Action: ARRANGE_POINTS

Module	dimred
Description	Usage
Arrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix.

Details and examples

Arrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix.

This action and PROJECT_POINTS are the workhorses for the implementation of SKETCHMAP that is provided within PLUMED. ARRANGE_POINTS allows you to find a set of low dimenionsional coordinates, $\{x_k\}_\textrm{min}$ , for a set of high-dimensional coordinates, $\{X_k\}$ , by minimising this stress function:

$\chi(\{x_k\}) = \sum_{i=2}^N \sum_{j=1}^i w_{ij} [ D(X_i,X_j) - d(x_i,x_j) ]^2$

The $D$ here indicates that we are calculating the dissimilarity between the point $X_i$ and $X_j$ , while the $d$ indicates that we are calculating the distance between the projections of points $i$ and $j$ . In minimising the expression above we are thus finding a set of low-dimensional projections for the high dimensional points that were input. The $w_{ij}$ is a weight that determines how important reproducing the distance between atom $i$ and $j$

The example input below illustrates how you can use ARRANGE_POINTS to project a high-dimensional representational of a trajectory in a low-dimensional space.

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

# Calcuate the instantaneous values of the three distances
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
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
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

# Collect the calulated distances for later analysis
ffThe COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Type    Description  
ff_data matrix the data that is being collected by this action
ff_logweights vector the logarithms of the weights of the data points: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and it has hidden defaults. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3
The COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Description  
ff.data the data that is being collected by this action
ff.logweights the logarithms of the weights of the data pointsff: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and uses the defaults shown here. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3  CLEAR the frequency with which data should all be deleted and restarted=0
# PLUMED interprets the command:
# ff: COLLECT_FRAMES STRIDE=1 ARG=d1,d2,d3
# as follows (Click the red comment above to revert to the short version of the input):
ff_d1The COLLECT action with label ff_d1 calculates the following quantities: Quantity    Type    Description  
ff_d1 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d1 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d2The COLLECT action with label ff_d2 calculates the following quantities: Quantity    Type    Description  
ff_d2 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d2 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d3The COLLECT action with label ff_d3 calculates the following quantities: Quantity    Type    Description  
ff_d3 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d3 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_dataThe VSTACK action with label ff_data calculates the following quantities: Quantity    Type    Description  
ff_data 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=ff_d1,ff_d2,ff_d3
ff_cweightThe CONSTANT action with label ff_cweight calculates the following quantities: Quantity    Type    Description  
ff_cweight scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=0
ff_logweightsThe COLLECT action with label ff_logweights calculates the following quantities: Quantity    Type    Description  
ff_logweights vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_cweight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_oneThe CONSTANT action with label ff_one calculates the following quantities: Quantity    Type    Description  
ff_one scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=1
ff_onesThe COLLECT action with label ff_ones calculates the following quantities: Quantity    Type    Description  
ff_ones vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_one STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
# --- End of included input --- ff_weightsThe CUSTOM action with label ff_weights calculates the following quantities: Quantity    Type    Description  
ff_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=ff_logweights FUNCthe function you wish to evaluate=exp(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Generate an initial projection of the high dimensional points using MDS
mdsThe CLASSICAL_MDS action with label mds calculates the following quantities: Quantity    Type    Description  
mds matrix the low dimensional projections for the input data points: CLASSICAL_MDSCreate a low-dimensional projection of a trajectory using the classical multidimensional This action is a shortcut. More details ARGthe arguments that you would like to make the histogram for=ff NLOW_DIMnumber of low-dimensional coordinates required=2
# PLUMED interprets the command:
# mds: CLASSICAL_MDS ARG=ff NLOW_DIM=2
# as follows (Click the red comment above to revert to the short version of the input):
ff_dataTThe TRANSPOSE action with label ff_dataT calculates the following quantities: Quantity    Type    Description  
ff_dataT 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=ff_data
mds_matThe DISSIMILARITIES action with label mds_mat calculates the following quantities: Quantity    Type    Description  
mds_mat matrix the dissimilarity matrix: DISSIMILARITIESCalculate the matrix of dissimilarities between a trajectory of atomic configurations. More details SQUARED calculate the squares of the dissimilarities (this option cannot be used with MATRIX_PRODUCT) ARGthe label of the two matrices from which the product is calculated=ff_data,ff_dataT
mds_rsumsThe MATRIX_VECTOR_PRODUCT action with label mds_rsums calculates the following quantities: Quantity    Type    Description  
mds_rsums 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=mds_mat,ff_ones
mds_nonesThe SUM action with label mds_nones calculates the following quantities: Quantity    Type    Description  
mds_nones scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_rsumsnThe CUSTOM action with label mds_rsumsn calculates the following quantities: Quantity    Type    Description  
mds_rsumsn 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=mds_rsums,mds_nones 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
mds_rsummatThe OUTER_PRODUCT action with label mds_rsummat calculates the following quantities: Quantity    Type    Description  
mds_rsummat 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=mds_rsumsn,ff_ones
mds_intThe CUSTOM action with label mds_int calculates the following quantities: Quantity    Type    Description  
mds_int 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=mds_rsummat,mds_mat FUNCthe function you wish to evaluate=-0.5*y+0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_intTThe TRANSPOSE action with label mds_intT calculates the following quantities: Quantity    Type    Description  
mds_intT 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=mds_int
mds_csumsThe MATRIX_VECTOR_PRODUCT action with label mds_csums calculates the following quantities: Quantity    Type    Description  
mds_csums 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=mds_intT,ff_ones
mds_csumsnThe CUSTOM action with label mds_csumsn calculates the following quantities: Quantity    Type    Description  
mds_csumsn 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=mds_csums,mds_nones 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
mds_csummatThe OUTER_PRODUCT action with label mds_csummat calculates the following quantities: Quantity    Type    Description  
mds_csummat 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=mds_csumsn,ff_ones
mds_cmatThe CUSTOM action with label mds_cmat calculates the following quantities: Quantity    Type    Description  
mds_cmat 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=mds_csummat,mds_intT FUNCthe function you wish to evaluate=y-x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_eigThe DIAGONALIZE action with label mds_eig calculates the following quantities: Quantity    Type    Description  
mds_eig.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
mds_eig.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
mds_eig.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
mds_eig.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=mds_cmat VECTORS the eigenvalues and vectors that you would like to calculate=1,2
mds-1The CUSTOM action with label mds-1 calculates the following quantities: Quantity    Type    Description  
mds-1 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=mds_eig.vecs-1,mds_eig.vals-1 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds-2The CUSTOM action with label mds-2 calculates the following quantities: Quantity    Type    Description  
mds-2 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=mds_eig.vecs-2,mds_eig.vals-2 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mdsThe VSTACK action with label mds calculates the following quantities: Quantity    Type    Description  
mds 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=mds-1,mds-2
# --- End of included input --- 
# Generate a matrix of w_ij values
weightsThe OUTER_PRODUCT action with label weights calculates the following quantities: Quantity    Type    Description  
weights 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=ff_weights,ff_weights
weights: 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=ff_weights,ff_weights  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y

# And produce the projections
projThe ARRANGE_POINTS action with label proj calculates the following quantities: Quantity    Type    Description  
proj.coord-1 vector the coordinates of the points in the low dimensional space  This is the 1th of these quantities
proj.coord-2 vector the coordinates of the points in the low dimensional space  This is the 2th of these quantities: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action has hidden defaults. More details ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=weights
proj: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action uses the defaults shown here. More details ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=weights  MINTYPE the method to use for the minimisation=conjgrad CGTOL the tolerance for the conjugate gradient minimization=1E-6 MAXITER maximum number of optimization cycles for optimisation algorithms=1000

# And print the projections to a file
DUMPVECTORPrint a vector to a file More details ARGthe labels of vectors/matrices that should be output in the file=proj.* FILE the file on which to write the vetors=colvar

Here projections are generated once at the end of the trajectory and are output to a file called colvar. Initial projections of all the points are generated using CLASSICAL_MDS. A better optimisation of the stress function above is then obtained by using the conjugate gradient algorithm. The MINTYPE option in ARRANGE_POINTS allows you to specify whether conjugate gradient, the smacof algorithm or the pointwise global optimisation algorithm that was discussed in the original paper on sketch-map that is referenced below are used to optimise the stress function.

Using RMSD distances

If you wish to use the coordinates of the atoms directly when computing the dissimilarities in the high dimensional space you use an input similar to the one shown below:

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

# Collect the positions of the atoms for later analysis
ffThe COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Type    Description  
ff_data matrix the data that is being collected by this action
ff_logweights vector the logarithms of the weights of the data points: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and it has hidden defaults. More details STRIDE the frequency with which data should be stored for analysis=1 ATOMSlist of atomic positions that you would like to collect and store for later analysis=1-10
The COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Description  
ff.data the data that is being collected by this action
ff.logweights the logarithms of the weights of the data pointsff: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and uses the defaults shown here. More details STRIDE the frequency with which data should be stored for analysis=1 ATOMSlist of atomic positions that you would like to collect and store for later analysis=1-10  CLEAR the frequency with which data should all be deleted and restarted=0 ALIGN if storing atoms how would you like the alignment to be done can be SIMPLE/OPTIMAL=OPTIMAL
# PLUMED interprets the command:
# ff: COLLECT_FRAMES STRIDE=1 ATOMS=1-10
# as follows (Click the red comment above to revert to the short version of the input):
ff_getposxThe POSITION action with label ff_getposx calculates the following quantities: Quantity    Type    Description  
ff_getposx.x vector the x-component of the atom position
ff_getposx.y vector the y-component of the atom position
ff_getposx.z vector the z-component of the atom position: POSITIONCalculate the components of the position of an atom or atoms. More details ATOMSthe atom numbers that you would like to use the positions of=1-10
ff_getposThe CONCATENATE action with label ff_getpos calculates the following quantities: Quantity    Type    Description  
ff_getpos vector the concatenated vector/matrix that was constructed from the input values: CONCATENATEJoin vectors or matrices together More details ARGthe values that should be concatenated together to form the output vector=ff_getposx.x,ff_getposx.y,ff_getposx.z
ff_cposxThe MEAN action with label ff_cposx calculates the following quantities: Quantity    Type    Description  
ff_cposx scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_getposx.x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ff_cposyThe MEAN action with label ff_cposy calculates the following quantities: Quantity    Type    Description  
ff_cposy scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_getposx.y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ff_cposzThe MEAN action with label ff_cposz calculates the following quantities: Quantity    Type    Description  
ff_cposz scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_getposx.z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ff_refxThe CUSTOM action with label ff_refx calculates the following quantities: Quantity    Type    Description  
ff_refx 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=ff_getposx.x,ff_cposx 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
ff_refyThe CUSTOM action with label ff_refy calculates the following quantities: Quantity    Type    Description  
ff_refy 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=ff_getposx.y,ff_cposy 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
ff_refzThe CUSTOM action with label ff_refz calculates the following quantities: Quantity    Type    Description  
ff_refz 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=ff_getposx.z,ff_cposz 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
ff_refThe CONCATENATE action with label ff_ref calculates the following quantities: Quantity    Type    Description  
ff_ref vector the concatenated vector/matrix that was constructed from the input values: CONCATENATEJoin vectors or matrices together More details ARGthe values that should be concatenated together to form the output vector=ff_refx,ff_refy,ff_refz
ff_refposThe COLLECT action with label ff_refpos calculates the following quantities: Quantity    Type    Description  
ff_refpos matrix the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details TYPE required if you are collecting an object with rank>0=matrix ARGthe label of the value whose time series is being stored for later analysis=ff_ref STRIDE the frequency with which the data should be collected and added to the quantity being averaged=0 CLEAR the frequency with which to clear all the accumulated data=0
ff_refposTThe TRANSPOSE action with label ff_refposT calculates the following quantities: Quantity    Type    Description  
ff_refposT 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=ff_refpos
ff_rmsdThe RMSD action with label ff_rmsd calculates the following quantities: Quantity    Type    Description  
ff_rmsd.dist scalar the RMSD distance the atoms have moved
ff_rmsd.disp vector the vector of displacements for the atoms: RMSD_VECTOR More details ARGthe labels of two actions that you are calculating the RMSD between=ff_getpos,ff_refpos DISPLACEMENT Calculate the vector of displacements instead of the length of this vector SQUARED  This should be set if you want mean squared displacement instead of RMSD  TYPE the manner in which RMSD alignment is performed=OPTIMAL
ff_fposThe COMBINE action with label ff_fpos calculates the following quantities: Quantity    Type    Description  
ff_fpos vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ff_refposT,ff_rmsd.disp PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ff_dataThe COLLECT action with label ff_data calculates the following quantities: Quantity    Type    Description  
ff_data matrix the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details TYPE required if you are collecting an object with rank>0=matrix ARGthe label of the value whose time series is being stored for later analysis=ff_fpos STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_cweightThe CONSTANT action with label ff_cweight calculates the following quantities: Quantity    Type    Description  
ff_cweight scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=0
ff_logweightsThe COLLECT action with label ff_logweights calculates the following quantities: Quantity    Type    Description  
ff_logweights vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_cweight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_oneThe CONSTANT action with label ff_one calculates the following quantities: Quantity    Type    Description  
ff_one scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=1
ff_onesThe COLLECT action with label ff_ones calculates the following quantities: Quantity    Type    Description  
ff_ones vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_one STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
# --- End of included input --- 
# Generate an initial projection of the high dimensional points using MDS
mdsThe CLASSICAL_MDS action with label mds calculates the following quantities: Quantity    Type    Description  
mds matrix the low dimensional projections for the input data points: CLASSICAL_MDSCreate a low-dimensional projection of a trajectory using the classical multidimensional This action is a shortcut. More details ARGthe arguments that you would like to make the histogram for=ff NLOW_DIMnumber of low-dimensional coordinates required=2
# PLUMED interprets the command:
# mds: CLASSICAL_MDS ARG=ff NLOW_DIM=2
# as follows (Click the red comment above to revert to the short version of the input):
ff_dataTThe TRANSPOSE action with label ff_dataT calculates the following quantities: Quantity    Type    Description  
ff_dataT 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=ff_data
mds_matThe DISSIMILARITIES action with label mds_mat calculates the following quantities: Quantity    Type    Description  
mds_mat matrix the dissimilarity matrix: DISSIMILARITIESCalculate the matrix of dissimilarities between a trajectory of atomic configurations. More details SQUARED calculate the squares of the dissimilarities (this option cannot be used with MATRIX_PRODUCT) ARGthe label of the two matrices from which the product is calculated=ff_data,ff_dataT
mds_rsumsThe MATRIX_VECTOR_PRODUCT action with label mds_rsums calculates the following quantities: Quantity    Type    Description  
mds_rsums 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=mds_mat,ff_ones
mds_nonesThe SUM action with label mds_nones calculates the following quantities: Quantity    Type    Description  
mds_nones scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_rsumsnThe CUSTOM action with label mds_rsumsn calculates the following quantities: Quantity    Type    Description  
mds_rsumsn 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=mds_rsums,mds_nones 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
mds_rsummatThe OUTER_PRODUCT action with label mds_rsummat calculates the following quantities: Quantity    Type    Description  
mds_rsummat 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=mds_rsumsn,ff_ones
mds_intThe CUSTOM action with label mds_int calculates the following quantities: Quantity    Type    Description  
mds_int 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=mds_rsummat,mds_mat FUNCthe function you wish to evaluate=-0.5*y+0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_intTThe TRANSPOSE action with label mds_intT calculates the following quantities: Quantity    Type    Description  
mds_intT 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=mds_int
mds_csumsThe MATRIX_VECTOR_PRODUCT action with label mds_csums calculates the following quantities: Quantity    Type    Description  
mds_csums 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=mds_intT,ff_ones
mds_csumsnThe CUSTOM action with label mds_csumsn calculates the following quantities: Quantity    Type    Description  
mds_csumsn 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=mds_csums,mds_nones 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
mds_csummatThe OUTER_PRODUCT action with label mds_csummat calculates the following quantities: Quantity    Type    Description  
mds_csummat 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=mds_csumsn,ff_ones
mds_cmatThe CUSTOM action with label mds_cmat calculates the following quantities: Quantity    Type    Description  
mds_cmat 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=mds_csummat,mds_intT FUNCthe function you wish to evaluate=y-x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_eigThe DIAGONALIZE action with label mds_eig calculates the following quantities: Quantity    Type    Description  
mds_eig.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
mds_eig.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
mds_eig.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
mds_eig.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=mds_cmat VECTORS the eigenvalues and vectors that you would like to calculate=1,2
mds-1The CUSTOM action with label mds-1 calculates the following quantities: Quantity    Type    Description  
mds-1 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=mds_eig.vecs-1,mds_eig.vals-1 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds-2The CUSTOM action with label mds-2 calculates the following quantities: Quantity    Type    Description  
mds-2 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=mds_eig.vecs-2,mds_eig.vals-2 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mdsThe VSTACK action with label mds calculates the following quantities: Quantity    Type    Description  
mds 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=mds-1,mds-2
# --- End of included input --- ff_weightsThe CUSTOM action with label ff_weights calculates the following quantities: Quantity    Type    Description  
ff_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=ff_logweights FUNCthe function you wish to evaluate=exp(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Generate a matrix of w_ij values
weightsThe OUTER_PRODUCT action with label weights calculates the following quantities: Quantity    Type    Description  
weights 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=ff_weights,ff_weights
weights: 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=ff_weights,ff_weights  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y

# And produce the projections
projThe ARRANGE_POINTS action with label proj calculates the following quantities: Quantity    Type    Description  
proj.coord-1 vector the coordinates of the points in the low dimensional space  This is the 1th of these quantities
proj.coord-2 vector the coordinates of the points in the low dimensional space  This is the 2th of these quantities: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action has hidden defaults. More details ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=weights
proj: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action uses the defaults shown here. More details ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=weights  MINTYPE the method to use for the minimisation=conjgrad CGTOL the tolerance for the conjugate gradient minimization=1E-6 MAXITER maximum number of optimization cycles for optimisation algorithms=1000

# And print the projections to a file
DUMPVECTORPrint a vector to a file More details ARGthe labels of vectors/matrices that should be output in the file=proj.* FILE the file on which to write the vetors=colvar

The dissimilarities between the atomic configurations here are computed as RMSD distances between atomic configurations.

Using transformed distances

In SKETCHMAP the stress function that is minimised is not the one given above. Instead of seeking to generate a projection, in which the distances between the projections are the same as the dissimilarities between the high-dimensional coordinates, the dissimilarities and distances are transformed by functions as illustrated below:

$\chi(\{x_k\}) = \sum_{i=2}^N \sum_{j=1}^i w_{ij} [ F[D(X_i,X_j)] - f[d(x_i,x_j)] ]^2$

The two functions $F$ and $f$ in this expression are usually different as you can see in the input below:

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

# Calcuate the instantaneous values of the three distances
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
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
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

# Collect the calulated distances for later analysis
ffThe COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Type    Description  
ff_data matrix the data that is being collected by this action
ff_logweights vector the logarithms of the weights of the data points: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and it has hidden defaults. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3
The COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Description  
ff.data the data that is being collected by this action
ff.logweights the logarithms of the weights of the data pointsff: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and uses the defaults shown here. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3  CLEAR the frequency with which data should all be deleted and restarted=0
# PLUMED interprets the command:
# ff: COLLECT_FRAMES STRIDE=1 ARG=d1,d2,d3
# as follows (Click the red comment above to revert to the short version of the input):
ff_d1The COLLECT action with label ff_d1 calculates the following quantities: Quantity    Type    Description  
ff_d1 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d1 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d2The COLLECT action with label ff_d2 calculates the following quantities: Quantity    Type    Description  
ff_d2 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d2 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d3The COLLECT action with label ff_d3 calculates the following quantities: Quantity    Type    Description  
ff_d3 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d3 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_dataThe VSTACK action with label ff_data calculates the following quantities: Quantity    Type    Description  
ff_data 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=ff_d1,ff_d2,ff_d3
ff_cweightThe CONSTANT action with label ff_cweight calculates the following quantities: Quantity    Type    Description  
ff_cweight scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=0
ff_logweightsThe COLLECT action with label ff_logweights calculates the following quantities: Quantity    Type    Description  
ff_logweights vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_cweight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_oneThe CONSTANT action with label ff_one calculates the following quantities: Quantity    Type    Description  
ff_one scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=1
ff_onesThe COLLECT action with label ff_ones calculates the following quantities: Quantity    Type    Description  
ff_ones vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_one STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
# --- End of included input --- ff_weightsThe CUSTOM action with label ff_weights calculates the following quantities: Quantity    Type    Description  
ff_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=ff_logweights FUNCthe function you wish to evaluate=exp(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Generate an initial projection of the high dimensional points using MDS
mdsThe CLASSICAL_MDS action with label mds calculates the following quantities: Quantity    Type    Description  
mds matrix the low dimensional projections for the input data points: CLASSICAL_MDSCreate a low-dimensional projection of a trajectory using the classical multidimensional This action is a shortcut. More details ARGthe arguments that you would like to make the histogram for=ff NLOW_DIMnumber of low-dimensional coordinates required=2
# PLUMED interprets the command:
# mds: CLASSICAL_MDS ARG=ff NLOW_DIM=2
# as follows (Click the red comment above to revert to the short version of the input):
ff_dataTThe TRANSPOSE action with label ff_dataT calculates the following quantities: Quantity    Type    Description  
ff_dataT 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=ff_data
mds_matThe DISSIMILARITIES action with label mds_mat calculates the following quantities: Quantity    Type    Description  
mds_mat matrix the dissimilarity matrix: DISSIMILARITIESCalculate the matrix of dissimilarities between a trajectory of atomic configurations. More details SQUARED calculate the squares of the dissimilarities (this option cannot be used with MATRIX_PRODUCT) ARGthe label of the two matrices from which the product is calculated=ff_data,ff_dataT
mds_rsumsThe MATRIX_VECTOR_PRODUCT action with label mds_rsums calculates the following quantities: Quantity    Type    Description  
mds_rsums 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=mds_mat,ff_ones
mds_nonesThe SUM action with label mds_nones calculates the following quantities: Quantity    Type    Description  
mds_nones scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_rsumsnThe CUSTOM action with label mds_rsumsn calculates the following quantities: Quantity    Type    Description  
mds_rsumsn 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=mds_rsums,mds_nones 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
mds_rsummatThe OUTER_PRODUCT action with label mds_rsummat calculates the following quantities: Quantity    Type    Description  
mds_rsummat 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=mds_rsumsn,ff_ones
mds_intThe CUSTOM action with label mds_int calculates the following quantities: Quantity    Type    Description  
mds_int 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=mds_rsummat,mds_mat FUNCthe function you wish to evaluate=-0.5*y+0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_intTThe TRANSPOSE action with label mds_intT calculates the following quantities: Quantity    Type    Description  
mds_intT 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=mds_int
mds_csumsThe MATRIX_VECTOR_PRODUCT action with label mds_csums calculates the following quantities: Quantity    Type    Description  
mds_csums 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=mds_intT,ff_ones
mds_csumsnThe CUSTOM action with label mds_csumsn calculates the following quantities: Quantity    Type    Description  
mds_csumsn 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=mds_csums,mds_nones 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
mds_csummatThe OUTER_PRODUCT action with label mds_csummat calculates the following quantities: Quantity    Type    Description  
mds_csummat 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=mds_csumsn,ff_ones
mds_cmatThe CUSTOM action with label mds_cmat calculates the following quantities: Quantity    Type    Description  
mds_cmat 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=mds_csummat,mds_intT FUNCthe function you wish to evaluate=y-x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_eigThe DIAGONALIZE action with label mds_eig calculates the following quantities: Quantity    Type    Description  
mds_eig.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
mds_eig.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
mds_eig.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
mds_eig.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=mds_cmat VECTORS the eigenvalues and vectors that you would like to calculate=1,2
mds-1The CUSTOM action with label mds-1 calculates the following quantities: Quantity    Type    Description  
mds-1 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=mds_eig.vecs-1,mds_eig.vals-1 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds-2The CUSTOM action with label mds-2 calculates the following quantities: Quantity    Type    Description  
mds-2 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=mds_eig.vecs-2,mds_eig.vals-2 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mdsThe VSTACK action with label mds calculates the following quantities: Quantity    Type    Description  
mds 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=mds-1,mds-2
# --- End of included input --- 
# Generate a matrix of w_ij values
weightsThe OUTER_PRODUCT action with label weights calculates the following quantities: Quantity    Type    Description  
weights 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=ff_weights,ff_weights
weights: 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=ff_weights,ff_weights  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y

# Transform the dissimilarities with the function F
fedThe MORE_THAN action with label fed calculates the following quantities: Quantity    Type    Description  
fed matrix the matrix 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 matrix: 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=mds_mat SQUARED is the input quantity the square of the value that you would like to apply the switching function to SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={SMAP R_0=4 A=3 B=2}

# And produce the projections
projThe ARRANGE_POINTS action with label proj calculates the following quantities: Quantity    Type    Description  
proj.coord-1 vector the coordinates of the points in the low dimensional space  This is the 1th of these quantities
proj.coord-2 vector the coordinates of the points in the low dimensional space  This is the 2th of these quantities: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action has hidden defaults. More details ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=fed WEIGHTS1the matrix with the weights of the target quantities=weights FUNC1a function that is applied on the distances between the points in the low dimensional space={SMAP R_0=4 A=1 B=2}
proj: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action uses the defaults shown here. More details ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=fed WEIGHTS1the matrix with the weights of the target quantities=weights FUNC1a function that is applied on the distances between the points in the low dimensional space={SMAP R_0=4 A=1 B=2}  MINTYPE the method to use for the minimisation=conjgrad CGTOL the tolerance for the conjugate gradient minimization=1E-6 MAXITER maximum number of optimization cycles for optimisation algorithms=1000

# And print the projections to a file
DUMPVECTORPrint a vector to a file More details ARGthe labels of vectors/matrices that should be output in the file=proj.* FILE the file on which to write the vetors=colvar

In the input above the function, $F$ , that is applied on the dissimilarities is implemented using a MORE_THAN action. The function, $f$ , that is applied on the distances in the low-dimensional space is specified using the FUNC keyword that is input to ARRANGE_POINTS.

Using multiple targets

At its most complex this action allows you to minimise a stress function such as the one below:

$\chi(\{x_k\}) = \sum_{i=2}^N \sum_{j=1}^i \sum_{n=1}^M w_{nij} [ F_n[D(X_i,X_j)] - f_n[d(x_i,x_j)] ]^2$

The input below shows how this can be implemted within PLUMED:

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

# Calcuate the instantaneous values of the three distances
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
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
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

# Collect the calulated distances for later analysis
ffThe COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Type    Description  
ff_data matrix the data that is being collected by this action
ff_logweights vector the logarithms of the weights of the data points: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and it has hidden defaults. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3
The COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Description  
ff.data the data that is being collected by this action
ff.logweights the logarithms of the weights of the data pointsff: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and uses the defaults shown here. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3  CLEAR the frequency with which data should all be deleted and restarted=0
# PLUMED interprets the command:
# ff: COLLECT_FRAMES STRIDE=1 ARG=d1,d2,d3
# as follows (Click the red comment above to revert to the short version of the input):
ff_d1The COLLECT action with label ff_d1 calculates the following quantities: Quantity    Type    Description  
ff_d1 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d1 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d2The COLLECT action with label ff_d2 calculates the following quantities: Quantity    Type    Description  
ff_d2 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d2 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d3The COLLECT action with label ff_d3 calculates the following quantities: Quantity    Type    Description  
ff_d3 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d3 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_dataThe VSTACK action with label ff_data calculates the following quantities: Quantity    Type    Description  
ff_data 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=ff_d1,ff_d2,ff_d3
ff_cweightThe CONSTANT action with label ff_cweight calculates the following quantities: Quantity    Type    Description  
ff_cweight scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=0
ff_logweightsThe COLLECT action with label ff_logweights calculates the following quantities: Quantity    Type    Description  
ff_logweights vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_cweight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_oneThe CONSTANT action with label ff_one calculates the following quantities: Quantity    Type    Description  
ff_one scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=1
ff_onesThe COLLECT action with label ff_ones calculates the following quantities: Quantity    Type    Description  
ff_ones vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_one STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
# --- End of included input --- ff_weightsThe CUSTOM action with label ff_weights calculates the following quantities: Quantity    Type    Description  
ff_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=ff_logweights FUNCthe function you wish to evaluate=exp(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Generate an initial projection of the high dimensional points using MDS
mdsThe CLASSICAL_MDS action with label mds calculates the following quantities: Quantity    Type    Description  
mds matrix the low dimensional projections for the input data points: CLASSICAL_MDSCreate a low-dimensional projection of a trajectory using the classical multidimensional This action is a shortcut. More details ARGthe arguments that you would like to make the histogram for=ff NLOW_DIMnumber of low-dimensional coordinates required=2
# PLUMED interprets the command:
# mds: CLASSICAL_MDS ARG=ff NLOW_DIM=2
# as follows (Click the red comment above to revert to the short version of the input):
ff_dataTThe TRANSPOSE action with label ff_dataT calculates the following quantities: Quantity    Type    Description  
ff_dataT 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=ff_data
mds_matThe DISSIMILARITIES action with label mds_mat calculates the following quantities: Quantity    Type    Description  
mds_mat matrix the dissimilarity matrix: DISSIMILARITIESCalculate the matrix of dissimilarities between a trajectory of atomic configurations. More details SQUARED calculate the squares of the dissimilarities (this option cannot be used with MATRIX_PRODUCT) ARGthe label of the two matrices from which the product is calculated=ff_data,ff_dataT
mds_rsumsThe MATRIX_VECTOR_PRODUCT action with label mds_rsums calculates the following quantities: Quantity    Type    Description  
mds_rsums 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=mds_mat,ff_ones
mds_nonesThe SUM action with label mds_nones calculates the following quantities: Quantity    Type    Description  
mds_nones scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_rsumsnThe CUSTOM action with label mds_rsumsn calculates the following quantities: Quantity    Type    Description  
mds_rsumsn 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=mds_rsums,mds_nones 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
mds_rsummatThe OUTER_PRODUCT action with label mds_rsummat calculates the following quantities: Quantity    Type    Description  
mds_rsummat 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=mds_rsumsn,ff_ones
mds_intThe CUSTOM action with label mds_int calculates the following quantities: Quantity    Type    Description  
mds_int 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=mds_rsummat,mds_mat FUNCthe function you wish to evaluate=-0.5*y+0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_intTThe TRANSPOSE action with label mds_intT calculates the following quantities: Quantity    Type    Description  
mds_intT 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=mds_int
mds_csumsThe MATRIX_VECTOR_PRODUCT action with label mds_csums calculates the following quantities: Quantity    Type    Description  
mds_csums 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=mds_intT,ff_ones
mds_csumsnThe CUSTOM action with label mds_csumsn calculates the following quantities: Quantity    Type    Description  
mds_csumsn 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=mds_csums,mds_nones 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
mds_csummatThe OUTER_PRODUCT action with label mds_csummat calculates the following quantities: Quantity    Type    Description  
mds_csummat 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=mds_csumsn,ff_ones
mds_cmatThe CUSTOM action with label mds_cmat calculates the following quantities: Quantity    Type    Description  
mds_cmat 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=mds_csummat,mds_intT FUNCthe function you wish to evaluate=y-x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_eigThe DIAGONALIZE action with label mds_eig calculates the following quantities: Quantity    Type    Description  
mds_eig.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
mds_eig.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
mds_eig.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
mds_eig.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=mds_cmat VECTORS the eigenvalues and vectors that you would like to calculate=1,2
mds-1The CUSTOM action with label mds-1 calculates the following quantities: Quantity    Type    Description  
mds-1 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=mds_eig.vecs-1,mds_eig.vals-1 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds-2The CUSTOM action with label mds-2 calculates the following quantities: Quantity    Type    Description  
mds-2 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=mds_eig.vecs-2,mds_eig.vals-2 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mdsThe VSTACK action with label mds calculates the following quantities: Quantity    Type    Description  
mds 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=mds-1,mds-2
# --- End of included input --- 
# Generate a matrix of w_ij values
weightsThe OUTER_PRODUCT action with label weights calculates the following quantities: Quantity    Type    Description  
weights 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=ff_weights,ff_weights
weights: 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=ff_weights,ff_weights  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y
w1The CUSTOM action with label w1 calculates the following quantities: Quantity    Type    Description  
w1 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=weights FUNCthe function you wish to evaluate=0.3*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
w2The CUSTOM action with label w2 calculates the following quantities: Quantity    Type    Description  
w2 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=weights FUNCthe function you wish to evaluate=(1-0.3)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Transform the dissimilarities with the function F
fedThe MORE_THAN action with label fed calculates the following quantities: Quantity    Type    Description  
fed matrix the matrix 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 matrix: 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=mds_mat SQUARED is the input quantity the square of the value that you would like to apply the switching function to SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={SMAP R_0=4 A=3 B=2}

# And produce the projections
projThe ARRANGE_POINTS action with label proj calculates the following quantities: Quantity    Type    Description  
proj.coord-1 vector the coordinates of the points in the low dimensional space  This is the 1th of these quantities
proj.coord-2 vector the coordinates of the points in the low dimensional space  This is the 2th of these quantities: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action has hidden defaults. More details ...
   ARGthe initial positions for the projections=mds-1,mds-2
   TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=w1 FUNC1a function that is applied on the distances between the points in the low dimensional space={CUSTOM FUNC=1-sqrt(x2) R_0=1.0}
   TARGET2the matrix of target quantities that you would like to match=fed WEIGHTS2the matrix with the weights of the target quantities=w2 FUNC2a function that is applied on the distances between the points in the low dimensional space={SMAP R_0=4 A=1 B=2}
...
proj: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action uses the defaults shown here. More details ...
   ARGthe initial positions for the projections=mds-1,mds-2
   TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=w1 FUNC1a function that is applied on the distances between the points in the low dimensional space={CUSTOM FUNC=1-sqrt(x2) R_0=1.0}
   TARGET2the matrix of target quantities that you would like to match=fed WEIGHTS2the matrix with the weights of the target quantities=w2 FUNC2a function that is applied on the distances between the points in the low dimensional space={SMAP R_0=4 A=1 B=2}
 MINTYPE the method to use for the minimisation=conjgrad CGTOL the tolerance for the conjugate gradient minimization=1E-6 MAXITER maximum number of optimization cycles for optimisation algorithms=1000
...

# And print the projections to a file
DUMPVECTORPrint a vector to a file More details ARGthe labels of vectors/matrices that should be output in the file=proj.* FILE the file on which to write the vetors=colvar

Here the sum over $M$ in the expression above has two terms. In the first of these terms $F_1$ is the identity so the input for TARGET1 is the output from EUCLIDEAN_DISTANCE. $f_1$ is similarly the identity. To implement the identity here we use the input to FUNC1 shown above. The input to this function is the input for one of the switching functions described in the documentation for LESS_THAN. What we compute for the transformed distance is $1-s(d)$ where $s(d)$ is the switching function that is specified in input. Consequently, applying the function 1-sqrt(x2) returns the distance.

The second term in our sum over $M$ in the input above has the dissimilarities and distances transformed by the functions that we introduced in the previous section.

Choosing an optimization algorithm

The inputs above use conjugate gradients to optimize the stress function and to find the low dimensional projection. If you wish you can change the algorithm used to optimize the sketch-map function. For example, in the input below the smacof algorithm is used in place of conjugate gradients.

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

# Calcuate the instantaneous values of the three distances
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
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
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

# Collect the calulated distances for later analysis
ffThe COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Type    Description  
ff_data matrix the data that is being collected by this action
ff_logweights vector the logarithms of the weights of the data points: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and it has hidden defaults. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3
The COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Description  
ff.data the data that is being collected by this action
ff.logweights the logarithms of the weights of the data pointsff: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and uses the defaults shown here. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3  CLEAR the frequency with which data should all be deleted and restarted=0
# PLUMED interprets the command:
# ff: COLLECT_FRAMES STRIDE=1 ARG=d1,d2,d3
# as follows (Click the red comment above to revert to the short version of the input):
ff_d1The COLLECT action with label ff_d1 calculates the following quantities: Quantity    Type    Description  
ff_d1 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d1 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d2The COLLECT action with label ff_d2 calculates the following quantities: Quantity    Type    Description  
ff_d2 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d2 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d3The COLLECT action with label ff_d3 calculates the following quantities: Quantity    Type    Description  
ff_d3 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d3 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_dataThe VSTACK action with label ff_data calculates the following quantities: Quantity    Type    Description  
ff_data 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=ff_d1,ff_d2,ff_d3
ff_cweightThe CONSTANT action with label ff_cweight calculates the following quantities: Quantity    Type    Description  
ff_cweight scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=0
ff_logweightsThe COLLECT action with label ff_logweights calculates the following quantities: Quantity    Type    Description  
ff_logweights vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_cweight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_oneThe CONSTANT action with label ff_one calculates the following quantities: Quantity    Type    Description  
ff_one scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=1
ff_onesThe COLLECT action with label ff_ones calculates the following quantities: Quantity    Type    Description  
ff_ones vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_one STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
# --- End of included input --- ff_weightsThe CUSTOM action with label ff_weights calculates the following quantities: Quantity    Type    Description  
ff_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=ff_logweights FUNCthe function you wish to evaluate=exp(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Generate an initial projection of the high dimensional points using MDS
mdsThe CLASSICAL_MDS action with label mds calculates the following quantities: Quantity    Type    Description  
mds matrix the low dimensional projections for the input data points: CLASSICAL_MDSCreate a low-dimensional projection of a trajectory using the classical multidimensional This action is a shortcut. More details ARGthe arguments that you would like to make the histogram for=ff NLOW_DIMnumber of low-dimensional coordinates required=2
# PLUMED interprets the command:
# mds: CLASSICAL_MDS ARG=ff NLOW_DIM=2
# as follows (Click the red comment above to revert to the short version of the input):
ff_dataTThe TRANSPOSE action with label ff_dataT calculates the following quantities: Quantity    Type    Description  
ff_dataT 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=ff_data
mds_matThe DISSIMILARITIES action with label mds_mat calculates the following quantities: Quantity    Type    Description  
mds_mat matrix the dissimilarity matrix: DISSIMILARITIESCalculate the matrix of dissimilarities between a trajectory of atomic configurations. More details SQUARED calculate the squares of the dissimilarities (this option cannot be used with MATRIX_PRODUCT) ARGthe label of the two matrices from which the product is calculated=ff_data,ff_dataT
mds_rsumsThe MATRIX_VECTOR_PRODUCT action with label mds_rsums calculates the following quantities: Quantity    Type    Description  
mds_rsums 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=mds_mat,ff_ones
mds_nonesThe SUM action with label mds_nones calculates the following quantities: Quantity    Type    Description  
mds_nones scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_rsumsnThe CUSTOM action with label mds_rsumsn calculates the following quantities: Quantity    Type    Description  
mds_rsumsn 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=mds_rsums,mds_nones 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
mds_rsummatThe OUTER_PRODUCT action with label mds_rsummat calculates the following quantities: Quantity    Type    Description  
mds_rsummat 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=mds_rsumsn,ff_ones
mds_intThe CUSTOM action with label mds_int calculates the following quantities: Quantity    Type    Description  
mds_int 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=mds_rsummat,mds_mat FUNCthe function you wish to evaluate=-0.5*y+0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_intTThe TRANSPOSE action with label mds_intT calculates the following quantities: Quantity    Type    Description  
mds_intT 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=mds_int
mds_csumsThe MATRIX_VECTOR_PRODUCT action with label mds_csums calculates the following quantities: Quantity    Type    Description  
mds_csums 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=mds_intT,ff_ones
mds_csumsnThe CUSTOM action with label mds_csumsn calculates the following quantities: Quantity    Type    Description  
mds_csumsn 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=mds_csums,mds_nones 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
mds_csummatThe OUTER_PRODUCT action with label mds_csummat calculates the following quantities: Quantity    Type    Description  
mds_csummat 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=mds_csumsn,ff_ones
mds_cmatThe CUSTOM action with label mds_cmat calculates the following quantities: Quantity    Type    Description  
mds_cmat 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=mds_csummat,mds_intT FUNCthe function you wish to evaluate=y-x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_eigThe DIAGONALIZE action with label mds_eig calculates the following quantities: Quantity    Type    Description  
mds_eig.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
mds_eig.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
mds_eig.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
mds_eig.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=mds_cmat VECTORS the eigenvalues and vectors that you would like to calculate=1,2
mds-1The CUSTOM action with label mds-1 calculates the following quantities: Quantity    Type    Description  
mds-1 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=mds_eig.vecs-1,mds_eig.vals-1 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds-2The CUSTOM action with label mds-2 calculates the following quantities: Quantity    Type    Description  
mds-2 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=mds_eig.vecs-2,mds_eig.vals-2 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mdsThe VSTACK action with label mds calculates the following quantities: Quantity    Type    Description  
mds 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=mds-1,mds-2
# --- End of included input --- 
# Generate a matrix of w_ij values
weightsThe OUTER_PRODUCT action with label weights calculates the following quantities: Quantity    Type    Description  
weights 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=ff_weights,ff_weights
weights: 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=ff_weights,ff_weights  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y

# And produce the projections
projThe ARRANGE_POINTS action with label proj calculates the following quantities: Quantity    Type    Description  
proj.coord-1 vector the coordinates of the points in the low dimensional space  This is the 1th of these quantities
proj.coord-2 vector the coordinates of the points in the low dimensional space  This is the 2th of these quantities: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action has hidden defaults. More details ...
  ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=weights
  MINTYPE the method to use for the minimisation=smacof
...
proj: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action uses the defaults shown here. More details ...
  ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat WEIGHTS1the matrix with the weights of the target quantities=weights
  MINTYPE the method to use for the minimisation=smacof
 SMACTOL the tolerance for the smacof algorithm=1E-4 SMACREG this is used to ensure that we don't divide by zero when updating weights for SMACOF algorithm=0.001 MAXITER maximum number of optimization cycles for optimisation algorithms=1000
...

# And print the projections to a file
DUMPVECTORPrint a vector to a file More details ARGthe labels of vectors/matrices that should be output in the file=proj.* FILE the file on which to write the vetors=colvar

Alternatively, the following example uses a combination of conjugate gradients and a pointwise global optimisation to optimize the stress function

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

# Calcuate the instantaneous values of the three distances
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
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
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

# Collect the calulated distances for later analysis
ffThe COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Type    Description  
ff_data matrix the data that is being collected by this action
ff_logweights vector the logarithms of the weights of the data points: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and it has hidden defaults. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3
The COLLECT_FRAMES action with label ff calculates the following quantities: Quantity    Description  
ff.data the data that is being collected by this action
ff.logweights the logarithms of the weights of the data pointsff: COLLECT_FRAMESCollect atomic positions or argument values from the trajectory for later analysis This action is a shortcut and uses the defaults shown here. More details STRIDE the frequency with which data should be stored for analysis=1 ARGthe labels of the values whose time series you would like to collect for later analysis=d1,d2,d3  CLEAR the frequency with which data should all be deleted and restarted=0
# PLUMED interprets the command:
# ff: COLLECT_FRAMES STRIDE=1 ARG=d1,d2,d3
# as follows (Click the red comment above to revert to the short version of the input):
ff_d1The COLLECT action with label ff_d1 calculates the following quantities: Quantity    Type    Description  
ff_d1 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d1 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d2The COLLECT action with label ff_d2 calculates the following quantities: Quantity    Type    Description  
ff_d2 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d2 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_d3The COLLECT action with label ff_d3 calculates the following quantities: Quantity    Type    Description  
ff_d3 vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=d3 STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_dataThe VSTACK action with label ff_data calculates the following quantities: Quantity    Type    Description  
ff_data 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=ff_d1,ff_d2,ff_d3
ff_cweightThe CONSTANT action with label ff_cweight calculates the following quantities: Quantity    Type    Description  
ff_cweight scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=0
ff_logweightsThe COLLECT action with label ff_logweights calculates the following quantities: Quantity    Type    Description  
ff_logweights vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_cweight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
ff_oneThe CONSTANT action with label ff_one calculates the following quantities: Quantity    Type    Description  
ff_one scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=1
ff_onesThe COLLECT action with label ff_ones calculates the following quantities: Quantity    Type    Description  
ff_ones vector the time series for the input quantity: COLLECTCollect data from the trajectory for later analysis More details ARGthe label of the value whose time series is being stored for later analysis=ff_one STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0
# --- End of included input --- ff_weightsThe CUSTOM action with label ff_weights calculates the following quantities: Quantity    Type    Description  
ff_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=ff_logweights FUNCthe function you wish to evaluate=exp(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

# Generate an initial projection of the high dimensional points using MDS
mdsThe CLASSICAL_MDS action with label mds calculates the following quantities: Quantity    Type    Description  
mds matrix the low dimensional projections for the input data points: CLASSICAL_MDSCreate a low-dimensional projection of a trajectory using the classical multidimensional This action is a shortcut. More details ARGthe arguments that you would like to make the histogram for=ff NLOW_DIMnumber of low-dimensional coordinates required=2
# PLUMED interprets the command:
# mds: CLASSICAL_MDS ARG=ff NLOW_DIM=2
# as follows (Click the red comment above to revert to the short version of the input):
ff_dataTThe TRANSPOSE action with label ff_dataT calculates the following quantities: Quantity    Type    Description  
ff_dataT 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=ff_data
mds_matThe DISSIMILARITIES action with label mds_mat calculates the following quantities: Quantity    Type    Description  
mds_mat matrix the dissimilarity matrix: DISSIMILARITIESCalculate the matrix of dissimilarities between a trajectory of atomic configurations. More details SQUARED calculate the squares of the dissimilarities (this option cannot be used with MATRIX_PRODUCT) ARGthe label of the two matrices from which the product is calculated=ff_data,ff_dataT
mds_rsumsThe MATRIX_VECTOR_PRODUCT action with label mds_rsums calculates the following quantities: Quantity    Type    Description  
mds_rsums 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=mds_mat,ff_ones
mds_nonesThe SUM action with label mds_nones calculates the following quantities: Quantity    Type    Description  
mds_nones scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=ff_ones PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_rsumsnThe CUSTOM action with label mds_rsumsn calculates the following quantities: Quantity    Type    Description  
mds_rsumsn 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=mds_rsums,mds_nones 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
mds_rsummatThe OUTER_PRODUCT action with label mds_rsummat calculates the following quantities: Quantity    Type    Description  
mds_rsummat 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=mds_rsumsn,ff_ones
mds_intThe CUSTOM action with label mds_int calculates the following quantities: Quantity    Type    Description  
mds_int 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=mds_rsummat,mds_mat FUNCthe function you wish to evaluate=-0.5*y+0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_intTThe TRANSPOSE action with label mds_intT calculates the following quantities: Quantity    Type    Description  
mds_intT 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=mds_int
mds_csumsThe MATRIX_VECTOR_PRODUCT action with label mds_csums calculates the following quantities: Quantity    Type    Description  
mds_csums 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=mds_intT,ff_ones
mds_csumsnThe CUSTOM action with label mds_csumsn calculates the following quantities: Quantity    Type    Description  
mds_csumsn 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=mds_csums,mds_nones 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
mds_csummatThe OUTER_PRODUCT action with label mds_csummat calculates the following quantities: Quantity    Type    Description  
mds_csummat 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=mds_csumsn,ff_ones
mds_cmatThe CUSTOM action with label mds_cmat calculates the following quantities: Quantity    Type    Description  
mds_cmat 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=mds_csummat,mds_intT FUNCthe function you wish to evaluate=y-x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds_eigThe DIAGONALIZE action with label mds_eig calculates the following quantities: Quantity    Type    Description  
mds_eig.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
mds_eig.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
mds_eig.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
mds_eig.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=mds_cmat VECTORS the eigenvalues and vectors that you would like to calculate=1,2
mds-1The CUSTOM action with label mds-1 calculates the following quantities: Quantity    Type    Description  
mds-1 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=mds_eig.vecs-1,mds_eig.vals-1 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mds-2The CUSTOM action with label mds-2 calculates the following quantities: Quantity    Type    Description  
mds-2 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=mds_eig.vecs-2,mds_eig.vals-2 FUNCthe function you wish to evaluate=sqrt(y)*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
mdsThe VSTACK action with label mds calculates the following quantities: Quantity    Type    Description  
mds 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=mds-1,mds-2
# --- End of included input --- 
# Generate a matrix of w_ij values
weightsThe OUTER_PRODUCT action with label weights calculates the following quantities: Quantity    Type    Description  
weights 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=ff_weights,ff_weights
weights: 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=ff_weights,ff_weights  FUNC the function of the input vectors that should be put in the elements of the outer product=x*y

# And produce the projections
projThe ARRANGE_POINTS action with label proj calculates the following quantities: Quantity    Type    Description  
proj.coord-1 vector the coordinates of the points in the low dimensional space  This is the 1th of these quantities
proj.coord-2 vector the coordinates of the points in the low dimensional space  This is the 2th of these quantities: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action has hidden defaults. More details ...
   ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat
   WEIGHTS1the matrix with the weights of the target quantities=weights MINTYPE the method to use for the minimisation=pointwise
...
proj: ARRANGE_POINTSArrange points in a low dimensional space so that the (transformed) distances between points in the low dimensional space match the dissimilarities provided in an input matrix. This action uses the defaults shown here. More details ...
   ARGthe initial positions for the projections=mds-1,mds-2 TARGET1the matrix of target quantities that you would like to match=mds_mat
   WEIGHTS1the matrix with the weights of the target quantities=weights MINTYPE the method to use for the minimisation=pointwise
 CGRID_SIZE number of points to use in each grid direction=10,10 BUFFER grid extent for search is (max projection - minimum projection) multiplied by this value=1.1 NCYCLES the number of cycles of global optimization to attempt=5 FGRID_SIZE interpolate the grid onto this number of points -- only works in 2D=0,0 CGTOL the tolerance for the conjugate gradient minimization=1E-6 MAXITER maximum number of optimization cycles for optimisation algorithms=1000
...

# And print the projections to a file
DUMPVECTORPrint a vector to a file More details ARGthe labels of vectors/matrices that should be output in the file=proj.* FILE the file on which to write the vetors=colvar

This is the algorithm that is to optimize the stress function within SKETCHMAP.

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	the initial positions for the projections
TARGET	matrix	the matrix of target quantities that you would like to match
WEIGHTS	matrix	the matrix with the weights of the target quantities

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 initial positions for the projections
TARGET	input	none	the matrix of target quantities that you would like to match
WEIGHTS	input	none	the matrix with the weights of the target quantities
MINTYPE	compulsory	conjgrad	the method to use for the minimisation
MAXITER	compulsory	1000	maximum number of optimization cycles for optimisation algorithms
CGTOL	compulsory	1E-6	the tolerance for the conjugate gradient minimization
NCYCLES	compulsory	5	the number of cycles of global optimization to attempt
BUFFER	compulsory	1.1	grid extent for search is (max projection - minimum projection) multiplied by this value
CGRID_SIZE	compulsory	10	number of points to use in each grid direction
FGRID_SIZE	compulsory	0	interpolate the grid onto this number of points -- only works in 2D
SMACTOL	compulsory	1E-4	the tolerance for the smacof algorithm
SMACREG	compulsory	0.001	this is used to ensure that we don't divide by zero when updating weights for SMACOF algorithm
FUNC	optional	not used	a function that is applied on the distances between the points in the low dimensional space

References

More information about how this action can be used is available in the following articles:

M. Ceriotti, G. A. Tribello, M. Parrinello, Simplifying the representation of complex free-energy landscapes using sketch-map. Proceedings of the National Academy of Sciences. 108, 13023–13028 (2011)

Quantity	Type	Description
d1	scalar	the DISTANCE between this pair of atoms

Quantity	Description
ff.data	the data that is being collected by this action
ff.logweights	the logarithms of the weights of the data points