Action: OUTER_PRODUCT

Module	matrixtools
Description	Usage
Calculate the outer product matrix of two vectors
output value	type
a matrix containing the outer product of the two input vectors that was obtained using the function that was input	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.

Further details and examples

Calculate the outer product matrix of two vectors

This action can be used to calculate the outer product of two vectors. As a (useless) example of what can be done with this action consider the following simple input:

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

d1The DISTANCE action with label d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
d1
vector
the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details 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
d2The DISTANCE action with label d2 calculates the following quantities:
 Quantity   
 Type   
 Description  
d2
vector
the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=5,6 ATOMS2the pair of atom that we are calculating the distance between=7,8 ATOMS3the pair of atom that we are calculating the distance between=9,10
ppThe OUTER_PRODUCT action with label pp calculates the following quantities:
 Quantity   
 Type   
 Description  
pp
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 This action has hidden defaults. More details ARGthe labels of the two vectors from which the outer product is being computed=d1,d2
pp: OUTER_PRODUCTCalculate the outer product matrix of two vectors This action uses the defaults shown here. More details ARGthe labels of the two vectors from which the outer product is being computed=d1,d2  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=pp FILEthe name of the file on which to output these quantities=colvar

This input outputs a $2 \times 3$ matrix. If we call the 2 dimensional vector output by the first DISTANCE action $d$ and the 3 dimensional vector output by the second DISTANCE action $h$ then the $(i,j)$ element of the matrix output by the action with the label pp is given by:

$$p_{ij} = d_i h_j$$

These outer product matrices are useful if you are trying to calculate an adjacency matrix that says atoms are connected if they are within a certain distance of each other and if they satisfy a certain criterion. For example, consider the following input:

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

# Determine if atoms are within 5.3 nm of each other
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 GROUPspecifies the list of atoms that should be assumed indistinguishable=1-100 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.={GAUSSIAN D_0=5.29 R_0=0.01 D_MAX=5.3}
# Calculate the coordination numbers
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 --- ccThe MATRIX_VECTOR_PRODUCT action with label cc calculates the following quantities:
 Quantity   
 Type   
 Description  
cc
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,ones
# Now use MORE_THAN to work out which atoms have a coordination number that is bigger than six
cfThe MORE_THAN action with label cf calculates the following quantities:
 Quantity   
 Type   
 Description  
cf
vector
the vector obtained by doing an element-wise application of a function that is one if the if the input is more than a threshold to the input vectors: MORE_THANUse a switching function to determine how many of the input variables are more than a certain cutoff. More details ARGthe values input to this function=cc SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL D_0=5.5 R_0=0.5}
# Now recalculate the contact matrix above as first step towards calculating adjacency matrix that measures if
# atoms are close to each other and both have a coordination number that is bigger than six
c2The CONTACT_MATRIX action with label c2 calculates the following quantities:
 Quantity   
 Type   
 Description  
c2
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 GROUPspecifies the list of atoms that should be assumed indistinguishable=1-100 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.={GAUSSIAN D_0=5.29 R_0=0.01 D_MAX=5.3}
# Now make a matrix in which element i,j is one if atom i and atom j both have a coordination number that is greater than 6
cfmThe OUTER_PRODUCT action with label cfm calculates the following quantities:
 Quantity   
 Type   
 Description  
cfm
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 This action has hidden defaults. More details ARGthe labels of the two vectors from which the outer product is being computed=cf,cf
cfm: OUTER_PRODUCTCalculate the outer product matrix of two vectors This action uses the defaults shown here. More details ARGthe labels of the two vectors from which the outer product is being computed=cf,cf  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y
# And multiply this by our contact matrix to determine the desired adjacency matrix
mThe CUSTOM action with label m calculates the following quantities:
 Quantity   
 Type   
 Description  
m
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=c2,cfm 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
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

This input calculates a adjacency matrix which has element $(i,j)$ equal to one if atoms $i$ and $j$ have coordination numbers that are greater than 6 and if they are within 5.3 nm of each other.

Notice that you can specify the function of the two input vectors that is to be calculated by using the FUNC keyword which accepts mathematical expressions of $x$ and $y$. In other words, the elements of the outer product are calculated using the lepton library that is used in the CUSTOM action. In addition, you can set FUNC=min or FUNC=max to set the elements of the outer product equal to the minimum of the two input variables or the maximum respectively.

Syntax

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