Cambridge Crystallographic Subroutine Library

CCSL Mark 4 Update 57 17

Appendix A

List of subroutines divided according to topic

Basic crystallography
Data collection & reduction
Manipulation of reflection indices
Structure factors
Fourier maps
Least Squares Refinement, general
Least Squares Refinement, specific
Crystal geometry
Mathematical functions
Trigonometry
Tests
Matrices & vectors
Special input/output
Graphical output
Logical operations
Miscellaneous
Magnetic routines
Multipole routines
Profile refinement
As yet unclassified

General Library

1. Basic crystallography

A. Setting up

SUBROUTINE FACGRP: Extracts factor groups from a space group.
SUBROUTINE FACTGP: Finds the factor elements which generate a space group from one of its sub-groups.
SUBROUTINE FIXUNI: Deals with one potential plane face of asymmetric unit, while the unit is being formed.
SUBROUTINE INPUTC: Reads one "C" card.
SUBROUTINE INPUTS: Reads and interprets one "S" card containing a space group operator. Can also interpret an S GRUP card containing a space group specification.
SUBROUTINE INPUTU: Reads and interprets a "U" card, giving a typical reflection to define the reciprocal asymmetric unit.
SUBROUTINE MAKGRP: Generates the subgroup of a space group from the given generators.
SUBROUTINE ORTHG: Calculates matrices for the transformation of vectors in real or reciprocal space, between crystallographic and orthogonal axes.
SUBROUTINE PLN3AD: A specialist routine used during the formation of the reciprocal unit cell, to offer up 3 planes as boundaries, in cubic space groups.
SUBROUTINE POLUNI: A specialist routine to "polish" the edges of a found asymmetric unit by specifying exactly how its faces and edges should be treated.

SUBROUTINE RECIP: SUBROUTINE REINDX; Reads the lattice parameters and forms the reciprocal cell. To reindex a set of reflections after a least squares cycle in which the propagation vector changes
SUBROUTINE SETFC: Calls all the setting up routines needed for nuclear structure factor calculations.
SUBROUTINE SHUFLE: Reorders the symmetry operators for various specialist applications.
SUBROUTINE SPACE: Interprets symbols from an S card which are the space group name.
SUBROUTINE SPGNAM: Decodes space group symbol or integer from S GRUP card
SUBROUTINE SYMCEN: A specialist routine used during the input of space group symmetry to discover whether there is a centre of symmetry.
SUBROUTINE SYMFRI: Reads and interprets an item "FRIE" on an I card.
SUBROUTINE SYMGEN: Produces the generators of a space group which has been read by SYMOP.
SUBROUTINE SYMOP: Reads all the symmetry operators or a space group specification from "S" cards, and generates the space group.
SUBROUTINE SYMTID: Tidies all the arrays connected with the space group symmetry.
SUBROUTINE SYMUNI: Selects a reciprocal space asymmetric unit fitting the symmetry.
SUBROUTINE TRYUNI: A specialist routine used in the setting up of the asymmetric unit, to try out a given set of planes as faces of the unit.
SUBROUTINE UNITID: A specialist routine called when an asymmetric unit has been found, to tidy the unit, its faces and edges.

B. Crystallographic

FUNCTION ANGRAD: Calculates the angle in radians between two vectors, in either space.
SUBROUTINE ASUNIT: Produces reflection indices in the asymmetric unit, related to those given.
SUBROUTINE CELMAT: Sets up the matrix to convert derivatives wrt A,B,C . . (cell quadratic products in real space) to derivatives wrt A*, B*, C*, . . in reciprocal space.
SUBROUTINE EQOP: Checks whether a rotation matrix and a translation vector of a symmetry operator are already in a list, and adds them if not. Also finds lattice translations.
SUBROUTINE EULSYM: Finds the Euler angles correponding to a symmetry rotation.
SUBROUTINE GENELM: Finds the generators of a subgroup of a space group.
LOGICAL FUNCTION ISPABS: Checks space group absences.
LOGICAL FUNCTION LATABS: Checks h,k,l for being a (nuclear) lattice absence.
SUBROUTINE LATGEN: Generates points on a lattice.
LOGICAL FUNCTION LATVEC: Tests for the presence of a lattice vector.
SUBROUTINE OPSYM: Prints out the symmetry operators in either real or reciprocal space.
SUBROUTINE ORTHO: Carries out conversions between crystallographic and orthogonal axes.
SUBROUTINE RECELL: Makes real or reciprocal space cell parameters from the others.
SUBROUTINE ROTOSM: Calculates the effect of the rotation matrix of a symmetry operator, on a vector given on orthogonal axes.
SUBROUTINE ROTSYM: Rotates the vector H into RH by the given symmetry operator.
FUNCTION SCLPRD: Forms the scalar product of two vectors referred to crystal axes.
SUBROUTINE SUBSYM: Replaces all the symmetry parameters by those of a subgroup.
SUBROUTINE SYMBAK: Restores the original symmetry operators after a call to SUBSYM.
SUBROUTINE SYMREF: Generates a set of equivalent reflections and related phases.
FUNCTION VCTMOD: Calculates the modulus of the vector H, in either space.

C. Utility

SUBROUTINE AXIS: Finds the axis of a given rotation matrix.
SUBROUTINE FCTOR: Finds the highest common factor of a set of indices and reduces them by that factor.
SUBROUTINE FRAC3: Makes all 3 elements of a vector fractional
SUBROUTINE INVENT: Given a plane U and an axis H, produces a direction ANS which is in the plane but not parallel to the axis.
FUNCTION NORDER: Returns the order of the Jth symmetry operator.

2. Data collection & reduction

A. Setting up

SUBROUTINE ARPRIN: A multi-mode routine to produce the output in ARRNGE type main programs.
SUBROUTINE ARREAD: Multiple entry routine to deal with reading items for ARRNGE type programs.
SUBROUTINE GAUSPT: Sets up Gauss points and weights for use in 3D integration.
SUBROUTINE ICDFMT: Interprets I and Q PROP cards for programs reading ARRNGE type data".
SUBROUTINE IICD3: Interprets I cards for ARRNGE-type MAIN programs, and sets them up.
SUBROUTINE INPUTD: Reads and interprets all D cards, for general diffraction information.
SUBROUTINE INPUTE: Reads and interprets an E card, and sets up extinction calculations.
SUBROUTINE INPUTG: Reads and interprets all "G" cards, for Gaussian integration of various integrals over a crystal defined by its plane faces.
SUBROUTINE SETABS: Sets up data for the calculation of absorption (or related) integrals.
SUBROUTINE SETDC: Reads D cards to set up crystal orientation and diffraction geometry.
SUBROUTINE SETGAU: Sets up the COMMON /GAUSS/ for Gaussian integration (for use in absorption correction type integrals).
SUBROUTINE SETLP: Prepares to calculate (X-ray) Lorentz and polarisation corrections.
SUBROUTINE SETPOL: Reads the polarisation and flipping efficiencies (for polarised neutrons).

B. Crystallographic

SUBROUTINE ABMULT: Forms transmission (=1/absorption) factors or related integrals.
SUBROUTINE ABSCOR: Applies absorption corrections to groups of equivalent reflections.
FUNCTION ABSOR: Forms a transmission (=1/absorption) factor or related integrals.
SUBROUTINE AINOUT: Multiple function routine called by ARRNGE type programs to process sort items.
SUBROUTINE ALRPOL: Calculates the reciprocals of Lorentz and polarisation factors.
SUBROUTINE ANGDIR: Calculates D3 or 4-circle angles from direction cosines.
SUBROUTINE BIGGAM: Deals with gammas whose value is greater than one, in SORGAM. There is also the entry SETGAM to set up the calculation.
SUBROUTINE EXTINC: Multi-entry routine to deal with all aspects of single crystal extinction corrections.
SUBROUTINE FGAMMA: Calculates gamma, the ratio of magnetic and nuclear scattering, and its standard deviation. FGAMMS does this in the presence of spin-independent multiple scattering.
SUBROUTINE GAMEX: Calculates an extinction corrected gamma from a flipping ratio.
SUBROUTINE GETDC: Calculates direction cosines of the incident and diffracted beams used by absorption correction type integrals
SUBROUTINE QARRIN: In the library, simply a dummy routine. If the user wishes some special new input format for "ARRNGE" type main programs, he provides a new version of QUARRIN.
SUBROUTINE STATIS: Calculates means and other statistics for a set of measurements of a single quantity.

C. Utility

FUNCTION INPUAR: Reads the data from files made by ARRNGE and other similar programs.

3. Manipulation of reflection indices

A. Setting up

SUBROUTINE PRMTIV: A specialist routine for use in generating h,k,l indices where the natural stepping vectors do not define a primitive cell.
SUBROUTINE SETGEN: Sets up the generation of a complete set of reflection indices.

B. Crystallographic

SUBROUTINE GENMUL: Gives next useful set of h,k,l and multiplicity, scanning the asymmetric unit of reciprocal space.
SUBROUTINE GETGEN: Gives the next useful set of h,k,l scanning the asymmetric unit of reciprocal space.
SUBROUTINE INBOX: Determines whether the given reflection is inside, on, or outside the reciprocal space asymmetric unit.

C. Utility

SUBROUTINE INDFIX: Converts 3 real items in H to be integers in K.
SUBROUTINE INDFLO: Converts 3 integers in K into floating point reals in H.
FUNCTION MATCH: Checks to see whether two sets of reflection indices match.
FUNCTION MATCHF: Checks to see whether two sets of floating point reflection indices match.
FUNCTION MULBOX: Tests indices for being in the asymmetric unit, and gives multiplicity.

4. Structure factors

A. Setting up

SUBROUTINE ATOPOS: Reads and interprets all given A cards.
SUBROUTINE INPUTA: Reads an A card and prepares it for further processing.
SUBROUTINE INPUTF: Reads and partially interprets an "F" card.
SUBROUTINE INPUTT: Reads and interprets one "T" card.
SUBROUTINE INPUTW: To read the "W" card indicated by ID, as far as atom label and word.
SUBROUTINE RADFUN: Reads coefficients for the expansion of an atomic wave function.
SUBROUTINE SETANI: Reads "T" cards to set up for calculation of anisotropic temperature factors.
SUBROUTINE SETFOR: Sets up data for scattering or form factor calculations.

B. Crystallographic

FUNCTION ANITF: Forms the contribution to the anisotropic temperature factor on an atom N from indices H.
SUBROUTINE ATOMS: Makes a real space unit cell full of related atomic positions.
FUNCTION CONATF: Produces for a single coefficient of an anisotropic temperature factor, its conversion factor from the internally used betas, in order to communicate with the user.
COMPLEX FUNCTION FCALC: Calculates the COMPLEX nuclear structure factor for the reflection H.
COMPLEX FUNCTION FORMFA: Calculates form or scattering factors.
FUNCTION FORMFC: Calculates form factor integrals from radial wave functions.

5. Fourier maps

A. Setting up

SUBROUTINE INPUTM: Reads and interprets all "M" cards.
SUBROUTINE MAJUST: A specialist routine used in the input of the Crystal Data File needing previously stored Fourier maps.
SUBROUTINE NEXCON: Sets up the "next" contour value to plot for Fouriers.
SUBROUTINE SETFOU: Sets up data for Fourier map calculations.
SUBROUTINE USYM: Transforms all the symmetry operators by pre- and post-multiplying them by U, the orientation matrix for a Fourier map.

B. Crystallographic

SUBROUTINE ATMPLO: Plots atom positions on a map.
SUBROUTINE ATOGEN: Generates a set of equivalent positions.
SUBROUTINE ERRMAP: Calculates the standard deviation of the density in a Fourier map.
SUBROUTINE FORIER: Controls Fourier calculations.
SUBROUTINE FOUR1D: Calculates a Fourier along a general line.
SUBROUTINE FOUR1Z: Calculates 1 layer of Fourier sum : a section if 3D, a projection if 2D, or a bounded section if "4D".
SUBROUTINE FOURGP: Calculates a Fourier on a general plane.
SUBROUTINE GETMAP: Retrieves 1 Fourier map previously filed using SAVMAP.
SUBROUTINE MAPCON: After a Fourier map has been plotted, sends to the plotter the list of contours which were plotted, with a frame.
SUBROUTINE MAPDRW: Draws an unframed contour map, in predetermined place.
SUBROUTINE MAPFRA: Draws a black frame round a potential contoured map, adding the labels X Y and a 1A scale.
SUBROUTINE MAPKEY: Plots a key to the atoms found by ATMPLO.
SUBROUTINE MAPTIT: Writes a title over a plotted map, with a frame.
SUBROUTINE PLTTXT: Plots a block of explanatory text under a plotted Fourier map.

SUBROUTINE PRNTMP: SUBROUTINE PROPAG; Multiple entry subroutine for propagation vector refinement Prints out a Fourier projection or one layer of a 3D Fourier.
SUBROUTINE QFOUIN: In the library, simply a dummy routine. If the user wishes some special new input format for Fourier routines, he provides a new version of QFOUIN.
SUBROUTINE READMP: Reads into the array DENS a map previously written to file, unformatted.
FUNCTION RESOL: Calculates a resolution function for use with Fourier inversion.
SUBROUTINE SAVMAP: Writes 1 layer of map to given file, plus information for later retrieval.
SUBROUTINE SYMEQU: Generates new indices and a phase, in Fourier calculations.
SUBROUTINE TBOUND: A specialist routine used duing the plotting of atomic positions in main program ATMPLO.

C. Utility

SUBROUTINE CHOOSF: Chooses modulus and phase for a particular Fourier.
SUBROUTINE DOSIDE: A specialist routine for contour plotting, to help to decide where a contour crosses the side of a square.
SUBROUTINE FOUINP: Reads one data item for a given type of Fourier, in a given format.

6. Least Squares Refinement, general

A. Setting up

SUBROUTINE CELREL: Transfers any relations which exist between cell parameters from their own COMMON to the general "contraint/fixing" COMMON.
SUBROUTINE F2VAR8: Records varying information for a particular family 2 (structure) parameter.
SUBROUTINE FIXPAR: Records an instruction to fix a LSQ parameter.
SUBROUTINE FIXREL: Takes a temporary set of fix/relate information and adds it to the permanent information.
SUBROUTINE FUDGIN: Interprets all L FUDG cards.
SUBROUTINE GEOMIN: Reads L cards for bond slack constraints.
SUBROUTINE IICD1: Interprets basic I cards to drive any LSQ.
SUBROUTINE LLSCAL: Multiple entry routine which deals with scale factors in Least Squares.
SUBROUTINE LLTFAC: Multiple entry routine which deals with overall isotropic temperature factors in Least Squares.
SUBROUTINE LSETSF: Sets up vocabulary for a specific LSQ problem involving structure factors.
SUBROUTINE LSETUP: Sets up specific LSQ problem - copies the vocabulary to standard COMMON.
SUBROUTINE RDFV: Reads all the user's L FIX and L VARY cards in sequence.
SUBROUTINE RDRELA: Reads and interprets all user-supplied L RELA cards for constraints.
SUBROUTINE RELPAR: In the setting up of LSQ applications, relates two parameters by a simple linear relationship.
SUBROUTINE RELSM3: Forms a complete set of relations imposed by symmetry on the given 3 parameters of a LSQ application.
SUBROUTINE RELSM6: Forms a complete set of relations imposed by symmetry on the given 6 parameters of a LSQ application.
SUBROUTINE SCLCHN: A specialist routine used during the setting up of constraints on LSQ variables. Scales a chain of connected variables by the given constant.
SUBROUTINE VARMAK: Makes variables for a LSQ cycle from given FIX/VARY and CONSTRAINT lists.
SUBROUTINE VOCAB: Adds a given set of vocabulary and meanings to the Least Squares total vocabulary.

B. Crystallographic

SUBROUTINE CELDER: From h,k,l calculates d* squared and its derivatives, and sets SSQRD.
SUBROUTINE F2NEW: Outputs a new LSQ family 2 (structure parameters) card (for A, T or F cards).
SUBROUTINE F2RELA: Collects all structure factor type constraints implied by the symmetry.
SUBROUTINE F2SHFT: Applies a shift to a particular family 2 (structure) parameter.
SUBROUTINE GEOMLS: Calculates bond lengths and derivatives for geometrical slack constraints.
SUBROUTINE LFCALC: Calculates a nuclear structure factor and its derivatives.
SUBROUTINE MATCEL: After a cycle of LSQ gives variance-covariance matrix for cell A* B* etc in both real and reciprocal space, and the same for abc, alpha,beta,gamma.
SUBROUTINE OTPUTI: Outputs a new I card after a LSQ refinement, updating the cycle number.
SUBROUTINE QLSQIN: In the library, simply a dummy routine. If the user wishes some special new input format for Least Squares routines, he provides a new version QLSQIN.
SUBROUTINE RFACS: A multiple entry routine to deal with all aspects of R Factor calculations and statistics for single crystal observations, and
SUBROUTINE XYZREL: Collects all position parameter constraints implied by the symmetry.

C. Utility

SUBROUTINE ADDCON: Adds a constraint to the list held in LSQ programs.
SUBROUTINE ADJUST: Applies a (possibly fudged) shift to a given LSQ parameter.
SUBROUTINE CELNEW: Writes out a new C card after cell parameter refinement.
SUBROUTINE CELSDP: Prints the esds of real cell parameters after a cycle of refinement.
SUBROUTINE CELSHF: Applies a shift to a cell quadratic product.
SUBROUTINE DEPRIN: Decodes an integer which describes the frequency of LSQ printing required, and outputs this frequency.
FUNCTION ELEMAT: Gets a matrix element from the triangular LSQ matrix.
SUBROUTINE FETSHF: Fettles a shift and esd for printing and counts, in the application of shifts in LSQ.
SUBROUTINE FIXVAR: Adds a request to fix (or vary) a parameter to the lists held in setting up LSQ environments.
SUBROUTINE FUDGET: Reads a fudge factor from a card having already read a parameter specification.
SUBROUTINE GEOMCO: Multiple entry routine for geometric slack constraints.
FUNCTION KPAK: Pack a LSQ parameter specification on to integer.
LOGICAL FUNCTION KSAME: Tells if two LSQ parameter specifications are the same, allowing wild card elements.
SUBROUTINE KUNPAK: Unpacks a LSQ parameter specification from single integer.
LOGICAL FUNCTION KWHOLE: Says if KK is a whole packed parameter specification, or whether there are wild card elements.
SUBROUTINE MATCOR: After a Least Squares cycle, prints correlations from the inverse matrix.
SUBROUTINE MATINV: Inverts the matrix in ALSQ, of which the upper triangle only is held.
SUBROUTINE MATSET: Sets up pointers into a Least Squares matrix, and clears the matrix and the corresponding right hand side vector.
SUBROUTINE MATSHF: From an inverted Least Squares matrix, calculates shifts in basic variables.
SUBROUTINE MATTOT: Add in contributions to LSQ matrix and RHS for one observation.
SUBROUTINE NEWCD: Opens a file on to which to write a new Crystal Data File after a Least Squares refinement. .CCN at RAL, .CRY at ILL, for unit NEWIN in /NEWOLD/
SUBROUTINE PARNAM: Obtains the printing name of a LSQ parameter.
SUBROUTINE PARRD: Reads a LSQ parameter specification from a given card at given point.
SUBROUTINE PARRUN: Controls the cycling over all parameters in LSQ (not for Profile Refinement).
SUBROUTINE PRBLOK: Prints a block of shifts in parameters all relating to the same atom in LSQ applications involving structure parameters.
SUBROUTINE PRIVAR: Prints a list of basic variables, and constraint relations, for LSQ.
SUBROUTINE PRIWRD: Finds the name of the packed (possibly part) LSQ parameter from the built-in table of parameter names.
LOGICAL FUNCTION PRNCYC: Decides whether printing (of various different quantities in LSQ) is needed during the current LSQ cycle.
SUBROUTINE PUNPAK: Unpacks a parameter specification from single integer.
SUBROUTINE RELATE: In LSQ programs, converts a vector of derivatives wrt variables into the vector of derivatives wrt basic variables.
SUBROUTINE SERROR: Called after VA05A to give the standard deviations of the parameters.
SUBROUTINE SHFESD: During the application of LSQ shifts, calculates the shift and ESD for a "redundant" variable.
LOGICAL FUNCTION SYMFIX: Says whether a LSQ parameter is fixed by symmetry or not.
SUBROUTINE TBLFND: Looks for an A4 NAME in every table it can find, trying to identify it as part of a LSQ parameter name.
SUBROUTINE VA05A: Minimises the sum of squares of given functions without requiring the explicit calculation of derivatives.
SUBROUTINE WGHTLS: Performs various operations to do with weights for LSQ, either for PR or simpler applications. applications.

FUNCTION WIYPOS: SUBROUTINE WGHTSF; GIVES EXP(Y*Y)ERFNC(Y) FOR +VE Y ONLY Deals with weights of LSQ observations for single crystal.

7. Least Squares Refinement, specific

A. Setting up

LOGICAL FUNCTION DFLTMG: Called as a substitute for DEFALT via VARMAK, giving default fix/vary for otherwise unspecified parameters for magnetic structures.
LOGICAL FUNCTION DFLTMP: Called as a substitute for DEFALT out of VARMAK, giving defaults fix/vary for otherwise unspecified parameters of multipole refinements.
LOGICAL FUNCTION DFLTSF: Called as a substitute for DEFALT out of SUBROUTINE VARMAK, giving default fix/vary information for structure parameters.
LOGICAL FUNCTION DFTRUE: Called as a substitute for DEFALT out of VARMAK in main programs, to vary an otherwise unspecified parameter.
SUBROUTINE INOBGR: Performs a preliminary pass of observations for GRLSQ, (group refinement, integrated intensity LSQ).
SUBROUTINE INPLSF: Reads in (nearly) all L cards for the particular LSQ type 'SF', for single crystal work.
SUBROUTINE MPOVAR: Records whether each multipole parameter is fixed or varied.
SUBROUTINE PARSDS: Collects together all parameter fixing and varying information for LSQ refinement of cell parameters using d spacings.
SUBROUTINE PARSFW: An older routine to set up variables from parameters for FWLSQ.
SUBROUTINE STLSFW: Sets up the main program FWLSQ to perform LSQ on Forsyth & Wells scattering factor coefficients.
SUBROUTINE STLSSF: Sets up any main program which does single crystal structure factor LSQ.
SUBROUTINE VARSDS: Makes variables for cell parameters and propagation vector for d-spacing LSQ.
SUBROUTINE VARSMG: Records variable pointers for all variables in magnetic structure-factor LSQ.
SUBROUTINE VARSMP: Records pointers for all variables in multipole LSQ.
SUBROUTINE VARSSF: Records variable pointers for all variables in structure-factor LSQ.

B. Crystallographic

SUBROUTINE APSHDS: Applies shifts for during d-spacing refinement.
SUBROUTINE APSHFW: Applies shifts for Forsyth & Wells scattering factor coefficient refinement.
SUBROUTINE APSHMP: Applies shifts to all variables in multipole LSQ, and prints the results.
SUBROUTINE APSHSF: Applies shifts to all variables in single crystal structure factor based LSQ, and prints the results.
SUBROUTINE APSHT2: Applies shifts for reciprocal cell quadratic products and zero during 2theta refinement.
SUBROUTINE CALCDS: Calculates d star squared, and its derivatives wrt reciprocal cell quadratic products.
SUBROUTINE CALCFW: Calculates the Forsyth & Wells exponential function which approximates to observed scattering factor curves.
SUBROUTINE CALCGR: Gives the calculated function for grouped single crystal Least Squares.
SUBROUTINE CALCMG: Calculates GCALC and its derivatives for structures which may have mixed magnetic and nuclear reflections.
SUBROUTINE CALCMP: Makes the calculated function and derivatives for single crystal LSQ with multipoles.
SUBROUTINE CALCSF: Makes the calculated function and derivatives for single crystal LSQ.
SUBROUTINE CALCT2: Calculates a function to match an observation for 2theta-type refinement of reciprocal cell parameters and a zero point.
SUBROUTINE CALPOL: Calculates scattered polarisations and their derivatives for structures which may have mixed magnetic and nuclear reflections.
SUBROUTINE CONVMP: Converts between user values and LSQ parameters for multipoles.
SUBROUTINE JMPOL: Writes to unit NEWIN all J MPOL cards after a multipole refinement.
SUBROUTINE LMPCAL: Calculates a structure factor and its derivatives using a multipole description of the form factors.
SUBROUTINE NWINDS: Outputs to unit NEWIN a new input dataset at the end of a refinement of cell parameters and propagation vector from d spacing values.
SUBROUTINE NWINFW: Writes out a new Crystal Data File for main program FWLSQ.
SUBROUTINE NWINMP: Writes to unit NEWIN a replacement Crystal Data File after multipole LSQ.
SUBROUTINE NWINSF: Outputs a replacement Crystal Data File after single crystal refinement.
SUBROUTINE NWINT2: Writes out a new Crystal Data File for main program T2LSQ.
SUBROUTINE PARSSF: Collects all parameter fix and vary information for single crystal LSQ.
SUBROUTINE PRMBLK: Applies shifts to multipole parameters, in both program and user units.
SUBROUTINE VARST2: Makes variables for zero and cell for T2 type LSQ

8. Crystal geometry

A. Setting up

SUBROUTINE ADDANG: Finds an angle in the tables for geometric constraints, or adds it if absent.
SUBROUTINE ADDATM: Finds an atom in the tables for geometric constraints, or adds it if absent.
SUBROUTINE ADDBON: Finds a bond in the tables for geometric constraints, or adds it if absent.
SUBROUTINE ADDTOR: Finds a torsion angle in the tables for geometric constraints, or adds it if absent.
SUBROUTINE RDANGL: Reads a specification of a bond angle, by reading the names of 2 intersecting bonds; makes the third bond involved.
SUBROUTINE RDATOM: Reads the specification of an atom for slack constraint purposes
SUBROUTINE RDBOND: Reads a specification of a bond, by reading the names of the atoms at each end.

B. Crystallographic

SUBROUTINE ANGLST: Lists all angles at one source atom made by a given list of bonds.
SUBROUTINE BNDLST: Writes out and saves a list of bonds from one atomic position.
SUBROUTINE BONCOS: Given 3 bonds forming a triangle, calculates the angle opposite the first, its sine and cosine, and its derivatives wrt all 3 bonds.
FUNCTION BONDA: Calculates the angle between two bonds.
SUBROUTINE BONDER: Calculate a bond and its derivatives for slack constraints.
SUBROUTINE BONTRI: Given two bonds with a common atom, completes the triangle and identifies the atom.
SUBROUTINE INCELL: Sets P to be the position in the central cell equivalent to X.
SUBROUTINE XROOT: Finds the symmetry operations which take the given source atom into the given coordinates.
SUBROUTINE XTRANS: Transforms a given atomic position by given symmetry operator and lattice and cell translations.

C. Utility

SUBROUTINE ATSPEC: Makes the 16-character specification of a symmetry related atom from its packed specification.

9. Mathematical functions

A. Setting up

SUBROUTINE SPLINE: Sets up a cubic spline to fit a curve.

C. Utility

FUNCTION ALNINT: Performs linear interpolation, suitable for profile backgrounds etc.
FUNCTION BJ: Calculates Bessel functions of order 1 or 2.
FUNCTION BRILL: Returns the value of the Brillouin function.
SUBROUTINE CGAMMA: Solves the quadratic equation for gamma in terms of the flipping ratio. The ENTRY CGAMMS is for when there is spin-independent multiple scattering.
SUBROUTINE DIJROT: Calculates the matrix D(i,j) for the Euler rotations alpha,beta,gamma of the eigenfunctions of angular momentum l.
FUNCTION ERFNC: Calculates the error function accurate to 3E-7, for + and - X.
FUNCTION EXPINT: Calculates an exponential radial integral.
FUNCTION FACT: Calculates factorial K.
SUBROUTINE FF01A: Modified Harwell routine for zero order Bessel functions.
SUBROUTINE FF02A: Modified Harwell routine for first order Bessel functions.
SUBROUTINE FRACT: Forms the fractional part of a real number.
SUBROUTINE FT01A: Modification of Harwell Fast Fourier Transform.
SUBROUTINE JTERMS: Calculates the terms in the 2D averaged spherically symmetric form factor summation which depend on S,K, and R only.
SUBROUTINE NB01A: Harwell routine NB01A to find the zero of a function.
FUNCTION RGAUSS: Returns a value random number with a gaussian distribution.
SUBROUTINE SPHARM: Calculates spherical harmonics.
FUNCTION SPLINT: Evaluates a cubic spline given spline values and first derivative values at the given knots.
SUBROUTINE STERMS: Calculates a term in the spherically symmetric form factor summation, for a 3D averaged form-factor involving Sk and r only.
SUBROUTINE TB02A: Interpolates in non-equal interval table.
SUBROUTINE TQLI: Performs the QL algorithm for eigenvalues and vectors of a real symmetric matrix previously reduced to tridiagonal form.
SUBROUTINE TRED2: Performs the Householder reduction of a real symmetric matrix to tridiagonal form.
FUNCTION VECOUP: Calculates Clebsch-Gordon vector coupling coefficients.
SUBROUTINE VOIGT: Calculates normalised Voigt function
SUBROUTINE WERF: Weighted error function ???
SUBROUTINE WTMEAN: Multiple entry routine for the calculation of weighted averages.

10. Trigonometry
FUNCTION ARCCOS: Calculates an arc cosine.
FUNCTION DEGREE: Converts from radians to degrees.
FUNCTION RADIAN: Converts from degrees to radians.
SUBROUTINE SINCOS: Calculates sin from cos or vice-versa.
SUBROUTINE TRIAN1: Applies the cosine formula for the solution of spherical triangles.
SUBROUTINE TRIG: Sets up cos(nx) and sin(nx) for a range of n by recursion.

11. Tests
LOGICAL FUNCTION BINDIG: Tests for the presence of a given binary digit within an integer.
SUBROUTINE EQPOS: Checks whether the given atom position already occurs in a given list, and adds the new one if not.
SUBROUTINE EQPPOS: Checks whether the given position vector is related by lattice translation to one already in the given list.
SUBROUTINE EQRLV: Checks whether vectors differ by a reciprocal lattice vector.
SUBROUTINE EQVEC: Finds a given vector in given table of vectors, or adds it as a new one.
LOGICAL FUNCTION EXCLD: Determines whether a number occurs within any of a set of given ranges.
LOGICAL FUNCTION GMSAME: Tells whether one vector is the same as another, to a given tolerance.
FUNCTION IATOM: Identifies an atom name in a given list.
FUNCTION ISCAT: Searches for a potential scattering factor name in the table.
FUNCTION LMATCH: Matches an A4 item in given table, adding it if it is not there already.
FUNCTION MINIM: Finds the position and value of the minimum in a list of integers.
FUNCTION NCFIND: Searches for a particular word in a table of words.
FUNCTION NFIND: Searches for integer N in a table.
SUBROUTINE PARITY: Finds out whether N is odd or even.
FUNCTION RANGE: Puts a number into a given range.
SUBROUTINE REJECT: Decides for ARRNGE-type main programs whether the record number of a reflection occurs in a list of those to be rejected.
LOGICAL FUNCTION SAID: Decides whether the character variables INCHAR and WANT are the same, ignoring any distinction between upper and lower case.
LOGICAL FUNCTION SAYS: Decides whether the string WANT matches a string of the same length,just read into /SCRACH/ ignoring any distinction between upper and lower case.
LOGICAL FUNCTION TESTOV: Tests a floating division for potential overflow.

12. Matrices & vectors
SUBROUTINE C1MSCA: Multiplies every element of the REAL matrix A by the COMPLEX scalar SCALE.
SUBROUTINE CGMADD: Sets COMPLEX matrix C = COMPLEX matrix A + COMPLEX matrix B.
SUBROUTINE CGMEQ: Sets COMPLEX matrix B equal to COMPLEX matrix A.
SUBROUTINE CGMPRD: Multiplies together two COMPLEX matrices.
SUBROUTINE CGMSCA: Multiplies every element of a COMPLEX matrix by a COMPLEX scale.
SUBROUTINE CGMSUB: Sets COMPLEX matrix C = COMPLEX matrix A - COMPLEX matrix B.
SUBROUTINE CGMUNI: Clears a COMPLEX square matrix to contain the unit matrix.
SUBROUTINE CGMZER: Clears to zero a complex matrix.
SUBROUTINE CMCONJ: Gives the conjugate of a COMPLEX matrix.
SUBROUTINE CMIMAG: Gives the imaginary parts of a COMPLEX matrix.
SUBROUTINE CMREAL: Gives the real parts of a COMPLEX matrix.
SUBROUTINE CMRSCA: Multiplies every element of a COMPLEX matrix by a REAL scale.
SUBROUTINE CRMPRD: Performs COMPLEX by REAL matrix multiplication.
COMPLEX FUNCTION CRSCLP: Finds the COMPLEX scalar product of a COMPLEX with a REAL vector.
FUNCTION DETER3: Forms the determinant of a 3 x 3 matrix.
SUBROUTINE GMADD: Sets matrix C = matrix A plus matrix B.
SUBROUTINE GMEQ: Sets matrix B = matrix A.
SUBROUTINE GMINV: Inverts matrix A into matrix B.
SUBROUTINE GMNORM: Normalises the rows of a matrix.
SUBROUTINE GMPRD: Sets matrix C = matrix A times matrix B.
SUBROUTINE GMREV: Reverses the signs of the elements of an NI X NJ matrix.
SUBROUTINE GMSCA: Multiplies every element of the matrix A by the scalar SCALE.
SUBROUTINE GMSUB: Sets matrix C = matrix A minus matrix B.
SUBROUTINE GMTRAN: Transposes a JJxII matrix A into B.
SUBROUTINE GMUNI: Writes a unit matrix into the square matrix A.
SUBROUTINE GMZER: Clears to zero the matrix A.
SUBROUTINE JGMADD: In integers, sets matrix C = matrix A plus matrix B.
SUBROUTINE JGMEQ: Equates an integer matrix to a given integer matrix.
SUBROUTINE JGMPRD: In integers, sets matrix C = matrix A times matrix B.
SUBROUTINE JGMREV: Reverses the signs of the elements of an integer matrix.
SUBROUTINE JGMSUB: In integers, sets matrix C = matrix A minus matrix B.
SUBROUTINE JGMZER: Clears an integer matrix to zero.
SUBROUTINE MB11A: Inverts a rectangular matrix whose order is the smaller dimension; used by the Harwell refinement routine VA05A.
SUBROUTINE RCMPRD: Performs the multiplication of a COMPLEX by a REAL matrix.
FUNCTION RSCALP: Forms the scalar product of two COMPLEX vectors.
FUNCTION SCALPR: Forms the scalar product of two orthogonal vectors (or of one from real space with one from reciprocal space).
SUBROUTINE SID: Solves a set of simultaneous linear equations.
SUBROUTINE SUMVEC: Calculates the sum of elements of a real array
SUBROUTINE TRANSC: Replaces a COMPLEX square matrix by its transposed conjugate.
SUBROUTINE TRANSQ: Replaces a real square matrix by its transpose.
SUBROUTINE TRINV3: Replaces a 3x3 matrix by the transpose of its inverse.
SUBROUTINE UNIVEC: Replaces a vector by a parallel unit vector, and gives its length.
SUBROUTINE VECPRD: Calculates the vector product of two 1x3 vectors.

13. Special input/output

A. Setting up

SUBROUTINE PREFIN: Makes the Crystal Data File readable in a random order by writing it to a scratch file.

C. Utility

SUBROUTINE ASK: Writes a message on unit ITO and reads an interactive answer to /SCRACH/.
SUBROUTINE BIGCHA: Writes on unit LPT up to 9 characters in large letters.
SUBROUTINE CARDIN: Finds the record number IDEN in the DIRECT ACCESS file on unit IO10, which is a copy of the Crystal Data File.
SUBROUTINE CDFIN: Reads in one Crystal Data File and copies it to direct access unit number IO10, starting at record number ID.
SUBROUTINE CDSCAN: Finds the next card which starts with the letter given in CH, and has then a word which is one of the collection given in WORDS.
SUBROUTINE CENTRE: Writes on unit LUNIT the given message, centred & preceded by N empty lines.
SUBROUTINE CLOFIL: Closes the FORTRAN unit LUN and returns the CCSL unit to the pool.
SUBROUTINE ERRATM: Writes an error message to say that the given name is not an atom name; there is a choice of subsequent action.
SUBROUTINE ERRCH2: Write an error message which involves a given WORD between 2 messages; there is a choice of subsequent action.
SUBROUTINE ERRCHK: (Possibly increases and) checks a value, giving if appropriate an error message; there is a choice of subsequent action.
SUBROUTINE ERRIN2: Writes an error message which involves a given integer INT between 2 messages; there is a choice of subsequent action.
SUBROUTINE ERRMES: Writes an error message, with choice of action on exit.

SUBROUTINE ERRRE2: SUBROUTINE ESDFMT; Writes X and its esd DX in the form X(DX) Writes an error message which involves a given real X between 2 messages; there is a choice of subsequent action.
SUBROUTINE EXPAND: Expands UNIX pathnames by substituting for environment variables
SUBROUTINE FETTLE: Decides field width and fractional part of real number in order to print it.
CHARACTER*10 FUNCTION FILNOM: Returns the name of the file on FORTRAN unit LUN.
SUBROUTINE FILPRO: Makes sense of general file names, under VMS AND UNIX.
SUBROUTINE FINDCD: Searches for a card starting with letter CH and with WORD in columns 3-6.
CHARACTER *4 FUNCTION GENNAM: Finds all the starting letters of an atom name.
SUBROUTINE INCREM: Increments a file name.
SUBROUTINE INITIL: Initialises the CCSL system.
SUBROUTINE INPUTI: Gathers information from a user's interactive instruction card.
SUBROUTINE INPUTN: Deals with the "N" card giving the Crystal Data File title.
SUBROUTINE INTCHR: Converts digits to characters, either left- or right-justified.
SUBROUTINE INTDIG: Unpacks an integer into its individual digits.
FUNCTION IPOPE: Machine specific routine to interpret error codes during file opening.
FUNCTION LENG: Determines the length of a text string, omitting trailing spaces.
FUNCTION LENGT: Determines the length of a character variable, omitting the final spaces.
LOGICAL FUNCTION LERCHK: FALSETRUE or TRUE according to whether NVALUE (possibly incremented) is greater than NBOUND
FUNCTION LETTER: Determines whether a character is a letter.
CHARACTER *4 FUNCTION MAKNAM: Makes an A4 name from the given character and the digits of the given number.
SUBROUTINE MESS: Writes on unit LUNIT the given message, preceded by N empty lines.
FUNCTION NCHINT: Converts an ASCII character into an integer
FUNCTION NDIGIT: Identifies a character as a digit or not.
SUBROUTINE NEWLIN: Writes a newline to the output unit LUNIT
SUBROUTINE NEWPAG: Writes a newpage carriage control ('1') to the output unit LUNIT
FUNCTION NOPFIL: Opens a file on a FORTRAN unit for the first time in this job.
FUNCTION NSYMBL: Finds whether the character I is one of the symbols recognised by the system.
SUBROUTINE NUMA1: Prepares a number for writing, probably on a plotter.
SUBROUTINE NUMDEN: Converts a real number to the numerator and denominator of a fraction.
LOGICAL FUNCTION ONCARD: Finds a card which starts with the given letter and word, and reads one number from it.
SUBROUTINE OPNFIL: Opens file L according to requirements given in M; L may be preset.
SUBROUTINE PRILIS: Prints a list of real numbers held in an array, 5 per line.
SUBROUTINE PRIPLN: Given the normal to a plane face in A, prints the equation of the plane.
SUBROUTINE PUTPAR: Distributes parameters read by RDNUMS amongst individually named variables.
SUBROUTINE RDDATA: Reads in free format h,k,l (possibly floating) and a list of values, allowing for a possible title.
SUBROUTINE RDINTG: Reads an integer in free format from a character string.
SUBROUTINE RDNUMS: Reads all the numbers on a line in free format.
SUBROUTINE RDREAL: Reads a real number in free format from a character string.
SUBROUTINE RDWORD: Reads the next word from a character string.
SUBROUTINE RDWRDS: Reads all the words on a line from column 3 onwards.
SUBROUTINE TESTP: Puts a given heading at top of every printer page, counting lines.
SUBROUTINE UPLOW: Makes first letter of C upper case, and any subsequent letters lower case.
SUBROUTINE UPONE: Puts character strings into all uppercase or all lower case depending on ISYS
SUBROUTINE UPPER: Replaces any lower case letters in C by upper case

14. Graphical output

A. Setting up

SUBROUTINE GETSCL: Chooses a sensible scale for a graph.
SUBROUTINE PINITL: Initialises the system in order to make graphical output.
SUBROUTINE STPLOT: Sets up the plotting of maps; fits elements of a picture together.

B. Crystallographic

SUBROUTINE PICMOV: If plotting to Tektronix, do nothing; if to plotter, move to next picture.
SUBROUTINE PLCONV: Performs the transformation of coordinates between different plotter spaces.
SUBROUTINE PLOTCT: Plots a single contour throughout a given array.
SUBROUTINE PLOTIT: Plots the graph of given vector y against x, with esds.
SUBROUTINE PLOTO: A multi-purpose graph-drawing routine.
SUBROUTINE PLTRIN: Defines a new coordinate transformation for plotting.
SUBROUTINE PMTINV: Specialist routine to invert a 2x3 matrix, such as those which transform plotting coordinates from one space to another.
SUBROUTINE PMTMUL: Specialist routine to multiply together two 2x3 matrices, such as those which transform plotting coordinates from one space to another.
SUBROUTINE SPCSET: Defines the "space" in which coordinates will be given for plotting.

C. Utility

SUBROUTINE ARROW: Draws an arrow centred at X,Y in the current space.
SUBROUTINE CIRCLE: Draws a circle of given radius and centre, with various options.
SUBROUTINE DPLOT: Does plotting in current coordinate system.
SUBROUTINE FRAME: Draws a rectangle in the plotting context.
SUBROUTINE KANGA1: Moves plotter pen (or equivalent) to X,Y in current coordinates.
SUBROUTINE KANGA2: Writes on a plot a string of characters, or simulates this in order to measure the length of the string.
SUBROUTINE KANGA3: Plots a special symbol.
SUBROUTINE PIGLET: A complete set of device-specific plotting commands.

15. Logical operations
SUBROUTINE BITSET: Sets or tests a single bit in a word.
SUBROUTINE GETSQ: Works out where a contour crosses the sides of a square of function values.
FUNCTION ITPOS: Sets ITPOS=a single bit (a one), in position IPOS, counting from the right.
SUBROUTINE LOCBIT: A specialist routine for contour plotting, which finds the "next" bit in the bit-map, removes it, and indicates where on the picture it was.
FUNCTION LOGAND: Performs logical "and" on 2 whole integers.
FUNCTION LOGOR: Performs logical "or" on 2 whole integers.
SUBROUTINE MAKEBM: A specialist contour plotting routine which makes a bit map to show where the contours are.

16. Miscellaneous
SUBROUTINE BATCH: Signals batch running, not interactive.
SUBROUTINE DUMMY: Does absolutely nothing; used as a default in routine calls.
SUBROUTINE FLIP: Exchanges the integers I and J.
FUNCTION JFIX: Rounds a real to be an integer.

FUNCTION NSIGFG: SUBROUTINE NPACK; Deals with the packing and unpacking of up to 10 integers in/out of one Returns the number of figures to print after the decimal point based on the ESD dx integer.
FUNCTION NTICK: Advances its argument by 1 and sets the function to that value also.
SUBROUTINE RESHUF: Reorders a real array, given a parallel pointer array out of SORTX.
SUBROUTINE SORTN: Sorts pointers to an integer array using Heapsort.
SUBROUTINE SORTX: Sorts pointers to a real array using Heapsort.

17. Magnetic routines

A. Setting up

SUBROUTINE INPUTQ: Reads individual "Q" cards
SUBROUTINE LOGMAG: Sets mnemonic logicals from the type of magnetic structure.
SUBROUTINE MAGCNC: To find magnetic constraints in a non-least squares calculation.
SUBROUTINE MAGCNL: Does the fixing associated with constraints found by MAGCON and PSICON.
SUBROUTINE MAGCON: Finds and reports the symmetry constraints on magnetic parameters.
SUBROUTINE PROPER: Determines whether the satellites generated by the propagation vector PROP have integer indices, and generates its "star".
SUBROUTINE PSICON: Determines the constraints on the phase factors in helimagnets.
SUBROUTINE READRT: Reads whatever follows on a "W atom-name ROTN" card.
SUBROUTINE SETFCM: Calls the routines needed to set up magnetic structure factor calculations (or non-magnetic also).
SUBROUTINE SPHPOL: Sets up spherical polar spin directions for magnetic structures.

B. Crystallographic

SUBROUTINE CALDSM: Calculates d star squared, and its derivatives wrt reciprocal cell quadratic products and components of propagation vector.
SUBROUTINE CENTRO: Executes the action of the centre of symmetry on a term in the magnetic structure factor for helimagnetic structures.
SUBROUTINE DOMAG: Multiple entry subroutine to deal with parameters for magnetic structures on Q cards (but not their fixing/varying).
SUBROUTINE FMCALC: Calculates magnetic interaction vectors and magnetic structure factors.
FUNCTION LMAGPR: Gives the fix/vary information for one of the family 2 parameters for magnetic atoms.
SUBROUTINE LMCALC: Calculates a magnetic structure factor and its derivatives.
LOGICAL FUNCTION MAGABS: Tests for systematic absence of magnetic reflections.
SUBROUTINE MAGDIR: Calculates various geometric corrections for various magnetic states. The ENTRY ENTMAG sets up the COMMON.
SUBROUTINE MAGDOM: In Least Squares refinement with magnetic scattering, forms the matrix needed for derivatives of Q with respect to a spin direction.
SUBROUTINE MAGSYM: Routine with 4 named entry points, MAGSYM, MELIN, NELIN and ROTMAG, to deal generally with magnetic symmetry. MAGSYM sets magnetic symmetry, MELIN puts in an operator for a generator, NELIN puts in non-symmetric rotation and ROTMAG rotates with a magnetic operator.
SUBROUTINE MAGVAR: Records the initial fixing, or subsequent varying of magnetic parameters.
SUBROUTINE MOLORB: To read molecular orbital wave-functions from "W atom-name FUNC" card.
SUBROUTINE PROPDR: Makes derivatives of d*sqrd with respect to the magnetic propagation vector
SUBROUTINE SATFND: Finds the indices HS of the satellite equivalent to H, offset by the propagation vector PROP from a reciprocal lattice point.
SUBROUTINE SATGEN: Generates a set of magnetic satellite reflections.
SUBROUTINE SPHELI: Imposes perpendicularity on the two components of a helix.

C. Utility

FUNCTION ASPHFF: Calculates an aspherical form factor for a cubic space group.
SUBROUTINE GENMAG: Generates the next set of magnetic h,k,l, scanning the asymmetric unit.
SUBROUTINE MTPROD: Puts entries into the table of time inversion operators.

18. Multipole routines

A. Setting up

SUBROUTINE INPUTJ: Reads individual J cards.
SUBROUTINE MPCON: Finds the symmetry constraints on multipoles.
SUBROUTINE MPFORM: Finds out which radial form factors to apply to which atom and L value.
SUBROUTINE ORTFUN: Finds the best set of orthonormal functions compatible with symmetry based on the users input, and hence defines the multipoles to refine.
SUBROUTINE PFSET: Directs the reading of J and W cards for multipole calculations.
SUBROUTINE REAORB: To change the orbital basis from Ylm and Yl-m to (Ylm +- Yl-m).

B. Crystallographic

SUBROUTINE MF5ADD: A specialist routine to deal with the refinement of multipoles. Converts each type of LSQ family 5 (multipoles) addressing to the other.
COMPLEX FUNCTION PFCALC: Calculates the COMPLEX nuclear structure factor for the reflection H, using a multipole expansion of the form factor.
SUBROUTINE PFORMF: Calculates radial form factors for multipole refinement.

C. Utility

SUBROUTINE NAMPOL: Creates the label for a given multipole.

P. Jane Brown (brown@ill.fr)