Shortcut: COVARIANCE_MATRIX

Module	matrixtools
Description	Usage
Calculate a covariance matix
output value	type
the covariance matrix	matrix

Further details and examples

Calculate a covariance matix

This shortcut takes multiple vectors in input as well as a vector of weights. A covariance matrix is then computed from this input data. The example below shows how this action can be used to calculate a gyration tensor that describes the shape for a cluster of atoms.

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

# Calculate the geometric center for 100 atoms
comThe CENTER_FAST action with label com calculates the following quantities:
 Quantity   
 Type   
 Description  
com
atoms
virtual atom calculated by CENTER_FAST action: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-100
# Calculate the vector connecting each of the 100 atoms to the geometric center
dThe DISTANCE action with label d calculates the following quantities:
 Quantity   
 Type   
 Description  
d.x
vector
the x-component of the vector connecting the two atoms
d.y
vector
the y-component of the vector connecting the two atoms
d.z
vector
the z-component of the vector connecting the two atoms: DISTANCESCalculate the distances between multiple piars of atoms This action is a shortcut. More details ATOMSthe pairs of atoms that you would like to calculate the angles for=1-100 ORIGINcalculate the distance of all the atoms specified using the ATOMS keyword from this point=com COMPONENTS calculate the x, y and z components of the distance separately and store them as label
# PLUMED interprets the command:
# d: DISTANCES ATOMS=1-100 ORIGIN=com COMPONENTS
# as follows (Click the red comment above to revert to the short version of the input):
d: DISTANCECalculate the distance/s between pairs of atoms. More details COMPONENTS calculate the x, y and z components of the distance separately and store them as label ATOMS1the pair of atom that we are calculating the distance between=com,1 ATOMS2the pair of atom that we are calculating the distance between=com,2 ATOMS3the pair of atom that we are calculating the distance between=com,3 ATOMS4the pair of atom that we are calculating the distance between=com,4 ATOMS5the pair of atom that we are calculating the distance between=com,5     # Action input conctinues with 95 further ATOMSn keywords, 
# --- End of included input --- # Now compute the covariance matrix
onesThe ONES action with label ones calculates the following quantities:
 Quantity   
 Type   
 Description  
ones
vector
a vector of ones with the required number of elements: ONESCreate a constant vector with all elements equal to one This action is a shortcut. More details SIZEthe number of ones that you would like to create=100
# PLUMED interprets the command:
# ones: ONES SIZE=100
# as follows (Click the red comment above to revert to the short version of the input):
onesThe CONSTANT action with label ones calculates the following quantities:
 Quantity   
 Type   
 Description  
ones
vector
the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NOLOG do not report all the read in scalars in the log VALUESthe numbers that are in your constant value=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
# --- End of included input --- covarThe COVARIANCE_MATRIX action with label covar calculates the following quantities:
 Quantity   
 Type   
 Description  
covar
matrix
the covariance matrix: COVARIANCE_MATRIXCalculate a covariance matix This action is a shortcut. More details ARGthe vectors of data from which we are calculating the covariance=d.x,d.y,d.z WEIGHTSthis keyword takes the label of an action that calculates a vector of values=ones
# PLUMED interprets the command:
# covar: COVARIANCE_MATRIX ARG=d.x,d.y,d.z WEIGHTS=ones
# as follows (Click the red comment above to revert to the short version of the input):
covar_wsumThe SUM action with label covar_wsum calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_wsum
scalar
the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
covar_weightsThe CUSTOM action with label covar_weights calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_weights
vector
the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=ones,covar_wsum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
covar_stackThe VSTACK action with label covar_stack calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_stack
matrix
a matrix that contains the input vectors in its columns: VSTACKCreate a matrix by stacking vectors together More details ARGthe values that you would like to stack together to construct the output matrix=d.x,d.y,d.z
covar_stackTThe TRANSPOSE action with label covar_stackT calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_stackT
matrix
the transpose of the input matrix: TRANSPOSECalculate the transpose of a matrix More details ARGthe label of the vector or matrix that should be transposed=covar_stack
covar_onesThe CONSTANT action with label covar_ones calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_ones
vector
the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=3
covar_matweightsThe OUTER_PRODUCT action with label covar_matweights calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_matweights
matrix
a matrix containing the outer product of the two input vectors that was obtained using the function that was input: OUTER_PRODUCTCalculate the outer product matrix of two vectors More details ARGthe labels of the two vectors from which the outer product is being computed=covar_ones,covar_weights
covar_wTThe CUSTOM action with label covar_wT calculates the following quantities:
 Quantity   
 Type   
 Description  
covar_wT
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=covar_matweights,covar_stackT FUNCthe function you wish to evaluate=x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
covarThe MATRIX_PRODUCT action with label covar calculates the following quantities:
 Quantity   
 Type   
 Description  
covar
matrix
the product of the two input matrices: MATRIX_PRODUCTCalculate the product of two matrices More details ARGthe label of the two matrices from which the product is calculated=covar_wT,covar_stack
# --- End of included input --- 

Syntax

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