Shortcut: KL_ENTROPY
| Module | gridtools |
|---|---|
| Description | Usage |
| Calculate the KL entropy of a distribution |   |
| output value | type |
| the value of the KL-Entropy | scalar |
Details and examples
Calculate the KL entropy of a distribution
This shortcut was implemented in order to make the implementation of CVs like those described in the paper that is cited below straightforward. An example input that can be used to implement one of the CVs that is introduced in that paper is shown below:
Click on the labels of the actions for more information on what each action computes
#SETTINGS INPUTFILES=regtest/gridtools/rt-weights-integral/kde.grid
# These two commands compute a set of weights that allow us to determine if each distance in our system is a bond d1The DISTANCE action with label d1 calculates the following quantities:: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=1,3 ATOMS3the pair of atom that we are calculating the distance between=1,4 ATOMS4the pair of atom that we are calculating the distance between=1,5 ATOMS5the pair of atom that we are calculating the distance between=2,3 ATOMS6the pair of atom that we are calculating the distance between=2,4 ATOMS7the pair of atom that we are calculating the distance between=2,5 ATOMS8the pair of atom that we are calculating the distance between=3,4 ATOMS9the pair of atom that we are calculating the distance between=3,5 ATOMS10the pair of atom that we are calculating the distance between=4,5 d1ltThe LESS_THAN action with label d1lt calculates the following quantities:
Quantity Type Description d1 vector the DISTANCE for each set of specified atoms : LESS_THANUse a switching function to determine how many of the input variables are less than a certain cutoff. More details ARGthe values input to this function=d1 SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL D_0=2.0 R_0=0.5 D_MAX=5.0}
Quantity Type Description d1lt vector the vector obtained by doing an element-wise application of a function that is one if the input is less than a threshold to the input vectors
# These commands caluclate the angle between the z axis and the bond directions d1cThe DISTANCE action with label d1c calculates the following quantities:: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=2,1 ATOMS2the pair of atom that we are calculating the distance between=3,1 ATOMS3the pair of atom that we are calculating the distance between=4,1 ATOMS4the pair of atom that we are calculating the distance between=5,1 ATOMS5the pair of atom that we are calculating the distance between=3,2 ATOMS6the pair of atom that we are calculating the distance between=4,2 ATOMS7the pair of atom that we are calculating the distance between=5,2 ATOMS8the pair of atom that we are calculating the distance between=4,3 ATOMS9the pair of atom that we are calculating the distance between=5,3 ATOMS10the pair of atom that we are calculating the distance between=5,4 COMPONENTS calculate the x, y and z components of the distance separately and store them as label d2The COMBINE action with label d2 calculates the following quantities:
Quantity Type Description d1c.x vector the x-component of the vector connecting the two atoms d1c.y vector the y-component of the vector connecting the two atoms d1c.z vector the z-component of the vector connecting the two atoms : COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d1c.x,d1c.y,d1c.z POWERS the powers to which you are raising each of the arguments in your function=2,2,2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO aaThe MATHEVAL action with label aa calculates the following quantities:
Quantity Type Description d2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors : MATHEVALAn alias to the CUSTOM function that can also be used to calaculate combinations of variables using a custom expression. More details ARGthe values input to this function=d1c.z,d2 FUNCthe function you wish to evaluate=acos(x/sqrt(y)) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO # These commands compute the torsion angle between the bond direction and the positive x direction around the z axis dd0The FIXEDATOM action with label dd0 calculates the following quantities:
Quantity Type Description aa vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors : FIXEDATOMAdd a virtual atom in a fixed position. This action has hidden defaults. More details ATcoordinates of the virtual atom=0,0,0 dd0: FIXEDATOMAdd a virtual atom in a fixed position. This action uses the defaults shown here. More details ATcoordinates of the virtual atom=0,0,0 SET_MASS mass of the virtual atom=1 SET_CHARGE charge of the virtual atom=0 ddxThe FIXEDATOM action with label ddx calculates the following quantities:
Quantity Type Description dd0 atoms virtual atom calculated by FIXEDATOM action : FIXEDATOMAdd a virtual atom in a fixed position. This action has hidden defaults. More details ATcoordinates of the virtual atom=1,0,0 ddx: FIXEDATOMAdd a virtual atom in a fixed position. This action uses the defaults shown here. More details ATcoordinates of the virtual atom=1,0,0 SET_MASS mass of the virtual atom=1 SET_CHARGE charge of the virtual atom=0 ddzThe FIXEDATOM action with label ddz calculates the following quantities:
Quantity Type Description ddx atoms virtual atom calculated by FIXEDATOM action : FIXEDATOMAdd a virtual atom in a fixed position. This action has hidden defaults. More details ATcoordinates of the virtual atom=0,0,1 ddz: FIXEDATOMAdd a virtual atom in a fixed position. This action uses the defaults shown here. More details ATcoordinates of the virtual atom=0,0,1 SET_MASS mass of the virtual atom=1 SET_CHARGE charge of the virtual atom=0
Quantity Type Description ddz atoms virtual atom calculated by FIXEDATOM action
ttThe TORSION action with label tt calculates the following quantities:: TORSIONCalculate one or multiple torsional angles. More details ... VECTORA1two atoms that define a vector=2,1 VECTORB1two atoms that define a vector=ddx,dd0 AXIS1two atoms that define an axis=ddz,dd0 VECTORA2two atoms that define a vector=3,1 VECTORB2two atoms that define a vector=ddx,dd0 AXIS2two atoms that define an axis=ddz,dd0 VECTORA3two atoms that define a vector=4,1 VECTORB3two atoms that define a vector=ddx,dd0 AXIS3two atoms that define an axis=ddz,dd0 VECTORA4two atoms that define a vector=5,1 VECTORB4two atoms that define a vector=ddx,dd0 AXIS4two atoms that define an axis=ddz,dd0 VECTORA5two atoms that define a vector=3,2 VECTORB5two atoms that define a vector=ddx,dd0 AXIS5two atoms that define an axis=ddz,dd0 VECTORA6two atoms that define a vector=4,2 VECTORB6two atoms that define a vector=ddx,dd0 AXIS6two atoms that define an axis=ddz,dd0 VECTORA7two atoms that define a vector=5,2 VECTORB7two atoms that define a vector=ddx,dd0 AXIS7two atoms that define an axis=ddz,dd0 VECTORA8two atoms that define a vector=4,3 VECTORB8two atoms that define a vector=ddx,dd0 AXIS8two atoms that define an axis=ddz,dd0 VECTORA9two atoms that define a vector=5,3 VECTORB9two atoms that define a vector=ddx,dd0 AXIS9two atoms that define an axis=ddz,dd0 VECTORA10two atoms that define a vector=5,4 VECTORB10two atoms that define a vector=ddx,dd0 AXIS10two atoms that define an axis=ddz,dd0 ...
Quantity Type Description tt vector the TORSION for each set of specified atoms
# We now compute our instaneous normalised histogram of the bond directions. Notice that the weights are used here so that we do not consider # non-bonded atoms huThe KDE action with label hu calculates the following quantities:: KDECreate a histogram from the input scalar/vector/matrix using KDE This action has hidden defaults. More details VOLUMESthis keyword take the label of an action that calculates a vector of values=d1lt ARGthe label for the value that should be used to construct the histogram=aa,tt GRID_BINthe number of bins for the grid=20,20 GRID_MIN the lower bounds for the grid=0,-pi GRID_MAX the upper bounds for the grid=pi,pi BANDWIDTHthe bandwidths for kernel density esimtation=0.2,0.2 hu: KDECreate a histogram from the input scalar/vector/matrix using KDE This action uses the defaults shown here. More details VOLUMESthis keyword take the label of an action that calculates a vector of values=d1lt ARGthe label for the value that should be used to construct the histogram=aa,tt GRID_BINthe number of bins for the grid=20,20 GRID_MIN the lower bounds for the grid=0,-pi GRID_MAX the upper bounds for the grid=pi,pi BANDWIDTHthe bandwidths for kernel density esimtation=0.2,0.2 KERNEL the kernel function you are using=GAUSSIAN deThe SUM action with label de calculates the following quantities:
Quantity Type Description hu grid a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments : SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=d1lt PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO hThe CUSTOM action with label h calculates the following quantities:
Quantity Type Description de scalar the SUM of the elements in the input value : CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=hu,de 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 # And lastly compute the KL_ENTROPY klThe KL_ENTROPY action with label kl calculates the following quantities:
Quantity Type Description h grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid : KL_ENTROPYCalculate the KL entropy of a distribution This action is a shortcut. More details ARGthe grid that you wish to use in the KL entropy calculation=h REFERENCEa file containing the reference density in grid format=
Quantity Type Description kl scalar the value of the KL-Entropy regtest/gridtools/rt-weights-integral/kde.gridClick here to see an extract from this file.VALUEthe name of the value that should be read from the grid=h # PLUMED interprets the command: # kl: KL_ENTROPY ARG=h REFERENCE=regtest/gridtools/rt-weights-integral/kde.grid VALUE=h # as follows (Click the red comment above to revert to the short version of the input): kl_refThe REFERENCE_GRID action with label kl_ref calculates the following quantities:×FILE: regtest/gridtools/rt-weights-integral/kde.grid
#! FIELDS aa tt h dh_aa dh_tt #! SET min_aa 0 #! SET max_aa pi #! SET nbins_aa 20 #! SET periodic_aa false #! SET min_tt -pi #! SET max_tt pi #! SET nbins_tt 20 #! 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0.00000 0.00000 0.00000 2.35619 2.82743 0.00000 0.00001 0.00000 2.51327 2.82743 0.00000 0.00004 0.00002 2.67035 2.82743 0.00001 0.00004 0.00004 2.82743 2.82743 0.00001 -0.00001 0.00005 2.98451 2.82743 0.00001 -0.00004 0.00003 3.14159 2.82743 0.00000 -0.00003 0.00001: REFERENCE_GRIDSetup a constant grid by either reading values from a file or definining a function in input More details VALUEthe name of the value that should be read from the grid=h FILEthe name of the file that contains the reference data=
Quantity Type Description kl_ref grid the constant function on the grid that was specified in input regtest/gridtools/rt-weights-integral/kde.gridClick here to see an extract from this file.kl_klThe CUSTOM action with label kl_kl calculates the following quantities:×FILE: regtest/gridtools/rt-weights-integral/kde.grid
#! FIELDS aa tt h dh_aa dh_tt #! SET min_aa 0 #! SET max_aa pi #! SET nbins_aa 20 #! SET periodic_aa false #! SET min_tt -pi #! SET max_tt pi #! SET nbins_tt 20 #! 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-0.14399 1.57080 0.31416 0.00333 -0.02610 -0.05657 1.72788 0.31416 0.00080 -0.00709 -0.01090 1.88496 0.31416 0.00065 0.00418 0.00558 2.04204 0.31416 0.00188 0.01068 0.02308 2.19911 0.31416 0.00337 0.00587 0.04129 2.35619 0.31416 0.00326 -0.00712 0.03987 2.51327 0.31416 0.00170 -0.01037 0.02078 2.67035 0.31416 0.00048 -0.00479 0.00584 2.82743 0.31416 0.00007 -0.00101 0.00089 2.98451 0.31416 0.00001 -0.00011 0.00007 3.14159 0.31416 0.00000 0.00000 0.00000 0.00000 0.62832 0.00000 0.00000 0.00000 0.15708 0.62832 0.00000 0.00000 0.00000 0.31416 0.62832 0.00000 0.00000 0.00000 0.47124 0.62832 0.00000 0.00000 0.00000 0.62832 0.62832 0.00000 0.00000 0.00000 0.78540 0.62832 0.00000 0.00000 0.00000 0.94248 0.62832 0.00000 0.00000 0.00000 1.09956 0.62832 0.00000 0.00000 0.00000 1.25664 0.62832 0.00000 0.00000 0.00000 1.41372 0.62832 0.00001 0.00011 0.00002 1.57080 0.62832 0.00011 0.00193 0.00049 1.72788 0.62832 0.00126 0.01707 0.00554 1.88496 0.62832 0.00775 0.07440 0.03406 2.04204 0.62832 0.02571 0.14573 0.11292 2.19911 0.62832 0.04601 0.08008 0.20204 2.35619 0.62832 0.04442 -0.09713 0.19509 2.51327 0.62832 0.02315 -0.14152 0.10165 2.67035 0.62832 0.00651 -0.06535 0.02858 2.82743 0.62832 0.00099 -0.01380 0.00434 2.98451 0.62832 0.00008 -0.00145 0.00036 3.14159 0.62832 0.00000 0.00000 0.00000 0.00000 0.94248 0.00000 0.00000 0.00000 0.15708 0.94248 0.00000 0.00000 0.00000 0.31416 0.94248 0.00000 0.00000 0.00000 0.47124 0.94248 0.00000 0.00000 0.00000 0.62832 0.94248 0.00000 0.00000 0.00000 0.78540 0.94248 0.00000 0.00000 0.00000 0.94248 0.94248 0.00000 0.00000 0.00000 1.09956 0.94248 0.00000 0.00000 0.00000 1.25664 0.94248 0.00000 0.00000 0.00000 1.41372 0.94248 0.00001 0.00013 -0.00002 1.57080 0.94248 0.00013 0.00224 -0.00044 1.72788 0.94248 0.00146 0.01975 -0.00506 1.88496 0.94248 0.00897 0.08609 -0.03107 2.04204 0.94248 0.02975 0.16862 -0.10302 2.19911 0.94248 0.05324 0.09265 -0.18433 2.35619 0.94248 0.05140 -0.11239 -0.17799 2.51327 0.94248 0.02678 -0.16374 -0.09274 2.67035 0.94248 0.00753 -0.07562 -0.02608 2.82743 0.94248 0.00114 -0.01596 -0.00396 2.98451 0.94248 0.00009 -0.00167 -0.00032 3.14159 0.94248 0.00000 0.00000 0.00000 0.00000 1.25664 0.00000 0.00000 0.00000 0.15708 1.25664 0.00000 0.00000 0.00000 0.31416 1.25664 0.00000 0.00000 0.00000 0.47124 1.25664 0.00000 0.00000 0.00000 0.62832 1.25664 0.00000 0.00000 0.00000 0.78540 1.25664 0.00000 0.00000 0.00000 0.94248 1.25664 0.00000 0.00000 0.00000 1.09956 1.25664 0.00000 0.00000 0.00000 1.25664 1.25664 0.00000 0.00000 0.00000 1.41372 1.25664 0.00000 0.00001 -0.00001 1.57080 1.25664 0.00001 0.00022 -0.00014 1.72788 1.25664 0.00014 0.00194 -0.00162 1.88496 1.25664 0.00088 0.00845 -0.00996 2.04204 1.25664 0.00292 0.01655 -0.03304 2.19911 1.25664 0.00522 0.00909 -0.05911 2.35619 1.25664 0.00504 -0.01103 -0.05708 2.51327 1.25664 0.00263 -0.01607 -0.02974 2.67035 1.25664 0.00074 -0.00742 -0.00836 2.82743 1.25664 0.00011 -0.00157 -0.00127 2.98451 1.25664 0.00001 -0.00016 -0.00010 3.14159 1.25664 0.00000 0.00000 0.00000 0.00000 1.57080 0.00000 0.00000 0.00000 0.15708 1.57080 0.00000 0.00000 0.00000 0.31416 1.57080 0.00000 0.00000 0.00000 0.47124 1.57080 0.00000 0.00000 0.00000 0.62832 1.57080 0.00000 0.00000 0.00000 0.78540 1.57080 0.00000 0.00000 0.00000 0.94248 1.57080 0.00000 0.00000 0.00000 1.09956 1.57080 0.00000 0.00000 0.00000 1.25664 1.57080 0.00000 0.00000 0.00000 1.41372 1.57080 0.00000 0.00000 -0.00000 1.57080 1.57080 0.00000 0.00000 -0.00000 1.72788 1.57080 0.00000 0.00002 -0.00002 1.88496 1.57080 0.00001 0.00007 -0.00014 2.04204 1.57080 0.00002 0.00014 -0.00047 2.19911 1.57080 0.00004 0.00008 -0.00083 2.35619 1.57080 0.00004 -0.00009 -0.00080 2.51327 1.57080 0.00002 -0.00013 -0.00042 2.67035 1.57080 0.00001 -0.00006 -0.00012 2.82743 1.57080 0.00000 -0.00001 -0.00002 2.98451 1.57080 0.00000 -0.00000 -0.00000 3.14159 1.57080 0.00000 0.00000 0.00000 0.00000 1.88496 0.00000 0.00000 0.00000 0.15708 1.88496 0.00000 0.00000 0.00000 0.31416 1.88496 0.00000 0.00000 0.00000 0.47124 1.88496 0.00000 0.00000 0.00000 0.62832 1.88496 0.00000 0.00000 0.00000 0.78540 1.88496 0.00000 0.00000 0.00000 0.94248 1.88496 0.00000 0.00000 0.00000 1.09956 1.88496 0.00000 0.00000 0.00000 1.25664 1.88496 0.00000 0.00000 0.00000 1.41372 1.88496 0.00000 0.00000 0.00000 1.57080 1.88496 0.00000 0.00000 0.00000 1.72788 1.88496 0.00000 0.00000 0.00000 1.88496 1.88496 0.00000 0.00000 0.00000 2.04204 1.88496 0.00000 0.00000 0.00000 2.19911 1.88496 0.00000 0.00000 0.00000 2.35619 1.88496 0.00000 0.00000 0.00000 2.51327 1.88496 0.00000 0.00000 0.00000 2.67035 1.88496 0.00000 0.00000 0.00000 2.82743 1.88496 0.00000 -0.00000 0.00000 2.98451 1.88496 0.00000 -0.00000 0.00000 3.14159 1.88496 0.00000 -0.00000 0.00000 0.00000 2.19911 0.00000 0.00000 0.00000 0.15708 2.19911 0.00000 0.00000 0.00000 0.31416 2.19911 0.00000 0.00000 0.00000 0.47124 2.19911 0.00000 0.00000 0.00000 0.62832 2.19911 0.00000 0.00000 0.00000 0.78540 2.19911 0.00000 0.00000 0.00000 0.94248 2.19911 0.00000 0.00000 0.00000 1.09956 2.19911 0.00000 0.00000 0.00000 1.25664 2.19911 0.00000 0.00000 0.00000 1.41372 2.19911 0.00000 0.00000 0.00000 1.57080 2.19911 0.00000 0.00000 0.00000 1.72788 2.19911 0.00000 0.00000 0.00000 1.88496 2.19911 0.00000 0.00000 0.00000 2.04204 2.19911 0.00000 0.00000 0.00000 2.19911 2.19911 0.00000 0.00000 0.00000 2.35619 2.19911 0.00000 0.00000 0.00000 2.51327 2.19911 0.00000 0.00000 0.00000 2.67035 2.19911 0.00000 0.00000 0.00000 2.82743 2.19911 0.00000 -0.00000 0.00000 2.98451 2.19911 0.00000 -0.00000 0.00000 3.14159 2.19911 0.00000 -0.00000 0.00000 0.00000 2.51327 0.00000 0.00000 0.00000 0.15708 2.51327 0.00000 0.00000 0.00000 0.31416 2.51327 0.00000 0.00000 0.00000 0.47124 2.51327 0.00000 0.00000 0.00000 0.62832 2.51327 0.00000 0.00000 0.00000 0.78540 2.51327 0.00000 0.00000 0.00000 0.94248 2.51327 0.00000 0.00000 0.00000 1.09956 2.51327 0.00000 0.00000 0.00000 1.25664 2.51327 0.00000 0.00000 0.00000 1.41372 2.51327 0.00000 0.00000 0.00000 1.57080 2.51327 0.00000 0.00000 0.00000 1.72788 2.51327 0.00000 0.00000 0.00000 1.88496 2.51327 0.00000 0.00000 0.00000 2.04204 2.51327 0.00000 0.00000 0.00000 2.19911 2.51327 0.00000 0.00000 0.00000 2.35619 2.51327 0.00000 0.00000 0.00000 2.51327 2.51327 0.00000 0.00000 0.00001 2.67035 2.51327 0.00000 0.00000 0.00001 2.82743 2.51327 0.00000 -0.00000 0.00001 2.98451 2.51327 0.00000 -0.00000 0.00001 3.14159 2.51327 0.00000 -0.00000 0.00000 0.00000 2.82743 0.00000 0.00000 0.00000 0.15708 2.82743 0.00000 0.00000 0.00000 0.31416 2.82743 0.00000 0.00000 0.00000 0.47124 2.82743 0.00000 0.00000 0.00000 0.62832 2.82743 0.00000 0.00000 0.00000 0.78540 2.82743 0.00000 0.00000 0.00000 0.94248 2.82743 0.00000 0.00000 0.00000 1.09956 2.82743 0.00000 0.00000 0.00000 1.25664 2.82743 0.00000 0.00000 0.00000 1.41372 2.82743 0.00000 0.00000 0.00000 1.57080 2.82743 0.00000 0.00000 0.00000 1.72788 2.82743 0.00000 0.00000 0.00000 1.88496 2.82743 0.00000 0.00000 0.00000 2.04204 2.82743 0.00000 0.00000 0.00000 2.19911 2.82743 0.00000 0.00000 0.00000 2.35619 2.82743 0.00000 0.00001 0.00000 2.51327 2.82743 0.00000 0.00004 0.00002 2.67035 2.82743 0.00001 0.00004 0.00004 2.82743 2.82743 0.00001 -0.00001 0.00005 2.98451 2.82743 0.00001 -0.00004 0.00003 3.14159 2.82743 0.00000 -0.00003 0.00001: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=h,kl_ref FUNCthe function you wish to evaluate=y*log(y/(0.5*(x+y))) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO klThe CUSTOM action with label kl calculates the following quantities:
Quantity Type Description kl_kl grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid : INTEGRATE_GRIDCalculate the numerical integral of the function stored on the grid More details ARGthe label of the function on a grid that is being integrated=kl_kl PERIODICif the value of the output integral has a periodid domain then you use this keyword to specify the periodicity=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=kl FILEthe name of the file on which to output these quantities=colvar
Quantity Type Description kl scalar an arbitrary function
The CV kl that is defined in the input above describes the disribution of bond directions that is observed in the structure. To compute it we first define the orientations
of all the bonds in our structure relative to the lab frame by computing the angle between each bond direction and the z axis and the torsional angle around the z axis between
our bond vector and the positive x direction. In other words, we compute two of the three spherical polar coordinates
for each of the bond directions in our crystal structure.
A normalised histogram that describes the instaneous distribution for these bond directions is then computed by using the KDE action. The final scalar value for the CV is computed by determining the Kullbeck-Leibler divergence between this instaneous distribution and a reference distribution that is provided in input.
Notice that this action will also works if you use KDEs computed using the SPHERICAL_KDE action in input as is illustrated in the following input:
Click on the labels of the actions for more information on what each action computes
#SETTINGS INPUTFILES=regtest/gridtools/rt-kldiv/averageSp_X240.grid
# These two commands compute a set of weights that allow us to determine if each distance in our system is a bond d1The DISTANCE action with label d1 calculates the following quantities:: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=1,3 ATOMS3the pair of atom that we are calculating the distance between=1,4 ATOMS4the pair of atom that we are calculating the distance between=1,5 ATOMS5the pair of atom that we are calculating the distance between=2,3 ATOMS6the pair of atom that we are calculating the distance between=2,4 ATOMS7the pair of atom that we are calculating the distance between=2,5 ATOMS8the pair of atom that we are calculating the distance between=3,4 ATOMS9the pair of atom that we are calculating the distance between=3,5 ATOMS10the pair of atom that we are calculating the distance between=4,5 d1ltThe LESS_THAN action with label d1lt calculates the following quantities:
Quantity Type Description d1 vector the DISTANCE for each set of specified atoms : LESS_THANUse a switching function to determine how many of the input variables are less than a certain cutoff. More details ARGthe values input to this function=d1 SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL D_0=2.0 R_0=0.5 D_MAX=5.0}
Quantity Type Description d1lt vector the vector obtained by doing an element-wise application of a function that is one if the input is less than a threshold to the input vectors
# These commands compute the directors of the bonds between the atoms d1cThe DISTANCE action with label d1c calculates the following quantities:: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=2,1 ATOMS2the pair of atom that we are calculating the distance between=3,1 ATOMS3the pair of atom that we are calculating the distance between=4,1 ATOMS4the pair of atom that we are calculating the distance between=5,1 ATOMS5the pair of atom that we are calculating the distance between=3,2 ATOMS6the pair of atom that we are calculating the distance between=4,2 ATOMS7the pair of atom that we are calculating the distance between=5,2 ATOMS8the pair of atom that we are calculating the distance between=4,3 ATOMS9the pair of atom that we are calculating the distance between=5,3 ATOMS10the pair of atom that we are calculating the distance between=5,4 COMPONENTS calculate the x, y and z components of the distance separately and store them as label d1lThe CUSTOM action with label d1l calculates the following quantities:
Quantity Type Description d1c.x vector the x-component of the vector connecting the two atoms d1c.y vector the y-component of the vector connecting the two atoms d1c.z vector the z-component of the vector connecting the two atoms : CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=d1c.x,d1c.y,d1c.z FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO d1nxThe CUSTOM action with label d1nx calculates the following quantities:
Quantity Type Description d1l 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=d1c.x,d1l 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 d1nyThe CUSTOM action with label d1ny calculates the following quantities:
Quantity Type Description d1nx 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=d1c.y,d1l 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 d1nzThe CUSTOM action with label d1nz calculates the following quantities:
Quantity Type Description d1ny 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=d1c.z,d1l 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 # Now compute our instaneous normalised histogram of the bond directions huThe SPHERICAL_KDE action with label hu calculates the following quantities:
Quantity Type Description d1nz vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors : SPHERICAL_KDECreate a histogram from the input scalar/vector/matrix using SPHERICAL_KDE More details HEIGHTS this keyword takes the label of an action that calculates a vector of values=d1lt ARGthe label for the value that should be used to construct the histogram=d1nx,d1ny,d1nz GRID_BINthe number of points on the fibonacci sphere at which the density should be evaluated=400 CONCENTRATIONthe concentration parameter for the Von Mises-Fisher distributions=100.0 deThe SUM action with label de calculates the following quantities:
Quantity Type Description hu grid a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments : SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=d1lt PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO hThe CUSTOM action with label h calculates the following quantities:
Quantity Type Description de scalar the SUM of the elements in the input value : CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=hu,de 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 # And lastly compute the KL_ENTROPY klThe KL_ENTROPY action with label kl calculates the following quantities:
Quantity Type Description h grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid : KL_ENTROPYCalculate the KL entropy of a distribution This action is a shortcut. More details ARGthe grid that you wish to use in the KL entropy calculation=h REFERENCEa file containing the reference density in grid format=
Quantity Type Description kl scalar the value of the KL-Entropy regtest/gridtools/rt-kldiv/averageSp_X240.gridClick here to see an extract from this file.VALUEthe name of the value that should be read from the grid=av_Sp_X # PLUMED interprets the command: # kl: KL_ENTROPY ARG=h REFERENCE=regtest/gridtools/rt-kldiv/averageSp_X240.grid VALUE=av_Sp_X # as follows (Click the red comment above to revert to the short version of the input): kl_refThe REFERENCE_GRID action with label kl_ref calculates the following quantities:×FILE: regtest/gridtools/rt-kldiv/averageSp_X240.grid
#! FIELDS X_vectors.x X_vectors.y X_vectors.z av_Sp_X dav_Sp_X_X_vectors.x dav_Sp_X_X_vectors.y dav_Sp_X_X_vectors.z #! 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0.727500 0.675310 0.000026 0.000156 0.000938 0.000870 0.363906 0.732500 -0.575340 0.000000 0.000000 0.000000 -0.000000 -0.651739 0.737500 0.177002 0.003898 -0.127021 0.143735 0.034497 0.595247 0.742500 0.307205 0.757066 22.532061 28.106077 11.628723 -0.229473 0.747500 -0.623366 0.000705 -0.008091 0.026357 -0.021980 -0.249722 0.752500 0.609412 0.000000 -0.000000 0.000000 0.000000 0.590581 0.757500 -0.278223 0.000243 0.007175 0.009203 -0.003380 -0.617830 0.762500 -0.192043 0.510182 -15.760260 19.450670 -4.898835 0.322854 0.767500 0.553813 0.008972 0.144833 0.344303 0.248442 0.134752 0.772500 -0.620553 0.000000 0.000000 0.000000 -0.000000 -0.513532 0.777500 0.363013 0.000012 -0.000318 0.000481 0.000225 0.617692 0.782500 0.078427 0.174349 5.384703 6.821413 0.683684 -0.398394 0.787500 -0.470240 0.052161 -1.039035 2.053845 -1.226413 -0.023629 0.792500 0.609414 0.000001 -0.000001 0.000022 0.000017 0.424466 0.797500 -0.428745 0.000001 0.000012 0.000023 -0.000012 -0.595942 0.802500 0.029095 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0.000029 -0.000016 -0.344416 0.882500 0.320267 0.000003 -0.000046 0.000118 0.000043 0.460795 0.887500 -0.003435 0.008239 0.189828 0.365613 -0.001415 -0.334850 0.892500 -0.302191 0.012365 -0.207029 0.551809 -0.186836 0.041829 0.897500 0.439026 0.000009 0.000019 0.000404 0.000198 0.259494 0.902500 -0.343739 0.000000 0.000004 0.000013 -0.000005 -0.413074 0.907500 0.076246 0.001248 -0.025770 0.056614 0.004757 0.346788 0.912500 0.216984 0.009876 0.171252 0.450614 0.107152 -0.106114 0.917500 -0.383319 0.000058 -0.000307 0.002651 -0.001107 -0.175351 0.922500 0.343869 0.000000 -0.000000 0.000002 0.000001 0.350175 0.927500 -0.130849 0.000158 0.002769 0.007333 -0.001035 -0.334864 0.932500 -0.135315 0.003983 -0.066694 0.185724 -0.026950 0.149837 0.937500 0.314074 0.000161 0.001204 0.007533 0.002524 0.097643 0.942500 -0.319624 0.000000 0.000000 0.000004 -0.000001 -0.275454 0.947500 0.162386 0.000018 -0.000252 0.000868 0.000149 0.297915 0.952500 0.063172 0.000873 0.012998 0.041557 0.002756 -0.167641 0.957500 -0.234713 0.000172 -0.001444 0.008246 -0.002021 -0.032856 0.962500 0.269285 0.000001 -0.000001 0.000029 0.000008 0.192138 0.967500 -0.164399 0.000003 0.000026 0.000131 -0.000022 -0.232769 0.972500 -0.007888 0.000099 -0.001149 0.004799 -0.000039 0.150622 0.977500 0.147671 0.000059 0.000443 0.002872 0.000434 -0.009990 0.982500 -0.185994 0.000001 -0.000001 0.000068 -0.000013 -0.100083 0.987500 0.121767 0.000000 -0.000002 0.000024 0.000003 0.121028 0.992500 -0.017203 0.000004 0.000027 0.000218 -0.000004 -0.058306 0.997500 -0.039926 0.000001 -0.000004 0.000072 -0.000003: REFERENCE_GRIDSetup a constant grid by either reading values from a file or definining a function in input More details VALUEthe name of the value that should be read from the grid=av_Sp_X FILEthe name of the file that contains the reference data=
Quantity Type Description kl_ref grid the constant function on the grid that was specified in input regtest/gridtools/rt-kldiv/averageSp_X240.gridClick here to see an extract from this file.kl_klThe CUSTOM action with label kl_kl calculates the following quantities:×FILE: regtest/gridtools/rt-kldiv/averageSp_X240.grid
#! FIELDS X_vectors.x X_vectors.y X_vectors.z av_Sp_X dav_Sp_X_X_vectors.x dav_Sp_X_X_vectors.y dav_Sp_X_X_vectors.z #! SET nbins 400 0.070666 -0.997500 0.000000 0.000001 0.000005 -0.000065 0.000000 -0.090139 -0.992500 -0.082575 0.000006 -0.000026 -0.000291 -0.000024 0.013780 -0.987500 0.157015 0.000001 0.000001 -0.000064 0.000010 0.113329 -0.982500 -0.147818 0.000000 0.000003 -0.000022 -0.000003 -0.207711 -0.977500 0.036741 0.000029 -0.000300 -0.001412 0.000053 0.196513 -0.972500 0.125006 0.000153 0.001506 -0.007450 0.000958 -0.065646 -0.967500 -0.244201 0.000011 -0.000037 -0.000538 -0.000136 -0.125036 -0.962500 0.240749 0.000000 -0.000001 -0.000006 0.000001 0.270932 -0.957500 -0.098944 0.000050 0.000675 -0.002385 -0.000246 -0.281499 -0.952500 -0.116199 0.001040 -0.014640 -0.049538 -0.006043 0.135527 -0.947500 0.289614 0.000100 0.000677 -0.004731 0.001446 0.100023 -0.942500 -0.318888 0.000000 0.000000 -0.000004 -0.000001 -0.301081 -0.937500 0.174482 0.000025 -0.000374 -0.001164 0.000217 0.352746 -0.932500 0.077550 0.003155 0.055643 -0.147095 0.012233 -0.214997 -0.927500 -0.305811 0.000829 -0.008912 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-0.167641 0.957500 -0.234713 0.000172 -0.001444 0.008246 -0.002021 -0.032856 0.962500 0.269285 0.000001 -0.000001 0.000029 0.000008 0.192138 0.967500 -0.164399 0.000003 0.000026 0.000131 -0.000022 -0.232769 0.972500 -0.007888 0.000099 -0.001149 0.004799 -0.000039 0.150622 0.977500 0.147671 0.000059 0.000443 0.002872 0.000434 -0.009990 0.982500 -0.185994 0.000001 -0.000001 0.000068 -0.000013 -0.100083 0.987500 0.121767 0.000000 -0.000002 0.000024 0.000003 0.121028 0.992500 -0.017203 0.000004 0.000027 0.000218 -0.000004 -0.058306 0.997500 -0.039926 0.000001 -0.000004 0.000072 -0.000003: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=h,kl_ref FUNCthe function you wish to evaluate=y*log(y/(0.5*(x+y))) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO klThe CUSTOM action with label kl calculates the following quantities:
Quantity Type Description kl_kl grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid : INTEGRATE_GRIDCalculate the numerical integral of the function stored on the grid More details ARGthe label of the function on a grid that is being integrated=kl_kl PERIODICif the value of the output integral has a periodid domain then you use this keyword to specify the periodicity=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=kl FILEthe name of the file on which to output these quantities=colvar
Quantity Type Description kl scalar an arbitrary function
Full list of keywords
The following table describes the keywords and options that can be used with this action
| Keyword | Type | Default | Description |
|---|---|---|---|
| ARG | compulsory | none | the grid that you wish to use in the KL entropy calculation |
| REFERENCE | compulsory | none | a file containing the reference density in grid format |
| VALUE | compulsory | none | the name of the value that should be read from the grid |
References
More information about how this action can be used is available in the following articles: