Fixed some examples in function documentation

src/function/Custom.cpp

@@ -249,7 +249,32 @@ PRINT ARG=onaxis,fromaxis
 ```
 
 The equations in this input were also used to combine [RMSD](RMSD.md) values from different snapshots of a protein so as to define
-progression (S) and distance (Z) variables in the paper that is cited in the bibliography.
+progression (S) and distance (Z) variables in the paper that is cited in the bibliography.  We can understand how these expressions
+are derived by noting that $x$, $y$ and $z$ are the distances between atoms 1 and 3, 2 and 3 and 1 and 2 respectively.  The projection
+of the vector connecting atom 1 to atom 3 onto the vector connecting atom 1 to atom 2 is thus $x\cos(\theta)$, where theta is the angle
+between the vector connecting atoms 1 and 3 and the vector connecting atoms 1 and 2.  We can arrive at the following expression for $x\cos(\theta)$
+by rearranging the cosine rule:
+
+$$
+x\cos(\theta) = \frac{y^2 - x^2}{z} - \frac{z}{2}
+$$
+
+Notice that the value called `onaxis` in the above input is thus $o=x\cos(\theta) + \frac{z}{2}$.  Adding the factor of $\frac{z}{2}$ ensures that the origin
+is at the center of the bond connecting atom 1 to atom 2.
+
+The value `fromaxis` measures the square of the distance from the the line.  It is calculated using pythagoras theorem as follows:
+
+$$
+f^2 = y^2 - x^2\cos^2(\theta) 
+$$
+
+Inserting $x\cos(\theta) = o - \frac{z}{2}$ into this expression gives:
+
+$$
+f^2 = y^2 - (o -\frac{z}{2})^2 = y^2 - o^2 + oz - \frac{z^2}{4}
+$$
+
+Inserting the fact that $oz = \frac{y^2 - x^2}{2}$, which comes from the expression for $o$ that was used to calculate `onaxis`, gets us to the expression that is used to calculate `fromaxis`.
 
 ## CUSTOM with vector arguments
 
@@ -326,8 +351,8 @@ PRINT ARG=angles FILE=colvar
 Notice that you can pass multiple $N\times M$ matrices in the input to a CUSTOM action as illustrated in the example below:
 
 ```plumed
-c1: CUSTOM VALUES=2,3,4,5 NROWS=2 NCOLS=2
-c2: CUSTOM VALUES=1,0,0,1 NROWS=2 NCOLS=2
+c1: CONSTANT VALUES=2,3,4,5 NROWS=2 NCOLS=2
+c2: CONSTANT VALUES=1,0,0,1 NROWS=2 NCOLS=2
 f: CUSTOM ARG=c1,c2 FUNC=x*y PERIODIC=NO
 PRINT ARG=f FILE=colvar
 ```

src/function/FunctionOfMatrix.h

@@ -182,6 +182,11 @@ FunctionOfMatrix<T>::FunctionOfMatrix(const ActionOptions&ao):
       }
     }
   }
+  bool allconstant=true;
+  for(unsigned i=argstart; i<getNumberOfArguments(); ++i) {
+      if( !getPntrToArgument(i)->isConstant() ) { allconstant=false; break; } 
+  } 
+  if( allconstant ) done_in_chain=false;
   // Now setup the action in the chain if we can
   nderivatives = buildArgumentStore(myfunc.getArgStart());
 }

src/function/Highest.cpp

@@ -93,7 +93,7 @@ Notice that you can also use a combination of scalars and vectors in the input t
 ```plumed
 c: CONSTANT VALUE=0.05
 d: DISTANCE ATOMS1=1,2 ATOMS2=3,4
-h: HIGHEST ARG=c,d
+h: HIGHEST ARG=d,c
 PRINT ARG=h FILE=colvar
 ``` 
 
@@ -187,7 +187,7 @@ Notice that you can also use a combination of scalars and vectors in the input t
 ```plumed
 c: CONSTANT VALUE=0.5
 d: DISTANCE ATOMS1=1,2 ATOMS2=3,4
-h: LOWEST ARG=c,d
+h: LOWEST ARG=d,c
 PRINT ARG=h FILE=colvar
 ``` 
 

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: MOMENTS ARG=d POWERS=2,3
+mv: 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_MATRIX SPECIES=1-100 SWITCH={RATIONAL R_0=0.1}
+c: CONTACT_MATRIX GROUP=1-100 SWITCH={RATIONAL R_0=0.1}
 s: SUM ARG=c PERIODIC=NO
 PRINT ARG=s FILE=colvar
 ```