.078760 2.5119E+02 1.7993E+06 2.1176E-04 0.7643 +475 6 3G - 8 3F 3-4 1333.353224 cm-1 195262.726142 196596.079366 4.0578E+00 1.7999E+06 4.3983E-06 1.0000 +475 6 3G - 8 3F 3-2 1333.354300 cm-1 195262.726142 196596.080442 5.2590E+03 1.7998E+06 3.1668E-03 1.0000 +475 6 3G - 8 3F 5-4 1333.354682 cm-1 195262.724684 196596.079366 4.9993E+03 1.7999E+06 3.4483E-03 1.0000 +475 6 3G - 8 3F 4-3 1333.355678 cm-1 195262.723082 196596.078760 4.7129E+03 1.7993E+06 3.0902E-03 0.9559 +475 6 3G - 8 3F 4-4 1333.356284 cm-1 195262.723082 196596.079366 1.3280E+02 1.7999E+06 1.1196E-04 0.5197 +476 6 3G - 8 3H Mean 1333.516941 cm-1 195262.724528 196596.241469 2.5630E+05 7.0248E+05 2.6402E-01 0.9935 +476 6 3G - 8 3H 3-4 1333.515765 cm-1 195262.726142 196596.241907 2.4523E+05 7.0248E+05 2.6574E-01 1.0000 +476 6 3G - 8 3H 5-5 1333.516382 cm-1 195262.724684 196596.241066 5.3169E+03 7.0248E+05 4.4813E-03 0.5153 +476 6 3G - 8 3H 5-6 1333.516823 cm-1 195262.724684 196596.241507 2.5797E+05 7.0248E+05 2.5696E-01 1.0000 +476 6 3G - 8 3H 5-4 1333.517222 cm-1 195262.724684 196596.241907 1.2739E+02 7.0248E+05 8.7847E-05 1.0000 +476 6 3G - 8 3H 4-5 1333.517984 cm-1 195262.723082 196596.241066 2.5260E+05 7.0248E+05 2.6021E-01 1.0200 +476 6 3G - 8 3H 4-4 1333.518824 cm-1 195262.723082 196596.241907 6.5517E+03 7.0248E+05 5.5220E-03 0.5195 +477 6 3G - 9 3F Mean 1693.220943 cm-1 195262.724528 196955.945471 2.8465E+03 1.2727E+06 1.1574E-03 0.9698 +477 6 3G - 9 3F 3-3 1693.218875 cm-1 195262.726142 196955.945017 1.4176E+02 1.2724E+06 7.4108E-05 0.7727 +477 6 3G - 9 3F 3-4 1693.219287 cm-1 195262.726142 196955.945429 2.2649E+00 1.2728E+06 1.5223E-06 1.0000 +477 6 3G - 9 3F 3-2 1693.220043 cm-1 195262.726142 196955.946185 2.9353E+03 1.2728E+06 1.0961E-03 1.0000 +477 6 3G - 9 3F 5-4 1693.220745 cm-1 195262.724684 196955.945429 2.7904E+03 1.2728E+06 1.1935E-03 1.0000 +477 6 3G - 9 3F 4-3 1693.221934 cm-1 195262.723082 196955.945017 2.6153E+03 1.2724E+06 1.0634E-03 0.9504 +477 6 3G - 9 3F 4-4 1693.222347 cm-1 195262.723082 196955.945429 7.4123E+01 1.2728E+06 3.8749E-05 0.5188 +478 6 3G - 9 3H Mean 1693.336037 cm-1 195262.724528 196956.060565 1.4472E+05 4.9674E+05 9.2454E-02 0.9935 +478 6 3G - 9 3H 3-4 1693.334730 cm-1 195262.726142 196956.060872 1.3847E+05 4.9674E+05 9.3058E-02 1.0000 +478 6 3G - 9 3H 5-5 1693.335598 cm-1 195262.724684 196956.060282 3.0021E+03 4.9674E+05 1.5692E-03 0.5153 +478 6 3G - 9 3H 5-6 1693.335907 cm-1 195262.724684 196956.060591 1.4566E+05 4.9674E+05 8.9980E-02 1.0000 +478 6 3G - 9 3H 5-4 1693.336188 cm-1 195262.724684 196956.060872 7.1930E+01 4.9674E+05 3.0762E-05 1.0000 +478 6 3G - 9 3H 4-5 1693.337199 cm-1 195262.723082 196956.060282 1.4263E+05 4.9674E+05 9.1120E-02 1.0200 +478 6 3G - 9 3H 4-4 1693.337790 cm-1 195262.723082 196956.060872 3.6992E+03 4.9674E+05 1.9336E-03 0.5195 +479 6 3G -10 3H Mean 1950.712369 cm-1 195262.724528 197213.436897 9.0832E+04 3.6446E+05 4.3726E-02 0.9935 +479 6 3G -10 3H 3-4 1950.710979 cm-1 195262.726142 197213.437121 8.6910E+04 3.6446E+05 4.4012E-02 1.0000 +479 6 3G -10 3H 5-5 1950.712006 cm-1 195262.724684 197213.436691 1.8843E+03 3.6446E+05 7.4217E-04 0.5153 +479 6 3G -10 3H 5-6 1950.712232 cm-1 195262.724684 197213.436916 9.1424E+04 3.6446E+05 4.2556E-02 1.0000 +479 6 3G -10 3H 5-4 1950.712437 cm-1 195262.724684 197213.437121 4.5148E+01 3.6446E+05 1.4549E-05 1.0000 +479 6 3G -10 3H 4-5 1950.713608 cm-1 195262.723082 197213.436691 8.9521E+04 3.6446E+05 4.3095E-02 1.0200 +479 6 3G -10 3H 4-4 1950.714039 cm-1 195262.723082 197213.437121 2.3219E+03 3.6446E+05 9.1453E-04 0.5195 +480 6 3H - 7 3G Mean 808.575643 cm-1 195262.794006 196071.369648 3.3374E+03 1.5756E+06 6.2597E-03 0.9935 +480 6 3H - 7 3G 4-4 808.573695 cm-1 195262.795043 196071.368738 6.9839E+01 1.5756E+06 1.6010E-04 0.5198 +480 6 3H - 7 3G 4-5 808.574703 cm-1 195262.795043 196071.369746 1.1105E+00 1.5756E+06 3.1115E-06 1.0000 +480 6 3H - 7 3G 4-3 808.575621 cm-1 195262.795043 196071.370664 3.3592E+03 1.5756E+06 5.9895E-03 1.0000 +480 6 3H - 7 3G 6-5 808.575651 cm-1 195262.794095 196071.369746 3.2481E+03 1.5756E+06 6.3005E-03 1.0000 +480 6 3H - 7 3G 5-4 808.575687 cm-1 195262.793051 196071.368738 3.2892E+03 1.5756E+06 6.1693E-03 1.0200 +480 6 3H - 7 3G 5-5 808.576695 cm-1 195262.793051 196071.369746 5.6645E+01 1.5756E+06 1.2985E-04 0.5155 +481 6 3H - 7 3I Mean 808.635312 cm-1 195262.794006 196071.429317 7.3786E+05 7.4121E+05 1.9988E+00 0.9955 +481 6 3H - 7 3I 4-5 808.634730 cm-1 195262.795043 196071.429773 7.1671E+05 7.4121E+05 2.0078E+00 1.0000 +481 6 3H - 7 3I 6-6 808.634796 cm-1 195262.794095 196071.428891 1.0560E+04 7.4121E+05 2.4205E-02 0.5129 +481 6 3H - 7 3I 6-7 808.635257 cm-1 195262.794095 196071.429352 7.4121E+05 7.4121E+05 1.9603E+00 1.0000 +481 6 3H - 7 3I 6-5 808.635677 cm-1 195262.794095 196071.429773 1.7016E+02 7.4121E+05 3.3002E-04 1.0000 +481 6 3H - 7 3I 5-6 808.635840 cm-1 195262.793051 196071.428891 7.3058E+05 7.4121E+05 1.9790E+00 1.0138 +481 6 3H - 7 3I 5-5 808.636722 cm-1 195262.793051 196071.429773 1.2537E+04 7.4121E+05 2.8736E-02 0.5153 +482 6 3H - 8 3I Mean 1333.457332 cm-1 195262.794006 196596.251337 2.1672E+05 4.9846E+05 2.1588E-01 0.9955 +482 6 3H - 8 3I 4-5 1333.456600 cm-1 195262.795043 196596.251643 2.1050E+05 4.9846E+05 2.1686E-01 1.0000 +482 6 3H - 8 3I 6-6 1333.456957 cm-1 195262.794095 196596.251052 3.1015E+03 4.9846E+05 2.6143E-03 0.5129 +482 6 3H - 8 3I 6-7 1333.457266 cm-1 195262.794095 196596.251361 2.1770E+05 4.9846E+05 2.1173E-01 1.0000 +482 6 3H - 8 3I 6-5 1333.457547 cm-1 195262.794095 196596.251643 4.9976E+01 4.9846E+05 3.5644E-05 1.0000 +482 6 3H - 8 3I 5-6 1333.458001 cm-1 195262.793051 196596.251052 2.1458E+05 4.9846E+05 2.1376E-01 1.0138 +482 6 3H - 8 3I 5-5 1333.458592 cm-1 195262.793051 196596.251643 3.6823E+03 4.9846E+05 3.1038E-03 0.5153 +483 6 3H - 9 3I Mean 1693.273660 cm-1 195262.794006 196956.067666 9.6356E+04 3.5197E+05 5.9527E-02 0.9955 +483 6 3H - 9 3I 4-5 1693.272837 cm-1 195262.795043 196956.067880 9.3593E+04 3.5197E+05 5.9797E-02 1.0000 +483 6 3H - 9 3I 6-6 1693.273370 cm-1 195262.794095 196956.067465 1.3790E+03 3.5197E+05 7.2086E-04 0.5129 +483 6 3H - 9 3I 6-7 1693.273587 cm-1 195262.794095 196956.067682 9.6793E+04 3.5197E+05 5.8382E-02 1.0000 +483 6 3H - 9 3I 6-5 1693.273785 cm-1 195262.794095 196956.067880 2.2221E+01 3.5197E+05 9.8287E-06 1.0000 +483 6 3H - 9 3I 5-6 1693.274414 cm-1 195262.793051 196956.067465 9.5406E+04 3.5197E+05 5.8940E-02 1.0138 +483 6 3H - 9 3I 5-5 1693.274829 cm-1 195262.793051 196956.067880 1.6372E+03 3.5197E+05 8.5583E-04 0.5153 +484 6 3H -10 3I Mean 1950.648157 cm-1 195262.794006 197213.442162 5.2498E+04 1.5881E+05 2.4438E-02 0.9955 +484 6 3H -10 3I 4-5 1950.647275 cm-1 195262.795043 197213.442318 5.0992E+04 2.5807E+05 2.4549E-02 1.0000 +484 6 3H -10 3I 6-6 1950.647921 cm-1 195262.794095 197213.442016 7.5132E+02 2.5807E+05 2.9594E-04 0.5128 +484 6 3H -10 3I 6-7 1950.648079 cm-1 195262.794095 197213.442174 5.2736E+04 0.0000E+00 2.3968E-02 1.0000 +484 6 3H -10 3I 6-5 1950.648223 cm-1 195262.794095 197213.442318 1.2106E+01 2.5807E+05 4.0349E-06 1.0000 +484 6 3H -10 3I 5-6 1950.648965 cm-1 195262.793051 197213.442016 5.1980E+04 2.5807E+05 2.4197E-02 1.0138 +484 6 3H -10 3I 5-5 1950.649267 cm-1 195262.793051 197213.442318 8.9202E+02 2.5807E+05 3.5136E-04 0.5153 +485 7 3S - 7 3P Mean 159.080971 cm-1 195868.236975 196027.317947 1.2105E+04 1.9947E+06 2.1505E+00 1.0000 +485 7 3S - 7 3P 1-2 159.078051 cm-1 195868.236975 196027.315027 1.2105E+04 1.9947E+06 1.1947E+00 1.0000 +485 7 3S - 7 3P 1-1 159.079665 cm-1 195868.236975 196027.316641 1.2105E+04 1.9947E+06 7.1685E-01 1.0000 +485 7 3S - 7 3P 1-0 159.099489 cm-1 195868.236975 196027.336465 1.2105E+04 1.9947E+06 2.3895E-01 1.0000 +486 7 3S - 8 3P Mean 698.476792 cm-1 195868.236975 196566.713767 4.3310E+03 1.3990E+06 3.9916E-02 1.0000 +486 7 3S - 8 3P 1-2 698.474847 cm-1 195868.236975 196566.711822 4.3310E+03 1.3990E+06 2.2176E-02 1.0000 +486 7 3S - 8 3P 1-1 698.475922 cm-1 195868.236975 196566.712897 4.3310E+03 1.3990E+06 1.3305E-02 1.0000 +486 7 3S - 8 3P 1-0 698.489129 cm-1 195868.236975 196566.726105 4.3310E+03 1.3990E+06 4.4352E-03 1.0000 +487 7 3S - 9 3P Mean 1067.095803 cm-1 195868.236975 196935.332779 5.3540E+03 1.0146E+06 2.1142E-02 1.0000 +487 7 3S - 9 3P 1-2 1067.094443 cm-1 195868.236975 196935.331418 5.3540E+03 1.0146E+06 1.1745E-02 1.0000 +487 7 3S - 9 3P 1-1 1067.095195 cm-1 195868.236975 196935.332170 5.3540E+03 1.0146E+06 7.0473E-03 1.0000 +487 7 3S - 9 3P 1-0 1067.104433 cm-1 195868.236975 196935.341408 5.3540E+03 1.0146E+06 2.3491E-03 1.0000 +488 7 3S -10 3P Mean 1330.096735 cm-1 195868.236975 197198.333711 4.7278E+03 7.5715E+05 1.2016E-02 1.0000 +488 7 3S -10 3P 1-2 1330.095747 cm-1 195868.236975 197198.332722 4.7278E+03 7.5715E+05 6.6756E-03 1.0000 +488 7 3S -10 3P 1-1 1330.096293 cm-1 195868.236975 197198.333268 4.7278E+03 7.5715E+05 4.0054E-03 1.0000 +488 7 3S -10 3P 1-0 1330.103006 cm-1 195868.236975 197198.339982 4.7278E+03 7.5716E+05 1.3351E-03 1.0000 +489 7 3P - 7 3D Mean 42.355679 cm-1 196027.317947 196069.673625 3.0529E+02 6.1663E+06 4.2579E-01 1.0000 +489 7 3P - 7 3D 0-1 42.340025 cm-1 196027.336465 196069.676490 1.6961E+02 6.1664E+06 4.2580E-01 1.0000 +489 7 3P - 7 3D 1-2 42.356409 cm-1 196027.316641 196069.673050 2.2896E+02 6.1661E+06 3.1933E-01 0.9999 +489 7 3P - 7 3D 2-3 42.357782 cm-1 196027.315027 196069.672809 3.0530E+02 6.1664E+06 3.5767E-01 1.0000 +489 7 3P - 7 3D 2-2 42.358023 cm-1 196027.315027 196069.673050 7.6318E+01 6.1661E+06 6.3864E-02 0.9999 +489 7 3P - 7 3D 1-1 42.359849 cm-1 196027.316641 196069.676490 1.2721E+02 6.1664E+06 1.0645E-01 1.0000 +489 7 3P - 7 3D 2-1 42.361463 cm-1 196027.315027 196069.676490 8.4805E+00 6.1664E+06 4.2580E-03 1.0000 +490 7 3P - 8 3S Mean 434.043864 cm-1 196027.317947 196461.361811 1.7296E+05 2.4913E+06 4.5869E-01 1.0000 +490 7 3P - 8 3S 0-1 434.025346 cm-1 196027.336465 196461.361811 1.9217E+04 2.4913E+06 4.5869E-01 1.0000 +490 7 3P - 8 3S 1-1 434.045170 cm-1 196027.316641 196461.361811 5.7652E+04 2.4913E+06 4.5869E-01 1.0000 +490 7 3P - 8 3S 2-1 434.046784 cm-1 196027.315027 196461.361811 9.6087E+04 2.4913E+06 4.5869E-01 1.0000 +491 7 3P - 8 3D Mean 567.744803 cm-1 196027.317947 196595.062750 5.7426E+04 4.1689E+06 4.4509E-01 1.0000 +491 7 3P - 8 3D 0-1 567.728203 cm-1 196027.336465 196595.064668 3.1904E+04 4.1690E+06 4.4510E-01 1.0000 +491 7 3P - 8 3D 1-2 567.745724 cm-1 196027.316641 196595.062365 4.3067E+04 4.1688E+06 3.3380E-01 0.9999 +491 7 3P - 8 3D 2-3 567.747176 cm-1 196027.315027 196595.062202 5.7427E+04 4.1690E+06 3.7388E-01 1.0000 +491 7 3P - 8 3D 2-2 567.747338 cm-1 196027.315027 196595.062365 1.4356E+04 4.1688E+06 6.6761E-02 0.9999 +491 7 3P - 8 3D 1-1 567.748027 cm-1 196027.316641 196595.064668 2.3928E+04 4.1690E+06 1.1127E-01 1.0000 +491 7 3P - 8 3D 2-1 567.749641 cm-1 196027.315027 196595.064668 1.5952E+03 4.1690E+06 4.4510E-03 1.0000 +492 7 3P - 9 3S Mean 834.669393 cm-1 196027.317947 196861.987340 9.8610E+04 1.7692E+06 7.0719E-02 1.0000 +492 7 3P - 9 3S 0-1 834.650875 cm-1 196027.336465 196861.987340 1.0957E+04 1.7692E+06 7.0721E-02 1.0000 +492 7 3P - 9 3S 1-1 834.670699 cm-1 196027.316641 196861.987340 3.2870E+04 1.7692E+06 7.0719E-02 1.0000 +492 7 3P - 9 3S 2-1 834.672313 cm-1 196027.315027 196861.987340 5.4783E+04 1.7692E+06 7.0718E-02 1.0000 +493 7 3P - 9 3D Mean 927.908965 cm-1 196027.317947 196955.226911 4.5472E+04 2.9483E+06 1.3193E-01 1.0000 +493 7 3P - 9 3D 0-1 927.891793 cm-1 196027.336465 196955.228258 2.5263E+04 2.9484E+06 1.3194E-01 1.0000 +493 7 3P - 9 3D 1-2 927.910001 cm-1 196027.316641 196955.226641 3.4102E+04 2.9482E+06 9.8944E-02 0.9999 +493 7 3P - 9 3D 2-3 927.911500 cm-1 196027.315027 196955.226527 4.5473E+04 2.9483E+06 1.1083E-01 1.0000 +493 7 3P - 9 3D 2-2 927.911615 cm-1 196027.315027 196955.226641 1.1367E+04 2.9482E+06 1.9788E-02 0.9999 +493 7 3P - 9 3D 1-1 927.911618 cm-1 196027.316641 196955.228258 1.8947E+04 2.9484E+06 3.2984E-02 1.0000 +493 7 3P - 9 3D 2-1 927.913232 cm-1 196027.315027 196955.228258 1.2631E+03 2.9484E+06 1.3193E-03 1.0000 +494 7 3P -10 3S Mean 1117.915311 cm-1 196027.317947 197145.233258 6.5217E+04 1.2990E+06 2.6073E-02 1.0000 +494 7 3P -10 3S 0-1 1117.896793 cm-1 196027.336465 197145.233258 7.2464E+03 1.2990E+06 2.6073E-02 1.0000 +494 7 3P -10 3S 1-1 1117.916617 cm-1 196027.316641 197145.233258 2.1739E+04 1.2990E+06 2.6073E-02 1.0000 +494 7 3P -10 3S 2-1 1117.918231 cm-1 196027.315027 197145.233258 3.6232E+04 1.2990E+06 2.6073E-02 1.0000 +495 7 3D - 7 3F Mean 1.503565 cm-1 196069.673625 196071.177191 1.1963E-02 2.6643E+06 1.1116E-02 0.9195 +495 7 3D - 7 3F 1-2 1.502240 cm-1 196069.676490 196071.178730 1.0927E-02 2.6646E+06 1.2087E-02 1.0000 +495 7 3D - 7 3F 2-3 1.503128 cm-1 196069.673050 196071.176178 8.7876E-03 2.6638E+06 8.1651E-03 0.7600 +495 7 3D - 7 3F 3-3 1.503369 cm-1 196069.672809 196071.176178 1.0863E-03 2.6638E+06 7.2096E-04 0.7516 +495 7 3D - 7 3F 3-4 1.504315 cm-1 196069.672809 196071.177123 1.3008E-02 2.6646E+06 1.1100E-02 1.0000 +495 7 3D - 7 3F 2-2 1.505680 cm-1 196069.673050 196071.178730 2.0234E-03 2.6646E+06 1.3429E-03 0.9999 +495 7 3D - 7 3F 3-2 1.505921 cm-1 196069.672809 196071.178730 5.7815E-05 2.6646E+06 2.7408E-05 1.0000 +496 7 3D - 8 3P Mean 497.040142 cm-1 196069.673625 196566.713767 4.5429E+04 1.3990E+06 1.6535E-01 1.0000 +496 7 3D - 8 3P 1-2 497.035332 cm-1 196069.676490 196566.711822 4.5430E+02 1.3990E+06 4.5931E-03 1.0000 +496 7 3D - 8 3P 1-1 497.036407 cm-1 196069.676490 196566.712897 1.1358E+04 1.3990E+06 6.8900E-02 1.0000 +496 7 3D - 8 3P 2-2 497.038772 cm-1 196069.673050 196566.711822 6.8140E+03 1.3990E+06 4.1335E-02 0.9999 +496 7 3D - 8 3P 3-2 497.039013 cm-1 196069.672809 196566.711822 3.8161E+04 1.3990E+06 1.6535E-01 1.0000 +496 7 3D - 8 3P 2-1 497.039847 cm-1 196069.673050 196566.712897 3.4070E+04 1.3990E+06 1.2401E-01 0.9999 +496 7 3D - 8 3P 1-0 497.049615 cm-1 196069.676490 196566.726105 4.5430E+04 1.3990E+06 9.1863E-02 1.0000 +497 7 3D - 8 3F Mean 526.405795 cm-1 196069.673625 196596.079420 1.0122E+05 1.7997E+06 7.6651E-01 0.9239 +497 7 3D - 8 3F 1-2 526.403952 cm-1 196069.676490 196596.080442 9.2036E+04 1.7998E+06 8.2967E-01 1.0000 +497 7 3D - 8 3F 2-3 526.405710 cm-1 196069.673050 196596.078760 7.5234E+04 1.7993E+06 5.6970E-01 0.7725 +497 7 3D - 8 3F 3-3 526.405951 cm-1 196069.672809 196596.078760 9.3036E+03 1.7993E+06 5.0321E-02 0.7642 +497 7 3D - 8 3F 3-4 526.406557 cm-1 196069.672809 196596.079366 1.0957E+05 1.7999E+06 7.6197E-01 1.0000 +497 7 3D - 8 3F 2-2 526.407392 cm-1 196069.673050 196596.080442 1.7042E+04 1.7998E+06 9.2177E-02 0.9999 +497 7 3D - 8 3F 3-2 526.407633 cm-1 196069.672809 196596.080442 4.8696E+02 1.7998E+06 1.8813E-03 1.0000 +498 7 3D - 9 3P Mean 865.659153 cm-1 196069.673625 196935.332779 2.7704E+04 1.0146E+06 3.3245E-02 1.0000 +498 7 3D - 9 3P 1-2 865.654929 cm-1 196069.676490 196935.331418 2.7705E+02 1.0146E+06 9.2350E-04 1.0000 +498 7 3D - 9 3P 1-1 865.655680 cm-1 196069.676490 196935.332170 6.9262E+03 1.0146E+06 1.3852E-02 1.0000 +498 7 3D - 9 3P 2-2 865.658368 cm-1 196069.673050 196935.331418 4.1554E+03 1.0146E+06 8.3108E-03 0.9999 +498 7 3D - 9 3P 3-2 865.658609 cm-1 196069.672809 196935.331418 2.3272E+04 1.0146E+06 3.3246E-02 1.0000 +498 7 3D - 9 3P 2-1 865.659120 cm-1 196069.673050 196935.332170 2.0777E+04 1.0146E+06 2.4932E-02 0.9999 +498 7 3D - 9 3P 1-0 865.664918 cm-1 196069.676490 196935.341408 2.7705E+04 1.0146E+06 1.8470E-02 1.0000 +499 7 3D - 9 3F Mean 886.271846 cm-1 196069.673625 196955.945471 7.2520E+04 1.2727E+06 1.9373E-01 0.9266 +499 7 3D - 9 3F 1-2 886.269695 cm-1 196069.676490 196955.946185 6.5739E+04 1.2728E+06 2.0906E-01 1.0000 +499 7 3D - 9 3F 2-3 886.271967 cm-1 196069.673050 196955.945017 5.4320E+04 1.2724E+06 1.4511E-01 0.7808 +499 7 3D - 9 3F 3-3 886.272208 cm-1 196069.672809 196955.945017 6.7191E+03 1.2724E+06 1.2821E-02 0.7727 +499 7 3D - 9 3F 3-4 886.272620 cm-1 196069.672809 196955.945429 7.8261E+04 1.2728E+06 1.9200E-01 1.0000 +499 7 3D - 9 3F 2-2 886.273135 cm-1 196069.673050 196955.946185 1.2173E+04 1.2728E+06 2.3228E-02 0.9999 +499 7 3D - 9 3F 3-2 886.273376 cm-1 196069.672809 196955.946185 3.4783E+02 1.2728E+06 4.7407E-04 1.0000 +500 7 3D -10 3P Mean 1128.660085 cm-1 196069.673625 197198.333711 1.8409E+04 7.5715E+05 1.2995E-02 1.0000 +500 7 3D -10 3P 1-2 1128.656233 cm-1 196069.676490 197198.332722 1.8409E+02 7.5715E+05 3.6098E-04 1.0000 +500 7 3D -10 3P 1-1 1128.656779 cm-1 196069.676490 197198.333268 4.6023E+03 7.5715E+05 5.4148E-03 1.0000 +500 7 3D -10 3P 2-2 1128.659672 cm-1 196069.673050 197198.332722 2.7611E+03 7.5715E+05 3.2485E-03 0.9999 +500 7 3D -10 3P 3-2 1128.659913 cm-1 196069.672809 197198.332722 1.5464E+04 7.5715E+05 1.2996E-02 1.0000 +500 7 3D -10 3P 2-1 1128.660218 cm-1 196069.673050 197198.333268 1.3806E+04 7.5715E+05 9.7460E-03 0.9999 +500 7 3D -10 3P 1-0 1128.663492 cm-1 196069.676490 197198.339982 1.8409E+04 7.5716E+05 7.2196E-03 1.0000 +501 7 3D -10 3F Mean 1143.678700 cm-1 196069.673625 197213.352326 5.2198E+04 9.3313E+05 8.3737E-02 0.9286 +501 7 3D -10 3F 1-2 1143.676354 cm-1 196069.676490 197213.352843 4.7217E+04 9.3321E+05 9.0174E-02 1.0000 +501 7 3D -10 3F 2-3 1143.678948 cm-1 196069.673050 197213.351998 3.9310E+04 9.3293E+05 6.3061E-02 0.7867 +501 7 3D -10 3F 3-3 1143.679189 cm-1 196069.672809 197213.351998 4.8633E+03 9.3293E+05 5.5727E-03 0.7787 +501 7 3D -10 3F 3-4 1143.679484 cm-1 196069.672809 197213.352292 5.6211E+04 9.3323E+05 8.2813E-02 1.0000 +501 7 3D -10 3F 2-2 1143.679793 cm-1 196069.673050 197213.352843 8.7432E+03 9.3321E+05 1.0019E-02 0.9999 +501 7 3D -10 3F 3-2 1143.680034 cm-1 196069.672809 197213.352843 2.4983E+02 9.3321E+05 2.0448E-04 1.0000 +502 7 3F - 8 3D Mean 523.885559 cm-1 196071.177191 196595.062750 1.4995E+04 4.1689E+06 5.8489E-02 0.9196 +502 7 3F - 8 3D 2-3 523.883472 cm-1 196071.178730 196595.062202 3.6974E+01 4.1690E+06 2.8268E-04 1.0000 +502 7 3F - 8 3D 2-2 523.883635 cm-1 196071.178730 196595.062365 1.8116E+03 4.1688E+06 9.8930E-03 0.9999 +502 7 3F - 8 3D 4-3 523.885079 cm-1 196071.177123 196595.062202 1.4974E+04 4.1690E+06 6.3600E-02 1.0000 +502 7 3F - 8 3D 2-1 523.885938 cm-1 196071.178730 196595.064668 1.6305E+04 4.1690E+06 5.3424E-02 1.0000 +502 7 3F - 8 3D 3-3 523.886024 cm-1 196071.176178 196595.062202 9.7261E+02 4.1690E+06 5.3114E-03 0.7516 +502 7 3F - 8 3D 3-2 523.886187 cm-1 196071.176178 196595.062365 1.1012E+04 4.1688E+06 4.2954E-02 0.7598 +503 7 3F - 8 3G Mean 525.033075 cm-1 196071.177191 196596.210266 1.4957E+05 1.0641E+06 1.0456E+00 0.9736 +503 7 3F - 8 3G 2-3 525.032216 cm-1 196071.178730 196596.210946 1.4109E+05 1.0641E+06 1.0740E+00 1.0000 +503 7 3F - 8 3G 4-4 525.032533 cm-1 196071.177123 196596.209656 4.9927E+03 1.0641E+06 2.7146E-02 0.5200 +503 7 3F - 8 3G 4-5 525.033208 cm-1 196071.177123 196596.210331 1.5363E+05 1.0641E+06 1.0209E+00 1.0000 +503 7 3F - 8 3G 3-4 525.033479 cm-1 196071.176178 196596.209656 1.3883E+05 1.0641E+06 9.7050E-01 0.9639 +503 7 3F - 8 3G 4-3 525.033823 cm-1 196071.177123 196596.210946 1.9595E+02 1.0641E+06 8.2865E-04 1.0000 +503 7 3F - 8 3G 3-3 525.034768 cm-1 196071.176178 196596.210946 9.2783E+03 1.0641E+06 5.0447E-02 0.7516 +504 7 3F - 9 3D Mean 884.049720 cm-1 196071.177191 196955.226911 8.6942E+03 2.9483E+06 1.1909E-02 0.9196 +504 7 3F - 9 3D 2-3 884.047797 cm-1 196071.178730 196955.226527 2.1439E+01 2.9483E+06 5.7560E-05 1.0000 +504 7 3F - 9 3D 2-2 884.047911 cm-1 196071.178730 196955.226641 1.0504E+03 2.9482E+06 2.0144E-03 0.9999 +504 7 3F - 9 3D 4-3 884.049403 cm-1 196071.177123 196955.226527 8.6827E+03 2.9483E+06 1.2951E-02 1.0000 +504 7 3F - 9 3D 2-1 884.049528 cm-1 196071.178730 196955.228258 9.4545E+03 2.9484E+06 1.0879E-02 1.0000 +504 7 3F - 9 3D 3-3 884.050349 cm-1 196071.176178 196955.226527 5.6395E+02 2.9483E+06 1.0815E-03 0.7516 +504 7 3F - 9 3D 3-2 884.050463 cm-1 196071.176178 196955.226641 6.3841E+03 2.9482E+06 8.7450E-03 0.7597 +505 7 3F - 9 3G Mean 884.861100 cm-1 196071.177191 196956.038291 1.0037E+05 7.5280E+05 2.4702E-01 0.9736 +505 7 3F - 9 3G 2-3 884.860039 cm-1 196071.178730 196956.038769 9.4677E+04 7.5280E+05 2.5372E-01 1.0000 +505 7 3F - 9 3G 4-4 884.860740 cm-1 196071.177123 196956.037863 3.3514E+03 7.5280E+05 6.4153E-03 0.5201 +505 7 3F - 9 3G 4-5 884.861214 cm-1 196071.177123 196956.038337 1.0309E+05 7.5280E+05 2.4119E-01 1.0000 +505 7 3F - 9 3G 4-3 884.861645 cm-1 196071.177123 196956.038769 1.3150E+02 7.5280E+05 1.9578E-04 1.0000 +505 7 3F - 9 3G 3-4 884.861685 cm-1 196071.176178 196956.037863 9.3169E+04 7.5280E+05 2.2930E-01 0.9640 +505 7 3F - 9 3G 3-3 884.862591 cm-1 196071.176178 196956.038769 6.2262E+03 7.5280E+05 1.1918E-02 0.7516 +506 7 3F -10 3G Mean 1142.243282 cm-1 196071.177191 197213.420472 6.9077E+04 5.5231E+05 1.0202E-01 0.9736 +506 7 3F -10 3G 2-3 1142.242091 cm-1 196071.178730 197213.420821 6.5159E+04 5.5231E+05 1.0479E-01 1.0000 +506 7 3F -10 3G 4-4 1142.243037 cm-1 196071.177123 197213.420161 2.3071E+03 5.5231E+05 2.6503E-03 0.5203 +506 7 3F -10 3G 4-5 1142.243382 cm-1 196071.177123 197213.420506 7.0951E+04 5.5231E+05 9.9617E-02 1.0000 +506 7 3F -10 3G 4-3 1142.243697 cm-1 196071.177123 197213.420821 9.0499E+01 5.5231E+05 8.0858E-05 1.0000 +506 7 3F -10 3G 3-4 1142.243983 cm-1 196071.176178 197213.420161 6.4125E+04 5.5231E+05 9.4710E-02 0.9640 +506 7 3F -10 3G 3-3 1142.244643 cm-1 196071.176178 197213.420821 4.2851E+03 5.5231E+05 4.9225E-03 0.7516 +507 7 3G - 8 3F Mean 524.709772 cm-1 196071.369648 196596.079420 8.2583E+03 1.7997E+06 3.4966E-02 0.9713 +507 7 3G - 8 3F 3-3 524.708096 cm-1 196071.370664 196596.078760 4.0608E+02 1.7993E+06 2.2106E-03 0.7642 +507 7 3G - 8 3F 3-4 524.708702 cm-1 196071.370664 196596.079366 6.5601E+00 1.7999E+06 4.5915E-05 1.0000 +507 7 3G - 8 3F 5-4 524.709620 cm-1 196071.369746 196596.079366 8.0820E+03 1.7999E+06 3.5997E-02 1.0000 +507 7 3G - 8 3F 3-2 524.709778 cm-1 196071.370664 196596.080442 8.5019E+03 1.7998E+06 3.3059E-02 1.0000 +507 7 3G - 8 3F 4-3 524.710022 cm-1 196071.368738 196596.078760 7.6202E+03 1.7993E+06 3.2264E-02 0.9560 +507 7 3G - 8 3F 4-4 524.710628 cm-1 196071.368738 196596.079366 2.1481E+02 1.7999E+06 1.1694E-03 0.5198 +508 7 3G - 8 3H Mean 524.871821 cm-1 196071.369648 196596.241469 2.0794E+05 7.0248E+05 1.3827E+00 0.9935 +508 7 3G - 8 3H 3-4 524.871243 cm-1 196071.370664 196596.241907 1.9896E+05 7.0248E+05 1.3917E+00 1.0000 +508 7 3G - 8 3H 5-5 524.871320 cm-1 196071.369746 196596.241066 4.3137E+03 7.0248E+05 2.3468E-02 0.5153 +508 7 3G - 8 3H 5-6 524.871761 cm-1 196071.369746 196596.241507 2.0930E+05 7.0248E+05 1.3457E+00 1.0000 +508 7 3G - 8 3H 5-4 524.872160 cm-1 196071.369746 196596.241907 1.0336E+02 7.0248E+05 4.6008E-04 1.0000 +508 7 3G - 8 3H 4-5 524.872328 cm-1 196071.368738 196596.241066 2.0494E+05 7.0248E+05 1.3627E+00 1.0200 +508 7 3G - 8 3H 4-4 524.873169 cm-1 196071.368738 196596.241907 5.3184E+03 7.0248E+05 2.8934E-02 0.5198 +509 7 3G - 9 3F Mean 884.575823 cm-1 196071.369648 196955.945471 4.2967E+03 1.2727E+06 6.4011E-03 0.9698 +509 7 3G - 9 3F 3-3 884.574353 cm-1 196071.370664 196955.945017 2.1396E+02 1.2724E+06 4.0983E-04 0.7726 +509 7 3G - 9 3F 3-4 884.574765 cm-1 196071.370664 196955.945429 3.4186E+00 1.2728E+06 8.4190E-06 1.0000 +509 7 3G - 9 3F 3-2 884.575521 cm-1 196071.370664 196955.946185 4.4304E+03 1.2728E+06 6.0616E-03 1.0000 +509 7 3G - 9 3F 5-4 884.575683 cm-1 196071.369746 196955.945429 4.2117E+03 1.2728E+06 6.6005E-03 1.0000 +509 7 3G - 9 3F 4-3 884.576278 cm-1 196071.368738 196955.945017 3.9481E+03 1.2724E+06 5.8818E-03 0.9505 +509 7 3G - 9 3F 4-4 884.576691 cm-1 196071.368738 196955.945429 1.1194E+02 1.2728E+06 2.1441E-04 0.5198 +510 7 3G - 9 3H Mean 884.690917 cm-1 196071.369648 196956.060565 1.2349E+05 4.9674E+05 2.8904E-01 0.9936 +510 7 3G - 9 3H 3-4 884.690208 cm-1 196071.370664 196956.060872 1.1816E+05 4.9674E+05 2.9092E-01 1.0000 +510 7 3G - 9 3H 5-5 884.690536 cm-1 196071.369746 196956.060282 2.5617E+03 4.9674E+05 4.9055E-03 0.5153 +510 7 3G - 9 3H 5-6 884.690845 cm-1 196071.369746 196956.060591 1.2430E+05 4.9674E+05 2.8131E-01 1.0000 +510 7 3G - 9 3H 5-4 884.691126 cm-1 196071.369746 196956.060872 6.1380E+01 4.9674E+05 9.6169E-05 1.0000 +510 7 3G - 9 3H 4-5 884.691544 cm-1 196071.368738 196956.060282 1.2171E+05 4.9674E+05 2.8486E-01 1.0200 +510 7 3G - 9 3H 4-4 884.692134 cm-1 196071.368738 196956.060872 3.1584E+03 4.9674E+05 6.0482E-03 0.5198 +511 7 3G -10 3F Mean 1141.982678 cm-1 196071.369648 197213.352326 2.5491E+03 9.3313E+05 2.2786E-03 0.9687 +511 7 3G -10 3F 3-3 1141.981334 cm-1 196071.370664 197213.351998 1.2807E+02 9.3293E+05 1.4719E-04 0.7788 +511 7 3G -10 3F 3-4 1141.981629 cm-1 196071.370664 197213.352292 2.0305E+00 9.3323E+05 3.0003E-06 1.0000 +511 7 3G -10 3F 3-2 1141.982179 cm-1 196071.370664 197213.352843 2.6316E+03 9.3321E+05 2.1603E-03 1.0000 +511 7 3G -10 3F 5-4 1141.982546 cm-1 196071.369746 197213.352292 2.5016E+03 9.3323E+05 2.3523E-03 1.0000 +511 7 3G -10 3F 4-3 1141.983260 cm-1 196071.368738 197213.351998 2.3351E+03 9.3293E+05 2.0873E-03 0.9465 +511 7 3G -10 3F 4-4 1141.983554 cm-1 196071.368738 197213.352292 6.6491E+01 9.3323E+05 7.6416E-05 0.5197 +512 7 3G -10 3H Mean 1142.067249 cm-1 196071.369648 197213.436897 7.8507E+04 3.6446E+05 1.1026E-01 0.9935 +512 7 3G -10 3H 3-4 1142.066457 cm-1 196071.370664 197213.437121 7.5117E+04 3.6446E+05 1.1098E-01 1.0000 +512 7 3G -10 3H 5-5 1142.066944 cm-1 196071.369746 197213.436691 1.6286E+03 3.6446E+05 1.8714E-03 0.5153 +512 7 3G -10 3H 5-6 1142.067170 cm-1 196071.369746 197213.436916 7.9019E+04 3.6446E+05 1.0731E-01 1.0000 +512 7 3G -10 3H 5-4 1142.067375 cm-1 196071.369746 197213.437121 3.9022E+01 3.6446E+05 3.6687E-05 1.0000 +512 7 3G -10 3H 4-5 1142.067953 cm-1 196071.368738 197213.436691 7.7373E+04 3.6446E+05 1.0867E-01 1.0200 +512 7 3G -10 3H 4-4 1142.068383 cm-1 196071.368738 197213.437121 2.0079E+03 3.6446E+05 2.3073E-03 0.5198 +513 7 3H - 8 3G Mean 524.795152 cm-1 196071.415114 196596.210266 3.8362E+03 1.0641E+06 1.7081E-02 0.9935 +513 7 3H - 8 3G 4-4 524.793889 cm-1 196071.415767 196596.209656 8.0310E+01 1.0641E+06 4.3705E-04 0.5199 +513 7 3H - 8 3G 4-5 524.794564 cm-1 196071.415767 196596.210331 1.2764E+00 1.0641E+06 8.4898E-06 1.0000 +513 7 3H - 8 3G 5-4 524.795144 cm-1 196071.414513 196596.209656 3.7808E+03 1.0641E+06 1.6834E-02 1.0200 +513 7 3H - 8 3G 6-5 524.795161 cm-1 196071.415170 196596.210331 3.7336E+03 1.0641E+06 1.7192E-02 1.0000 +513 7 3H - 8 3G 4-3 524.795179 cm-1 196071.415767 196596.210946 3.8612E+03 1.0641E+06 1.6343E-02 1.0000 +513 7 3H - 8 3G 5-5 524.795819 cm-1 196071.414513 196596.210331 6.5111E+01 1.0641E+06 3.5433E-04 0.5152 +514 7 3H - 8 3I Mean 524.836224 cm-1 196071.415114 196596.251337 2.7950E+05 4.9846E+05 1.7973E+00 0.9955 +514 7 3H - 8 3I 4-5 524.835876 cm-1 196071.415767 196596.251643 2.7149E+05 4.9846E+05 1.8055E+00 1.0000 +514 7 3H - 8 3I 6-6 524.835882 cm-1 196071.415170 196596.251052 4.0001E+03 4.9846E+05 2.1765E-02 0.5129 +514 7 3H - 8 3I 6-7 524.836191 cm-1 196071.415170 196596.251361 2.8077E+05 4.9846E+05 1.7628E+00 1.0000 +514 7 3H - 8 3I 6-5 524.836472 cm-1 196071.415170 196596.251643 6.4455E+01 4.9846E+05 2.9676E-04 1.0000 +514 7 3H - 8 3I 5-6 524.836539 cm-1 196071.414513 196596.251052 2.7674E+05 4.9846E+05 1.7796E+00 1.0138 +514 7 3H - 8 3I 5-5 524.837130 cm-1 196071.414513 196596.251643 4.7492E+03 4.9846E+05 2.5841E-02 0.5153 +515 7 3H - 9 3G Mean 884.623177 cm-1 196071.415114 196956.038291 1.7320E+03 7.5280E+05 2.7141E-03 0.9935 +515 7 3H - 9 3G 4-4 884.622096 cm-1 196071.415767 196956.037863 3.6271E+01 7.5280E+05 6.9468E-05 0.5202 +515 7 3H - 9 3G 4-5 884.622570 cm-1 196071.415767 196956.038337 5.7630E-01 7.5280E+05 1.3490E-06 1.0000 +515 7 3H - 9 3G 4-3 884.623002 cm-1 196071.415767 196956.038769 1.7433E+03 7.5280E+05 2.5969E-03 1.0000 +515 7 3H - 9 3G 6-5 884.623167 cm-1 196071.415170 196956.038337 1.6857E+03 7.5280E+05 2.7318E-03 1.0000 +515 7 3H - 9 3G 5-4 884.623351 cm-1 196071.414513 196956.037863 1.7070E+03 7.5280E+05 2.6749E-03 1.0200 +515 7 3H - 9 3G 5-5 884.623824 cm-1 196071.414513 196956.038337 2.9397E+01 7.5280E+05 5.6302E-05 0.5151 +516 7 3H - 9 3I Mean 884.652552 cm-1 196071.415114 196956.067666 1.3094E+05 3.5197E+05 2.9635E-01 0.9955 +516 7 3H - 9 3I 4-5 884.652113 cm-1 196071.415767 196956.067880 1.2718E+05 3.5197E+05 2.9769E-01 1.0000 +516 7 3H - 9 3I 6-6 884.652295 cm-1 196071.415170 196956.067465 1.8739E+03 3.5197E+05 3.5887E-03 0.5129 +516 7 3H - 9 3I 6-7 884.652512 cm-1 196071.415170 196956.067682 1.3153E+05 3.5197E+05 2.9065E-01 1.0000 +516 7 3H - 9 3I 6-5 884.652710 cm-1 196071.415170 196956.067880 3.0195E+01 3.5197E+05 4.8930E-05 1.0000 +516 7 3H - 9 3I 5-6 884.652953 cm-1 196071.414513 196956.067465 1.2965E+05 3.5197E+05 2.9344E-01 1.0138 +516 7 3H - 9 3I 5-5 884.653367 cm-1 196071.414513 196956.067880 2.2248E+03 3.5197E+05 4.2607E-03 0.5153 +517 7 3H -10 3I Mean 1142.027048 cm-1 196071.415114 197213.442162 7.2318E+04 1.5881E+05 9.8217E-02 0.9955 +517 7 3H -10 3I 4-5 1142.026551 cm-1 196071.415767 197213.442318 7.0245E+04 2.5807E+05 9.8663E-02 1.0000 +517 7 3H -10 3I 6-6 1142.026846 cm-1 196071.415170 197213.442016 1.0350E+03 2.5807E+05 1.1894E-03 0.5129 +517 7 3H -10 3I 6-7 1142.027004 cm-1 196071.415170 197213.442174 7.2647E+04 0.0000E+00 9.6328E-02 1.0000 +517 7 3H -10 3I 6-5 1142.027148 cm-1 196071.415170 197213.442318 1.6677E+01 2.5807E+05 1.6216E-05 1.0000 +517 7 3H -10 3I 5-6 1142.027503 cm-1 196071.414513 197213.442016 7.1605E+04 2.5807E+05 9.7248E-02 1.0138 +517 7 3H -10 3I 5-5 1142.027806 cm-1 196071.414513 197213.442318 1.2288E+03 2.5807E+05 1.4121E-03 0.5153 +518 7 3I - 8 3H Mean 524.812152 cm-1 196071.429317 196596.241469 1.1856E+03 7.0248E+05 5.4591E-03 0.9955 +518 7 3I - 8 3H 5-5 524.811294 cm-1 196071.429773 196596.241066 1.7046E+01 7.0248E+05 9.2758E-05 0.5156 +518 7 3I - 8 3H 5-6 524.811734 cm-1 196071.429773 196596.241507 1.9576E-01 7.0248E+05 1.2589E-06 1.0000 +518 7 3I - 8 3H 5-4 524.812134 cm-1 196071.429773 196596.241907 1.1910E+03 7.0248E+05 5.3026E-03 1.0000 +518 7 3I - 8 3H 7-6 524.812154 cm-1 196071.429352 196596.241507 1.1628E+03 7.0248E+05 5.4839E-03 1.0000 +518 7 3I - 8 3H 6-5 524.812175 cm-1 196071.428891 196596.241066 1.1739E+03 7.0248E+05 5.4052E-03 1.0138 +518 7 3I - 8 3H 6-6 524.812616 cm-1 196071.428891 196596.241507 1.4358E+01 7.0248E+05 7.8131E-05 0.5128 +519 8 3S - 8 3P Mean 105.351957 cm-1 196461.361811 196566.713767 6.0678E+03 1.3990E+06 2.4579E+00 1.0000 +519 8 3S - 8 3P 1-2 105.350012 cm-1 196461.361811 196566.711822 6.0678E+03 1.3990E+06 1.3655E+00 1.0000 +519 8 3S - 8 3P 1-1 105.351087 cm-1 196461.361811 196566.712897 6.0678E+03 1.3990E+06 8.1930E-01 1.0000 +519 8 3S - 8 3P 1-0 105.364294 cm-1 196461.361811 196566.726105 6.0678E+03 1.3990E+06 2.7310E-01 1.0000 +520 8 3S - 9 3P Mean 473.970968 cm-1 196461.361811 196935.332779 2.0002E+03 1.0146E+06 4.0035E-02 1.0000 +520 8 3S - 9 3P 1-2 473.969608 cm-1 196461.361811 196935.331418 2.0002E+03 1.0146E+06 2.2241E-02 1.0000 +520 8 3S - 9 3P 1-1 473.970360 cm-1 196461.361811 196935.332170 2.0002E+03 1.0146E+06 1.3345E-02 1.0000 +520 8 3S - 9 3P 1-0 473.979598 cm-1 196461.361811 196935.341408 2.0002E+03 1.0146E+06 4.4483E-03 1.0000 +521 8 3S -10 3P Mean 736.971900 cm-1 196461.361811 197198.333711 2.5922E+03 7.5715E+05 2.1460E-02 1.0000 +521 8 3S -10 3P 1-2 736.970912 cm-1 196461.361811 197198.332722 2.5922E+03 7.5715E+05 1.1922E-02 1.0000 +521 8 3S -10 3P 1-1 736.971458 cm-1 196461.361811 197198.333268 2.5922E+03 7.5715E+05 7.1534E-03 1.0000 +521 8 3S -10 3P 1-0 736.978171 cm-1 196461.361811 197198.339982 2.5922E+03 7.5716E+05 2.3845E-03 1.0000 +522 8 3P - 8 3D Mean 28.348982 cm-1 196566.713767 196595.062750 1.5918E+02 4.1689E+06 4.9557E-01 1.0000 +522 8 3P - 8 3D 0-1 28.338564 cm-1 196566.726105 196595.064668 8.8434E+01 4.1690E+06 4.9559E-01 1.0000 +522 8 3P - 8 3D 1-2 28.349468 cm-1 196566.712897 196595.062365 1.1938E+02 4.1688E+06 3.7167E-01 0.9999 +522 8 3P - 8 3D 2-3 28.350380 cm-1 196566.711822 196595.062202 1.5918E+02 4.1690E+06 4.1629E-01 1.0000 +522 8 3P - 8 3D 2-2 28.350543 cm-1 196566.711822 196595.062365 3.9792E+01 4.1688E+06 7.4332E-02 0.9999 +522 8 3P - 8 3D 1-1 28.351771 cm-1 196566.712897 196595.064668 6.6326E+01 4.1690E+06 1.2390E-01 1.0000 +522 8 3P - 8 3D 2-1 28.352846 cm-1 196566.711822 196595.064668 4.4217E+00 4.1690E+06 4.9559E-03 1.0000 +523 8 3P - 9 3S Mean 295.273572 cm-1 196566.713767 196861.987340 9.3840E+04 1.7692E+06 5.3776E-01 1.0000 +523 8 3P - 9 3S 0-1 295.261235 cm-1 196566.726105 196861.987340 1.0427E+04 1.7692E+06 5.3778E-01 1.0000 +523 8 3P - 9 3S 1-1 295.274442 cm-1 196566.712897 196861.987340 3.1280E+04 1.7692E+06 5.3776E-01 1.0000 +523 8 3P - 9 3S 2-1 295.275518 cm-1 196566.711822 196861.987340 5.2133E+04 1.7692E+06 5.3776E-01 1.0000 +524 8 3P - 9 3D Mean 388.513144 cm-1 196566.713767 196955.226911 2.7822E+04 2.9483E+06 4.6048E-01 1.0000 +524 8 3P - 9 3D 0-1 388.502154 cm-1 196566.726105 196955.228258 1.5457E+04 2.9484E+06 4.6050E-01 1.0000 +524 8 3P - 9 3D 1-2 388.513744 cm-1 196566.712897 196955.226641 2.0865E+04 2.9482E+06 3.4534E-01 0.9999 +524 8 3P - 9 3D 2-3 388.514705 cm-1 196566.711822 196955.226527 2.7822E+04 2.9483E+06 3.8681E-01 1.0000 +524 8 3P - 9 3D 2-2 388.514819 cm-1 196566.711822 196955.226641 6.9550E+03 2.9482E+06 6.9068E-02 0.9999 +524 8 3P - 9 3D 1-1 388.515361 cm-1 196566.712897 196955.228258 1.1593E+04 2.9484E+06 1.1513E-01 1.0000 +524 8 3P - 9 3D 2-1 388.516436 cm-1 196566.711822 196955.228258 7.7284E+02 2.9484E+06 4.6049E-03 1.0000 +525 8 3P -10 3S Mean 578.519491 cm-1 196566.713767 197145.233258 5.5365E+04 1.2990E+06 8.2649E-02 1.0000 +525 8 3P -10 3S 0-1 578.507153 cm-1 196566.726105 197145.233258 6.1515E+03 1.2990E+06 8.2647E-02 1.0000 +525 8 3P -10 3S 1-1 578.520361 cm-1 196566.712897 197145.233258 1.8455E+04 1.2990E+06 8.2649E-02 1.0000 +525 8 3P -10 3S 2-1 578.521436 cm-1 196566.711822 197145.233258 3.0758E+04 1.2990E+06 8.2649E-02 1.0000 +526 8 3D - 8 3F Mean 1.016670 cm-1 196595.062750 196596.079420 6.6712E-03 1.7997E+06 1.3560E-02 0.9238 +526 8 3D - 8 3F 1-2 1.015774 cm-1 196595.064668 196596.080442 6.0664E-03 1.7998E+06 1.4679E-02 1.0000 +526 8 3D - 8 3F 2-3 1.016395 cm-1 196595.062365 196596.078760 4.9577E-03 1.7993E+06 1.0077E-02 0.7723 +526 8 3D - 8 3F 3-3 1.016558 cm-1 196595.062202 196596.078760 6.1324E-04 1.7993E+06 8.9034E-04 0.7643 +526 8 3D - 8 3F 3-4 1.017164 cm-1 196595.062202 196596.079366 7.2219E-03 1.7999E+06 1.3481E-02 1.0000 +526 8 3D - 8 3F 2-2 1.018077 cm-1 196595.062365 196596.080442 1.1233E-03 1.7998E+06 1.6309E-03 0.9999 +526 8 3D - 8 3F 3-2 1.018240 cm-1 196595.062202 196596.080442 3.2098E-05 1.7998E+06 3.3287E-05 1.0000 +527 8 3D - 9 3P Mean 340.270029 cm-1 196595.062750 196935.332779 2.6504E+04 1.0146E+06 2.0583E-01 1.0000 +527 8 3D - 9 3P 1-2 340.266750 cm-1 196595.064668 196935.331418 2.6504E+02 1.0146E+06 5.7176E-03 1.0000 +527 8 3D - 9 3P 1-1 340.267502 cm-1 196595.064668 196935.332170 6.6261E+03 1.0146E+06 8.5765E-02 1.0000 +527 8 3D - 9 3P 2-2 340.269053 cm-1 196595.062365 196935.331418 3.9753E+03 1.0146E+06 5.1454E-02 0.9999 +527 8 3D - 9 3P 3-2 340.269216 cm-1 196595.062202 196935.331418 2.2264E+04 1.0146E+06 2.0584E-01 1.0000 +527 8 3D - 9 3P 2-1 340.269805 cm-1 196595.062365 196935.332170 1.9877E+04 1.0146E+06 1.5437E-01 0.9999 +527 8 3D - 9 3P 1-0 340.276740 cm-1 196595.064668 196935.341408 2.6504E+04 1.0146E+06 1.1435E-01 1.0000 +528 8 3D - 9 3F Mean 360.882722 cm-1 196595.062750 196955.945471 4.8613E+04 1.2727E+06 7.8323E-01 0.9266 +528 8 3D - 9 3F 1-2 360.881517 cm-1 196595.064668 196955.946185 4.4069E+04 1.2728E+06 8.4526E-01 1.0000 +528 8 3D - 9 3F 2-3 360.882652 cm-1 196595.062365 196955.945017 3.6407E+04 1.2724E+06 5.8657E-01 0.7807 +528 8 3D - 9 3F 3-3 360.882814 cm-1 196595.062202 196955.945017 4.5043E+03 1.2724E+06 5.1837E-02 0.7727 +528 8 3D - 9 3F 3-4 360.883227 cm-1 196595.062202 196955.945429 5.2464E+04 1.2728E+06 7.7628E-01 1.0000 +528 8 3D - 9 3F 2-2 360.883820 cm-1 196595.062365 196955.946185 8.1603E+03 1.2728E+06 9.3911E-02 0.9999 +528 8 3D - 9 3F 3-2 360.883982 cm-1 196595.062202 196955.946185 2.3317E+02 1.2728E+06 1.9167E-03 1.0000 +529 8 3D -10 3P Mean 603.270961 cm-1 196595.062750 197198.333711 1.6855E+04 7.5715E+05 4.1647E-02 1.0000 +529 8 3D -10 3P 1-2 603.268054 cm-1 196595.064668 197198.332722 1.6855E+02 7.5715E+05 1.1568E-03 1.0000 +529 8 3D -10 3P 1-1 603.268600 cm-1 196595.064668 197198.333268 4.2139E+03 7.5715E+05 1.7353E-02 1.0000 +529 8 3D -10 3P 2-2 603.270357 cm-1 196595.062365 197198.332722 2.5281E+03 7.5715E+05 1.0411E-02 0.9999 +529 8 3D -10 3P 3-2 603.270520 cm-1 196595.062202 197198.332722 1.4159E+04 7.5715E+05 4.1649E-02 1.0000 +529 8 3D -10 3P 2-1 603.270903 cm-1 196595.062365 197198.333268 1.2641E+04 7.5715E+05 3.1234E-02 0.9999 +529 8 3D -10 3P 1-0 603.275313 cm-1 196595.064668 197198.339982 1.6855E+04 7.5716E+05 2.3137E-02 1.0000 +530 8 3D -10 3F Mean 618.289576 cm-1 196595.062750 197213.352326 3.6472E+04 9.3313E+05 2.0019E-01 0.9286 +530 8 3D -10 3F 1-2 618.288175 cm-1 196595.064668 197213.352843 3.2993E+04 9.3321E+05 2.1559E-01 1.0000 +530 8 3D -10 3F 2-3 618.289633 cm-1 196595.062365 197213.351998 2.7462E+04 9.3293E+05 1.5074E-01 0.7866 +530 8 3D -10 3F 3-3 618.289796 cm-1 196595.062202 197213.351998 3.3983E+03 9.3293E+05 1.3324E-02 0.7787 +530 8 3D -10 3F 3-4 618.290090 cm-1 196595.062202 197213.352292 3.9278E+04 9.3323E+05 1.9799E-01 1.0000 +530 8 3D -10 3F 2-2 618.290478 cm-1 196595.062365 197213.352843 6.1094E+03 9.3321E+05 2.3953E-02 0.9999 +530 8 3D -10 3F 3-2 618.290641 cm-1 196595.062202 197213.352843 1.7457E+02 9.3321E+05 4.8888E-04 1.0000 +531 8 3F - 9 3D Mean 359.147491 cm-1 196596.079420 196955.226911 9.6344E+03 2.9483E+06 7.9963E-02 0.9238 +531 8 3F - 9 3D 2-3 359.146085 cm-1 196596.080442 196955.226527 2.3650E+01 2.9483E+06 3.8473E-04 1.0000 +531 8 3F - 9 3D 2-2 359.146199 cm-1 196596.080442 196955.226641 1.1587E+03 2.9482E+06 1.3464E-02 0.9999 +531 8 3F - 9 3D 4-3 359.147161 cm-1 196596.079366 196955.226527 9.5782E+03 2.9483E+06 8.6563E-02 1.0000 +531 8 3F - 9 3D 3-3 359.147767 cm-1 196596.078760 196955.226527 6.3257E+02 2.9483E+06 7.3502E-03 0.7642 +531 8 3F - 9 3D 2-1 359.147816 cm-1 196596.080442 196955.228258 1.0430E+04 2.9484E+06 7.2716E-02 1.0000 +531 8 3F - 9 3D 3-2 359.147881 cm-1 196596.078760 196955.226641 7.1583E+03 2.9482E+06 5.9412E-02 0.7721 +532 8 3F - 9 3G Mean 359.958871 cm-1 196596.079420 196956.038291 6.9358E+04 7.5280E+05 1.0315E+00 0.9714 +532 8 3F - 9 3G 2-3 359.958327 cm-1 196596.080442 196956.038769 6.5571E+04 7.5280E+05 1.0619E+00 1.0000 +532 8 3F - 9 3G 4-4 359.958497 cm-1 196596.079366 196956.037863 2.3211E+03 7.5280E+05 2.6849E-02 0.5201 +532 8 3F - 9 3G 4-5 359.958971 cm-1 196596.079366 196956.038337 7.1399E+04 7.5280E+05 1.0094E+00 1.0000 +532 8 3F - 9 3G 3-4 359.959103 cm-1 196596.078760 196956.037863 6.4008E+04 7.5280E+05 9.5195E-01 0.9562 +532 8 3F - 9 3G 4-3 359.959403 cm-1 196596.079366 196956.038769 9.1071E+01 7.5280E+05 8.1935E-04 1.0000 +532 8 3F - 9 3G 3-3 359.960009 cm-1 196596.078760 196956.038769 4.3847E+03 7.5280E+05 5.0720E-02 0.7642 +533 8 3F -10 3G Mean 617.341052 cm-1 196596.079420 197213.420472 4.9935E+04 5.5231E+05 2.5249E-01 0.9714 +533 8 3F -10 3G 2-3 617.340379 cm-1 196596.080442 197213.420821 4.7207E+04 5.5231E+05 2.5991E-01 1.0000 +533 8 3F -10 3G 4-4 617.340795 cm-1 196596.079366 197213.420161 1.6715E+03 5.5231E+05 6.5735E-03 0.5203 +533 8 3F -10 3G 4-5 617.341140 cm-1 196596.079366 197213.420506 5.1404E+04 5.5231E+05 2.4708E-01 1.0000 +533 8 3F -10 3G 3-4 617.341401 cm-1 196596.078760 197213.420161 4.6085E+04 5.5231E+05 2.3302E-01 0.9563 +533 8 3F -10 3G 4-3 617.341455 cm-1 196596.079366 197213.420821 6.5566E+01 5.5231E+05 2.0055E-04 1.0000 +533 8 3F -10 3G 3-3 617.342061 cm-1 196596.078760 197213.420821 3.1567E+03 5.5231E+05 1.2414E-02 0.7642 +534 8 3G - 9 3F Mean 359.735206 cm-1 196596.210266 196955.945471 5.9009E+03 1.2727E+06 5.3155E-02 0.9698 +534 8 3G - 9 3F 3-3 359.734070 cm-1 196596.210946 196955.945017 2.9384E+02 1.2724E+06 3.4032E-03 0.7727 +534 8 3G - 9 3F 3-4 359.734483 cm-1 196596.210946 196955.945429 4.6947E+00 1.2728E+06 6.9908E-05 1.0000 +534 8 3G - 9 3F 5-4 359.735098 cm-1 196596.210331 196955.945429 5.7839E+03 1.2728E+06 5.4808E-02 1.0000 +534 8 3G - 9 3F 3-2 359.735238 cm-1 196596.210946 196955.946185 6.0844E+03 1.2728E+06 5.0334E-02 1.0000 +534 8 3G - 9 3F 4-3 359.735360 cm-1 196596.209656 196955.945017 5.4226E+03 1.2724E+06 4.8847E-02 0.9506 +534 8 3G - 9 3F 4-4 359.735773 cm-1 196596.209656 196955.945429 1.5379E+02 1.2728E+06 1.7812E-03 0.5200 +535 8 3G - 9 3H Mean 359.850299 cm-1 196596.210266 196956.060565 9.3856E+04 4.9674E+05 1.3277E+00 0.9935 +535 8 3G - 9 3H 3-4 359.849926 cm-1 196596.210946 196956.060872 8.9803E+04 4.9674E+05 1.3364E+00 1.0000 +535 8 3G - 9 3H 5-5 359.849950 cm-1 196596.210331 196956.060282 1.9470E+03 4.9674E+05 2.2535E-02 0.5153 +535 8 3G - 9 3H 5-6 359.850260 cm-1 196596.210331 196956.060591 9.4468E+04 4.9674E+05 1.2922E+00 1.0000 +535 8 3G - 9 3H 5-4 359.850541 cm-1 196596.210331 196956.060872 4.6651E+01 4.9674E+05 4.4178E-04 1.0000 +535 8 3G - 9 3H 4-5 359.850625 cm-1 196596.209656 196956.060282 9.2500E+04 4.9674E+05 1.3085E+00 1.0200 +535 8 3G - 9 3H 4-4 359.851216 cm-1 196596.209656 196956.060872 2.4015E+03 4.9674E+05 2.7796E-02 0.5200 +536 8 3G -10 3F Mean 617.142060 cm-1 196596.210266 197213.352326 3.3074E+03 9.3313E+05 1.0123E-02 0.9687 +536 8 3G -10 3F 3-3 617.141052 cm-1 196596.210946 197213.351998 1.6616E+02 9.3293E+05 6.5388E-04 0.7787 +536 8 3G -10 3F 3-4 617.141346 cm-1 196596.210946 197213.352292 2.6345E+00 9.3323E+05 1.3329E-05 1.0000 +536 8 3G -10 3F 3-2 617.141897 cm-1 196596.210946 197213.352843 3.4143E+03 9.3321E+05 9.5972E-03 1.0000 +536 8 3G -10 3F 5-4 617.141961 cm-1 196596.210331 197213.352292 3.2457E+03 9.3323E+05 1.0450E-02 1.0000 +536 8 3G -10 3F 4-3 617.142342 cm-1 196596.209656 197213.351998 3.0300E+03 9.3293E+05 9.2740E-03 0.9466 +536 8 3G -10 3F 4-4 617.142636 cm-1 196596.209656 197213.352292 8.6301E+01 9.3323E+05 3.3961E-04 0.5200 +537 8 3G -10 3H Mean 617.226631 cm-1 196596.210266 197213.436897 6.2632E+04 3.6446E+05 3.0116E-01 0.9935 +537 8 3G -10 3H 3-4 617.226175 cm-1 196596.210946 197213.437121 5.9927E+04 3.6446E+05 3.0312E-01 1.0000 +537 8 3G -10 3H 5-5 617.226359 cm-1 196596.210331 197213.436691 1.2993E+03 3.6446E+05 5.1116E-03 0.5153 +537 8 3G -10 3H 5-6 617.226585 cm-1 196596.210331 197213.436916 6.3040E+04 3.6446E+05 2.9310E-01 1.0000 +537 8 3G -10 3H 5-4 617.226789 cm-1 196596.210331 197213.437121 3.1131E+01 3.6446E+05 1.0021E-04 1.0000 +537 8 3G -10 3H 4-5 617.227034 cm-1 196596.209656 197213.436691 6.1727E+04 3.6446E+05 2.9681E-01 1.0200 +537 8 3G -10 3H 4-4 617.227464 cm-1 196596.209656 197213.437121 1.6026E+03 3.6446E+05 6.3049E-03 0.5200 +538 8 3H - 9 3G Mean 359.796822 cm-1 196596.241469 196956.038291 3.3100E+03 7.5280E+05 3.1354E-02 0.9935 +538 8 3H - 9 3G 4-4 359.795957 cm-1 196596.241907 196956.037863 6.9315E+01 7.5280E+05 8.0251E-04 0.5201 +538 8 3H - 9 3G 4-5 359.796430 cm-1 196596.241907 196956.038337 1.1013E+00 7.5280E+05 1.5584E-05 1.0000 +538 8 3H - 9 3G 5-4 359.796797 cm-1 196596.241066 196956.037863 3.2621E+03 7.5280E+05 3.0901E-02 1.0200 +538 8 3H - 9 3G 6-5 359.796830 cm-1 196596.241507 196956.038337 3.2214E+03 7.5280E+05 3.1559E-02 1.0000 +538 8 3H - 9 3G 4-3 359.796862 cm-1 196596.241907 196956.038769 3.3315E+03 7.5280E+05 3.0000E-02 1.0000 +538 8 3H - 9 3G 5-5 359.797271 cm-1 196596.241066 196956.038337 5.6179E+01 7.5280E+05 6.5043E-04 0.5152 +539 8 3H - 9 3I Mean 359.826197 cm-1 196596.241469 196956.067666 1.2261E+05 3.5197E+05 1.6773E+00 0.9955 +539 8 3H - 9 3I 6-6 359.825958 cm-1 196596.241507 196956.067465 1.7547E+03 3.5197E+05 2.0312E-02 0.5129 +539 8 3H - 9 3I 4-5 359.825973 cm-1 196596.241907 196956.067880 1.1909E+05 3.5197E+05 1.6849E+00 1.0000 +539 8 3H - 9 3I 6-7 359.826175 cm-1 196596.241507 196956.067682 1.2316E+05 3.5197E+05 1.6450E+00 1.0000 +539 8 3H - 9 3I 6-5 359.826373 cm-1 196596.241507 196956.067880 2.8274E+01 3.5197E+05 2.7694E-04 1.0000 +539 8 3H - 9 3I 5-6 359.826399 cm-1 196596.241066 196956.067465 1.2140E+05 3.5197E+05 1.6608E+00 1.0138 +539 8 3H - 9 3I 5-5 359.826814 cm-1 196596.241066 196956.067880 2.0833E+03 3.5197E+05 2.4116E-02 0.5153 +540 8 3H -10 3G Mean 617.179003 cm-1 196596.241469 197213.420472 1.6574E+03 5.5231E+05 5.3359E-03 0.9935 +540 8 3H -10 3G 4-4 617.178254 cm-1 196596.241907 197213.420161 3.4716E+01 5.5231E+05 1.3660E-04 0.5202 +540 8 3H -10 3G 4-5 617.178599 cm-1 196596.241907 197213.420506 5.5147E-01 5.5231E+05 2.6521E-06 1.0000 +540 8 3H -10 3G 4-3 617.178914 cm-1 196596.241907 197213.420821 1.6682E+03 5.5231E+05 5.1053E-03 1.0000 +540 8 3H -10 3G 6-5 617.178999 cm-1 196596.241507 197213.420506 1.6131E+03 5.5231E+05 5.3707E-03 1.0000 +540 8 3H -10 3G 5-4 617.179094 cm-1 196596.241066 197213.420161 1.6335E+03 5.5231E+05 5.2588E-03 1.0200 +540 8 3H -10 3G 5-5 617.179440 cm-1 196596.241066 197213.420506 2.8131E+01 5.5231E+05 1.1069E-04 0.5154 +541 8 3H -10 3I Mean 617.200693 cm-1 196596.241469 197213.442162 7.1250E+04 1.5881E+05 3.3130E-01 0.9955 +541 8 3H -10 3I 4-5 617.200412 cm-1 196596.241907 197213.442318 6.9207E+04 2.5807E+05 3.3280E-01 1.0000 +541 8 3H -10 3I 6-6 617.200509 cm-1 196596.241507 197213.442016 1.0197E+03 2.5807E+05 4.0120E-03 0.5129 +541 8 3H -10 3I 6-7 617.200667 cm-1 196596.241507 197213.442174 7.1573E+04 0.0000E+00 3.2493E-01 1.0000 +541 8 3H -10 3I 6-5 617.200811 cm-1 196596.241507 197213.442318 1.6431E+01 2.5807E+05 5.4702E-05 1.0000 +541 8 3H -10 3I 5-6 617.200950 cm-1 196596.241066 197213.442016 7.0547E+04 2.5807E+05 3.2803E-01 1.0138 +541 8 3H -10 3I 5-5 617.201252 cm-1 196596.241066 197213.442318 1.2106E+03 2.5807E+05 4.7631E-03 0.5153 +542 8 3I - 9 3H Mean 359.809227 cm-1 196596.251337 196956.060565 1.5391E+03 4.9674E+05 1.5077E-02 0.9955 +542 8 3I - 9 3H 5-5 359.808639 cm-1 196596.251643 196956.060282 2.2128E+01 4.9674E+05 2.5617E-04 0.5153 +542 8 3I - 9 3H 5-6 359.808949 cm-1 196596.251643 196956.060591 2.5412E-01 4.9674E+05 3.4768E-06 1.0000 +542 8 3I - 9 3H 5-4 359.809229 cm-1 196596.251643 196956.060872 1.5461E+03 4.9674E+05 1.4645E-02 1.0000 +542 8 3I - 9 3H 6-5 359.809230 cm-1 196596.251052 196956.060282 1.5239E+03 4.9674E+05 1.4928E-02 1.0138 +542 8 3I - 9 3H 7-6 359.809230 cm-1 196596.251361 196956.060591 1.5095E+03 4.9674E+05 1.5145E-02 1.0000 +542 8 3I - 9 3H 6-6 359.809539 cm-1 196596.251052 196956.060591 1.8638E+01 4.9674E+05 2.1577E-04 0.5130 +543 9 3S - 9 3P Mean 73.345439 cm-1 196861.987340 196935.332779 3.3076E+03 1.0146E+06 2.7643E+00 1.0000 +543 9 3S - 9 3P 1-2 73.344079 cm-1 196861.987340 196935.331418 3.3076E+03 1.0146E+06 1.5357E+00 1.0000 +543 9 3S - 9 3P 1-1 73.344830 cm-1 196861.987340 196935.332170 3.3076E+03 1.0146E+06 9.2143E-01 1.0000 +543 9 3S - 9 3P 1-0 73.354069 cm-1 196861.987340 196935.341408 3.3076E+03 1.0146E+06 3.0714E-01 1.0000 +544 9 3S -10 3P Mean 336.346371 cm-1 196861.987340 197198.333711 1.0185E+03 7.5715E+05 4.0481E-02 1.0000 +544 9 3S -10 3P 1-2 336.345383 cm-1 196861.987340 197198.332722 1.0185E+03 7.5715E+05 2.2489E-02 1.0000 +544 9 3S -10 3P 1-1 336.345929 cm-1 196861.987340 197198.333268 1.0185E+03 7.5715E+05 1.3494E-02 1.0000 +544 9 3S -10 3P 1-0 336.352642 cm-1 196861.987340 197198.339982 1.0185E+03 7.5716E+05 4.4979E-03 1.0000 +545 9 3P - 9 3D Mean 19.894132 cm-1 196935.332779 196955.226911 8.9249E+01 2.9483E+06 5.6423E-01 1.0000 +545 9 3P - 9 3D 0-1 19.886850 cm-1 196935.341408 196955.228258 4.9584E+01 2.9484E+06 5.6425E-01 1.0000 +545 9 3P - 9 3D 1-2 19.894471 cm-1 196935.332170 196955.226641 6.6934E+01 2.9482E+06 4.2316E-01 0.9999 +545 9 3P - 9 3D 2-3 19.895109 cm-1 196935.331418 196955.226527 8.9251E+01 2.9483E+06 4.7397E-01 1.0000 +545 9 3P - 9 3D 2-2 19.895223 cm-1 196935.331418 196955.226641 2.2311E+01 2.9482E+06 8.4630E-02 0.9999 +545 9 3P - 9 3D 1-1 19.896088 cm-1 196935.332170 196955.228258 3.7188E+01 2.9484E+06 1.4106E-01 1.0000 +545 9 3P - 9 3D 2-1 19.896840 cm-1 196935.331418 196955.228258 2.4792E+00 2.9484E+06 5.6425E-03 1.0000 +546 9 3P -10 3S Mean 209.900479 cm-1 196935.332779 197145.233258 5.4399E+04 1.2990E+06 6.1690E-01 1.0000 +546 9 3P -10 3S 0-1 209.891850 cm-1 196935.341408 197145.233258 6.0444E+03 1.2990E+06 6.1691E-01 1.0000 +546 9 3P -10 3S 1-1 209.901088 cm-1 196935.332170 197145.233258 1.8133E+04 1.2990E+06 6.1690E-01 1.0000 +546 9 3P -10 3S 2-1 209.901840 cm-1 196935.331418 197145.233258 3.0222E+04 1.2990E+06 6.1691E-01 1.0000 +547 9 3D -10 3P Mean 243.106800 cm-1 196955.226911 197198.333711 1.6240E+04 7.5715E+05 2.4708E-01 1.0000 +547 9 3D -10 3P 1-2 243.104464 cm-1 196955.228258 197198.332722 1.6240E+02 7.5715E+05 6.8634E-03 1.0000 +547 9 3D -10 3P 1-1 243.105010 cm-1 196955.228258 197198.333268 4.0601E+03 7.5715E+05 1.0295E-01 1.0000 +547 9 3D -10 3P 2-2 243.106081 cm-1 196955.226641 197198.332722 2.4359E+03 7.5715E+05 6.1768E-02 0.9999 +547 9 3D -10 3P 3-2 243.106196 cm-1 196955.226527 197198.332722 1.3642E+04 7.5715E+05 2.4709E-01 1.0000 +547 9 3D -10 3P 2-1 243.106627 cm-1 196955.226641 197198.333268 1.2179E+04 7.5715E+05 1.8530E-01 0.9999 +547 9 3D -10 3P 1-0 243.111723 cm-1 196955.228258 197198.339982 1.6240E+04 7.5716E+05 1.3727E-01 1.0000 +548 9 3D -10 3F Mean 258.125414 cm-1 196955.226911 197213.352326 2.5573E+04 9.3313E+05 8.0536E-01 0.9285 +548 9 3D -10 3F 1-2 258.124585 cm-1 196955.228258 197213.352843 2.3135E+04 9.3321E+05 8.6736E-01 1.0000 +548 9 3D -10 3F 2-3 258.125357 cm-1 196955.226641 197213.351998 1.9254E+04 9.3293E+05 6.0636E-01 0.7865 +548 9 3D -10 3F 3-3 258.125472 cm-1 196955.226527 197213.351998 2.3828E+03 9.3293E+05 5.3600E-02 0.7787 +548 9 3D -10 3F 3-4 258.125766 cm-1 196955.226527 197213.352292 2.7541E+04 9.3323E+05 7.9653E-01 1.0000 +548 9 3D -10 3F 2-2 258.126202 cm-1 196955.226641 197213.352843 4.2839E+03 9.3321E+05 9.6365E-02 0.9999 +548 9 3D -10 3F 3-2 258.126317 cm-1 196955.226527 197213.352843 1.2241E+02 9.3321E+05 1.9668E-03 1.0000 +549 9 3F -10 3G Mean 257.475001 cm-1 196955.945471 197213.420472 3.5490E+04 5.5231E+05 1.0316E+00 0.9699 +549 9 3F -10 3G 2-3 257.474636 cm-1 196955.946185 197213.420821 3.3605E+04 5.5231E+05 1.0637E+00 1.0000 +549 9 3F -10 3G 4-4 257.474732 cm-1 196955.945429 197213.420161 1.1898E+03 5.5231E+05 2.6900E-02 0.5203 +549 9 3F -10 3G 4-5 257.475077 cm-1 196955.945429 197213.420506 3.6592E+04 5.5231E+05 1.0111E+00 1.0000 +549 9 3F -10 3G 3-4 257.475144 cm-1 196955.945017 197213.420161 3.2617E+04 5.5231E+05 9.4811E-01 0.9508 +549 9 3F -10 3G 4-3 257.475392 cm-1 196955.945429 197213.420821 4.6674E+01 5.5231E+05 8.2073E-04 1.0000 +549 9 3F -10 3G 3-3 257.475804 cm-1 196955.945017 197213.420821 2.2721E+03 5.5231E+05 5.1369E-02 0.7727 +550 9 3G -10 3F Mean 257.314035 cm-1 196956.038291 197213.352326 4.1634E+03 9.3313E+05 7.3303E-02 0.9687 +550 9 3G -10 3F 3-3 257.313230 cm-1 196956.038769 197213.351998 2.0916E+02 9.3293E+05 4.7347E-03 0.7787 +550 9 3G -10 3F 3-4 257.313524 cm-1 196956.038769 197213.352292 3.3162E+00 9.3323E+05 9.6515E-05 1.0000 +550 9 3G -10 3F 5-4 257.313955 cm-1 196956.038337 197213.352292 4.0856E+03 9.3323E+05 7.5669E-02 1.0000 +550 9 3G -10 3F 3-2 257.314074 cm-1 196956.038769 197213.352843 4.2978E+03 9.3321E+05 6.9491E-02 1.0000 +550 9 3G -10 3F 4-3 257.314135 cm-1 196956.037863 197213.351998 3.8144E+03 9.3293E+05 6.7157E-02 0.9467 +550 9 3G -10 3F 4-4 257.314429 cm-1 196956.037863 197213.352292 1.0867E+02 9.3323E+05 2.4599E-03 0.5201 +551 9 3G -10 3H Mean 257.398606 cm-1 196956.038291 197213.436897 4.6982E+04 3.6446E+05 1.2990E+00 0.9935 +551 9 3G -10 3H 3-4 257.398352 cm-1 196956.038769 197213.437121 4.4953E+04 3.6446E+05 1.3075E+00 1.0000 +551 9 3G -10 3H 5-5 257.398354 cm-1 196956.038337 197213.436691 9.7462E+02 3.6446E+05 2.2048E-02 0.5153 +551 9 3G -10 3H 5-6 257.398579 cm-1 196956.038337 197213.436916 4.7288E+04 3.6446E+05 1.2642E+00 1.0000 +551 9 3G -10 3H 5-4 257.398784 cm-1 196956.038337 197213.437121 2.3352E+01 3.6446E+05 4.3222E-04 1.0000 +551 9 3G -10 3H 4-5 257.398827 cm-1 196956.037863 197213.436691 4.6303E+04 3.6446E+05 1.2802E+00 1.0200 +551 9 3G -10 3H 4-4 257.399258 cm-1 196956.037863 197213.437121 1.2025E+03 3.6446E+05 2.7203E-02 0.5201 +552 9 3H -10 3G Mean 257.359908 cm-1 196956.060565 197213.420472 2.6091E+03 5.5231E+05 4.8306E-02 0.9935 +552 9 3H -10 3G 4-4 257.359289 cm-1 196956.060872 197213.420161 5.4650E+01 5.5231E+05 1.2367E-03 0.5203 +552 9 3H -10 3G 4-5 257.359634 cm-1 196956.060872 197213.420506 8.6813E-01 5.5231E+05 2.4010E-05 1.0000 +552 9 3H -10 3G 5-4 257.359879 cm-1 196956.060282 197213.420161 2.5714E+03 5.5231E+05 4.7608E-02 1.0200 +552 9 3H -10 3G 6-5 257.359915 cm-1 196956.060591 197213.420506 2.5393E+03 5.5231E+05 4.8621E-02 1.0000 +552 9 3H -10 3G 4-3 257.359949 cm-1 196956.060872 197213.420821 2.6261E+03 5.5231E+05 4.6219E-02 1.0000 +552 9 3H -10 3G 5-5 257.360224 cm-1 196956.060282 197213.420506 4.4284E+01 5.5231E+05 1.0021E-03 0.5153 +553 9 3H -10 3I Mean 257.381597 cm-1 196956.060565 197213.442162 5.9988E+04 1.5881E+05 1.6040E+00 0.9955 +553 9 3H -10 3I 6-6 257.381425 cm-1 196956.060591 197213.442016 8.5852E+02 2.5807E+05 1.9424E-02 0.5129 +553 9 3H -10 3I 4-5 257.381446 cm-1 196956.060872 197213.442318 5.8268E+04 2.5807E+05 1.6113E+00 1.0000 +553 9 3H -10 3I 6-7 257.381583 cm-1 196956.060591 197213.442174 6.0260E+04 0.0000E+00 1.5731E+00 1.0000 +553 9 3H -10 3I 6-5 257.381727 cm-1 196956.060591 197213.442318 1.3834E+01 2.5807E+05 2.6484E-04 1.0000 +553 9 3H -10 3I 5-6 257.381734 cm-1 196956.060282 197213.442016 5.9396E+04 2.5807E+05 1.5882E+00 1.0138 +553 9 3H -10 3I 5-5 257.382037 cm-1 196956.060282 197213.442318 1.0193E+03 2.5807E+05 2.3061E-02 0.5153 +554 9 3I -10 3H Mean 257.369231 cm-1 196956.067666 197213.436897 1.4604E+03 3.6446E+05 2.7960E-02 0.9955 +554 9 3I -10 3H 5-5 257.368811 cm-1 196956.067880 197213.436691 2.0997E+01 3.6446E+05 4.7510E-04 0.5152 +554 9 3I -10 3H 5-6 257.369036 cm-1 196956.067880 197213.436916 2.4113E-01 3.6446E+05 6.4480E-06 1.0000 +554 9 3I -10 3H 6-5 257.369225 cm-1 196956.067465 197213.436691 1.4460E+03 3.6446E+05 2.7685E-02 1.0138 +554 9 3I -10 3H 7-6 257.369234 cm-1 196956.067682 197213.436916 1.4323E+03 3.6446E+05 2.8087E-02 1.0000 +554 9 3I -10 3H 5-4 257.369241 cm-1 196956.067880 197213.437121 1.4670E+03 3.6446E+05 2.7158E-02 1.0000 +554 9 3I -10 3H 6-6 257.369451 cm-1 196956.067465 197213.436916 1.7685E+01 3.6446E+05 4.0016E-04 0.5129 +555 9 3K -10 3I Mean 257.371756 cm-1 196956.070406 197213.442162 6.8757E+02 1.5881E+05 1.3483E-02 0.9967 +555 9 3K -10 3I 6-6 257.371452 cm-1 196956.070564 197213.442016 7.2210E+00 2.5807E+05 1.6339E-04 0.5129 +555 9 3K -10 3I 6-7 257.371610 cm-1 196956.070564 197213.442174 6.2573E-02 0.0000E+00 1.6336E-06 1.0000 +555 9 3K -10 3I 6-5 257.371754 cm-1 196956.070564 197213.442318 6.8987E+02 2.5807E+05 1.3208E-02 1.0000 +555 9 3K -10 3I 8-7 257.371757 cm-1 196956.070417 197213.442174 6.7761E+02 0.0000E+00 1.3528E-02 1.0000 +555 9 3K -10 3I 7-6 257.371759 cm-1 196956.070257 197213.442016 6.8264E+02 2.5807E+05 1.3386E-02 1.0101 +555 9 3K -10 3I 7-7 257.371917 cm-1 196956.070257 197213.442174 6.2371E+00 0.0000E+00 1.4112E-04 0.5110 +556 10 3S -10 3P Mean 53.100453 cm-1 197145.233258 197198.333711 1.9254E+03 7.5715E+05 3.0700E+00 1.0000 +556 10 3S -10 3P 1-2 53.099464 cm-1 197145.233258 197198.332722 1.9254E+03 7.5715E+05 1.7056E+00 1.0000 +556 10 3S -10 3P 1-1 53.100010 cm-1 197145.233258 197198.333268 1.9254E+03 7.5715E+05 1.0233E+00 1.0000 +556 10 3S -10 3P 1-0 53.106724 cm-1 197145.233258 197198.339982 1.9254E+03 7.5716E+05 3.4111E-01 1.0000 \ No newline at end of file diff --git a/bin/rgb_hex/hex2rgb.m b/bin/rgb_hex/hex2rgb.m new file mode 100644 index 0000000..0bf72b8 --- /dev/null +++ b/bin/rgb_hex/hex2rgb.m @@ -0,0 +1,107 @@ +function [ rgb ] = hex2rgb(hex,range) +% hex2rgb converts hex color values to rgb arrays on the range 0 to 1. +% +% +% * * * * * * * * * * * * * * * * * * * * +% SYNTAX: +% rgb = hex2rgb(hex) returns rgb color values in an n x 3 array. Values are +% scaled from 0 to 1 by default. +% +% rgb = hex2rgb(hex,256) returns RGB values scaled from 0 to 255. +% +% +% * * * * * * * * * * * * * * * * * * * * +% EXAMPLES: +% +% myrgbvalue = hex2rgb('#334D66') +% = 0.2000 0.3020 0.4000 +% +% +% myrgbvalue = hex2rgb('334D66') % <-the # sign is optional +% = 0.2000 0.3020 0.4000 +% +% +% myRGBvalue = hex2rgb('#334D66',256) +% = 51 77 102 +% +% +% myhexvalues = ['#334D66';'#8099B3';'#CC9933';'#3333E6']; +% myrgbvalues = hex2rgb(myhexvalues) +% = 0.2000 0.3020 0.4000 +% 0.5020 0.6000 0.7020 +% 0.8000 0.6000 0.2000 +% 0.2000 0.2000 0.9020 +% +% +% myhexvalues = ['#334D66';'#8099B3';'#CC9933';'#3333E6']; +% myRGBvalues = hex2rgb(myhexvalues,256) +% = 51 77 102 +% 128 153 179 +% 204 153 51 +% 51 51 230 +% +% HexValsAsACharacterArray = {'#334D66';'#8099B3';'#CC9933';'#3333E6'}; +% rgbvals = hex2rgb(HexValsAsACharacterArray) +% +% * * * * * * * * * * * * * * * * * * * * +% Chad A. Greene, April 2014 +% +% Updated August 2014: Functionality remains exactly the same, but it's a +% little more efficient and more robust. Thanks to Stephen Cobeldick for +% the improvement tips. In this update, the documentation now shows that +% the range may be set to 256. This is more intuitive than the previous +% style, which scaled values from 0 to 255 with range set to 255. Now you +% can enter 256 or 255 for the range, and the answer will be the same--rgb +% values scaled from 0 to 255. Function now also accepts character arrays +% as input. +% +% * * * * * * * * * * * * * * * * * * * * +% See also rgb2hex, dec2hex, hex2num, and ColorSpec. +% + +%% Input checks: + +assert(nargin>0&nargin<3,'hex2rgb function must have one or two inputs.') + +if nargin==2 + assert(isscalar(range)==1,'Range must be a scalar, either "1" to scale from 0 to 1 or "256" to scale from 0 to 255.') +end + +%% Tweak inputs if necessary: + +if iscell(hex) + assert(isvector(hex)==1,'Unexpected dimensions of input hex values.') + + % In case cell array elements are separated by a comma instead of a + % semicolon, reshape hex: + if isrow(hex) + hex = hex'; + end + + % If input is cell, convert to matrix: + hex = cell2mat(hex); +end + +if strcmpi(hex(1,1),'#') + hex(:,1) = []; +end + +if nargin == 1 + range = 1; +end + +%% Convert from hex to rgb: + +switch range + case 1 + rgb = reshape(sscanf(hex.','%2x'),3,[]).'/255; + + case {255,256} + rgb = reshape(sscanf(hex.','%2x'),3,[]).'; + + otherwise + error('Range must be either "1" to scale from 0 to 1 or "256" to scale from 0 to 255.') +end + +end + diff --git a/bin/rgb_hex/license.txt b/bin/rgb_hex/license.txt new file mode 100644 index 0000000..9436ea6 --- /dev/null +++ b/bin/rgb_hex/license.txt @@ -0,0 +1,25 @@ +Copyright (c) 2014, Chad Greene +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + +* Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. + +* Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution +* Neither the name of The University of Texas at Austin nor the names of its + contributors may be used to endorse or promote products derived from this + software without specific prior written permission. +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE +FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR +SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, +OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/bin/rgb_hex/rgb2hex.m b/bin/rgb_hex/rgb2hex.m new file mode 100644 index 0000000..7581cf2 --- /dev/null +++ b/bin/rgb_hex/rgb2hex.m @@ -0,0 +1,64 @@ +function [ hex ] = rgb2hex(rgb) +% rgb2hex converts rgb color values to hex color format. +% +% This function assumes rgb values are in [r g b] format on the 0 to 1 +% scale. If, however, any value r, g, or b exceed 1, the function assumes +% [r g b] are scaled between 0 and 255. +% +% * * * * * * * * * * * * * * * * * * * * +% SYNTAX: +% hex = rgb2hex(rgb) returns the hexadecimal color value of the n x 3 rgb +% values. rgb can be an array. +% +% * * * * * * * * * * * * * * * * * * * * +% EXAMPLES: +% +% myhexvalue = rgb2hex([0 1 0]) +% = #00FF00 +% +% myhexvalue = rgb2hex([0 255 0]) +% = #00FF00 +% +% myrgbvalues = [.2 .3 .4; +% .5 .6 .7; +% .8 .6 .2; +% .2 .2 .9]; +% myhexvalues = rgb2hex(myrgbvalues) +% = #334D66 +% #8099B3 +% #CC9933 +% #3333E6 +% +% * * * * * * * * * * * * * * * * * * * * +% Chad A. Greene, April 2014 +% +% Updated August 2014: Functionality remains exactly the same, but it's a +% little more efficient and more robust. Thanks to Stephen Cobeldick for +% his suggestions. +% +% * * * * * * * * * * * * * * * * * * * * +% See also hex2rgb, dec2hex, hex2num, and ColorSpec. + +%% Check inputs: + +assert(nargin==1,'This function requires an RGB input.') +assert(isnumeric(rgb)==1,'Function input must be numeric.') + +sizergb = size(rgb); +assert(sizergb(2)==3,'rgb value must have three components in the form [r g b].') +assert(max(rgb(:))<=255& min(rgb(:))>=0,'rgb values must be on a scale of 0 to 1 or 0 to 255') + +%% If no value in RGB exceeds unity, scale from 0 to 255: +if max(rgb(:))<=1 + rgb = round(rgb*255); +else + rgb = round(rgb); +end + +%% Convert (Thanks to Stephen Cobeldick for this clever, efficient solution): + +hex(:,2:7) = reshape(sprintf('%02X',rgb.'),6,[]).'; +hex(:,1) = '#'; + + +end diff --git a/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo.html b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo.html new file mode 100644 index 0000000..d649e9b --- /dev/null +++ b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo.html @@ -0,0 +1,255 @@ + + + + + rgb2hex and hex2rgb

rgb2hex and hex2rgb

These functions convert RGB color triplets to hexadecimal format, or hexadecimal format to RGB color triplets.

Contents

Syntax

rgb2hex(rgb)
+hex2rgb(hex)
+hex2rgb(hex,range)

Description

rgb2hex(rgb) converts RGB color triplets to hexadecimal format. If no value in the rgb matrix exceeds unity, values are assumed to be scaled from 0 to 1. If any value in rgb exceeds unity, values are assumed to be scaled from 0 to 255.

hex2rgb(hex) converts hexadecimal to rgb color triplets scale from 0 to 1.

hex2rgb(hex,range) specifies a range as 1 or 256 for scaling output RGB values. A previous version of this function required a range of 255 when scaling from 0 to 255, but letting range equal 256 may be more intuitive, so either input will work now. Whether you enter a range of 255 or 256, RGB values will be scaled from 0 to 255. Default range is 1 to Matlab syntax, meaning values are scaled from 0 to 1.

Examples of rgb2hex

What is the hexadecimal value of pure green?

greenHex = rgb2hex([0 1 0])
+
+greenHex =
+
+#00FF00
+
+

What if the rgb values are scaled from 0 to 255?

greenHexIsStill = rgb2hex([0 255 0])
+
+greenHexIsStill =
+
+#00FF00
+
+

This function works for multiple entries too:

myrgbvalues = [.2 .3 .4;
+               .5 .6 .7;
+               .8 .6 .2;
+               .2 .2 .9];
+myhexvalues = rgb2hex(myrgbvalues)
+
+myhexvalues =
+
+#334D66
+#8099B3
+#CC9933
+#3333E6
+
+

Or similarly,

rgb2hex(jet(5))
+
+ans =
+
+#0080FF
+#00FFFF
+#80FF80
+#FFFF00
+#FF8000
+
+

Examples of hex2rgb

Say some online color program gives you some hex value that you'd like to use in your next Matlab plot. The number '#334D66' is something that Matlab can understand, so we use hex2rgb:

hex2rgb('#334D66')
+
+ans =
+
+    0.2000    0.3020    0.4000
+
+

The hex2rgb function may also be used inside a plot command:

plot(1:10,(1:10).^2,'color',hex2rgb('#334D66'),'linewidth',5)
+

The pound sign is optional:

myrgbvalue = hex2rgb('334D66')
+
+myrgbvalue =
+
+    0.2000    0.3020    0.4000
+
+

Values may be scaled from 0 to 255:

myRGBvalue = hex2rgb('#334D66',256)
+
+myRGBvalue =
+
+    51    77   102
+
+

Input hex values can be in a matrix:

myhexvalues = ['#334D66';'#8099B3';'#CC9933';'#3333E6'];
+myrgbvalues = hex2rgb(myhexvalues)
+
+myrgbvalues =
+
+    0.2000    0.3020    0.4000
+    0.5020    0.6000    0.7020
+    0.8000    0.6000    0.2000
+    0.2000    0.2000    0.9020
+
+

Input hex values may also be in a character array:

HexValsAsACharacterArray = {'#334D66';'#8099B3';'#CC9933';'#3333E6'};
+rgbvals = hex2rgb(HexValsAsACharacterArray)
+
+rgbvals =
+
+    0.2000    0.3020    0.4000
+    0.5020    0.6000    0.7020
+    0.8000    0.6000    0.2000
+    0.2000    0.2000    0.9020
+
+

Character arrays can be useful when plotting and labelling:

x = 1:4;
+y = -x;
+scatter(x,y,1e3,rgbvals,'filled')
+axis([0 5 -5 0])
+text(x,y,HexValsAsACharacterArray,'horizontalalignment','center')
+

Author Info

These functions were written by Chad A. Greene of the University of Texas at Austin's Institute for Geophysics (UTIG) in April of 2014. On advice from Stephen Cobeldick, some changes were made in August 2014. Functionality has not changed with these updates, but the functions are now faster and more robust. Thanks Stephen.


Published with MATLAB® R2012b

\ No newline at end of file diff --git a/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo.png b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo.png new file mode 100644 index 0000000..8db0e71 Binary files /dev/null and b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo.png differ diff --git a/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo_01.png b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo_01.png new file mode 100644 index 0000000..9141ceb Binary files /dev/null and b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo_01.png differ diff --git a/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo_02.png b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo_02.png new file mode 100644 index 0000000..83bc150 Binary files /dev/null and b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/html/rgb2hex_hex2rgb_demo_02.png differ diff --git a/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/rgb2hex_hex2rgb_demo.m b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/rgb2hex_hex2rgb_demo.m new file mode 100644 index 0000000..4d71f09 --- /dev/null +++ b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/rgb2hex_hex2rgb_demo.m @@ -0,0 +1,103 @@ +%% |rgb2hex| and |hex2rgb| +% These functions convert RGB color triplets to hexadecimal format, or +% hexadecimal format to RGB color triplets. + +%% Syntax +% +% rgb2hex(rgb) +% hex2rgb(hex) +% hex2rgb(hex,range) + +%% Description +% +% |rgb2hex(rgb)| converts RGB color triplets to hexadecimal format. If no +% value in the |rgb| matrix exceeds unity, values are assumed to be scaled +% from 0 to 1. If any value in |rgb| exceeds unity, values are assumed to +% be scaled from 0 to 255. +% +% |hex2rgb(hex)| converts hexadecimal to rgb color triplets scale from 0 to +% 1. +% +% |hex2rgb(hex,range)| specifies a range as 1 or 256 for scaling output RGB values. +% A previous version of this function required a range of 255 when scaling from 0 to 255, +% but letting range equal 256 may be more intuitive, so either input will work now. +% Whether you enter a range of 255 or 256, RGB values will be scaled from 0 to 255. +% Default range is 1 to Matlab syntax, meaning values are scaled from 0 to 1. + +%% Examples of |rgb2hex| +% What is the hexadecimal value of pure green? + +greenHex = rgb2hex([0 1 0]) + +%% +% What if the rgb values are scaled from 0 to 255? + +greenHexIsStill = rgb2hex([0 255 0]) + +%% +% This function works for multiple entries too: + +myrgbvalues = [.2 .3 .4; + .5 .6 .7; + .8 .6 .2; + .2 .2 .9]; +myhexvalues = rgb2hex(myrgbvalues) + +%% +% Or similarly, + +rgb2hex(jet(5)) + +%% Examples of |hex2rgb| +% Say gives you some hex value that you'd like to use in +% your next Matlab plot. The number |'#334D66'| is something that Matlab +% can understand, so we use |hex2rgb|: + +hex2rgb('#334D66') + +%% +% The |hex2rgb| function may also be used inside a |plot| command: + +plot(1:10,(1:10).^2,'color',hex2rgb('#334D66'),'linewidth',5) + +%% +% The pound sign is optional: + +myrgbvalue = hex2rgb('334D66') + +%% +% Values may be scaled from 0 to 255: + +myRGBvalue = hex2rgb('#334D66',256) + +%% +% Input hex values can be in a matrix: + +myhexvalues = ['#334D66';'#8099B3';'#CC9933';'#3333E6']; +myrgbvalues = hex2rgb(myhexvalues) + +%% +% Input hex values may also be in a character array: + +HexValsAsACharacterArray = {'#334D66';'#8099B3';'#CC9933';'#3333E6'}; +rgbvals = hex2rgb(HexValsAsACharacterArray) + +%% +% Character arrays can be useful when plotting and labelling: + +x = 1:4; +y = -x; +scatter(x,y,1e3,rgbvals,'filled') +axis([0 5 -5 0]) +text(x,y,HexValsAsACharacterArray,'horizontalalignment','center') + +%% Author Info +% These functions were written by Chad A. Greene of the University of Texas +% at Austin's Institute for Geophysics +% () in April of 2014. +% On advice from +% , some changes were made in August 2014. Functionality +% has not changed with these updates, but the functions are now faster and +% more robust. Thanks Stephen. \ No newline at end of file diff --git a/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/rgb2hex_hex2rgb_demo.mlx b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/rgb2hex_hex2rgb_demo.mlx new file mode 100644 index 0000000..96f346a Binary files /dev/null and b/bin/rgb_hex/rgb2hex_and_hex2rgb_documentation/rgb2hex_hex2rgb_demo.mlx differ diff --git a/bin/rgb_hsl/hsl2rgb.m b/bin/rgb_hsl/hsl2rgb.m new file mode 100644 index 0000000..00b4d07 --- /dev/null +++ b/bin/rgb_hsl/hsl2rgb.m @@ -0,0 +1,51 @@ +function rgb=hsl2rgb(hsl_in) +%Converts Hue-Saturation-Luminance Color value to Red-Green-Blue Color value +% +%Usage +% RGB = hsl2rgb(HSL) +% +% converts HSL, a M [x N] x 3 color matrix with values between 0 and 1 +% into RGB, a M [x N] X 3 color matrix with values between 0 and 1 +% +%See also rgb2hsl, rgb2hsv, hsv2rgb + +% (C) Vladimir Bychkovsky, June 2008 +% written using: +% - an implementation by Suresh E Joel, April 26,2003 +% - Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV + +hsl=reshape(hsl_in, [], 3); + +H=hsl(:,1); +S=hsl(:,2); +L=hsl(:,3); + +lowLidx=L < (1/2); +q=(L .* (1+S) ).*lowLidx + (L+S-(L.*S)).*(~lowLidx); +p=2*L - q; +hk=H; % this is already divided by 360 + +t=zeros([length(H), 3]); % 1=R, 2=B, 3=G +t(:,1)=hk+1/3; +t(:,2)=hk; +t(:,3)=hk-1/3; + +underidx=t < 0; +overidx=t > 1; +t=t+underidx - overidx; + +range1=t < (1/6); +range2=(t >= (1/6) & t < (1/2)); +range3=(t >= (1/2) & t < (2/3)); +range4= t >= (2/3); + +% replicate matricies (one per color) to make the final expression simpler +P=repmat(p, [1,3]); +Q=repmat(q, [1,3]); +rgb_c= (P + ((Q-P).*6.*t)).*range1 + ... + Q.*range2 + ... + (P + ((Q-P).*6.*(2/3 - t))).*range3 + ... + P.*range4; + +rgb_c=round(rgb_c.*10000)./10000; +rgb=reshape(rgb_c, size(hsl_in)); \ No newline at end of file diff --git a/bin/rgb_hsl/hsltest.m b/bin/rgb_hsl/hsltest.m new file mode 100644 index 0000000..3f802bd --- /dev/null +++ b/bin/rgb_hsl/hsltest.m @@ -0,0 +1,157 @@ +% A few crude tests for rgb2hsl.m and hsl2rgb.m +% If you find a bug in the conversion add a test here that exposes it. +% +% (C) Vladimir Bychkovsky June 2008 +% + +% ideas for improvement: +% - factor out the testing code +% - rewrite using some sort of Matlab unit testing frame work + +function hsltest() +% --------- Test rgb2hsl conversions ------------ +rgb=[0,0,0]; +test_hsl=[0,0,0]; +hsl=rgb2hsl(rgb); +if min(hsl==test_hsl)==0 + fprintf('E'); + rgb + test_hsl + hsl + return; +else + fprintf('.'); +end + +rgb=[0.5,0,0]; +test_hsl=[0,1,0.25]; +hsl=rgb2hsl(rgb); +if min(hsl==test_hsl)==0 + fprintf('E'); + rgb + test_hsl + hsl + return; +else + fprintf('.'); +end + + +rgb=[0.5,0.3,0]; +test_hsl=[36.0/360,1,0.25]; +hsl=rgb2hsl(rgb); +if min(hsl==test_hsl)==0 + fprintf('E'); + rgb + test_hsl + hsl + return; +else + fprintf('.'); +end + +rgb=[0.5,0.5,0.5]; +test_hsl=[0,0,0.5]; +hsl=rgb2hsl(rgb); +if min(hsl==test_hsl)==0 + fprintf('E'); + rgb + test_hsl + hsl + return; +else + fprintf('.'); +end + +% 2d test +rgb=[0.5,0.5,0.5;... + 0.5,0.3,0]; +test_hsl=[0,0,0.5; + 36.0/360,1,0.25]; +hsl=rgb2hsl(rgb); +if min(min(hsl==test_hsl))==0 + fprintf('E'); + rgb + test_hsl + hsl + return; +else + fprintf('.'); +end + +% 3d test +rgb_in=rand(4,4,3); +rgb_r=reshape(rgb_in, [],3); +hsl_r=rgb2hsl(rgb_r); +test_hsl=reshape(hsl_r, size(rgb_in)); + +hsl=rgb2hsl(rgb_in); +if min(reshape(hsl==test_hsl, [],1))==0 + fprintf('E'); + rgb + test_hsl + hsl + return; +else + fprintf('.'); +end + +%----------- Test HSL to RGB ---------- +test_rgb=[0,0,0]; +test_hsl=rgb2hsl(test_rgb); +rgb=hsl2rgb(test_hsl); +if min(reshape(rgb==test_rgb, [],1))==0 + fprintf('E'); + test_hsl + rgb + test_rgb + return; +else + fprintf('.'); +end + +test_rgb=[1,0,0]; +test_hsl=rgb2hsl(test_rgb); +rgb=hsl2rgb(test_hsl); +if min(reshape(rgb==test_rgb, [],1))==0 + fprintf('E'); + test_hsl + rgb + test_rgb + return; +else + fprintf('.'); +end + +test_rgb=[0.0,1.0,0.0]; +test_hsl=rgb2hsl(test_rgb); +rgb=hsl2rgb(test_hsl); +if min(reshape(rgb==test_rgb, [],1))==0 + fprintf('E'); + test_hsl + rgb + test_rgb + return; +else + fprintf('.'); +end + + +% 2d test +test_rgb=floor(rand(5,5,3).*100)./100; +test_hsl=rgb2hsl(test_rgb); +rgb=hsl2rgb(test_hsl); +if min(reshape(rgb==test_rgb, [],1))==0 + fprintf('E'); + test_hsl + rgb + test_rgb + return; +else + fprintf('.'); +end + + + +fprintf('\nDone.\n'); + diff --git a/bin/rgb_hsl/rgb2hsl.m b/bin/rgb_hsl/rgb2hsl.m new file mode 100644 index 0000000..738e1a8 --- /dev/null +++ b/bin/rgb_hsl/rgb2hsl.m @@ -0,0 +1,45 @@ +function hsl=rgb2hsl(rgb_in) +%Converts Red-Green-Blue Color value to Hue-Saturation-Luminance Color value +% +%Usage +% HSL = rgb2hsl(RGB) +% +% converts RGB, a M [x N] x 3 color matrix with values between 0 and 1 +% into HSL, a M [x N] X 3 color matrix with values between 0 and 1 +% +%See also hsl2rgb, rgb2hsv, hsv2rgb + +% (C) Vladimir Bychkovsky, June 2008 +% written using: +% - an implementation by Suresh E Joel, April 26,2003 +% - Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV + +rgb=reshape(rgb_in, [], 3); + +mx=max(rgb,[],2);%max of the 3 colors +mn=min(rgb,[],2);%min of the 3 colors + +L=(mx+mn)/2;%luminance is half of max value + min value +S=zeros(size(L)); + +% this set of matrix operations can probably be done as an addition... +zeroidx= (mx==mn); +S(zeroidx)=0; + +lowlidx=L <= 0.5; +calc=(mx-mn)./(mx+mn); +idx=lowlidx & (~ zeroidx); +S(idx)=calc(idx); + +hilidx=L > 0.5; +calc=(mx-mn)./(2-(mx+mn)); +idx=hilidx & (~ zeroidx); +S(idx)=calc(idx); + +hsv=rgb2hsv(rgb); +H=hsv(:,1); + +hsl=[H, S, L]; + +hsl=round(hsl.*100000)./100000; +hsl=reshape(hsl, size(rgb_in)); \ No newline at end of file diff --git a/bin/subaxis/license.txt b/bin/subaxis/license.txt new file mode 100644 index 0000000..a09622a --- /dev/null +++ b/bin/subaxis/license.txt @@ -0,0 +1,24 @@ +Copyright (c) 2014, Aslak Grinsted +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in + the documentation and/or other materials provided with the distribution + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +POSSIBILITY OF SUCH DAMAGE. diff --git a/bin/subaxis/parseArgs.m b/bin/subaxis/parseArgs.m new file mode 100644 index 0000000..f43d22b --- /dev/null +++ b/bin/subaxis/parseArgs.m @@ -0,0 +1,159 @@ +function ArgStruct=parseArgs(args,ArgStruct,varargin) +% Helper function for parsing varargin. +% +% +% ArgStruct=parseArgs(varargin,ArgStruct[,FlagtypeParams[,Aliases]]) +% +% * ArgStruct is the structure full of named arguments with default values. +% * Flagtype params is params that don't require a value. (the value will be set to 1 if it is present) +% * Aliases can be used to map one argument-name to several argstruct fields +% +% +% example usage: +% -------------- +% function parseargtest(varargin) +% +% %define the acceptable named arguments and assign default values +% Args=struct('Holdaxis',0, ... +% 'SpacingVertical',0.05,'SpacingHorizontal',0.05, ... +% 'PaddingLeft',0,'PaddingRight',0,'PaddingTop',0,'PaddingBottom',0, ... +% 'MarginLeft',.1,'MarginRight',.1,'MarginTop',.1,'MarginBottom',.1, ... +% 'rows',[],'cols',[]); +% +% %The capital letters define abrreviations. +% % Eg. parseargtest('spacingvertical',0) is equivalent to parseargtest('sv',0) +% +% Args=parseArgs(varargin,Args, ... % fill the arg-struct with values entered by the user +% {'Holdaxis'}, ... %this argument has no value (flag-type) +% {'Spacing' {'sh','sv'}; 'Padding' {'pl','pr','pt','pb'}; 'Margin' {'ml','mr','mt','mb'}}); +% +% disp(Args) +% +% +% +% +% Aslak Grinsted 2004 + +% ------------------------------------------------------------------------- +% Copyright (C) 2002-2004, Aslak Grinsted +% This software may be used, copied, or redistributed as long as it is not +% sold and this copyright notice is reproduced on each copy made. This +% routine is provided as is without any express or implied warranties +% whatsoever. + +persistent matlabver + +if isempty(matlabver) + matlabver=ver('MATLAB'); + matlabver=str2double(matlabver.Version); +end + +Aliases={}; +FlagTypeParams=''; + +if (length(varargin)>0) + FlagTypeParams=lower(strvcat(varargin{1})); %#ok + if length(varargin)>1 + Aliases=varargin{2}; + end +end + + +%---------------Get "numeric" arguments +NumArgCount=1; +while (NumArgCount<=size(args,2))&&(~ischar(args{NumArgCount})) + NumArgCount=NumArgCount+1; +end +NumArgCount=NumArgCount-1; +if (NumArgCount>0) + ArgStruct.NumericArguments={args{1:NumArgCount}}; +else + ArgStruct.NumericArguments={}; +end + + +%--------------Make an accepted fieldname matrix (case insensitive) +Fnames=fieldnames(ArgStruct); +for i=1:length(Fnames) + name=lower(Fnames{i,1}); + Fnames{i,2}=name; %col2=lower + Fnames{i,3}=[name(Fnames{i,1}~=name) ' ']; %col3=abreviation letters (those that are uppercase in the ArgStruct) e.g. SpacingHoriz->sh + %the space prevents strvcat from removing empty lines + Fnames{i,4}=isempty(strmatch(Fnames{i,2},FlagTypeParams)); %Does this parameter have a value? +end +FnamesFull=strvcat(Fnames{:,2}); %#ok +FnamesAbbr=strvcat(Fnames{:,3}); %#ok + +if length(Aliases)>0 + for i=1:length(Aliases) + name=lower(Aliases{i,1}); + FieldIdx=strmatch(name,FnamesAbbr,'exact'); %try abbreviations (must be exact) + if isempty(FieldIdx) + FieldIdx=strmatch(name,FnamesFull); %&??????? exact or not? + end + Aliases{i,2}=FieldIdx; + Aliases{i,3}=[name(Aliases{i,1}~=name) ' ']; %the space prevents strvcat from removing empty lines + Aliases{i,1}=name; %dont need the name in uppercase anymore for aliases + end + %Append aliases to the end of FnamesFull and FnamesAbbr + FnamesFull=strvcat(FnamesFull,strvcat(Aliases{:,1})); %#ok + FnamesAbbr=strvcat(FnamesAbbr,strvcat(Aliases{:,3})); %#ok +end + +%--------------get parameters-------------------- +l=NumArgCount+1; +while (l<=length(args)) + a=args{l}; + if ischar(a) + paramHasValue=1; % assume that the parameter has is of type 'param',value + a=lower(a); + FieldIdx=strmatch(a,FnamesAbbr,'exact'); %try abbreviations (must be exact) + if isempty(FieldIdx) + FieldIdx=strmatch(a,FnamesFull); + end + if (length(FieldIdx)>1) %shortest fieldname should win + [mx,mxi]=max(sum(FnamesFull(FieldIdx,:)==' ',2));%#ok + FieldIdx=FieldIdx(mxi); + end + if FieldIdx>length(Fnames) %then it's an alias type. + FieldIdx=Aliases{FieldIdx-length(Fnames),2}; + end + + if isempty(FieldIdx) + error(['Unknown named parameter: ' a]) + end + for curField=FieldIdx' %if it is an alias it could be more than one. + if (Fnames{curField,4}) + if (l+1>length(args)) + error(['Expected a value for parameter: ' Fnames{curField,1}]) + end + val=args{l+1}; + else %FLAG PARAMETER + if (l=6 + ArgStruct.(Fnames{curField,1})=val; %try the line below if you get an error here + else + ArgStruct=setfield(ArgStruct,Fnames{curField,1},val); %#ok <-works in old matlab versions + end + end + l=l+1+paramHasValue; %if a wildcard matches more than one + else + error(['Expected a named parameter: ' num2str(a)]) + end +end \ No newline at end of file diff --git a/bin/subaxis/subaxis.m b/bin/subaxis/subaxis.m new file mode 100644 index 0000000..fb1476f --- /dev/null +++ b/bin/subaxis/subaxis.m @@ -0,0 +1,106 @@ +function h=subaxis(varargin) +%SUBAXIS Create axes in tiled positions. (just like subplot) +% Usage: +% h=subaxis(rows,cols,cellno[,settings]) +% h=subaxis(rows,cols,cellx,celly[,settings]) +% h=subaxis(rows,cols,cellx,celly,spanx,spany[,settings]) +% +% SETTINGS: Spacing,SpacingHoriz,SpacingVert +% Padding,PaddingRight,PaddingLeft,PaddingTop,PaddingBottom +% Margin,MarginRight,MarginLeft,MarginTop,MarginBottom +% Holdaxis +% +% all units are relative (i.e. from 0 to 1) +% +% Abbreviations of parameters can be used.. (Eg MR instead of MarginRight) +% (holdaxis means that it wont delete any axes below.) +% +% +% Example: +% +% >> subaxis(2,1,1,'SpacingVert',0,'MR',0); +% >> imagesc(magic(3)) +% >> subaxis(2,'p',.02); +% >> imagesc(magic(4)) +% +% 2001-2014 / Aslak Grinsted (Feel free to modify this code.) + +f=gcf; + + + +UserDataArgsOK=0; +Args=get(f,'UserData'); +if isstruct(Args) + UserDataArgsOK=isfield(Args,'SpacingHorizontal')&isfield(Args,'Holdaxis')&isfield(Args,'rows')&isfield(Args,'cols'); +end +OKToStoreArgs=isempty(Args)|UserDataArgsOK; + +if isempty(Args)&&(~UserDataArgsOK) + Args=struct('Holdaxis',0, ... + 'SpacingVertical',0.05,'SpacingHorizontal',0.05, ... + 'PaddingLeft',0,'PaddingRight',0,'PaddingTop',0,'PaddingBottom',0, ... + 'MarginLeft',.1,'MarginRight',.1,'MarginTop',.1,'MarginBottom',.1, ... + 'rows',[],'cols',[]); +end +Args=parseArgs(varargin,Args,{'Holdaxis'},{'Spacing' {'sh','sv'}; 'Padding' {'pl','pr','pt','pb'}; 'Margin' {'ml','mr','mt','mb'}}); + +if (length(Args.NumericArguments)>2) + Args.rows=Args.NumericArguments{1}; + Args.cols=Args.NumericArguments{2}; +%remove these 2 numerical arguments + Args.NumericArguments={Args.NumericArguments{3:end}}; +end + +if OKToStoreArgs + set(f,'UserData',Args); +end + + +switch length(Args.NumericArguments) + case 0 + return % no arguments but rows/cols.... + case 1 + if numel(Args.NumericArguments{1}) > 1 % restore subplot(m,n,[x y]) behaviour + [x1 y1] = ind2sub([Args.cols Args.rows],Args.NumericArguments{1}(1)); % subplot and ind2sub count differently (column instead of row first) --> switch cols/rows + [x2 y2] = ind2sub([Args.cols Args.rows],Args.NumericArguments{1}(end)); + else + x1=mod((Args.NumericArguments{1}-1),Args.cols)+1; x2=x1; + y1=floor((Args.NumericArguments{1}-1)/Args.cols)+1; y2=y1; + end +% x1=mod((Args.NumericArguments{1}-1),Args.cols)+1; x2=x1; +% y1=floor((Args.NumericArguments{1}-1)/Args.cols)+1; y2=y1; + case 2 + x1=Args.NumericArguments{1};x2=x1; + y1=Args.NumericArguments{2};y2=y1; + case 4 + x1=Args.NumericArguments{1};x2=x1+Args.NumericArguments{3}-1; + y1=Args.NumericArguments{2};y2=y1+Args.NumericArguments{4}-1; + otherwise + error('subaxis argument error') +end + + +cellwidth=((1-Args.MarginLeft-Args.MarginRight)-(Args.cols-1)*Args.SpacingHorizontal)/Args.cols; +cellheight=((1-Args.MarginTop-Args.MarginBottom)-(Args.rows-1)*Args.SpacingVertical)/Args.rows; +xpos1=Args.MarginLeft+Args.PaddingLeft+cellwidth*(x1-1)+Args.SpacingHorizontal*(x1-1); +xpos2=Args.MarginLeft-Args.PaddingRight+cellwidth*x2+Args.SpacingHorizontal*(x2-1); +ypos1=Args.MarginTop+Args.PaddingTop+cellheight*(y1-1)+Args.SpacingVertical*(y1-1); +ypos2=Args.MarginTop-Args.PaddingBottom+cellheight*y2+Args.SpacingVertical*(y2-1); + +if Args.Holdaxis + h=axes('position',[xpos1 1-ypos2 xpos2-xpos1 ypos2-ypos1]); +else + h=subplot('position',[xpos1 1-ypos2 xpos2-xpos1 ypos2-ypos1]); +end + + +set(h,'box','on'); +%h=axes('position',[x1 1-y2 x2-x1 y2-y1]); +set(h,'units',get(gcf,'defaultaxesunits')); +set(h,'tag','subaxis'); + + + +if (nargout==0), clear h; end; + diff --git a/bin/suptitle.m b/bin/suptitle.m index 1bb801b..71247d7 100644 --- a/bin/suptitle.m +++ b/bin/suptitle.m @@ -1,4 +1,4 @@ -function hout=suptitle(str) +function hout=suptitle(str,varargin) %SUPTITLE puts a title above all subplots. % % SUPTITLE('text') adds text to the top of the figure @@ -9,7 +9,6 @@ % Copyright 2003-2010 The MathWorks, Inc. - % Warning: If the figure or axis units are non-default, this % will break. @@ -22,7 +21,11 @@ titleypos = .95; % Fontsize for supertitle -fs = get(gcf,'defaultaxesfontsize')+4; +if nargin > 1 + fs = varargin{1}; +else + fs = get(gcf,'defaultaxesfontsize')+4; +end % Fudge factor to adjust y spacing between subplots fudge=1; diff --git a/bin/wavelength2color/README.md b/bin/wavelength2color/README.md new file mode 100644 index 0000000..48649e7 --- /dev/null +++ b/bin/wavelength2color/README.md @@ -0,0 +1,2 @@ +# wavelength2rgb +Converts a wavelength provided in nm into a representative color. diff --git a/bin/wavelength2color/wavelength2color.m b/bin/wavelength2color/wavelength2color.m new file mode 100644 index 0000000..6a6c78b --- /dev/null +++ b/bin/wavelength2color/wavelength2color.m @@ -0,0 +1,111 @@ +% Function: wavelength2color.m +% Author: Urs Hofmann +% Mail: hofmannu@biomed.ee.ethz.ch +% Date: 08.07.2020 +% Version: 1.0 + +% Description: converts a wavelength in nm into a color +% input arguments: +% - maxIntensity: maximum intensity of colorspace +% - gammaVal +% - used colorSpace (either 'rgb', or 'hsv') + +% example usage +% wavelength2color(532, 'gammaVal', 1, 'maxIntensity', 255, 'colorSpace', 'rgb') + +% principle stolen from: +% https://academo.org/demos/wavelength-to-colour-relationship/ + +function colorCode = wavelength2color(wavelength, varargin) + + % default arguments + maxIntensity = 1; + gammaVal = 0.8; + colorSpace = 'rgb'; + + for iargin=1:2:(nargin-1) + switch varargin{iargin} + case 'maxIntensity' + maxIntensity = varargin{iargin + 1}; + case 'gammaVal' + gammaVal = varargin{iargin + 1}; + case 'colorSpace' + switch varargin{iargin + 1} + case 'rgb' + colorSpace = 'rgb'; + case 'hsv' + colorSpace = 'hsv'; + otherwise + error('Invalid colorspace defined'); + end + otherwise + error('Invalid argument passed'); + end + end + + function outputVal = adjust(inputVal, factor) + + if (inputVal == 0) + outputVal = 0; + else + outputVal = (inputVal * factor)^gammaVal; + end + + end + + if (wavelength >= 380) && (wavelength < 440) + r = -(wavelength - 440) / (440 - 380); + g = 0; + b = 1; + elseif (wavelength >= 440) && (wavelength < 490) + r = 0; + g = (wavelength - 440) / (490 - 440); + b = 1; + elseif (wavelength >= 490) && (wavelength < 510) + r = 0; + g = 1; + b = -(wavelength - 510) / (510 - 490); + elseif (wavelength >= 510) && (wavelength < 580) + r = (wavelength - 510) / (580 - 510); + g = 1; + b = 0; + elseif (wavelength >= 580) && (wavelength < 645) + r = 1; + g = -(wavelength - 645) / (645 - 580); + b = 0; + elseif (wavelength >= 645) && (wavelength < 780) + r = 1; + g = 0; + b = 0; + else + r = 0; + g = 0; + b = 0; + end + + if (wavelength >= 380) && (wavelength < 420) + factor = 0.3 + 0.7 * (wavelength - 380) / (420 - 380); + elseif (wavelength >= 420) && (wavelength < 700) + factor = 1; + elseif (wavelength >= 700) && (wavelength < 780) + factor = 0.3 + 0.7 * (780 - wavelength) / (780 - 700); + else + factor = 0; + end + + r = adjust(r, factor); + g = adjust(g, factor); + b = adjust(b, factor); + + rgbCode = [r, g, b]; + + switch colorSpace + case 'rgb' + colorCode = rgbCode; + case 'hsv' + colorCode = rgb2hsv(rgbCode); + end + + colorCode = colorCode * maxIntensity; + +end \ No newline at end of file diff --git a/dev/add_unc.m b/dev/add_unc.m new file mode 100644 index 0000000..5ae863f --- /dev/null +++ b/dev/add_unc.m @@ -0,0 +1,47 @@ +function val_unc = add_unc(varargin) +% Accepts tuples of the form [x,x_unc] and returns the pair [val,unc]. +% Acts as if all uncertainties are non-negative and adds in quadrature. +%``` Basic function +% x = [0,0.5]; +% y = [-1,0.2]; +% val_unc = add_unc(x,y); +% isequal(val_unc,[-1, sqrt(0.5^2+0.7^2)]) +%``` +% Also works for: +%``` differences +% x = [0,0.5]; +% y = [-1,0.2]; +% val_unc = add_unc(x,-y); +% isequal(val_unc,[1,sqrt(0.5^2+0.2^2)]) +%``` +%``` multiple inputs +% x = [0,0.5]; +% y = [-1,0.2]; +% z = [5,1]; +% val_unc = add_unc(x,y,z); +% isequal(val_unc,[4,sqrt(0.5^2+0.2^2+1)]) +%``` +% Possible improvements: +% Vectorize to accept two Mx2 arrays or an Nx2 and 1x2 array. +% Implement proper type checking + + if nargin == 1 + warning("Not enough inputs to add_unc"); + if length(varargin{1}) == 2 + val_unc = varargin{1}; + else + warning("Input to add_unc was not a [v,u] pair"); + end + elseif nargin == 2 + val_unc = add_unc_pair(varargin{1},varargin{2}); + else + val_unc = add_unc(varargin{1},add_unc(varargin{2:end})); + end + + +end + +function val_unc = add_unc_pair(x,y) + val_unc =[x(1) + y(1),sqrt(abs(x(2)).^2+abs(y(2)).^2)]; +end +% add_unc = @(x,y) [x(1)+y(1),abs(x(2))+abs(y(2))]; \ No newline at end of file diff --git a/lib/MBeautifier/beautify_path.m b/dev/beautify_path.m similarity index 100% rename from lib/MBeautifier/beautify_path.m rename to dev/beautify_path.m diff --git a/dev/ci_plot.m b/dev/ci_plot.m new file mode 100644 index 0000000..47b9d0c --- /dev/null +++ b/dev/ci_plot.m @@ -0,0 +1,72 @@ +function [plt,f] = ci_plot(X,Y,I,varargin) +% a widget to plot lines with some surrounding interval such as standard +% error or confidence interval. + p = inputParser; +% defaultFontSize = 12; +% defaultFont = 'times'; + addParameter(p,'mask',ones(size(X))); + addParameter(p,'LogScale',0); + addParameter(p,'FaceAlpha',0.2); + addParameter(p,'Ymin',nan); + addParameter(p,'LineCol',[0,0,0]); + addParameter(p,'AreaCol',0.5*[1,1,1]); + addParameter(p,'LineWidth',2); + addParameter(p,'LineStyle','-'); + addParameter(p,'mode','Interval'); + parse(p,varargin{:}); + areacol = p.Results.AreaCol; + fill_alpha = p.Results.FaceAlpha; + linecol = p.Results.LineCol; + plotmode = p.Results.mode; + ymin = p.Results.Ymin; + lw = p.Results.LineWidth; + logscale = p.Results.LogScale; + lstyle = p.Results.LineStyle; + + X = col_vec(X); + + + if any(size(I)==1) + Y_upper = col_vec(Y)+col_vec(I); + Y_lower = col_vec(Y)-col_vec(I); +% end + elseif any(size(I) == 2) %upper and lower CI specified + if size(I,1) == 2 + I = I'; + end + if strcmp(plotmode,'Interval') % supplied vals are the CI widths + Y_upper = col_vec(Y)+col_vec(I(:,2)); + Y_lower = col_vec(Y)-col_vec(I(:,1)); + elseif strcmp(plotmode,'Absolute') + Y_upper = I(:,1); + Y_lower = I(:,2); + else + error('Plot mode specification error') + end + else + error('CI size specification error') + end + + if logscale + if isnan(ymin) + ymin = 0.1*min(Y(Y>0)); + end + Y_lower(Y_lowernum_blobs? +% Many of the vectors will be close to each other + +% Adajcency matrix method +% All of the values above the threshold are considered 'on'. Two pixels +% i and j are connected iff they are both on and adjacent. +% The elements $(Im^n)_{i,j})$ of powers of Im give the number of paths +% of length n from i to j. +% The exponential of the matrix is a weighted sum of path-connectedness +% with factorially decaying weights. +% Therefore, elements of the exponential exp(Im) are 0 iff two nodes do +% not share any connection. +% The number of zero eigenvalues of Im is equal to the number of +% connected components. The null space of Im span (???) and have (???) +% interpretation in the graph. + +% We can compute the adjacency matrix (Are there memory savings by +% dynamic programming) by + % for each pix, subtract from neighbour (vert and horiz) and they are + % connected iff sum(im(i,j),im(i,j+1)) == 2 for j +% L(:,1). +% Optional kwargs: +% mode 'open' Strict inequality m < A < M +% 'closed' Inclusive limits m <= A <= M +% 'upper' Reverse inequality m < A <= M +% Example: +% ``` +% A = 1:6; +% L = [0,3 +% 5,6]; +% isequal(in_intervals(A,L),[1,1,0,0,1,0]) +% ``` + +p = inputParser; +addParameter(p,'mode','default'); +parse(p,varargin{:}); +mode = p.Results.mode; + +if numel(lims) < 2 + error('Limits must be pairs of values'); +end + +if iscolumn(lims) + lims = lims'; +end + +logical_out = false(size(A)); +if strcmp(mode,'default') + for l_ax = 1:size(lims,1) + logical_out = logical_out | (A>=min(lims(l_ax,:)))&(Amin(lims(l_ax,:)))&(A=min(lims(l_ax,:)))&(A<=max(lims(l_ax,:))); + end +elseif strcmp(mode,'upper') + for l_ax = 1:size(lims,1) + logical_out = logical_out | (A>min(lims(l_ax,:)))&(A<=max(lims(l_ax,:))); + end +end + + + +end \ No newline at end of file diff --git a/dev/index_bin_search.m b/dev/index_bin_search.m new file mode 100644 index 0000000..eade953 --- /dev/null +++ b/dev/index_bin_search.m @@ -0,0 +1,66 @@ +function bin_idx=index_bin_search(data,edges) +if ~iscolumn(data) || ~iscolumn(edges) + error('inputs must be column vectors') +end + +% number of bins is edges-1 + 2 extra for below lowest and above highest +num_edges=size(edges,1); +num_data=size(data,1); +bin_idx=zeros(num_data,1); +for ii=1:num_data + data_val=data(ii); + closest_idx=binary_search_first_elm(edges,data_val,1,num_edges); + closest_idx=closest_idx+1; + %if closest is on the edge check if it should go up or down + if closest_idx==2 + if data_valedges(num_edges) + closest_idx=closest_idx+1; + end + end + bin_idx(ii)=closest_idx; +end + +end + + + +%modified from mathworks submission by Benjamin Bernard +%from https://au.mathworks.com/matlabcentral/fileexchange/37915-binary-search-for-closest-value-in-an-array +function idx_closest = binary_search_first_elm(vec, val,lower_idx,upper_idx) +% Returns index of vec that is closest to val, searching between min_idx start_idx . +%If several entries +% are equally close, return the first. Works fine up to machine error (e.g. +% [v, i] = closest_value([4.8, 5], 4.9) will return [5, 2], since in float +% representation 4.9 is strictly closer to 5 than 4.8). +% =============== +% Parameter list: +% =============== +% arr : increasingly ordered array +% val : scalar in R +% use for debug in loop %fprintf('%i, %i, %i\n',btm,top,mid) + +top = upper_idx(1); +btm = lower_idx(1); + +% Binary search for index +while top > btm + 1 + mid = floor((top + btm)/2); + % Replace >= here with > to obtain the last index instead of the first. + if vec(mid) <= val %modified to work to suit histogram + btm = mid; + else + top = mid; + end +end + +% Replace < here with <= to obtain the last index instead of the first. +%if top - btm == 1 && abs(arr(top) - val) < abs(arr(btm) - val) +% btm = top; +%end + +idx_closest=btm; +end \ No newline at end of file diff --git a/dev/index_bin_search.prj b/dev/index_bin_search.prj new file mode 100644 index 0000000..1d1bb35 --- /dev/null +++ b/dev/index_bin_search.prj @@ -0,0 +1,1124 @@ + + + + false + false + option.WorkingFolder.Project + + option.BuildFolder.Project + + + true + true + true + true + option.GlobalDataSyncMethod.SyncAlways + true + option.DynamicMemoryAllocation.Threshold + 65536 + option.RowMajor.ColumnMajor + true + false + false + 200000 + option.FilePartitionMethod.MapMFileToCFile + true + false + + false + false + true + false + + + false + option.VerificationMode.None + option.VerificationStatus.Passed + false + false + + + + + + + + + false + 40000 + 50 + true + option.PreserveVariableNames.None + true + 10 + 200 + 4000 + true + 64 + true + true + option.ConstantInputs.CheckValues + true + false + false + true + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + false + option.WorkingFolder.Project + + option.BuildFolder.Project + + + true + false + true + 5 + true + option.DynamicMemoryAllocation.Threshold + 65536 + option.RowMajor.ColumnMajor + true + false + false + 200000 + false + option.FilePartitionMethod.MapMFileToCFile + true + option.CommentStyle.Auto + false + true + false + true + true + true + option.ParenthesesLevel.Nominal + 31 + option.DataTypeReplacement.CBuiltIn + false + + + + + + + + + + + + + $M$N + $M$N + $M$N + $M$N + $M$N + $M$N + emxArray_$M$N + emx$M$N + + false + false + false + true + false + false + false + false + + false + true + true + false + + false + false + option.VerificationMode.None + option.VerificationStatus.Inactive + + + + + + + + + C99 (ISO) + None + + true + Automatically locate an installed toolchain + Faster Builds + + true + + option.target.TargetType.MatlabHost + + Generic + MATLAB Host Computer + + true + 8 + 16 + 32 + 32 + 64 + 32 + 64 + 64 + 64 + 64 + 64 + option.HardwareEndianness.Little + true + true + option.HardwareAtomicIntegerSize.Char + option.HardwareAtomicFloatSize.None + option.HardwareDivisionRounding.Zero + Generic + MATLAB Host 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codegen\mex\index_bin_search + MEX_FILE + 2243334596 + codegen\mex\index_bin_search + 203116070 + basic_usage_histcn_search + false + <?xml version="1.0" encoding="UTF-8" standalone="yes"?><checksum><includedFiles><file>C:\Users\Bryce\Dropbox\UNI\projects\programs\Core_BEC_Analysis\dev\index_bin_search.m</file></includedFiles><value>863651712</value></checksum> + <?xml version="1.0" encoding="UTF-8" standalone="yes"?><sourceModel><primarySourceFiles><file>C:\Users\Bryce\Dropbox\UNI\projects\programs\Core_BEC_Analysis\dev\index_bin_search.m</file></primarySourceFiles><fixedPointSourceFiles/><fixedPointSourceRegistered>false</fixedPointSourceRegistered><fixedPointSourceSelected>false</fixedPointSourceSelected></sourceModel> + false + false + false + false + true + true + index_bin_search_mex + index_bin_search + option.target.artifact.mex + ${PROJECT_ROOT}\index_bin_search_mex.mexw64 + false + + -1 + + 200 + 1024 + false + false + false + false + false + + + + false + false + true + option.deeplearning.targetlibrary.none + false + true + true + option.tensorrt.datatype.fp32 + + 1 + true + option.cudnn.datatype.fp32 + option.arm-compute.version.18_05 + option.arm-compute.architecture.unspecified + option.TargetLang.C + true + false + + option.FixedPointMode.None + false + + + 16 + 4 + 0 + fimath('RoundingMethod', 'Floor', 'OverflowAction', 'Wrap', 'ProductMode', 'FullPrecision', 'MaxProductWordLength', 128, 'SumMode', 'FullPrecision', 'MaxSumWordLength', 128) + option.FixedPointTypeSource.SimAndDerived + + false + false + false + false + true + + + + + + + + + true + false + _fixpt + + false + false + option.DefaultFixedPointSignedness.Automatic + option.FixedPointTypeProposalMode.ProposeFractionLengths + false + option.fixedPointAction.none + + + + + + + + false + option.FixedPointAnalysisMode.Sim + false + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 1573438466220 + + + + ${PROJECT_ROOT}\basic_usage_histcn_search.m + + + + + + + + + double + :inf x 1 + + + true + false + false + + + + + + + C:\Users\Bryce\Dropbox\UNI\projects\programs\Core_BEC_Analysis\dev\index_bin_search_mex.mexw64 + + + + C:\Program Files\MATLAB\R2019a + + + + + + + + + + true + + + + + true + + + + + true + + + + + true + + + + + true + + + + + false + false + true + false + false + false + false + false + 10.0 + false + true + win64 + true + + + \ No newline at end of file diff --git a/dev/ring_removal.m b/dev/ring_removal.m new file mode 100644 index 0000000..9a1af84 --- /dev/null +++ b/dev/ring_removal.m @@ -0,0 +1,20 @@ +function data = ring_removal(data,t_lim) +%small function to remove ringing from reconstructed data +out_counts_txy = cell(size(data.counts_txy)); +out_num_counts = zeros(size(data.num_counts)); +for ii = 1:length(data.counts_txy) + num_counts = data.num_counts(ii); + if num_counts == 0 + out_counts_txy{ii} = data.counts_txy{ii}; + continue + end + counts=data.counts_txy{ii}; + t_dif = -counts(1:end-1,1)+counts(2:end,1); + t_dif_mask = logical([1;abs(t_dif)>t_lim]); + out_counts_txy{ii} = counts(t_dif_mask,:); + masked_counts = sum(~t_dif_mask); + out_num_counts(ii) = num_counts-masked_counts; +end +data.counts_txy = out_counts_txy; +data.num_counts = out_num_counts; +end \ No newline at end of file diff --git a/dev/sat_pulse_centre.m b/dev/sat_pulse_centre.m new file mode 100644 index 0000000..9ac99d3 --- /dev/null +++ b/dev/sat_pulse_centre.m @@ -0,0 +1,15 @@ +function [val,idx] = sat_pulse_centre(T,Y,minval,upperval) + %[val,idx] = sat_pulse_centre(T,Y,minval,thr) + % A function to find the centre of a saturated peak. + % Works by capping the flux at some value below the saturated level, + % then finding the centre of mass of the thresholded density. + + Y = col_vec(Y); + T = col_vec(T); + m = rescale(Y)>upperval; + Y(m) = upperval*max(Y); + Y(rescale(Y)thr) = +m = rescale(Y)>thr; +Ydash = Y; +Ydash(m) = thr*max(Y); +idx = mean(T(m)); +val = mean(T.*Ydash)/sum(Ydash); + +A = .4e-6; +tau = 2.; +quash_fun = @(t) [zeros(size(t)),A*exp(-t/tau)]; +tdash = 0:mean(diff(T)):10; +qe_quash = 1-conv(Y,quash_fun(tdash),'same'); +qe_quash(qe_quash<0) = 0; + +Y_sat = qe_quash.*Y; +[v_sat,i_sat] = sat_pulse_centre(T,Y_sat,0.1); + +m_sat = rescale(Y_sat)>thr; +Ydash_sat = Y_sat; +Ydash_sat(m_sat) = thr*max(Y_sat); +idx_sat = mean(T(m_sat)); +val_sat = mean(T.*Ydash_sat)/sum(Ydash_sat); + +cli_header('Saturated peak centering:'); +cli_header(1,'Support COM error: %.3e',idx_sat-centre_val); +cli_header(1,'Threshold COM error: %.3e',val_sat-centre_val); + +stfig('Saturated centering tests'); +clf +subplot(2,2,1) +hold on +plot(T,Y) +plot(T,Ydash) +plot(T(m),thr*max(Y)*ones(size(T(m))),'k') +plot(idx,0,'rx') +plot(val,0,'ko') +title('Raw profile') + +ylabel('Density') +xlabel('T') +subplot(2,2,2) +plot(quash_fun(tdash)) +title('Accumulation function') + +subplot(2,2,3) +plot(T,qe_quash) +title('QE loss envelope') + +subplot(2,2,4) +hold on +plot(T,Y_sat) +plot(T,Y,'k:') +plot(T,Ydash_sat) +plot(T(m_sat),thr*max(Y_sat)*ones(size(T(m_sat))),'k') +plot(T(i_sat),0,'rx') +plot(v_sat,0,'ko') +xlim([-5,5]) +title('Saturated peak') + +% first: threshold, find COM + + \ No newline at end of file diff --git a/dev/term2vec.m b/dev/term2vec.m new file mode 100644 index 0000000..9cff058 --- /dev/null +++ b/dev/term2vec.m @@ -0,0 +1,22 @@ +function state_out = term2vec(state) + % accepts n^SL_J_mJ string and returns [n l s j mj] vector - note the + % ordering + % Also turns a vector into term strings if needed? + % outputs in form + term_symbols = 'SPDFGHIJKL'; + if isstring(state) || ischar(state) + state_out = [str2num(state(1)),strfind(term_symbols,state(4))-1,0.5*(str2num(state(3))-1),str2num(state(6)),str2num(state(8))]; + else + % it's a vector, so make it into a string + state_out = ''; + + if len(state) == 3 + state_out = sprintf('%u_%u%s',state(1),2*state(2)+1,state(3)); + elseif len(state) == 4 + state_out = sprintf('%u_%u%s_%u',state(1),2*state(2)+1,state(3),state(4)); + elseif len(state) == 5 + state_out = sprintf('%u_%u%s_%u_%u',state(1),2*state(2)+1,state(3),state(4),state(5)); + end + + end +end \ No newline at end of file diff --git a/dev/thermometry_fits.m b/dev/thermometry_fits.m new file mode 100644 index 0000000..cc3517e --- /dev/null +++ b/dev/thermometry_fits.m @@ -0,0 +1,273 @@ +function shot_data = thermometry_fits(data,opts) + + cache_opts=[]; + if isfield(opts.temp,'cache_opts'), cache_opts=opts.temp.cache_opts; end + cache_opts.verbose=1; + + opts.shot_range = nan; + + + opts.shotnums = data.tdc.shot_num; + if ~isnan(opts.temp.shot_nums) + shot_nums = opts.temp.shot_nums; + shot_nums = shot_nums(shot_nums < max(opts.shotnums) & shot_nums >= 1); + opts.shotnums = shot_nums; + end + cli_header(1,'Fitting thermal profiles'); + shot_data = thermo_fit_core(data,opts); + + + %% + % for these temperatures, k_B*T ~ 5e-30, and hbar*omega_trap ~ 1.5e-31 + % so this is right about the crossover + + cli_header(2,'Done.'); +end + +function shot_data = thermo_fit_core(data,opts) + mcp_data = data.tdc; + mcp_data.all_ok = ones(size(mcp_data.N_atoms)); + num_shots = length(opts.shotnums); + + opts.c.fall_time = sqrt(2*opts.c.fall_distance/opts.c.g0); + opts.c.fall_velocity = 9.796*opts.c.fall_time; + + % Options for binning and show_TXY + opts.t0 = 0.4145; % Centre of first pulse (sec) + opts.pulsedt = .008; %time between pulses (sec) + opts.num_bins = [50,50,50]; + opts.hist_2d = false; + opts.draw_plots = false; + opts.centre_bec = true; + opts.verbose = false; + opts.xylim = [-0.03,.03;-.03,.03]; + opts.pulse_twindow = .003; + +% min_flux = 1e4; +% num_pulses = 75; + single_shot_plot = opts.single_shot_plot; + do_refits = true; + min_shot_counts = 1e2; + + x_refit_lvl = 0.15; + y_refit_lvl = 0.15; + + const.g0 = 9.796; + const.mhe = 6.6433e-27; + const.kb=1.380e-23; + + A = 5e3; + T_guess=250; %nK + x_guess.bose = [A,0,T_guess,0]; + x_guess.gauss = x_guess.bose; + +% gfit_guess(3) = sqrt(const.mhe*gfit_guess(3)/const.kb); + g_tol = 1e-4; + n_p = @(p,v) p(1)*g_bose(exp(-const.mhe*abs((v-p(2))).^2/(2*const.kb*p(3)*1e-9)),g_tol)+p(4); + gfun = @(b,x) b(1).*exp(-const.mhe*((x-b(2)).^2)./(2*const.kb*b(3)*1e-9))+b(4); + fit_options = statset('TolFun',1e-6); + + shot_data=[]; + shot_data.pulse_data = cell(num_shots,1); + shot_data.ok_mask = zeros(num_shots,1); + shot_data.shot_num= ones(num_shots,1); + shot_data.num_counts= ones(num_shots,1); + shot_data.T = nan(num_shots,2); %val, SE + + for idx=1:num_shots + i = opts.shotnums(idx); + warning('off') + if mod(idx,10)==0 + cli_header('Working on shot %u/%u (%u)...',idx,num_shots,i); + end + try + mask = zeros(size(data.tdc.N_atoms)); + mask(i) = 1; +% this_txy = data.tdc.counts_txy{i}; + tshot = struct_mask(data.tdc,logical(mask)); + topts.draw_plots = false; + topts.num_bins = [100,100,100]; + topts.verbose = 0; + pulse_data = show_txy_raw(tshot,topts); + if tshot.N_atoms < min_shot_counts + warning('on') + warning('Insufficient counts in shot %u',i) + warning('off') + shot_data.ok_mask(i,:) = 0; + else + +% pulse_data.x_cens = zeros(opts.num_bins(2)); +% pulse_data.y_cens= zeros(opts.num_bins(3)); +% pulse_data.x_flux= zeros(num_pulses,opts.num_bins(2)); +% pulse_data.y_flux= zeros(num_pulses,opts.num_bins(3)); +% pulse_data.txy = cell(num_pulses,1); +% pulse_data.num= zeros(num_pulses,1); +% pulse_data.cen= zeros(num_pulses,3); +% pulse_data.std= zeros(num_pulses,3); + +% for pulse_num = 1:num_pulses +% if pulse_num == 80 +% fprintf('Hi'); +% end +% opts.lims = [opts.t0+(pulse_num-1)*opts.pulsedt,opts.t0+(pulse_num)*opts.pulsedt; +% opts.xylim(1,:); +% opts.xylim(2,:)]; +% +% % h_data = show_txy_raw(tshot,opts); +% pulse_data.x_cens = h_data.centres{2}; +% pulse_data.y_cens = h_data.centres{3}; +% pulse_data.x_flux(pulse_num,:) = h_data.flux_1d{2}; +% pulse_data.y_flux(pulse_num,:) = h_data.flux_1d{3}; +% pulse_data.txy{pulse_num} = h_data.txy; +% pulse_data.num(pulse_num) = size(h_data.txy,1); +% pulse_data.cen(pulse_num,:) = h_data.pulse_cen; +% pulse_data.std(pulse_num,:) = h_data.pulse_std; +% end % loop over pulses + + X = pulse_data.centres{2}; + x_mean_flux = pulse_data.flux_1d{2}; + v_x = X/opts.c.fall_time; + [max_flux,max_loc] = max(x_mean_flux); + flux_cen_v = v_x(max_loc); + x_mask = x_mean_flux < .05*max_flux; + x_guess.bose = [A,0,T_guess,0]; + x_guess.gauss = x_guess.bose; + x_guess.bose(2) = flux_cen_v; + x_guess.gauss(2) = flux_cen_v; + + gauss_guess_fun = gfun(x_guess.gauss,v_x(x_mask)); + bose_guess_fun = n_p(x_guess.bose,v_x(x_mask)); + + bose_rescale = mean(bose_guess_fun'./x_mean_flux(x_mask)); + gauss_rescale = mean(gauss_guess_fun'./x_mean_flux(x_mask)); + x_guess.bose(1) = x_guess.bose(1)/bose_rescale; + x_guess.gauss(1) = x_guess.gauss(1)/gauss_rescale; + gauss_guess_fun = gfun(x_guess.gauss,v_x(x_mask)); + bose_guess_fun = n_p(x_guess.bose,v_x(x_mask)); + + if sum(x_mask) < 10 + warning('on') + warning('Too few points to fix in shot %u X',i) + shot_data.ok_mask(i) = 0; + else + if opts.do_fits + +% x_guess.bose=fit_guess; + x_mdl = fitnlm(v_x(x_mask),x_mean_flux(x_mask),n_p,x_guess.bose,... + 'Options',fit_options); + x_coef.bose= x_mdl.Coefficients.Estimate; + x_SE = x_mdl.Coefficients.SE; + bose_resid_x =(col_vec(n_p(x_coef.bose,v_x))-col_vec(x_mean_flux)); + x.bose.rel_err = col_vec(bose_resid_x)./col_vec(x_mean_flux); + + % Fit Gaussian functions +% x_guess.gauss=gfit_guess; + + x_mdlfit.gauss = fitnlm(v_x(x_mask),x_mean_flux(x_mask),gfun,x_guess.gauss,... + 'Options',fit_options); + x_coef.gauss = x_mdlfit.gauss.Coefficients.Estimate; + gauss_resid_x = (col_vec(gfun(x_coef.gauss,v_x))-col_vec(x_mean_flux)); + x.gauss.rel_err = col_vec(gauss_resid_x)./col_vec(x_mean_flux); + + % re-fit +% x_refit_mask = abs(x.gauss.rel_err) < x_refit_lvl | abs(x.bose.rel_err) < x_refit_lvl; + x_refit_mask = abs(x.bose.rel_err) < x_refit_lvl; + if sum(x_refit_mask) > sum(x_mask) && do_refits + % New things to fit + x_mask = x_refit_mask & abs(v_x) > .01; + x_mdl = fitnlm(v_x(x_mask),x_mean_flux(x_mask),n_p,x_guess.bose,... + 'Options',fit_options); + x_coef.bose= x_mdl.Coefficients.Estimate; + x_SE = x_mdl.Coefficients.SE; + bose_resid_x =(n_p(x_coef.bose,v_x)-x_mean_flux); + x.bose.rel_err = bose_resid_x./x_mean_flux; + end + temp_x =(abs(x_coef.gauss(3)));% *const.mhe/const.kb; + temp_x_SE =(abs(x_mdlfit.gauss.Coefficients.SE(3))) *const.mhe/const.kb; + shot_data.T(idx,:) = 1e-9*[temp_x,temp_x_SE]; + end + shot_data.ok_mask(i) = 1; + end + + + + [~, msgid] = lastwarn; %were there warnings in that attempt? + if strcmp(msgid,'stats:nlinfit:IllConditionedJacobian') +% cli_header(2,'Shot %u Gaussian poorly fitted\n',i); + % shot_data.ok_mask(i) = 0; + warning('Restting warning...'); + end + + shot_data.shot_num(i) = i; + shot_data.num_counts(i) = mcp_data.N_atoms(i); +% shot_data.pulse_counts(idx,:) = pulse_data.num; + if opts.do_fits + pulse_data.gauss.residual.x = gauss_resid_x; + pulse_data.bose.residual.x = bose_resid_x; + pulse_data.x_mask = x_mask; + end + + + if single_shot_plot + cli_header(2,'Plotting...'); + stfig('Pulse data'); + clf + subplot(2,1,1) + hold on + plot(v_x,x_mean_flux,'k:') + plot(v_x(x_mask),x_mean_flux(x_mask),'k*') + plot(v_x(x_mask),gauss_guess_fun,'go') + plot(v_x(x_mask),bose_guess_fun,'bo') +% plot(v_x(x_mask),x_mean_flux(x_mask),n_p,fit_guess) + if opts.do_fits +% plot(v_x(x_refit_mask),x_mean_flux(x_refit_mask),'ko') + plot(v_x,n_p(x_coef.bose,(v_x)),'k-.') + plot(v_x,n_p(x_coef.gauss,(v_x)),'r-.') + end +% ylim([100,max(2*x_mean_flux)]) + legend('Flux','Fit domain 1','GFit guess','BFit guess','Polylog','Gaussian') + plot(v_x,gfun(x_guess.gauss,v_x),'g:') + plot(v_x,n_p(x_guess.bose,v_x),'b:') + xlabel('$v_x$') + ylabel('Flux') + set(gca,'Yscale','log') + title('Mean X profile') + + subplot(2,1,2) + hold on + if opts.do_fits + plot(v_x(x_mask),(n_p(x_coef.bose,abs(v_x(x_mask)))'-x_mean_flux(x_mask))./x_mean_flux(x_mask),'ro') +% suptitle(sprintf('Shot %u: T$_P$ =(%.2e,%.2e), T$_G$ =(%.2e,%.2e), N=%u',i,x_coef.bose(3),y_coef.bose(3),gauss_temp_x,gauss_temp_y,tshot.N_atoms)); + end + legend('Polylog','Gaussian','Location','NorthEast') + ylim([-1,1]) + xlabel('$v_x$') + ylabel('$\Delta/y$') + title('Normalised residuals') + + + drawnow + + end % single shot plot + + end %if enough counts + + catch + warning('on') + warning('Error in shot %u',i); + shot_data.ok_mask(i) = 0; + + end %try shot + end %loop over shots +% if opts.visual +% stfig('PAL results'); +% clf +% hold on +% errorbar(1:length(shot_data.T),1e9*shot_data.T(:,1),1e9*shot_data.T(:,2),'kx') +% xlabel('Shot number') +% ylabel('T (nK)') +% set(gca,'FontSize',16) +% end +% title('$v_y$ residuals') + +end \ No newline at end of file diff --git a/lib/CLI_tools/cli_header.m b/lib/CLI_tools/cli_header.m new file mode 100644 index 0000000..1a4d51d --- /dev/null +++ b/lib/CLI_tools/cli_header.m @@ -0,0 +1,43 @@ +function msg_out = cli_header(varargin) + % A function that makes nice sub headers in the console + % Works OK with numeric substitution, but needs a length checking + % function. + + % Examples: +% header('Header examples') +% header(2,'Some options:') +% header(3,'%u %u,...',[1,2]) + + % Improvements; +% switch to varargin +% Tests + args = varargin; + if iscell(varargin{1}) + fprintf("cli_header accepts varargin, cell args will be removed next version.\n") + args = varargin{1}; + end + v = 1; + if numel(args) == 1 %text only + msg = args{1}; + lvl = 0;%If no header level is passed, assumed to be top-level + + else + if isfloat(args{1}) %Passing header level + lvl = args{1}; + msg = args{2}; + if numel(args)>2 + v = 3; + end + else % No header level passed, but other values present + lvl = 0; + msg = args{1}; + v = 2; + end + end + msg_out = sprintf(msg,args{v:end}); +% blank = '------------------------------------------------------------'; + blank = ' '; + marker = blank(1:2*lvl+1); + fprintf([marker,' - ',msg_out,'\n']) + +end \ No newline at end of file diff --git a/lib/command_line_format_tools/fwtext.m b/lib/CLI_tools/fwtext.m similarity index 100% rename from lib/command_line_format_tools/fwtext.m rename to lib/CLI_tools/fwtext.m diff --git a/lib/command_line_format_tools/header.m b/lib/CLI_tools/header.m similarity index 76% rename from lib/command_line_format_tools/header.m rename to lib/CLI_tools/header.m index 925b5e6..0ceecd3 100644 --- a/lib/command_line_format_tools/header.m +++ b/lib/CLI_tools/header.m @@ -2,7 +2,7 @@ function header(vargin) % A function that makes nice sub headers in the console % Works OK with numeric substitution, but needs a length checking % function. - warning('this function has been migrated to cli_header and will be removed in a future release\n please change to the new function name') + warning('this function has been migrated to cli_header and will be removed in a future release') cli_header(vargin) end \ No newline at end of file diff --git a/lib/CLI_tools/sltext.m b/lib/CLI_tools/sltext.m new file mode 100644 index 0000000..6d30463 --- /dev/null +++ b/lib/CLI_tools/sltext.m @@ -0,0 +1,28 @@ +function sltext(args) + % A function that makes nice headers in the console + % Works OK with numeric substitution, but needs a length checking + % function. + if ischar(args) + msg = args; + vals = []; + elseif iscell(args) + msg = args{1}; + vals = args{2:end}; + end + msg_out = sprintf(msg,vals); + msg_len=length(msg_out); + blank = '\n------------------------------------------------------------\n'; + width = length(blank); + + if msg_len ==0 + elseif mod(msg_len,2) ==0 && msg_len ~=0 + msg0 = width/2 - msg_len/2; + msg1 = width/2 + msg_len/2; + blank(msg0:msg1+1) = [' ',msg_out,' ']; + else + msg0 = width/2 - (msg_len-1)/2; + msg1 = width/2 + (msg_len+1)/2; + blank(msg0:msg1+1) = [' ',msg_out,' ']; + end + fprintf(blank,vals); +end \ No newline at end of file diff --git a/lib/CLI_tools/sshow/sshow.m b/lib/CLI_tools/sshow/sshow.m index 1c68d54..39b91da 100644 --- a/lib/CLI_tools/sshow/sshow.m +++ b/lib/CLI_tools/sshow/sshow.m @@ -1,42 +1,30 @@ -function sshow(varargin) +function sshow(s) % Displays the tree structure of a struct variable and the types of its % terminal nodes (leaves). % Input: s - struct -% Ourput: nothing - for now, may eventually return a tree -% Improvements: - % Show variable dimensions as in MATLAB's default display +% Ourput: nothing - for now, will eventually return a tree +% Improvements: Show variable dimensions as in MATLAB's default display % Return a representation of the branch structure - % Align the name/type columns more cleanly - % Output field contents (if singleton) or first few (if - % array/cell?) - % Display warning if non-struct passed as input - - + % +sshow_core(s,0); + +end + +function sshow_core(s,depth) -if nargin == 1 - depth =0; - sname = inputname(1); - fprintf('Contents of structure %s:\n',sname) - sshow(varargin{1},0); -else - depth = varargin{2}; - s = varargin{1}; if isstruct(s) fnames = fields(s); nfields = numel(fnames); - buffer = ' >'; + buffer = ' '; for k=1:depth - buffer = [' ',buffer]; + buffer = [buffer,' ']; end for fieldnum = 1:nfields - fprintf([buffer,' ',fnames{fieldnum},'\n']) - sshow(s.(fnames{fieldnum}),depth+1) + fprintf([buffer,'- ',fnames{fieldnum},'\n']) + sshow_core(s.(fnames{fieldnum}),depth+1) end else - fprintf('\b - %s\n',class(s)) + fprintf('\b - %ux%u %s\n',size(s,1),size(s,2),class(s)) end -end - - end \ No newline at end of file diff --git a/lib/command_line_format_tools/sshow/sshow_test.m b/lib/CLI_tools/sshow/sshow_test.m similarity index 100% rename from lib/command_line_format_tools/sshow/sshow_test.m rename to lib/CLI_tools/sshow/sshow_test.m diff --git a/lib/bec_cals/bec_properties.m b/lib/bec_cals/bec_properties.m index 20c0c07..c8e6f03 100644 --- a/lib/bec_cals/bec_properties.m +++ b/lib/bec_cals/bec_properties.m @@ -1,110 +1,190 @@ -function details=bec_properties(omega,atom_number,mass,a_scat_len) +function details=bec_properties(omega,atom_number,varargin) % calculate key properties of bose-einstein condensates % input -% omega-[scalar or 1x3] in hz -% atom number - scalar -% output -% -% todo: Vectorize omega x atom_num +% omega - [m x 1 or m x 3] scalar array in hz +% atom number - [n x 1] scalar array +% optional keyword arguments +% mass - particle mass (default const.mhe = 6.6433e-27 kg +% a_scat_len - s-wave scattering length, default 7.512e-9 m +% temperature - Default 0 K +% Returns a number of quantities indexed by [n,m,:] where dependent on +% number and frequency, or indexed by [m,:] where independent of number +% Usage notes: +% omega MUST be row-indexed by the trap instance and column-indexed by +% the trap axis (ie, [wx_1,wy_1,wz_1;wx_2,wy_2,wz_2;...]) OR a column +% vector of isotropic frequencies [w1;w2;w3;...;wn]. The single-trap +% case requires an input of a scalar or 1x3 array. +% Possible improvements: +% Vectorize over kwarg inputs +% Implement better testing warning('do not trust this function, it has not been tested well enough') +warning('bec_properties now accepts kwargs (trap_freqs, total_number,varargin)') + %if the constants strucure already exists do not run % set up the constants global const if isempty(const) - hebec_constants + const = hebec_constants; end +p = inputParser; +% defaultFontSize = 12; +% defaultFont = 'times'; +addParameter(p,'temperature',0); +addParameter(p,'mass',const.mhe); +addParameter(p,'th_frac',nan); +addParameter(p,'a_scat_len',const.ahe_scat); +parse(p,varargin{:}); +temperature = p.Results.temperature; +mass = p.Results.mass; +a_scat_len = p.Results.a_scat_len; +th_frac = p.Results.th_frac; + + +% isotropic = false; % input parsing % omega -omega=col_vec(omega); -if numel(omega)==1 - omega=cat(1,omega,omega,omega); -elseif numel(omega)~=3 - error('omega must be 1, or 3 elements') -end - -if sum(omega<0)>0 && sum(imag(omega)>0)>0 - error('omega must be positive real') +if isvector(omega) + omega_vec = true; + omega=col_vec(omega); + if numel(omega)==1 + omega=cat(1,omega,omega,omega); + elseif numel(omega)~=3 && numel(omega)~=1 + error('omega must be 1, or 3 elements') + end + if sum(omega<0)>0 && sum(imag(omega)>0)>0 + error('omega must be positive real') + end +else +% omega is a matrix + omega_vec = false; + if size(omega,2) == 1 + omega = cat(2,omega,omega,omega); + end + omega = omega'; %each omega is now a col_vec end omega=2*pi*omega; -%mass -if nargin<3 || isnan(mass) || isempty(mass) - mass=const.mhe; -end - -%scat_len -if nargin<4 || isnan(a_scat_len) || isempty(a_scat_len) - a_scat_len=7.512000000000000e-09; -end - % begin calculation - - details=[]; -omega_bar=prod(omega)^(1/3); +omega_bar=prod(omega).^(1/3); omega_mean=mean(omega); - -tc_non_interacting=const.hb *omega_bar*(atom_number^(1/3))/((zeta(3)^(1/3))*const.kb); +atom_number = col_vec(atom_number); +zeta_3 = 1.202056903; +tc_non_interacting=const.hb *omega_bar.*(atom_number.^(1/3))/((zeta_3^(1/3))*const.kb); %fprintf('tc non interaging %g \n',tc_non_interacting) %pethick eq2 .91 -tc_finite_number=tc_non_interacting*(1-0.73*omega_mean/((atom_number^(1/3))*omega_bar)); +tc_finite_number=tc_non_interacting.*(1-0.73*omega_mean./((atom_number.^(1/3))*omega_bar)); %fprintf('tc finite number %g \n',tc_finite_number) -abar=sqrt(const.hb/(mass*omega_bar)); +oscillator_length = sqrt(const.hb./(mass*omega))'; +abar=sqrt(const.hb./(mass*omega_bar)); %pethick eq11.14 -tc_finite_interacting=tc_finite_number-tc_non_interacting*... - (1.33*a_scat_len*atom_number^(1/6)/(abar)); +tc_finite_interacting=tc_finite_number-tc_non_interacting.*... + (1.33*a_scat_len*atom_number.^(1/6)./(abar)); -%fprintf('tc finite non interacting %g \n',tc_finite_interacting) +%fprintf('tc finite non interacting %g \n',tc_finite_interacting) +if isnan(th_frac) + condensed_fraction = 1 - (temperature./tc_finite_interacting).^3; +else + condensed_fraction = 1 - th_frac; +end +ideal_condensed_fraction = 1 - (temperature./tc_non_interacting).^3; +condensed_number = atom_number.*condensed_fraction; % other things we can calculate % chemical potential %pethick eq6.35 mu_chem_pot=((15^(2/5))/2)... - *((atom_number*a_scat_len/abar)^(2/5))*... + *((condensed_number *a_scat_len/abar).^(2/5))*... const.hb*omega_bar; -details.mu_chem_pot=mu_chem_pot; + %pethick eq6.33 -r_tf_radi=sqrt(2*mu_chem_pot./(mass.*omega.^2)); +if omega_vec + r_tf_radi=sqrt(2*mu_chem_pot./(mass.*omega'.^2)); +else %more complicated if omega is tensor: need to return n x m x 3 array + m = size(omega,2); + n = size(atom_number,1); + r_tf_radi = nan(n,m,3); + for mm = 1:m + r_tf_radi(:,mm,:) = mu_chem_pot(:,mm)./(mass*omega(:,mm).^2)'; + end + r_tf_radi=sqrt(2*r_tf_radi); +end + +if omega_vec + r_bar=prod(r_tf_radi,2).^(1/3); + r_mean=mean(r_tf_radi,2); + tf_volume=(4/3)*pi*prod(r_tf_radi,2); +else + r_bar=prod(r_tf_radi,3).^(1/3); + r_mean=mean(r_tf_radi,3); + tf_volume=(4/3)*pi*prod(r_tf_radi,3); +end -r_bar=prod(r_tf_radi)^(1/3); -r_mean=mean(r_tf_radi); %pethick eq6.33 u_eff_interaction=4*pi*const.hb^2*a_scat_len/mass; -n_max_peak_density=mu_chem_pot/u_eff_interaction; +n_peak_density=mu_chem_pot/u_eff_interaction; % %find the average density inside the elipsoid -tf_volume=(4/3)*pi*prod(r_tf_radi); -n_mean_density=atom_number/tf_volume; -tan_constant = (n_max_peak_density)*((64*pi^2)/7)*a_scat_len^2; +n_mean_density=condensed_number ./tf_volume; %Pethick % Smith 6.31 +tan_contact= condensed_number .*(n_peak_density)*((64*pi^2)/7)*a_scat_len^2; %Chang 2016 & Ross 2020(ish) -details.tc.non_interacting=tc_non_interacting; -details.tc.finite_number=tc_finite_number; -details.tc.finite_interacting=tc_finite_interacting; -details.omega_mean=omega_mean; -details.omega_bar=omega_bar; +LHY_correction.mean = 2.5*(128/(15*sqrt(pi)))*sqrt(n_mean_density*a_scat_len^3); +LHY_correction.peak = 2.5*(128/(15*sqrt(pi)))*sqrt(n_peak_density*a_scat_len^3); + + +speed_of_sound = sqrt(u_eff_interaction*n_peak_density/mass); %Pethick and Smith 8.92 +% oscillator_length = abar; +healing_length = 1./(8*pi*a_scat_len*n_peak_density); % Pethick % Smith 6.62 + +% landau_critical_velocity = +% Baym & Pethick 2012 https://arxiv.org/pdf/1206.7066.pdf + + +% scalar outputs +details.u_eff_interaction=u_eff_interaction; +details.lambda_db = deBroglie_wavelength(temperature); +% number-dependent outputs +details.mu_chem_pot=mu_chem_pot; + +details.tf_volume=tf_volume; +details.density_peak=n_peak_density; +details.density_mean=n_mean_density; +details.tan_contact= tan_contact; +details.healing_length = healing_length; +details.speed_of_sound = speed_of_sound; +details.condensed_fraction.interacting = condensed_fraction; +details.condensed_fraction.non_interacting = ideal_condensed_fraction; details.tf_radi=r_tf_radi; details.tf_radi_bar=r_bar; details.tf_radi_mean=r_mean; -details.tf_volume=tf_volume; -details.density_peak=n_max_peak_density; -details.density_mean=n_mean_density; -details.u_eff_interaction=u_eff_interaction; -details.tan_contact= tan_constant; +% Number-independent outputs +details.oscillator_length = oscillator_length; %geometric means +details.omega_mean=omega_mean'; +details.omega_bar=omega_bar'; + +% struct outputs +details.tc.non_interacting=tc_non_interacting; +details.tc.finite_number=tc_finite_number; +details.tc.finite_interacting=tc_finite_interacting; +details.LHY_correction= LHY_correction; +details.inputs.omega = omega; +details.inputs.atom_number = atom_number; +details.inputs.mass = mass; end diff --git a/lib/bec_cals/bec_tc.m b/lib/bec_cals/bec_tc.m index b29b8d6..bad6a4d 100644 --- a/lib/bec_cals/bec_tc.m +++ b/lib/bec_cals/bec_tc.m @@ -1,8 +1,8 @@ function [tc_out,details]=bec_tc(omega,atom_number,mass) % input % omega-[scalar or 1x3] in hz +warning('this function will be merged into bec_properties, please move your code use') -warning('do not trust this function, it has not been tested') %if the constants strucure already exists do not run global const if isempty(const) diff --git a/lib/bec_cals/fake_shot.m b/lib/bec_cals/fake_shot.m new file mode 100644 index 0000000..0a51ac4 --- /dev/null +++ b/lib/bec_cals/fake_shot.m @@ -0,0 +1,326 @@ +function shot_data = fake_shot(total_number,trap_freqs,const,varargin) + +% fake_shot(total_number,trap_freqs,const,varargin) generates data that +% mimics the k-space density of thermal and quantum depleted fractions, +% plus a spatially uniform dark count rate. Returns a structure with fields: +% k_cart Nx3 k-vector where N = num counts generated +% k Lists all k-vector magnitudes (k.detections) and the +% maximum index of the thermal, depleted, and background +% counts (k.partitions) +% stats Various properties of the generated data +% Mandatory inputs: +% total_number +% trap_freqs +% const struct - table of physical constants (consistent with +% hebec_constants) +% Example: +% ``` +% const = hebec_constants() +% shot_data = fake_shot(5e5,[420,420,42],const,'temperature',1e-7,'QE',0.1); +% ``` + +% Parse the inputs + p = inputParser; + % defaultFontSize = 12; + % defaultFont = 'times'; + addParameter(p,'temperature',0); + addParameter(p,'background_rate',0); + addParameter(p,'QE',1); + addParameter(p,'contact_scale',1); + addParameter(p,'k_max',1e7); + addParameter(p,'k_min',1e6); + addParameter(p,'verbose',0); + addParameter(p,'visual',0); + addParameter(p,'phi_range',nan); + parse(p,varargin{:}); + temperature = p.Results.temperature; + background_rate = p.Results.background_rate; + contact_scale = p.Results.contact_scale; + QE = p.Results.QE; + k_max = p.Results.k_max; + k_min = p.Results.k_min; + verbose = p.Results.verbose; + visual= p.Results.visual; + phi_range= p.Results.phi_range; + +% Calculate some useful objects + w_HO = 2*pi*geomean(trap_freqs); + total_number = ceil(total_number); + critical_temperature = (0.94*const.hbar*w_HO*total_number^(1/3))/const.kb; + if temperature > critical_temperature + error('T > T_c, many calculations will fail'); + end + condensed_fraction = 1-(temperature/critical_temperature)^3; + condensed_number = ceil(condensed_fraction*total_number); + + bec_prop = bec_properties(trap_freqs,total_number,'temperature',temperature); + interparticle_distance = (1/bec_prop.density_peak)^(1/3); + n0 = bec_prop.density_peak; + contact = contact_scale*(64*pi^2*const.ahe_scat^2)*n0*condensed_number/7; + lambda_db = deBroglie_wavelength(temperature); + + % factor of 2 comes from integrating n(k) + num_depletion_before_cut = ceil(1*(contact/(2*pi^2*k_min))); + num_depletion_after_cut = 1*(contact/(2*pi^2*k_min) - contact/(2*pi^2*k_max)); + k_thermal = 10/lambda_db; + num_depletion_outside_thermal = 1*(contact/(2*pi^2*k_thermal) - contact/(2*pi^2*k_max)); + condensed_number = condensed_number - num_depletion_before_cut; + thermal_number = total_number - condensed_number; % should be non-negative + detector_volume = (2*k_max)^3; + n_background = round(background_rate*detector_volume); + + % Generate the samples + uniform_seed = rand(ceil(num_depletion_before_cut),1); + alpha = 2; %for the power-law transform - note that this produces the *counts* which are then converted to density + depletion_kvec = k_min*(1 - uniform_seed).^(-1/(alpha - 1)); + depletion_dirs = randn(ceil(num_depletion_before_cut),3); + depletion_dirs = depletion_dirs./vecnorm(depletion_dirs')'; + depletion_counts = depletion_kvec.*depletion_dirs; + + sigma_thermal_v = sqrt(const.kb*temperature/const.mhe); + thermal_counts = const.mhe*sigma_thermal_v*randn(thermal_number,3)/const.hbar; + + background_counts = 2*k_max*(rand(n_background,3)-0.5); % 3D uniform distribution in a box + + % Account for detector efficiency + QE_samples = 1:ceil(QE*length(depletion_counts)); + depletion_counts = depletion_counts(QE_samples,:); + thermal_counts = thermal_counts(1:ceil(QE*length(thermal_counts)),:); + + depletion_kvec = depletion_kvec(QE_samples); + thermal_kvec = vecnorm(thermal_counts,2,2); + background_kvec = vecnorm(background_counts,2,2);% + + % trim to detector + depletion_mask = (depletion_kvec > k_min & depletion_kvec < k_max); + thermal_mask = (thermal_kvec > k_min & thermal_kvec < k_max); + background_mask = (background_kvec > k_min & background_kvec < k_max); + + % write some output for feedback + if verbose + cli_header('Setting up sims with N=%u, T=%.2f nK w_HO = 2pi*%.1f Hz',total_number,1e9*temperature, w_HO/(2*pi)); + if verbose>1 + cli_header(1,'Wavevector range %.2e, %.2e',k_min,k_max); + cli_header(1,'Background density %.2e produces %.2e counts', background_rate,n_background); + cli_header(1,'Cond frac of %.2f produces %.2f counts', condensed_fraction,condensed_number); + cli_header(1,' With peak density %.2e', n0); + cli_header(1,' and thermal population is %.2f counts', thermal_number); + cli_header(1,'The deBroglie wavelength is %.2f micron', 1e6*lambda_db); + cli_header(1,'Interparticle spacing at peak is %.2e m', interparticle_distance); + cli_header(1,'The total contact is %.2e (%.1fx Tan theory)',contact,contact_scale); + cli_header(1,'The Contact region will be from k >> (%.2e,%.2e)',1/interparticle_distance,1/lambda_db); + cli_header(1,'Av num in %.2e1 + cli_header(1,'%u depletion outside thermal',sum(depletion_mask)); + end + end + + if ~isnan(phi_range) + qd_phi = atan(depletion_counts(:,3)./sqrt(depletion_counts(:,1).^2+depletion_counts(:,2).^2)); + th_phi = atan(thermal_counts(:,3)./sqrt(thermal_counts(:,1).^2+thermal_counts(:,2).^2)); + bg_phi = atan(background_counts(:,3)./sqrt(background_counts(:,1).^2+background_counts(:,2).^2)); + depletion_mask_phi = abs(qd_phi) > phi_range(1) & abs(qd_phi) < phi_range(2); + thermal_mask_phi = abs(th_phi) > phi_range(1) & abs(th_phi) < phi_range(2); + background_mask_phi = abs(bg_phi) > phi_range(1) & abs(bg_phi) < phi_range(2); + + depletion_mask = depletion_mask_phi & depletion_mask; + thermal_mask = thermal_mask_phi & thermal_mask; + background_mask = background_mask_phi & background_mask; + if verbose>1 + cli_header('Masking out counts outside %.2fdg<|phi|<%.2fdg, leaving %u/%u counts',rad2deg(phi_range(1)),rad2deg(phi_range(2)),... + sum(depletion_mask_phi)+sum(thermal_mask_phi)+sum(background_mask_phi),length(depletion_mask)+length(thermal_mask)+length(background_mask)); + cli_header(1,'Final detections (%u therm, %u dep, %u backg)',sum(thermal_mask),sum(depletion_mask),sum(background_mask)); + end + end + + depletion_counts = depletion_counts(depletion_mask,:); + thermal_counts = thermal_counts(thermal_mask,:); + background_counts = background_counts(background_mask,:); + + depletion_kvec = depletion_kvec(depletion_mask); + thermal_kvec = thermal_kvec(thermal_mask); + background_kvec = background_kvec(background_mask); + + k_cloud = [thermal_counts;depletion_counts]; + k_cart = [k_cloud;background_counts]; + k_detections = vecnorm(k_cart,2,2); + + + %Make some plots for display + + k_plot = linspace(k_min,k_max,3e2); + p_plot = const.hb*k_plot; + v_plot = p_plot/const.mhe; + + g_tol = 1e-5; + density_scale = (2*pi)^-3; + % constants out front to convert from p to k + thermal_BoseEinstein = QE*(const.hbar)^3 * (1/(lambda_db*const.mhe*w_HO)^3)*g_bose(exp(-(p_plot).^2/(2*const.mhe*const.kb*temperature)),g_tol); + thermal_MaxwellBoltzmann = QE *thermal_number*(const.hbar/const.mhe)^3 * 1/sqrt(2*pi)* (const.mhe/(const.kb*temperature)) * exp(-(1/2)*((p_plot).^2)/(2*const.mhe*const.kb*temperature)); + thermal_chang = QE*thermal_number*g_bose(exp(-((k_plot*lambda_db).^2)/(4*pi)),g_tol)/(1.202*(2*pi/lambda_db)^3); + + depletion_profile = QE*density_scale * contact./(k_plot.^4); + + + % K cartesian coordinates + shot_data.k_cart = k_cart; + % k radial vectors + shot_data.k.detections = k_detections; + % Indices to re-partition the counts according to their sources + shot_data.k.partitions = [size(thermal_counts,1),size(depletion_counts,1),size(background_counts,1)]; + % plotting stuff +% shot_data.hist.edges = log_edges; +% shot_data.hist.centres = log_bin_centres; +% shot_data.hist.volumes = log_bin_volumes; +% shot_data.hist.counts = hist_allcounts; + + shot_data.stats.N=total_number; + shot_data.stats.T=temperature; + shot_data.stats.data_domain = [k_min,k_max]; + shot_data.stats.background_density = background_rate; + shot_data.stats.background_counts = n_background; + shot_data.stats.cond_pop = condensed_number; + shot_data.stats.peak_density = n0; + shot_data.stats.thermal_pop = thermal_number; + shot_data.stats.deBroglie_wavelength = lambda_db; + shot_data.stats.contact = contact; + shot_data.stats.contact_scale = contact_scale; + shot_data.stats.k_ranges(1,:) = [k_min,inf,num_depletion_before_cut,100*num_depletion_before_cut/total_number]; + shot_data.stats.k_ranges(2,:) = [k_min,k_max,num_depletion_after_cut,100*num_depletion_after_cut/total_number]; + shot_data.stats.k_ranges(3,:) = [10/lambda_db,k_max,num_depletion_outside_thermal,100*num_depletion_outside_thermal/total_number]; + shot_data.stats.QE = QE; + shot_data.stats.total_atoms = [thermal_number,num_depletion_before_cut,n_background; + length(thermal_kvec),length(depletion_counts),length(background_kvec)]; + shot_data.stats.QD_detect_region = sum(depletion_mask); + shot_data.stats.noise_detect_region = sum(background_mask); + shot_data.properties = bec_prop; + shot_data.detection_density = nan; + + if visual +% xplt = linspace(1,100,101); + log_edges = logspace(min(log10(k_detections)),max(log10(k_detections)),100); + hist_signal = histcounts(depletion_kvec,log_edges); + hist_noise = histcounts(background_kvec,log_edges); + hist_thermal = histcounts(thermal_kvec,log_edges); + [hist_allcounts,hcs] = histcounts(k_detections,log_edges); + % these are in kspace so let's integrate in spherical coordinates + log_bin_volumes= (4*pi/3)*(log_edges(2:end).^3-log_edges(1:end-1).^3); + log_bin_centres= 0.5*(log_edges(2:end)+log_edges(1:end-1)); + noise_density = (hist_noise./log_bin_volumes); + detection_density = hist_allcounts./log_bin_volumes; +% shot_data.hist.density = detection_density; +% shot_data.hist.edges = log_edges; + plot_profile = thermal_chang + depletion_profile + background_rate; + + stfig('Data generation'); + clf + +% subplot(2,2,1) +% title('Detection counts') +% hold on +% plot((log_bin_centres),(hist_signal),'--') +% plot((log_bin_centres),(hist_noise),':') +% plot((log_bin_centres),(hist_thermal),'-.') +% plot((log_bin_centres),(hist_allcounts)) +% +% legend('Depletion','Noise floor','Thermal','Combined','Location','Best') +% set(gca,'Xscale','log') +% set(gca,'Yscale','log') +% box off + subplot(2,1,1) + title('Simulated detection densities') + hold on + plot((log_bin_centres),(hist_thermal./log_bin_volumes),'-.','LineWidth',2) + plot((log_bin_centres),(hist_signal./log_bin_volumes),'-.','LineWidth',2) + plot((log_bin_centres),noise_density,'-.','LineWidth',2) + plot((log_bin_centres),(detection_density),'LineWidth',2) + plot(k_plot,depletion_profile,':','LineWidth',2) +% plot(k_plot,thermal_MaxwellBoltzmann,':','LineWidth',2) +% plot(k_plot,thermal_BoseEinstein,':','LineWidth',2) + plot(k_plot,thermal_chang,':','LineWidth',2) + plot(k_plot,plot_profile,'LineWidth',2) + legend('Thermal','Depletion','Noise floor','All counts','QD thry','Thermal thry','Full thry',... + 'Location','Best') + ylim([.3*min(plot_profile),10*max(plot_profile)]) + xlabel('k ($ m^{-1}$)') + ylabel('n(k) ($m^{3}$)') + set(gca,'Xscale','log') + set(gca,'Yscale','log') + set(gca,'FontSize',16) +% set(gca,'ColorOrder',cmap(randsample(1:10,10),:)); + box off + +% subplot(2,2,3) +% hold on +% plot((log_bin_centres),(hist_thermal./log_bin_volumes),'-.') +% plot((log_bin_centres),(hist_signal./log_bin_volumes),'-.') +% plot((log_bin_centres),noise_density,'-.') +% plot((log_bin_centres),(detection_density)) +% plot(k_plot,depletion_profile,':') +% plot(k_plot,thermal_MaxwellBoltzmann,':') +% plot(k_plot,thermal_BoseEinstein,':') +% plot(k_plot,plot_profile) +% % legend('Thermal','Depletion','Noise floor','All counts','QD thry','MB thry','BE thry','Full thry',... +% % 'Location','Best') +% ylim([.3e-20,1.5*max(plot_profile)]) +% xlabel('k ($ m^{-1}$)') +% ylabel('n(k) ($ m^{3}$)') +% set(gca,'FontSize',16) +% % set(gca,'ColorOrder',cmap(randsample(1:10,10),:)); +% box off + + subplot(2,1,2) + hold on + plot((log_bin_centres),log_bin_centres.^4.*(hist_thermal./log_bin_volumes),'-.','LineWidth',2) + plot((log_bin_centres),log_bin_centres.^4.*(hist_signal./log_bin_volumes),'-.','LineWidth',2) + plot((log_bin_centres),log_bin_centres.^4.*noise_density,'-.','LineWidth',2) + plot((log_bin_centres),log_bin_centres.^4.*(detection_density),'LineWidth',2) + plot(k_plot,k_plot.^4.*depletion_profile,':','LineWidth',2) +% plot(k_plot,k_plot.^4.*thermal_MaxwellBoltzmann,':') + plot(k_plot,k_plot.^4.*thermal_chang,':','LineWidth',2) + plot(k_plot,k_plot.^4.*plot_profile,'LineWidth',2) +% legend('Thermal','Depletion','Noise floor','All counts','QD thry','MB thry','BE thry','Full thry',... +% 'Location','Best') + ylim([.5*min(k_plot.^4.*plot_profile),10*max(k_plot.^4.*plot_profile)]) + xlabel('k ($ m^{-1}$)') + ylabel('n(k) ($m^{3}$)') + set(gca,'Xscale','log') + set(gca,'Yscale','log') + set(gca,'FontSize',16) + + +% subplot(2,2,3) +% title('Scaled densities') +% hold on +% plot((log_bin_centres),(hist_signal./log_bin_volumes).*log_bin_centres.^4,'--') +% plot((log_bin_centres),noise_density.*log_bin_centres.^4,'--') +% plot((log_bin_centres),(hist_thermal./log_bin_volumes).*log_bin_centres.^4,'--') +% plot((log_bin_centres),(hist_allcounts./log_bin_volumes).*log_bin_centres.^4) +% plot(k_plot,contact*ones(size(k_plot))/(2*pi)^3) +% legend('Depletion','Background','Thermal','Detections','Theory',... +% 'Location','Best') +% set(gca,'Xscale','log') +% set(gca,'Yscale','log') +% box off +% +% subplot(2,2,4) +% hold on +% plot(k_plot,intCDF(k_plot,k_detections)) +% plot(k_plot,intCDF(k_plot,thermal_kvec)) +% plot(k_plot,intCDF(k_plot,background_kvec)) +% plot(k_plot,(intCDF(k_plot,k_detections)-intCDF(k_plot,background_kvec))) +% plot(k_plot,(intCDF(k_plot,depletion_kvec))) +% +% legend('Total','Thermal','Background','Total - Background','Depletion','Location','Best') +% ylabel('N(k1 +% For considerably faster results, use a lower g_tol (I have used as low as 1e-5 for +% some applications) +% USER CONSTS FOR ALGORITHM CONVERGENCE +% TODO +% - optional args +% - tolerance or number of terms +% - aproximate expressions +% - consider if better to use something off file exchange +% - https://au.mathworks.com/matlabcentral/fileexchange/23060-polylogarithm-de-jonquiere-s-function +% - approx expansions https://github.com/wme7/Polylog +% - https://au.mathworks.com/matlabcentral/fileexchange/37229-enhanced-computation-of-polylogarithm-aka-de-jonquieres-function +% - fix error where sumation does not terminate if any of the z vector input has not converged + +if nargin==2 + tol_err = varargin{1}; +else + tol_err=1e-16; % incremental error from evaluating series sum +end + +zmask = Z >= 0.99999; +if any(zmask) + warning('g_bose will not converge for Z>=1 !') + Z(zmask) = nan; +end +% else + +GZ=0; % initialise output +err=inf; % initialise incremental error + +n_ser=0; % summand order +while err>tol_err + n_ser=n_ser+1; + GZ_temp=GZ; % save last order series sum + + % evaluate next series term + GZ=GZ+(Z.^n_ser)/(n_ser^(3/2)); + + % evaluate error from this term + if n_ser>1 % skip evaluateion (div) for first iter + err=max(abs(GZ-GZ_temp)./GZ_temp); % incremental fractional diff + end +end +end \ No newline at end of file diff --git a/lib/bec_cals/replay_pid15624.log b/lib/bec_cals/replay_pid15624.log new file mode 100644 index 0000000..e588f1d --- /dev/null +++ b/lib/bec_cals/replay_pid15624.log @@ -0,0 +1,7669 @@ +JvmtiExport can_access_local_variables 0 +JvmtiExport can_hotswap_or_post_breakpoint 0 +JvmtiExport can_post_on_exceptions 0 +# 130 ciObject found +instanceKlass com/icl/saxon/StandardURIResolver +instanceKlass javax/xml/transform/ErrorListener +instanceKlass javax/xml/transform/URIResolver +instanceKlass javax/xml/transform/sax/TransformerHandler +instanceKlass javax/xml/transform/Transformer +instanceKlass com/icl/saxon/sort/NodeOrderComparer +instanceKlass com/mathworks/install/input/ComponentData 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 100 100 1 1 100 100 100 100 1 1 100 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 100 100 100 100 1 1 1 100 100 1 1 1 1 1 1 1 1 1 12 12 12 1 12 12 12 1 1 1 1 1 1 1 1 1 1 1 12 1 12 100 12 1 12 1 12 1 12 1 12 100 12 1 100 12 1 12 1 1 1 1 1 12 1 7 12 12 12 7 12 1 12 7 12 12 12 1 100 12 12 1 12 1 12 1 1 1 1 1 12 12 12 12 12 1 12 12 1 1 12 12 1 100 12 1 1 7 12 12 12 12 1 1 12 1 1 1 1 1 100 12 12 1 12 7 12 12 12 12 12 1 1 1 12 1 12 12 12 12 1 12 12 12 12 7 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +staticfield java/lang/invoke/MethodHandleNatives COUNT_GWT Z 1 +staticfield java/lang/invoke/MethodHandleNatives $assertionsDisabled Z 1 +ciInstanceKlass java/lang/invoke/LambdaForm 1 1 986 7 100 9 10 10 9 9 10 100 10 9 10 9 10 7 9 10 9 9 9 10 7 10 10 10 10 10 10 10 9 10 8 10 10 10 10 7 10 10 8 10 10 10 100 8 10 10 10 10 10 7 10 7 10 10 9 9 10 10 100 10 10 10 10 10 10 10 10 10 10 8 10 10 8 8 9 9 9 10 10 10 9 10 10 10 10 10 10 10 10 8 8 8 8 8 8 8 8 10 9 10 10 10 10 10 10 10 7 10 10 9 10 10 10 10 10 10 8 10 100 100 10 10 10 10 11 11 11 7 10 10 10 10 7 10 8 10 10 8 10 10 10 7 10 8 10 9 10 10 8 8 10 10 8 8 8 10 10 9 10 8 8 9 10 10 8 8 8 100 8 100 8 100 8 10 8 10 9 10 10 9 10 10 10 10 10 10 10 10 10 10 8 100 10 10 9 10 8 8 100 8 8 9 8 8 8 10 8 8 8 10 10 8 8 8 10 8 10 8 8 8 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 8 10 11 11 9 9 9 9 9 10 10 8 10 8 9 7 10 100 10 7 10 9 10 10 10 10 9 10 10 9 10 9 10 9 7 9 9 10 100 10 10 10 10 9 100 1 100 1 100 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 3 1 1 1 3 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 100 100 1 1 1 1 1 1 100 1 1 1 1 1 1 1 100 100 100 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 100 1 100 100 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +staticfield java/lang/invoke/LambdaForm COMPILE_THRESHOLD I 0 +staticfield java/lang/invoke/LambdaForm INTERNED_ARGUMENTS [[Ljava/lang/invoke/LambdaForm$Name; 5 [[Ljava/lang/invoke/LambdaForm$Name; +staticfield java/lang/invoke/LambdaForm IMPL_NAMES Ljava/lang/invoke/MemberName$Factory; java/lang/invoke/MemberName$Factory +staticfield java/lang/invoke/LambdaForm LF_identityForm [Ljava/lang/invoke/LambdaForm; 6 [Ljava/lang/invoke/LambdaForm; +staticfield java/lang/invoke/LambdaForm LF_zeroForm [Ljava/lang/invoke/LambdaForm; 6 [Ljava/lang/invoke/LambdaForm; +staticfield java/lang/invoke/LambdaForm NF_identity [Ljava/lang/invoke/LambdaForm$NamedFunction; 6 [Ljava/lang/invoke/LambdaForm$NamedFunction; +staticfield java/lang/invoke/LambdaForm NF_zero [Ljava/lang/invoke/LambdaForm$NamedFunction; 6 [Ljava/lang/invoke/LambdaForm$NamedFunction; +staticfield java/lang/invoke/LambdaForm DEBUG_NAME_COUNTERS Ljava/util/HashMap; null +staticfield java/lang/invoke/LambdaForm TRACE_INTERPRETER Z 0 +staticfield java/lang/invoke/LambdaForm $assertionsDisabled Z 1 +ciInstanceKlass java/lang/invoke/MethodType 1 1 610 7 10 10 10 9 10 7 9 9 10 9 8 10 10 9 9 10 7 10 8 10 10 10 100 8 10 100 10 10 10 10 11 9 11 7 10 9 10 10 10 10 10 9 7 10 7 10 10 10 10 10 10 10 10 10 10 8 8 10 9 100 10 10 10 10 10 10 10 10 10 8 10 10 10 10 10 11 10 10 10 10 10 7 10 10 10 10 9 7 10 10 10 10 10 10 10 10 8 8 10 8 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 9 7 10 10 10 10 10 8 10 11 9 10 10 10 10 10 10 10 10 10 9 9 10 9 10 7 10 7 9 8 10 10 8 100 100 10 100 1 1 1 1 1 5 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 100 1 1 1 1 1 1 1 100 1 1 100 1 1 1 1 1 1 100 100 1 100 1 1 1 1 1 100 1 1 100 1 1 1 1 1 100 1 1 100 1 1 1 12 12 12 12 7 12 12 12 7 12 7 12 1 7 12 12 7 7 12 1 1 12 12 12 1 1 12 1 12 12 12 7 12 12 12 1 7 12 12 12 12 12 12 12 12 1 12 1 12 12 100 12 12 12 12 12 12 12 12 1 1 12 12 1 12 12 12 12 100 12 12 12 1 12 12 7 12 12 12 12 12 12 12 12 12 1 12 12 12 12 1 12 7 12 12 7 12 12 12 1 1 12 1 100 12 12 12 12 12 12 12 12 12 100 12 12 12 12 12 12 1 12 12 12 7 12 12 1 7 12 12 12 12 12 100 12 12 12 12 100 12 12 100 12 12 7 12 12 12 1 1 12 12 12 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +staticfield java/lang/invoke/MethodType internTable Ljava/lang/invoke/MethodType$ConcurrentWeakInternSet; java/lang/invoke/MethodType$ConcurrentWeakInternSet +staticfield java/lang/invoke/MethodType NO_PTYPES [Ljava/lang/Class; 0 [Ljava/lang/Class; +staticfield java/lang/invoke/MethodType objectOnlyTypes [Ljava/lang/invoke/MethodType; 20 [Ljava/lang/invoke/MethodType; +staticfield java/lang/invoke/MethodType serialPersistentFields [Ljava/io/ObjectStreamField; 0 [Ljava/io/ObjectStreamField; +staticfield java/lang/invoke/MethodType rtypeOffset J 12 +staticfield java/lang/invoke/MethodType ptypesOffset J 16 +staticfield java/lang/invoke/MethodType $assertionsDisabled Z 1 +ciInstanceKlass java/lang/BootstrapMethodError 0 0 39 10 10 10 10 10 100 100 1 1 1 5 0 1 1 1 1 1 1 1 1 100 100 1 1 12 12 12 100 12 12 1 1 1 1 1 1 1 1 +instanceKlass java/lang/invoke/VolatileCallSite +instanceKlass java/lang/invoke/MutableCallSite +instanceKlass java/lang/invoke/ConstantCallSite +ciInstanceKlass java/lang/invoke/CallSite 1 1 322 10 10 9 10 10 100 7 10 7 10 10 10 100 100 10 10 10 8 10 10 10 9 10 10 10 10 100 8 10 10 10 100 10 9 10 10 10 10 9 9 10 10 9 10 10 10 10 10 10 7 10 10 10 10 10 10 7 100 8 10 10 10 10 10 7 100 8 10 10 100 8 10 7 10 10 10 8 10 10 8 10 10 100 10 8 10 10 100 100 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 100 1 1 1 1 1 100 100 100 100 100 100 100 1 1 1 1 1 1 1 1 100 100 1 1 12 12 12 12 12 1 1 12 1 12 12 12 1 1 100 12 12 1 12 12 12 12 12 100 12 12 1 1 12 12 1 12 12 12 12 12 100 12 7 12 12 7 12 12 7 12 12 12 12 12 7 12 12 1 12 12 12 12 12 12 1 1 1 12 12 100 12 12 1 1 1 12 1 1 12 1 12 12 7 12 12 12 12 12 1 12 12 12 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +staticfield java/lang/invoke/CallSite GET_TARGET Ljava/lang/invoke/MethodHandle; java/lang/invoke/DirectMethodHandle +staticfield java/lang/invoke/CallSite THROW_UCS Ljava/lang/invoke/MethodHandle; java/lang/invoke/MethodHandleImpl$AsVarargsCollector +staticfield java/lang/invoke/CallSite TARGET_OFFSET J 12 +ciInstanceKlass java/lang/invoke/ConstantCallSite 1 1 42 10 9 10 100 10 9 100 10 10 7 7 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 12 12 12 1 12 12 1 12 1 1 1 1 1 1 +ciInstanceKlass java/lang/invoke/MutableCallSite 0 0 57 10 10 9 10 10 10 9 10 10 100 10 100 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 100 12 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 +ciInstanceKlass java/lang/invoke/VolatileCallSite 0 0 33 10 10 10 10 10 10 100 100 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 1 1 1 1 1 1 1 +instanceKlass java/lang/StringBuilder +instanceKlass java/lang/StringBuffer +ciInstanceKlass java/lang/AbstractStringBuilder 1 1 318 7 10 9 9 10 10 10 7 3 10 3 100 10 100 10 10 10 10 100 10 10 10 8 10 10 10 10 10 10 10 10 10 10 10 7 10 11 10 8 100 10 8 10 10 8 8 10 10 11 3 8 10 10 7 5 0 8 10 10 10 10 10 10 10 10 100 10 8 8 10 10 10 8 8 8 10 10 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 100 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 12 12 12 12 12 7 12 1 12 1 1 12 12 7 12 12 1 12 12 1 12 7 12 12 12 12 12 12 100 1 12 12 1 1 1 12 12 1 1 12 12 1 12 12 1 1 12 12 100 12 12 12 12 12 1 1 1 12 12 12 1 1 1 12 12 1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +ciInstanceKlass java/lang/StringBuffer 1 1 371 10 10 10 11 10 10 9 9 10 10 9 10 100 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 10 10 8 10 8 10 8 10 10 10 10 7 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 10 9 9 9 7 7 100 100 1 1 1 1 1 5 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 7 12 1 12 100 12 1 100 12 1 12 1 12 12 100 12 100 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 1 12 7 12 7 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +staticfield java/lang/StringBuffer serialPersistentFields [Ljava/io/ObjectStreamField; 3 [Ljava/io/ObjectStreamField; +ciInstanceKlass java/lang/StringBuilder 1 1 326 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 9 9 10 10 10 10 10 10 10 100 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 7 100 100 1 1 1 5 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 1 12 12 12 100 12 12 12 100 12 12 12 1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +ciInstanceKlass sun/misc/Unsafe 1 1 390 10 10 10 10 100 8 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 100 10 10 7 7 8 10 10 7 10 9 7 9 7 9 7 9 7 9 7 9 7 9 7 9 7 9 10 9 9 9 9 9 9 9 9 9 10 9 7 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 7 12 7 12 7 12 1 1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 100 12 100 12 12 12 12 12 12 12 12 12 12 12 1 12 1 1 12 1 12 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 12 12 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +staticfield sun/misc/Unsafe theUnsafe Lsun/misc/Unsafe; sun/misc/Unsafe +staticfield sun/misc/Unsafe ARRAY_BOOLEAN_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_BYTE_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_SHORT_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_CHAR_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_INT_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_LONG_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_FLOAT_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_DOUBLE_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_OBJECT_BASE_OFFSET I 16 +staticfield sun/misc/Unsafe ARRAY_BOOLEAN_INDEX_SCALE I 1 +staticfield sun/misc/Unsafe ARRAY_BYTE_INDEX_SCALE I 1 +staticfield sun/misc/Unsafe ARRAY_SHORT_INDEX_SCALE I 2 +staticfield sun/misc/Unsafe ARRAY_CHAR_INDEX_SCALE I 2 +staticfield sun/misc/Unsafe ARRAY_INT_INDEX_SCALE I 4 +staticfield sun/misc/Unsafe ARRAY_LONG_INDEX_SCALE I 8 +staticfield sun/misc/Unsafe ARRAY_FLOAT_INDEX_SCALE I 4 +staticfield sun/misc/Unsafe ARRAY_DOUBLE_INDEX_SCALE I 8 +staticfield sun/misc/Unsafe ARRAY_OBJECT_INDEX_SCALE I 4 +staticfield sun/misc/Unsafe ADDRESS_SIZE I 8 +instanceKlass org/eclipse/jgit/util/io/AutoLFInputStream +instanceKlass org/eclipse/jgit/lib/ObjectStream +instanceKlass org/tmatesoft/svn/core/internal/wc/SVNFileUtil$2 +instanceKlass org/tmatesoft/svn/core/internal/util/SVNLogInputStream +instanceKlass sun/nio/ch/ChannelInputStream +instanceKlass org/apache/xerces/impl/XMLEntityManager$RewindableInputStream +instanceKlass java/io/SequenceInputStream +instanceKlass org/apache/commons/io/input/ClosedInputStream 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10 8 10 8 10 9 10 10 10 10 10 10 7 10 10 10 10 10 7 8 10 10 10 8 10 7 10 10 10 10 7 10 100 10 10 10 10 10 8 7 10 100 100 10 10 10 7 10 10 10 10 10 10 10 10 10 10 10 7 10 11 11 11 7 11 7 10 10 10 10 7 11 10 10 10 10 10 10 10 8 10 10 10 10 10 10 10 10 100 8 10 10 10 8 8 10 10 100 8 10 10 10 10 10 10 10 10 8 10 10 9 9 10 9 10 9 10 10 10 10 10 10 9 10 9 9 10 10 10 8 100 7 100 100 7 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 0 1 1 1 1 1 1 1 1 1 100 100 1 1 1 1 1 100 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 100 100 1 100 1 1 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 1 1 1 1 1 100 100 1 1 100 100 100 1 1 100 1 1 1 1 12 12 12 12 12 12 12 12 1 1 12 12 12 1 12 12 12 12 1 1 12 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 12 12 12 12 12 12 12 1 12 12 12 12 12 1 1 12 12 1 12 1 12 12 12 1 1 12 12 12 12 1 1 12 1 1 12 7 12 100 12 1 12 12 12 12 12 12 12 12 7 12 12 12 1 7 12 7 12 12 1 12 1 12 1 100 12 12 12 12 12 12 12 12 1 12 12 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java/lang/AbstractStringBuilder ensureCapacityInternal (I)V 4 17 java/lang/AbstractStringBuilder newCapacity (I)I 4 20 java/util/Arrays copyOf ([CI)[C diff --git a/lib/bootstrap_error b/lib/bootstrap_error index 26da190..d0b3ee5 160000 --- a/lib/bootstrap_error +++ b/lib/bootstrap_error @@ -1 +1 @@ -Subproject commit 26da1903be81b5889f249c8974928b65e6192f51 +Subproject commit d0b3ee594263915e14faf90328803db949d407dd diff --git a/lib/bound.m b/lib/bound.m deleted file mode 100644 index 0ca0ac2..0000000 --- a/lib/bound.m +++ /dev/null @@ -1,4 +0,0 @@ -function y = bound(x,lower,upper) - % limits the retuned value to lower or upper - y=min(max(x,lower),upper); -end \ No newline at end of file diff --git a/lib/cell_manipulation/nucellf.m b/lib/cell_manipulation/nucellf.m deleted file mode 100644 index a3d1dec..0000000 --- a/lib/cell_manipulation/nucellf.m +++ /dev/null @@ -1,6 +0,0 @@ -function out = nucellf(fn,cell) - % A shortcut to call a cellfun with non-uniform output - % Replaces A = cellfun(@(x) foo(x),cell, 'UniformOutput',false) - % with A = nucellf(@(x) foo(x),cell) - out = cellfun(fn,cell, 'UniformOutput',false); -end \ No newline at end of file diff --git a/lib/coldatom_tools/deBroglie_wavelength.m b/lib/coldatom_tools/deBroglie_wavelength.m new file mode 100644 index 0000000..dd351e0 --- /dev/null +++ b/lib/coldatom_tools/deBroglie_wavelength.m @@ -0,0 +1,20 @@ +function lambda = deBroglie_wavelength(temperature, varargin) +% Returns the de Broglie wavelength at temperature T (in kelvin). +% Returns inf if passed T=0. +% If only one argument is passed, assumes 4He mass. Eg +% ``` +% lambda_db(300) == 5.0367e-11 +% ``` +% Accepts particle mass as second argument, for example 3He +% ``` +% lambda_db(300,4.9825e-27) == 5.8158e-11 + +% ``` + if nargin>1 + mass = varargin{1}; + else + mass = 6.64332e-27; + end + lambda = sqrt((2*pi*(1.0540e-34)^2) ./ (mass * 1.3806e-23 *temperature)); + +end \ No newline at end of file diff --git a/lib/coldatom_tools/doppler_broadening.m b/lib/coldatom_tools/doppler_broadening.m new file mode 100644 index 0000000..973606e --- /dev/null +++ b/lib/coldatom_tools/doppler_broadening.m @@ -0,0 +1,13 @@ +function FWHM = doppler_broadening(T,varargin) + if nargin < 2 + m = 6.6433e-27; + else + m = varargin{1}; + end + kB = 1.380649e-23; + c = 299792458; + % the multiplicative factor to obtain FWHM of a delta-function distribution + % at frequency f0 for atoms of mass m at temperature T. + % eg doppler_width = doppler_broadening(T,m)*f0 + FWHM = sqrt(8*kB*T*log(2)/(m*c^2)); +end \ No newline at end of file diff --git a/lib/coldatom_tools/doppler_limit.m b/lib/coldatom_tools/doppler_limit.m new file mode 100644 index 0000000..19a311c --- /dev/null +++ b/lib/coldatom_tools/doppler_limit.m @@ -0,0 +1,6 @@ +function T_dop = doppler_limit(gamma) + % accepts gamma in Hz + hbar = 1.054571817e-34; + kB = 1.380649e-23; + T_dop = 2*pi*hbar*gamma/(2*kB); +end \ No newline at end of file diff --git a/lib/f2wl.m b/lib/coldatom_tools/f2wl.m similarity index 100% rename from lib/f2wl.m rename to lib/coldatom_tools/f2wl.m diff --git a/lib/freq_to_recoil_vel_he.m b/lib/coldatom_tools/freq_to_recoil_vel_he.m similarity index 100% rename from lib/freq_to_recoil_vel_he.m rename to lib/coldatom_tools/freq_to_recoil_vel_he.m diff --git a/lib/command_line_format_tools/cli_header.m b/lib/command_line_format_tools/cli_header.m index 19d1307..ecfdba6 100644 --- a/lib/command_line_format_tools/cli_header.m +++ b/lib/command_line_format_tools/cli_header.m @@ -30,33 +30,24 @@ function cli_header(varargin) msg_level = 0;%If no header level is passed, assumed to be top-level if iscell(varargin{1}) fprintf("cli_header accepts varargin, cell args will be removed next version.\n") - args = varargin{1}; end - v=1; - if numel(args) == 1 %text only - msg = args{1}; - + if nargin == 1 %text only + msg = varargin{1}; msg_level = 0;%If no header level is passed, assumed to be top-level argument_index=2; - - else - if isfloat(varargin{1}) %Passing header level + else %passed level, or args, or both + if isnumeric(varargin{1}) % Header level passed as argument msg_level = varargin{1}; msg = varargin{2}; - if nargin>2 - vals = varargin{3:end}; - end - - argument_index = 1; - + argument_index = 3; else % No header level passed, but other values present msg_level = 0; - msg = args{1}; + msg = varargin{1}; argument_index = 2; end end - msg_out = sprintf(msg,args{argument_index:end}); + msg_out = sprintf(msg,varargin{argument_index:end}); % blank = '------------------------------------------------------------'; blank = ' '; marker = blank(1:2*msg_level+1); diff --git a/lib/command_line_format_tools/sltext.m b/lib/command_line_format_tools/sltext.m index f7cf3b3..13833ba 100644 --- a/lib/command_line_format_tools/sltext.m +++ b/lib/command_line_format_tools/sltext.m @@ -1,4 +1,4 @@ function out=sltext(args) warning('sltext has been migrated to cli_cen_text please update your usage') - out=cli_cen_text(args) + out=cli_cen_text(args); end \ No newline at end of file diff --git a/lib/command_line_format_tools/sshow/sshow.m b/lib/command_line_format_tools/sshow/sshow.m deleted file mode 100644 index 89da042..0000000 --- a/lib/command_line_format_tools/sshow/sshow.m +++ /dev/null @@ -1,45 +0,0 @@ -function sshow(s) - -% Displays the tree structure of a struct variable and the types of its -% terminal nodes (leaves). -% Input: s - struct -% Ourput: nothing - for now, will eventually return a tree -% Improvements: Show variable dimensions as in MATLAB's default display - % Return a representation of the branch structure - % -sname = inputname(1); -fprintf('Structure %s:\n',sname) -sshow_core(s,0); - -end - -function sshow_core(s,depth) - if isstruct(s) - fnames = fields(s); - nfields = numel(fnames); - if depth >0 - buffer = ' |- '; - else - buffer = '--'; - end - for k=1:depth - buffer = [' ',buffer]; - end - for fieldnum = 1:nfields - this_name = fnames{fieldnum}; - txt = ' '; - txt(1:length(this_name)) = this_name; - - datlabel = [' - ',class(s.(fnames{fieldnum}))]; - if isstruct(s.(fnames{fieldnum})) - datlabel = ''; - end - -% fprintf([buffer,' ',datlabel,' - ',fnames{fieldnum},'\n']) - fprintf([buffer,' ',txt,datlabel,'\n']) - sshow_core(s.(fnames{fieldnum}),depth+1) - end - else -% fprintf('\b - %s\n',class(s)) - end -end \ No newline at end of file diff --git a/lib/command_line_format_tools/string_value_with_unc.m b/lib/command_line_format_tools/string_value_with_unc.m index 7635e92..45d5bfd 100644 --- a/lib/command_line_format_tools/string_value_with_unc.m +++ b/lib/command_line_format_tools/string_value_with_unc.m @@ -6,6 +6,7 @@ % Inputs: % value - numeric, value % unc - nmeric, uncertianty in the value +% String value pairs % type - to use the ± notation as in 10±3 pass 's','standard','pm' to use the () notation as in 10(3) pass , 'b','brackets' % @@ -15,11 +16,11 @@ % % Example: -% string_value_with_unc(50.1234,0.15,'s') +% string_value_with_unc(50.1234,0.15,'type','s') % '50.12±0.15' -% string_value_with_unc(8.547896541,0.001,'b') +% string_value_with_unc(8.547896541,0.001,'type','b') % '8.5479(10)' -% string_value_with_unc(854738.96541,200,'b') +% string_value_with_unc(854738.96541,200,'type','b') % '854700(200)' % Other m-files required: none @@ -45,11 +46,22 @@ type_ok_fun=@(x) sum(strcmp(validtypes,x))==1; p = inputParser; addParameter(p,'type','standard',type_ok_fun); -addParameter(p,'separator',true,@(x) is_c_logical(x) || (ischar(x) && numel(x)==1) ); +addParameter(p,'separator',false,@(x) is_c_logical(x) || (ischar(x) && numel(x)==1) ); addParameter(p,'remove_common_factors',0,is_c_logical); +addParameter(p,'power_type','sci',@(x) sum(strcmp({'sci','eng'},x))==1); parse(p,varargin{:}); -type=p.Results.type; +error_type=p.Results.type; +power_type=p.Results.power_type; + +if sum(strcmp(power_type,{'s','sci','10'}))>0 + power_type=true; +elseif sum(strcmp(power_type,{'e','eng'}))>0 + power_type=false; +else + warning('power_type not valid, using default') + power_type=true; +end rem_com_fac=p.Results.remove_common_factors; @@ -89,10 +101,12 @@ rounded_val=(10^decimal_place_unc)*round(value*(10^(-decimal_place_unc))); % standard plus-minus format -if sum(strcmp(type,{'s','standard','pm'}))>0 +if sum(strcmp(error_type,{'s','standard','pm'}))>0 if rem_com_fac - error('remove common factors feature is not yet implemented') + %error('remove common factors feature is not yet implemented') + rounded_unc=rounded_unc*10^(-unc_first_decimal_place); + rounded_val=rounded_val*10^(-unc_first_decimal_place); end if use_sep @@ -108,11 +122,26 @@ unc_str=sprintf('%.*f',max([0,-decimal_place_unc]),rounded_unc); val_str=sprintf(sprintf('%%.%uf',max([0,-decimal_place_unc])),rounded_val); end - out_string=cat(2,val_str,'±',unc_str); + if rem_com_fac + if power_type + out_string=cat(2,'(',val_str,'±',unc_str,')·10^',sprintf('%u',unc_first_decimal_place)); + else + out_string=cat(2,'(',val_str,'±',unc_str,')e',sprintf('%u',unc_first_decimal_place)); + end + else + out_string=cat(2,val_str,'±',unc_str); + end %metrology brackets notation -elseif sum(strcmp(type,{'b','brackets'}))>0 +elseif sum(strcmp(error_type,{'b','brackets'}))>0 + + if rem_com_fac + %error('remove common factors feature is not yet implemented') + rounded_unc=rounded_unc*10^(-unc_first_decimal_place); + rounded_val=rounded_val*10^(-unc_first_decimal_place); + end + unc_str=sprintf('%.0f',rounded_unc*(10^(max([0,-decimal_place_unc])))); if use_sep val_str=num_with_sep(rounded_val,... @@ -122,7 +151,18 @@ else val_str=sprintf(sprintf('%%.%uf',max([0,-decimal_place_unc])),rounded_val); end - out_string=cat(2,val_str,'(',unc_str,')'); + + if rem_com_fac + if power_type + out_string=cat(2,val_str,'(',unc_str,')','·10^',sprintf('%u',unc_first_decimal_place)); + else + out_string=cat(2,'(',val_str,'±',unc_str,')e',sprintf('%u',unc_first_decimal_place)); + end + else + out_string=cat(2,val_str,'(',unc_str,')'); + end + + else error('did not pass valid format string') end diff --git a/lib/command_line_format_tools/test_string_value_with_unc.m b/lib/command_line_format_tools/test_string_value_with_unc.m index f284baf..cb7fe48 100644 --- a/lib/command_line_format_tools/test_string_value_with_unc.m +++ b/lib/command_line_format_tools/test_string_value_with_unc.m @@ -3,61 +3,71 @@ string_value_with_unc(50,1) -out_string=string_value_with_unc(50,1,'s'); +out_string=string_value_with_unc(50,1,'type','s'); if ~strcmp(out_string,'50.0±1.0') error('test failed') end -out_string=string_value_with_unc(50.1234,1,'s'); +out_string=string_value_with_unc(50.1234,1,'type','s'); if ~strcmp(out_string,'50.1±1.0') error('test failed') end -out_string=string_value_with_unc(50.1234,1.8235,'s'); +out_string=string_value_with_unc(50.1234,1.8235,'type','s'); if ~strcmp(out_string,'50±2') error('test failed') end -out_string=string_value_with_unc(50.1234,5.1235,'s'); +out_string=string_value_with_unc(50.1234,5.1235,'type','s'); if ~strcmp(out_string,'50±5') error('test failed') end -out_string=string_value_with_unc(50.1234,0.15,'s'); +out_string=string_value_with_unc(50.1234,0.15,'type','s'); if ~strcmp(out_string,'50.12±0.15') error('test failed') end -out_string=string_value_with_unc(854738.96541,200,'s'); +out_string=string_value_with_unc(854738.96541,200,'type','s','separator',','); if ~strcmp(out_string, '854,700±200') error('test failed') end -out_string=string_value_with_unc(8.547896541,0.001,'s',0); +out_string=string_value_with_unc(8.547896541,0.001,'type','s'); if ~strcmp(out_string,'8.5479±0.0010') error('test failed') end -out_string=string_value_with_unc(8.547896541,0.001,'s',1); +out_string=string_value_with_unc(8.547896541,0.001,'type','s','separator',','); if ~strcmp(out_string,'8.547,9±0.001,0') error('test failed') end -out_string=string_value_with_unc(8.547896541,0.001,'b'); +out_string=string_value_with_unc(8.547896541,0.001,'type','b'); if ~strcmp(out_string,'8.547,9(10)') error('test failed') end -out_string=string_value_with_unc(854738.96541,200,'b'); +out_string=string_value_with_unc(854738.96541,200,'type','b'); if ~strcmp(out_string,'854,700(200)') error('test failed') end -out_string=string_value_with_unc(8.547896541,0.0000005,'b'); +out_string=string_value_with_unc(8.547896541,0.0000005,'type','b'); if ~strcmp(out_string,'8.547,896,5(5)') error('test failed') end -out_string=string_value_with_unc(854738.96541,130,'b'); +out_string=string_value_with_unc(854738.96541,130,'type','b'); if ~strcmp(out_string,'854,740(130)') error('test failed') -end \ No newline at end of file +end +%% Common factors +fac=1e6; +out_string=string_value_with_unc(854738.96541*fac,130*fac,'type','s','separator',false) + +fac=1e6; +out_string=string_value_with_unc(854738.96541*fac,130*fac,'type','b','separator',false) + +fac=1e6; +out_string=string_value_with_unc(854738.96541*fac,110*fac,'type','s','separator',false) + diff --git a/lib/correlations/Correlations.fig b/lib/correlations/Correlations.fig new file mode 100644 index 0000000..b9b2315 Binary files /dev/null and b/lib/correlations/Correlations.fig differ diff --git a/lib/correlations/UpperTriangle.m b/lib/correlations/UpperTriangle.m new file mode 100644 index 0000000..8b991a9 --- /dev/null +++ b/lib/correlations/UpperTriangle.m @@ -0,0 +1,11 @@ +function pairs=UpperTriangle(n) +%upper tirangle pairs (above the diagonal) +pairs=zeros(2,CountUpperTriangle(n)); +count=1; +for i=1:n + for j=1+i:n + pairs(:,count)=[i;j]; + count=count+1; + end +end +end \ No newline at end of file diff --git a/lib/correlations/calc_any_g2_type.m b/lib/correlations/calc_any_g2_type.m new file mode 100644 index 0000000..3ebc4f7 --- /dev/null +++ b/lib/correlations/calc_any_g2_type.m @@ -0,0 +1,452 @@ +function out=calc_any_g2_type(corr_opts,counts) +%caucluates normalized g2 functions for a lot of different cases +%uses a lot of correlators from https://github.com/spicydonkey/correlation-funs (with some modifications) +%input +%counts_txy- cell array (n_shots*[1 or 2]) of txy data (n counts * 3) +% txy must be sorted in time for prewindowing option +% cell array can be n_shots*2 for two port xcorr +%corr_opts.type- what type of g2 fo you want to calculate +% '1d_cart_cl' %window out the other 2 axes and then do a 1d correlation in the remaining +% '1d_cart_bb' %differences are cacluated as the vector sum instead of difference +% 'radial_cl' %Euclidean distance/L2 norm of the differences +% 'radial_bb' %differences are calculates as the vector sum +% '3d_cart_cl' +% '3d_cart_bb' +%output +%norm g2 amplitude +%norm g2 vector with cordinates + +%improvements +%- fit g2 amplitude +%- implement all the options +%- think more carefully about how the coicidences should be normalized +% - results should be invariant under +% - QE change +% - Change in how the shot is cut up +% - implement bootstraping +% - most usefull at the shot level (more practical to implement & more informative) +% - different smoothing for G2(in-shot) G2(between-shot) + +%find the num of counts in each shot +num_counts=cellfun(@(x)size(x,1),counts); + +if isfield(corr_opts,'timer') && corr_opts.timer + tic +end + +if ~isfield(corr_opts,'fit') + corr_opts.fit=false; +end + +if ~isfield(corr_opts,'calc_err') + corr_opts.calc_err = false; +end + +if ~isfield(corr_opts,'direction_labels') %the label for each direction + direction_label={'x','y','z'}; +else + direction_label=corr_opts.direction_labels; +end + +% set the number of updates in a smart way +% should input check everything used here +if ~isfield(corr_opts,'progress_updates') || isnan(corr_opts.progress_updates) + update_time=2; + pairs_per_sec=5e7*(1+corr_opts.do_pre_mask*10); + dyn_updates=round(update_time*size(counts,2)*... + mean((corr_opts.attenuate_counts*num_counts(1,:)).^2)/(pairs_per_sec)); + corr_opts.progress_updates=min(100,max(5,dyn_updates)); +end + +if isfield(corr_opts,'norm_samp_factor') + if corr_opts.norm_samp_factor<0.01 || corr_opts.norm_samp_factor>2e7 + error('corr_opts.norm_samp_factor exceeds limits'); + end +else + corr_opts.norm_samp_factor=3; +end + +if ~isfield(corr_opts,'sort_norm') + corr_opts.sort_norm=false; +end + +if ~isfield(corr_opts,'fig') + corr_opts.fig='corr. output'; +end + +if ~isfield(corr_opts,'param_num') + corr_opt.param_num = 2; +end + +if corr_opt.param_num == 4 %full freedom gaussian fit + fun1d = @(b,x) b(1).*exp(-((x-b(2)).^2)./(2*b(3).^2))+b(4); + inital_guess=[2.5,0,0.01,1]; +elseif corr_opt.param_num == 3 %gaussian fit with fixed offset + fun1d = @(b,x) b(1).*exp(-((x-b(2)).^2)./(2*b(3).^2))+1; + inital_guess=[2.5,0,0.01]; +elseif corr_opt.param_num == 2 %centered gaussian fit with fixed offset + fun1d = @(b,x) b(1).*exp(-((x).^2)./(2*b(2).^2))+1; + inital_guess=[2.5,0.01]; +else + warning('Invalid number of fit parameters, using 2 instead') + fun1d = @(b,x) b(1).*exp(-((x).^2)./(2*b(2).^2))+1; + inital_guess=[2.5,0.01]; +end +fo = statset('TolFun',10^-6,... + 'TolX',1e-4,... + 'MaxIter',1e4,... + 'UseParallel',1); + + +if isequal(corr_opts.type,'1d_cart_cl') || isequal(corr_opts.type,'1d_cart_bb') + direction_label=direction_label{corr_opts.one_d_dimension}; + + if isequal(corr_opts.type,'1d_cart_cl') + corr_opts.cl_or_bb=false; + elseif isequal(corr_opts.type,'1d_cart_bb') + corr_opts.cl_or_bb=true; + end + fprintf('calculating intra-shot correlations \n') + shotscorr=corr_1d_cart(corr_opts,counts); + if corr_opts.calc_err + shotscorr_err=corr_err(@corr_1d_cart,corr_opts,counts); + end + if corr_opts.plots + stfig(corr_opts.fig,'add_stack',1); + clf + set(gcf,'color','w'); + subplot(1,3,1) + if corr_opts.calc_err + errorbar(shotscorr.x_centers,shotscorr.one_d_corr_density,shotscorr_err.results.se_fun_whole_unweighted,'kx-') + else + plot(shotscorr.x_centers,shotscorr.one_d_corr_density,'.k-','MarkerSize',10) + end + title('In Shot X Dist (windowed)') + ylabel(sprintf('$G^{(2)}(\\Delta %s)$ coincedence density',direction_label)) + xlabel(sprintf('$\\Delta %s$ Seperation',direction_label)) + pause(1e-6); + end + norm_sort_dir=corr_opts.sorted_dir; + if ~corr_opts.sort_norm,norm_sort_dir=nan; end + if size(counts,1)>1 + chunk_num = round(size(counts,2)); + counts_chunked(1,:)=chunk_data(counts(1,:),corr_opts.norm_samp_factor,norm_sort_dir,chunk_num); + counts_chunked(2,:)=chunk_data(counts(2,:),corr_opts.norm_samp_factor,norm_sort_dir,chunk_num); +% counts_chunked=counts_chunked(:,1:end-1); + else + counts_chunked=chunk_data(counts,corr_opts.norm_samp_factor,norm_sort_dir); + end + corr_opts.do_pre_mask=corr_opts.sort_norm; %can only do premask if data is sorted + fprintf('calculating inter-shot correlations \n') + normcorr=corr_1d_cart(corr_opts,counts_chunked); + if corr_opts.calc_err + normcorr_err=corr_err(@corr_1d_cart,corr_opts,counts_chunked); + end + if corr_opts.plots + subplot(1,3,2) + if corr_opts.calc_err + errorbar(normcorr.x_centers,normcorr.one_d_corr_density,normcorr_err.results.se_fun_whole_unweighted,'kx-') + else + plot(normcorr.x_centers,normcorr.one_d_corr_density,'.k-','MarkerSize',10) + end + title('Between Shot X Dist (windowed)') + ylabel(sprintf('$G^{(2)}(\\Delta %s)$ coincedence density',direction_label)) + xlabel(sprintf('$\\Delta %s$ Seperation',direction_label)) + subplot(1,3,3) + xg2=shotscorr.one_d_corr_density./normcorr.one_d_corr_density; + if corr_opts.calc_err + xg2_err=xg2.*sqrt((shotscorr_err.results.se_fun_whole_unweighted'./shotscorr.one_d_corr_density).^2+(normcorr_err.results.se_fun_whole_unweighted'./normcorr.one_d_corr_density).^2); + errorbar(shotscorr.x_centers,xg2,xg2_err,'kx-') + else + plot(shotscorr.x_centers,xg2,'.k-','MarkerSize',10) + end + title('Norm. Corr.') + ylabel(sprintf('$G^{(2)}(\\Delta %s)$ coincedence density',direction_label)) + ylabel(sprintf('$g^{(2)}(\\Delta %s)$',direction_label)) + xlabel(sprintf('$\\Delta %s$ Seperation',direction_label)) + pause(1e-6); + end + out.in_shot_corr.x_centers=shotscorr.x_centers; + out.in_shot_corr.one_d_corr_density=shotscorr.one_d_corr_density; + out.between_shot_corr.x_centers=normcorr.x_centers; + out.between_shot_corr.one_d_corr_density=normcorr.one_d_corr_density; + out.norm_g2.x_centers=shotscorr.x_centers; + out.norm_g2.g2_amp=xg2; + if corr_opts.fit + if ~corr_opts.calc_err + fit=fitnlm(shotscorr.x_centers,xg2,... + fun1d,... + inital_guess,... + 'Options',fo); + else + w = 1./xg2_err.^2; + fit=fitnlm(shotscorr.x_centers,xg2,... + fun1d,... + inital_guess,... + 'Weight',w,... + 'Options',fo); + end + out.fit = fit; + if corr_opts.plots + hold on + xx = linspace(min(shotscorr.x_centers),max(shotscorr.x_centers),3e3)'; + [ypred,ypredci] = predict(fit,xx,'Simultaneous',true); + plot(xx,ypred,'b-', xx,ypredci,'r-'); + end + end + [g2peak,indx] = max(xg2); + if corr_opts.calc_err + out.in_shot_corr.corr_unc = shotscorr_err; + out.between_shot_corr.corr_unc = normcorr_err; + out.norm_g2.g2_unc = xg2_err; + g2peak_unc = xg2_err(indx); + out.norm_g2.g2peak_unc = g2peak_unc; + fprintf('g2 peak amplitude %s\n',string_value_with_unc(g2peak,g2peak_unc,'type','b','separator',0)) + else + fprintf('g2 peak amplitude %4.2f \n',g2peak) + end + out.norm_g2.g2peak=g2peak; + + + +elseif isequal(corr_opts.type,'radial_cl') || isequal(corr_opts.type,'radial_bb') + if isequal(corr_opts.type,'radial_cl') + corr_opts.cl_or_bb=false; + elseif isequal(corr_opts.type,'radial_bb') + corr_opts.cl_or_bb=true; + end + fprintf('calculating intra-shot correlations \n') + shotscorr=corr_radial(corr_opts,counts); + if corr_opts.calc_err + shotscorr_err=corr_err(@corr_radial,corr_opts,counts); + end + if corr_opts.plots + stfig(corr_opts.fig,'add_stack',1); + clf + set(gcf,'color','w'); + subplot(1,3,1) + if corr_opts.calc_err + errorbar(shotscorr.rad_centers,shotscorr.rad_corr_density,shotscorr_err.results.se_fun_whole_unweighted,'kx-') + else + plot(shotscorr.rad_centers,shotscorr.rad_corr_density,'.k-','MarkerSize',10) + end + title('In Shot X Dist (windowed)') + ylabel('$G^{(2)}(\Delta r)$ coincedence density') + xlabel('$\delta r$ Seperation') + pause(1e-6); + end + norm_sort_dir=corr_opts.sorted_dir; + if ~corr_opts.sort_norm,norm_sort_dir=nan; end + if size(counts,1)>1 + chunk_num = round(size(counts,2)/100); + counts_chunked(1,:)=chunk_data(counts(1,:),corr_opts.norm_samp_factor,norm_sort_dir,chunk_num); + counts_chunked(2,:)=chunk_data(counts(2,:),corr_opts.norm_samp_factor,norm_sort_dir,chunk_num); +% counts_chunked=counts_chunked(:,1:end-1); + else + counts_chunked=chunk_data(counts,corr_opts.norm_samp_factor,norm_sort_dir); + end + corr_opts.do_pre_mask=corr_opts.sort_norm; %can only do premask if data is sorted + + fprintf('calculating inter-shot correlations \n') + normcorr=corr_radial(corr_opts,counts_chunked); + if corr_opts.calc_err + normcorr_err=corr_err(@corr_radial,corr_opts,counts_chunked); + end + if corr_opts.plots + subplot(1,3,2) + if corr_opts.calc_err + errorbar(normcorr.rad_centers,normcorr.rad_corr_density,normcorr_err.results.se_fun_whole_unweighted,'kx-') + else + plot(normcorr.rad_centers,normcorr.rad_corr_density,'.k-','MarkerSize',10) + end + title('Between Shot X Dist (windowed)') + ylabel('$G^{(2)}(\Delta r)$ coincedence density') + xlabel('$\delta r$ Seperation') + subplot(1,3,3) + xg2=shotscorr.rad_corr_density./normcorr.rad_corr_density; + if corr_opts.calc_err + xg2_err=xg2.*sqrt((shotscorr_err.results.se_fun_whole_unweighted'./shotscorr.rad_corr_density).^2+(normcorr_err.results.se_fun_whole_unweighted'./normcorr.rad_corr_density).^2); + errorbar(shotscorr.rad_centers,xg2,xg2_err,'kx-') + else + plot(shotscorr.rad_centers,xg2,'.k-','MarkerSize',10) + end + title('Norm. Corr.') + ylabel('$g^{(2)} (\Delta r)$') + xlabel('$\delta r$ Seperation') + pause(1e-6); + end + out.in_shot_corr.rad_centers=shotscorr.rad_centers; + out.in_shot_corr.one_d_corr_density=shotscorr.rad_corr_density; + out.between_shot_corr.rad_centers=normcorr.rad_centers; + out.between_shot_corr.one_d_corr_density=normcorr.rad_corr_density; + out.norm_g2.rad_centers=shotscorr.rad_centers; + out.norm_g2.g2_amp=xg2; + [g2peak,indx] = max(xg2); + if corr_opts.fit + if ~corr_opts.calc_err + fit=fitnlm(shotscorr.rad_centers,xg2,... + fun1d,... + inital_guess,... + 'Options',fo); + else + w = 1./xg2_err.^2; + fit=fitnlm(shotscorr.rad_centers,xg2,... + fun1d,... + inital_guess,... + 'Weight',w,... + 'Options',fo); + end + out.fit = fit; + if corr_opts.plots + hold on + xx = linspace(0,max(shotscorr.rad_centers),3e3)'; + [ypred,ypredci] = predict(fit,xx,'Simultaneous',true); + plot(xx,ypred,'b-', xx,ypredci,'r-'); + end + end + if corr_opts.calc_err + out.in_shot_corr.corr_unc = shotscorr_err; + out.between_shot_corr.corr_unc = normcorr_err; + out.norm_g2.g2_unc = xg2_err; + g2peak_unc = xg2_err(indx); + out.norm_g2.g2peak_unc = g2peak_unc; + fprintf('g2 peak amplitude %s\n',string_value_with_unc(g2peak,g2peak_unc,'type','b','separator',0)) + else + fprintf('g2 peak amplitude %4.2f \n',g2peak) + end + out.norm_g2.g2peak=g2peak; + + +elseif isequal(corr_opts.type,'3d_cart_cl') || isequal(corr_opts.type,'3d_cart_bb') + out = cell(1,3); + for dimension = 1:3 + if corr_opts.calc_err + lin_style = {'kx-','bx-','rx-'}; + else + lin_style = {'.k-','.b-','.r-'}; + end + corr_opts.one_d_dimension = dimension; + if isequal(corr_opts.type,'3d_cart_cl') + corr_opts.cl_or_bb=false; + elseif isequal(corr_opts.type,'3d_cart_bb') + corr_opts.cl_or_bb=true; + end + shotscorr=corr_1d_cart(corr_opts,counts); + if corr_opts.calc_err + shotscorr_err=corr_err(@corr_1d_cart,corr_opts,counts); + end + %shotscorr_high=corr_1d_cart_high_mem(corr_opts,counts); + if corr_opts.plots + if dimension == 1 + stfig(corr_opts.fig,'add_stack',1); + clf + set(gcf,'color','w'); + end + subplot(1,3,1) + hold on + if corr_opts.calc_err + errorbar(shotscorr.x_centers,shotscorr.one_d_corr_density,shotscorr_err.results.se_fun_whole_unweighted,lin_style{dimension}) + else + plot(shotscorr.x_centers,shotscorr.one_d_corr_density,lin_style{dimension},'MarkerSize',10) + end + title('In Shot X Dist (windowed)') + ylabel('$G^{(2)}(\Delta)$ coincedence density') + xlabel('$\Delta$ Seperation') + pause(1e-6); + end + norm_sort_dir=corr_opts.sorted_dir; + if ~corr_opts.sort_norm,norm_sort_dir=nan; end + if size(counts,1)>1 + chunk_num = round(size(counts,2)); + counts_chunked(1,:)=chunk_data(counts(1,:),corr_opts.norm_samp_factor,norm_sort_dir,chunk_num); + counts_chunked(2,:)=chunk_data(counts(2,:),corr_opts.norm_samp_factor,norm_sort_dir,chunk_num); + % counts_chunked=counts_chunked(:,1:end-1); + else + counts_chunked=chunk_data(counts,corr_opts.norm_samp_factor,norm_sort_dir); + end + corr_opts.do_pre_mask=corr_opts.sort_norm; %can only do premask if data is sorted + fprintf('calculating inter-shot correlations \n') + normcorr=corr_1d_cart(corr_opts,counts_chunked); + if corr_opts.calc_err + normcorr_err=corr_err(@corr_1d_cart,corr_opts,counts_chunked); + end + if corr_opts.plots + subplot(1,3,2) + hold on + if corr_opts.calc_err + errorbar(normcorr.x_centers,normcorr.one_d_corr_density,normcorr_err.results.se_fun_whole_unweighted,lin_style{dimension}) + else + plot(normcorr.x_centers,normcorr.one_d_corr_density,lin_style{dimension},'MarkerSize',10) + end + title('Between Shot X Dist (windowed)') + ylabel('$G^{(2)}(\Delta)$ coincedence density') + xlabel('$\Delta$ Seperation') + subplot(1,3,3) + hold on + xg2=shotscorr.one_d_corr_density./normcorr.one_d_corr_density; + if corr_opts.calc_err + xg2_err=xg2.*sqrt((shotscorr_err.results.se_fun_whole_unweighted'./shotscorr.one_d_corr_density).^2+(normcorr_err.results.se_fun_whole_unweighted'./normcorr.one_d_corr_density).^2); + errorbar(shotscorr.x_centers,xg2,xg2_err,lin_style{dimension}) + else + plot(shotscorr.x_centers,xg2,lin_style{dimension},'MarkerSize',10) + end + title('Norm. Corr.') + ylabel('$g^{(2)}(\Delta)$') + xlabel('$\Delta$ Seperation') + pause(1e-6); + end + out{dimension}.in_shot_corr.x_centers=shotscorr.x_centers; + out{dimension}.in_shot_corr.one_d_corr_density=shotscorr.one_d_corr_density; + out{dimension}.between_shot_corr.x_centers=normcorr.x_centers; + out{dimension}.between_shot_corr.one_d_corr_density=normcorr.one_d_corr_density; + out{dimension}.norm_g2.x_centers=shotscorr.x_centers; + out{dimension}.norm_g2.g2_amp=xg2; + [g2peak,indx] = max(xg2); + if corr_opts.fit + if ~corr_opts.calc_err + fit=fitnlm(shotscorr.x_centers,xg2,... + fun1d,... + inital_guess,... + 'Options',fo); + else + w = 1./xg2_err.^2; + fit=fitnlm(shotscorr.x_centers,xg2,... + fun1d,... + inital_guess,... + 'Weight',w,... + 'Options',fo); + end + out{dimension}.fit = fit; + if corr_opts.plots + hold on + xx = linspace(0,max(shotscorr.x_centers),3e3)'; + [ypred,ypredci] = predict(fit,xx,'Simultaneous',true); + plot(xx,ypred,'b-', xx,ypredci,'r-'); + end + end + if corr_opts.calc_err + out{dimension}.in_shot_corr.corr_unc = shotscorr_err; + out{dimension}.between_shot_corr.corr_unc = normcorr_err; + out{dimension}.norm_g2.g2_unc = xg2_err; + g2peak_unc = xg2_err(indx); + out{dimension}.norm_g2.g2peak_unc = g2peak_unc; + fprintf('g2 peak amplitude %s\n',string_value_with_unc(g2peak,g2peak_unc,'type','b','separator',0)) + else + fprintf('g2 peak amplitude %4.2f \n',g2peak) + end + out{dimension}.norm_g2.g2peak=g2peak; + end + if corr_opts.plots + subplot(1,3,2) + legend(sprintf('$\\Delta %s$ Seperation',direction_label{1}),... + sprintf('$\\Delta %s$ Seperation',direction_label{2}),... + sprintf('$\\Delta %s$ Seperation',direction_label{3})) + end +end + +if isfield(corr_opts,'timer') && corr_opts.timer + toc +end + +end + diff --git a/lib/correlations/chunk_data.m b/lib/correlations/chunk_data.m new file mode 100644 index 0000000..1ace6f5 --- /dev/null +++ b/lib/correlations/chunk_data.m @@ -0,0 +1,50 @@ +function counts_chunked=chunk_data(counts,norm_samp_factor,sort_dir,num_chunks) + %data chunking function for normalization + %see calc_any_g2_type for usage + + %input + %norm_samp_factor-should be about the correlation amp for equal noise contibution from in-shot & between shot + %data.txy + %data.data.num_counts + %to do + % -documentation + + num_counts=cellfun(@(x)size(x,1),counts); + + num_shots = size(counts,2); + + total_counts=sum(num_counts); + + if nargin<4 + norm_chunk_size=round(mean(num_counts)*sqrt(norm_samp_factor)); + num_chunks=ceil(total_counts/norm_chunk_size); + else + norm_chunk_size=floor(total_counts/num_chunks); + end + + if num_chunks3 +% norm_chunk_size=round(randn(1)+mean(num_counts)); +% end + min_idx=(ii-1)*norm_chunk_size+1; + if ii==iimax + max_idx=total_counts; + else + max_idx=ii*norm_chunk_size; + end + tmp_data=all_counts(min_idx:max_idx,:); + if ~isnan(sort_dir) + [~,order]=sort(tmp_data(:,sort_dir)); + tmp_data=tmp_data(order,:); + end + counts_chunked{ii}=tmp_data; + end + if size(vertcat(counts_chunked{:}),1)~=total_counts + warning('lost counts') + end +end + diff --git a/lib/correlations/combinatorial_algorithm_g_function.pdf b/lib/correlations/combinatorial_algorithm_g_function.pdf new file mode 100644 index 0000000..c12f1e6 Binary files /dev/null and b/lib/correlations/combinatorial_algorithm_g_function.pdf differ diff --git a/lib/correlations/corr_1d_cart.m b/lib/correlations/corr_1d_cart.m new file mode 100644 index 0000000..a66500b --- /dev/null +++ b/lib/correlations/corr_1d_cart.m @@ -0,0 +1,320 @@ +function out=corr_1d_cart(corr_opts,counts) +% corr_1d_cart - %a low/high memory implementation of the one D correlation +% Notes: +% This g2 correlator is very fast and can be thought as taking a tube along the full 3d cartesian g2 but without having +% to deal with how slow that is. It does this by windowing the pair differences in two dimensions then histograming the +% differences in the remaining dimension(one_d_dimension). Because the correlation is effectively integerated in those +% two window dimensions the window width (one_d_window) must be a small fraction of the correlation length (in those dimensions) +%to avoid suppressing the measured corelation amplitude. +% +% Usage: +% pass in a cell array of counts and then calculate the correlations using a +% bin on the fly method (low mem) or a bin all diferences (high mem) +% differences can be prewindowed using fast_sorted_mask (optional) in both cases to reduce memory & comp requirements. +% differences are then windowed in two dimensions and the correlation calculated in the remaining axis. +% conforms to output formats of import_mcp_tdc_data +% +% Syntax: out=corr_1d_cart(corr_opts,counts_txy) +% +% Inputs: +% counts_txy - as a cell array of zxy counts size=[num_counts,3] +% must be ordered in z for pre window optimzation +% corr_opts - structure of input options +% .one_d_window - [[tmin,tmax];[xmin,xmax];[ymin,ymax]]; %limiits in the one_d_dimension are ignored +% .cl_or_bb - colinear(false) or bb (true) +% .one_d_edges - edges of histogram bins for the correlation +% .one_d_dimension - dimension to calculate correlation +% .one_d_smoothing - [float] gaussian smoothing for the coincidence density output use nan or 0 for no +% smoothing +% .attenuate_counts - value 0-1 the ammount of data to keep, like simulating a lower QE +% .do_pre_mask - logical, use fast sorted mask to window to a range of +% one_d_window in the sorted axis arround each count +% .sorted_dir - must be passed when corr_opts.do_pre_mask used, usualy 1 for time +% .low_mem - use lowmem(true) or highmem(false) options, use nan to set dynamicaly using the +% remaining memory on your computer. +% +% Outputs: +% out - output structure +% .one_d_corr_density - (optional smoothed) coincidence density +% .one_d_corr_density_raw - raw coincidence density +% .x_centers - centers of the histogram vector +% .pairs - total number of pairs +% +% Example: +% [TO DO] +% +% Other m-files required: fast_sorted_mask +% Subfunctions: none +% MAT-files required: none +% See also: corr_unit_testing, calc_any_g2_type, import_mcp_tdc_data +% +% Known BUGS/ Possible Improvements +% - lowmem option seems to be much faster at the moment (with less cpu usage) +% - see if better to prevent prevent diff vector initalization when using high meme with prewindowing to save memory +% - auto memory option does not work on linux, should defalult to low_mem +% - input checking +% - document output better +% - more outputs +% - for the high memory option I dont have to store the prewindowed dimension +% - might be a little messy to implement +% +% Author: Bryce Henson +% email: Bryce.Henson@live.com +% Last revision:2018-12-18 + +%------------- BEGIN CODE -------------- +if size(counts,1)==2 + corr_opts.between_sets = true; +else + corr_opts.between_sets = false; +end + + +if ~isfield(corr_opts,'attenuate_counts') + corr_opts.attenuate_counts=1; +else + if corr_opts.attenuate_counts>1 || corr_opts.attenuate_counts<0 + error('invalid attenuation value, pass a value between 0 and 1\n') + end +end + +if ~isfield(corr_opts,'cl_or_bb') + error('corr_opts.cl_or_bb not specified!do you want co-linear(false) or back-to-back (true)? ') +end + +if isfield(corr_opts,'do_pre_mask') && ~isfield(corr_opts,'sorted_dir') + error('you must pass corr_opts.sorted_dir with corr_opts.do_pre_mask') +elseif ~isfield(corr_opts,'do_pre_mask') + corr_opts.do_pre_mask=false; +end + +if ~isfield(corr_opts,'progress_updates') + corr_opts.progress_updates=50; +end + +num_counts=cellfun(@(x)size(x,1),counts); +if ~isfield(corr_opts,'low_mem') || isnan(corr_opts.low_mem) + mem_temp=memory; + max_arr_size=floor(mem_temp.MaxPossibleArrayBytes/(8*2)); %divide by 8 for double array size and 2 as a saftey factor + + if corr_opts.do_pre_mask + premask_factor=1; %premasking currently uses the same amount of memory + %premasking could in principle dramaticaly reduce the number of pairs that are stored in memory + %this might be a factor of ~1/100 to be implemnted in future + else + premask_factor=1; + end + %use the corr_opts.norm_samp_factor so that both corr/uncorr parts are calculated with the same function + corr_opts.low_mem=((max(num_counts,[],'all')*corr_opts.norm_samp_factor*premask_factor)^2)>max_arr_size; + if corr_opts.print_update + if corr_opts.low_mem,fprintf('auto detection:using the low memory option\n'), end + if ~corr_opts.low_mem,fprintf('auto detection:using the high memory option\n'), end + end +end + +%for the dimension of interest we set the window to be the region specified in corr_opts.one_d_edges +%this simplifies the code and can speed up the historgraming +corr_opts.one_d_window(corr_opts.one_d_dimension,:)=[min(corr_opts.one_d_edges),max(corr_opts.one_d_edges)]; + +updates=corr_opts.progress_updates; %number of updates in the progress bar to give the user, can slow thigs down if too high + + +shots =size(counts,2); +update_interval=ceil(shots/updates); +N = ceil(shots/update_interval); +% dvs = divisors(shots); +% [~,idx]=min(abs(dvs-N)); +% N=dvs(idx); +if ~isfield(corr_opts,'print_update') + corr_opts.print_update = true; +end +if corr_opts.print_update + parfor_progress_imp(N); +end + +pairs_count=zeros(1,shots); +delta_multiplier=[1,-1]; +delta_multiplier=delta_multiplier(1+corr_opts.cl_or_bb); %gives 1 when cl and -1 when bb + +%build a queue of the dimensions that should be masked in before the histogram +%should not mask in corr_opts.one_d_dimension & corr_opts.sorted_dir (if corr_opts.do_pre_mask ) +mask_dimensions=[1,2,3]; +mask_dimensions_logic=[true,true,true]; %logic to avoid clashes when corr_opts.one_d_dimension==corr_opts.sorted_dir +mask_dimensions_logic(corr_opts.one_d_dimension)=false; +if corr_opts.do_pre_mask && ~corr_opts.between_sets, mask_dimensions_logic(corr_opts.sorted_dir)=false; end +mask_dimensions=mask_dimensions(mask_dimensions_logic); + +[one_d_bins,corr_opts.one_d_edges]=histcounts([],corr_opts.one_d_edges); + + +if corr_opts.low_mem %calculate with the low memory mode + % the low memory mode is serial and is a bit easier on mem requirements + one_d_bins=col_vec(one_d_bins); + for shotnum=1:shots + if corr_opts.between_sets + shot_txy_1=counts{1,shotnum}; + shot_txy_2=counts{2,shotnum}; + num_counts_shot_1=num_counts(1,shotnum); + num_counts_shot_2=num_counts(2,shotnum); + else + shot_txy=counts{shotnum}; + num_counts_shot=num_counts(shotnum); + end + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + if corr_opts.between_sets + mask1=rand(num_counts_shot_1,1)corr_opts.one_d_window(mask_dim,1) ... + & delta(:,mask_dim)corr_opts.one_d_window(mask_dim,1) ... + & -delta(:,mask_dim)4x speedup on corr unit testing + one_d_bins=one_d_bins+hist_adaptive_method(delta(one_d_mask_pos,corr_opts.one_d_dimension),corr_opts.one_d_edges); + one_d_bins=one_d_bins+hist_adaptive_method(-delta(one_d_mask_neg,corr_opts.one_d_dimension),corr_opts.one_d_edges); + % old brute histogram approach + %one_d_bins=one_d_bins+histcounts(delta(one_d_mask_pos,corr_opts.one_d_dimension),corr_opts.one_d_edges)'; + %one_d_bins=one_d_bins+histcounts(-delta(one_d_mask_neg,corr_opts.one_d_dimension),corr_opts.one_d_edges)'; + end + if mod(shotnum,update_interval)==0 && corr_opts.print_update + parfor_progress_imp; + end + end%loop over shots + + +else%calculate with the high memory mode + one_d_bins=zeros(shots,size(one_d_bins,2)); + for shotnum=1:shots + shot_txy=counts{shotnum}; + num_counts_shot=num_counts(shotnum); + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + mask=rand(num_counts_shot,1)corr_opts.one_d_window(mask_dim,1) ... + & delta(:,mask_dim)corr_opts.one_d_window(mask_dim,1) ... + & -delta(:,mask_dim)min_lim & delta_brute(:,corr_opts.sorted_dir)1 || corr_opts.attenuate_counts<0 + error('invalid attenuation value, pass a value between 0 and 1\n') + end +end + +if ~isfield(corr_opts,'cl_or_bb') + error('corr_opts.cl_or_bb not specified!do you want co-linear or back-to-back? ') +end + +updates=corr_opts.progress_updates; %number of updates in the progress bar to give the user, can slow thigs down if too high + +%find un-norm g2 +shots =size(counts_txy,2); +update_interval=ceil(shots/updates); +parfor_progress_imp(ceil(shots/update_interval)); + +[one_d_bins,corr_opts.one_d_edges]=histcounts([],corr_opts.one_d_edges); +one_d_bins=zeros(shots,size(one_d_bins,2)); + +pairs_count=zeros(1,shots); +for shotnum=1:shots + shot_txy=counts_txy{shotnum}; + num_counts_shot=size(shot_txy,1); + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + mask=rand(num_counts_shot,1)corr_opts.one_d_window(2,1) & delta(:,2)corr_opts.one_d_window(3,1) & delta(:,3)corr_opts.one_d_window(2,1) & -delta(:,2)corr_opts.one_d_window(3,1) & -delta(:,3)corr_opts.one_d_window(1,1) & delta(:,1)corr_opts.one_d_window(3,1) & delta(:,3)corr_opts.one_d_window(1,1) & -delta(:,1)corr_opts.one_d_window(3,1) & -delta(:,3)corr_opts.one_d_window(1,1) & delta(:,1)corr_opts.one_d_window(2,1) & delta(:,2)corr_opts.one_d_window(1,1) & -delta(:,1)corr_opts.one_d_window(2,1) & -delta(:,2)1 || corr_opts.attenuate_counts<0 + error('invalid attenuation value, pass a value between 0 and 1\n') + end +end + +if ~isfield(corr_opts,'cl_or_bb') + error('corr_opts.cl_or_bb not specified!do you want co-linear or back-to-back? ') +end + +if isfield(corr_opts,'do_pre_mask') && ~isfield(corr_opts,'sorted_dir') + error('you must pass corr_opts.sorted_dir with corr_opts.do_pre_mask') +elseif ~isfield(corr_opts,'do_pre_mask') + corr_opts.do_pre_mask=false; +end + +%for the dimension of interest we set the window to be the redion specified in corr_opts.one_d_edges +%this simplifies the code and can speed up the historgraming +corr_opts.one_d_window(corr_opts.one_d_dimension,:)=[min(corr_opts.one_d_edges),max(corr_opts.one_d_edges)]; + +updates=corr_opts.progress_updates; %number of updates in the progress bar to give the user, can slow thigs down if too high + +%find un-norm g2 +shots =size(counts_txy,2); +update_interval=ceil(shots/updates); +parfor_progress_imp(ceil(shots/update_interval)); + +[one_d_bins,corr_opts.one_d_edges]=histcounts([],corr_opts.one_d_edges); +one_d_bins=zeros(shots,size(one_d_bins,2)); + +pairs_count=zeros(1,shots); +for shotnum=1:shots + shot_txy=counts_txy{shotnum}; + num_counts_shot=size(shot_txy,1); + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + mask=rand(num_counts_shot,1)corr_opts.one_d_window(2,1) & delta(:,2)corr_opts.one_d_window(3,1) & delta(:,3)corr_opts.one_d_window(2,1) & -delta(:,2)corr_opts.one_d_window(3,1) & -delta(:,3)corr_opts.one_d_window(1,1) & delta(:,1)corr_opts.one_d_window(3,1) & delta(:,3)corr_opts.one_d_window(1,1) & -delta(:,1)corr_opts.one_d_window(3,1) & -delta(:,3)corr_opts.one_d_window(1,1) & delta(:,1)corr_opts.one_d_window(2,1) & delta(:,2)corr_opts.one_d_window(1,1) & -delta(:,1)corr_opts.one_d_window(2,1) & -delta(:,2)1 || corr_opts.attenuate_counts<0 + error('invalid attenuation value, pass a value between 0 and 1\n') + end +end + +if ~isfield(corr_opts,'cl_or_bb') + error('corr_opts.cl_or_bb not specified!do you want co-linear(false) or back-to-back (true)? ') +end + +if isfield(corr_opts,'do_pre_mask') && ~isfield(corr_opts,'sorted_dir') + error('you must pass corr_opts.sorted_dir with corr_opts.do_pre_mask') +elseif ~isfield(corr_opts,'do_pre_mask') + corr_opts.do_pre_mask=false; +end + +if ~isfield(corr_opts,'progress_updates') + corr_opts.progress_updates=50; +end + +num_counts=cellfun(@(x)size(x,1),counts); +if ~isfield(corr_opts,'low_mem') || isnan(corr_opts.low_mem) + mem_temp=memory; + max_arr_size=floor(mem_temp.MaxPossibleArrayBytes/(8*2)); %divide by 8 for double array size and 2 as a saftey factor + + if corr_opts.do_pre_mask + premask_factor=1; %premasking currently uses the same amount of memory + %premasking could in principle dramaticaly reduce the number of pairs that are stored in memory + %this might be a factor of ~1/100 to be implemnted in future + else + premask_factor=1; + end + %use the corr_opts.norm_samp_factor so that both corr/uncorr parts are calculated with the same function + corr_opts.low_mem=((max(num_counts,[],'all')*corr_opts.norm_samp_factor*premask_factor)^2)>max_arr_size; + + if corr_opts.low_mem,fprintf('auto detection:using the low memory option\n'), end + if ~corr_opts.low_mem,fprintf('auto detection:using the high memory option\n'), end +end + +%for the dimension of interest we set the window to be the region specified in corr_opts.one_d_edges +%this simplifies the code and can speed up the historgraming +% corr_opts.one_d_window(corr_opts.one_d_dimension,:)=[min(corr_opts.one_d_edges),max(corr_opts.one_d_edges)]; + +updates=corr_opts.progress_updates; %number of updates in the progress bar to give the user, can slow thigs down if too high + + +shots =size(counts,2); +update_interval=ceil(shots/updates); +N = ceil(shots/update_interval); +% dvs = divisors(shots); +% [~,idx]=min(abs(dvs-N)); +% N=dvs(idx); +if ~isfield(corr_opts,'print_update') + corr_opts.print_update = true; +end +if corr_opts.print_update + parfor_progress_imp(N); +end + +pairs_count=zeros(1,shots); +delta_multiplier=[1,-1]; +delta_multiplier=delta_multiplier(1+corr_opts.cl_or_bb); %gives 1 when cl and -1 when bb + +%build a queue of the dimensions that should be masked in before the histogram +%should not mask in corr_opts.one_d_dimension & corr_opts.sorted_dir (if corr_opts.do_pre_mask ) +mask_dimensions=[1,2,3]; +mask_dimensions_logic=[true,true,true]; %logic to avoid clashes when corr_opts.one_d_dimension==corr_opts.sorted_dir +if corr_opts.do_pre_mask, mask_dimensions_logic(corr_opts.sorted_dir)=false; end +mask_dimensions=mask_dimensions(mask_dimensions_logic); + +[three_d_bins,corr_opts.one_d_edges]=histcn([],corr_opts.three_d_edges(:,1),corr_opts.three_d_edges(:,2),... + corr_opts.three_d_edges(:,3)); + + +if corr_opts.low_mem %calculate with the low memory mode + % the low memory mode is serial and is a bit easier on mem requirements + three_d_bins=col_vec(three_d_bins); + for shotnum=1:shots + if corr_opts.between_sets + shot_txy_1=counts{1,shotnum}; + shot_txy_2=counts{2,shotnum}; + num_counts_shot_1=num_counts(1,shotnum); + num_counts_shot_2=num_counts(2,shotnum); + else + shot_txy=counts{shotnum}; + num_counts_shot=num_counts(shotnum); + end + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + if corr_opts.between_sets + mask1=rand(num_counts_shot,1)corr_opts.three_d_window(mask_dim,1) ... + & delta(:,mask_dim)corr_opts.three_d_window(mask_dim,1) ... + & -delta(:,mask_dim)4x speedup on corr unit testing + three_d_bins=three_d_bins+histcn(delta(one_d_mask_pos,:),corr_opts.three_d_edges(:,1),corr_opts.three_d_edges(:,2),... + corr_opts.three_d_edges(:,3)); + three_d_bins=three_d_bins+histcn(-delta(one_d_mask_neg,:),corr_opts.three_d_edges(:,1),corr_opts.three_d_edges(:,2),... + corr_opts.three_d_edges(:,3)); + % old brute histogram approach + %one_d_bins=one_d_bins+histcounts(delta(one_d_mask_pos,corr_opts.one_d_dimension),corr_opts.one_d_edges)'; + %one_d_bins=one_d_bins+histcounts(-delta(one_d_mask_neg,corr_opts.one_d_dimension),corr_opts.one_d_edges)'; + end + if mod(shotnum,update_interval)==0 && corr_opts.print_update + parfor_progress_imp; + end + end%loop over shots + + +else%calculate with the high memory mode + three_d_bins=zeros(shots,size(three_d_bins,2)); + for shotnum=1:shots + shot_txy=counts{shotnum}; + num_counts_shot=num_counts(shotnum); + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + mask=rand(num_counts_shot,1)corr_opts.three_d_window(mask_dim,1) ... + & delta(:,mask_dim)corr_opts.three_d_window(mask_dim,1) ... + & -delta(:,mask_dim)min_lim & delta_brute(:,corr_opts.sorted_dir)corr_opts.one_d_window(2,1) & delta(:,2)corr_opts.one_d_window(3,1) & delta(:,3)corr_opts.one_d_window(2,1) & -delta(:,2)corr_opts.one_d_window(3,1) & -delta(:,3)corr_opts.one_d_window(1,1) & delta(:,1)corr_opts.one_d_window(3,1) & delta(:,3)corr_opts.one_d_window(1,1) & -delta(:,1)corr_opts.one_d_window(3,1) & -delta(:,3)corr_opts.one_d_window(1,1) & delta(:,1)corr_opts.one_d_window(2,1) & delta(:,2)corr_opts.one_d_window(1,1) & -delta(:,1)corr_opts.one_d_window(2,1) & -delta(:,2)1 || corr_opts.attenuate_counts<0 + error('invalid attenuation value, pass a value between 0 and 1\n') + end +end + +if ~isfield(corr_opts,'cl_or_bb') + error('corr_opts.cl_or_bb not specified!do you want co-linear or back-to-back? ') +end + +if isfield(corr_opts,'do_pre_mask') && ~isfield(corr_opts,'sorted_dir') + error('you must pass corr_opts.sorted_dir with corr_opts.do_pre_mask') +elseif ~isfield(corr_opts,'do_pre_mask') + corr_opts.do_pre_mask=false; +end + +if ~isfield(corr_opts,'redges') + error('no radial edges specified') +else + if min(corr_opts.redges)<0 + error('redges should only be positive') + end +end + +if ~isfield(corr_opts,'progress_updates') + corr_opts.progress_updates=50; +end + +num_counts=cellfun(@(x)size(x,1),counts); +if ~isfield(corr_opts,'low_mem') || isnan(corr_opts.low_mem) + mem_temp=memory; + max_arr_size=floor(mem_temp.MaxPossibleArrayBytes/(8*2)); %divide by 8 for double array size and 2 as a saftey factor + + if corr_opts.do_pre_mask + premask_factor=1; %premasking currently uses the same amount of memory + %premasking could in principle dramaticaly reduce the number of pairs that are stored in memory + %this might be a factor of ~1/100 to be implemnted in future + else + premask_factor=1; + end + %use the corr_opts.norm_samp_factor so that both corr/uncorr parts are calculated with the same function + corr_opts.low_mem=((max(num_counts)*corr_opts.norm_samp_factor*premask_factor)^2)>max_arr_size; + if corr_opts.print_update + if corr_opts.low_mem,fprintf('auto detection:using the low memory option\n'), end + if ~corr_opts.low_mem,fprintf('auto detection:using the high memory option\n'), end + end +end + +% convert edges to col vec +corr_opts.redges=col_vec(corr_opts.redges); + +%set the prewindow to be the max radial edge +prewindow=[-1,1]*max(corr_opts.redges); + +updates=corr_opts.progress_updates; %number of updates in the progress bar to give the user, can slow thigs down if too high +shots =size(counts,2); +update_interval=ceil(shots/updates); +if corr_opts.print_update + parfor_progress_imp(ceil(shots/update_interval)); +end + +pairs_count=zeros(1,shots); +delta_multiplier=[1,-1]; +delta_multiplier=delta_multiplier(1+corr_opts.cl_or_bb); %gives 1 when cl and -1 when bb + +[rad_bins,corr_opts.redges]=histcounts([],corr_opts.redges); +%this is slightly wrong it should be r^3 weighted - maybe (JR) +out.rad_centers=(corr_opts.redges(2:end)+corr_opts.redges(1:end-1))/2; + +if corr_opts.low_mem %calculate with the low memory mode + rad_bins=col_vec(rad_bins); + for shotnum=1:shots + if corr_opts.between_sets + shot_txy_1=counts{1,shotnum}; + shot_txy_2=counts{2,shotnum}; + num_counts_shot_1=num_counts(1,shotnum); + num_counts_shot_2=num_counts(2,shotnum); + else + shot_txy=counts{shotnum}; + num_counts_shot=num_counts(shotnum); + end + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + if corr_opts.between_sets + mask1=rand(num_counts_shot_1,1)0 +% fprintf('warning duplicate count') +% end + +% %%you can check that the sorted mask this is equivelent to the below brute approach +% delta_brute=shot_txy(ii,:)-delta_multiplier*shot_txy(ii+1:num_counts_shot,:); +% min_lim=corr_opts.one_d_window(corr_opts.sorted_dir,1); +% max_lim=corr_opts.one_d_window(corr_opts.sorted_dir,2); +% mask=delta_brute(:,corr_opts.sorted_dir)>min_lim & delta_brute(:,corr_opts.sorted_dir)0 + delpos=mvnrnd(zeros(3,1),diag(corr_width),corr_counts); + %%THE WRONG WAY !!! + %delpos=reshape(randn(sum(coor_chance)*3,1),[sum(coor_chance),3]).*repmat([corr_widthz,corr_widthx,corr_widthy],[corr_counts,1]); + shot_with_corr=[shot;shot(coor_chance,:)+delpos]; + else + shot_with_corr=shot; + end + + det_chance=rand(size(shot_with_corr,1),1)1 + det_counts=shot_with_corr(det_chance,:); + %sort in time to make sure everything is robust to that + [~,sort_idx]=sort(det_counts(:,1)); + det_counts=det_counts(sort_idx,:); + counts_txy{n}=det_counts; + else + counts_txy{n}={}; + end + num_counts(n)=num_det; +end + +total_counts=sum(num_counts); +density=mean(num_counts)/(therm_width^3); +mode_volume=prod(corr_width); +mode_occ=density*mode_volume; + +fprintf('estimated mode occupancy %2.3e \n',mode_occ) +fprintf('estimated corr amp %.3f \n',1+1/mode_occ) +fprintf('total counts over all shots %2.3e \n',total_counts) +fprintf('mean per shot %2.3e \n',total_counts/number_shots) +fprintf('rough pairs per shot %2.3e \n',count_upper_triangle(total_counts/number_shots)) +fprintf('rough total pairs %2.3e \n',count_upper_triangle(total_counts/number_shots)*number_shots) + +fake_data.counts_txy=counts_txy; +fake_data.num_counts=num_counts; + +end \ No newline at end of file diff --git a/lib/correlations/fake_cl_corr_medium_hot.m b/lib/correlations/fake_cl_corr_medium_hot.m new file mode 100644 index 0000000..f79a8f9 --- /dev/null +++ b/lib/correlations/fake_cl_corr_medium_hot.m @@ -0,0 +1,65 @@ +function fake_data=fake_cl_corr_medium_hot(number_shots,qe) +% test function on that makes some colinearly correlated data g(2)~2 +%return data in the same structure that import_mcp_tdc_data produces + +shot_counts=20000; %number of counts in each shot +corr_frac=1; +therm_width=0.5; %isotropic in 3d +corr_width(1)=0.001; +corr_width(2)=0.001; +corr_width(3)=0.001; + + +% shot_counts=10000; %number of counts in each shot +% corr_frac=1; +% therm_width=0.5; %isotropic in 3d +% corr_widthx=0.001; +% corr_widthy=0.001; +% corr_widthz=0.001; + +fake_data=[]; +num_corrected=round(shot_counts/(1+corr_frac)); +for n=1:number_shots + shot=mvnrnd(zeros(3,1),diag([1,1,1])*therm_width,num_corrected); + %shot=reshape(randn(num_corrected*3,1)*therm_width,[num_corrected,3]); %THE WRONG WAY !!! + coor_chance=rand(num_corrected,1)0 + delpos=mvnrnd(zeros(3,1),diag(corr_width),corr_counts); + %%THE WRONG WAY !!! + %delpos=reshape(randn(sum(coor_chance)*3,1),[sum(coor_chance),3]).*repmat([corr_widthz,corr_widthx,corr_widthy],[corr_counts,1]); + shot_with_corr=[shot;shot(coor_chance,:)+delpos]; + else + shot_with_corr=shot; + end + + det_chance=rand(size(shot_with_corr,1),1)1 + det_counts=shot_with_corr(det_chance,:); + %sort in time to make sure everything is robust to that + [~,sort_idx]=sort(det_counts(:,1)); + det_counts=det_counts(sort_idx,:); + counts_txy{n}=det_counts; + else + counts_txy{n}={}; + end + num_counts(n)=num_det; +end + +total_counts=sum(num_counts); +density=mean(num_counts)/(therm_width^3); +mode_volume=prod(corr_width); +mode_occ=density*mode_volume; + +fprintf('estimated mode occupancy %2.3e \n',mode_occ) +fprintf('estimated corr amp %.3f \n',1+1/mode_occ) +fprintf('total counts over all shots %2.3e \n',total_counts) +fprintf('mean per shot %2.3e \n',total_counts/number_shots) +fprintf('rough pairs per shot %2.3e \n',count_upper_triangle(total_counts/number_shots)) +fprintf('rough total pairs %2.3e \n',count_upper_triangle(total_counts/number_shots)*number_shots) + +fake_data.counts_txy=counts_txy; +fake_data.num_counts=num_counts; + +end \ No newline at end of file diff --git a/lib/correlations/fake_super_cl_corr.m b/lib/correlations/fake_super_cl_corr.m new file mode 100644 index 0000000..d31796b --- /dev/null +++ b/lib/correlations/fake_super_cl_corr.m @@ -0,0 +1,65 @@ +function fake_data=fake_super_cl_corr(number_shots,qe) +% test function on that makes some colinearly correlated data g(2)~2 +%return data in the same structure that import_mcp_tdc_data produces + +shot_counts=2000; %number of counts in each shot +corr_frac=1; +therm_width=0.5; %isotropic in 3d +corr_width(1)=0.0015; +corr_width(2)=0.0015; +corr_width(3)=0.0015; + + +% shot_counts=10000; %number of counts in each shot +% corr_frac=1; +% therm_width=0.5; %isotropic in 3d +% corr_widthx=0.001; +% corr_widthy=0.001; +% corr_widthz=0.001; + +fake_data=[]; +num_corrected=round(shot_counts/(1+corr_frac)); +for n=1:number_shots + shot=mvnrnd(zeros(3,1),diag([1,1,1])*therm_width,num_corrected); + %shot=reshape(randn(num_corrected*3,1)*therm_width,[num_corrected,3]); %THE WRONG WAY !!! + coor_chance=rand(num_corrected,1)0 + delpos=mvnrnd(zeros(3,1),diag(corr_width),corr_counts); + %%THE WRONG WAY !!! + %delpos=reshape(randn(sum(coor_chance)*3,1),[sum(coor_chance),3]).*repmat([corr_widthz,corr_widthx,corr_widthy],[corr_counts,1]); + shot_with_corr=[shot;shot(coor_chance,:)+delpos]; + else + shot_with_corr=shot; + end + + det_chance=rand(size(shot_with_corr,1),1)1 + det_counts=shot_with_corr(det_chance,:); + %sort in time to make sure everything is robust to that + [~,sort_idx]=sort(det_counts(:,1)); + det_counts=det_counts(sort_idx,:); + counts_txy{n}=det_counts; + else + counts_txy{n}={}; + end + num_counts(n)=num_det; +end + +total_counts=sum(num_counts); +density=mean(num_counts)/(therm_width^3); +mode_volume=prod(corr_width); +mode_occ=density*mode_volume; + +fprintf('estimated mode occupancy %2.3e \n',mode_occ) +fprintf('estimated corr amp %.3f \n',1+1/mode_occ) +fprintf('total counts over all shots %2.3e \n',total_counts) +fprintf('mean per shot %2.3e \n',total_counts/number_shots) +fprintf('rough pairs per shot %2.3e \n',CountUpperTriangle(total_counts/number_shots)) +fprintf('rough total pairs %2.3e \n',CountUpperTriangle(total_counts/number_shots)*number_shots) + +fake_data.counts_txy=counts_txy; +fake_data.num_counts=num_counts; + +end \ No newline at end of file diff --git a/lib/correlations/fake_therm_cl_corr_small_cold.m b/lib/correlations/fake_therm_cl_corr_small_cold.m new file mode 100644 index 0000000..30c8639 --- /dev/null +++ b/lib/correlations/fake_therm_cl_corr_small_cold.m @@ -0,0 +1,47 @@ +function fake_data=fake_therm_cl_corr_small_cold(number_shots,qe) +% test function on that makes some colinearly correlated data g(2)~1.85 +%return data in the same structure that import_mcp_tdc_data produces + +shot_counts=360; %number of counts in each shot +corr_frac=1; +therm_width=0.5; %isotropic in 3d +corr_widthx=0.1; +corr_widthy=0.1; +corr_widthz=0.1; + +fake_data=[]; +num_corrected=round(shot_counts/(1+corr_frac)); +for n=1:number_shots + shot=reshape(randn(num_corrected*3,1)*therm_width,[num_corrected,3]); + coor_chance=rand(num_corrected,1)0 + delpos=reshape(randn(sum(coor_chance)*3,1),[sum(coor_chance),3]).*repmat([corr_widthz,corr_widthx,corr_widthy],[sum(coor_chance),1]); + shot_with_corr=[shot;shot(coor_chance,:)+delpos]; + else + shot_with_corr=shot; + end + + det_chance=rand(size(shot_with_corr,1),1)1 + det_counts=shot_with_corr(det_chance,:); + %sort in time to make sure everything is robust to that + [~,sort_idx]=sort(det_counts(:,1)); + det_counts=det_counts(sort_idx,:); + counts_txy{n}=det_counts; + else + counts_txy{n}={}; + end + num_counts(n)=num_det; +end + +total_counts=sum(num_counts); +fprintf('total counts over all shots %2.3e \n',total_counts) +fprintf('mean per shot %2.3e \n',total_counts/number_shots) +fprintf('rough pairs per shot %2.3e \n',CountUpperTriangle(total_counts/number_shots)) +fprintf('rough total pairs %2.3e \n',CountUpperTriangle(total_counts/number_shots)*number_shots) + +fake_data.counts_txy=counts_txy; +fake_data.num_counts=num_counts; + +end \ No newline at end of file diff --git a/lib/correlations/fake_therm_cl_corr_small_hot.m b/lib/correlations/fake_therm_cl_corr_small_hot.m new file mode 100644 index 0000000..b209f4a --- /dev/null +++ b/lib/correlations/fake_therm_cl_corr_small_hot.m @@ -0,0 +1,48 @@ +function fake_data=fake_therm_cl_corr_small_hot(number_shots,qe) +% test function on that makes some colinearly correlated data with g(2)~1.8 +%returns data in the same structure/format that import_mcp_tdc_data produces + +%dont change there or the corr amp will change +shot_counts=100; %number of counts in each shot +corr_frac=0.017; +therm_width=1; %isotropic in 3d +corr_widthx=0.1; +corr_widthy=0.1; +corr_widthz=0.1; + +fake_data=[]; +num_corrected=round(shot_counts/(1+corr_frac)); +for n=1:number_shots + shot=reshape(randn(num_corrected*3,1)*therm_width,[num_corrected,3]); + coor_chance=rand(num_corrected,1)0 + delpos=reshape(randn(sum(coor_chance)*3,1),[sum(coor_chance),3]).*repmat([corr_widthz,corr_widthx,corr_widthy],[sum(coor_chance),1]); + shot_with_corr=[shot;shot(coor_chance,:)+delpos]; + else + shot_with_corr=shot; + end + + det_chance=rand(size(shot_with_corr,1),1)1 + det_counts=shot_with_corr(det_chance,:); + %sort in time to make sure everything is robust to that + [~,sort_idx]=sort(det_counts(:,1)); + det_counts=det_counts(sort_idx,:); + counts_txy{n}=det_counts; + else + counts_txy{n}={}; + end + num_counts(n)=num_det; +end + +total_counts=sum(num_counts); +fprintf('total counts over all shots %2.3e \n',total_counts) +fprintf('mean per shot %2.3e \n',total_counts/number_shots) +fprintf('rough pairs per shot %2.3e \n',CountUpperTriangle(total_counts/number_shots)) +fprintf('rough total pairs %2.3e \n',CountUpperTriangle(total_counts/number_shots)*number_shots) + +fake_data.counts_txy=counts_txy; +fake_data.num_counts=num_counts; + +end \ No newline at end of file diff --git a/lib/correlations/generate_thermal_data/generate_thermal_corr_data.m b/lib/correlations/generate_thermal_data/generate_thermal_corr_data.m new file mode 100644 index 0000000..c6d87cb --- /dev/null +++ b/lib/correlations/generate_thermal_data/generate_thermal_corr_data.m @@ -0,0 +1,125 @@ + + +uniform_region=10; +g1_sigma=0.4; +corr_sigma=0.01; +headroom=1.2; +peak_value=headroom*1/(g1_sigma*sqrt(2*pi)); +% initalize data structure; +thermal_data=[]; +thermal_data.xcord=[]; +%thermal_data.therm_amp=[]; +thermal_data.xcord=0; +plot_handle=stfig('conditional prop plot'); +max_order=4; +clf + +%% plot the thermal pdf + +stfig('conditional prop plot'); +xsamp=linspace(-5,5,1e3); +plot(xsamp,g1(xsamp,g1_sigma)) + +%% +fprintf('\ncounts %05u',numel(thermal_data.xcord)) +while true +trying_to_sample=true; +tries=1; +while trying_to_sample + sample_x_cord=uniform_region*(rand(1)-0.5)*2; + sample_amp=rand(1)*peak_value; + pdf_amp=conditional_amp(sample_x_cord,thermal_data,g1_sigma,corr_sigma,max_order); + if sample_amp0 && ordermax>1 + delta_mat = bsxfun(@minus, x_in, thermal_data.xcord'); + % if numel(thermal_data.xcord)<2 + % thermal_data.xcord=thermal_data.xcord(2:end); + % else + % delta_mat=triu(delta_mat,1); + % end + for order=2:ordermax + amp_corr_tmp=gn_amp(delta_mat,order,corr_sigma).*big_g2_uncorr(delta_mat,order,g1_sigma); %xin col, xcounts rows + amp_corr=amp_corr+sum(amp_corr_tmp,2); + end +else + amp_corr=0; +end +amp_out=amp_corr; +end diff --git a/lib/correlations/generate_thermal_data/generate_thermal_corr_data_naive.m b/lib/correlations/generate_thermal_data/generate_thermal_corr_data_naive.m new file mode 100644 index 0000000..c567291 --- /dev/null +++ b/lib/correlations/generate_thermal_data/generate_thermal_corr_data_naive.m @@ -0,0 +1,111 @@ + +% THIS ALGO DOES NOT WORK! +% the fairly direct approach to the conditional probability ends up narrowing up with a width about the correlation +% length and does not produce a thermal density distribution + +% %% start with some seed data (does not work) +% num_seed=1e2; +% thermal_data.xcord=normrnd(0,g1_sigma,num_seed,1); +% thermal_data.therm_amp=g1(thermal_data.xcord,g1_sigma); + + +uniform_region=5; +g1_sigma=1; +corr_sigma=0.2; +peak_value=1/(g1_sigma*sqrt(2*pi)); +headroom=1.1; +% initalize data structure; +thermal_data=[]; +thermal_data.xcord=[]; +thermal_data.therm_amp=[]; + +plot_handle=stfig('conditional prop plot'); +clf + +%% plot the thermal pdf + +stfig('conditional prop plot'); +xsamp=linspace(-5,5,1e4); +plot(xsamp,g1(xsamp,g1_sigma)) + + +%% +while true + +trying_to_sample=true; +tries=1; +while trying_to_sample + sample_x_cord=uniform_region*(rand(1)-0.5)*2; + sample_amp=rand(1)*headroom*peak_value; + pdf_amp=conditional_amp(sample_x_cord,thermal_data,g1_sigma,corr_sigma); + if sample_amp0 + delta_mat = bsxfun(@minus, x_in, thermal_data.xcord'); + % if numel(thermal_data.xcord)<2 + % thermal_data.xcord=thermal_data.xcord(2:end); + % else + % delta_mat=triu(delta_mat,1); + % end + amp_corr=gn_amp(delta_mat,2,corr_sigma); %xin col, xcounts rows + amp_corr=amp_corr.*repmat(thermal_data.therm_amp',[size(x_in,1),1]); + amp_corr=sum(amp_corr,2); +else + amp_corr=0; +end +amp_out=amp_corr+thermal_amp; +end \ No newline at end of file diff --git a/lib/correlations/generate_thermal_data/readme.md b/lib/correlations/generate_thermal_data/readme.md new file mode 100644 index 0000000..7ef0ef9 --- /dev/null +++ b/lib/correlations/generate_thermal_data/readme.md @@ -0,0 +1,75 @@ +# thermal correlation sampling +Bryce Henson + +Want to sample (m) counts from a thermal distribution up to some maximum order (p) +probability distrbution(PD) +contitional probability distrbution(CPD) + + +## rough algo sketch +- starting with a gaussian distrbution sample a single count,using rejection sampling with a proposal density that encloses this distribution +- this then changes the probability distribution by adding a gaussian of the g2 corr. length, and with the amplitude of the thermal distribution at that location +- now readjust the proposal density so that it encloses the probability distrbution + - will require finding the sum of the thermal PD and all the correlation orders + - could sample the entire distribution at less than a correlation length( maybe divided by max corr. order) + - could frame as a search problem starting from each count + - maybe there is a nice property of gaussians that we can exploit +- now repeat + - sample a count using rejection sampling + - give a sample of x + - generate a random number between 0 and the proposal density amplitude + - calcluate the contitional proabablity + - thermal + - correlation enghancements + - g2 from differences to all other counts + - g3 ect... up to order p + - if conditional probablity lies abvove the random number then sucess store that count and the thermap PD amp + - otherwise repeat + - readjust the proposal density so that it encloses the conditional proabablity + + + +## some thoughts on complexity +- restrict the interval + +for only g2, n counts +- Sampling + - sample from the prop.dist (c1) + - calculate the thermal dist (c2) + - calculate distance differences (n) and coresponding gaussian amp to give conditional proabablity + - sampling eff int.PD/int. prop.den +- sample the CPD to adjust the prop.dist. n(c2+n) +- repeat unitl have m counts + +sum_n=1^m [n+ (n(c2+n))] +to leading term +m^3 + + +for max order p +sum_n=1^m [sum_i=1^p (n^i) + (n(c2+sum_i=1^p (n^i)))] +to leading order +sum_n=1^m [n^p + (n(c2+n^p))] +m^(p+1) + + +for g3 1e3 counts +1e12 operations +5GFLOPS/core for i7 +200s +for 1e5 counts +634y + + +## results +- the implmentation of above just produces this divergence of the CPD which does not produce a thermal density dist +- seeding with some uncorrelated gaussians does not help + +## future thoughts +- i think the answer may lie in the usage og the g2 function +- this algo seems to say that the G^(2)_corr. is equal to gauss(\delta x,\sigma)+1 +- in reality it is the ratio of G^(2)_corr./G^(2)_uncorr. =gauss(\delta x,\sigma)+1 +- the G^(2)_uncorr should be related to the http://mathworld.wolfram.com/NormalDifferenceDistribution.html +- so it is wrong to call the g^(2) the probability of detection relative to the (uncorr) themal distribution + + diff --git a/lib/correlations/jth_neibour/corr_radial_deuar.m b/lib/correlations/jth_neibour/corr_radial_deuar.m new file mode 100644 index 0000000..14cff9f --- /dev/null +++ b/lib/correlations/jth_neibour/corr_radial_deuar.m @@ -0,0 +1,224 @@ +function out=corr_radial_deuar(corr_opts,counts_txy) +% deuar_corr - %a low/high memory implementation of the deuar correlator +% Notes: +% This is a 'non traditional' correlaor that is used to see how 'bloby' the data is. Uses the distribution of the +% ordered differeces. eg the mean distance of the 4th nearest data point. +% +% Usage: +% How to interpret the results of this correlator +% ? How to interpret the width, can this be converted to blob width. +% ? can it be used to find gaps in data +% +% Syntax: out=corr_1d_cart(corr_opts,counts_txy) +% +% Inputs: +% counts_txy - as a cell array of zxy counts size=[num_counts,3] +% must be ordered in z for pre window optimzation +% corr_opts - structure of input options +% .one_d_smoothing - [float] gaussian smoothing for the coincidence density output use nan or 0 for no +% smoothing +% .attenuate_counts - value 0-1 the ammount of data to keep, like simulating a lower QE +% .do_pre_mask - logical, use fast sorted mask to window to a range of +% one_d_window in the sorted axis arround each count +% .sorted_dir - must be passed when corr_opts.do_pre_mask used, usualy 1 for time +% .low_mem - use lowmem(true) or highmem(false) options, use nan to set dynamicaly using the +% remaining memory on your computer. +% +% Outputs: +% out - output structure +% .one_d_corr_density - (optional smoothed) coincidence density +% .one_d_corr_density_raw - raw coincidence density +% .x_centers - centers of the histogram vector +% .pairs - total number of pairs +% +% Example: +% [TO DO] +% +% Other m-files required: fast_sorted_mask +% Subfunctions: none +% MAT-files required: none +% See also: corr_unit_testing, calc_any_g2_type, import_mcp_tdc_data +% +% Known BUGS/ Possible Improvements +% - decrease memory requirements +% - implement standard deviation +% - implemnt histogram of the nth distance +% - understand how to normalize with different atom numbers +% - implement low memory option with mean/histogram on the fly +% - need to figure out how to normalize shots first +% - do after the high memory option is working + +% +% Author: Bryce Henson +% email: Bryce.Henson@live.com +% Last revision:2018-12-18 + +%------------- BEGIN CODE -------------- + +if ~isfield(corr_opts,'attenuate_counts') + corr_opts.attenuate_counts=1; +else + if corr_opts.attenuate_counts>1 || corr_opts.attenuate_counts<0 + error('invalid attenuation value, pass a value between 0 and 1\n') + end +end + +if ~isfield(corr_opts,'cl_or_bb') + error('corr_opts.cl_or_bb not specified!do you want co-linear or back-to-back? ') +end + +if isfield(corr_opts,'do_pre_mask') && ~isfield(corr_opts,'sorted_dir') + error('you must pass corr_opts.sorted_dir with corr_opts.do_pre_mask') +elseif ~isfield(corr_opts,'do_pre_mask') + corr_opts.do_pre_mask=false; +end + +if ~isfield(corr_opts,'progress_updates') + corr_opts.progress_updates=50; +end + +num_counts=cellfun(@(x)size(x,1),counts_txy); +%if ~isfield(corr_opts,'low_mem') || isnan(corr_opts.low_mem) +%TO BE USED WHEN LOW MEM IS IMPLEMENTED +% mem_temp=memory; +% max_arr_size=floor(mem_temp.MaxPossibleArrayBytes/(8*2)); %divide by 8 for double array size and 2 as a saftey factor +% %premasking can dramaticaly reduce the number of pairs that are stored in memory +% %this might be a factor of ~1/100 +% if corr_opts.do_pre_mask +% premask_factor=1e-2; +% else +% premask_factor=1; +% end +% %use the corr_opts.norm_samp_factor so that both corr/uncorr parts are calculated with the same function +% corr_opts.low_mem=((max(num_counts)*corr_opts.norm_samp_factor*premask_factor)^2)>max_arr_size; +% +% if corr_opts.low_mem,fprintf('auto detection:using the low memory option\n'), end +% if ~corr_opts.low_mem,fprintf('auto detection:using the high memory option\n'), end +%end +corr_opts.low_mem=false; + +shots =size(counts_txy,2); +updates=corr_opts.progress_updates; %number of updates in the progress bar to give the user, can slow thigs down if too high +update_interval=ceil(shots/updates); +parfor_progress_imp(ceil(shots/update_interval)); + +pairs_count=zeros(1,shots); +delta_multiplier=[1,-1]; +delta_multiplier=delta_multiplier(1+corr_opts.cl_or_bb); %gives 1 when cl and -1 when bb + +ordered_delta=cell(shots,1); %each cell should countain an num_counts by num_counts array with the ordered radial differences + + +if corr_opts.low_mem %calculate with the low memory mode + error('low mem option not yet implemented') + % will require some more thinking , high memory is easier to implement + +else%calculate with the high memory mode + for shotnum=1:shots + shot_txy=counts_txy{shotnum}; + num_counts_shot=num_counts(shotnum); + ordered_delta_shot=nan(num_counts_shot,num_counts_shot); + if corr_opts.attenuate_counts~=1 %randomly keep corr_opts.attenuate_counts fraction of the data + mask=rand(num_counts_shot,1)min_lim & delta_brute(:,corr_opts.sorted_dir)1 + det_counts=shot_with_blob(det_chance,:); + %sort in time to make sure everything is robust to that + [~,sort_idx]=sort(det_counts(:,1)); + det_counts=det_counts(sort_idx,:); + counts_txy{n}=det_counts; + else + counts_txy{n}={}; + end + num_counts(n)=num_det; +end + +fake_data.counts_txy=counts_txy; +fake_data.num_counts=num_counts; + +end \ No newline at end of file diff --git a/lib/fast_search_histogram b/lib/fast_search_histogram index 464ee81..a6af668 160000 --- a/lib/fast_search_histogram +++ b/lib/fast_search_histogram @@ -1 +1 @@ -Subproject commit 464ee8173129ed902a97f070c4e542b68921f478 +Subproject commit a6af668129597d808747060d47e661f659cdf9f3 diff --git a/lib/fast_sorted_mask b/lib/fast_sorted_mask index 201a025..9e42724 160000 --- a/lib/fast_sorted_mask +++ b/lib/fast_sorted_mask @@ -1 +1 @@ -Subproject commit 201a0259a65cc8109a991b809b5393a9764c0d60 +Subproject commit 9e42724710a58a972a7805a5424d575b4428ac1f diff --git a/lib/fft_tx/test_fft_tx.m b/lib/fft_tx/test_fft_tx.m index bab83a2..78ecbed 100644 --- a/lib/fft_tx/test_fft_tx.m +++ b/lib/fft_tx/test_fft_tx.m @@ -2,6 +2,21 @@ %to do %- tests for unevenly sampled data +addpath('./lib/') %add the path to set_up_project_path, this will change if Core_BEC_Analysis is included as a submodule + % in this case it should be './lib/Core_BEC_Analysis/lib/' +set_up_project_path(pwd) + +%% Basic usage +% a very simple use case +time_vec=linspace(0,1e3,1e6); +amp_strong=10; +testfun=@(t) amp_strong*sin(2*pi*t*100+pi)+1*sin(2*pi*t*133+pi); +val=testfun(time_vec); +out=fft_tx(time_vec,val,'padding',10,'window','gauss','win_param',{5}); +stfig('fft output') +plot(out(1,:),abs(out(2,:)),'k') + + %% EVENLY SAMPLED %test that freq amplitude values are correct in the evenly sampled case %---start user var--- @@ -86,18 +101,6 @@ fprintf('TEST: peak amp within tolerance: %s\n',logic_str{1+(abs(max_amp/amp_strong-1) opts_cent.threshold(axis); + locs = find(mask); + margins = [min(locs(2:end-1)), max(locs(2:end-1))]; + if isempty(margins) + centre_OK(this_idx) = 0; + else + t_margins = bin_centres(margins); + bec_centres(this_idx, axis) = mean(t_margins); + bec_widths(this_idx, axis) = diff(t_margins); + centre_OK(this_idx) = 1; + end + if opts_cent.visual > 1 + subplot(3, 1, axis); + plot(bin_centres, flux, 'k') + hold on + plot(bin_centres(mask), flux(mask), 'r') + end + end +end +% if opts_cent.visual +% for splt = 1:3 +% subplot(3,1,splt) +% ylabel('Counts') +% end +% end + +if opts_cent.visual + f=stfig('BEC centering'); +% f=sfigure(2); + clf + xmin = -3e-3; + xmax = 3e-3; + c_edges = 0.5*linspace(xmin,xmax,30); + w_edges = 1.5*linspace(xmin,xmax,30); + + subplot(3,2,1) + hold on + plot(bec_centres(:,1)-mean(bec_centres(:,1)),'r.') + plot(bec_centres(:,2)-mean(bec_centres(:,2)),'b.') + plot(bec_centres(:,3)-mean(bec_centres(:,3)),'k.') + title('BEC centre deviation') + xlabel('Shot number') + ylabel('Centre offset from mean') + legend('T','X','Y') + subplot(3,2,2) + hold on + histogram(bec_centres(:,1)-mean(bec_centres(:,1)),c_edges,'FaceColor','r','FaceAlpha',0.2) + histogram(bec_centres(:,2)-mean(bec_centres(:,2)),c_edges,'FaceColor','b','FaceAlpha',0.2) + histogram(bec_centres(:,3)-mean(bec_centres(:,3)),c_edges,'FaceColor','k','FaceAlpha',0.2) + xlim([min(c_edges),max(c_edges)]) + legend('T','X','Y') + title('BEC centre deviation') + ylabel('Centre offset from mean') + ylabel('Number of shots') + + subplot(3,2,3) + hold on + plot(bec_widths(:,1)-mean(bec_widths(:,1)),'r.') + plot(bec_widths(:,2)-mean(bec_widths(:,2)),'b.') + plot(bec_widths(:,3)-mean(bec_widths(:,3)),'k.') + legend('T','X','Y') + title('BEC width variation') + xlabel('Shot number') + ylabel('Width variation from mean') + subplot(3,2,4) + hold on + histogram(bec_widths(:,1)-mean(bec_widths(:,1)),w_edges,'FaceColor','r','FaceAlpha',0.2) + histogram(bec_widths(:,2)-mean(bec_widths(:,2)),w_edges,'FaceColor','b','FaceAlpha',0.2) + histogram(bec_widths(:,3)-mean(bec_widths(:,3)),w_edges,'FaceColor','k','FaceAlpha',0.2) + xlim([min(w_edges),max(w_edges)]) + legend('T','X','Y') + title('BEC width variation') + ylabel('Width offset from mean') + ylabel('Number of shots') + + % plot(bec_widths) + if opts_cent.savefigs + cli_header(1,'Saving images...'); + saveas(f,fullfile(opts_cent.data_out,'centering.fig')); + saveas(f,fullfile(opts_cent.data_out,'centering.eps')); + saveas(f,fullfile(opts_cent.data_out,'centering.svg')); + cli_header(2,'Done.'); + end +end + +cli_header(2, 'Done!'); +end \ No newline at end of file diff --git a/lib/g_bose.m b/lib/g_bose.m deleted file mode 100644 index 8a97a44..0000000 --- a/lib/g_bose.m +++ /dev/null @@ -1,32 +0,0 @@ -function GZ = g_bose(Z) -% function [GZ,err,n_ser] = g_bose(Z) -% Polylog of order 3/2 - Bose-Einstein distribution integral -% Converges for Z in [0,1) - runtime diverges as Z->1 - -% USER CONSTS FOR ALGORITHM CONVERGENCE -tol_err=1e-20; % incremental error from evaluating series sum - -zmask = Z >= 0.9999; -if any(zmask) - warning('g_bose will not converge for Z>=1 !') - Z(zmask) = nan; -end -% else - -GZ=0; % initialise output -err=inf; % initialise incremental error - -n_ser=0; % summand order -while err>tol_err - n_ser=n_ser+1; - GZ_temp=GZ; % save last order series sum - - % evaluate next series term - GZ=GZ+(Z.^n_ser)/(n_ser^(3/2)); - - % evaluate error from this term - if n_ser>1 % skip evaluateion (div) for first iter - err=max(abs(GZ-GZ_temp)./GZ_temp); % incremental fractional diff - end -end -end \ No newline at end of file diff --git a/lib/gauss_filt_unifrom.m b/lib/gauss_filt_unifrom.m new file mode 100644 index 0000000..7b82514 --- /dev/null +++ b/lib/gauss_filt_unifrom.m @@ -0,0 +1,4 @@ +function out_vec=gauss_filt_unifrom(in_vec,sigma) +in_vec=col_vec(in_vec); +out_vec=gaussfilt(1:numel(in_vec),in_vec,sigma); +end \ No newline at end of file diff --git a/lib/getlims.m b/lib/getlims.m deleted file mode 100644 index 9f2bfae..0000000 --- a/lib/getlims.m +++ /dev/null @@ -1,11 +0,0 @@ -function lims = getlims(data) -% A really quick function to return the [min,max] in each axis of data -% where the COLUMNS of data are the data coordinates - naxis = size(data,2); - lims = zeros(naxis,2); - for axis = 1:naxis - axmin = min(data(axis,:)); - axmax = max(data(axis,:)); - lims(axis,:) = [axmin,axmax]; - end -end \ No newline at end of file diff --git a/lib/hebec_constants.m b/lib/hebec_constants.m index 76542ee..bd5eb93 100644 --- a/lib/hebec_constants.m +++ b/lib/hebec_constants.m @@ -6,8 +6,8 @@ % - add references for all values % - include transitions - -global const +function const = hebec_constants() +% global const %fundamental const.c = 299792458; %speed of light (m/s) const.h = 6.626070040*10^-34; %Planck constant (J s) @@ -19,12 +19,14 @@ const.mub =9.274009994*10^-24; %Bohr magneton*(J/T) const.electron = 1.60217657*10^-19;%(*charge of electron*) const.me = 9.10938291*10^-31;%(*mass of electron*) +const.mp = 1.67262158*10^-27;%(*mass of proton*) const.grav=6.67430*10^-11; %Newtonian constant of gravitation %https://physics.nist.gov/cgi-bin/cuu/Value?bg %Helium % const.ahe_scat=15*10^-9; const.ahe_scat=7.512000000000000e-09; %m^2 Moal et al https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.023203 -const.b_freq=2.802*1e6*1e4; %hz/T +const.b_freq=2*const.mub/const.h /(1e4); %for the metastable state - hz/G +% calculated for the metastable state const.mhe = 1.66*10^-27*4.002;%(*helium mass*) const.interaction_energy = 4*pi*const.hb^2*const.ahe_scat/const.mhe; % interaction strength [] @@ -38,3 +40,36 @@ %customary const.a0 = 0.529*10^-10;%(*bohr radius*) +%experiment +const.fall_distance = 0.8587; + +const.mu = 9.27e-28; %J/G +const.h = 6.62607015e-34; +const.hbar = const.h/(2*pi); +const.f_mu = const.mu/const.h; +const.w_mu = const.mu/const.hbar; +const.c = 299792458; +const.q = 1.602e-19; +% Notation & lookup +const.terms = {'S','P','D','F','G','H','I','K'}; +%% Reference values +const.f_table.g_2_3P_2.e_5_3S_1 = 727.3032446e12; +% Misc transitions - what do the stars mean? +const.f_table.g_2_3P_2.e_5_3P_0 = 1e9*const.c/404.628937550957; +const.f_table.g_2_3P_2.e_5_3P_1 = 1e9*const.c/404.629844755577; +const.f_table.g_2_3P_2.e_5_3P_2 = 1e9*const.c/404.629918705477; +% Historically controversial transitions +const.f_table.g_2_3P_2.e_5_3D_3 = 744.39620968e12; +const.f_table.g_2_3P_2.e_5_3D_2 = 744.39622889e12; +const.f_table.g_2_3P_2.e_5_3D_1 = 744.39651246e12; +% Singlet-triplet transitions +const.f_table.g_2_3P_2.e_5_1S_0 = 1e9*const.c/406.8886971706; +const.f_table.g_2_3P_2.e_5_1P_1 = 1e9*const.c/402.322271224483; +const.f_table.g_2_3P_2.e_5_1D_2 = 744.43034335e12; % 402.7nm + +%Fitted valuse for the 5^3D's +const.f_table.g_2_3P_2.e_5_3D_3 = 744.39620836e12; +const.f_table.g_2_3P_2.e_5_3D_2 = 744.39622758e12; +const.f_table.g_2_3P_2.e_5_3D_1 = 744.39651114e12; + +end diff --git a/lib/import_mcp_tdc_data/import_mcp_tdc_data.m b/lib/import_mcp_tdc_data/import_mcp_tdc_data.m index 7520c62..c353e47 100644 --- a/lib/import_mcp_tdc_data/import_mcp_tdc_data.m +++ b/lib/import_mcp_tdc_data/import_mcp_tdc_data.m @@ -203,7 +203,7 @@ end %ineffecient to read back what whas just written txydata=txy_importer([import_opts.dir,import_opts.file_name],num2str(import_opts.shot_num(ii))); - txydata=masktxy(txydata,import_opts.txylim); %mask for counts in the window txylim + txydata=masktxy_square(txydata,import_opts.txylim); %mask for counts in the window txylim %rotate the counts into the trap axis alpha=-import_opts.dld_xy_rot; mcp_tdc_data.counts_txy{ii}=txydata*[1 0 0;0 cos(alpha) -sin(alpha); 0 sin(alpha) cos(alpha)]; diff --git a/lib/import_mcp_tdc_data/is_dld_done_writing.m b/lib/import_mcp_tdc_data/is_dld_done_writing.m index 102df4c..7cba8df 100644 --- a/lib/import_mcp_tdc_data/is_dld_done_writing.m +++ b/lib/import_mcp_tdc_data/is_dld_done_writing.m @@ -21,16 +21,16 @@ if logic_file_done_writing %checks that the last charater of the file is a newline %modified from https://stackoverflow.com/questions/2659375/matlab-command-to-access-the-last-line-of-each-file - fid = fopen(file_pointer,'r'); %# Open the file as a binary - offset = 30; %# Offset from the end of file (bytes) - fseek(fid,-offset,'eof'); %# Seek to the file end, minus the offset - new_char = fread(fid,1,'*char'); %# Read one character + fid = fopen(file_pointer,'r'); % Open the file as a binary + offset = 30; % Offset from the end of file (bytes) + fseek(fid,-offset,'eof'); % Seek to the file end, minus the offset + new_char = fread(fid,1,'*char'); % Read one character last_char=''; %initalize to deal with empty file case while numel(new_char)>0 - last_char = new_char; %# Add the character to a string - new_char = fread(fid,1,'*char'); %# Read one character + last_char = new_char; % Add the character to a string + new_char = fread(fid,1,'*char'); % Read one character end - fclose(fid); %# Close the file + fclose(fid); % Close the file logic_file_done_writing=isequal(last_char,newline); end diff --git a/lib/logical_tools/is_even.m b/lib/logical_tools/is_even.m new file mode 100644 index 0000000..c9ca382 --- /dev/null +++ b/lib/logical_tools/is_even.m @@ -0,0 +1,3 @@ +function logical=is_even(in) +logical=mod(in,2) ==0; +end \ No newline at end of file diff --git a/lib/logical_tools/is_odd.m b/lib/logical_tools/is_odd.m new file mode 100644 index 0000000..8128cdb --- /dev/null +++ b/lib/logical_tools/is_odd.m @@ -0,0 +1,3 @@ +function logical=is_odd(in) +logical=mod(in,2) ==1; +end \ No newline at end of file diff --git a/lib/mask_square.m b/lib/mask_square.m new file mode 100644 index 0000000..5e8c4a1 --- /dev/null +++ b/lib/mask_square.m @@ -0,0 +1,28 @@ +function masked=mask_square(in,limits,invert) +%simple masking function that gets used a lot in our data processing +% limits =[[tmin,tmax];[xmin,xmax];[ymin,ymax]] (in seconds and meters) +% invert - to flip this to an exclusion region instead of a include +%TODO +% could get a speedup buy checking if any of the limits are inf and then not doing that check + +if nargin<3 + invert = 0; +end + +counts_size=size(in); +if counts_size(2)~=3 + error('wrong txy size') +end +if ~isequal(size(limits),[3,2]) + error('wrong txylim size') +end + +mask=in(:,1)>limits(1,1) & in(:,1)limits(2,1) & in(:,2)limits(3,1) & in(:,3)1 % the mean of the finite difference can be usefull for some indication of the nonlinearity of the function + do_mean=true; + mean_val=x_in*nan; +else + do_mean=false; +end + +% find the dimensionality of the output of the function +x_in_single=x_in(1,all_other_dims_input{:}); +fun_out_tmp=fun_in(x_in_single); +fun_out_size=size(fun_out_tmp); +if isequal(fun_out_size,[1,1]) + fun_out_dims={}; + deriv=nan(size(x_in)); %intialize output +else + fun_out_dims=repmat({':'},[1,size(fun_out_size,2)]); + deriv=nan([size(x_in),fun_out_size]); +end + + + +delta_tensor_template=zeros(x_in_size(2:end)); +delta_tensor_template=permute(delta_tensor_template,[x_in_dims,1:x_in_dims-1]); +sub_tmp=cell([1,x_in_dims-1]); +for ii=1:num_inputs + x_in_single=x_in(ii,all_other_dims_input{:}); + for jj=1:num_elements + [sub_tmp{:}]=ind2sub(x_in_size(2:end),jj); + delta_tensor=delta_tensor_template; + delta_tensor(1,sub_tmp{:})=delta_val; + fdp=fun_in(x_in_single+delta_tensor); + fdn=fun_in(x_in_single-delta_tensor); + deriv(ii,sub_tmp{:},fun_out_dims{:})= (fdp-fdn)/(2*delta_val); + if do_mean + mean_val(ii,sub_tmp{:},fun_out_dims{:})= (fdp+fdn)/(2*delta_val); + end + end +end + + +end \ No newline at end of file diff --git a/lib/num_grad_vecs.m b/lib/num_grad_vecs.m new file mode 100644 index 0000000..a4cdcde --- /dev/null +++ b/lib/num_grad_vecs.m @@ -0,0 +1,37 @@ +function deriv=num_grad_vecs(fun,x_mat,delta,vectorized_logical) +%finds the 2 point derivative of the output of a function with repsect to each input +% of a function which takes a row vector and returns a scalar +% the rows of x_mat specifies the position at which to evaluate the derivatives in each input +% the sperate inputs are stacked in the first dimension +% each row is therefore independent to one another +% if you sepcify vectorized logical the function is assumed to operate independently on rows of the the input matrix X +% which can be usefull to vectorize the evaluation +% eg test_fun=@(x) sqrt(x(:,1).^2+x(:,2).^2+x(:,3).^2); + +% sometimes this can be usefull to prevent false minima +%delta=delta*(0.5+rand(1)); + + + +if nargin<4 || isnan(vectorized_logical) || isempty(vectorized_logical) + vectorized_logical=0; +end + +dim=size(x_mat,2); +num_pts=size(x_mat,1); +deriv=x_mat*NaN; +if vectorized_logical + for ii=1:dim + deriv(:,ii)= (fun(x_mat+repmat([zeros(1,ii-1),delta,zeros(1,dim-ii)],num_pts,1))... + -fun(x_mat-repmat([zeros(1,ii-1),delta,zeros(1,dim-ii)],num_pts,1)))/(2*delta); + end +else + for ii=1:dim + for jj=1:num_pts + deriv(jj,ii)= (fun(x_mat(jj,:)+[zeros(1,ii-1),delta,zeros(1,dim-ii)])... + -fun(x_mat(jj,:)-[zeros(1,ii-1),delta,zeros(1,dim-ii)]))/(2*delta); + end + end +end + +end \ No newline at end of file diff --git a/lib/num_hessian_vecs.m b/lib/num_hessian_vecs.m new file mode 100644 index 0000000..379e277 --- /dev/null +++ b/lib/num_hessian_vecs.m @@ -0,0 +1,49 @@ +function H=num_hessian_vecs(fun,x_list,delta) + + +%here I find the numerical hessian of the the passed scalar function potential +%it requires(1+2*3+4*3) 19 evaluations of the potential +%better than the 9*4=36 for naive simple implementation +%for the xx,yy,zz derivatives only need 1+2*3=7 +%evaluations each (instead of 4*3=12) +%df/dxdx=f(x+2h)-2f(x)+f(x-2h)/h^2 +%delta=delta*(0.5+rand(1)); %noise up the step to prevent false minima + +num_pts=size(x_list,1); +dim=size(x_list,2); +fx=fun(x_list); +H=zeros(dim,dim,num_pts); +for i=1:dim + for j=1:dim + if i~=j && j>i + %next we calculate the dj term at plus i + dj_plus_i=(fun(x_list... + +repmat([zeros(1,j-1),delta,zeros(1,dim-j)],num_pts,1)... + +repmat([zeros(1,i-1),delta,zeros(1,dim-i)],num_pts,1))... + -fun(x_list... + -repmat([zeros(1,j-1),delta,zeros(1,dim-j)],num_pts,1)... + +repmat([zeros(1,i-1),delta,zeros(1,dim-i)],num_pts,1)))... + /(2*delta); + + %next we calculate the dj term at minus i + dj_minus_i=(fun(x_list... + +repmat([zeros(1,j-1),delta,zeros(1,dim-j)],num_pts,1)... + -repmat([zeros(1,i-1),delta,zeros(1,dim-i)],num_pts,1))... + -fun(x_list... + -repmat([zeros(1,j-1),delta,zeros(1,dim-j)],num_pts,1)... + -repmat([zeros(1,i-1),delta,zeros(1,dim-i)],num_pts,1)))... + /(2*delta); + H(i,j,:)=(dj_plus_i- dj_minus_i)/(2*delta); + elseif j 0 + f = fopen('parfor_progress.txt', 'w'); + if f<0 + error('Do you have write permissions for %s?', pwd); + end + fprintf(f, '%d\n', N); % Save N at the top of progress.txt + fclose(f); + + if nargout == 0 + disp([' 0%[>', repmat(' ', 1, w), ']']); + end +elseif N == 0 + delete('parfor_progress.txt'); + percent = 100; + + if nargout == 0 + disp([repmat(char(8), 1, (w+9)), char(10), '100%[', repmat('=', 1, w+1), ']']); + end +else + if ~exist('parfor_progress.txt', 'file') + error('parfor_progress.txt not found. Run PARFOR_PROGRESS(N) before PARFOR_PROGRESS to initialize parfor_progress.txt.'); + end + + f = fopen('parfor_progress.txt', 'a'); + fprintf(f, '1\n'); + fclose(f); + + f = fopen('parfor_progress.txt', 'r'); + progress = fscanf(f, '%d'); + fclose(f); + percent = (length(progress)-1)/progress(1)*100; + + if nargout == 0 + perc = sprintf('%3.0f%%', percent); % 4 characters wide, percentage + disp([repmat(char(8), 1, (w+9)), char(10), perc, '[', repmat('=', 1, round(percent*w/100)), '>', repmat(' ', 1, w - round(percent*w/100)), ']']); + end +end diff --git a/lib/parfor_progress_improved/parfor_progress_imp.m b/lib/parfor_progress_improved/parfor_progress_imp.m new file mode 100644 index 0000000..63290f4 --- /dev/null +++ b/lib/parfor_progress_improved/parfor_progress_imp.m @@ -0,0 +1,182 @@ +function percent = parfor_progress_imp(N) +%PARFOR_PROGRESS Progress monitor (progress bar) that works with parfor. +% PARFOR_PROGRESS works by creating a file called parfor_progress.txt in +% your working directory, and then keeping track of the parfor loop's +% progress within that file. This workaround is necessary because parfor +% workers cannot communicate with one another so there is no simple way +% to know which iterations have finished and which haven't. +% +% PARFOR_PROGRESS(N) initializes the progress monitor for a set of N +% upcoming calculations. +% +% PARFOR_PROGRESS updates the progress inside your parfor loop and +% displays an updated progress bar. +% +% PARFOR_PROGRESS(0) deletes parfor_progress.txt and finalizes progress +% bar. +% +% To suppress output from any of these functions, just ask for a return +% variable from the function calls, like PERCENT = PARFOR_PROGRESS which +% returns the percentage of completion. +% +% Example: +% +% N = 100; +% parfor_progress(N); +% parfor i=1:N +% pause(rand); % Replace with real code +% parfor_progress; +% end +% parfor_progress(0); +% +% See also PARFOR. + +% By Jeremy Scheff - jdscheff@gmail.com - http://www.jeremyscheff.com/ + +% modified to use a binary file using the comment by philip +% https://au.mathworks.com/matlabcentral/fileexchange/32101-progress-monitor-progress-bar-that-works-with-parfor +%"Nice contribution. However, as Timo already found out, while fitting a huge amount of data +%I noticed that the progress monitor gets extremely slow for very long loops. In the beginning +%it is not so bad but with every loop iteration the call to 'fscanf' gets slower and slower. +%I fixed this by reading & writing to a simple binary file (i am writing the expected loop length +%to the first 4 bytes and the current progress to the next 4 bytes - if you think that uint32 is +%not enough, feel free to use uint64). In addition, the filename is now stored in the folder +%determined by matlab's 'tempname'-function (less filesystem clutter if the delete fails & e.g. tempdir +%on an ssd is much faster than working dir somewhere on the network)." + +% this makes this improved version about 30 times faster than stock + +narginchk(0,1) + +if nargin < 1 + N = -1; +end + +percent = 0; +w = 50; % Width of progress bar + +if N > 0 + f = fopen(fullfile(tempdir,'parfor_progress.bin'), 'w'); + if f<0 + error('Do you have write permissions for %s?', pwd); + end + fwrite(f,N,'uint32'); + fwrite(f,0,'uint32'); + fclose(f); + + if nargout == 0 + disp([' 0%[>', repmat(' ', 1, w), ']']); + end +elseif N == 0 + delete(fullfile(tempdir,'parfor_progress.bin')); + percent = 100; + + if nargout == 0 + disp([repmat(char(8), 1, (w+9)), char(10), '100%[', repmat('=', 1, w+1), ']']); + end +else + fname = fullfile(tempdir,'parfor_progress.bin'); + if ~exist(fname, 'file') + error('parfor_progress.bin not found. Run PARFOR_PROGRESS(N) before PARFOR_PROGRESS to initialize parfor_progress.bin.'); + end + + f = fopen(fname, 'r+'); + A = fread(f,2,'uint32'); + todo = A(1); + progress = A(2) + 1; + fseek(f, 4, 'bof'); + fwrite(f,progress,'uint32'); + fclose(f); + + percent = progress/todo * 100; + + if nargout == 0 + perc = sprintf('%3.0f%%', percent); % 4 characters wide, percentage + disp([repmat(char(8), 1, (w+9)), char(10), perc, '[', repmat('=', 1, round(percent*w/100)), '>', repmat(' ', 1, w - round(percent*w/100)), ']']); + end +end + +end + + +% % function percent = parfor_progress(N) +% % %PARFOR_PROGRESS Progress monitor (progress bar) that works with parfor. +% % % PARFOR_PROGRESS works by creating a file called parfor_progress.txt in +% % % your working directory, and then keeping track of the parfor loop's +% % % progress within that file. This workaround is necessary because parfor +% % % workers cannot communicate with one another so there is no simple way +% % % to know which iterations have finished and which haven't. +% % % +% % % PARFOR_PROGRESS(N) initializes the progress monitor for a set of N +% % % upcoming calculations. +% % % +% % % PARFOR_PROGRESS updates the progress inside your parfor loop and +% % % displays an updated progress bar. +% % % +% % % PARFOR_PROGRESS(0) deletes parfor_progress.txt and finalizes progress +% % % bar. +% % % +% % % To suppress output from any of these functions, just ask for a return +% % % variable from the function calls, like PERCENT = PARFOR_PROGRESS which +% % % returns the percentage of completion. +% % % +% % % Example: +% % % +% % % N = 100; +% % % parfor_progress(N); +% % % parfor i=1:N +% % % pause(rand); % Replace with real code +% % % parfor_progress; +% % % end +% % % parfor_progress(0); +% % % +% % % See also PARFOR. +% % +% % % By Jeremy Scheff - jdscheff@gmail.com - http://www.jeremyscheff.com/ +% % +% % error(nargchk(0, 1, nargin, 'struct')); +% % +% % if nargin < 1 +% % N = -1; +% % end +% % percent = 0; +% % w = 50; % Width of progress bar +% % if N > 0 +% % f = fopen(fullfile(tempdir,'parfor_progress.bin'), 'w'); +% % if f<0 +% % error('Do you have write permissions for %s?', pwd); +% % end +% % fwrite(f,N,'uint32'); +% % fwrite(f,0,'uint32'); +% % fclose(f); +% % +% % if nargout == 0 +% % disp([' 0%[>', repmat(' ', 1, w), ']']); +% % end +% % elseif N == 0 +% % delete(fullfile(tempdir,'parfor_progress.bin')); +% % percent = 100; +% % +% % if nargout == 0 +% % disp([repmat(char(8), 1, (w+9)), char(10), '100%[', repmat('=', 1, w+1), ']']); +% % end +% % else +% % fname = fullfile(tempdir,'parfor_progress.bin'); +% % if ~exist(fname, 'file') +% % error('parfor_progress.bin not found. Run PARFOR_PROGRESS(N) before PARFOR_PROGRESS to initialize parfor_progress.bin.'); +% % end +% % f = fopen(fname, 'r+'); +% % A = fread(f,2,'uint32'); +% % todo = A(1); +% % progress = A(2) + 1; +% % fseek(f, 4, 'bof'); +% % fwrite(f,progress,'uint32'); +% % fclose(f); +% % +% % percent = progress/todo * 100; +% % +% % if nargout == 0 +% % perc = sprintf('%3.0f%%', percent); % 4 characters wide, percentage +% % disp([repmat(char(8), 1, (w+9)), char(10), perc, '[', repmat('=', 1, round(percent*w/100)), '>', repmat(' ', 1, w - round(percent*w/100)), ']']); +% % end +% % end diff --git a/lib/parfor_progress_improved/test_parfor_progress_improved.m b/lib/parfor_progress_improved/test_parfor_progress_improved.m new file mode 100644 index 0000000..51bdcfa --- /dev/null +++ b/lib/parfor_progress_improved/test_parfor_progress_improved.m @@ -0,0 +1,78 @@ +% basic usage + +% only update some of the time so it wont slow down some fast inner loop +tic +updates=100; +itt = 100000; +update_frac=itt/updates; +parfor_progress_imp(updates); +parfor i=1:itt + pause(10*rand/itt); % Replace with real code + if rand<(1/update_frac) + parfor_progress_imp; + end +end +parfor_progress_imp(0); +toc + + +%% +% can also be used in nested loops + +tic +updates=100; +itt_outer = 100000; +itt_inner=10; +update_frac=(itt*itt_inner)/updates; +parfor_progress_imp(updates); +parfor i=1:itt_outer + for x=1:itt_inner + pause(10*rand/itt); % Replace with real code + if rand<(1/update_frac) + parfor_progress_imp; + end + end +end +parfor_progress_imp(0); +toc + +%% and you can deterministicly update instead of randomly +tic +updates=100; +itt_outer = 100; +itt_inner=100; +update_frac=(itt*itt_inner)/updates; +parfor_progress_imp(itt_outer*itt_inner/30); +for i=1:itt_outer + for x=1:itt_inner + pause(0.001); % Replace with real code + if mod(x,30)==0 + parfor_progress_imp; + end + end +end +parfor_progress_imp(0); +toc + +%% Benchamrk against original +tic +itt = 100; +parfor_progress_imp(itt); +parfor i=1:itt + parfor_progress_imp; +end +parfor_progress_imp(0); +toc + +%% + +tic +itt = 100; +parfor_progress(itt); +parfor i=1:itt + parfor_progress; +end +parfor_progress_imp(0); +toc + + diff --git a/lib/pooled_mean_and_std/pooled_mean_and_std.m b/lib/pooled_mean_and_std/pooled_mean_and_std.m new file mode 100644 index 0000000..13ae10a --- /dev/null +++ b/lib/pooled_mean_and_std/pooled_mean_and_std.m @@ -0,0 +1,57 @@ +function [mean_out,std_out]=pooled_mean_and_std(mean_obs,std_obs,num_obs) +% pooled_mean_and_std - compute the standard deviation in a combned data set +% from the standard deviations measured from data subsets +% uses expressions from +% https://en.wikipedia.org/wiki/Pooled_variance +% https://stats.stackexchange.com/questions/55999/is-it-possible-to-find-the-combined-standard-deviation +% this is an exact equivelence not an approximation + +% Syntax: pooled_mean_and_std(mean_obs,std_obs,num_obs) +% Inputs: +% mean_obs - vector of the mean of each subset observation +% std_obs - vector of the standard deviation in the subset observation +% num_obs - vector of the population in each subset +% +% Outputs: +% mean_out - col vector of the mean in the combined data set +% std_out - col vector of the standard deviation in the combined data set +% +% Example: +% for example see test_pooled_mean_and_std +% +% Other m-files required: vol_vec +% Also See: test_pooled_mean_and_std +% Subfunctions: none +% MAT-files required: none +% +% Known BUGS/ Possible Improvements +% - none so far +% +% Author: Bryce Henson +% email: Bryce.Henson@live.com +% Last revision:2019-11-19 + +%------------- BEGIN CODE -------------- + +mean_obs=col_vec(mean_obs); +std_obs=col_vec(std_obs); +num_obs=col_vec(num_obs); + + +total_num_obs=sum(num_obs); + +mean_out=sum(mean_obs.*num_obs)/total_num_obs; + +% std_out=sqrt( (1/(total_num_obs-1))*... +% ( sum((num_obs-1).*(std_obs.^2) + num_obs.*(mean_obs.^2) ) -... +% (mean_out.^2)*sum(num_obs) ... +% )... +% ) +% an equivelent way that is a little easier to understand +std_out=sqrt( (1/(total_num_obs-1))*... + ( sum((num_obs-1).*(std_obs.^2) + num_obs.*((mean_obs-mean_out).^2) ) ... + )... + ); + + +end \ No newline at end of file diff --git a/lib/pooled_mean_and_std/test_pooled_mean_and_std.m b/lib/pooled_mean_and_std/test_pooled_mean_and_std.m new file mode 100644 index 0000000..d01a0e1 --- /dev/null +++ b/lib/pooled_mean_and_std/test_pooled_mean_and_std.m @@ -0,0 +1,84 @@ +%test_pooled_mean_and_std + + + +sub_samples=5; +sigma_sub=rand(sub_samples,1)*10; +mean_sub=rand(sub_samples,1)*1; +num_obs_sub=randi([100,10000],sub_samples,1); +observations=cell(sub_samples,1); + +for ii=1:sub_samples + observations{ii}=normrnd(mean_sub(ii),sigma_sub(ii),num_obs_sub(ii),1); +end + +sub_mean=cellfun(@mean, observations); +sub_std=cellfun(@std, observations); +sub_obs=cellfun(@numel, observations); + +[pooled_mean,pooled_std]=pooled_mean_and_std(sub_mean,sub_std,sub_obs); + +combined_obs=cat(1,observations{:}); +combined_mean=mean(combined_obs); +combined_std=std(combined_obs); + + +logic_str = {'FAIL','pass'}; +test_tol=1e-6; + +fprintf('INFO: mean combined = %.6f\n',combined_mean) +fprintf('INFO: mean pooled = %.6f\n',pooled_mean) +is_mean_right= frac_diff(pooled_mean,combined_mean)limit_max(:)) + error('min is greater than max limit') + end + if any(abs(limit_min(:)-limit_max(:)) 1 + + if all(size(this_data,2) > 1) out.(this_field) =this_data(m,:); else out.(this_field) =this_data(m); diff --git a/lib/simple_utilities/test_logspace_mat.m b/lib/simple_utilities/test_logspace_mat.m new file mode 100644 index 0000000..2250c8b --- /dev/null +++ b/lib/simple_utilities/test_logspace_mat.m @@ -0,0 +1,22 @@ +%test_logspace_mat + +mat_in=magic(5); +a=linspace_mat(mat_in,mat_in+1,10); +isequal(col_vec(squeeze(a(1,1,:))),col_vec(linspace(mat_in(1,1),mat_in(1,1)+1,10))) + + +%% how it deals with vectors +% does the linspace in the singelton dimension + +mat_in=[1,2,3]' +a=linspace_mat(mat_in,mat_in+1,10) + + +mat_in=[1,2,3] +a=linspace_mat(mat_in,mat_in+1,10) + + +%% if you turn off the vector fix then it does the linspace in the 3rd dim +% (which i dont see being usefull) +mat_in=[1,2,3]' +a=linspace_mat(mat_in,mat_in+1,10,[],0) diff --git a/lib/simple_utilities/test_rand_interval.m b/lib/simple_utilities/test_rand_interval.m new file mode 100644 index 0000000..2a77be4 --- /dev/null +++ b/lib/simple_utilities/test_rand_interval.m @@ -0,0 +1,43 @@ +%test_rand_interval + +out_interval=[1,2]; +test_out=rand_interval(out_interval,[1,10]) +if sum(test_out>out_interval(2))>0 || sum(test_out0 + error('outside limits') +end + + + +%% constructing the limits matrix is the hardest part of using this function +out_size=[1,2]; +out_interval=cat(2,cat(3,2,3), cat(3,1,2)) +out_interval=reshape([[2,3];[1,2]],cat(2,out_size,2)) +test_out=rand_interval(out_interval,out_size) + + +%% in higher dimensions it can get a bit painfull but carefully used reshape makes it easier + +out_interval=cat(1,cat(2,cat(3,1,2), cat(3,2,3)),cat(2,cat(3,3,4), cat(3,4,5))); +out_size=[2,2]; +out_interval=reshape([[1,2];[2,3];[3,4];[4,5]],cat(2,out_size,2)); +test_out=rand_interval(out_interval,out_size) + +%% you dont even need to pass the output size if you are specifying the limits for each element +out_size=[2,2]; +out_interval=reshape([[1,2];[2,3];[3,4];[4,5]],cat(2,out_size,2)); +test_out=rand_interval(out_interval) + + + +%% the function will check that the limits are sensible and that max and min are not equal (will produce a warning) + +out_size=[2,2]; +out_interval=reshape([[1,1];[2,3];[3,4];[4,5]],cat(2,out_size,2)); +test_out=rand_interval(out_interval,out_size) + +%% check that the test for min greater than max works (should produce a error) +out_size=[2,2]; +out_interval=reshape([[2,1];[2,3];[3,4];[4,5]],cat(2,out_size,2)); +test_out=rand_interval(out_interval,out_size) + + diff --git a/lib/smooth_hist/smooth_hist.m b/lib/smooth_hist/smooth_hist.m index 47de825..8b82ee5 100644 --- a/lib/smooth_hist/smooth_hist.m +++ b/lib/smooth_hist/smooth_hist.m @@ -44,10 +44,14 @@ addOptional(p,'bin_num',nan,@isnumeric); addOptional(p,'bin_factor',nan,@isnumeric); addOptional(p,'max_bins',2e6,@isnumeric); +addOptional(p,'doplot',false,is_c_logical); parse(p,varargin{:}); parsed_input= p.Results; -sigma=parsed_input.sigma; +if nargout==0 + parsed_input.doplot=true; +end + if sum(~isnan([parsed_input.bin_factor,parsed_input.bin_width,parsed_input.bin_num]))>1 error('must pass only one of ''bin_factor'' or ''bin_width'' or ''bin_num'' ') @@ -62,12 +66,18 @@ error('cant specify bin width using bin_factor when sigma is zero') end -if isempty(parsed_input.lims) || sum(isnan(parsed_input.lims)) == 0 +if isempty(parsed_input.lims) || sum(isnan(parsed_input.lims)) ~= 0 bin_limits=[nanmin(xdata),nanmax(xdata)]; else bin_limits=parsed_input.lims; end +if isnan(parsed_input.sigma) && sum(~isnan([parsed_input.bin_width,parsed_input.bin_num,parsed_input.bin_factor]))==0 + %using default bin factor + parsed_input.sigma=range(bin_limits)*5e-3; + parsed_input.bin_factor=5; +end + if ~isnan(parsed_input.bin_factor) bin_width=parsed_input.sigma/parsed_input.bin_factor; x_bin_num=floor(range(bin_limits)/bin_width); @@ -79,11 +89,17 @@ x_bin_num=parsed_input.bin_num; end +if x_bin_num==0 + error("auto binning has returned no bins, try seting the limits with the 'lim'") +end + if x_bin_num>parsed_input.max_bins warning('%s: number of bins exceeds %g will reduce bin number to this',mfilename,parsed_input.max_bins) x_bin_num=parsed_input.max_bins; end +sigma=parsed_input.sigma; + bin_width=range(bin_limits)/x_bin_num; if bin_width>sigma*5 warning('bin width was much larger than sigma will not smooth',mfilename) @@ -96,7 +112,7 @@ %function that resturns a gaussian smoothed histogram edges=linspace(min(bin_limits),max(bin_limits),x_bin_num+1)'; centers=(edges(2:end)+edges(1:end-1))./2; -hist_counts_raw=hist_adaptive_method(xdata,edges,parsed_input.sorted); +hist_counts_raw=hist_adaptive_method(xdata,edges,parsed_input.sorted,1); out_struct.counts.below=hist_counts_raw(1); out_struct.counts.above=hist_counts_raw(end); @@ -114,5 +130,11 @@ out_struct.bin.edge=edges; out_struct.bin.centers=centers; +if parsed_input.doplot + stfig('smooth histogram') + plot(out_struct.bin.centers,out_struct.count_rate.smooth,'k') +end + + end diff --git a/lib/stash_opts/stash_opts.m b/lib/stash_opts/stash_opts.m index 2d71c77..4bcb243 100644 --- a/lib/stash_opts/stash_opts.m +++ b/lib/stash_opts/stash_opts.m @@ -1,5 +1,5 @@ function flag = stash_opts(stash_dir,opts) -% A quick function for storing the configuration files used in a given data +% A quick function for caching the configuration files used in a given data % run for structured recollection by get_stashed_opts() later on. % Required inputs: A structure s with mandatory fields: % stash_dir The destination for storage (full form) diff --git a/lib/stfig/stfig.m b/lib/stfig/stfig.m index 4262231..893fff7 100644 --- a/lib/stfig/stfig.m +++ b/lib/stfig/stfig.m @@ -117,6 +117,7 @@ handle_out=figure('Name',fig_str,'NumberTitle','off'); end set(handle_out,'color','w') +% set(handle_out,'DefaultAxesXLabelFontSize','20') if focus_back_to_cwin drawnow commandwindow diff --git a/lib/test_num_grad_tensors.m b/lib/test_num_grad_tensors.m new file mode 100644 index 0000000..03293d9 --- /dev/null +++ b/lib/test_num_grad_tensors.m @@ -0,0 +1,28 @@ +%test_num_grad_tensors + + + +test_fun=@(x) sum(x(:).^2); + +x_in=rand(3,2,4); +num_grad_tensors(test_fun,x_in,0.1) + +%% +x_in=rand(1,1); +df_out=num_grad_tensors(test_fun,x_in,0.1) +isalmost(df_out,2*x_in,eps(10)) + +%% +x_in=rand(2,3); +[df_out,mean_out]=num_grad_tensors(test_fun,x_in,0.1) +diff(mean_out,1,2) +isalmost(df_out,2*x_in,eps(100)) + + + +%% + +test_fun=@(x) [[1,2];[3,4]]*sum(x(:).^2); + +x_in=rand(3,2,4); +num_grad_tensors(test_fun,x_in,0.1) \ No newline at end of file diff --git a/lib/test_num_grad_vec.m b/lib/test_num_grad_vec.m new file mode 100644 index 0000000..df96693 --- /dev/null +++ b/lib/test_num_grad_vec.m @@ -0,0 +1,17 @@ +%test_num_grad_vecs + + + +test_fun=@(x) sqrt(x(:,1).^2+x(:,2).^2+x(:,3).^2); + + +num_grad_vecs(test_fun,[[1,2,3];[4,5,6]],1e-3) + +%% +num_grad_vecs(test_fun,[1,2,3],1e-3) + +num_grad_vecs(test_fun,[4,5,6],1e-3) + +num_grad_vecs(test_fun,[[1,2,3];[4,5,6]],1e-3) + +isequal(num_grad_vecs(test_fun,[[1,2,3];[4,5,6]],1e-3,1),num_grad_vecs(test_fun,[[1,2,3];[4,5,6]],1e-3,0)) diff --git a/lib/text_to_window_function/test_text_to_window_fun.m b/lib/text_to_window_function/test_text_to_window_fun.m new file mode 100644 index 0000000..0652659 --- /dev/null +++ b/lib/text_to_window_function/test_text_to_window_fun.m @@ -0,0 +1,53 @@ + +%test if the text to windowing function works + + + +%% fake dataset +%fake_data=fake_cl_corr(100,1); +%fake_data=fake_therm_cl_corr_small_hot(5000,1) +%fake_data=fake_therm_cl_corr_small_cold(5000,1); +%fake_data=fake_super_cl_corr(1000,1); +%fake_data=fake_cl_corr_medium_hot(5000,0.1); +data_faker=@() fake_super_cl_corr(5000,1); + +fake_data=data_faker(); + +total_counts=sum(fake_data.num_counts); +%% Spliting data +fprintf('spliting data\n') +data_up_down={}; +for ii=1:size(fake_data.counts_txy,2) + shot_txy=fake_data.counts_txy{ii}; + mask=rand(size(shot_txy,1),1)>0.5; + data_up_down.up_counts{ii}=shot_txy(mask,:); + data_up_down.down_counts{ii}=shot_txy(~mask,:); +end + +%% make windowing text function +fprintf('calculating text mask\n') +windowing_function=text_to_window_fun([],0); +%% +fprintf('applying text mask\n') +for ii=1:size(data_up_down.up_counts,2) + down_counts=data_up_down.down_counts{ii}; + mask=windowing_function(down_counts); + %simple mask + %mask=(down_counts(:,2)<0 & down_counts(:,3)<0) | (down_counts(:,2)>0 & down_counts(:,3)>0 & down_counts(:,3)<0.5) ; + data_up_down.down_counts_mask{ii}=down_counts(mask,:); +end + + +%% Verify the mask has been applied +x_edges=linspace(-1,1,50); +y_edges=linspace(-1,1,50); + +all_mask_counts=vertcat(data_up_down.down_counts_mask{:}); +bins=histcn(all_mask_counts(:,2:3),x_edges,y_edges); +sfigure(1) +clf +imagesc(bins') +set(gca,'YDir','normal') +title('Mask port all counts') +colormap(viridis) +pause(1e-3) \ No newline at end of file diff --git a/lib/text_to_window_function/text_to_window_fun.m b/lib/text_to_window_function/text_to_window_fun.m new file mode 100644 index 0000000..1860c75 --- /dev/null +++ b/lib/text_to_window_function/text_to_window_fun.m @@ -0,0 +1,109 @@ +function windowing_function=text_to_window_fun(input,verbose) +%inputs +%input domain +%text + +%to do +%implement changeable domain +%smart hole detection + +input.text='He*'; +input.domain=[-1,1]; +%develop a windowing function from some text + +%% + +text_image=ones(180,350); +text_image=insertText(text_image,[-50,-80],input.text,'FontSize',200,'BoxOpacity',0,'Font','Arial' ); +text_image=imresize(text_image,10,'bicubic'); +text_image = imbinarize(text_image); +text_image= squeeze(text_image(:,:,1)); +text_image=imcomplement(text_image); + +[B,L] = bwboundaries(text_image); %why does the output not label holes! + +if verbose>1 + figure(3) + set(gcf,'color','w') + clf + subplot(1,2,1) + imagesc(text_image) + colormap('gray') + %% + subplot(1,2,2) + imshow(label2rgb(L, @jet, [.5 .5 .5])) + hold on + for k = 1:length(B) + boundary = B{k}; + plot(boundary(:,2), boundary(:,1), 'w', 'LineWidth', 2) + end + + + %% + figure(4) + subplot(1,3,1) + boundary = B{4}; + plot(polyshape(boundary(:,2), boundary(:,1))) + %plot(boundary(:,2), boundary(:,1), 'k', 'LineWidth', 2) + + + subplot(1,3,2) + poly_simple=[]; + [poly_simple(:,2),poly_simple(:,1)]=reducem(boundary(:,2), boundary(:,1),5); + plot(polyshape(poly_simple(:,2), poly_simple(:,1))) +end + + + +%% Make a cell array of the simplified polydons and scale to the unit interval +text_segments= {}; +text_segments.holes=logical([0,0,0,1]); +text_segments.polygons={}; +image_size=size(text_image); +image_size(1)=-image_size(1); +image_shift=[0.46,-0.5]; +image_rescale=[2,2]; +for ii=1:size(B,1) + boundary = B{ii}; + poly_simple=[]; + [poly_simple(:,2),poly_simple(:,1)]=reducem(boundary(:,2), boundary(:,1),5); + %plot(polyshape(poly_simple(:,2), poly_simple(:,1))) + poly_simple=poly_simple./repmat(image_size,[size(poly_simple,1),1]); + poly_simple=poly_simple+repmat(image_shift,[size(poly_simple,1),1]); + poly_simple=poly_simple.*repmat(image_rescale,[size(poly_simple,1),1]); + text_segments.polygons{ii}=poly_simple; +end + + +windowing_function=@(txy_in) window_poly_fun(txy_in,text_segments); + +if verbose>1 + figure(5) + clf + hold on + for ii=1:numel(text_segments.polygons) + plot(polyshape(text_segments.polygons{ii}(:,2), text_segments.polygons{ii}(:,1))) + end + hold off + + + %% Test the method + txy_rand=(rand(1e6,3)-0.5)*2; + + mask=windowing_function(txy_rand) ;%& ~mask_in_holes(2,:); + plot(txy_rand(mask,2),txy_rand(mask,3),'.') +end + +end + +function mask=window_poly_fun(txy_in,text_segments) + mask_in_holes=zeros(size(text_segments.holes,2),size(txy_in,1)); + for kk=1:numel(text_segments.polygons) + polygons=text_segments.polygons{kk}; + mask_in_holes(kk,:)=inpolygon(txy_in(:,2),txy_in(:,3),polygons(:,2),polygons(:,1)); + end + %find the case that the count is in any of the segments but in none of the holes + mask=any(mask_in_holes(~text_segments.holes,:),1) & ~any(mask_in_holes(text_segments.holes,:),1) ;%& ~mask_in_holes(2,:); +end + + diff --git a/lib/txy_to_vel.m b/lib/txy_to_vel.m deleted file mode 100644 index 5bf853e..0000000 --- a/lib/txy_to_vel.m +++ /dev/null @@ -1,51 +0,0 @@ -function vzxy_out=txy_to_vel(txy_in,out_time,gravity,fall_distance) -% gravity is assumed to be in -ve z - -if size(txy_in,2)~=3 - error('wrong txy size') -end -if ~isscalar(out_time) - error('time_offset should be scalar') -end -if ~isscalar(gravity) - error('gravity should be scalar') -end - -gravity=-abs(gravity); - - -%convert the position data into velocity - -% the z/time axis is slightly complicated because -% z=z(0) + vz(0)t+1/2 g t^2 -% want to solve for v(0) given x(t_fall) the fall distance and gravity(in -ve x) , say bec pos is x=0 at t=0 -% and is released at t=0 -% -fall_dist=vz(0)t+1/2 g t^2 -% vz(0)=-fall_dist/t -1/2 g t - -% lets compare this to what i have calculated in the past -% fall_time=sqrt(2*fall_dist/g) -% vel_fall=sqrt(2*fall_dist*g) -% vz(0)~(t-fall_time)*vel_fall/fall_time -% vz(0)~(t-sqrt(2*fall_dist/g))*sqrt(2*fall_dist*g)/sqrt(2*fall_dist/g) -% vz(0)~(t-sqrt(2*fall_dist/g))*g -% vz(0)~ g t -sqrt(2*g*fall_dist) - -% initalize the output array -vzxy_out=txy_in*nan; -% now we dont have the fall time directly, we can use the offset from the output time (generaly atom laser -% pulse time) - -fall_time=txy_in(:,1)-out_time; - -vel_z=-fall_distance./fall_time-(1/2)*gravity*fall_time; - -% then we want to convert the x,y data into velocity using the fall time -% bacause the TOF changes a little for each count we can correct for this - -vzxy_out(:,[2,3])=txy_in(:,[2,3])./repmat(fall_time,1,2); -vzxy_out(:,1)=vel_z; - - - -end \ No newline at end of file diff --git a/lib/txy_to_vel/txy_to_vel.m b/lib/txy_to_vel/txy_to_vel.m index 8ea1f29..002c1f8 100644 --- a/lib/txy_to_vel/txy_to_vel.m +++ b/lib/txy_to_vel/txy_to_vel.m @@ -4,7 +4,7 @@ if size(txy_in,2)~=3 error('wrong txy size') end -if ~isscalar(out_time) +if ~isscalar(out_time) && size(txy_in(:,1))~=size(out_time) error('time_offset should be scalar') end if ~isscalar(gravity) @@ -12,6 +12,7 @@ end gravity=-abs(gravity); +fall_distance=abs(fall_distance); %convert the position data into velocity @@ -21,6 +22,7 @@ % want to solve for v(0) given x(t_fall) the fall distance and gravity(in -ve x) , say bec pos is x=0 at t=0 % and is released at t=0 % -fall_dist=vz(0)t+1/2 g t^2 +% vz(0)t=-fall_dist-1/2 g t^2 % vz(0)=-fall_dist/t -1/2 g t % lets compare this to what i have calculated in the past @@ -31,14 +33,31 @@ % vz(0)~(t-sqrt(2*fall_dist/g))*g % vz(0)~ g t -sqrt(2*g*fall_dist) +% We can also use the expression +% tau = sqrt(2*fall_distance/g); % the COM fall time +% fall_times = (-v - sqrt(v.^2 + 2*g*fall_distance))/g; +% recover_v = g*(tau^2-fall_times.^2)./(2*fall_times); +% This result can be found by: +% 1. Solve for the arrival time in terms of fall distance and initial +% vertical velocity via the quadratic formula, +% 2. Square the expression and substitute from 1 to eliminate the radical +% 3. Solve the resulting quadratic for v(0) in terms of gravity and +% measured times. This agrees within machine precision. For example: +% n = 1e4; +% v = randn(n,1); +% s = -0.8587; +% g = -9.796; +% tau = sqrt(2*s/g); +% fall_times = (-v - sqrt(v.^2 + 2*g*s))/g; +% recover_v = g*(tau^2-fall_times.^2)./(2*fall_times); +% % Correct to within a few x machine precision + % initalize the output array vzxy_out=txy_in*nan; % now we dont have the fall time directly, we can use the offset from the output time (generaly atom laser % pulse time) - fall_time=txy_in(:,1)-out_time; - -vel_z=fall_distance./fall_time+(1/2)*gravity*fall_time; +vel_z = -fall_distance./fall_time - (1/2)*gravity*fall_time; % then we want to convert the x,y data into velocity using the fall time % bacause the TOF changes a little for each count we can correct for this diff --git a/lib/txy_tools/getlims.m b/lib/txy_tools/getlims.m new file mode 100644 index 0000000..01a6dcb --- /dev/null +++ b/lib/txy_tools/getlims.m @@ -0,0 +1,23 @@ +function lims = getlims(data) +% getlims(x) returns the [min,max] along the columns of x +% Motivation: Where x is an [N x D] array of N samples in D dimensions, +% return the bounds of the interval where the data points are found +% eg +% ''' +% d1 = [1 0 0]; +% d2 = [0,-1,3]; +% d3 = [2,-.5,1]; +% x = [d1;d2;d3]; +% isequal(getlims(x),[0,2;-1,0;0,3]); +% ``` +if isrow(data) + data = data'; +end + naxis = size(data,2); + lims = zeros(naxis,2); + for axis = 1:naxis + axmin = min(data(:,axis)); + axmax = max(data(:,axis)); + lims(axis,:) = [axmin,axmax]; + end +end \ No newline at end of file diff --git a/lib/txy_tools/hotspot_mask.m b/lib/txy_tools/hotspot_mask.m new file mode 100644 index 0000000..76e007f --- /dev/null +++ b/lib/txy_tools/hotspot_mask.m @@ -0,0 +1,50 @@ +function data=hotspot_mask(data,anal_opts) +% this code deletes the hot spots from our detector +% it makes a flat-feild image look like swiss cheese +% code sniped from forbidden_heating_method +% TODO +% - automate the mask devlopment process +% - +% +if nargin<2 || isempty(anal_args) + % default hot spot deletion + % good as of 2019-11-20 + tlim=[0,inf]; + tmp_xlim=[-50e-3, 50e-3]; + tmp_ylim=[-50e-3, 50e-3]; + anal_opts=[]; + anal_opts.hotspot_mask.square_mask=[tlim;tmp_xlim;tmp_ylim]; + anal_opts.hotspot_mask.circ_mask=[[0,0,38e-3,1]; + [32e-3,3.6e-3,3e-3,0]; + [35.6e-3,5.6e-3,4e-3,0]; + [25.36e-3,-19.8e-3,3e-3,0]; + [13.68e-3,31.6e-3,2e-3,0]; + [28.4e-3,-13.68e-3,2e-3,0]; + [32.08e-3,-12.24e-3,2e-3,0]; + [28.88e-3,-21.84e-3,2e-3,0]; + [18.8e-3,-28.72e-3,2e-3,0]; + [2.48e-3,-34.8e-3,2e-3,0]; + ]; +end + + +num_shots=numel(data.mcp_tdc.counts_txy); +empty_shots=cellfun(@isempty,data.mcp_tdc.counts_txy); +data.mcp_tdc.masked.counts_txy={}; +data.mcp_tdc.masked.num_counts=data.mcp_tdc.num_counts*nan; +fprintf('hotspot masking shots %04u:%04u',num_shots,0) +for ii=1:num_shots + txy_shot=data.mcp_tdc.counts_txy{ii}; + if ~isempty(txy_shot) + txy_shot=masktxy_square(txy_shot,anal_opts.hotspot_mask.square_mask); + txy_shot=masktxy_2d_circle(txy_shot,anal_opts.hotspot_mask.circ_mask); + data.mcp_tdc.masked.num_counts(ii)=numel(txy_shot); + data.mcp_tdc.masked.counts_txy{ii}=txy_shot; + else + warning('empty shot') + end + if mod(ii,10)==0,fprintf('\b\b\b\b%04u',ii),end +end + + +end \ No newline at end of file diff --git a/lib/txy_tools/k2r.m b/lib/txy_tools/k2r.m new file mode 100644 index 0000000..19a8ec6 --- /dev/null +++ b/lib/txy_tools/k2r.m @@ -0,0 +1,30 @@ +function [r,T] = k2r(varargin) + % Rough - correct in horizontal ballistic picture (does not account for + % gravity) for estimating only, generally. + % Use txy_to_vel for more precise conversion. + + % Converts a distance (in m) to a wavenumber (m^-1) after a falltime + % (default 417.6 ms) for particle of mass m (default 6.64e-27 kg) + % Also returns the time separation in the case that particles are + % moving purely horizontally + % + % Syntax: [r,t] = k2r(k) + % r = k2r(k,m) + % Test: k2r(r2k(1)) == 1 + % k2r(1) == 1.6069e8 + + t = 0.4176; %fall time + k = varargin{1}; + h = 6.63e-34; + v_c = 4.9*t^2; % center of mass velocity + hbar = h/(2*pi); + if nargin == 1 % just passed distance, no mass + m = 6.64e-27; %kg + else + m = varargin{2}; + end + + r = hbar*k*t/m; + T = r/v_c; +end + \ No newline at end of file diff --git a/lib/txy_tools/mask_square_num.m b/lib/txy_tools/mask_square_num.m new file mode 100644 index 0000000..14b7605 --- /dev/null +++ b/lib/txy_tools/mask_square_num.m @@ -0,0 +1,17 @@ +function masked_num = mask_square_num(in,lim,varargin) +%performs a mask square and counts the total number of counts in that +%masked region + +if length(varargin)<1 + invert = 0; +else + invert = varargin{1}; +end + +masked_num = zeros(1,length(in)); + +for ii = 1:length(in) + this_counts = in{ii}; + masked_counts = mask_square(this_counts,lim,invert); + masked_num(ii) = size(masked_counts,1); +end \ No newline at end of file diff --git a/lib/txy_tools/masktxy_square.m b/lib/txy_tools/masktxy_square.m index c4876ed..1b6fc60 100644 --- a/lib/txy_tools/masktxy_square.m +++ b/lib/txy_tools/masktxy_square.m @@ -1,17 +1,7 @@ function txymasked=masktxy_square(txyin,txylim) %simple masking function that gets used a lot in our data processing %txylim=[[tmin,tmax];[xmin,xmax];[ymin,ymax]] (in seconds and meters) -txy_size=size(txyin); -if txy_size(2)~=3 - error('wrong txy size') -end -if ~isequal(size(txylim),[3,2]) - error('wrong txylim size') -end -mask=txyin(:,1)>txylim(1,1) & txyin(:,1)txylim(2,1) & txyin(:,2)txylim(3,1) & txyin(:,3) 1 +% opts = varargin{2}; +% end +% +% if ~isfield(opts,'min_counts') +% opts.min_counts = 5; +% end +% +% if ~isfield(opts,'centre_bec') +% opts.centre_bec = false; +% end + const = hebec_constants(); + fall_time = sqrt(2*const.fall_distance/const.g0); + if isstruct(data_input) %passed a bundle of shots + shots_in = length(data_input.shot_num); + OK_num = ~isnan(data_input.shot_num); + OK_counts = ~isnan(data_input.num_counts); + OK_txy = cellfun(@(x) numel(x) > min_counts, data_input.counts_txy); + mask = OK_num & OK_counts & OK_txy; + data_work = struct_mask(data_input,mask); + num_shots = sum(mask); + all_together = vertcat(data_work.counts_txy{:}); + elseif ismatrix(data_input) && size(data_input,2) == 3 % passed a raw TXY array + shots_in = 1; + num_shots = 1; + data_work.num_counts = size(data_input,1); + data_work.shot_num = 1; + all_together = data_input; + end + + if isnan(lims(1,2)) +% lims(1,2) = max(all_together(:,1)); + lims = getlims(all_together); + end + txy = masktxy_square(all_together,lims); + R = [cos(theta),sin(theta); + -sin(theta),cos(theta)]; + txy(:,[2,3]) = (R*txy(:,[2,3])')'; + if iscell(txy) + txy = cell2mat(txy); + end + + + v_com_xy = [0,0]; + if txy2v + if isnan(t_COM) + warning('Release time not specified, will make a guess') + t_COM = mean(txy(:,1)); %this will be incorrect + end + txy = txy2vzxy(txy,'t_COM',t_COM); + v_com_xy = mean(txy(:,2:3)); + txy(:,2:3) = txy(:,2:3) - v_com_xy; + h_data.pulse_cen = mean(txy); + h_data.pulse_std = std(txy); + if ~isnan(v_mask) + txy = mask_square(txy,v_mask); + end + end + bounds = getlims(txy); + bounds(2:3,:) = bounds(2:3,:) + v_com_xy'; + if auto_align + C = cov(txy(:,2:3)); + [evec,~] = eig(C); + [~,y_index] = max(abs(evec*[0;1])); + if y_index == 1 % first evec is in y dir + txy(:,2:3) = txy(:,[3,2])*evec; + elseif y_index == 2 + txy(:,2:3) = txy(:,2:3)*evec; + end + end + if verbose + fprintf('DISPLAYING TXY DATA:\n') + fprintf('%u shots passed\n',shots_in) + fprintf('%u total counts\n',sum(data_work.num_counts)) + fprintf('Mean %.2f std %.2f stderr %.2f\n',mean(data_work.num_counts),std(data_work.num_counts),std(data_work.num_counts)/length(data_work.shot_num)) + fprintf('%u windowed counts\n',size(txy,1)) +% fprintf('t_COM (%.3f,%.3f,%.3f)\n',h_data.pulse_cen'); +% fprintf('VAR (%.3f,%.3f,%.3f)\n',h_data.pulse_std'); + end %verbose + + + bounds = lims; + t_edges = linspace(bounds(1,1),bounds(1,2)*1.01,num_bins(1)+1); + x_edges = linspace(bounds(2,1),bounds(2,2)*1.01,num_bins(2)+1); + y_edges = linspace(bounds(3,1),bounds(3,2)*1.01,num_bins(3)+1); + [voxel_counts,bin_edges,bin_cents,~] = histcn(txy,t_edges,x_edges,y_edges); + bin_volumes = (OuterProduct(diff(t_edges)'.*diff(x_edges),diff(y_edges'))); + voxel_counts = voxel_counts/num_shots; % av counts per voxel + bin_flux = voxel_counts./bin_volumes; + + h_data.flux3 = bin_flux; + h_data.counts3 = voxel_counts; + h_data.volumes = bin_volumes; + h_data.mean_counts = sum(h_data.counts3,'all'); + + if txy2v + profile_labels = {'Z','X','Y'}; + axis_labels = {'$v_z$ (m/s)','$v_x$ (m/s)','$v_y$ (m/s)'}; + else + profile_labels = {'T','X','Y'}; + axis_labels = {'T (s)','X (cm)','Y (cm)'}; + end + + + h_data.edges = cell(3,1); + h_data.counts_1d = cell(3,1); + h_data.centres = cell(3,1); + h_data.flux_1d = cell(3,1); + h_data.num_shots = num_shots; + if size(txy,1) < min_counts + warning('Counts too low'); + end + + ax_order = 1:3; % to align the X and Y axes in the figure + hist_ax_order = [1 3 2]; + + for axis = 1:3 + ax_excl = 1:3; + ax_1d = ax_order(axis); + ax_excl(axis) = []; + h_data.edges{axis} = bin_edges{axis}; + h_data.centres{axis} = bin_cents{axis}; + h_data.counts_1d{axis} = histcounts(txy(:,axis),bin_edges{axis}); +% h_data.counts_1d{axis} = col_vec(squeeze(sum(voxel_counts,ax_excl))); + h_data.mean_1d = h_data.counts_1d{axis}/num_shots; + h_data.flux_1d{axis} = h_data.counts_1d{axis}./diff(h_data.edges{axis}); + if axis ~= 1 + h_data.flux_1d{axis} = h_data.flux_1d{axis}/diff(bounds(1,:)); + end + end + + + h_data.X_c = [0,0,0]; + thr = .00; +% for ax=1:3 +% mask = rescale(h_data.flux_1d{ax}) > thr; +% X=h_data.centres{ax}; +% h_data.X_c(ax) = median(X(mask)); +% end + + h_data.counts_2d = cell(3,1); + for txy_count = 1:3 + h_data.counts_2d{txy_count} = squeeze(sum(voxel_counts,txy_count)); + end + h_data.txy = txy; + %% PLOTTING + grid_height = 2; + grid_width = 3; + + subplot_indices = {[10],[2,3],[4,7],[5,6,8,9],[11],[12]}; + subplot_counter = 0; + + if draw_plots + stfig(sprintf('BEC TXY display %s',label)); + clf +% tiledlayout(grid_height,grid_width) + for axis_count = 1:3 + subplot_counter = subplot_counter + 1; + subplot(4,3,subplot_indices{subplot_counter}) + axis = ax_order(axis_count); +% nexttile + + hold on + if axis ~=1 + fact = 1e2; + else + fact = 1; + end + plot(fact*h_data.centres{axis},(h_data.flux_1d{axis})/1e3) +% title(sprintf('%s profile',profile_labels{axis})) + if axis_count == 1 + ylabel('Flux (Hz)') + end + if axis_count ~= 1 + ylabel('Flux (m$^2$ s)$^{-1}$') + end +% yticks([]) + + xlim(fact*[min(lims(axis,:)),max(lims(axis,:))]) + if log_plot + set(gca,'Yscale','log') + end + if axis_count == 3 + camroll(90) + end +% if axis_count ~=2 +% set(gca,'XAxisLocation','top') +% end + if axis_count == 1 + xticks([]) + camroll(90) + else + xlabel(sprintf('%s',axis_labels{axis})) + end + set(gca,'FontSize',fontsize) + end +% h_data.flux_1d = h_data.flux_1d{1,3,2}; + + + axis_labels = {'T(s)','X (cm)','Y (cm)'}; + for txy_count = 1:3 + kept_axes = ax_order; + ax_sel = hist_ax_order(txy_count); + kept_axes(txy_count) = []; + +% nexttile + subplot_counter = subplot_counter + 1; + subplot(4,3,subplot_indices{subplot_counter}) + if blur_size == 1 + V = h_data.counts_2d{ax_sel}; + else + V = imgaussfilt(h_data.counts_2d{excl_axis},blur_size); + end + if txy_count == 1 + V = V'; + kept_axes = fliplr(kept_axes); + ax_labels = {axis_labels{2},axis_labels{3}}; + edges_2d{1} = h_data.edges{kept_axes(1)}; + edges_2d{2} = h_data.edges{kept_axes(2)}; + fact = 1; + else + fact = 1e2; + ax_labels = {axis_labels{txy_count},axis_labels{1}}; + kept_axes(2) = txy_count; + edges_2d{1} = h_data.edges{kept_axes(1)}; + edges_2d{2} = fact*h_data.edges{txy_count}; + end + if log_hist + V = log(V); + end + + + imagesc(edges_2d{2},edges_2d{1},V) + + if txy_count == 1 + xticks([]) + else + xlabel(sprintf('%s',ax_labels{1})) + +% if txy_count ~= 1 +% ylabel(sprintf('%s',ax_labels{2})) +% end + end + if txy_count ~=3 + yticks([]) + else + set(gca,'YAxisLocation','right') + ylabel('T (s)') + end + xlim(fact*lims(kept_axes(2),:)) + ylim(lims(kept_axes(1),:)) + set(gca,'YDir','normal') + + set(gca,'FontSize',fontsize) + end + + +% if plot_3d > 1 +% stfig('3D BEC display'); +% clf +% nexttile +% end + if ~keep_3d + h_data = rmfield(h_data,'flux3'); + h_data = rmfield(h_data,'counts3'); + h_data = rmfield(h_data,'volumes'); + end + + if ~keep_txy + h_data = rmfield(h_data,'txy'); + end + colormap(viridis) + suptitle(label) + + end + +end \ No newline at end of file diff --git a/lib/txy_tools/txy2vzxy.m b/lib/txy_tools/txy2vzxy.m new file mode 100644 index 0000000..fc91a09 --- /dev/null +++ b/lib/txy_tools/txy2vzxy.m @@ -0,0 +1,47 @@ +function v_out = txy2vel(txy_in,varargin) +% A function that converts txy data to velocity-space. +% Takes either a standard tdc struct and appends a field vel_zxy +% OR accepts an Nx3 array of txy data and returns one of the same size. +% Required inputs: +% tdc_struct - A struct with field (at least) counts_txy, an Nx1 cell of n_i x 3 arrays +% Optional inputs: +% COM - centre of mass of cloud. Good idea to specify if pulses are saturated. +% defaults to the mean position of all txy points (shotwise) +% gravity - defaults to hebec_constant value + c = hebec_constants(); + p = inputParser; + addParameter(p,'gravity',c.g0); + addParameter(p,'fall_distance',c.fall_distance); + addParameter(p,'release_time',0); + addParameter(p,'t_COM',nan); + parse(p,varargin{:}); + g = p.Results.gravity; + s = p.Results.fall_distance; + t0 = p.Results.release_time; + t_COM = p.Results.t_COM; + +% if isstruct(txy_in) +% mode = 'struct'; +% elseif isvector(txy_in) +% mode = 'time'; +% elseif ismatrix(txy_in) +% mode = 'array'; +% else +% error('TXY data type not recognized'); +% end +% if strcmP(mode,'array') + if isnan(t_COM) %if nothing passed + t_COM = mean(txy_in(:,1)); + warning('t_COM argument not passed, using mean arrival time') + end +% end + + fall_times = txy_in(:,1) - t0; + vz = -g*(t_COM^2-fall_times.^2)./(2*fall_times); + % Correct to within machine precision + v_out = [vz, txy_in(:,2:3)./fall_times]; + +% function vzxy_out=txy_to_vel(txy_in,out_time,gravity,fall_distance) + +end + diff --git a/lib/angle_between_vec.m b/lib/vectors/angle_between_vec.m similarity index 100% rename from lib/angle_between_vec.m rename to lib/vectors/angle_between_vec.m diff --git a/lib/vectors/compute_polar_angle_between_vec.m b/lib/vectors/compute_polar_angle_between_vec.m new file mode 100644 index 0000000..66c1ab9 --- /dev/null +++ b/lib/vectors/compute_polar_angle_between_vec.m @@ -0,0 +1,89 @@ +function angle_out=compute_polar_angle_between_vec(in_vec,point_ref_vec,angle_ref_vec) + +% given some vector v, a pointing reference u and a angle reference w +% find the polar angle of the vector v about u such that the vector w would retun zero angle +% two ways to tackle the probjem +% both will require finding the component of w that is perpendicular to u +% w_perp(u)=w-(w·u)u + +% the geometric way +% we calculate the component of v that is perpendicular to u +% v_perp(u) +% then find the angle between v_perp(u) & w_perp(u) +% this gives the magnitude of the angle with no regards for the sign +% to get the sign we compute sign(u · ( v_perp(u) × w_perp(u))) + + +% cord transform +% we find a transformation such that the identity vectors i is mapped to the +% w_perp(u) vector, k goes to u and then j is maped to the othogonal to these two +% transformation*I=vecnorm([w_perp(u);u×w_perp(u);u]) +% and simply +% transformation=vecnorm([w_perp(u);u×w_perp(u);u]) +% then this transformation is applied to the input +% the resulting vectors are then converted to spherical cordinates +% this approach seems easier to get wrong so we take the geometric approach + +% TODO +% - try normalizing input vector length for better numerical performance + + + +%handle matching input sizes +if size(point_ref_vec)~=size(angle_ref_vec) + error('reference vectors must be the same size') +end +if size(in_vec,2)~=size(angle_ref_vec,2) + error('inputs must have the same size in the 2nd dimension') +end + +if size(in_vec,1)~=size(angle_ref_vec,1) + if ~xor(size(in_vec,1)==1,size(angle_ref_vec,1)==1) + error('first diemension of inputs must be matched or input_vector/reference must have length of 1') + end + if size(in_vec,1)==1 + in_vec=repmat(in_vec,[size(angle_ref_vec,1),1]); + elseif size(angle_ref_vec,1)==1 + angle_ref_vec=repmat(angle_ref_vec,[size(in_vec,1),1]); + point_ref_vec=repmat(point_ref_vec,[size(in_vec,1),1]); + end +end + +if ~isequal(size(point_ref_vec),size(angle_ref_vec),size(in_vec)) + error('inputs not matched after code should have matched them') +end + +% precomputation normalizing (not strictly needed) +in_vec=in_vec./repmat(vecnorm(in_vec,2,2),[1,3]); +angle_ref_vec=angle_ref_vec./repmat(vecnorm(angle_ref_vec,2,2),[1,3]); +point_ref_vec=point_ref_vec./repmat(vecnorm(point_ref_vec,2,2),[1,3]); + + +% find the component of the angle reference vector that is perp. to the pointing reference vector (jector rejection) +% this is through http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/dotprod/dotprod.html +comp_angle_ref_perp_point_ref=angle_ref_vec-vector_projection(angle_ref_vec,point_ref_vec); + +%find the component of the input vector that is perp. to the pointing reference vector +comp_in_vec_perp_point_ref=in_vec-vector_projection(in_vec,point_ref_vec); + + +% now compute the angle between these +angle_mag=angle_between_vec(comp_angle_ref_perp_point_ref,comp_in_vec_perp_point_ref); +angle_sign=sign(dot(point_ref_vec,cross(comp_in_vec_perp_point_ref,comp_angle_ref_perp_point_ref),2)); +angle_sign(angle_sign==0)=1; +angle_out=angle_mag.*angle_sign; +angle_out=wrapTo2Pi(angle_out); + +%check that the point_ref_vec is not aligned with angle_ref_vec +ref_vec_angles=angle_between_vec(angle_ref_vec,point_ref_vec); +angle_out(abs(ref_vec_angles)< 5*eps(2*pi))=nan; + +% check that the input vector has a length +in_len=vecnorm(in_vec,2,2); +angle_out(in_len==0)=nan; + + + +end + + diff --git a/lib/test_angle_between_vec.m b/lib/vectors/test_angle_between_vec.m similarity index 100% rename from lib/test_angle_between_vec.m rename to lib/vectors/test_angle_between_vec.m diff --git a/lib/vectors/test_compute_polar_angle_between_vec.m b/lib/vectors/test_compute_polar_angle_between_vec.m new file mode 100644 index 0000000..f69958c --- /dev/null +++ b/lib/vectors/test_compute_polar_angle_between_vec.m @@ -0,0 +1,49 @@ +%test_compute_polar_angle_between_vec + +% life lesson +% dont test code with vectors with approx unit norm + +rad2deg(compute_polar_angle_between_vec([0,1,0]*100,[1,0,0]*100,[0,0,1]*100) ) +rad2deg(compute_polar_angle_between_vec([0,1,1]*100,[1,0,0]*100,[0,0,1]*100) ) +rad2deg(compute_polar_angle_between_vec([0,0,-1]*100,[1,0,0]*100,[0,0,1]*100) ) +rad2deg(compute_polar_angle_between_vec([0,-1,0]*100,[1,0,0]*100,[0,0,1]*100) ) + + +%% + +rad2deg(compute_polar_angle_between_vec([[0,1,0];[0,1,1];[0,0,-1];[0,-1,0]],[1,0,0],[0,0,1]) ) + + +%% +rad2deg(compute_polar_angle_between_vec([1,1,0], [[1,0,0];[1,1,0]], [[0,0,1];[0,0,1]] ) ) + +%% +rad2deg(compute_polar_angle_between_vec([1,1,1], [[1,0,0];[1,1,0]], [[0,0,1];[0,0,1]] ) ) + +%% hangling when the angle reference and pointing reference point in the same dir +% single input +rad2deg(compute_polar_angle_between_vec([1,1,1],[1,0,0],[2,0,0]) ) + +% multi input +rad2deg(compute_polar_angle_between_vec([1,1,1],[[1,0,0];[1,0,0]],[[2,0,0];[0,0,1]]) ) + +%% zero vector + +rad2deg(compute_polar_angle_between_vec([0,0,0],[0,1,0],[0,0,1]) ) +rad2deg(compute_polar_angle_between_vec([1,0,0],[0,0,0],[0,0,1]) ) +rad2deg(compute_polar_angle_between_vec([1,0,0],[0,1,0],[0,0,0]) ) + + +%% vector scaling +% should be invariant under scaling +scale_factor=1e-320; +%scale_factor=1e120; +invec=[0.5+pi/1e3,sqrt(2),-1]*100; +pointrefvec=[1+48/7812,pi/1e4,pi/1e4]*100; +anglerefvec=[sqrt(7)/100,sqrt(2)/100,pi]*100; +baseline=rad2deg(compute_polar_angle_between_vec(invec,pointrefvec,anglerefvec) ) +baseline-rad2deg(compute_polar_angle_between_vec(scale_factor.*invec,pointrefvec,anglerefvec) ) +baseline-rad2deg(compute_polar_angle_between_vec(invec,scale_factor.*(pointrefvec),anglerefvec) ) +baseline-rad2deg(compute_polar_angle_between_vec(invec,pointrefvec,scale_factor.*anglerefvec) ) + +% this can be slightly improved by turning on intermediate normalization but its already very good \ No newline at end of file diff --git a/lib/vectors/test_vector_projection.m b/lib/vectors/test_vector_projection.m new file mode 100644 index 0000000..a718212 --- /dev/null +++ b/lib/vectors/test_vector_projection.m @@ -0,0 +1,5 @@ +% test_vector_projection + +out1=vector_projection([1,2,3],[4,5,6]) +% analytic answer from mathematica +out1-[128/77, 160/77, 192/77] \ No newline at end of file diff --git a/lib/vectors/vector_projection.m b/lib/vectors/vector_projection.m new file mode 100644 index 0000000..9e59da5 --- /dev/null +++ b/lib/vectors/vector_projection.m @@ -0,0 +1,34 @@ +function vector_out=vector_projection(vec_a,vec_b) +% calculate the vector projection of vector a onto vector b +% Inputs +% vec_a - [n x m] matrix where m is the dimensionality of the vector and n is the number of independent vectors +% Outputs: +% vector_out - projection of a onto b calculated row-wise + +% Other m-files required: none +% Also See: angle_between_vec,compute_polar_angle_between_vec +% Subfunctions: none +% MAT-files required: none +% +% Known BUGS/ Possible Improvements +% - +% +% Author: Bryce Henson +% email: Bryce.Henson@live.com +% Last revision:2019-10-30 + + +if size(vec_a)~=size(vec_b) + error('vectors must be the same size') +end + +%algo 1 +vector_out=vec_b.*dot(vec_a,vec_b,2)./(vecnorm(vec_b,2,2).^2); + +% algo 2 +% this seems to have very slightly better numerical perfromance +% vector_out2=(dot(vec_a,vec_b,2)./vecnorm(vec_b,2,2)).*(vec_b./vecnorm(vec_b,2,2)); + + + +end \ No newline at end of file diff --git a/scratch/DopplerWidth.m b/scratch/DopplerWidth.m deleted file mode 100644 index e69de29..0000000 diff --git a/vprint.m b/vprint.m new file mode 100644 index 0000000..3cfe9cc --- /dev/null +++ b/vprint.m @@ -0,0 +1,6 @@ +function str = vprint(str,verbose,level) + if verbose>level + str = cli_header(str,level); + end + +end \ No newline at end of file