Shortcut: PIECEWISE

Module	function
Description	Usage
Compute a piece wise straight line through its arguments that passes through a set of ordered control points.

Input

The arguments that serve as the input for this action are specified using one or more of the keywords in the following table.

Further details and examples

Compute a piece wise straight line through its arguments that passes through a set of ordered control points.

This action can be used to calculate a piecewise linear function of an input argument such as the one given below:

$$f(x) = \begin{cases} 10 & \textrm{if} \quad x<1 \\ 10 + \frac{\pi - 10}{2-1}(x-1) & \textrm{if} \quad 1 \le x < 2 \\ \pi + \frac{10 - \pi}{3-2}(x-2) & \textrm{if} \quad 2 \le x \le 3 \\ 10 & \textrm{otherwise} \end{cases}$$

The example shown below illustrates how one can use PLUMED to evaluate the function described above for the distance between atom 1 and atom 2.

Click on the labels of the actions for more information on what each action computes

dist1The DISTANCE action with label dist1 calculates the following quantities:
 Quantity   
 Type   
 Description  
dist1
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,10
pwThe PIECEWISE action with label pw calculates the following quantities:
 Quantity   
 Type   
 Description  
pw
scalar
the value calculated by this action: PIECEWISECompute a piece wise straight line through its arguments that passes through a set of ordered control points. More details POINT0This keyword is used to specify the various points in the function above=1,10 POINT1This keyword is used to specify the various points in the function above=2,PI POINT2This keyword is used to specify the various points in the function above=3,10 ARGthe values input to this function=dist1
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=pw FILEthe name of the file on which to output these quantities=colvar

As you can see from the example above, the control points for the picewise function are passed using the POINT0=... POINT1=... syntax. You can specify as many of these control points as you want. These control points then serce as the $x_i$ and $y_i$ values in the following expression.

For variables less than the first (greater than the last) point, the value of the first (last) point is used.

$$\frac{y_{i+1}-y_i}{x_{i+1}-x_i}(s-x_i)+y_i ; if x_i<s<x_{i+1}$$

If the input value of $s$ is smaller than the lowest specified $x_i$ value then this action outputs the $y_i$ value that corresponds to the smallest of the input $x_i$ values. Similarly, if the input value of $s$ is larger than the highest specified $x_i$ value the $y_i$ value that corresponds to the largest of the input $x_i$ values is output.

Using multiple scalars in input

The following example illustrates what happens when multiple scalar arguments are passed to this action:

Click on the labels of the actions for more information on what each action computes

dist1The DISTANCE action with label dist1 calculates the following quantities:
 Quantity   
 Type   
 Description  
dist1
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,10
dist2The DISTANCE action with label dist2 calculates the following quantities:
 Quantity   
 Type   
 Description  
dist2
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=2,11

ppwwThe PIECEWISE action with label ppww calculates the following quantities:
 Quantity   
 Type   
 Description  
ppww.dist1_pfunc
scalar
one or multiple instances of this quantity can be referenced elsewhere in the input file.  These quantities will be named with the arguments of the function followed by the character string _pfunc.  These quantities tell the user the values of the piece wise functions of each of the arguments. This particular component measures this quantity for the input CV named dist1
ppww.dist2_pfunc
scalar
one or multiple instances of this quantity can be referenced elsewhere in the input file.  These quantities will be named with the arguments of the function followed by the character string _pfunc.  These quantities tell the user the values of the piece wise functions of each of the arguments. This particular component measures this quantity for the input CV named dist2: PIECEWISECompute a piece wise straight line through its arguments that passes through a set of ordered control points. More details POINT0This keyword is used to specify the various points in the function above=1,10 POINT1This keyword is used to specify the various points in the function above=2,PI POINT2This keyword is used to specify the various points in the function above=3,10 ARGthe values input to this function=dist1,dist2
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=ppww.dist1_pfunc,ppww.dist2_pfunc

In essence the piecewise function is applied to each of the input arguments in turn. Hence, in the example above the PIECEWISE command outputs two values. The first of these ppww.dist1_pfunc is the result that is obtained when the piecewise function is applied to the argument dist1. The second is then the result that is obtained when the piecewise function is applied to the argument dist2.

Non rank zero arguments

This argument currently cannot accept non-rank zero arguments. However, it would be extremely straightforward to add functionality to ensure that if a PIECEWISE command receives a vector, matrix or function on grid in input it will output a vector, matrix or function on grid that is obtained by applying the piecewise function elementwise to each of the elements of the input vector, matrix or function.

Syntax

The following table describes the keywords and options that can be used with this action