# correl (c43b2)

Correlation Functions

The CORREL commands may be used to obtain a set of time series

for a given property from a trajectory. Once obtained, the time series

may be manipulated as required, saved or plotted, or to generate

correlation functions ( C(tau) = <A(t).A(t+tau)> ). The correlation

functions may be manipulated, saved, plotted, and transformed to find

spectral density (Fourier transform of C(tau)), etc and determine the

correlation times.

Reorienting a coordinate trajectory is possible using the

COMPARE command. For details

* Syntax | The syntax of the correlation command

* General | General information regarding the correlation section

* Enter | How to specify time series

* Trajectory | How to reference to trajectory files

* Edit | How the edit the time series specifications

* Mantime | How to manipulate time series

* Corfun | How to generate correlation functions.

* Spectrum | How to get a spectrum from a correlation function

* Cluster | How to cluster time series data into similar groups

* IO | Input/output guide to correlation functions and series

* Examples | Just what it says

The CORREL commands may be used to obtain a set of time series

for a given property from a trajectory. Once obtained, the time series

may be manipulated as required, saved or plotted, or to generate

correlation functions ( C(tau) = <A(t).A(t+tau)> ). The correlation

functions may be manipulated, saved, plotted, and transformed to find

spectral density (Fourier transform of C(tau)), etc and determine the

correlation times.

Reorienting a coordinate trajectory is possible using the

COMPARE command. For details

**»**dynamc Merge.* Syntax | The syntax of the correlation command

* General | General information regarding the correlation section

* Enter | How to specify time series

* Trajectory | How to reference to trajectory files

* Edit | How the edit the time series specifications

* Mantime | How to manipulate time series

* Corfun | How to generate correlation functions.

* Spectrum | How to get a spectrum from a correlation function

* Cluster | How to cluster time series data into similar groups

* IO | Input/output guide to correlation functions and series

* Examples | Just what it says

Top

Syntax for the CORREL command and subcommands

[SYNTAX CORRelation functions]

Syntax:

CORREL [ MAXTimesteps int ] [ MAXSeries int ] [ MAXAtoms ] [ COVAriance] -

default 512 default 2 default 100

[ nonbond-spec ] [ hbond-spec ] [ image-spec ] [NOUPdate]

[ INBFrq 0 ] [ IHBFrq 0 ] [ IMGFrq 0 ]

hbond-spec

nonbond-spec

image-spec

Subcommands:

miscellaneous-commands

COOR coordinate-manipulation-command

{ DUPLicate time-series-name }

{ }

ENTEr name { [ BONDs repeat(2x(atom-spec)) ] [ GEOMetry ] } c

{ [ ANGLe repeat(3x(atom-spec)) ] [ ENERgy ] } c

{ [ DIHEd repeat(4x(atom-spec)) [NOTR] ] } c

{ [ IMPRo repeat(4x(atom-spec)) ] } c

{ }

{ [ ATOM ] [ X ] repeat(atom-spec) [ MASS ] } e

{ [ FLUC ] [ Y ] } c

{ [ Z ] }

{ [ R ] }

{ [ XYZ ] }

{ }

{ VECT [ X ] repeat(2x(atom-spec)) } e

{ [ Y ] }

{ [ Z ] }

{ [ R ] }

{ [ XYZ ] }

{ }

{ ATOM DOTProduct repeat(2x(atom-spec)) [NORMal] [MASS]} e

{ FLUC DOTProduct repeat(2x(atom-spec)) [NORMal] [MASS]} e

{ VECT DOTProduct repeat(4x(atom-spec)) [NORMal] } e

{ }

{ ATOM CROSsproduct rep.(2x(atom-spec)) [NORMal] [MASS]} e

{ FLUC CROSsproduct rep.(2x(atom-spec)) [NORMal] [MASS]} e

{ VECT CROSsproduct rep.(4x(atom-spec)) [NORMal] } e

{ }

{ HBONd [4x(atom-spec)]*++ [ ENERgy ] } c

{ [ DISTance] }

{ [ HANGle ] }

{ [ AANGle ] }

{ }

{ DISTance repeat(2x(atom-spec)) } c

{ }

{ [ GYRAtion ] [ CUT real ] [ MASS ] s** } c

{ [ DENSity ] s** } c

{ }

{ RMS [ MASS ] [ ORIEnt ] s** } c

{ DRMS [atom-selection [atom-selection]] } c

{ SECS [CUTHB real] } c

{ MODE mode-number s** } c**

{ TEMPerature [ NDEGF int ] s** } v

{ ENERGY } c

{ HELIx [ SELE atom-selection END ] } c

{ INERtia [ SELE atom-selection END ][ TRACe | ALL] } c

{ PUCK RESI <resid> [SEGI <segid>] } c

{

{ PUCK ATOM [ Q ] repeat(6x(atom-spec)) }

{ [ THETa ] }

{ [ PHI ] }

{

{ USER user-value [ repeat(atom-spec) ] s** } e

{ SURF [ RPRPobe real] [ WEIG ] [ACCE|CONT] [RESI] } c

{ [ SELE atom-selection END ] }

{ }

{ CELL cell-spec }

{ TIME [ AKMA ] }

{ ZERO }

{ }

{ DIPO [ SELE atom-selection END ] [ OXYZ ] [ MASS ] }

{ VECM repeat(2x(atom-spec)) }

{ }

{ SDIP [ SHELL int ] [ OXYZ ] [ MASS ] } c***

{ [ BULK ] }

{ SATM [ SHELL int ] atom-spec } c***

{ [ BULK ] }

{ OMSC ETA friction-coefficient } c

{ }

{ PRDI proto_num [ MASS ] } c****

{ }

{ PRVE proto_num [ MASS ] } v*

{ }

( code: c-coordinates, v-velocities, e-either )

c** MODE time series is allowed only if CORREL is invoked from VIBRAN.

s** these utilize the first atom selection in the next TRAJ command.

c*** needs a CHARMM executable with SHELL functionality

c****,v* needs a CHARMM executable with PROTo functionality

*++ Hydrogen bond atom order is one of:

Donor,Hydrogen,Acceptor,Acceptor-antecedent

Donor,Hydrogen,Acceptor

Donor,Acceptor

cell-spec::= one of { A B C ALPHa BETA GAMMa ALL SHAPe }

atom-spec::= {residue-number atom-name}

{ segid resid atom-name }

{ BYNUm atom-number }

{ SELE atom-selection END} ***

atom-selection::=

*** Note: If an atom-selection is used for atom-spec's, then

all atom-spec's must be contained within one atom-selection

*** WARNING: For angles and dihedrals, if SELE is used to

specify atoms, then the order that the atoms are

used to determine the angle value is the order that

the atoms are in the psf/coord array. Recommend that

BYNUm is used to specify the correct order of atoms.

TRAJectory [ FIRStu int ] [ NUNIt int ] [ BEGIn int ] [ STOP int ]

[ SKIP int ] [ VELOcity ] [first-atom-selection]

[ ORIEnt [MASS] second-atom-selection ]

{ ALL } [P2] [UNIT int]

SHOW { time-series-name }

{ CORRelation-function } (defines ?P2, ?AVER, ?FLUC)

{ ALL }

EDIT { time-series-name } edit-spec

{ CORRelation-function }

edit-spec::= [INDEx int] [VECCod int] [CLASs int] [SECOnd int]

[TOTAl int] [SKIP int] [DELTa real]

[VALUe real] [NAME new-name] [OFFSet real]

READ { time-series-name } unit-spec edit-spec { [FILE] }

{ CORRelation-funct } { CARD }

{ DUMB [COLUmn int] }

{ ALL } { [FILE] }

WRITe { time-series-name } unit-spec { CARD }

{ CORRelation-function } { PLOT }

{ DUMB [ TIME ] }

MANTIME time-series-name

{ DAVErage } ! Q(t) = Q(t) - <Q(t)>,

<Q(t)> implies time average

{ NORMal } ! Q(t) = Q(t) / |Q(t)|

{ SQUAre } ! Q(t) = Q(t) ** 2

{ COS } ! Q(t) = COS(Q(t)) (in degrees)

{ ACOS } ! Q(t) = ACOS(Q(t)) (in degrees)

{ COS2 } ! Q(t) = 3*COS(Q(t))**2 - 1 (in degrees)

{ AVERage integer } ! Q(t) = < Q(ti) >(ti=t-NUTIL+1,t)

{ SQRT } ! Q(t) = SQRT(Q(t))

{ FLUCt name2 } ! print zero time fluctuations

{ DINItial } ! Q(t) = Q(t) - Q(1)

{ DELN integer } ! Q(t) = Q(t) - <Q(ti)>(ti=t-NUTIL+1,t)

{ OSC } ! print oscillations

{ COPY name2 [FIRSt int] [LAST int] }

! Q(t) = Q2(t1), t1=FIRST,..,LAST

{ ADD name2 } ! Q(t) = Q(t) + Q2(t)

{ RATIo name2 } ! Q(t) = Q(t) / Q2(t)

{ DOTProdcut name2 } ! Q(T) x-comp=Q(T).Q2(T)

Q2(T)x-comp=angle Q(T) vs Q2(T) degrees

{ CROSproduct name2 } ! Q(T) = Q(T)xQ2(T)

{ KMULt name2 } ! Q(t) = Q(t) * Q2(t)

{ PROB integer } ! Q(t) = PROB(Q(t))

{ HIST min max nbins } ! Q(ibin) = Fraction of Q(t) values in ibin

{ WHIS name2 min max nbins } ! Q(ibin) = Fraction of Q(t)*Q2(t) values in ibin

{ STATe rmin rmax } ! Q(T) = 1.0 , rmin < Q(T) < rmax

0.0 , Q(T) < rmim

0.0 , Q(T) > rmax

{ HEAViside } ! Q(T) = 1.0 ,Q(T)> 0

0.0, Q(T)<0

{ POLY integer } ! fit time series to polynomial (0-10)

[REPLace] [WEIGh name]

{ CONTinuous [real] } ! make a (dihedral) time series continuous

Q(t) = Q(t)+ n(t)*2*real, n(t)=integer

(default real is 180.0)

{ MAP real1 real2 } ! Q(t)is mapped to [real1,real2]

! (typically [0,360] -

! default or both have to be specified!

{ LOG } ! Q(t) = LOG(Q(t))

{ EXP } ! Q(t) = EXP(Q(t))

{ IPOWer integer } ! Q(t) = Q(t) ** integer

{ MULT real } ! Q(t) = real * Q(t)

{ DIVIde real } ! Q(t) = Q(t) / real

{ SHIFt real } ! Q(t) = Q(t) + real

{ DMIN } ! Q(t) = Q(t) - QMIN

{ ABS } ! Q(t) = ABS(Q(t))

{ DIVFirst } ! Q(t) = Q(t) / Q(1)

{ DIVMaximum } ! Q(t) = Q(t) / ABS(Q(MAX))

{ INTEgrate } ! Q(t) = Integral(0 to t) (Q(t)dt)

{ MOVIng integer } ! Q(t) = < Q(ti) >(ti=t-integer+1,t) (t)

{ TEST real } ! Q(t) = COS(2*PI*t*real/TTOT)

{ ZERO } ! Q(t) = 0.0

{ DERIvative } ! Q(t) = (Q(t+dt)-Q(t))/dt

{ SPHErical } ! Q(t) = Q(t) 3-component vector series

! converted to spherical coord:

! (x,y,z)-> (r,phi,theta)

DCOR 2x(time-series-name) ! Calculate dependence between two time

! series, which can be of different

! respective dimensions. Time series can

! contain any variable. The only requirement

! is that both time series should be of

! equal length. » dcor

CORFUN 2x(time-series-name)

{ [ PRODuct ] [ FFT ] [ LTC ] [ P1 ] [ NONOrm ] } [ XNORm real ] [ TOTAl int ]

{ [ DIREct] [ NLTC ] [ P2 ] }

{ }

{ DIFFerence }

SPECtrum [FOLD] [RAMP] [SWITch] [SIZE integer]

CLUSter time-series-name RADIus <real> [ MAXCluster <int> ] -

[ MAXIteration <int> ] [ MAXError <real> ] -

[ NFEAture <int> ] [ UNICluster <int> ] -

[ UNIMember <int> ] [ UNIInitial <int>] -

[ CSTEP <int> ] [ BEGIn <int> ] -

[ STOP <int> ] [ ANGLE ]

END ! return to main command parser

Syntax for the CORREL command and subcommands

[SYNTAX CORRelation functions]

Syntax:

CORREL [ MAXTimesteps int ] [ MAXSeries int ] [ MAXAtoms ] [ COVAriance] -

default 512 default 2 default 100

[ nonbond-spec ] [ hbond-spec ] [ image-spec ] [NOUPdate]

[ INBFrq 0 ] [ IHBFrq 0 ] [ IMGFrq 0 ]

hbond-spec

**»**hbonds .nonbond-spec

**»**nbonds .image-spec

**»**images Update.Subcommands:

miscellaneous-commands

COOR coordinate-manipulation-command

{ DUPLicate time-series-name }

{ }

ENTEr name { [ BONDs repeat(2x(atom-spec)) ] [ GEOMetry ] } c

{ [ ANGLe repeat(3x(atom-spec)) ] [ ENERgy ] } c

{ [ DIHEd repeat(4x(atom-spec)) [NOTR] ] } c

{ [ IMPRo repeat(4x(atom-spec)) ] } c

{ }

{ [ ATOM ] [ X ] repeat(atom-spec) [ MASS ] } e

{ [ FLUC ] [ Y ] } c

{ [ Z ] }

{ [ R ] }

{ [ XYZ ] }

{ }

{ VECT [ X ] repeat(2x(atom-spec)) } e

{ [ Y ] }

{ [ Z ] }

{ [ R ] }

{ [ XYZ ] }

{ }

{ ATOM DOTProduct repeat(2x(atom-spec)) [NORMal] [MASS]} e

{ FLUC DOTProduct repeat(2x(atom-spec)) [NORMal] [MASS]} e

{ VECT DOTProduct repeat(4x(atom-spec)) [NORMal] } e

{ }

{ ATOM CROSsproduct rep.(2x(atom-spec)) [NORMal] [MASS]} e

{ FLUC CROSsproduct rep.(2x(atom-spec)) [NORMal] [MASS]} e

{ VECT CROSsproduct rep.(4x(atom-spec)) [NORMal] } e

{ }

{ HBONd [4x(atom-spec)]*++ [ ENERgy ] } c

{ [ DISTance] }

{ [ HANGle ] }

{ [ AANGle ] }

{ }

{ DISTance repeat(2x(atom-spec)) } c

{ }

{ [ GYRAtion ] [ CUT real ] [ MASS ] s** } c

{ [ DENSity ] s** } c

{ }

{ RMS [ MASS ] [ ORIEnt ] s** } c

{ DRMS [atom-selection [atom-selection]] } c

{ SECS [CUTHB real] } c

{ MODE mode-number s** } c**

{ TEMPerature [ NDEGF int ] s** } v

{ ENERGY } c

{ HELIx [ SELE atom-selection END ] } c

{ INERtia [ SELE atom-selection END ][ TRACe | ALL] } c

{ PUCK RESI <resid> [SEGI <segid>] } c

{

{ PUCK ATOM [ Q ] repeat(6x(atom-spec)) }

{ [ THETa ] }

{ [ PHI ] }

{

{ USER user-value [ repeat(atom-spec) ] s** } e

{ SURF [ RPRPobe real] [ WEIG ] [ACCE|CONT] [RESI] } c

{ [ SELE atom-selection END ] }

{ }

{ CELL cell-spec }

{ TIME [ AKMA ] }

{ ZERO }

{ }

{ DIPO [ SELE atom-selection END ] [ OXYZ ] [ MASS ] }

{ VECM repeat(2x(atom-spec)) }

{ }

{ SDIP [ SHELL int ] [ OXYZ ] [ MASS ] } c***

{ [ BULK ] }

{ SATM [ SHELL int ] atom-spec } c***

{ [ BULK ] }

{ OMSC ETA friction-coefficient } c

{ }

{ PRDI proto_num [ MASS ] } c****

{ }

{ PRVE proto_num [ MASS ] } v*

{ }

( code: c-coordinates, v-velocities, e-either )

c** MODE time series is allowed only if CORREL is invoked from VIBRAN.

s** these utilize the first atom selection in the next TRAJ command.

c*** needs a CHARMM executable with SHELL functionality

**»**shellc****,v* needs a CHARMM executable with PROTo functionality

**»**proto*++ Hydrogen bond atom order is one of:

Donor,Hydrogen,Acceptor,Acceptor-antecedent

Donor,Hydrogen,Acceptor

Donor,Acceptor

cell-spec::= one of { A B C ALPHa BETA GAMMa ALL SHAPe }

atom-spec::= {residue-number atom-name}

{ segid resid atom-name }

{ BYNUm atom-number }

{ SELE atom-selection END} ***

atom-selection::=

**»**select*** Note: If an atom-selection is used for atom-spec's, then

all atom-spec's must be contained within one atom-selection

*** WARNING: For angles and dihedrals, if SELE is used to

specify atoms, then the order that the atoms are

used to determine the angle value is the order that

the atoms are in the psf/coord array. Recommend that

BYNUm is used to specify the correct order of atoms.

TRAJectory [ FIRStu int ] [ NUNIt int ] [ BEGIn int ] [ STOP int ]

[ SKIP int ] [ VELOcity ] [first-atom-selection]

[ ORIEnt [MASS] second-atom-selection ]

{ ALL } [P2] [UNIT int]

SHOW { time-series-name }

{ CORRelation-function } (defines ?P2, ?AVER, ?FLUC)

{ ALL }

EDIT { time-series-name } edit-spec

{ CORRelation-function }

edit-spec::= [INDEx int] [VECCod int] [CLASs int] [SECOnd int]

[TOTAl int] [SKIP int] [DELTa real]

[VALUe real] [NAME new-name] [OFFSet real]

READ { time-series-name } unit-spec edit-spec { [FILE] }

{ CORRelation-funct } { CARD }

{ DUMB [COLUmn int] }

{ ALL } { [FILE] }

WRITe { time-series-name } unit-spec { CARD }

{ CORRelation-function } { PLOT }

{ DUMB [ TIME ] }

MANTIME time-series-name

{ DAVErage } ! Q(t) = Q(t) - <Q(t)>,

<Q(t)> implies time average

{ NORMal } ! Q(t) = Q(t) / |Q(t)|

{ SQUAre } ! Q(t) = Q(t) ** 2

{ COS } ! Q(t) = COS(Q(t)) (in degrees)

{ ACOS } ! Q(t) = ACOS(Q(t)) (in degrees)

{ COS2 } ! Q(t) = 3*COS(Q(t))**2 - 1 (in degrees)

{ AVERage integer } ! Q(t) = < Q(ti) >(ti=t-NUTIL+1,t)

{ SQRT } ! Q(t) = SQRT(Q(t))

{ FLUCt name2 } ! print zero time fluctuations

{ DINItial } ! Q(t) = Q(t) - Q(1)

{ DELN integer } ! Q(t) = Q(t) - <Q(ti)>(ti=t-NUTIL+1,t)

{ OSC } ! print oscillations

{ COPY name2 [FIRSt int] [LAST int] }

! Q(t) = Q2(t1), t1=FIRST,..,LAST

{ ADD name2 } ! Q(t) = Q(t) + Q2(t)

{ RATIo name2 } ! Q(t) = Q(t) / Q2(t)

{ DOTProdcut name2 } ! Q(T) x-comp=Q(T).Q2(T)

Q2(T)x-comp=angle Q(T) vs Q2(T) degrees

{ CROSproduct name2 } ! Q(T) = Q(T)xQ2(T)

{ KMULt name2 } ! Q(t) = Q(t) * Q2(t)

{ PROB integer } ! Q(t) = PROB(Q(t))

{ HIST min max nbins } ! Q(ibin) = Fraction of Q(t) values in ibin

{ WHIS name2 min max nbins } ! Q(ibin) = Fraction of Q(t)*Q2(t) values in ibin

{ STATe rmin rmax } ! Q(T) = 1.0 , rmin < Q(T) < rmax

0.0 , Q(T) < rmim

0.0 , Q(T) > rmax

{ HEAViside } ! Q(T) = 1.0 ,Q(T)> 0

0.0, Q(T)<0

{ POLY integer } ! fit time series to polynomial (0-10)

[REPLace] [WEIGh name]

{ CONTinuous [real] } ! make a (dihedral) time series continuous

Q(t) = Q(t)+ n(t)*2*real, n(t)=integer

(default real is 180.0)

{ MAP real1 real2 } ! Q(t)is mapped to [real1,real2]

! (typically [0,360] -

! default or both have to be specified!

{ LOG } ! Q(t) = LOG(Q(t))

{ EXP } ! Q(t) = EXP(Q(t))

{ IPOWer integer } ! Q(t) = Q(t) ** integer

{ MULT real } ! Q(t) = real * Q(t)

{ DIVIde real } ! Q(t) = Q(t) / real

{ SHIFt real } ! Q(t) = Q(t) + real

{ DMIN } ! Q(t) = Q(t) - QMIN

{ ABS } ! Q(t) = ABS(Q(t))

{ DIVFirst } ! Q(t) = Q(t) / Q(1)

{ DIVMaximum } ! Q(t) = Q(t) / ABS(Q(MAX))

{ INTEgrate } ! Q(t) = Integral(0 to t) (Q(t)dt)

{ MOVIng integer } ! Q(t) = < Q(ti) >(ti=t-integer+1,t) (t)

{ TEST real } ! Q(t) = COS(2*PI*t*real/TTOT)

{ ZERO } ! Q(t) = 0.0

{ DERIvative } ! Q(t) = (Q(t+dt)-Q(t))/dt

{ SPHErical } ! Q(t) = Q(t) 3-component vector series

! converted to spherical coord:

! (x,y,z)-> (r,phi,theta)

DCOR 2x(time-series-name) ! Calculate dependence between two time

! series, which can be of different

! respective dimensions. Time series can

! contain any variable. The only requirement

! is that both time series should be of

! equal length. » dcor

CORFUN 2x(time-series-name)

{ [ PRODuct ] [ FFT ] [ LTC ] [ P1 ] [ NONOrm ] } [ XNORm real ] [ TOTAl int ]

{ [ DIREct] [ NLTC ] [ P2 ] }

{ }

{ DIFFerence }

SPECtrum [FOLD] [RAMP] [SWITch] [SIZE integer]

CLUSter time-series-name RADIus <real> [ MAXCluster <int> ] -

[ MAXIteration <int> ] [ MAXError <real> ] -

[ NFEAture <int> ] [ UNICluster <int> ] -

[ UNIMember <int> ] [ UNIInitial <int>] -

[ CSTEP <int> ] [ BEGIn <int> ] -

[ STOP <int> ] [ ANGLE ]

END ! return to main command parser

Top

General discussion regarding time series and correlation functions

Discussion:

The CORREL command invokes the CORREL subcommand parser.

The keyword values MAXTimesteps, MAXSeries, and MAXAtoms may be

specified for space allocation greater than the default options.

If there in insufficient virtual address memory for the space request,

it may be possible to achive the desired results by removing the

nonbond lists before running the CORREL command.

The MAXTimesteps value is the largest number of steps any

time series will contain. The MAXSeries keyword is the largest number

of timeseries that will be contained at any time within CORREL.

A vector time series will counts as 3 time series in allocating space.

The MAXAtoms keyword allocates space for the atoms that are specified

in the ENTER commands (also duplicating a time series requires more space

for atoms). For bonds, angles, dihedrals, and improper dihedral

specifications, one extra value is needed for each entry to hold the

CODES value (so each bond uses 3 atom entries, 4 for angles...).

The ENTER defines a time series. Many time series may be specified.

A time series is defined by the following items;

Name - Each time series must have a unique (4 character) name.

Class code - The type of time series (BOND, USER, ATOM,...)

Number of steps - The number of time steps currently valid

Velocity code - Was the time series read from velocities?

Skip value - What multiple of delta do the time steps represent?

Delta - Integration time step

Offset - Time of first element

Secondary code - Depends on Class code (Geometry/Energy)(X/Y/Z...)

Vector code - 1=simple time series, 3=vector, 0=Y or Z part of vector

Value - Utility series value, depends on Class code

Mass weighting - Are the elements to be mass weighted (only for ATOM)

Average - Time series average

Fluctuation - Time series fluctuation about the average

Atom pointer - Pointer into first specified atom in atom list

Atom count - Number atom entries given in the ENTER command

Time series - Series values from (1,NTOT)

The TRAJectory command processes all of the time series which

have a NTOT (number of steps) count of zero. For this process,

the main coordinates are used for reading the trajectory. If flutucations

are requested, the comparison coordinates MUST be filled with the

reference (or average) coordinates before invoking the TRAJectory

command. Allowing multiple TRAJectory commands separated by enter

commands make it possible to compute correlation function between

positions and velocities, or even for different trajectories.

The EDIT command allows the user to directly modify the time

series specifications.

The MANTIME command allows the user to manipulate the time

series values (and sometimes some of the specifications).

The SHOW command will display the specification data for all

of the time series.

General discussion regarding time series and correlation functions

Discussion:

The CORREL command invokes the CORREL subcommand parser.

The keyword values MAXTimesteps, MAXSeries, and MAXAtoms may be

specified for space allocation greater than the default options.

If there in insufficient virtual address memory for the space request,

it may be possible to achive the desired results by removing the

nonbond lists before running the CORREL command.

The MAXTimesteps value is the largest number of steps any

time series will contain. The MAXSeries keyword is the largest number

of timeseries that will be contained at any time within CORREL.

A vector time series will counts as 3 time series in allocating space.

The MAXAtoms keyword allocates space for the atoms that are specified

in the ENTER commands (also duplicating a time series requires more space

for atoms). For bonds, angles, dihedrals, and improper dihedral

specifications, one extra value is needed for each entry to hold the

CODES value (so each bond uses 3 atom entries, 4 for angles...).

The ENTER defines a time series. Many time series may be specified.

A time series is defined by the following items;

Name - Each time series must have a unique (4 character) name.

Class code - The type of time series (BOND, USER, ATOM,...)

Number of steps - The number of time steps currently valid

Velocity code - Was the time series read from velocities?

Skip value - What multiple of delta do the time steps represent?

Delta - Integration time step

Offset - Time of first element

Secondary code - Depends on Class code (Geometry/Energy)(X/Y/Z...)

Vector code - 1=simple time series, 3=vector, 0=Y or Z part of vector

Value - Utility series value, depends on Class code

Mass weighting - Are the elements to be mass weighted (only for ATOM)

Average - Time series average

Fluctuation - Time series fluctuation about the average

Atom pointer - Pointer into first specified atom in atom list

Atom count - Number atom entries given in the ENTER command

Time series - Series values from (1,NTOT)

The TRAJectory command processes all of the time series which

have a NTOT (number of steps) count of zero. For this process,

the main coordinates are used for reading the trajectory. If flutucations

are requested, the comparison coordinates MUST be filled with the

reference (or average) coordinates before invoking the TRAJectory

command. Allowing multiple TRAJectory commands separated by enter

commands make it possible to compute correlation function between

positions and velocities, or even for different trajectories.

The EDIT command allows the user to directly modify the time

series specifications.

The MANTIME command allows the user to manipulate the time

series values (and sometimes some of the specifications).

The SHOW command will display the specification data for all

of the time series.

Top

Specifying time series

The ENTER command defines a new time series. Each time series

specified by different enter commands must have a unique name (up to

4 characters). With this command, a time series may be defined and

then must be later filled with a TRAJectory command (or a MANTIME COPY,

or a READ time-series command). Alternativly, a time series may be retrieved

from an existing file, or duplicated from another time series that

currently exists.

The time series names "ALL" and "CORR" may not be used, and

are reserved for selecting all of the time series or the correlation

function respectivly.

The ENTER options are;

-----------------------------------------------------------------------------

DUPLicate time-series-name

This causes an exact copy of an existing time series to be

created (except with a different name). This may be useful where

several different type of manipulations are required on a single

time series.

-----------------------------------------------------------------------------

READ unit-number [CARD] [edit-spec]

This causes a time series to be created and all data then

read in from an existing time series file. All time series (up to the

maximum allowed) will be read with this command.

-----------------------------------------------------------------------------

[ BONDS repeat(2x(atom-spec)) ] [ GEOMETRY ]

[ ANGLE repeat(3x(atom-spec)) ] [ ENERGY ]

[ DIHEd repeat(4x(atom-spec)) [NOTR] ]

[ IMPRo repeat(4x(atom-spec)) ]

These specifications cause a particular internal coordinate

(or an average of several) to define the time series. It is not necessary

that the specified atoms have a corresponding PSF entry, but if ENERGY is

requested, the specified atoms must be able to produce a valid parameter

code. The default is GEOMETRY. With geometry, any 4 atoms may be specified.

A velocity trajectory should not be used to fill these types of time series.

The NOTR option for dihedral prevents the analysis of dihedral transitions.

-----------------------------------------------------------------------------

[ ATOM ] [ X ] repeat(atom-spec) [ MASS ]

[ FLUC ] [ Y ]

[ Z ]

[ R ]

[ XYZ ]

These ENTER commands define a time series, Q(t), based on atom

positions or velocities. The ATOM option uses the (X,Y,Z,R,or XYZ) values

directly. The FLUCtuation option subtracts off the reference values

(contained in the comparison coordinates). For example, if the average

structure is desired as the reference value, then the command:

COOR DYNA COMP trajectory-spec

would be required before invoking the TRAJECTORY command.

If more than one atom is specified, then Q(t) values are

averaged over atoms. If MASS is specified, then mass weighting is used in

this averaging of Q(t) values. The properties X,Y,Z, and R cause a scalar

time series to be created with the requested property. The XYZ option causes

a vector time series to be created.

ATOM: Q(t) = X(t)

FLUC: Q(t) = X(t) - Xref

-----------------------------------------------------------------------------

VECT [ X ] repeat(2x(atom-spec))

[ Y ]

[ Z ]

[ R ]

[ XYZ ]

The VECTor command is similar to the ATOM and FLUCuation

commands listed above, except the values are given by the difference

in position or velocity of 2 atoms. If more than one pair of atoms

is specified, then the values for each vector are averaged.

Q(t) = X1(t) - X2(t)

-----------------------------------------------------------------------------

ATOM DOTProduct repeat(2x(atom-spec))

FLUC DOTProduct repeat(2x(atom-spec))

VECT DOTProduct repeat(4x(atom-spec))

ATOM CROSsproduct repeat(2x(atom-spec))

FLUC CROSsproduct repeat(2x(atom-spec))

VECT CROSsproduct repeat(4x(atom-spec))

These ENTER commands produce a scalar time series for

velocities or positions with the following definitions;

ATOM DOTP: Q(t) = ( r1(t) | r2(t) )

FLUC DOTP: Q(t) = ( (r1(t)-r1(ref)) | (r2(t)-r2(ref)) )

VECT DOTP: Q(t) = ( (r1(t)-r2(t)) | (r3(t)-r4(4)) )

If more than one set of atoms is specified, then the vector values

are averaged. The dotproduct is then computed from the

averaged vectors. NOTE: the vectors are averaged, NOT the resultant

dotproducts or crossproducts. For the FLUC option, the reference

coordinates must be in the comparison coordinate set.

-----------------------------------------------------------------------------

[ GYRAtion ] [ CUT real ]

[ DENSity ]

These commands define a scalar time series for a coordinate

trajectory. The density calculation is based about the origin on all

atoms within the CUT value; the radius of gyration is for all atoms

within distance CUT of the geometric center of the molecule, and no

mass weighting is applied.

-----------------------------------------------------------------------------

MODE mode-number

This option generates a scalar time series which is obtained

by projecting the velocities onto the specified normal mode, or to

project the coordinate diplacement from the reference strucure. The

result is given by;

velocity: Q(t) = < root(mass)*v(t) | q >

position: Q(t) = < root(mass(i))*(r(t)-r(ref)) | q >

-----------------------------------------------------------------------------

TEMPerature

The time series is the temperature at each point.

If NDEFG is specified as a positive value, then this is used instead of

the NDEGF values from the trajectory file. If a negative NDEGF value

is specified, then NDEGF will be set to 3 times the number of selected

atoms in the trajectory associated trajectory command.

-----------------------------------------------------------------------------

HELIx atom-selection

The x,y, and z components of the normalized vector defining the

axis af a cylindrical surface best fitting the selected atoms.

So you end up with a three-dimesnional vector series.

Intended for say alpha helices where the selection would be something

like: SELE ATOM * * CA .AND. RESID 23:36 END, to give the axis of

an alpha helix running from residue 23 to residue 36.

-----------------------------------------------------------------------------

INERtia atom-selection [ TRACe | ALL ]

The x,y, and z components of the normalized vector defining

the principal axis obtained from diagonalizing the moment of inertia

tensor for the selected atoms at each time point. The eigenvector

corresponding to the smallest eigenvalue is returned, and 180 deg flips

of the axis are explicitly prohibited (nonphysical).

The optional TRACe keyword returns the sorted eigenvalues as a

three column time series, instead of the principal axis vector.

The optional ALL keyword (ALL and TRACe are mutually exclusive)

returns all three principal axes as a vector with 9 components (x1,y1,z1,...)

sorted with the main axis first.

NB! There may be problems, in particular for flexible systems, with

exchange of the two minor axes; the code tries to correct for this

(messages about this are printed at PRNLEV 7), but it may not always be

right...

-----------------------------------------------------------------------------

CELL cell-spec

If the cell-spec is one of the 6 unit cell parameters A, B, C,

ALPHA, BETA, or GAMMA, then a single time series corresponding to that

component is return. The keyword ALL returns a 6 element time series,

with the columns in the order given above. The SHAPE keyword returns

the shape matrix for the unit cell at each time point, in lower diagonal

form. The shape matrix has the angles as cosines, while ALPHA, BETA, and

GAMMA are in degrees.

-----------------------------------------------------------------------------

RMS [ORIE]

The RMS deviation from the COMPARISON coordinate set is

computed for the atoms in the first selection on the TRAJ command,

with a superposition to obtain a best fit to the same atoms in the

COMParison coordinate set if ORIEnt is specified.

If the TRAJ command also contains an ORIENT second_selection, this second

selection will first have been used for a superposition onto the COMP

coordinates.

-----------------------------------------------------------------------------

DRMS [[2x](atom-selection)]

For each frame, the RMS difference between interatomic distances computed

for the comparison coordinates and the coordinates in the trajectory, using

all atom pairs having one atom in each selection. If no selection is given, all

atoms are used; if only one selection is given, all atom pairs within this

selection are used. If an atom i appears in both selections the distance

r(i)-r(i) will not be included in the calculation.

No other corrections are made wrt connectivity.

----------------------------------------------------------------------------

SECS [CUTHB real]

Computes secondary structure content in first selection of TRAJ command, in

context of second selection of TRAJ command:

First component=fraction residues in alpha helix.

Second component=fraction residues in beta sheet.

The hydrogen-acceptor distance can be set with option CUTHB; default is 2.6, which

may need to be slightly increased.

Averaging the timeseries over a few frames (MANTIME ... AVERAGE) helps to

reduce apparent loss of structure due to small structural fluctutations.

Based on Kabsch&Sander definitions. Uses SECS routine of corman,

with its defaults (» corman ).

----------------------------------------------------------------------------

PUCK RESI <resid> [SEGI <segid>]

The sugar pucker phase and amplitude are calculated for

the (deoxy)ribose of the specified residue; the first segment is

the default. This gives a two-dimensional vector, with component 1

being the phase (degrees) and component 2 the pucker amplitude

(Angstroms), as defined by Cremer&Pople (JACS 1975).

-----------------------------------------------------------------------------

PUCK ATOM [ Q ] repeat(6x(atom-spec))

[ THETa ]

[ PHI ]

Reports the Cremer & Pople puckering coordinates Q, THETa, and PHI for

a six member ring of atoms. If Q, THETa, or PHI are not defined, all three

coordinates are reported.

-----------------------------------------------------------------------------

USER user-value [ repeat(atom-spec) ]

The USRTIM routine is called for each coordinate or velocity

set. The user value and atom list is also passed along. See the

description in (USERSB.SRC)USRTIM for more details.

Q(t) = Whatever you want!

-----------------------------------------------------------------------------

SURF [RPRObe real] [WEIG] [ACCE|CONT] [RESI] [SELE atom-selection END]

Computes the solvent accessible surface area vs time for the selected

atoms in the context of the FIRST selection given to the TRAJ command. Uses the

analytical method (

Keyword Default Meaning

RPRObe 1.6 probe radius

WEIG .FALSE. use WMAIN instead of LJ radii from parameter file

ACCE|CONT ACCE accessible or contact surface

RESI .FALSE. give ASA per residue in the selected set (creates a vector

timeseries with one component for each residue)

Example:

* Compute individual ASAs for 8 Trp residues in protein context given by all

* residues with at least one atom within 8A of the Trp rings

*

! r1 .. r8 are previously defined as 8 different Trp rings

define trps sele r1 .or. r2 .or. r3 .or. r4 .or. r5 .or. r6 .or. r7 .or. r8 end

define environment sele .byres. (segid cht .and. ( trps .around. 8.0 ) ) end

long ! allows all ASA values at each time point to be written on one line

correl maxseries 10 maxtime 50000 maxatom 200

enter asa surf rprobe 1.4 sele trps end resi

traj firstu 51 nunit 1 begin 100000 skip 500 sele environment end stop 125000

write asa dumb time unit 21

*hi

end

-----------------------------------------------------------------------------

TIME [ AKMA ]

The time is returned in picoseconds unless AKMA is specified.

Q(t) = t

-----------------------------------------------------------------------------

ZERO

A zero time series is specified ( Q(t)=0 ).

This option is useful for cases where time series will be read with

the DUMB option. For these cases, the EDIT command may also be needed

to get desired results.

-----------------------------------------------------------------------------

DIPO [ SELE atom-selection END ]

Computes the dipole moment of all atoms specified in the atom

selection. The OXYZ and MASS keywords have the same meaning as defined

in COOR DIPO.

-----------------------------------------------------------------------------

VECM [ SELE atom-selection END ]

Generates a series like VECT XYZ, but IMAGE aware (which need to

be set up appropriately). If CUTIM is chosen appropriately (e.g., L/2

for a cubic box), the vector in the timeseries will always represent the

minimum image pair of the two atoms.

-----------------------------------------------------------------------------

SDIP [ SHELL int ]

[ BULK ]

Computes the dipole moment of a water/solvent shell. Returns

X/Y/Z and the number of atoms in the shell.

The OXYZ and MASS keywords have the same meaning as defined in COOR DIPO.

-----------------------------------------------------------------------------

SATM [ SHELL int ] atom-spec

[ BULK ]

The series contains zero or one depending on whether the atom is

in the specified shell (or the bulk).

for further details.

-----------------------------------------------------------------------------

PRDI int [ MASS ]

This tree-dimensional time series contains the sum of all

single dipole moments for each set in a given prototype set (

Proto:» chmdoc/proto ). This differs from the overall dipole moment

for all sets only if the single sets carry a net charge. In this case

the dipole moment of each set is calculated relative to a given

reference point. If the MASS keyword is present, this point of

reference is the center of mass of a given set, while in its absence

the center of geometry is used. (Note: Almost equivalent functionality

can be obtained with the DIPO series.)

-----------------------------------------------------------------------------

PRVE int [ MASS ]

Is similar to PRDI but calculates the sum of the center of

geometry (or center of mass with keyword MASS) velocities of a given

prototype set.

-----------------------------------------------------------------------------

OMSC ETA real

The series computes the cumulative Onsager-Machlup score

(*note Onsager-Machlup score:» chmdoc/dims Onsager-Machlup

score.). ETA is the friction coefficient of the dynamics (in 1/ps). As

a first guess one may use the value used for the Langevin dynamics

('FBETA').

OMSC can only be used as the single time series in a CORREL

command. In particular, it is incompatible with RMS because they both

use the same reference array for different things (RMS stores the

comparison structure, OMSC the previous frame to compute velocities

X(t) - X(t-1).)

Output:

The standard output (at PRNLEV 3 or higher) consists of lines

OMSCORE> step-score normalized-cumulative-score

The OM score for the first step is calculated and used to normalize

all following scores. The numbers can become rather large and using

the normalized score avoids using LONG in the output. Otherwise the

output format overflows and only ******** would be printed.

With the CORREL WRITE command, the normalized-cumulative-score for N-1

steps is written to an CORREL output file. The first step contains the

normalization factor s(t=0). You may have to postprocess the file

(using for instance awk) after having written the output file

omscore.dat with CORREL's WRITE name DUMB TIME ...:

awk 'NR == 1 {s0 = $2}; {t=$1; s=s0*$2; print t," ",s}' \

omscore.dat > omscore_nn.dat

Note that it only makes sense to compare OM-scores for trajectories of

the same system and of the same length.

Specifying time series

The ENTER command defines a new time series. Each time series

specified by different enter commands must have a unique name (up to

4 characters). With this command, a time series may be defined and

then must be later filled with a TRAJectory command (or a MANTIME COPY,

or a READ time-series command). Alternativly, a time series may be retrieved

from an existing file, or duplicated from another time series that

currently exists.

The time series names "ALL" and "CORR" may not be used, and

are reserved for selecting all of the time series or the correlation

function respectivly.

The ENTER options are;

-----------------------------------------------------------------------------

DUPLicate time-series-name

This causes an exact copy of an existing time series to be

created (except with a different name). This may be useful where

several different type of manipulations are required on a single

time series.

-----------------------------------------------------------------------------

READ unit-number [CARD] [edit-spec]

This causes a time series to be created and all data then

read in from an existing time series file. All time series (up to the

maximum allowed) will be read with this command.

-----------------------------------------------------------------------------

[ BONDS repeat(2x(atom-spec)) ] [ GEOMETRY ]

[ ANGLE repeat(3x(atom-spec)) ] [ ENERGY ]

[ DIHEd repeat(4x(atom-spec)) [NOTR] ]

[ IMPRo repeat(4x(atom-spec)) ]

These specifications cause a particular internal coordinate

(or an average of several) to define the time series. It is not necessary

that the specified atoms have a corresponding PSF entry, but if ENERGY is

requested, the specified atoms must be able to produce a valid parameter

code. The default is GEOMETRY. With geometry, any 4 atoms may be specified.

A velocity trajectory should not be used to fill these types of time series.

The NOTR option for dihedral prevents the analysis of dihedral transitions.

-----------------------------------------------------------------------------

[ ATOM ] [ X ] repeat(atom-spec) [ MASS ]

[ FLUC ] [ Y ]

[ Z ]

[ R ]

[ XYZ ]

These ENTER commands define a time series, Q(t), based on atom

positions or velocities. The ATOM option uses the (X,Y,Z,R,or XYZ) values

directly. The FLUCtuation option subtracts off the reference values

(contained in the comparison coordinates). For example, if the average

structure is desired as the reference value, then the command:

COOR DYNA COMP trajectory-spec

would be required before invoking the TRAJECTORY command.

If more than one atom is specified, then Q(t) values are

averaged over atoms. If MASS is specified, then mass weighting is used in

this averaging of Q(t) values. The properties X,Y,Z, and R cause a scalar

time series to be created with the requested property. The XYZ option causes

a vector time series to be created.

ATOM: Q(t) = X(t)

FLUC: Q(t) = X(t) - Xref

-----------------------------------------------------------------------------

VECT [ X ] repeat(2x(atom-spec))

[ Y ]

[ Z ]

[ R ]

[ XYZ ]

The VECTor command is similar to the ATOM and FLUCuation

commands listed above, except the values are given by the difference

in position or velocity of 2 atoms. If more than one pair of atoms

is specified, then the values for each vector are averaged.

Q(t) = X1(t) - X2(t)

-----------------------------------------------------------------------------

ATOM DOTProduct repeat(2x(atom-spec))

FLUC DOTProduct repeat(2x(atom-spec))

VECT DOTProduct repeat(4x(atom-spec))

ATOM CROSsproduct repeat(2x(atom-spec))

FLUC CROSsproduct repeat(2x(atom-spec))

VECT CROSsproduct repeat(4x(atom-spec))

These ENTER commands produce a scalar time series for

velocities or positions with the following definitions;

ATOM DOTP: Q(t) = ( r1(t) | r2(t) )

FLUC DOTP: Q(t) = ( (r1(t)-r1(ref)) | (r2(t)-r2(ref)) )

VECT DOTP: Q(t) = ( (r1(t)-r2(t)) | (r3(t)-r4(4)) )

If more than one set of atoms is specified, then the vector values

are averaged. The dotproduct is then computed from the

averaged vectors. NOTE: the vectors are averaged, NOT the resultant

dotproducts or crossproducts. For the FLUC option, the reference

coordinates must be in the comparison coordinate set.

-----------------------------------------------------------------------------

[ GYRAtion ] [ CUT real ]

[ DENSity ]

These commands define a scalar time series for a coordinate

trajectory. The density calculation is based about the origin on all

atoms within the CUT value; the radius of gyration is for all atoms

within distance CUT of the geometric center of the molecule, and no

mass weighting is applied.

-----------------------------------------------------------------------------

MODE mode-number

This option generates a scalar time series which is obtained

by projecting the velocities onto the specified normal mode, or to

project the coordinate diplacement from the reference strucure. The

result is given by;

velocity: Q(t) = < root(mass)*v(t) | q >

position: Q(t) = < root(mass(i))*(r(t)-r(ref)) | q >

-----------------------------------------------------------------------------

TEMPerature

The time series is the temperature at each point.

If NDEFG is specified as a positive value, then this is used instead of

the NDEGF values from the trajectory file. If a negative NDEGF value

is specified, then NDEGF will be set to 3 times the number of selected

atoms in the trajectory associated trajectory command.

-----------------------------------------------------------------------------

HELIx atom-selection

The x,y, and z components of the normalized vector defining the

axis af a cylindrical surface best fitting the selected atoms.

So you end up with a three-dimesnional vector series.

Intended for say alpha helices where the selection would be something

like: SELE ATOM * * CA .AND. RESID 23:36 END, to give the axis of

an alpha helix running from residue 23 to residue 36.

-----------------------------------------------------------------------------

INERtia atom-selection [ TRACe | ALL ]

The x,y, and z components of the normalized vector defining

the principal axis obtained from diagonalizing the moment of inertia

tensor for the selected atoms at each time point. The eigenvector

corresponding to the smallest eigenvalue is returned, and 180 deg flips

of the axis are explicitly prohibited (nonphysical).

The optional TRACe keyword returns the sorted eigenvalues as a

three column time series, instead of the principal axis vector.

The optional ALL keyword (ALL and TRACe are mutually exclusive)

returns all three principal axes as a vector with 9 components (x1,y1,z1,...)

sorted with the main axis first.

NB! There may be problems, in particular for flexible systems, with

exchange of the two minor axes; the code tries to correct for this

(messages about this are printed at PRNLEV 7), but it may not always be

right...

-----------------------------------------------------------------------------

CELL cell-spec

If the cell-spec is one of the 6 unit cell parameters A, B, C,

ALPHA, BETA, or GAMMA, then a single time series corresponding to that

component is return. The keyword ALL returns a 6 element time series,

with the columns in the order given above. The SHAPE keyword returns

the shape matrix for the unit cell at each time point, in lower diagonal

form. The shape matrix has the angles as cosines, while ALPHA, BETA, and

GAMMA are in degrees.

-----------------------------------------------------------------------------

RMS [ORIE]

The RMS deviation from the COMPARISON coordinate set is

computed for the atoms in the first selection on the TRAJ command,

with a superposition to obtain a best fit to the same atoms in the

COMParison coordinate set if ORIEnt is specified.

If the TRAJ command also contains an ORIENT second_selection, this second

selection will first have been used for a superposition onto the COMP

coordinates.

-----------------------------------------------------------------------------

DRMS [[2x](atom-selection)]

For each frame, the RMS difference between interatomic distances computed

for the comparison coordinates and the coordinates in the trajectory, using

all atom pairs having one atom in each selection. If no selection is given, all

atoms are used; if only one selection is given, all atom pairs within this

selection are used. If an atom i appears in both selections the distance

r(i)-r(i) will not be included in the calculation.

No other corrections are made wrt connectivity.

----------------------------------------------------------------------------

SECS [CUTHB real]

Computes secondary structure content in first selection of TRAJ command, in

context of second selection of TRAJ command:

First component=fraction residues in alpha helix.

Second component=fraction residues in beta sheet.

The hydrogen-acceptor distance can be set with option CUTHB; default is 2.6, which

may need to be slightly increased.

Averaging the timeseries over a few frames (MANTIME ... AVERAGE) helps to

reduce apparent loss of structure due to small structural fluctutations.

Based on Kabsch&Sander definitions. Uses SECS routine of corman,

with its defaults (» corman ).

----------------------------------------------------------------------------

PUCK RESI <resid> [SEGI <segid>]

The sugar pucker phase and amplitude are calculated for

the (deoxy)ribose of the specified residue; the first segment is

the default. This gives a two-dimensional vector, with component 1

being the phase (degrees) and component 2 the pucker amplitude

(Angstroms), as defined by Cremer&Pople (JACS 1975).

-----------------------------------------------------------------------------

PUCK ATOM [ Q ] repeat(6x(atom-spec))

[ THETa ]

[ PHI ]

Reports the Cremer & Pople puckering coordinates Q, THETa, and PHI for

a six member ring of atoms. If Q, THETa, or PHI are not defined, all three

coordinates are reported.

-----------------------------------------------------------------------------

USER user-value [ repeat(atom-spec) ]

The USRTIM routine is called for each coordinate or velocity

set. The user value and atom list is also passed along. See the

description in (USERSB.SRC)USRTIM for more details.

Q(t) = Whatever you want!

-----------------------------------------------------------------------------

SURF [RPRObe real] [WEIG] [ACCE|CONT] [RESI] [SELE atom-selection END]

Computes the solvent accessible surface area vs time for the selected

atoms in the context of the FIRST selection given to the TRAJ command. Uses the

analytical method (

**»**corman .).Keyword Default Meaning

RPRObe 1.6 probe radius

WEIG .FALSE. use WMAIN instead of LJ radii from parameter file

ACCE|CONT ACCE accessible or contact surface

RESI .FALSE. give ASA per residue in the selected set (creates a vector

timeseries with one component for each residue)

Example:

* Compute individual ASAs for 8 Trp residues in protein context given by all

* residues with at least one atom within 8A of the Trp rings

*

! r1 .. r8 are previously defined as 8 different Trp rings

define trps sele r1 .or. r2 .or. r3 .or. r4 .or. r5 .or. r6 .or. r7 .or. r8 end

define environment sele .byres. (segid cht .and. ( trps .around. 8.0 ) ) end

long ! allows all ASA values at each time point to be written on one line

correl maxseries 10 maxtime 50000 maxatom 200

enter asa surf rprobe 1.4 sele trps end resi

traj firstu 51 nunit 1 begin 100000 skip 500 sele environment end stop 125000

write asa dumb time unit 21

*hi

end

-----------------------------------------------------------------------------

TIME [ AKMA ]

The time is returned in picoseconds unless AKMA is specified.

Q(t) = t

-----------------------------------------------------------------------------

ZERO

A zero time series is specified ( Q(t)=0 ).

This option is useful for cases where time series will be read with

the DUMB option. For these cases, the EDIT command may also be needed

to get desired results.

-----------------------------------------------------------------------------

DIPO [ SELE atom-selection END ]

Computes the dipole moment of all atoms specified in the atom

selection. The OXYZ and MASS keywords have the same meaning as defined

in COOR DIPO.

**»**corman for further details.-----------------------------------------------------------------------------

VECM [ SELE atom-selection END ]

Generates a series like VECT XYZ, but IMAGE aware (which need to

be set up appropriately). If CUTIM is chosen appropriately (e.g., L/2

for a cubic box), the vector in the timeseries will always represent the

minimum image pair of the two atoms.

-----------------------------------------------------------------------------

SDIP [ SHELL int ]

[ BULK ]

Computes the dipole moment of a water/solvent shell. Returns

X/Y/Z and the number of atoms in the shell.

**»**shell for further details.The OXYZ and MASS keywords have the same meaning as defined in COOR DIPO.

**»**corman . for further details.-----------------------------------------------------------------------------

SATM [ SHELL int ] atom-spec

[ BULK ]

The series contains zero or one depending on whether the atom is

in the specified shell (or the bulk).

**»**shell .for further details.

-----------------------------------------------------------------------------

PRDI int [ MASS ]

This tree-dimensional time series contains the sum of all

single dipole moments for each set in a given prototype set (

Proto:» chmdoc/proto ). This differs from the overall dipole moment

for all sets only if the single sets carry a net charge. In this case

the dipole moment of each set is calculated relative to a given

reference point. If the MASS keyword is present, this point of

reference is the center of mass of a given set, while in its absence

the center of geometry is used. (Note: Almost equivalent functionality

can be obtained with the DIPO series.)

-----------------------------------------------------------------------------

PRVE int [ MASS ]

Is similar to PRDI but calculates the sum of the center of

geometry (or center of mass with keyword MASS) velocities of a given

prototype set.

-----------------------------------------------------------------------------

OMSC ETA real

The series computes the cumulative Onsager-Machlup score

(*note Onsager-Machlup score:» chmdoc/dims Onsager-Machlup

score.). ETA is the friction coefficient of the dynamics (in 1/ps). As

a first guess one may use the value used for the Langevin dynamics

('FBETA').

OMSC can only be used as the single time series in a CORREL

command. In particular, it is incompatible with RMS because they both

use the same reference array for different things (RMS stores the

comparison structure, OMSC the previous frame to compute velocities

X(t) - X(t-1).)

Output:

The standard output (at PRNLEV 3 or higher) consists of lines

OMSCORE> step-score normalized-cumulative-score

The OM score for the first step is calculated and used to normalize

all following scores. The numbers can become rather large and using

the normalized score avoids using LONG in the output. Otherwise the

output format overflows and only ******** would be printed.

With the CORREL WRITE command, the normalized-cumulative-score for N-1

steps is written to an CORREL output file. The first step contains the

normalization factor s(t=0). You may have to postprocess the file

(using for instance awk) after having written the output file

omscore.dat with CORREL's WRITE name DUMB TIME ...:

awk 'NR == 1 {s0 = $2}; {t=$1; s=s0*$2; print t," ",s}' \

omscore.dat > omscore_nn.dat

Note that it only makes sense to compare OM-scores for trajectories of

the same system and of the same length.

Top

Specification of the Trajectory Files

The TRAJectory command reads a number of trajectory files whose

Fortran unit numbers are specified sequentially. The first unit is given

by the FIRSTU keyword and must be specified. NUNIT gives the number of

units to be scanned, and defaults to 1.

BEGIN, STOP, and SKIP are used to specify which steps in the

trajectory are actually used. BEGIN specifies the first step number to

be used. STOP specifies the last. SKIP is used to select steps

periodically as follows: only those steps whose step number is evenly

divisible by STEP are selected. The default value for BEGIN is the first

step in the trajectory; for STOP, it is the last step in the trajectory;

and for SKIP, the default is 1.

The first atom selection in the TRAJectory command is meaningful

only for those time series that require an atom selection. These are

time series defined by the following ENTER commands: GYRAtion, DENSity,

RMS, MODE, TEMPerature, and optionally USER.

General reorienting of a coordinate trajectory is possible using the

MERGE command. For details

It is also possible to perform a simple rms best fit of each frame with the

reference coordinates (comparison set) using the ORIEnt option. For this

option a second atom selection MUST be provided and a MASS keyword is an

option that allows for a mass weighting of the best fit. This superposition is

performed before any other manipulation on each frame to be analyzed.

If VELOcity is specified, a velocity trajectory will be looked

for. Otherwise, a coordinate trajectory is expected.

Any time series that has a zero count (NTOT=0) will be

filled by this comand. The time series count will then be filled

with the total number of steps processed for each of these series.

Any time series with a nonzero count (NTOT>0) will not be affected

by this command. The count may be set to zero for a time series with

the EDIT command.

Upon conclusion, the average and flucutation as well as some

other data is presented on each of the processed time series.

If any of the time series to be filled require a reference

coordinate set, then the comparison coordinates MUST be filled with the

reference (or average) coordinates before invoking the TRAJectory

command. Upon completion, the main coordinates contain the last coordinate

set read from the trajectory, and the comparison coordinates are unaffected.

Specification of the Trajectory Files

The TRAJectory command reads a number of trajectory files whose

Fortran unit numbers are specified sequentially. The first unit is given

by the FIRSTU keyword and must be specified. NUNIT gives the number of

units to be scanned, and defaults to 1.

BEGIN, STOP, and SKIP are used to specify which steps in the

trajectory are actually used. BEGIN specifies the first step number to

be used. STOP specifies the last. SKIP is used to select steps

periodically as follows: only those steps whose step number is evenly

divisible by STEP are selected. The default value for BEGIN is the first

step in the trajectory; for STOP, it is the last step in the trajectory;

and for SKIP, the default is 1.

The first atom selection in the TRAJectory command is meaningful

only for those time series that require an atom selection. These are

time series defined by the following ENTER commands: GYRAtion, DENSity,

RMS, MODE, TEMPerature, and optionally USER.

General reorienting of a coordinate trajectory is possible using the

MERGE command. For details

**»**dynamc Merge.It is also possible to perform a simple rms best fit of each frame with the

reference coordinates (comparison set) using the ORIEnt option. For this

option a second atom selection MUST be provided and a MASS keyword is an

option that allows for a mass weighting of the best fit. This superposition is

performed before any other manipulation on each frame to be analyzed.

If VELOcity is specified, a velocity trajectory will be looked

for. Otherwise, a coordinate trajectory is expected.

Any time series that has a zero count (NTOT=0) will be

filled by this comand. The time series count will then be filled

with the total number of steps processed for each of these series.

Any time series with a nonzero count (NTOT>0) will not be affected

by this command. The count may be set to zero for a time series with

the EDIT command.

Upon conclusion, the average and flucutation as well as some

other data is presented on each of the processed time series.

If any of the time series to be filled require a reference

coordinate set, then the comparison coordinates MUST be filled with the

reference (or average) coordinates before invoking the TRAJectory

command. Upon completion, the main coordinates contain the last coordinate

set read from the trajectory, and the comparison coordinates are unaffected.

Top

Editing a time series

The EDIT command allows the time series specifications

to be modified directly.

WARNING:: This command gives the user direct access to most time

series specification. There is NO checking to see if what is being done

makes sense. As such, this command is versitile and dangerous.

The EDIT command must be followed by a valid time series name.

All subsequent keywords will be based on that time series.

The series name "ALL" will cause the edit spec to operate on all

the time series. The name "CORR" will cause the edit to occur on the

correlation function.

The following may be specified for a time series;

INDEx integer - May be specified to modify X,Y, or Z (1,2,3 resp)

of a vector timeseries. Otherwise, all are modified.

The index number is in fact an offset from the specified

time series, where a value of 1 represents the selected

time series. A value of 5 will cause the edit operation

to modify the fourth time series from the specified.

CLASs integer - May be used to specify a class code (consult source).

TOTAl integer - The total number of valid steps may be altered, but

none of the values are modified. By setting this

value to zero, the time series is then ready again

for the next TRAJectory command.

SKIP integer - May be specified to reset the SKIP value. This may be

useful after reading an external time series.

DELTa real - May be specified to modify the basic time step. The

actual time step for a series is (SKIP*DELTA).

OFFSet real - The time of the first element in the time series.

VECCod integer - User may specify a vector code. This may be useful

in merging 3 separate time series into a vector

time series (or the reverse). In fact any number of

time series may be grouped together with this option.

For example, if a table with 5 time series is desired,

setting VECCOD to 5 for the first one and the writing

this time series will output all 5.

VALUe real - This allows the user to modify the series utility

value. Its function depends on the Class code.

This value is currently used for (USER, GYRAtion,

DENSity, MODE, and TIME)

SECOndary int - The secondary class code may be modified (consult source).

Editing a time series

The EDIT command allows the time series specifications

to be modified directly.

WARNING:: This command gives the user direct access to most time

series specification. There is NO checking to see if what is being done

makes sense. As such, this command is versitile and dangerous.

The EDIT command must be followed by a valid time series name.

All subsequent keywords will be based on that time series.

The series name "ALL" will cause the edit spec to operate on all

the time series. The name "CORR" will cause the edit to occur on the

correlation function.

The following may be specified for a time series;

INDEx integer - May be specified to modify X,Y, or Z (1,2,3 resp)

of a vector timeseries. Otherwise, all are modified.

The index number is in fact an offset from the specified

time series, where a value of 1 represents the selected

time series. A value of 5 will cause the edit operation

to modify the fourth time series from the specified.

CLASs integer - May be used to specify a class code (consult source).

TOTAl integer - The total number of valid steps may be altered, but

none of the values are modified. By setting this

value to zero, the time series is then ready again

for the next TRAJectory command.

SKIP integer - May be specified to reset the SKIP value. This may be

useful after reading an external time series.

DELTa real - May be specified to modify the basic time step. The

actual time step for a series is (SKIP*DELTA).

OFFSet real - The time of the first element in the time series.

VECCod integer - User may specify a vector code. This may be useful

in merging 3 separate time series into a vector

time series (or the reverse). In fact any number of

time series may be grouped together with this option.

For example, if a table with 5 time series is desired,

setting VECCOD to 5 for the first one and the writing

this time series will output all 5.

VALUe real - This allows the user to modify the series utility

value. Its function depends on the Class code.

This value is currently used for (USER, GYRAtion,

DENSity, MODE, and TIME)

SECOndary int - The secondary class code may be modified (consult source).

Top

Manipulating the Time Series

The MANTIME command allows the user to manipulate selected

time series, Q(t), and performs the operation requested by the option

and leaves the resultant time series as the active time series.

This helps in performing various permuations of manipulations to increase

the options without increasing the number of ENTER commands.

The keyword ordering must be followed exactly.

DAVErage subtracts the average of the time series from all elements.

NORMal normalises the vectorial time series.

(i.e. creates the unit vector by dividing all elements for

a given value of t by r(t) = sqrt(x**2 + y**2 + z**2) ).

SQUAre squares all the elements

COS obtains the cosine of all elements.

ACOS obtains the arc-cosine of all elements.

COS2 calculates 3*cos**2 - 1 for all elements.

AVERage integer calculates the average for every <integer> consecutive

points and increases the time interval by a factor of

<integer>. Note: NTOT is divided by <integer>.

SQRT obtains square root for all elements.

Negative elements are set to -SQRT(-q(t)).

FLUCt name The Q(t) remains unchanged.

A second (b) timeseries must be specified.

The zero time fluctuations are computed and printed

out. The following variables are computed:

A = <Qa(t) . Qb(t)>

B = sqrt <Qa(t)**2>

C = sqrt <Qb(t)**2>

D = A/(B*C)

DINItial subtracts the value of the first element from all elements.

Q(t) = Q(t) - Q(1)

DELN integer Q(I) = Q(I) - <Q(I)> I FROM 1 TO N, FROM N+1 TO N+N ETC.

(untested).

OSC counts the number of oscillations in Q(t) / unit time step.

The Q(t) remains unchanged.

COPY name This copies the second time series to the first. NTOT

of the first is set to that of the second. If FIRSt or LAST is

specified, a subset (I=FIRST,,,LAST, with a total of

FIRST-LAST+1 points) of the second series is copied.

Defaults for FIRSt and LAST are 1 and NTOT of the second

series.

ADD name Q(t) = Q(t) + Q2(t); add the second time series to the first

RATIo name Q(t) = Q(t) / Q2(t)

CROSsprod name Q(T) = Q(T) x Q2(T); the 3D crossproduct of the two

3D vectors formed by the selected and named timeseries

DOTProd name Q(T) = x-comp of Q(T)= Q(T) . Q2(T)

x-comp of Q2(T) angle in degrees between the two vectors

NOTE! Modifies Q2 as well as Q

to get just the x-comp you may then edit the selected series:

EDIT series VECCOD 1

KMULt name Q(t) = Q(t) * Q2(t)

PROB integer give the probability to find a specific value of the

time series. <integer> subdivisions of the time series

are considered so that there are integer+1 values.

HIST min max nbins

Q(ibin) = Fraction of Q(t) values within ibin

This command replaces a time series with a

histogram of the time series divided into "nbins" with

a range from "min" to "max". The histogram values sum to 1.

POLY integer [REPLace] [WEIGh name]

fit time series to polynomial. The order should

be in the range of 0 to 10.

Order 0 will provide just the average,

Order 1 will fit the time series to a stright line.

Order 2 will fit to a quadratic function.

The REPLace option will replace the time series with

fitted one. The WEIGht option will wait all data

by the values in a second time series.

CONTinuous real Q(t) = Q(t) + n(t) , where n(t) is an integer such that

the ABS(Q(t)-Q(t-1))<=real

The default value is 180.0, which is appropriate for

making a dihedral time series continuous. A different

positive value may be selected (such as a box size...).

LOG Q(t) = LOG(Q(t))

EXP Q(t) = EXP(Q(t))

IPOWer integer Q(t) = Q(t) ** integer

MULT real Q(t) = Q(t) * <real>

DIVI real Q(t) = Q(t) / <real>

SHIFt real Q(t) = Q(t) + <real>

DMIN Q(t) = Q(t) - QMIN, QMIN being the minimum of the time series.

ABS Q(t) = ABS(Q(t))

DIVFirst Q(t) = Q(t) / Q(1)

DIVMax Q(t) = Q(t)/ ABS(Q(t) with max norm)

INTEgrate Q(t) = Integral(0-t) [ Q(t) dt ]

MOVIng integer Q(t) = Q(t) = < Q(ti) >(ti=t-integer+1,t) (t)

At each time, computed the moving average of the last

<integer> points. It <integer> is zero or negative, the

moving average is taken over all the preceding points.

TEST real Q(t) = COS ( 2 * PI * <real> / NTOT )

ZERO Q(t) = 0

This option zeroes the specified time series.

DERIvative Q(t) = (Q(t+dt)-Q(t))/dt, the last point is set to the one

before last

Manipulating the Time Series

The MANTIME command allows the user to manipulate selected

time series, Q(t), and performs the operation requested by the option

and leaves the resultant time series as the active time series.

This helps in performing various permuations of manipulations to increase

the options without increasing the number of ENTER commands.

The keyword ordering must be followed exactly.

DAVErage subtracts the average of the time series from all elements.

NORMal normalises the vectorial time series.

(i.e. creates the unit vector by dividing all elements for

a given value of t by r(t) = sqrt(x**2 + y**2 + z**2) ).

SQUAre squares all the elements

COS obtains the cosine of all elements.

ACOS obtains the arc-cosine of all elements.

COS2 calculates 3*cos**2 - 1 for all elements.

AVERage integer calculates the average for every <integer> consecutive

points and increases the time interval by a factor of

<integer>. Note: NTOT is divided by <integer>.

SQRT obtains square root for all elements.

Negative elements are set to -SQRT(-q(t)).

FLUCt name The Q(t) remains unchanged.

A second (b) timeseries must be specified.

The zero time fluctuations are computed and printed

out. The following variables are computed:

A = <Qa(t) . Qb(t)>

B = sqrt <Qa(t)**2>

C = sqrt <Qb(t)**2>

D = A/(B*C)

DINItial subtracts the value of the first element from all elements.

Q(t) = Q(t) - Q(1)

DELN integer Q(I) = Q(I) - <Q(I)> I FROM 1 TO N, FROM N+1 TO N+N ETC.

(untested).

OSC counts the number of oscillations in Q(t) / unit time step.

The Q(t) remains unchanged.

COPY name This copies the second time series to the first. NTOT

of the first is set to that of the second. If FIRSt or LAST is

specified, a subset (I=FIRST,,,LAST, with a total of

FIRST-LAST+1 points) of the second series is copied.

Defaults for FIRSt and LAST are 1 and NTOT of the second

series.

ADD name Q(t) = Q(t) + Q2(t); add the second time series to the first

RATIo name Q(t) = Q(t) / Q2(t)

CROSsprod name Q(T) = Q(T) x Q2(T); the 3D crossproduct of the two

3D vectors formed by the selected and named timeseries

DOTProd name Q(T) = x-comp of Q(T)= Q(T) . Q2(T)

x-comp of Q2(T) angle in degrees between the two vectors

NOTE! Modifies Q2 as well as Q

to get just the x-comp you may then edit the selected series:

EDIT series VECCOD 1

KMULt name Q(t) = Q(t) * Q2(t)

PROB integer give the probability to find a specific value of the

time series. <integer> subdivisions of the time series

are considered so that there are integer+1 values.

HIST min max nbins

Q(ibin) = Fraction of Q(t) values within ibin

This command replaces a time series with a

histogram of the time series divided into "nbins" with

a range from "min" to "max". The histogram values sum to 1.

POLY integer [REPLace] [WEIGh name]

fit time series to polynomial. The order should

be in the range of 0 to 10.

Order 0 will provide just the average,

Order 1 will fit the time series to a stright line.

Order 2 will fit to a quadratic function.

The REPLace option will replace the time series with

fitted one. The WEIGht option will wait all data

by the values in a second time series.

CONTinuous real Q(t) = Q(t) + n(t) , where n(t) is an integer such that

the ABS(Q(t)-Q(t-1))<=real

The default value is 180.0, which is appropriate for

making a dihedral time series continuous. A different

positive value may be selected (such as a box size...).

LOG Q(t) = LOG(Q(t))

EXP Q(t) = EXP(Q(t))

IPOWer integer Q(t) = Q(t) ** integer

MULT real Q(t) = Q(t) * <real>

DIVI real Q(t) = Q(t) / <real>

SHIFt real Q(t) = Q(t) + <real>

DMIN Q(t) = Q(t) - QMIN, QMIN being the minimum of the time series.

ABS Q(t) = ABS(Q(t))

DIVFirst Q(t) = Q(t) / Q(1)

DIVMax Q(t) = Q(t)/ ABS(Q(t) with max norm)

INTEgrate Q(t) = Integral(0-t) [ Q(t) dt ]

MOVIng integer Q(t) = Q(t) = < Q(ti) >(ti=t-integer+1,t) (t)

At each time, computed the moving average of the last

<integer> points. It <integer> is zero or negative, the

moving average is taken over all the preceding points.

TEST real Q(t) = COS ( 2 * PI * <real> / NTOT )

ZERO Q(t) = 0

This option zeroes the specified time series.

DERIvative Q(t) = (Q(t+dt)-Q(t))/dt, the last point is set to the one

before last

Top

Calculating a Correlation Function

CORFUN: This option takes the specified time series and calculates the

desired correlation function from it. The resultant correlation function

is saved in a time series named "CORR" which may then be used in subsequent

CORREL manipulation or write commands. If multiple CORFUN commands are

requested, then the "CORR" time series is overwritten.

Command line substitution parameter CFNORM is set to the value that would be

used as the multiplicative normalization factor of the correlation function.

In the following, Qa and Qb refer to the time series that were

extracted using the CORREL command.

PRODuct This option (default) generates a correlation function that is the

product of the time series elements.

C(tau) = < Q1(t)*Q2(t+tau) >

DIFFerence

The difference option is an alternative of the product option

and it generates a function that is useful in calculating

diffusion constants (slope at long tau).

C(tau) = < ( Q1(t) - Q2(t+tau) ) **2 >

FFT This option is to calculate the correlation function using the FFT

method. There are certain limitations on the prime factors

in the total number of points.

DIRECT This option is to calculate the correlation function using the

direct multiplication method.

P1 This option gives the direct correlation function, <Qa(0).Qb(t)>.

If Qa and Qb are unit vectors, then this is also the first

order Legendre Polynomial

P2 This is to obtain the correlation function of second order Legendre

Polynomial, (3 <[Qa(0).Qb(t)]**2> - 1)/2. For all applications

that I can think of, Qa and Qb will be unit vectors. For P2, LTC = 0

and NORM = 1

NLTC no long tail correction.

LTC long tail correction (subtracts <Qa>**2 if autocorrelation,

<Qa>*<Qb> if cross correlation. There is no LTC for P2

so NLTC and LTC give same result.)

This feature is to be used with care. If the Qa and Qb are

fluctuations from the mean (i.e. FLCT or MANTIME DELTA), then

this can serve as a correction for roundoff error. Otherwise,

they are not centered about the mean, this correction causes

the C.F. to be a less accurate calculation of fluctuations from

the mean, i.e.

<Qa(0).Qb(t)> - LTC = <Qa(0).Qb(t)> - <Qa>*<Qb>

= <delta Qa(0) . delta Qb(t)>

NONORM Correlations are not normalized. This is useful for adding

correlations computed in different trajectories.

(P2 is not normalized)

The correlation functions are normalized unless NONORM is specified.

XNORm Use this value if not zero as normalization factor (multiplies all

values in correlation function). Overrides NONORM setting.

TOTAL integer

The TOTAL value determines the number of points to keep in

the correlation function. The number of points may not be

grater than the number of points in the time series. A reasonable

value is about 1/4 to 1/3 the length of the time series.

Correlation function values near the end have little weight.

The default value is the nearest power of two less than half of

the time series length.

The defaults are FFT, P1, NLTC.

Note: The correlation time which is given by the program is calculated

by an exponential fit to the first NTOT/8 points or up to the

first crossing of the time axis. This value should be considered

a (poor) estimate, it is meaningful only for correlation functions

which decay exponentially to zero with no oscillations.

For P1,

C(t) = (c(t) - ltc)/N

ltc and Normalization factors, N, are:

LTC, autocorrelation:

ltc = <Qa>**2 for P1

= 0 for P2

N = C(0) - ltc

= <Qa**2> - ltc

LTC, cross-correlations:

ltc = <Qa>*<Qb>

N = sqrt[ (<Qa**2> - <Qa>**2) * (<Qb**2> - <Qb>**2) ]

NLTC, autocorrelation:

ltc = 0

N = C(0)

NLTC, cross-correlations:

ltc = 0

N = sqrt [<Qa**2>*<Qb**2>]

Calculating a Correlation Function

CORFUN: This option takes the specified time series and calculates the

desired correlation function from it. The resultant correlation function

is saved in a time series named "CORR" which may then be used in subsequent

CORREL manipulation or write commands. If multiple CORFUN commands are

requested, then the "CORR" time series is overwritten.

Command line substitution parameter CFNORM is set to the value that would be

used as the multiplicative normalization factor of the correlation function.

In the following, Qa and Qb refer to the time series that were

extracted using the CORREL command.

PRODuct This option (default) generates a correlation function that is the

product of the time series elements.

C(tau) = < Q1(t)*Q2(t+tau) >

DIFFerence

The difference option is an alternative of the product option

and it generates a function that is useful in calculating

diffusion constants (slope at long tau).

C(tau) = < ( Q1(t) - Q2(t+tau) ) **2 >

FFT This option is to calculate the correlation function using the FFT

method. There are certain limitations on the prime factors

in the total number of points.

DIRECT This option is to calculate the correlation function using the

direct multiplication method.

P1 This option gives the direct correlation function, <Qa(0).Qb(t)>.

If Qa and Qb are unit vectors, then this is also the first

order Legendre Polynomial

P2 This is to obtain the correlation function of second order Legendre

Polynomial, (3 <[Qa(0).Qb(t)]**2> - 1)/2. For all applications

that I can think of, Qa and Qb will be unit vectors. For P2, LTC = 0

and NORM = 1

NLTC no long tail correction.

LTC long tail correction (subtracts <Qa>**2 if autocorrelation,

<Qa>*<Qb> if cross correlation. There is no LTC for P2

so NLTC and LTC give same result.)

This feature is to be used with care. If the Qa and Qb are

fluctuations from the mean (i.e. FLCT or MANTIME DELTA), then

this can serve as a correction for roundoff error. Otherwise,

they are not centered about the mean, this correction causes

the C.F. to be a less accurate calculation of fluctuations from

the mean, i.e.

<Qa(0).Qb(t)> - LTC = <Qa(0).Qb(t)> - <Qa>*<Qb>

= <delta Qa(0) . delta Qb(t)>

NONORM Correlations are not normalized. This is useful for adding

correlations computed in different trajectories.

(P2 is not normalized)

The correlation functions are normalized unless NONORM is specified.

XNORm Use this value if not zero as normalization factor (multiplies all

values in correlation function). Overrides NONORM setting.

TOTAL integer

The TOTAL value determines the number of points to keep in

the correlation function. The number of points may not be

grater than the number of points in the time series. A reasonable

value is about 1/4 to 1/3 the length of the time series.

Correlation function values near the end have little weight.

The default value is the nearest power of two less than half of

the time series length.

The defaults are FFT, P1, NLTC.

Note: The correlation time which is given by the program is calculated

by an exponential fit to the first NTOT/8 points or up to the

first crossing of the time axis. This value should be considered

a (poor) estimate, it is meaningful only for correlation functions

which decay exponentially to zero with no oscillations.

For P1,

C(t) = (c(t) - ltc)/N

ltc and Normalization factors, N, are:

LTC, autocorrelation:

ltc = <Qa>**2 for P1

= 0 for P2

N = C(0) - ltc

= <Qa**2> - ltc

LTC, cross-correlations:

ltc = <Qa>*<Qb>

N = sqrt[ (<Qa**2> - <Qa>**2) * (<Qb**2> - <Qb>**2) ]

NLTC, autocorrelation:

ltc = 0

N = C(0)

NLTC, cross-correlations:

ltc = 0

N = sqrt [<Qa**2>*<Qb**2>]

Top

Generating a Spectrum from Correlation Functions

There is a command, SPECtral-density, which may be used to generate

a spectrum from a correlation function. The synatax is;

SPECtrum [SIZE integer] [FOLD] [RAMP] [SWITch]

Generating a Spectrum from Correlation Functions

There is a command, SPECtral-density, which may be used to generate

a spectrum from a correlation function. The synatax is;

SPECtrum [SIZE integer] [FOLD] [RAMP] [SWITch]

Top

Clustering Time Series Data

This command clusters time series data obtained within the CORREL

facility. The time series must first be defined using CORREL's ENTEr

command and the data read in via TRAJ or READ. The CLUSter command

clusters these data into groups with similar time series values, with

each cluster being defined by a "cluster center". The cluster centers are

output to UNICluster, and a list of time points and assigned clusters is

given in the cluster membership file (UNIMember).

For example, if you want to find similar conformations of a peptide

using dihedral angles, you would first define the set of dihedral angles to

be considered, say angle(1) -> angle(M), as M time series. If the time series

were each N time steps long, then you would be clustering N "patterns", with

each pattern M "features" long.

Consecutive time series are clustered. If the first time series

is, for example, "ts1" then the "veccod" of this time series can be

changed to the number of time series to be clustered:

CORREL ...

ENTE ts1 ...

ENTE ts2 ...

...

ENTE tsM ...

EDIT ts1 veccod M

TRAJ ... (or READ ...)

CLUSTER ts1 ...

END

Alternatively, NFEAture M can be specified in the CLUSter command line.

Note that vector time series count as three features.

The Clustering Algorithm

ART-2' is a step-wise optimal clustering algorithm based on a

self-organizing neural net (Carpenter & Grossberg, 1987; Pao, 1989;

Karpen et al., 1993). The algorithm optimizes cluster assignment subject

to a constraint on cluster radius, such that no member of a cluster is more

than a specified distance from the cluster center. This optimization is

carried out as an iterative minimization procedure that minimizes the

Euclidean distance between the cluster center and its members.

A self-organizing net is created with each output node representing

a cluster. The number of pattern features is equal to the number of input

nodes. The weights of the connections between the input layer (layer i)

and the output layer (layer j) are denoted by b(j,i). For each cluster j,

b(j,i), i = 1, nfeature, is the cluster center. To create the net (which is

synonomous to learning the classification scheme or cluster centers) the

following algorithm is implemented:

1. To initialize the network, assign b(1,i) equal to the first

pattern tq(1,i) for i = 1, nfeature.

2. For each pattern number k, calculate the Euclidean distance (rms)

between the pattern tq(k,i) and all cluster centers b(j,i), where

j is the cluster index.

rms(j,k) = sqrt[sum [(b(j,i)-tq(k,i))**2] for i = 1, nfeature]

3. Find cluster j such that rms(j,k) < rms(i,k) for all i<>j. If

rms(j,k) <= Threshold, then update b(j,i):

b(j,i) = ((m-1)*b(j,i) + tq(k,i))/m,

where m is the number of prior updates of b(j,i). Note that

b(j,i) is the average of feature i for all patterns currently

assigned to cluster j.

4. If rms > Threshold for all prior cluster centers (j=1,numclusters),

then create a new cluster center by increasing the number of

output nodes by one, and assign the weights b(numclusters,i) of

this node the value of the pattern tq(k,i).

5. Repeat 2.-4. until all patterns have been input.

6. Compare the new set of cluster centers with the last set. If

the difference between them is less than MAXError, then halt

clustering.

7. If the difference between the sets of cluster centers is greater

than MAXError, then use the new set of cluster centers as the

starting cluster centers, and repeat steps 2.-6. Else, clustering

is complete.

Note that the cluster centers currently being calculated in step 3

are only used for the comparison in step 2 during the first

iteration with no initial cluster centers. Otherwise, the centers

calculated in the previous iteration (or read from UNIInit) are

used in the comparison in step 2. Hence, in the initial "learning"

phase, cluster centers are recalculated as each new member is added.

In subsequent "refining" phases, cluster centers are not updated

until all conformations are read in and assigned.

References:

1) Carpenter, G. A., & Grossberg, S. 1987. ART 2: Self-organization of stable

category recognition codes for analog input patterns. Appl. Optics 26:4919-

4930.

2) Pao, Y.-H. 1989. Adaptive Pattern Recognition and Neural Networks, Addison-

Wesley, New York.

3) Karpen, M. E., Tobias, D. T., & Brooks III, C. L. 1993. Statistical

clustering techniques for analysis of long molecular dynamics trajectories.

I: Analysis of 2.2 ns trajectories of YPGDV. Biochemistry 32:412-420.

CLUSter Parameters

CLUSter time-series-name RADIus <real> [ MAXCluster <int> ] -

[ MAXIteration <int> ] [ MAXError <real> ] -

[ NFEAture <int> ] [ UNICluster <int> ] -

[ UNIMember <int> ] [ UNIInitial <int>] -

[ CSTEP <int> ] [ BEGIn <int> ] -

[ STOP <int> ] [ ANGLE ]

1. time-series-name: The name of the first time series (as defined by

the ENTE command) to be clustered.

2. RADIus: Maximum radius of cluster. The rms cutoff or threshold for

assignment to a cluster.

3. MAXCluster: Maximum number of clusters (default = 50).

4. MAXIteration: The maximum number of iterations allowed. If the

clustering has not converged by this number of iterations, all

clusters are output (default = 20).

5. MAXError: If the rms difference between the position of the cluster

centers for the last two iterations is less than maxerror, the system

is considered converged and the clustering is halted (default = 0.001).

6. NFEAture: This variable gives the number of features in the input

pattern, that is, the number of time series to be clustered at a time.

The default is the veccod parameter associated with 'time-series-name'.

NFEATure time series are clustered, starting with 'time-series-name'

and continuing with the next nfeature-1 series specified in subsequent

'ENTE' commands (default = veccod of time-series-name).

7. UNICluster: The unit number of the output cluster file. If UNIC = -1

(the default), the cluster parameters are output to the standard output.

8. UNIMember: The unit number of the output membership file. This file

lists each time point and the cluster(s) associated with the specified

time series at that time point. If UNIM = -1 (the default), the

membership list is not output.

9. UNIInit: The unit number of the file with the initial cluster centers.

If UNII = -1 (the default), no initial cluster centers are specified.

10. CSTEp: This variable gives the spacing between time series in the

input vector. For each timepoint k, the set of patterns clustered is

tq(k,1) -> tq(k,nfeature), tq(k,1 + cstep) -> tq(k,nfeature + cstep),

...,tq(k,nserie - nfeature + 1) -> tq(k,nserie) (default = nfeature).

11. BEGIn: Indicates frame in time series where clustering begins

(default = 1).

12. STOP: Indicates the frame in the time series where clustering ends

(default = minimum length (TOTAl in SHOW) of time series).

13. ANGLe: A logical flag which when true specifies angle data is to be

clustered, taking angle periodicity into account (default = .FALSE.).

Caveats

The clustering algorithm is initial-guess dependent, i.e., it is

dependent on the input order of the patterns. The order of presentation

in CLUSter is simply the consecutive frames of the time series. To check

for stable clustering, cluster centers can be calculated from time series

with the time frames randomized. This is not currently implemented in

and then randomize row position outside of CHARMM.

It is relatively straight forward to compare features derived from

similar measures (i.e., time series with the same "class codes", for

example all DIHE/GEOM). In some applications it may be desired to "mix"

units in the pattern, for example, cluster a set of time series derived

from both atomic positions and energies. How best to compare "apples &

oranges" is a problem from measurement theory, and is application-specific.

Normalizing the variables such that they have unit variance is one

possibility, and this can be done by 1) determining the standard deviation

of the time series (FLUC given by the SHOW command), and 2) using this

value in the MANTim DIVI command. Since only differences between features

are used in the clustering algorithm, shifting the time series to zero

mean is not necessary.

Duda & Hart have a good discussion of the issues involved in

clustering and normalization:

Duda, R. O., & Hart, P. E., Pattern Classification and Scene Analysis,

Wiley, New York, pp. (1973).

Cluster Output

The following data are output to UNIC for each cluster:

Cluster Index - The clusters are numbered starting with 1.

No. of Members - Number of patterns assigned to the cluster.

Cumulative No. of Members - The total number of patterns within the

cluster radius. This can be higher than the No. of Members due

to patterns being within the maximum radius of more than one cluster.

Standard Deviation of Patterns within Cluster -

For cluster j with the number of features = Nfeature, this is

sqrt(sum((tq(k,i) - b(j,i))**2)/Nfeature*N(j)) where the sum is

over i = 1, Nfeature and over all k such that tq(k) is a member

of j. N(j) = the number of members in cluster j. Note that

b(j,i) = <tq(k,i)> (averaged over k in cluster j).

Maximum Distance - the longest distance between the cluster center and

an assigned pattern, normalized by sqrt(Nfeature).

Cluster Centers - (b(j,i), i = 1, Nfeature)

The following data are output to UNIM:

Cluster index of the assigned cluster

Time series time step

Time series index of first time series in pattern

Distance of pattern from cluster center, normalized by sqrt(Nfeature)

Clustering Time Series Data

This command clusters time series data obtained within the CORREL

facility. The time series must first be defined using CORREL's ENTEr

command and the data read in via TRAJ or READ. The CLUSter command

clusters these data into groups with similar time series values, with

each cluster being defined by a "cluster center". The cluster centers are

output to UNICluster, and a list of time points and assigned clusters is

given in the cluster membership file (UNIMember).

For example, if you want to find similar conformations of a peptide

using dihedral angles, you would first define the set of dihedral angles to

be considered, say angle(1) -> angle(M), as M time series. If the time series

were each N time steps long, then you would be clustering N "patterns", with

each pattern M "features" long.

Consecutive time series are clustered. If the first time series

is, for example, "ts1" then the "veccod" of this time series can be

changed to the number of time series to be clustered:

CORREL ...

ENTE ts1 ...

ENTE ts2 ...

...

ENTE tsM ...

EDIT ts1 veccod M

TRAJ ... (or READ ...)

CLUSTER ts1 ...

END

Alternatively, NFEAture M can be specified in the CLUSter command line.

Note that vector time series count as three features.

The Clustering Algorithm

ART-2' is a step-wise optimal clustering algorithm based on a

self-organizing neural net (Carpenter & Grossberg, 1987; Pao, 1989;

Karpen et al., 1993). The algorithm optimizes cluster assignment subject

to a constraint on cluster radius, such that no member of a cluster is more

than a specified distance from the cluster center. This optimization is

carried out as an iterative minimization procedure that minimizes the

Euclidean distance between the cluster center and its members.

A self-organizing net is created with each output node representing

a cluster. The number of pattern features is equal to the number of input

nodes. The weights of the connections between the input layer (layer i)

and the output layer (layer j) are denoted by b(j,i). For each cluster j,

b(j,i), i = 1, nfeature, is the cluster center. To create the net (which is

synonomous to learning the classification scheme or cluster centers) the

following algorithm is implemented:

1. To initialize the network, assign b(1,i) equal to the first

pattern tq(1,i) for i = 1, nfeature.

2. For each pattern number k, calculate the Euclidean distance (rms)

between the pattern tq(k,i) and all cluster centers b(j,i), where

j is the cluster index.

rms(j,k) = sqrt[sum [(b(j,i)-tq(k,i))**2] for i = 1, nfeature]

3. Find cluster j such that rms(j,k) < rms(i,k) for all i<>j. If

rms(j,k) <= Threshold, then update b(j,i):

b(j,i) = ((m-1)*b(j,i) + tq(k,i))/m,

where m is the number of prior updates of b(j,i). Note that

b(j,i) is the average of feature i for all patterns currently

assigned to cluster j.

4. If rms > Threshold for all prior cluster centers (j=1,numclusters),

then create a new cluster center by increasing the number of

output nodes by one, and assign the weights b(numclusters,i) of

this node the value of the pattern tq(k,i).

5. Repeat 2.-4. until all patterns have been input.

6. Compare the new set of cluster centers with the last set. If

the difference between them is less than MAXError, then halt

clustering.

7. If the difference between the sets of cluster centers is greater

than MAXError, then use the new set of cluster centers as the

starting cluster centers, and repeat steps 2.-6. Else, clustering

is complete.

Note that the cluster centers currently being calculated in step 3

are only used for the comparison in step 2 during the first

iteration with no initial cluster centers. Otherwise, the centers

calculated in the previous iteration (or read from UNIInit) are

used in the comparison in step 2. Hence, in the initial "learning"

phase, cluster centers are recalculated as each new member is added.

In subsequent "refining" phases, cluster centers are not updated

until all conformations are read in and assigned.

References:

1) Carpenter, G. A., & Grossberg, S. 1987. ART 2: Self-organization of stable

category recognition codes for analog input patterns. Appl. Optics 26:4919-

4930.

2) Pao, Y.-H. 1989. Adaptive Pattern Recognition and Neural Networks, Addison-

Wesley, New York.

3) Karpen, M. E., Tobias, D. T., & Brooks III, C. L. 1993. Statistical

clustering techniques for analysis of long molecular dynamics trajectories.

I: Analysis of 2.2 ns trajectories of YPGDV. Biochemistry 32:412-420.

CLUSter Parameters

CLUSter time-series-name RADIus <real> [ MAXCluster <int> ] -

[ MAXIteration <int> ] [ MAXError <real> ] -

[ NFEAture <int> ] [ UNICluster <int> ] -

[ UNIMember <int> ] [ UNIInitial <int>] -

[ CSTEP <int> ] [ BEGIn <int> ] -

[ STOP <int> ] [ ANGLE ]

1. time-series-name: The name of the first time series (as defined by

the ENTE command) to be clustered.

2. RADIus: Maximum radius of cluster. The rms cutoff or threshold for

assignment to a cluster.

3. MAXCluster: Maximum number of clusters (default = 50).

4. MAXIteration: The maximum number of iterations allowed. If the

clustering has not converged by this number of iterations, all

clusters are output (default = 20).

5. MAXError: If the rms difference between the position of the cluster

centers for the last two iterations is less than maxerror, the system

is considered converged and the clustering is halted (default = 0.001).

6. NFEAture: This variable gives the number of features in the input

pattern, that is, the number of time series to be clustered at a time.

The default is the veccod parameter associated with 'time-series-name'.

NFEATure time series are clustered, starting with 'time-series-name'

and continuing with the next nfeature-1 series specified in subsequent

'ENTE' commands (default = veccod of time-series-name).

7. UNICluster: The unit number of the output cluster file. If UNIC = -1

(the default), the cluster parameters are output to the standard output.

8. UNIMember: The unit number of the output membership file. This file

lists each time point and the cluster(s) associated with the specified

time series at that time point. If UNIM = -1 (the default), the

membership list is not output.

9. UNIInit: The unit number of the file with the initial cluster centers.

If UNII = -1 (the default), no initial cluster centers are specified.

10. CSTEp: This variable gives the spacing between time series in the

input vector. For each timepoint k, the set of patterns clustered is

tq(k,1) -> tq(k,nfeature), tq(k,1 + cstep) -> tq(k,nfeature + cstep),

...,tq(k,nserie - nfeature + 1) -> tq(k,nserie) (default = nfeature).

11. BEGIn: Indicates frame in time series where clustering begins

(default = 1).

12. STOP: Indicates the frame in the time series where clustering ends

(default = minimum length (TOTAl in SHOW) of time series).

13. ANGLe: A logical flag which when true specifies angle data is to be

clustered, taking angle periodicity into account (default = .FALSE.).

Caveats

The clustering algorithm is initial-guess dependent, i.e., it is

dependent on the input order of the patterns. The order of presentation

in CLUSter is simply the consecutive frames of the time series. To check

for stable clustering, cluster centers can be calculated from time series

with the time frames randomized. This is not currently implemented in

and then randomize row position outside of CHARMM.

It is relatively straight forward to compare features derived from

similar measures (i.e., time series with the same "class codes", for

example all DIHE/GEOM). In some applications it may be desired to "mix"

units in the pattern, for example, cluster a set of time series derived

from both atomic positions and energies. How best to compare "apples &

oranges" is a problem from measurement theory, and is application-specific.

Normalizing the variables such that they have unit variance is one

possibility, and this can be done by 1) determining the standard deviation

of the time series (FLUC given by the SHOW command), and 2) using this

value in the MANTim DIVI command. Since only differences between features

are used in the clustering algorithm, shifting the time series to zero

mean is not necessary.

Duda & Hart have a good discussion of the issues involved in

clustering and normalization:

Duda, R. O., & Hart, P. E., Pattern Classification and Scene Analysis,

Wiley, New York, pp. (1973).

Cluster Output

The following data are output to UNIC for each cluster:

Cluster Index - The clusters are numbered starting with 1.

No. of Members - Number of patterns assigned to the cluster.

Cumulative No. of Members - The total number of patterns within the

cluster radius. This can be higher than the No. of Members due

to patterns being within the maximum radius of more than one cluster.

Standard Deviation of Patterns within Cluster -

For cluster j with the number of features = Nfeature, this is

sqrt(sum((tq(k,i) - b(j,i))**2)/Nfeature*N(j)) where the sum is

over i = 1, Nfeature and over all k such that tq(k) is a member

of j. N(j) = the number of members in cluster j. Note that

b(j,i) = <tq(k,i)> (averaged over k in cluster j).

Maximum Distance - the longest distance between the cluster center and

an assigned pattern, normalized by sqrt(Nfeature).

Cluster Centers - (b(j,i), i = 1, Nfeature)

The following data are output to UNIM:

Cluster index of the assigned cluster

Time series time step

Time series index of first time series in pattern

Distance of pattern from cluster center, normalized by sqrt(Nfeature)

Top

Input/Output of time series and correlation functions.

1) The SHOW command

{ ALL }

SHOW { time-series-name }

{ CORRelation-function }

The SHOW command displays to print unit various data regarding

the specified time series. This command is automatically run after the

ENTER and EDIT commands as a verification of the last action.

2) The READ command

READ { time-series-name } unit-spec edit-spec { [FILE] }

{ CORRelation-funct } { CARD }

{ DUMB [COLUmn int] }

The READ command allows a time series or correlation function to

be directly read. The file formats for time series and correlation

functions is identical. There are three basic methods by which time

series may be read: FILE (default), CARD, and DUMB. The FILE and CARD

options expect a file of specific type generated by the corresponding

WRITE command. The DUMB option will read a free field card file with

NO title or other header. The COLUmn option (default 1) may be specified

to start reading the time series from any specified column. The DUMB

option will usually include some edit specifications to properly set

the time steps (etc.).

3) The WRITe command

{ ALL } { [FILE] }

WRITe { time-series-name } unit-spec { CARD }

{ CORRelation-function } { PLOT }

{ DUMB [ TIME ] }

The WRITe command will write out time series or a correlation function.

All of the write options expect a title to follow this command.

There are several file formats; FILE (default), CARD, PLOT, and DUMB.

The FILE and CARD options will write out all data regarding the specified

time series with the expectation for later retrival by Charmm or another

program. The PLOT option will create a BINARY file for plotting by PLT2.

The first line of the title is used as the plot title, but this may be

reset in PLT2.

The DUMB options will simply write out the values with no title

or header to a card file, one value to a line. If the TIME option is

specified, the time value will preceed the time series values (as needed

for an X-Y plot). If the time series is a vector type, then all component

values will be given on each line. Unless LONG (» miscom ) is in effect

the output is limited to 8 values/line. DUMB option is useful for making plot

files, or for feeding the data to other programs.

With the EDIT command, a user may merge 3 separate sequential

time series into a vector time series (or the reverse). In fact any number

of time series may be grouped together with this option. For example,

if a table with 5 time series is desired, setting VECCOD to 5 for the

first one and the writing this time series will output all 5.

Input/Output of time series and correlation functions.

1) The SHOW command

{ ALL }

SHOW { time-series-name }

{ CORRelation-function }

The SHOW command displays to print unit various data regarding

the specified time series. This command is automatically run after the

ENTER and EDIT commands as a verification of the last action.

2) The READ command

READ { time-series-name } unit-spec edit-spec { [FILE] }

{ CORRelation-funct } { CARD }

{ DUMB [COLUmn int] }

The READ command allows a time series or correlation function to

be directly read. The file formats for time series and correlation

functions is identical. There are three basic methods by which time

series may be read: FILE (default), CARD, and DUMB. The FILE and CARD

options expect a file of specific type generated by the corresponding

WRITE command. The DUMB option will read a free field card file with

NO title or other header. The COLUmn option (default 1) may be specified

to start reading the time series from any specified column. The DUMB

option will usually include some edit specifications to properly set

the time steps (etc.).

3) The WRITe command

{ ALL } { [FILE] }

WRITe { time-series-name } unit-spec { CARD }

{ CORRelation-function } { PLOT }

{ DUMB [ TIME ] }

The WRITe command will write out time series or a correlation function.

All of the write options expect a title to follow this command.

There are several file formats; FILE (default), CARD, PLOT, and DUMB.

The FILE and CARD options will write out all data regarding the specified

time series with the expectation for later retrival by Charmm or another

program. The PLOT option will create a BINARY file for plotting by PLT2.

The first line of the title is used as the plot title, but this may be

reset in PLT2.

The DUMB options will simply write out the values with no title

or header to a card file, one value to a line. If the TIME option is

specified, the time value will preceed the time series values (as needed

for an X-Y plot). If the time series is a vector type, then all component

values will be given on each line. Unless LONG (» miscom ) is in effect

the output is limited to 8 values/line. DUMB option is useful for making plot

files, or for feeding the data to other programs.

With the EDIT command, a user may merge 3 separate sequential

time series into a vector time series (or the reverse). In fact any number

of time series may be grouped together with this option. For example,

if a table with 5 time series is desired, setting VECCOD to 5 for the

first one and the writing this time series will output all 5.

Top

Examples

These examples are meant to be a partial guide in setting up

input files for CORREL. The test cases may be examined for a wider

set of applications.

Example (1)

CORREL MAXSERIES 1 MAXTIMESTEPS 500 MAXATOMS 5

ENTER AAAA TORSION MAIN 28 N MAIN 28 CA MAIN 28 C MAIN 29 N GEOMETRY

TRAJECTORY FIRSTU 51 NUNIT 5 BEGIN 26000 STOP 31000 SKIP 10

MANTIME AAAA DAVER

WRITE AAAA UNIT 20 DUMB TIME

* title

WRITE AAAA CARD UNIT 10

* title for card

* file containing the time series

CORFUN AAAA AAAA FFT NLTC P0

WRITE CORREL UNIT 21 DUMB TIME

* title

WRITE CORREL FILE UNIT 11

* title for binary correlation function

Extracts the time series, PHI(t), for phi dihedral of residue 28.

Makes the time series the fluctuation from the mean, delta PHI(t).

Makes a plot file of delta PHI(t) vs. time.

Makes binary file of delta PHI(t).

Calculates C(t) = <delta PHI(0) . delta PHI(t)> / <PHI**2> by FFT

with no long tail correction.

Makes a plot file of C(t) vs. t.

Makes a binary file of C(t).

Example (2)

CORREL MAXSERIES 2 MAXTIMESTEPS 500 MAXATOMS 10

ENTER PHI TORSION MAIN 27 C MAIN 28 N MAIN 28 CA MAIN 28 C GEOMETRY

ENTER PSI TORSION MAIN 28 N MAIN 28 CA MAIN 28 C MAIN 29 N GEOMETRY

TRAJECTORY FIRSTU 51 NUNIT 5 BEGIN 26000 STOP 31000 SKIP 10

MANTIME PHI DAVER

MANTIME PSI DAVER

CORFUN PHI PSI FFT NLTC P0 NONORM

WRITE CORREL FILE UNIT 11

* title for cross correlation binary file

WRITE CORREL PLOT UNIT 12

* plot title

Extracts the time series PHI(t), for phi dihedral, and PSI(t), for

the psi dihedral, of residue 28.

Makes the time series the fluctuation from the mean.

Calculates C(t) = <delta PHI(0) . delta PSI(t)> by FFT with no

long tail correction.

Makes a binary file of C(t).

Makes a binary PLT2 file for plotting

Example (3) Fluorescence Depolarization, for example

CORREL MAXSERIES 6 MAXTIMESTEPS 500 MAXATOMS 8

ENTER V1 VECTOR XYZ MAIN 28 NE1 MAIN 28 CZ3 MAIN 28 NE1 MAIN 28 CE3

ENTER V2 VECTOR XYZ MAIN 28 CD1 MAIN 28 CH2 MAIN 28 CD1 MAIN 28 CZ3

TRAJECTORY FIRSTU 51 NUNIT 5 BEGIN 26000 STOP 31000 SKIP 10

MANTIME V1 NORMAL

MANTIME V2 NORMAL

SHOW ALL

CORFUN V1 V2 FFT P2

WRITE CORREL PLOT UNIT 21

* title for plot

Extracts the time series, consisting of the average of the vectors

NE1 - CZ3 and NE1 - CE3 == V1(t) and of the average of CD1 - CH2 and

CD1 - CZ3 == V2(t).

Makes V1(t) and V2(t) unit vectors.

Displays data regarding both time series

Calculates P2(t) = (3< (V1(0)*V2(t))**2 > - 1) / 2

Makes a binary plot file for PLT2

Examples

These examples are meant to be a partial guide in setting up

input files for CORREL. The test cases may be examined for a wider

set of applications.

Example (1)

CORREL MAXSERIES 1 MAXTIMESTEPS 500 MAXATOMS 5

ENTER AAAA TORSION MAIN 28 N MAIN 28 CA MAIN 28 C MAIN 29 N GEOMETRY

TRAJECTORY FIRSTU 51 NUNIT 5 BEGIN 26000 STOP 31000 SKIP 10

MANTIME AAAA DAVER

WRITE AAAA UNIT 20 DUMB TIME

* title

WRITE AAAA CARD UNIT 10

* title for card

* file containing the time series

CORFUN AAAA AAAA FFT NLTC P0

WRITE CORREL UNIT 21 DUMB TIME

* title

WRITE CORREL FILE UNIT 11

* title for binary correlation function

Extracts the time series, PHI(t), for phi dihedral of residue 28.

Makes the time series the fluctuation from the mean, delta PHI(t).

Makes a plot file of delta PHI(t) vs. time.

Makes binary file of delta PHI(t).

Calculates C(t) = <delta PHI(0) . delta PHI(t)> / <PHI**2> by FFT

with no long tail correction.

Makes a plot file of C(t) vs. t.

Makes a binary file of C(t).

Example (2)

CORREL MAXSERIES 2 MAXTIMESTEPS 500 MAXATOMS 10

ENTER PHI TORSION MAIN 27 C MAIN 28 N MAIN 28 CA MAIN 28 C GEOMETRY

ENTER PSI TORSION MAIN 28 N MAIN 28 CA MAIN 28 C MAIN 29 N GEOMETRY

TRAJECTORY FIRSTU 51 NUNIT 5 BEGIN 26000 STOP 31000 SKIP 10

MANTIME PHI DAVER

MANTIME PSI DAVER

CORFUN PHI PSI FFT NLTC P0 NONORM

WRITE CORREL FILE UNIT 11

* title for cross correlation binary file

WRITE CORREL PLOT UNIT 12

* plot title

Extracts the time series PHI(t), for phi dihedral, and PSI(t), for

the psi dihedral, of residue 28.

Makes the time series the fluctuation from the mean.

Calculates C(t) = <delta PHI(0) . delta PSI(t)> by FFT with no

long tail correction.

Makes a binary file of C(t).

Makes a binary PLT2 file for plotting

Example (3) Fluorescence Depolarization, for example

CORREL MAXSERIES 6 MAXTIMESTEPS 500 MAXATOMS 8

ENTER V1 VECTOR XYZ MAIN 28 NE1 MAIN 28 CZ3 MAIN 28 NE1 MAIN 28 CE3

ENTER V2 VECTOR XYZ MAIN 28 CD1 MAIN 28 CH2 MAIN 28 CD1 MAIN 28 CZ3

TRAJECTORY FIRSTU 51 NUNIT 5 BEGIN 26000 STOP 31000 SKIP 10

MANTIME V1 NORMAL

MANTIME V2 NORMAL

SHOW ALL

CORFUN V1 V2 FFT P2

WRITE CORREL PLOT UNIT 21

* title for plot

Extracts the time series, consisting of the average of the vectors

NE1 - CZ3 and NE1 - CE3 == V1(t) and of the average of CD1 - CH2 and

CD1 - CZ3 == V2(t).

Makes V1(t) and V2(t) unit vectors.

Displays data regarding both time series

Calculates P2(t) = (3< (V1(0)*V2(t))**2 > - 1) / 2

Makes a binary plot file for PLT2