Action: TRANSPOSE

Module	matrixtools
Description	Usage
Calculate the transpose of a matrix
output value	type
the transpose of the input matrix	vector/matrix

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	vector/matrix	the label of the vector or matrix that should be transposed

Further details and examples

Calculate the transpose of a matrix

This action takes a matrix in input and calculates the input matrix's tranpose. The following example shows how you can use this to calculate coordination numbers of species A with species B and vice versa.

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

# Calculate the contact matrix between the two groups
c1The CONTACT_MATRIX action with label c1 calculates the following quantities: Quantity    Type    Description  
c1 matrix a matrix containing the weights for the bonds between each pair of atoms: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPAwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPB=1-10 GROUPBwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPA=11-30 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=0.1}
# Calculate the cooordination numbers for the atoms in group A by multiplying by a vector of ones
onesBThe ONES action with label onesB calculates the following quantities: Quantity    Type    Description  
onesB 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=20
# PLUMED interprets the command:
# onesB: ONES SIZE=20
# as follows (Click the red comment above to revert to the short version of the input):
onesBThe CONSTANT action with label onesB calculates the following quantities: Quantity    Type    Description  
onesB 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
# --- End of included input --- coordAThe MATRIX_VECTOR_PRODUCT action with label coordA calculates the following quantities: Quantity    Type    Description  
coordA vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=c1,onesB
# Transpose the contact matrix
c1TThe TRANSPOSE action with label c1T calculates the following quantities: Quantity    Type    Description  
c1T 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=c1
# Calculate the coordination number for the atoms in group B by multiplying the transpose by a vector of ones
onesAThe ONES action with label onesA calculates the following quantities: Quantity    Type    Description  
onesA 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=10
# PLUMED interprets the command:
# onesA: ONES SIZE=10
# as follows (Click the red comment above to revert to the short version of the input):
onesAThe CONSTANT action with label onesA calculates the following quantities: Quantity    Type    Description  
onesA 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
# --- End of included input --- coordBThe MATRIX_VECTOR_PRODUCT action with label coordB calculates the following quantities: Quantity    Type    Description  
coordB vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=c1T,onesA
# Output the two vectors of coordination numbers to a file
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=coordA,coordB FILEthe name of the file on which to output these quantities=colvar

Another useful example where the transpose can be used is shown below. In this input the DISTANCE command is used to calculate the orientation of a collection of molecules. We then can then use the VSTACK, TRANSPOSE and the MATRIX_PRODUCT commands to calculate the dot products between all these vectors

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

# Calculate the vectors connecting these three pairs of atoms
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: 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=1,2 ATOMS2the pair of atom that we are calculating the distance between=3,4 ATOMS3the pair of atom that we are calculating the distance between=5,6
# Construct a matrix that contains all the components of the vectors calculated
vThe VSTACK action with label v calculates the following quantities: Quantity    Type    Description  
v 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
# Transpose v
vTThe TRANSPOSE action with label vT calculates the following quantities: Quantity    Type    Description  
vT 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=v
# And now calculate the 3x3 matrix of dot products
mThe MATRIX_PRODUCT action with label m calculates the following quantities: Quantity    Type    Description  
m 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=v,vT
# And output the matrix product to a file
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=m FILEthe name of the file on which to output these quantities=colvar

Syntax

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

Keyword	Type	Default	Description
ARG	input	none	the label of the vector or matrix that should be transposed
MATRIX	optional	not used	the input matrix (can use ARG instead)

Keys	Action
`?`	Open this help
`n`	Next page
`p`	Previous page
`s`	Search

Quantity	Type	Description
c1	matrix	a matrix containing the weights for the bonds between each pair of atoms