Shortcut: PCAVARS

Module	mapping
Description	Usage
Projection on principal component eigenvectors or other high dimensional linear subspace

Details and examples

Projection on principal component eigenvectors or other high dimensional linear subspace

As discussed in the documenation for RMSD and the refdist module there are various different ways of calculating the distance between the instantaneous structure adopted by the system and some high-dimensional, reference configuration. The problem with all these methods, as one gets further and further from the reference configuration, the distance from it becomes a progressively poorer and poorer collective variable. This happens because the ``number" of structures at a distance $d$ from a reference configuration is proportional to $d^N$ in an $N$ dimensional space. Consequently, when $d$ is small the distance from the reference configuration may well be a good collective variable. However, when $d$ is large it is unlikely that the distance from the reference structure is a good CV. When the distance is large there will almost certainly be markedly different configurations that have the same CV value and hence barriers in transverse degrees of freedom.

For these reasons dimensionality reduction is often employed so a projection $\mathbf{s}$ of a high-dimensional configuration $\mathbf{X}$ in a lower dimensionality space is found using a function:

$\mathbf{s} = F(\mathbf{X}-\mathbf{X}^{ref})$

where here we have introduced some high-dimensional reference configuration $\mathbf{X}^{ref}$ . By far the simplest way to do this is to use some linear operator for $F$ . That is to say we find a low-dimensional projection by rotating the basis vectors using some linear algebra:

$\mathbf{s}_i = \sum_k A_{ik} ( X_{k} - X_{k}^{ref} )$

Here $\mathbf{X}-\mathbf{X}^{ref}$ is the displacement from the refernece configuration in the high dimenisonal space, which you can calculate using the RMSD action or by simply calculating difference between the instaneous values for a collection of variables and the values of the variables for a particular reference configuration. $A$ is then a $d$ by $D$ matrix where $D$ is the dimensionality of the high dimensional space and $d$ is the dimensionality of the lower dimensional subspace. This matrix, $A$ , can be found by various means including principal component analysis (PCA) and normal mode analysis. In both these methods the rows of $A$ would be the principle eigenvectors of a square matrix. For PCA the covariance while for normal modes the Hessian.

Examples

The following input calculates a projection on a linear subspace where the displacements from the reference configuration are calculated using RMSD and TYPE=OPTIMAL. Consequently, both translation of the center of mass of the atoms and rotation of the reference frame are removed from the displacements that appear in the equatiosn above. The matrix $A$ and the reference configuration $R^{ref}$ are specified in the pdb input file reference.pdb and the value of all projections (and the residual) are output to a file called colvar2.

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

#SETTINGS INPUTFILES=regtest/mapping/rt-pca/reference.pdb
pca2The PCAVARS action with label pca2 calculates the following quantities: Quantity    Type    Description  
pca2_eig vector the projections on the eigenvalues
pca2_residual scalar the residual distance that is not projected on any of the eigenvalues: PCAVARSProjection on principal component eigenvectors or other high dimensional linear subspace This action is a shortcut. More details REFERENCEa pdb file containing the set of reference configurations=regtest/mapping/rt-pca/reference.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca/reference.pdb
    ATOM      2  CH3 ACE     1      12.932 -14.718  -6.016  1.00  1.00
ATOM      5  C   ACE     1      21.312  -9.928  -5.946  1.00  1.00
ATOM      9  CA  ALA     2      19.462 -11.088  -8.986  1.00  1.00
ATOM     13  HB2 ALA     2      21.112 -10.688 -12.476  1.00  1.00
ATOM     15  C   ALA     2      19.422   7.978 -14.536  1.00  1.00
ATOM     20 HH31 NME     3      20.122  -9.928 -17.746  1.00  1.00
ATOM     21 HH32 NME     3      18.572 -13.148 -16.346  1.00  1.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1      0.1414  0.3334 -0.0302  1.00  0.00
ATOM      5  C   ACE     1      0.0893 -0.1095 -0.1434  1.00  0.00
ATOM      9  CA  ALA     2      0.0207 -0.321   0.0321  1.00  0.00
ATOM     13  HB2 ALA     2      0.0317 -0.6085  0.0783  1.00  0.00
ATOM     15  C   ALA     2      0.1282 -0.4792  0.0797  1.00  0.00
ATOM     20 HH31 NME     3      0.0053 -0.465   0.0309  1.00  0.00
ATOM     21 HH32 NME     3     -0.1019 -0.4261 -0.0082  1.00  0.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1     -0.0380 -0.2736 -0.0003  1.00  0.00
ATOM      5  C   ACE     1     -0.0656 -0.2138  0.0075  1.00  0.00
ATOM      9  CA  ALA     2     -0.0286 -0.2116 -0.0579  1.00  0.00
ATOM     13  HB2 ALA     2     -0.0235 -0.2794 -0.0388  1.00  0.00
ATOM     15  C   ALA     2     -0.0512 -0.3078 -0.0076  1.00  0.00
ATOM     20 HH31 NME     3      0.0798 -0.2642 -0.1300  1.00  0.00
ATOM     21 HH32 NME     3      0.1136 -0.0846 -0.1385  1.00  0.00
END
  
 TYPE the manner in which distances are calculated=OPTIMAL
# PLUMED interprets the command:
# pca2: PCAVARS REFERENCE=regtest/mapping/rt-pca/reference.pdb TYPE=OPTIMAL
# as follows (Click the red comment above to revert to the short version of the input):
The PCAVARS action with label pca2 calculates the following quantities: Quantity    Description  
pca2.eig the projections on the eigenvalues
pca2.residual the residual distance that is not projected on any of the eigenvaluespca2_atThe RMSD action with label pca2_at calculates the following quantities: Quantity    Type    Description  
pca2_at.dist scalar the RMSD distance the atoms have moved
pca2_at.disp vector the vector of displacements for the atoms: RMSDCalculate the RMSD with respect to a reference structure. More details DISPLACEMENT Calculate the vector of displacements instead of the length of this vector SQUARED  This should be setted if you want MSD instead of RMSD  NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1 REFERENCEa file in pdb format containing the reference structure and the atoms involved in the CV=regtest/mapping/rt-pca/reference.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca/reference.pdb
    ATOM      2  CH3 ACE     1      12.932 -14.718  -6.016  1.00  1.00
ATOM      5  C   ACE     1      21.312  -9.928  -5.946  1.00  1.00
ATOM      9  CA  ALA     2      19.462 -11.088  -8.986  1.00  1.00
ATOM     13  HB2 ALA     2      21.112 -10.688 -12.476  1.00  1.00
ATOM     15  C   ALA     2      19.422   7.978 -14.536  1.00  1.00
ATOM     20 HH31 NME     3      20.122  -9.928 -17.746  1.00  1.00
ATOM     21 HH32 NME     3      18.572 -13.148 -16.346  1.00  1.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1      0.1414  0.3334 -0.0302  1.00  0.00
ATOM      5  C   ACE     1      0.0893 -0.1095 -0.1434  1.00  0.00
ATOM      9  CA  ALA     2      0.0207 -0.321   0.0321  1.00  0.00
ATOM     13  HB2 ALA     2      0.0317 -0.6085  0.0783  1.00  0.00
ATOM     15  C   ALA     2      0.1282 -0.4792  0.0797  1.00  0.00
ATOM     20 HH31 NME     3      0.0053 -0.465   0.0309  1.00  0.00
ATOM     21 HH32 NME     3     -0.1019 -0.4261 -0.0082  1.00  0.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1     -0.0380 -0.2736 -0.0003  1.00  0.00
ATOM      5  C   ACE     1     -0.0656 -0.2138  0.0075  1.00  0.00
ATOM      9  CA  ALA     2     -0.0286 -0.2116 -0.0579  1.00  0.00
ATOM     13  HB2 ALA     2     -0.0235 -0.2794 -0.0388  1.00  0.00
ATOM     15  C   ALA     2     -0.0512 -0.3078 -0.0076  1.00  0.00
ATOM     20 HH31 NME     3      0.0798 -0.2642 -0.1300  1.00  0.00
ATOM     21 HH32 NME     3      0.1136 -0.0846 -0.1385  1.00  0.00
END
  
 TYPE the manner in which RMSD alignment is performed=OPTIMAL
pca2_peigThe CONSTANT action with label pca2_peig calculates the following quantities: Quantity    Type    Description  
pca2_peig matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=0.0465854,0.0294206,0.00681978,0.0104438,0.0422365,0.00174613,-0.0335718,0.109841,-0.0360757,-0.105756,-0.200475,-0.157876,-0.153198,-0.140382,-0.00994964,-0.0472443,0.0105756,0.0257966,0.0262578,0.0101803,-0.00270156,-0.0206199,-0.0355965,-0.0155192,-0.0127518,-0.0277826,0.0433018,0.0616427,-0.148463,-0.116014,-0.11482,-0.151611,-0.167021,-0.143363,-0.0459064,-0.000162789,0.00406972,-0.0314182,-0.021054,-0.00412398,-0.0705418,-0.0751541 NROWS the number of rows in your input matrix=2 NCOLS the number of columns in your matrix=21
pca2_eigThe MATRIX_VECTOR_PRODUCT action with label pca2_eig calculates the following quantities: Quantity    Type    Description  
pca2_eig 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=pca2_peig,pca2_at.disp
pca2_eig-1The SELECT_WITH_MASK action with label pca2_eig-1 calculates the following quantities: Quantity    Type    Description  
pca2_eig-1 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=pca2_eig COMPONENTSthe components in the input value that you woul like to build a new vector from=1
pca2_eig-2The SELECT_WITH_MASK action with label pca2_eig-2 calculates the following quantities: Quantity    Type    Description  
pca2_eig-2 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=pca2_eig COMPONENTSthe components in the input value that you woul like to build a new vector from=2
pca2_eig2The CUSTOM action with label pca2_eig2 calculates the following quantities: Quantity    Type    Description  
pca2_eig2 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=pca2_eig FUNCthe function you wish to evaluate=x*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pca2_eigsum2The SUM action with label pca2_eigsum2 calculates the following quantities: Quantity    Type    Description  
pca2_eigsum2 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=pca2_eig2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pca2_residualThe CUSTOM action with label pca2_residual calculates the following quantities: Quantity    Type    Description  
pca2_residual scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pca2_at.dist,pca2_eigsum2 FUNCthe function you wish to evaluate=sqrt(x-y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=pca2.* FILEthe name of the file on which to output these quantities=colvar2

As you can see from the example above, the reference configurations are specified using a pdb file. The first configuration that you provide is the reference configuration, which is referred to in the above expressions as $X^{ref}$ . Subsequent configurations give the directions of row vectors that are contained in the matrix $A$ above. These directions are specified by giving a second configuration that describes the components of $A$ explicitly.

When you use an input like the one in the example above PLUMED assumes that the atoms for which RMSD displacements are being computed together form a molecule. A procedure akin to that in WHOLEMOLECULES is thus performed to ensure that any bonds that are broken by the periodic boundary conditions are reformed. If you would like to turn this feature off for any reason you add the NOPBC flag to the input line as shown below:

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

#SETTINGS INPUTFILES=regtest/mapping/rt-pca/reference.pdb
pca2The PCAVARS action with label pca2 calculates the following quantities: Quantity    Type    Description  
pca2_eig vector the projections on the eigenvalues
pca2_residual scalar the residual distance that is not projected on any of the eigenvalues: PCAVARSProjection on principal component eigenvectors or other high dimensional linear subspace This action is a shortcut. More details REFERENCEa pdb file containing the set of reference configurations=regtest/mapping/rt-pca/reference.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca/reference.pdb
    ATOM      2  CH3 ACE     1      12.932 -14.718  -6.016  1.00  1.00
ATOM      5  C   ACE     1      21.312  -9.928  -5.946  1.00  1.00
ATOM      9  CA  ALA     2      19.462 -11.088  -8.986  1.00  1.00
ATOM     13  HB2 ALA     2      21.112 -10.688 -12.476  1.00  1.00
ATOM     15  C   ALA     2      19.422   7.978 -14.536  1.00  1.00
ATOM     20 HH31 NME     3      20.122  -9.928 -17.746  1.00  1.00
ATOM     21 HH32 NME     3      18.572 -13.148 -16.346  1.00  1.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1      0.1414  0.3334 -0.0302  1.00  0.00
ATOM      5  C   ACE     1      0.0893 -0.1095 -0.1434  1.00  0.00
ATOM      9  CA  ALA     2      0.0207 -0.321   0.0321  1.00  0.00
ATOM     13  HB2 ALA     2      0.0317 -0.6085  0.0783  1.00  0.00
ATOM     15  C   ALA     2      0.1282 -0.4792  0.0797  1.00  0.00
ATOM     20 HH31 NME     3      0.0053 -0.465   0.0309  1.00  0.00
ATOM     21 HH32 NME     3     -0.1019 -0.4261 -0.0082  1.00  0.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1     -0.0380 -0.2736 -0.0003  1.00  0.00
ATOM      5  C   ACE     1     -0.0656 -0.2138  0.0075  1.00  0.00
ATOM      9  CA  ALA     2     -0.0286 -0.2116 -0.0579  1.00  0.00
ATOM     13  HB2 ALA     2     -0.0235 -0.2794 -0.0388  1.00  0.00
ATOM     15  C   ALA     2     -0.0512 -0.3078 -0.0076  1.00  0.00
ATOM     20 HH31 NME     3      0.0798 -0.2642 -0.1300  1.00  0.00
ATOM     21 HH32 NME     3      0.1136 -0.0846 -0.1385  1.00  0.00
END
  
 NOPBC do not use periodic boundary conditions when computing this quantity TYPE the manner in which distances are calculated=OPTIMAL
# PLUMED interprets the command:
# pca2: PCAVARS REFERENCE=regtest/mapping/rt-pca/reference.pdb NOPBC TYPE=OPTIMAL
# as follows (Click the red comment above to revert to the short version of the input):
The PCAVARS action with label pca2 calculates the following quantities: Quantity    Description  
pca2.eig the projections on the eigenvalues
pca2.residual the residual distance that is not projected on any of the eigenvaluespca2_atThe RMSD action with label pca2_at calculates the following quantities: Quantity    Type    Description  
pca2_at.dist scalar the RMSD distance the atoms have moved
pca2_at.disp vector the vector of displacements for the atoms: RMSDCalculate the RMSD with respect to a reference structure. More details DISPLACEMENT Calculate the vector of displacements instead of the length of this vector SQUARED  This should be setted if you want MSD instead of RMSD  NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1 REFERENCEa file in pdb format containing the reference structure and the atoms involved in the CV=regtest/mapping/rt-pca/reference.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca/reference.pdb
    ATOM      2  CH3 ACE     1      12.932 -14.718  -6.016  1.00  1.00
ATOM      5  C   ACE     1      21.312  -9.928  -5.946  1.00  1.00
ATOM      9  CA  ALA     2      19.462 -11.088  -8.986  1.00  1.00
ATOM     13  HB2 ALA     2      21.112 -10.688 -12.476  1.00  1.00
ATOM     15  C   ALA     2      19.422   7.978 -14.536  1.00  1.00
ATOM     20 HH31 NME     3      20.122  -9.928 -17.746  1.00  1.00
ATOM     21 HH32 NME     3      18.572 -13.148 -16.346  1.00  1.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1      0.1414  0.3334 -0.0302  1.00  0.00
ATOM      5  C   ACE     1      0.0893 -0.1095 -0.1434  1.00  0.00
ATOM      9  CA  ALA     2      0.0207 -0.321   0.0321  1.00  0.00
ATOM     13  HB2 ALA     2      0.0317 -0.6085  0.0783  1.00  0.00
ATOM     15  C   ALA     2      0.1282 -0.4792  0.0797  1.00  0.00
ATOM     20 HH31 NME     3      0.0053 -0.465   0.0309  1.00  0.00
ATOM     21 HH32 NME     3     -0.1019 -0.4261 -0.0082  1.00  0.00
END
REMARK TYPE=DIRECTION
ATOM      2  CH3 ACE     1     -0.0380 -0.2736 -0.0003  1.00  0.00
ATOM      5  C   ACE     1     -0.0656 -0.2138  0.0075  1.00  0.00
ATOM      9  CA  ALA     2     -0.0286 -0.2116 -0.0579  1.00  0.00
ATOM     13  HB2 ALA     2     -0.0235 -0.2794 -0.0388  1.00  0.00
ATOM     15  C   ALA     2     -0.0512 -0.3078 -0.0076  1.00  0.00
ATOM     20 HH31 NME     3      0.0798 -0.2642 -0.1300  1.00  0.00
ATOM     21 HH32 NME     3      0.1136 -0.0846 -0.1385  1.00  0.00
END
  
 NOPBC ignore the periodic boundary conditions when calculating distances TYPE the manner in which RMSD alignment is performed=OPTIMAL
pca2_peigThe CONSTANT action with label pca2_peig calculates the following quantities: Quantity    Type    Description  
pca2_peig matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=0.0465854,0.0294206,0.00681978,0.0104438,0.0422365,0.00174613,-0.0335718,0.109841,-0.0360757,-0.105756,-0.200475,-0.157876,-0.153198,-0.140382,-0.00994964,-0.0472443,0.0105756,0.0257966,0.0262578,0.0101803,-0.00270156,-0.0206199,-0.0355965,-0.0155192,-0.0127518,-0.0277826,0.0433018,0.0616427,-0.148463,-0.116014,-0.11482,-0.151611,-0.167021,-0.143363,-0.0459064,-0.000162789,0.00406972,-0.0314182,-0.021054,-0.00412398,-0.0705418,-0.0751541 NROWS the number of rows in your input matrix=2 NCOLS the number of columns in your matrix=21
pca2_eigThe MATRIX_VECTOR_PRODUCT action with label pca2_eig calculates the following quantities: Quantity    Type    Description  
pca2_eig 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=pca2_peig,pca2_at.disp
pca2_eig-1The SELECT_WITH_MASK action with label pca2_eig-1 calculates the following quantities: Quantity    Type    Description  
pca2_eig-1 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=pca2_eig COMPONENTSthe components in the input value that you woul like to build a new vector from=1
pca2_eig-2The SELECT_WITH_MASK action with label pca2_eig-2 calculates the following quantities: Quantity    Type    Description  
pca2_eig-2 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=pca2_eig COMPONENTSthe components in the input value that you woul like to build a new vector from=2
pca2_eig2The CUSTOM action with label pca2_eig2 calculates the following quantities: Quantity    Type    Description  
pca2_eig2 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=pca2_eig FUNCthe function you wish to evaluate=x*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pca2_eigsum2The SUM action with label pca2_eigsum2 calculates the following quantities: Quantity    Type    Description  
pca2_eigsum2 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=pca2_eig2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pca2_residualThe CUSTOM action with label pca2_residual calculates the following quantities: Quantity    Type    Description  
pca2_residual scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pca2_at.dist,pca2_eigsum2 FUNCthe function you wish to evaluate=sqrt(x-y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=pca2.* FILEthe name of the file on which to output these quantities=colvar2

Notice that the PCAVARS command is a shortcut. If you look at how the shortcut in the above input is expanded you should be able to see how the command works by calculating the RMSD displacement between the instantaneous and reference configuration and how those displacements are then projected on the eigenvector that was specified in the second frame of the pdb input above. Understanding the expanded version of this shortcut command allows you to recognise that you can project the displacement vector on any arbitrary vector. For example in the input below two reference structures are provided in the pdb file. PLUMED calculates the RMSD distance between these two reference configurations during setup and sets up a unit vector called eig that points along the director connecting the two RMSD structure. During the calculation the vector connecting the instantaneous configuration and the first of the two reference configurations in computed. This vector is then projected on the unit vector connecting the two initial structures:

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

#SETTINGS INPUTFILES=regtest/mapping/rt-pca-two-frames/two-frames.pdb

# Read in two reference configuratioms from PDB file
ref1The PDB2CONSTANT action with label ref1 calculates the following quantities: Quantity    Type    Description  
ref1 matrix a value that is constructed from the information in the PDB file: PDB2CONSTANTCreate a constant value from a PDB input file This action is a shortcut. More details REFERENCEa file in pdb format containing the reference structure=regtest/mapping/rt-pca-two-frames/two-frames.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-two-frames/two-frames.pdb
    ATOM      5  CLP ALA     1      -1.819  -0.143   1.679  1.00  1.00
ATOM      6  OL  ALA     1      -1.177  -0.889   2.401  1.00  1.00
ATOM      7  NL  ALA     1      -1.313   0.341   0.529  1.00  1.00
ATOM      8  HL  ALA     1      -1.845   0.961  -0.011  1.00  1.00
ATOM      9  CA  ALA     1      -0.003  -0.019   0.021  1.00  1.00
ATOM     10  HA  ALA     1       0.205  -1.051   0.259  1.00  1.00
ATOM     11  CB  ALA     1       0.009   0.135  -1.509  1.00  1.00
ATOM     15  CRP ALA     1       1.121   0.799   0.663  1.00  1.00
ATOM     16  OR  ALA     1       1.723   1.669   0.043  1.00  1.00
ATOM     17  NR  ALA     1       1.423   0.519   1.941  1.00  1.00
ATOM     18  HR  ALA     1       0.873  -0.161   2.413  1.00  1.00
ATOM     19  CR  ALA     1       2.477   1.187   2.675  1.00  1.00
END
ATOM      5  CLP ALA     1      -1.941   1.459   0.447  1.00  1.00
ATOM      6  OL  ALA     1      -1.481   2.369  -0.223  1.00  1.00
ATOM      7  NL  ALA     1      -1.303   0.291   0.647  1.00  1.00
ATOM      8  HL  ALA     1      -1.743  -0.379   1.229  1.00  1.00
ATOM      9  CA  ALA     1      -0.011  -0.077   0.099  1.00  1.00
ATOM     10  HA  ALA     1       0.155  -1.099   0.417  1.00  1.00
ATOM     11  CB  ALA     1       0.001  -0.097  -1.439  1.00  1.00
ATOM     15  CRP ALA     1       1.191   0.673   0.683  1.00  1.00
ATOM     16  OR  ALA     1       2.015   0.103   1.375  1.00  1.00
ATOM     17  NR  ALA     1       1.303   1.983   0.393  1.00  1.00
ATOM     18  HR  ALA     1       0.553   2.411  -0.109  1.00  1.00
ATOM     19  CR  ALA     1       2.395   2.811   0.843  1.00  1.00
END
  
 NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1
# PLUMED interprets the command:
# ref1: PDB2CONSTANT REFERENCE=regtest/mapping/rt-pca-two-frames/two-frames.pdb NUMBER=1
# as follows (Click the red comment above to revert to the short version of the input):
ref1The CONSTANT action with label ref1 calculates the following quantities: Quantity    Type    Description  
ref1 matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NROWS the number of rows in your input matrix=1 NCOLS the number of columns in your matrix=36 VALUESthe numbers that are in your constant value=-0.19585,-0.13165,-0.14525,-0.19845,-0.01425,0.00655,-0.01305,0.09815,0.15835,0.12835,0.07335,0.23375,-0.0422,-0.1168,0.0062,0.0682,-0.0298,-0.133,-0.0144,0.052,0.139,0.024,-0.044,0.0908,0.0753667,0.147567,-0.0396333,-0.0936333,-0.0904333,-0.0666333,-0.243433,-0.0262333,-0.0882333,0.101567,0.148767,0.174967
# --- End of included input --- ref1TThe TRANSPOSE action with label ref1T calculates the following quantities: Quantity    Type    Description  
ref1T 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=ref1
ref2The PDB2CONSTANT action with label ref2 calculates the following quantities: Quantity    Type    Description  
ref2 matrix a value that is constructed from the information in the PDB file: PDB2CONSTANTCreate a constant value from a PDB input file This action is a shortcut. More details REFERENCEa file in pdb format containing the reference structure=regtest/mapping/rt-pca-two-frames/two-frames.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-two-frames/two-frames.pdb
    ATOM      5  CLP ALA     1      -1.819  -0.143   1.679  1.00  1.00
ATOM      6  OL  ALA     1      -1.177  -0.889   2.401  1.00  1.00
ATOM      7  NL  ALA     1      -1.313   0.341   0.529  1.00  1.00
ATOM      8  HL  ALA     1      -1.845   0.961  -0.011  1.00  1.00
ATOM      9  CA  ALA     1      -0.003  -0.019   0.021  1.00  1.00
ATOM     10  HA  ALA     1       0.205  -1.051   0.259  1.00  1.00
ATOM     11  CB  ALA     1       0.009   0.135  -1.509  1.00  1.00
ATOM     15  CRP ALA     1       1.121   0.799   0.663  1.00  1.00
ATOM     16  OR  ALA     1       1.723   1.669   0.043  1.00  1.00
ATOM     17  NR  ALA     1       1.423   0.519   1.941  1.00  1.00
ATOM     18  HR  ALA     1       0.873  -0.161   2.413  1.00  1.00
ATOM     19  CR  ALA     1       2.477   1.187   2.675  1.00  1.00
END
ATOM      5  CLP ALA     1      -1.941   1.459   0.447  1.00  1.00
ATOM      6  OL  ALA     1      -1.481   2.369  -0.223  1.00  1.00
ATOM      7  NL  ALA     1      -1.303   0.291   0.647  1.00  1.00
ATOM      8  HL  ALA     1      -1.743  -0.379   1.229  1.00  1.00
ATOM      9  CA  ALA     1      -0.011  -0.077   0.099  1.00  1.00
ATOM     10  HA  ALA     1       0.155  -1.099   0.417  1.00  1.00
ATOM     11  CB  ALA     1       0.001  -0.097  -1.439  1.00  1.00
ATOM     15  CRP ALA     1       1.191   0.673   0.683  1.00  1.00
ATOM     16  OR  ALA     1       2.015   0.103   1.375  1.00  1.00
ATOM     17  NR  ALA     1       1.303   1.983   0.393  1.00  1.00
ATOM     18  HR  ALA     1       0.553   2.411  -0.109  1.00  1.00
ATOM     19  CR  ALA     1       2.395   2.811   0.843  1.00  1.00
END
  
 NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=2
# PLUMED interprets the command:
# ref2: PDB2CONSTANT REFERENCE=regtest/mapping/rt-pca-two-frames/two-frames.pdb NUMBER=2
# as follows (Click the red comment above to revert to the short version of the input):
ref2The CONSTANT action with label ref2 calculates the following quantities: Quantity    Type    Description  
ref2 matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NROWS the number of rows in your input matrix=1 NCOLS the number of columns in your matrix=36 VALUESthe numbers that are in your constant value=-0.20355,-0.15755,-0.13975,-0.18375,-0.01055,0.00605,-0.00935,0.10965,0.19205,0.12085,0.04585,0.23005,0.0588333,0.149833,-0.0579667,-0.124967,-0.0947667,-0.196967,-0.0967667,-0.0197667,-0.0767667,0.111233,0.154033,0.194033,0.00835,-0.05865,0.02835,0.08655,-0.02645,0.00535,-0.18025,0.03195,0.10115,0.00295,-0.04725,0.04795
# --- End of included input --- # Calculate the displacement vector that takes you from ref1 to ref2
eiguThe RMSD action with label eigu calculates the following quantities: Quantity    Type    Description  
eigu.dist scalar the RMSD distance the atoms have moved
eigu.disp vector the vector of displacements for the atoms: RMSDCalculate the RMSD with respect to a reference structure. More details ARGinstead of using the REFERENCE option you can use this action to specify the labels of two actions that you are calculating the RMSD between=ref1T,ref2 DISPLACEMENT Calculate the vector of displacements instead of the length of this vector TYPE the manner in which RMSD alignment is performed=OPTIMAL
# Normalise the reference vector
eigu2The CUSTOM action with label eigu2 calculates the following quantities: Quantity    Type    Description  
eigu2 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=eigu.disp FUNCthe function you wish to evaluate=x*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
eign2The SUM action with label eign2 calculates the following quantities: Quantity    Type    Description  
eign2 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=eigu2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
eigThe CUSTOM action with label eig calculates the following quantities: Quantity    Type    Description  
eig 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=eigu.disp,eign2 FUNCthe function you wish to evaluate=x/sqrt(y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
eigTThe TRANSPOSE action with label eigT calculates the following quantities: Quantity    Type    Description  
eigT 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=eig
# Everything prior to this point is only done in setup.  From here onwards we have the commands that are done during the main calculate loop.

# Calculate the RMSD displacement between the instaneous structure and the first reference structure
rmsdThe RMSD action with label rmsd calculates the following quantities: Quantity    Type    Description  
rmsd.dist scalar the RMSD distance the atoms have moved
rmsd.disp vector the vector of displacements for the atoms: RMSDCalculate the RMSD with respect to a reference structure. This action is a shortcut. More details REFERENCEa file in pdb format containing the reference structure and the atoms involved in the CV=regtest/mapping/rt-pca-two-frames/two-frames.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-two-frames/two-frames.pdb
    ATOM      5  CLP ALA     1      -1.819  -0.143   1.679  1.00  1.00
ATOM      6  OL  ALA     1      -1.177  -0.889   2.401  1.00  1.00
ATOM      7  NL  ALA     1      -1.313   0.341   0.529  1.00  1.00
ATOM      8  HL  ALA     1      -1.845   0.961  -0.011  1.00  1.00
ATOM      9  CA  ALA     1      -0.003  -0.019   0.021  1.00  1.00
ATOM     10  HA  ALA     1       0.205  -1.051   0.259  1.00  1.00
ATOM     11  CB  ALA     1       0.009   0.135  -1.509  1.00  1.00
ATOM     15  CRP ALA     1       1.121   0.799   0.663  1.00  1.00
ATOM     16  OR  ALA     1       1.723   1.669   0.043  1.00  1.00
ATOM     17  NR  ALA     1       1.423   0.519   1.941  1.00  1.00
ATOM     18  HR  ALA     1       0.873  -0.161   2.413  1.00  1.00
ATOM     19  CR  ALA     1       2.477   1.187   2.675  1.00  1.00
END
ATOM      5  CLP ALA     1      -1.941   1.459   0.447  1.00  1.00
ATOM      6  OL  ALA     1      -1.481   2.369  -0.223  1.00  1.00
ATOM      7  NL  ALA     1      -1.303   0.291   0.647  1.00  1.00
ATOM      8  HL  ALA     1      -1.743  -0.379   1.229  1.00  1.00
ATOM      9  CA  ALA     1      -0.011  -0.077   0.099  1.00  1.00
ATOM     10  HA  ALA     1       0.155  -1.099   0.417  1.00  1.00
ATOM     11  CB  ALA     1       0.001  -0.097  -1.439  1.00  1.00
ATOM     15  CRP ALA     1       1.191   0.673   0.683  1.00  1.00
ATOM     16  OR  ALA     1       2.015   0.103   1.375  1.00  1.00
ATOM     17  NR  ALA     1       1.303   1.983   0.393  1.00  1.00
ATOM     18  HR  ALA     1       0.553   2.411  -0.109  1.00  1.00
ATOM     19  CR  ALA     1       2.395   2.811   0.843  1.00  1.00
END
  
 NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1 TYPE the manner in which RMSD alignment is performed=OPTIMAL DISPLACEMENT Calculate the vector of displacements instead of the length of this vector SQUARED  This should be setted if you want MSD instead of RMSD 
# PLUMED interprets the command:
# rmsd: RMSD REFERENCE=regtest/mapping/rt-pca-two-frames/two-frames.pdb NUMBER=1 TYPE=OPTIMAL DISPLACEMENT SQUARED
# as follows (Click the red comment above to revert to the short version of the input):
rmsd_refThe CONSTANT action with label rmsd_ref calculates the following quantities: Quantity    Type    Description  
rmsd_ref matrix the constant value that was read from the plumed input: PDB2CONSTANTCreate a constant value from a PDB input file More details REFERENCEa file in pdb format containing the reference structure=regtest/mapping/rt-pca-two-frames/two-frames.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-two-frames/two-frames.pdb
    ATOM      5  CLP ALA     1      -1.819  -0.143   1.679  1.00  1.00
ATOM      6  OL  ALA     1      -1.177  -0.889   2.401  1.00  1.00
ATOM      7  NL  ALA     1      -1.313   0.341   0.529  1.00  1.00
ATOM      8  HL  ALA     1      -1.845   0.961  -0.011  1.00  1.00
ATOM      9  CA  ALA     1      -0.003  -0.019   0.021  1.00  1.00
ATOM     10  HA  ALA     1       0.205  -1.051   0.259  1.00  1.00
ATOM     11  CB  ALA     1       0.009   0.135  -1.509  1.00  1.00
ATOM     15  CRP ALA     1       1.121   0.799   0.663  1.00  1.00
ATOM     16  OR  ALA     1       1.723   1.669   0.043  1.00  1.00
ATOM     17  NR  ALA     1       1.423   0.519   1.941  1.00  1.00
ATOM     18  HR  ALA     1       0.873  -0.161   2.413  1.00  1.00
ATOM     19  CR  ALA     1       2.477   1.187   2.675  1.00  1.00
END
ATOM      5  CLP ALA     1      -1.941   1.459   0.447  1.00  1.00
ATOM      6  OL  ALA     1      -1.481   2.369  -0.223  1.00  1.00
ATOM      7  NL  ALA     1      -1.303   0.291   0.647  1.00  1.00
ATOM      8  HL  ALA     1      -1.743  -0.379   1.229  1.00  1.00
ATOM      9  CA  ALA     1      -0.011  -0.077   0.099  1.00  1.00
ATOM     10  HA  ALA     1       0.155  -1.099   0.417  1.00  1.00
ATOM     11  CB  ALA     1       0.001  -0.097  -1.439  1.00  1.00
ATOM     15  CRP ALA     1       1.191   0.673   0.683  1.00  1.00
ATOM     16  OR  ALA     1       2.015   0.103   1.375  1.00  1.00
ATOM     17  NR  ALA     1       1.303   1.983   0.393  1.00  1.00
ATOM     18  HR  ALA     1       0.553   2.411  -0.109  1.00  1.00
ATOM     19  CR  ALA     1       2.395   2.811   0.843  1.00  1.00
END
  
 NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1
WHOLEMOLECULESThis action is used to rebuild molecules that can become split by the periodic boundary conditions. More details ENTITY0the atoms that make up a molecule that you wish to align=5,6,7,8,9,10,11,15,16,17,18,19
The WHOLEMOLECULES action with label  calculates somethingrmsd_cposThe POSITION action with label rmsd_cpos calculates the following quantities: Quantity    Type    Description  
rmsd_cpos.x vector the x-component of the atom position
rmsd_cpos.y vector the y-component of the atom position
rmsd_cpos.z vector the z-component of the atom position: POSITIONCalculate the components of the position of an atom or atoms. More details NOPBC ignore the periodic boundary conditions when calculating distances ATOMSthe atom numbers that you would like to use the positions of=5,6,7,8,9,10,11,15,16,17,18,19
rmsd_posThe CONCATENATE action with label rmsd_pos calculates the following quantities: Quantity    Type    Description  
rmsd_pos 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=rmsd_cpos.x,rmsd_cpos.y,rmsd_cpos.z
rmsd: RMSDCalculate the RMSD with respect to a reference structure. More details ARGinstead of using the REFERENCE option you can use this action to specify the labels of two actions that you are calculating the RMSD between=rmsd_pos,rmsd_ref DISPLACEMENT Calculate the vector of displacements instead of the length of this vector ALIGN the weights to use when aligning to the reference structure=1,1,1,1,1,1,1,1,1,1,1,1 DISPLACE the weights to use when calculating the displacement from the reference structure=1,1,1,1,1,1,1,1,1,1,1,1 SQUARED  This should be setted if you want MSD instead of RMSD  TYPE the manner in which RMSD alignment is performed=OPTIMAL
# --- End of included input --- # Project the displacement computed above on the director of the vector that connects reference structure ref1 to refeference structure ref2
pcaThe MATRIX_VECTOR_PRODUCT action with label pca calculates the following quantities: Quantity    Type    Description  
pca 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=eigT,rmsd.disp

# Print the final CV to a file
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=pca FILEthe name of the file on which to output these quantities=colvar

You can also project vectors of differences of arguments on reference vectors. For example, the input below can be used to look at the projection of the vector connecting the instantanous configuraiton to a reference point in CV on a reference vector that has been specified in the PDB file.

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

#SETTINGS INPUTFILES=regtest/mapping/rt-pca-args/epath.pdb

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
pcaThe PCAVARS action with label pca calculates the following quantities: Quantity    Type    Description  
pca_eig vector the projections on the eigenvalues
pca_residual scalar the residual distance that is not projected on any of the eigenvalues: PCAVARSProjection on principal component eigenvectors or other high dimensional linear subspace This action is a shortcut and it has hidden defaults. More details ARGif there are arguments to be used specify them here=d1,d2,d3 REFERENCEa pdb file containing the set of reference configurations=regtest/mapping/rt-pca-args/epath.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-args/epath.pdb
    REMARK d1=0.1221 d2=0.0979 d3=0.1079
END
REMARK d1=0.078811 d2=-0.945732 d3=-0.315244
END
  
The PCAVARS action with label pca calculates the following quantities: Quantity    Description  
pca.eig the projections on the eigenvalues
pca.residual the residual distance that is not projected on any of the eigenvaluespca: PCAVARSProjection on principal component eigenvectors or other high dimensional linear subspace This action is a shortcut and uses the defaults shown here. More details ARGif there are arguments to be used specify them here=d1,d2,d3 REFERENCEa pdb file containing the set of reference configurations=regtest/mapping/rt-pca-args/epath.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-args/epath.pdb
    REMARK d1=0.1221 d2=0.0979 d3=0.1079
END
REMARK d1=0.078811 d2=-0.945732 d3=-0.315244
END
  
  TYPE the manner in which distances are calculated=OPTIMAL-FAST
# PLUMED interprets the command:
# pca: PCAVARS ARG=d1,d2,d3 REFERENCE=regtest/mapping/rt-pca-args/epath.pdb
# as follows (Click the red comment above to revert to the short version of the input):
pca_ref_d1The CONSTANT action with label pca_ref_d1 calculates the following quantities: Quantity    Type    Description  
pca_ref_d1 scalar the constant value that was read from the plumed input: PDB2CONSTANTCreate a constant value from a PDB input file More details NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1 REFERENCEa file in pdb format containing the reference structure=regtest/mapping/rt-pca-args/epath.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-args/epath.pdb
    REMARK d1=0.1221 d2=0.0979 d3=0.1079
END
REMARK d1=0.078811 d2=-0.945732 d3=-0.315244
END
  
 ARGread this single argument from the input rather than the atomic structure=d1
pca_ref_d2The CONSTANT action with label pca_ref_d2 calculates the following quantities: Quantity    Type    Description  
pca_ref_d2 scalar the constant value that was read from the plumed input: PDB2CONSTANTCreate a constant value from a PDB input file More details NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1 REFERENCEa file in pdb format containing the reference structure=regtest/mapping/rt-pca-args/epath.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-args/epath.pdb
    REMARK d1=0.1221 d2=0.0979 d3=0.1079
END
REMARK d1=0.078811 d2=-0.945732 d3=-0.315244
END
  
 ARGread this single argument from the input rather than the atomic structure=d2
pca_ref_d3The CONSTANT action with label pca_ref_d3 calculates the following quantities: Quantity    Type    Description  
pca_ref_d3 scalar the constant value that was read from the plumed input: PDB2CONSTANTCreate a constant value from a PDB input file More details NUMBER if there are multiple structures in the pdb file you can specify that you want the RMSD from a specific structure by specifying its place in the file here=1 REFERENCEa file in pdb format containing the reference structure=regtest/mapping/rt-pca-args/epath.pdb Click here to see an extract from this file.
    ×  FILE: regtest/mapping/rt-pca-args/epath.pdb
    REMARK d1=0.1221 d2=0.0979 d3=0.1079
END
REMARK d1=0.078811 d2=-0.945732 d3=-0.315244
END
  
 ARGread this single argument from the input rather than the atomic structure=d3
pca_argdistThe MATRIX_PRODUCT_DIAGONAL action with label pca_argdist calculates the following quantities: Quantity    Type    Description  
pca_argdist scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: EUCLIDEAN_DISTANCECalculate the euclidean distance between two vectors of arguments More details SQUARED The squared distance should be calculated ARG1The poin that we are calculating the distance from=d1,d2,d3 ARG2The point that we are calculating the distance to=pca_ref_d1,pca_ref_d2,pca_ref_d3
pca_peigThe CONSTANT action with label pca_peig calculates the following quantities: Quantity    Type    Description  
pca_peig matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=0.078811,-0.945732,-0.315244 NROWS the number of rows in your input matrix=1 NCOLS the number of columns in your matrix=3
pca_eigThe MATRIX_VECTOR_PRODUCT action with label pca_eig calculates the following quantities: Quantity    Type    Description  
pca_eig 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=pca_peig,pca_argdist_diffT
pca_eig-1The SELECT_WITH_MASK action with label pca_eig-1 calculates the following quantities: Quantity    Type    Description  
pca_eig-1 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=pca_eig COMPONENTSthe components in the input value that you woul like to build a new vector from=1
pca_eig2The CUSTOM action with label pca_eig2 calculates the following quantities: Quantity    Type    Description  
pca_eig2 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=pca_eig FUNCthe function you wish to evaluate=x*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pca_eigsum2The SUM action with label pca_eigsum2 calculates the following quantities: Quantity    Type    Description  
pca_eigsum2 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=pca_eig2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pca_residualThe CUSTOM action with label pca_residual calculates the following quantities: Quantity    Type    Description  
pca_residual scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pca_argdist,pca_eigsum2 FUNCthe function you wish to evaluate=sqrt(x-y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=pca_eig-1,pca_residual FILEthe name of the file on which to output these quantities=colvar

The first set of argument values in this input file are the reference values for the arguments. The second any subsquent sets of arguments give the coefficients that should be used when constructing linear combinations.

Notice, lastly, that you can also use a combination of argument values and atomic positions when specifying the reference configuration and the reference directions. If you are doing something this complicated, however, you are perhaps better working with the PLUMED input directly rather than this shortcut as you will need to take special measures to ensure that all your CVs are in the same units.

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	scalar/vector	if there are arguments to be used specify them here

Output components

This action calculates the values in the following table. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Description
eig	vector	the projections on the eigenvalues
residual	scalar	the residual distance that is not projected on any of the eigenvalues

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	if there are arguments to be used specify them here
REFERENCE	compulsory	none	a pdb file containing the set of reference configurations
TYPE	compulsory	OPTIMAL-FAST	the manner in which distances are calculated
NOPBC	optional	false	do not use periodic boundary conditions when computing this quantity

Quantity	Type	Description
pca2_eig	vector	the projections on the eigenvalues
pca2_residual	scalar	the residual distance that is not projected on any of the eigenvalues

Quantity	Description
pca2.eig	the projections on the eigenvalues
pca2.residual	the residual distance that is not projected on any of the eigenvalues

Quantity	Description
pca.eig	the projections on the eigenvalues
pca.residual	the residual distance that is not projected on any of the eigenvalues