Action: INVERT_MATRIX

Module	matrixtools
Description	Usage
Calculate the inverse of the input matrix
output value	type
the inverse of the input matrix	matrix

Details and examples

Calculate the inverse of the input matrix

This action allows you to calculate the inverse of a real symmetric matrix. If the matrix is not symmetric then the dgetrf and dgetri functions from the LAPACK library are used. If the matrix is symmetric then we use dsyevr to find the eigenvalues. The inverse matrix of the input matrix $M$ with eigendecomposition.:

$$M = Q \Lambda Q^{-1}$$

is then found as:

$$M^{-1} = Q \Lambda^{-1} Q^{-1}$$

where $\Lambda^{-1}$ is the inverse of the (diagonal) matrix of eigenvalues $\Lambda$ and $Q$ is the matrix of eigenvectors.

The following example shows how this action is used in practise:

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

cThe DISTANCE_MATRIX action with label c calculates the following quantities:
 Quantity   
 Type   
 Description  
c
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=1-4
c: 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=1-4  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
ciThe INVERT_MATRIX action with label ci calculates the following quantities:
 Quantity   
 Type   
 Description  
ci
matrix
the inverse of the input matrix: INVERT_MATRIXCalculate the inverse of the input matrix More details ARGthe input matrix=c
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=ci 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

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

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