bathyCI.m

function bathyErr = bathyCI(resid,J,w,flag)
% 
%   bathyErr = bathyCI(resid,J,w)
%
%  altered version of nlparci specifically modified to handle the bathy
%  estimation problem for cBathy and to account for the weighted
%  contribution to the sum of squares.  The only change is to reduce the
%  number of degrees of freedom depending on the weights, w.
%
%  Inputs:
%   resid   - Nx1 vector or prediction residuals from k-estimates
%   J       - if flag = 1,Jacobian (both these are from nlinfit)
%           - if flag = 0, expected input is J'*J, from LMFnlsq.m
%   w       - weights used in weighted nlinfit
%   flag    - 1 = use statistics toolbox, 0 = don't use stats toolbox
%  Output:
%   bathyErr - 95% confidence interval on depth estimate.
%
%  Scalped from nlparci for special case of single parameter (bathy)
%  estimation.  Holman, 2012.

alpha = 0.05;

n = sum(w)/max(w);  % Holman kludge
v = n-1;

if flag == 1 % use the stats toolbox if you have it
    
    % Calculate covariance matrix
    [~,R] = qr(J,0);
    Rinv = R\eye(size(R));
    diagInfo = sum(Rinv.*Rinv,2);
    
    rmse = norm(resid) / sqrt(v);
    se = sqrt(diagInfo) * rmse;
    
    % Calculate bathyError from t-stats.
    bathyErr = se * tinv(1-alpha/2,v);
    
elseif flag || ~isempty(ver('stats')) % if you don't have the stats toolbox, or you don't want to use it
    
    rmse = norm(resid) / sqrt(v);
    se = rmse*sqrt(diag(inv(J)));
    bathyErr = se*tstat3( v, 1-alpha/2, 'inv' );
    
end
%
%   Copyright (C) 2017  Coastal Imaging Research Network
%                       and Oregon State University

%    This program is free software: you can redistribute it and/or  
%    modify it under the terms of the GNU General Public License as 
%    published by the Free Software Foundation, version 3 of the 
%    License.

%    This program is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.

%    You should have received a copy of the GNU General Public License
%    along with this program.  If not, see
%                                <http://www.gnu.org/licenses/>.

% CIRN: https://coastal-imaging-research-network.github.io/
% CIL:  http://cil-www.coas.oregonstate.edu
%
%key cBathy
%