Shortcut: EUCLIDEAN_DISTANCE

Module	refdist
Description	Usage
Calculate the euclidean distance between two vectors of arguments
output value	type
the euclidean distances between the input vectors	scalar/vector

Further details and examples

Calculate the euclidean distance between two vectors of arguments

If we have two $n$ -dimensional vectors $u$ and $v$ we can calculate the Euclidean distance between the two points as

$d = \sqrt{ \sum_{i=1}^n (u_i - v_i)^2 }$

which can be expressed in matrix form as:

$d^2 = (u-v)^T (u-v)$

The inputs below shows an example where this is used to calculate the Euclidean distance between the instaneous values of some torsional angles and some reference values for these torsion. In this first example the input values are vectors:

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

cThe CONSTANT action with label c calculates the following quantities: Quantity    Type    Description  
c vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=1,2,3
c: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=1,2,3  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d 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 ATOMS3the pair of atom that we are calculating the distance between=5,6
ddThe EUCLIDEAN_DISTANCE action with label dd calculates the following quantities: Quantity    Type    Description  
dd scalar the euclidean distances between the input vectors: EUCLIDEAN_DISTANCECalculate the euclidean distance between two vectors of arguments This action is a shortcut. More details ARG1The poin that we are calculating the distance from=c ARG2The point that we are calculating the distance to=d
# PLUMED interprets the command:
# dd: EUCLIDEAN_DISTANCE ARG1=c ARG2=d
# as follows (Click the red comment above to revert to the short version of the input):
dd_diffThe TRANSPOSE action with label dd_diff calculates the following quantities: Quantity    Type    Description  
dd_diff matrix the transpose of the input matrix: DISPLACEMENTCalculate the displacement vector between the pair of input vectors More details ARG1The point that we are calculating the distance from=c ARG2The point that we are calculating the distance to=d
dd_diffTThe TRANSPOSE action with label dd_diffT calculates the following quantities: Quantity    Type    Description  
dd_diffT vector 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=dd_diff
dd_2The MATRIX_PRODUCT_DIAGONAL action with label dd_2 calculates the following quantities: Quantity    Type    Description  
dd_2 scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MATRIX_PRODUCT_DIAGONALCalculate the product of two matrices and return a vector that contains the diagonal elements of the ouptut vector More details ARGthe two vectors/matrices whose product are to be taken=dd_diff,dd_diffT
ddThe CUSTOM action with label dd calculates the following quantities: Quantity    Type    Description  
dd scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=dd_2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=dd FILEthe name of the file on which to output these quantities=colvar

while this second example does the same thing but uses scalars in input.

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

c1The CONSTANT action with label c1 calculates the following quantities: Quantity    Type    Description  
c1 scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUEthe single number that you would like to store=1
c1: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUEthe single number that you would like to store=1  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
d1The DISTANCE action with label d1 calculates the following quantities: Quantity    Type    Description  
d1 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2
c2The CONSTANT action with label c2 calculates the following quantities: Quantity    Type    Description  
c2 scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUEthe single number that you would like to store=2
c2: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUEthe single number that you would like to store=2  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
d2The DISTANCE action with label d2 calculates the following quantities: Quantity    Type    Description  
d2 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=3,4
c3The CONSTANT action with label c3 calculates the following quantities: Quantity    Type    Description  
c3 scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUEthe single number that you would like to store=3
c3: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUEthe single number that you would like to store=3  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
d3The DISTANCE action with label d3 calculates the following quantities: Quantity    Type    Description  
d3 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=5,6
ddThe EUCLIDEAN_DISTANCE action with label dd calculates the following quantities: Quantity    Type    Description  
dd scalar the euclidean distances between the input vectors: EUCLIDEAN_DISTANCECalculate the euclidean distance between two vectors of arguments This action is a shortcut. More details ARG1The poin that we are calculating the distance from=c1,c2,c3 ARG2The point that we are calculating the distance to=d1,d2,d3
# PLUMED interprets the command:
# dd: EUCLIDEAN_DISTANCE ARG1=c1,c2,c3 ARG2=d1,d2,d3
# as follows (Click the red comment above to revert to the short version of the input):
dd_diffThe VSTACK action with label dd_diff calculates the following quantities: Quantity    Type    Description  
dd_diff matrix a matrix that contains the input vectors in its columns: DISPLACEMENTCalculate the displacement vector between the pair of input vectors More details ARG1The point that we are calculating the distance from=c1,c2,c3 ARG2The point that we are calculating the distance to=d1,d2,d3
dd_diffTThe TRANSPOSE action with label dd_diffT calculates the following quantities: Quantity    Type    Description  
dd_diffT vector 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=dd_diff
dd_2The MATRIX_PRODUCT_DIAGONAL action with label dd_2 calculates the following quantities: Quantity    Type    Description  
dd_2 scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MATRIX_PRODUCT_DIAGONALCalculate the product of two matrices and return a vector that contains the diagonal elements of the ouptut vector More details ARGthe two vectors/matrices whose product are to be taken=dd_diff,dd_diffT
ddThe CUSTOM action with label dd calculates the following quantities: Quantity    Type    Description  
dd scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=dd_2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=dd FILEthe name of the file on which to output these quantities=colvar

Calculating multiple distances

Suppose that we now have $m$ reference configurations we can define the following $m$ distances from these reference configurations:

$d_j^2 = (u-v_j)^T (u-v_j)$

Lets suppose that we put the $m$ , $n$ -dimensional $(u-v_j)$ vectors in this expression into a $n\times m$ matrix, $A$ , by using the DISPLACEMENT command. It is then straightforward to show that the $d_j^2$ values in the above expression are then the diagonal elements of the matrix product $A^T A$ .

We can use this idea to calculate multiple EUCLIDEAN_DISTANCE values in the following inputs. This first example calculates the three distances between the instaneoues values of two torsions and three reference configurations.

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

ref_psiThe CONSTANT action with label ref_psi calculates the following quantities: Quantity    Type    Description  
ref_psi vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=2.25,1.3,-1.5
ref_psi: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=2.25,1.3,-1.5  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
ref_phiThe CONSTANT action with label ref_phi calculates the following quantities: Quantity    Type    Description  
ref_phi vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=-1.91,-0.6,2.4
ref_phi: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=-1.91,-0.6,2.4  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0

psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=1,2,3,4
phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=13,14,15,16

ddThe EUCLIDEAN_DISTANCE action with label dd calculates the following quantities: Quantity    Type    Description  
dd vector the euclidean distances between the input vectors: EUCLIDEAN_DISTANCECalculate the euclidean distance between two vectors of arguments This action is a shortcut. More details ARG1The poin that we are calculating the distance from=psi,phi ARG2The point that we are calculating the distance to=ref_psi,ref_phi
# PLUMED interprets the command:
# dd: EUCLIDEAN_DISTANCE ARG1=psi,phi ARG2=ref_psi,ref_phi
# as follows (Click the red comment above to revert to the short version of the input):
dd_diffThe VSTACK action with label dd_diff calculates the following quantities: Quantity    Type    Description  
dd_diff matrix a matrix that contains the input vectors in its columns: DISPLACEMENTCalculate the displacement vector between the pair of input vectors More details ARG1The point that we are calculating the distance from=psi,phi ARG2The point that we are calculating the distance to=ref_psi,ref_phi
dd_diffTThe TRANSPOSE action with label dd_diffT calculates the following quantities: Quantity    Type    Description  
dd_diffT 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=dd_diff
dd_2The MATRIX_PRODUCT_DIAGONAL action with label dd_2 calculates the following quantities: Quantity    Type    Description  
dd_2 vector a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MATRIX_PRODUCT_DIAGONALCalculate the product of two matrices and return a vector that contains the diagonal elements of the ouptut vector More details ARGthe two vectors/matrices whose product are to be taken=dd_diff,dd_diffT
ddThe CUSTOM action with label dd calculates the following quantities: Quantity    Type    Description  
dd 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=dd_2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=dd FILEthe name of the file on which to output these quantities=colvar

This section example calculates the three distances between a single reference value for the two torsions and three instances of this pair of torsions.

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

ref_psiThe CONSTANT action with label ref_psi calculates the following quantities: Quantity    Type    Description  
ref_psi scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=2.25
ref_psi: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=2.25  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
ref_phiThe CONSTANT action with label ref_phi calculates the following quantities: Quantity    Type    Description  
ref_phi scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=-1.91
ref_phi: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=-1.91  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0

psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=1,2,3,4 ATOMS2the four atoms involved in the torsional angle=5,6,7,8 ATOMS3the four atoms involved in the torsional angle=9,10,11,12
phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=13,14,15,16 ATOMS2the four atoms involved in the torsional angle=17,18,19,20 ATOMS3the four atoms involved in the torsional angle=21,22,23,24

ddThe EUCLIDEAN_DISTANCE action with label dd calculates the following quantities: Quantity    Type    Description  
dd vector the euclidean distances between the input vectors: EUCLIDEAN_DISTANCECalculate the euclidean distance between two vectors of arguments This action is a shortcut. More details ARG1The poin that we are calculating the distance from=psi,phi ARG2The point that we are calculating the distance to=ref_psi,ref_phi
# PLUMED interprets the command:
# dd: EUCLIDEAN_DISTANCE ARG1=psi,phi ARG2=ref_psi,ref_phi
# as follows (Click the red comment above to revert to the short version of the input):
dd_diffThe VSTACK action with label dd_diff calculates the following quantities: Quantity    Type    Description  
dd_diff matrix a matrix that contains the input vectors in its columns: DISPLACEMENTCalculate the displacement vector between the pair of input vectors More details ARG1The point that we are calculating the distance from=psi,phi ARG2The point that we are calculating the distance to=ref_psi,ref_phi
dd_diffTThe TRANSPOSE action with label dd_diffT calculates the following quantities: Quantity    Type    Description  
dd_diffT 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=dd_diff
dd_2The MATRIX_PRODUCT_DIAGONAL action with label dd_2 calculates the following quantities: Quantity    Type    Description  
dd_2 vector a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MATRIX_PRODUCT_DIAGONALCalculate the product of two matrices and return a vector that contains the diagonal elements of the ouptut vector More details ARGthe two vectors/matrices whose product are to be taken=dd_diff,dd_diffT
ddThe CUSTOM action with label dd calculates the following quantities: Quantity    Type    Description  
dd 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=dd_2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=dd FILEthe name of the file on which to output these quantities=colvar

This final example then computes three distances between three pairs of torsional angles and threee reference values for these three values.

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

ref_psiThe CONSTANT action with label ref_psi calculates the following quantities: Quantity    Type    Description  
ref_psi vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=2.25,1.3,-1.5
ref_psi: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=2.25,1.3,-1.5  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
ref_phiThe CONSTANT action with label ref_phi calculates the following quantities: Quantity    Type    Description  
ref_phi vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUESthe numbers that are in your constant value=-1.91,-0.6,2.4
ref_phi: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUESthe numbers that are in your constant value=-1.91,-0.6,2.4  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0

psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=1,2,3,4 ATOMS2the four atoms involved in the torsional angle=5,6,7,8 ATOMS3the four atoms involved in the torsional angle=9,10,11,12
phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=13,14,15,16 ATOMS2the four atoms involved in the torsional angle=17,18,19,20 ATOMS3the four atoms involved in the torsional angle=21,22,23,24

ddThe EUCLIDEAN_DISTANCE action with label dd calculates the following quantities: Quantity    Type    Description  
dd vector the euclidean distances between the input vectors: EUCLIDEAN_DISTANCECalculate the euclidean distance between two vectors of arguments This action is a shortcut. More details ARG1The poin that we are calculating the distance from=psi,phi ARG2The point that we are calculating the distance to=ref_psi,ref_phi
# PLUMED interprets the command:
# dd: EUCLIDEAN_DISTANCE ARG1=psi,phi ARG2=ref_psi,ref_phi
# as follows (Click the red comment above to revert to the short version of the input):
dd_diffThe VSTACK action with label dd_diff calculates the following quantities: Quantity    Type    Description  
dd_diff matrix a matrix that contains the input vectors in its columns: DISPLACEMENTCalculate the displacement vector between the pair of input vectors More details ARG1The point that we are calculating the distance from=psi,phi ARG2The point that we are calculating the distance to=ref_psi,ref_phi
dd_diffTThe TRANSPOSE action with label dd_diffT calculates the following quantities: Quantity    Type    Description  
dd_diffT 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=dd_diff
dd_2The MATRIX_PRODUCT_DIAGONAL action with label dd_2 calculates the following quantities: Quantity    Type    Description  
dd_2 vector a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MATRIX_PRODUCT_DIAGONALCalculate the product of two matrices and return a vector that contains the diagonal elements of the ouptut vector More details ARGthe two vectors/matrices whose product are to be taken=dd_diff,dd_diffT
ddThe CUSTOM action with label dd calculates the following quantities: Quantity    Type    Description  
dd 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=dd_2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=dd 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
ARG1	compulsory	none	The poin that we are calculating the distance from
ARG2	compulsory	none	The point that we are calculating the distance to
SQUARED	optional	false	The squared distance should be calculated

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

Quantity	Type	Description
c	vector	the constant value that was read from the plumed input