Shortcut: DETERMINANT

Module	matrixtools
Description	Usage
Calculate the determinant of a matrix
output value	type
the determinant of the matrix	scalar

Details and examples

Calculate the determinant of a matrix

This shorctu allows you to calculate the determinant of a square matrix. The following example shows how the action is used:

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

d1The DISTANCE_MATRIX action with label d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
d1
matrix
a matrix containing the weights for the bonds between each pair of atoms: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action has hidden defaults. More details ATOMSYou should use GROUP instead of this keyword which was used in older versions of PLUMED and is provided for back compatibility only=1-5
d1: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details ATOMSYou should use GROUP instead of this keyword which was used in older versions of PLUMED and is provided for back compatibility only=1-5  NL_CUTOFF The cutoff for the neighbor list=0.0 NL_STRIDE The frequency with which we are updating the atoms in the neighbor list=1 CUTOFF ignore distances that have a value larger than this cutoff=-1
detThe DETERMINANT action with label det calculates the following quantities:
 Quantity   
 Type   
 Description  
det
scalar
the determinant of the matrix: DETERMINANTCalculate the determinant of a matrix This action is a shortcut. More details ARGThe matrix that we are calculating the determinant for=d1
# PLUMED interprets the command:
# det: DETERMINANT ARG=d1
# as follows (Click the red comment above to revert to the short version of the input):
det_diagThe DIAGONALIZE action with label det_diag calculates the following quantities:
 Quantity   
 Type   
 Description  
det_diag.vals-1
scalar
the eigevalues of the input matrix  This is the 1th of these quantities
det_diag.vecs-1
vector
the eigenvectors of the input matrix  This is the 1th of these quantities
det_diag.vals-2
scalar
the eigevalues of the input matrix  This is the 2th of these quantities
det_diag.vecs-2
vector
the eigenvectors of the input matrix  This is the 2th of these quantities
det_diag.vals-3
scalar
the eigevalues of the input matrix  This is the 3th of these quantities
det_diag.vecs-3
vector
the eigenvectors of the input matrix  This is the 3th of these quantities
det_diag.vals-4
scalar
the eigevalues of the input matrix  This is the 4th of these quantities
det_diag.vecs-4
vector
the eigenvectors of the input matrix  This is the 4th of these quantities
det_diag.vals-5
scalar
the eigevalues of the input matrix  This is the 5th of these quantities
det_diag.vecs-5
vector
the eigenvectors of the input matrix  This is the 5th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=d1 VECTORS the eigenvalues and vectors that you would like to calculate=all
detThe CUSTOM action with label det calculates the following quantities:
 Quantity   
 Type   
 Description  
det
scalar
an arbitrary function: PRODUCTCalculate the product of the input quantities More details ARGThe set of scalars that you would like to multiply together=(det_diag\.vals-[0-9])
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=det FILEthe name of the file on which to output these quantities=colvar

If you look at the expanded version of the input above you can see that PLUMED calculates the determinant by first diagonalising the input matrix and then calculating the product of the eigenvalues.

Input

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

Keyword	Type	Description
ARG	matrix	The matrix that we are calculating the determinant for

Full list of keywords

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

Keyword	Type	Default	Description
ARG	input	none	The matrix that we are calculating the determinant for