Fixed some mistakes in manual for functions

src/function/Between.cpp

@@ -21,6 +21,7 @@
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
 #include "Between.h"
 #include "FunctionShortcut.h"
+#include "FunctionOfScalar.h"
 #include "FunctionOfVector.h"
 #include "FunctionOfMatrix.h"
 #include "core/ActionRegister.h"
@@ -66,7 +67,7 @@ The $\sigma$ values in the expressions above is calculated from the parameters $
 Also note that the Kernel function $K$ that is used in the first example is a Gaussian. The actual integral that is evaluated is thus:
 
 $$
-w(s) = \frac{1}{\sqrt{2\pi}\sigma} \int_a^b \exp\left( -\frac{(x-s)^2}{2\sigma^2} \textrm{d}x
+w(s) = \frac{1}{\sqrt{2\pi}\sigma} \int_a^b \exp\left( -\frac{(x-s)^2}{2\sigma^2}\right) \textrm{d}x
 $$
 
 The Gaussian kernel in this expression can be replaced by a triangular Kernel by changing the input to:
@@ -158,6 +159,8 @@ Transform all the elements of a matrix using a switching function that is oen wh
 
 typedef FunctionShortcut<Between> BetweenShortcut;
 PLUMED_REGISTER_ACTION(BetweenShortcut,"BETWEEN")
+typedef FunctionOfScalar<Between> ScalarBetween;
+PLUMED_REGISTER_ACTION(ScalarBetween,"BETWEEN_SCALAR")
 typedef FunctionOfVector<Between> VectorBetween;
 PLUMED_REGISTER_ACTION(VectorBetween,"BETWEEN_VECTOR")
 typedef FunctionOfMatrix<Between> MatrixBetween;

src/function/Combine.cpp

@@ -98,7 +98,7 @@ COMBINE action that takes vectors and scalars in input.
 ```plumed
 p: CONSTANT VALUE=2
 d: DISTANCE ATOMS1=1,2 ATOMS2=3,4 ATOMS3=5,6 ATOMS4=7,8
-c: COMBINE ARG=d,p COEFFICIENTS=4,-1 POWERS=2.5,1 
+c: COMBINE ARG=d,p COEFFICIENTS=4,-1 POWERS=2.5,1 PERIODIC=NO
 PRINT ARG=c FILE=colvar
 ```
 
@@ -117,7 +117,7 @@ Lastly, notice that if you pass a single vector in input to COMBINE as in the fo
 
 ```plumed
 d: DISTANCE ATOMS1=1,2 ATOMS2=3,4 ATOMS3=5,6 ATOMS4=7,8
-c: COMBINE ARG=d COEFFICIENTS=4 POWERS=2.5 PARAMETERS=0.5
+c: COMBINE ARG=d COEFFICIENTS=4 POWERS=2.5 PARAMETERS=0.5 PERIODIC=NO
 PRINT ARG=c FILE=colvar
 ```
 

src/function/Custom.cpp

@@ -101,7 +101,7 @@ that you can use in in the input to the `FUNC` keyword for CUSTOM.
 | cos(x)        | The cosine of x | 
 | sec(x)        | The reciprocal of the cosine of $x$. $\frac{1}{\cos(x)}$ |
 | csc(x)        | The reciprocal of the sine of $x$. $\frac{1}{\sin(x)}$ |
-| tan(x)        | The tangent of x i.e. $\frac{\sin(x)}(\cos(x)}$ | 
+| tan(x)        | The tangent of x i.e. $\frac{\sin(x)}{\cos(x)}$ | 
 | cot(x)        | The reciprocal of the tangent of $x$. $\frac{1}{\tan(x)}$ |
 | asin(x)       | The principal arc sine of x. Returns $-\frac{\pi}{2} \le y \le \frac{\pi}{2}$ which gives $x = \sin(y)$ |
 | acos(x)       | The principal arc cosine of x. Returns $0 \le y \le \pi$ which gives $x=\cos(y)$ | 
@@ -110,8 +110,8 @@ that you can use in in the input to the `FUNC` keyword for CUSTOM.
 | sinh(x)       | The hyperbolic sine of $x$ |
 | cosh(x)       | the hyperbolic cosine of $x$ |
 | tanh(x)       | The hyperbolic tangent of $x$ |
-| erf(x)        | The [error function](https://en.wikipedia.org/wiki/Error_function) $\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} \txtrm{d}t$ |
-| erfc(x)       | The complementary error function $1-\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} \txtrm{d}t$ |
+| erf(x)        | The [error function](https://en.wikipedia.org/wiki/Error_function) $\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} \textrm{d}t$ |
+| erfc(x)       | The complementary error function $1-\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} \textrm{d}t$ |
 | step(x)       | 1 if $x \ge 0$ and 0 otherwise |
 | delta(x)      | inf if $x=0$ and 0 otherwise |
 | nandelta(x)   | nan if $x=0$ and 0 otherwise |
@@ -120,7 +120,7 @@ that you can use in in the input to the `FUNC` keyword for CUSTOM.
 | recip(x)      | The reciprocal of x i.e. $\frac{1}{x}$ |
 | min(x,y)      | If $x<y$ this function returns $x$.  If $y\le x$ this function returns $y$ |  
 | max(x,y)      | If $x>y$ this function returns $x$.  If $y\ge x$ this function returns $y$ |
-| abs(x)        | The absolute value of x i.e. $|x|$ |
+| abs(x)        | The absolute value of x |
 | floor(x)      | The largest integer that is less than $x$ |
 | ceil(x)       | The smallest integer that is greater than $x$ |
 | select(x,y,z) | If $x==0$ this returns $z$ otherwise this returns $y$ |
@@ -208,7 +208,7 @@ Notice that you can use CUSTOM to implement a [MOVINGRESTRAINT](MOVINGRESTRAINT.
 ```plumed
 t: TIME 
 d: DISTANCE ATOMS=1,2 
-f: CUSTOM ARG=d,t FUNC=100*(d-((0.2-0.1)*t/100))^2 PERIODIC=NO
+f: CUSTOM ARG=d,t FUNC=100*(x-((0.2-0.1)*y/100))^2 PERIODIC=NO
 BIASVALUE ARG=f
 ```
 
@@ -310,9 +310,9 @@ d: DISTANCE COMPONENTS ATOMS1=1,2 ATOMS2=3,4 ATOMS3=5,6 ATOMS4=7,8
 # Calculate the norm of these four vectors 
 norm: CUSTOM ARG=d.x,d.y,d.z FUNC=sqrt(x*x+y*y+z*z) PERIODIC=NO
 # Now calculate the directors of the vectors
-norm_x: CUSTOM ARG=d.x,norm FUNC=x/y PEROIDIC=NO
-norm_y: CUSTOM ARG=d.y,norm FUNC=x/y PEROIDIC=NO
-norm_z: CUSTOM ARG=d.z,norm FUNC=x/y PEROIDIC=NO
+norm_x: CUSTOM ARG=d.x,norm FUNC=x/y PERIODIC=NO
+norm_y: CUSTOM ARG=d.y,norm FUNC=x/y PERIODIC=NO
+norm_z: CUSTOM ARG=d.z,norm FUNC=x/y PERIODIC=NO
 # And combine all these directors in a matrix
 stack: VSTACK ARG=norm_x,norm_y,norm_z 
 # Now calculate the matrix of dot products between directors (these are the cosines of the angles)
@@ -328,7 +328,7 @@ Notice that you can pass multiple $N\times M$ matrices in the input to a CUSTOM
 ```plumed
 c1: CUSTOM VALUES=2,3,4,5 NROWS=2 NCOLS=2
 c2: CUSTOM VALUES=1,0,0,1 NROWS=2 NCOLS=2
-f: CUSTOM ARG=c1,c2 FUNC=x*y PEIRODIC=NO
+f: CUSTOM ARG=c1,c2 FUNC=x*y PERIODIC=NO
 PRINT ARG=f FILE=colvar
 ```
 

src/function/FuncPathMSD.cpp

@@ -43,9 +43,9 @@ calculate the progress along the path and the distance from it in p1
 
 ```plumed
 #SETTINGS INPUTFILES=regtest/trajectories/path_msd/frame_1.dat,regtest/trajectories/path_msd/frame_21.dat,regtest/trajectories/path_msd/frame_42.dat
-t1: RMSD REFERENCE=regtest/trajectories/path_msd/frame_1.pdb TYPE=OPTIMAL SQUARED
-t2: RMSD REFERENCE=regtest/trajectories/path_msd/frame_21.pdb TYPE=OPTIMAL SQUARED
-t3: RMSD REFERENCE=regtest/trajectories/path_msd/frame_42.pdb TYPE=OPTIMAL SQUARED
+t1: RMSD REFERENCE=regtest/trajectories/path_msd/frame_1.dat TYPE=OPTIMAL SQUARED
+t2: RMSD REFERENCE=regtest/trajectories/path_msd/frame_21.dat TYPE=OPTIMAL SQUARED
+t3: RMSD REFERENCE=regtest/trajectories/path_msd/frame_42.dat TYPE=OPTIMAL SQUARED
 p1: FUNCPATHMSD ARG=t1,t2,t3 LAMBDA=500.0
 PRINT ARG=t1,t2,t3,p1.s,p1.z STRIDE=1 FILE=colvar FMT=%8.4f
 ```

src/function/Moments.cpp

@@ -56,7 +56,7 @@ Notice that you can also achieve the same result using the following input:
 
 ```plumed
 d: DISTANCE ATOMS1=1,2 ATOMS2=1,3 ATOMS3=1,4 ATOMS4=1,5
-sort: SORT ARG=d
+sort: MOMENTS ARG=d POWERS=2,3
 PRINT ARG=mv.moment-2,mv.moment-3 FILE=colvar
 ```
 

src/function/Sum.cpp

@@ -46,7 +46,7 @@ This example calculates and outputs the number of distances that are less than 0
 You can do something similar by summing the elements of a matrix as shown below:
 
 ```plumed
-c: CONTACT_MAP SPECIES=1-100 SWITCH={RATIONAL R_0=0.1}
+c: CONTACT_MATRIX SPECIES=1-100 SWITCH={RATIONAL R_0=0.1}
 s: SUM ARG=c PERIODIC=NO
 PRINT ARG=s FILE=colvar
 ```

src/generic/Constant.cpp

@@ -115,7 +115,7 @@ in the following input the values `d` and `f` are  evaluated on every step.  `c`
 p: CONSTANT VALUE=1.0
 c: CUSTOM ARG=p FUNC=2*x+1 PERIODIC=NO
 d: DISTANCE ATOMS=1,2
-f: CUSTOM ARG=p,d FUNX=x*y PERIODIC=NO
+f: CUSTOM ARG=p,d FUNC=x*y PERIODIC=NO
 PRINT ARG=f FILE=colvar STRIDE=1
 ```