Action: DIAGONALIZE

Module	matrixtools
Description	Usage
Calculate the eigenvalues and eigenvectors of a square matrix

Details and examples

Calculate the eigenvalues and eigenvectors of a square matrix

This action allows you to use the dsyevr function from the LAPACK library to calculate the eigenvalues and eigenvectors of a real symmetric matrix. For example, the following input can be used to calculate and print all four eigenvalues of the input DISTANCE_MATRIX.

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

dThe DISTANCE_MATRIX action with label d calculates the following quantities:
 Quantity   
 Type   
 Description  
d
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 GROUPthe atoms for which you would like to calculate the adjacency matrix=1-4
d: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-4  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
diagThe DIAGONALIZE action with label diag calculates the following quantities:
 Quantity   
 Type   
 Description  
diag.vals-1
scalar
the eigevalues of the input matrix  This is the 1th of these quantities
diag.vecs-1
vector
the eigenvectors of the input matrix  This is the 1th of these quantities
diag.vals-2
scalar
the eigevalues of the input matrix  This is the 2th of these quantities
diag.vecs-2
vector
the eigenvectors of the input matrix  This is the 2th of these quantities
diag.vals-3
scalar
the eigevalues of the input matrix  This is the 3th of these quantities
diag.vecs-3
vector
the eigenvectors of the input matrix  This is the 3th of these quantities
diag.vals-4
scalar
the eigevalues of the input matrix  This is the 4th of these quantities
diag.vecs-4
vector
the eigenvectors of the input matrix  This is the 4th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix This action has hidden defaults. More details ARGthe input matrix=d
diag: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix This action uses the defaults shown here. More details ARGthe input matrix=d  VECTORS the eigenvalues and vectors that you would like to calculate=all
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=diag.vals-1,diag.vals-2,diag.vals-3,diag.vals-4 FILEthe name of the file on which to output these quantities=colvar

If you wish to calculate only a subset of the eigenvalues and eigenvectors you would use an input like the one shown below. This input calculates and outputs the largest eigenvalue and its corresponding eigenvector.

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

dThe DISTANCE_MATRIX action with label d calculates the following quantities:
 Quantity   
 Type   
 Description  
d
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 GROUPthe atoms for which you would like to calculate the adjacency matrix=1-4
d: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-4  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
diagThe DIAGONALIZE action with label diag calculates the following quantities:
 Quantity   
 Type   
 Description  
diag.vals-1
scalar
the eigevalues of the input matrix  This is the 1th of these quantities
diag.vecs-1
vector
the eigenvectors of the input matrix  This is the 1th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=d VECTORS the eigenvalues and vectors that you would like to calculate=1
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=diag.vals-1,diag.vecs-1 FILEthe name of the file on which to output these quantities=colvar

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 input matrix

Output components

This action calculates the values in the following table. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Description
vals	scalar	the eigevalues of the input matrix
vecs	vector	the eigenvectors of the input matrix

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 input matrix
VECTORS	compulsory	all	the eigenvalues and vectors that you would like to calculate

deprecated keywords

The keywords in the following table can still be used with this action but have been deprecated

Keyword	Description
MATRIX	You should use ARG instead of this keyword which was used in older versions of PLUMED and is provided for back compatibility only