SFCHECK

Version 7.2.02 (01.10.2006) - Features

A program for assessing the agreement between the atomic model and X-ray data or EM map. The program requires one or two input files, with the coordinates of the model (in PDB or CIF or BLANC format) and structure factors (in CIF or PDB or BLANC or MTZ format) or EM (ccp4 format), and runs completely automatically, gives information about R-factor, correlation, Luzzati plot, Wilson plot, Boverall,pseudo-translation, twinning test ..., local error estimation by residues. Sfcheck can compute omit phases and use these instead of phases of model. For output Sfcheck generates a PostScript file. Sfcheck can also create output CIF file with omit phases or with detwinned data. When input file is EM map program can create new mirror or/and scaled map.

CONTENTS


Reference

   Authors:      A.A.Vagin, J.Richelle, S.J.Wodak. 
                email: alexei@ysbl.york.ac.uk
    A.A.Vaguine, J.Richelle, S.J.Wodak. SFCHECK: a unified set of 
    procedure for evaluating the quality of macromolecular stracture-factor
    data and their agreement with atomic model.
    Acta Cryst.(1999). D55, 191-205

Installation

Copy file sfcheck.tar.gz

and uncompress it (`gunzip sfcheck.tar.gz')

After untaring `sfcheck.tar' (command: tar xvf sfcheck.tar) you will get a sfcheck directory, with src, doc and bin subdirectory. To build the executable, go to src

1. setenv BLANC_FORT
define compiler with options,for example:
for linux and mac:
setenv BLANC_FORT "f77 -fno-globals -fno-automatic -O1 -w"
for linux intel compiler:
setenv BLANC_FORT "ifort -static -O1"
for mac ibm compiler:
setenv BLANC_FORT " xlf -qextname -qarch=auto -qtune=auto -qstrict -O3"
else
setenv BLANC_FORT "f77 -O1"
2. sfcheck.setup
the executable (sfcheck) will finish up in the bin directory; providing the full pathname (.../sfcheck/bin/sfcheck) one can execute it from anywhere without having to define an environmental variable. CCP4 version (which can read MTZ file ) will be prepared automaticly if ccp4 is installed
sfcheck for Fortran 90 with memory allocation:
in main_sfcheck_ccp4.f:
comment line:
REAL POOL(MEMORY)
uncomment lines:
C REAL, ALLOCATABLE :: POOL(:)
C VERS = 'M'
C IF(.NOT.ALLOCATED(POOL)) ALLOCATE(POOL(MEMORY_IN),STAT=ISTAT)
C DEALLOCATE(POOL)
for ccp4 version, CCP4 must be prepared with the same compiler

Also you can download binaries (executable files):

( all with memory allocation option)

sfcheck_linux.gz
sfcheck_mac.gz
sfcheck_macintel.gz
sfcheck for windows

New style to use


You can use this version as previous one:

1. by command (batch) file
2. interactively
3. by ccp4i

New style to use:

 You can use program by command string with options (without any keywords):

  sfcheck -f file_sf_mtz_or_cif_or_map  -m model_pdb_or_cif
          -out out    -nomit Nomit
          -mem Nm     -na Na
          -scl map_scale_factor  -map  -invert -origin
          -h             -r
          -po path_out -ps path_scrath
          -lf label_F  -lsf label_sigF
          -li label_I  -lsi label_sigI
          -lfree label_free_flag -lp label_phases

     h      = help and information about mtz labels
     r      = rest some special files(.dst,...)
     out    = y - see nomit option
              a - program creates CIFile (sfcheck.hkl)
                  with anisothermal corrected Fobs
              u - CIFile with detwinned data
     map    = extract density map will be created (sfcheck_ext.map)
              or new map if input was map (sfcheck.map).
              Useful to prepare mirror or/and scaled map
     invert = mirror map will be used 
     origin = set origin of map 0 0 0
     nomit  = number of cycles of omit procedure.
              2 is a good choice.It takes time
              if OUT = Y, program creates CIFile (sfcheck.hkl)
              with omit phases
     Nm     = memory request in Mb (for f90 only)
     Na     = maximal number of atoms in the model
     label_* = labels for mtz_file


     For example:

        sfcheck -f file.mtz

            or

        sfcheck -m file.pdb

            or

        sfcheck -f file.mtz  -m file.pdb

            or

        sfcheck -f file.mtz  -m file.pdb -nomit 2 -map  -out y

            or
            
        sfcheck -f file.mtz -lf FP -lsf SIGFP

            or

        sfcheck -f file.mtz -h

Output information produced by SFCHECK

    1.Crystal: 
        cell parameters and space group
 
    2.Model: 
        number of atoms
        number of water molecules
        solvent content  
        <B> for model
        Matthews coefficient and corresponding solvent %
        reported resolution 
        reported R-factor
 
    3.Refinement:
        refinement program
        resolution range for refinement
        reported sigma cut-off for refinement
        reported R-factor
        reported Rfree
 
    4.Structure factors:
        number of reflections
        number of reflections with I > sigma
        number of reflections with I > 3sigma
        resolution range
        completeness
        R-standard (sum(sigma)/sum(F))
        Wilson plot (amplitudes vs. resolution)
        overall B-factor by Patterson origin peak and by Wilson plot
        optical resolution 
        expected minimal error in coordinates
        Anisotropic distribution of Structure Factors -ratio of Eigen values 
 
    5.Model vs. structure factors:
        R-factor
        Correlation coefficient
        R-factor for reported resolution range and sigma cut-off
        Rfree    
        Luzzati plot (R-factor vs. resolution)
        coordinate error from Luzzati plot
        expected maximal error in coordinates
        DPI
        Patterson scaleing   - scale , Badd
        Anisothermal scaling - betas: b11,b22,b33,b12,b13,b23
        Solvent correction - Ks,Bs
 
    Optical resolution
 
      Optical resolution is defined as an expected minimum distance
      between two resolved peaks in the electron density map.

      With a single-Gaussian approximation of the shape of atomic peak
      the minimum distance between two resolved peaks is twice the standard 
      deviation "sigma" or the width of atomic peak W (W = 2 sigma).
      Expected width of atomic peak W is computed as

       W = sqrt ( 2 (sigma_patt2 + sigma_res2) )

       where  sigma_patt - standard deviation of the Gaussian corresponded 
                         to the Patterson origin peak. 

            sigma_res  - standard deviation of the Gaussian corresponded
                         to the origin peak of spherical interference function
                         which is Fourier transform of the sphere in 
                         the reciprocal space with radius 1/d_min.

                         sigma_res = 0.356 d_min.         
                        
                         d_min is minimum d-spacing, "nominal resolution".

      The "expected optical resolution for complete data set" is  
      calculated as above but using all reflections, with values for
      missing reflection being the average value in the corresponding
      resolution shell.
      Plot of Optical resolution for an atom with B=0 demonstrates
      behavior of the part of Optical resolution corresponded on the 
      series termination.

      (for the proof see Appendix)
  
    Patterson scaling
 
      Scaling in SFCHECK is based on the Patterson origin peak which is
      approximated as a gaussian. Compared to the conventional scaling 
      by the Wilson plot, this method is particularly advantageous when
      only low resolution data are available.
      The program gives overall B-factors estimated by both methods.
 
    Low resolution cut-off
 
      Disordered solvent contributes to diffraction at low resolution.
      However, removing of low resolution data from calculations results
      in a series termination effect which is noticeable in the electron
      density at the surface of the molecule. To reduce the influence of
      low resolution terms, SFCHECK applies the "soft" low resolution 
      cut-off to structure factors according to the formula:
 
        Fnew = Fold (1-exp(-Boff*s2)) , where Boff = 2dmax2
  
      Program uses Boff = 256
 
    Scaling
      
      Program scales Fobs and Fcalc by the Patterson origin peak using all
      data applying Boff.
      First, computes Boveralls for observed and calculed amplitudes.
      Second, makes the width of the calculated peak equal to the 
      observed, i.e. computes an additional termal factor Badd:
        
            Badd = Boverall_obs - Boverall_calc
  
      Third, computes the scale factor for Fcalc:
 
                                  sum(Fobs2*(1-exp(-Boff*s2)))
            scale = sqrt ( --------------------------------------------- )
                           sum(Fcalc2*exp(-Badd*s2)*(1-exp(-Boff*s2)))
 
      Finally we have:
 
            Fcalc_scaled = Fcalc * scale * exp(-Badd*s2)   
 
      The program computes R-factor and Correlation coefficient for all
      data applying the soft low resolution cut-off as described above. 
      The program also computes R-factor and Correlation coefficient for
      the reported resolution range and reported sigma cut-off without
      applying Boff. If the Fobs file contains reflections marked with
      the Rfree flag, the program computes Rfree.
  
    Completeness 
 
      Missing data are restored by using the average values of 
      intensities for the corresponding resolution shell.
      The program produces a plot of completeness vs. resolution and
      a plot of the average radial completeness in polar coordinates
      theta and phi.
 
    Expected minimal error  
 
      The minimal coordinate error is estimated using experimental 
      sigmas(F). The standard deviation of atomic coordinates is 
      
         sig_min(r) = sqrt(3)*sigma(slope)/curvature
 
              where  sigma(slope) is a slope of electron density in the 
                                  x direction ( along A).             
                     curvature is an average curvature of the electron 
                                  density in the atomic peak center.
         
      and computed as:
  
       sigma(slope) = (2pi*sqrt(sum(h2*(sigF)2)))/(VOL*A)
 
                     VOL - volume of cell
                     A   - cell parameter
                     h   - Miller index        
                     summation over all reflections
 
                    ( Cruickshank,D.W.J. (1949) Acta.Cryst 2, 65.) 
 
       curvature  = (2pi2*sum(h2*F))/(VOL*A2)
         
                    ( Murshudov et al., (1997) Acta.Cryst D532, 240.) 
  
      If there is no experimental sigma for observaed data, the program
      uses  sigma = Fobs * 0.04 for all reflections.
            
    Expected maximal error
 
      Expected maximal error in coordinates is estimated  by the difference
      between !Fobs! and !Fcalc!:
 
       sig_max(r) = sqrt(3)*sigma(slope)/curvature
 
       sigma(slope) = (2pi*sqrt(sum(h2*(Fobs-Fcalc)2)))/(VOL*A)
 
       curvature  = (2pi2*sum(h2*F))/(VOL*A2)
  
      For missing reflections the program uses the average value of 
      sigma(Fobs) for the corresponding resolution shell instead 
      of (Fobs-Fcalc).
 
    DPI - diffraction-data precision indicator
      
      The Cruickshank's method of estimation of coordinate error.
                   ( the Refinement of Macromolecular structure Proceeding
                     of CCP4 Study weekend. pp11-22 1996)
                 
        sig(x) = sqr(Natoms/(Nobs-4Natoms)) C-1/3 dmin Rfact
 
                where  C     - fractional completeness.
                       Rfact - convential crystallographic R-factor
                       Nobs  - number of reflections 
                       Dmin  - maximal resolution
        
       If Rfree flags are specified, the program uses the Murshudov's approach 
       to calculate DPI: 
                   (Newsletter on protein crystallography., Daresbury
                    Laboratory, (1997) 33, pp 25-30.)
 
        sig(x) = sqr(Natoms/Nobs) C-1/3 dmin Rfree
    
    Luzzati plot (R-factor vs. resolution)
 
       Program computes the average radial error <delta> in coordinates 
       by Luzzati plot.
                          <delta(r)> = 1.6 sig(x)
 
    Solvent content  
 
       Solvent content is the fraction of the unit cell volume not occupied
       by the model. The model consists of ALL atoms present in the coordinate 
       file.
 
 
    Residual factor Rmerge 
 
                            sum_i (sum_j |Ij - <I>|)
                Rmerge(I) = --------------------------
                                 sum_i (sum_j (<I>))
 
                Ij  = the intensity of the jth observation of reflection i
                <I> = the mean of the intensities of all observations of
                       reflection i
 
                sum_i is taken over all reflections
                sum_j is taken over all observations of each reflection

Local error esimationt

    Local error estimation (plotted for each residue, for the backbone
    and for the side chain):
       1. Amplitude of displacement of atoms from electron density
       2. Density correlation coefficient
       3. Density index 
       4. B-factor
       5. Index of connectivity
 
    Displacement
 
      Displacement of atoms from electron density is estimated from the
      difference (Fobs - Fcal) map. The displacement vector is the ratio of
      the gradient of difference density to the curvature. The amplitude of
      the displacement vector is an indicator of the positional error.
 
    Correlation coefficient
 
      The density correlation coefficient is calculated for each residue
      from atomic densities of (2Fobs-Fcalc) map - "Robs" and the model
      map (Fcalc) - "Rcalc" :
 
      D_corr =  <Robs><Rcalc>/sqrt(<Robs2><Rcalc2>)
 
          where <Robs> is the mean of "obsereved" densities of atoms of residue
                (backbone or side chain).
  
                <Rcalc> is the mean of "calculateded" densities of atoms of 
                residue.
 
          Value of density for some atom from map R(x) is:
 
                   sum_i ( R(xi) * Ratom(xi - xa) )
          Dens =  ---------------------------------- 
                       sum_i ( Ratom(xi - xa) ) 
 
            where  Ratom(x) is atomic electron density for x-th point of grid.
                   xa - vector of the centre of atom.
                   xi - vector of the i-th point of grid.
                   Sum is taken over all grid points which have distance
                   from the centre of atom less than Radius_limit.
                   For all atoms Radius_limit = 2.5 A.
 
    Index of density and index of connectivity
 
      The index of connectivity is the product of the (2Fobs-Fcal) electron 
      density values for the backbone atoms N, CA and C, i.e. the geometric
      mean value for these atoms. Low values of this index indicate breaks 
      in the backbone electron density which may be due to flexibility of 
      the chain or incorrect tracing.  The index of density is a similar 
      indicator which is calculated for all atoms of a given residue.

Omit procedure

 
      An omit map is a way to reduce the model bias in the electron
      density calculated with model phases. SFCHECK produces the so
      called total omit map by an automatic procedure. First, the
      initial (Fobs, PHImodel) map is divided into N boxes. For each
      box, the electron density in it is set to zero and new phases are
      calculated from this modified map. A new map is calculated using
      these phases and Fobs. This map contains the omit map for the
      given box which is stored until the procedure is repeated for
      all boxes. At the end, all the boxes with omit maps compose
      the total omit map. Phases calculated from the total omit map
      are combined with the initial phases. The whole procedure may
      be repeated (keyword NOMIT). Note: it is time consuming!
      Program can create output file with omit phases (see keyword OUT)

Partional information

 
      Program can use only one input file of coordinates or structure 
      factors. In this case program gives information derived from
      input file without local estimation.

Twinning test

 
     Program checks for merohedral twinning.

     Perfect twinning test: <I2>/<I>2 

     Also (if it's possible)
     Program will compute Partial Twinning test:

          H = !I(h1)-I(h2)!/(I(h1)+I(h2))
        
     Alpha (twinning fraction) = 1/2 - <H>

     If  0.05 <Alpha< 0.45 program can create output file
     with detwinned data (see keyword OUT)

Keywords

It is easy to use SFCHECK interactively, but can be used in batch. The best and easiest way to prepare a command file is to run SFCHECK once by dialogue. If a sfcheck.log file was assigned (first request), the program creates a command (batch) file (sfcheck.bat) automatically.

See some command (batch) file examples.

All keywords must be preceded by an underscore (e.g. _DOC). The available keywords are:

First keyword always must be defined:

DOC

One or both of these keywords must be defined:

FILE_C
FILE_F

Other keywords

NOMIT OUT MAP PATH_SCR TEST SCL INVER

To get started with SFCHECK interactively, you first have to answer this question:

  1. Do you want to have FILE-DOCUMENT sfcheck.log? < N | Y >

    _DOC:

    Default: <N>

    N
    do not produce DOC-file
    Y
    produce DOC-file

    The DOC-file contains the protocol of the running of the program. With the DOC-file, the program creates a command (batch) file: sfcheck.bat.

    Also you can use this keyword DOC to redirect output files:

        sfcheck.log
        sfcheck.bat
        sfchek_XXX.ps
        sfcheck.hkl
        sfcheck_ext.map
        sfcheck.map
      

    to special directory ( _DOC Y>path or _DOC >path). Examples:

    
      _DOC  Y>/y/people/alexei/
        or
      _DOC   >/y/people/alexei/
    
    

FILE_C <file>

Default: < >

the name of the input file with the model coordinates (allowed formats: PDB, CIF or BLANC),

FILE_F <file>

Default: < >

the name of the input file with Fobs (allowed formats: ASCII (CIF or PDB) or BLANC or MTZ) or EM map (ccp4 format).

When using an MTZ file, MTZ keywords must be used (or program will use default values).

Other keywords

NOMIT <nmon>

Default: <0>

<nomit> is the number of cycles of omit procedure. 2 is good choice.

OUT <N | Y | U | A>

Default: <N>

A
create new CIFile (sfcheck.hkl) with anisothermal corrected Fobs
Y
create new CIFile with Fobs and omit phases
U
new CIFile with detwinned data

MAP <N | Y>

Default: <N>

Y
extract density (around model) map will be created (sfcheck_ext.map) or new map if input was map (sfcheck.map)

PATH_SCR <path>

Default: < >

path
path to scratch file directory

SCL <scale>

Default: <1 >

map scale factor

INVER <N | Y>

Default: <N>

Y
Y - mirror map will be used

TEST <N | Y>

Default: <N>

Y
not delete some special files

Output files

 
       The output information is represented in the PostScript file:
 
           sfcheck_<identifier>.ps
           sfcheck_map.ps (if input was map)
  
       A simple ASCII version of this file is in:
 
           sfcheck.log 
  
       Also the program can create:
 
           a new formatted CIFile of Fobs: sfcheck.hkl (keyword OUT)
 
           a file of density around model:   sfcheck_ext.map (keyword MAP) 
           /CCP4 format for CCP4 distribution or BLANC format/
           a  new map if input was map:    sfcheck.map
 
       Some other files will not be deleted if keyword TEST = Y.
       These files have internal format of the BLANC program 
       suite (see file README by ftp from anonymous @ftp.ysbl.yorK.ac.uk) 
       and can be used by programs of this suite.
 
           sfcheck_fob.dat     - BLANC_Fobserved_file 
           sfcheck_ph.dat      - BLANC_phases of the model
           sfcheck_omit_ph.dat - BLANC_omit_phases
           sfcheck_detwin.dat  - BLANC_detwinned_Fobs

How to redirect output and scratch files

You can use keyword PATH_SCR to redirect all scratch files to special directory.Example:

  _PATH_SCR  /y/people/alexei/

You can use keyword DOC to redirect output files:


   sfcheck_<identifier>.ps
   sfcheck.hkl
   sfcheck_ext.map
   sfcheck.map

 and also (if keyword TEST = Y )

   sfcheck_fob.dat
   sfcheck_ph.dat
   sfcheck_omit_ph.dat
   sfcheck_detwin.dat

to special directory.Examples:


_DOC  Y>path
 or
_DOC   >path

SFCHECK version for CCP4

 
     You can have CCP4 version of SFCHECK which can read MTZ file
     or EM map (format CCP4) and create file with extract density 
     around model or new mirror or/and scaled map (format CCP4). 
  
  1. This possibility uses CCP4 libraries. 
     You must make setup CCP4 before.

  2. Keywords for reading MTZ file.

        
           Next keywords are necessary only for MTZ file
      
        F               - label of F or F(+)')
        SIGF            - label of sigma F or sigma F(+)')
        F-              - label of F(+)')
        SIGF-           - label of sigma F(-)')
        FREE            - label of Free_flag')
        I               - label of I or I(+)')
        SIGI            - label of sigma I or  sigma I(+)')
        I-              - label of I(-)')
        SIGI-           - label of sigma I(-)')

Command (batch) file examples


# --------------------------------
sfcheck <<stop
# --------------------------------
#
_DOC  Y
#
_FILE_C  model.pdb
_FILE_F fobs.cif
#
#
_END
stop

BATCH example for omit procedure :


  In this case all output files will be in directory: /y/people/alexei/
  and all scratch files will be created in directory: /y/people/alexei/work/

# --------------------------------
sfcheck <<stop
# --------------------------------
#
_DOC  >/y/people/alexei/ 
#
_FILE_C  model.pdb
_FILE_F fobs.cif
#
#
_NOMIT 2
_OUT   Y
_path_scr /y/people/alexei/work/
_END
stop

BATCH example with MTZ file:

  In this case coordinate file doesn't used.
# --------------------------------
sfcheck <<stop
# --------------------------------
#
_DOC  Y
#
_FILE_C  
_FILE_F p1.mtz
#
_F     FO
_SIGF  SDFO
_END
stop

File formats


     1. Input PDB_file of coordinates

        Input PDB_file of coordinates must contain the CRYST1 card with
        the unit cell and the space group name.
        Program can use the information from HEADER,SCALE,MTRIX,REMARK cards.

     2. Input formatted file of structure factors

        This file of structure factors must be in PDB-format or CIFile
        which contains indices and structure factors or intensities.
        (also simple formatted file with "h,k,l,!F!,sig(F)" or "h,k,l,!F!" 
        and without titles is acceptable)
        The best is CIFile.

        A. Example of a CIfile of structure factor amplitudes:

          data_structure_9ins
          _entry.id  9ins  
          _struct.title ' insuline 9ins' 
          _cell.length_a      100.000
          _cell_length_b      100.000
          _cell.length_c      100.000
          _cell.angle_alpha    90.000
          _cell.angle_beta     90.000
          _cell.angle_gamma    90.000
          _symmetry.space_group_name_H-M  'P 1 21 1'
          loop_
          _refln.index_h
          _refln.index_k
          _refln.index_l
          _refln.F_meas_au
          _refln.F_meas_au_sigma
             2  3   4    12.3   1.2
            -2 -3  -4    11.4   1.1
           . . . . . . . . . . . . .
C
                or just:

          data_structure_9ins
          loop_
          _refln.index_h
          _refln.index_k
          _refln.index_l
          _refln.F_meas_au
          _refln.F_meas_au_sigma
             2  3   4    12.3   1.2
            -2 -3  -4    11.4   1.1
            . . . . . . . . . . . . .

           For intensities use:

           _refln.intensity_meas 
           _refln.intensity_sigma 

        B. Example of a PDB file of structure factor amplitudes:

        HEADER   R2SARSF   15-JAN-91
        COMPND   RIBONUCLEASE SA (E.C.3.1.4.8) COMPLEX WITH 3'-*GUANYLIC ACID 
        SOURCE   (STREPTOMYCES $AUREOFACIENS)
        AUTHOR   J.SEVCIK,E.J.DODSON,G.G.DODSON
        CRYST1  64.900   78.320   38.790  90.00  90.00  90.00 P 21 21 21    8
        CONTNT   H,K,L,S,FOBS,SIGMA(FOBS)
        FORMAT   (2(I3,2I4,2F7.0,F6.0,9X))
        COORDS   2SAR
        REMARK  1 TWO REFLECTIONS PER RECORD.
        REMARK  2 DMIN=1.85, DMAX=16.28
        CHKSUM  1 MIN H=0,MAX H=34,MIN K=0,MAX K=41,MIN L=0,MAX L=20
        CHKSUM  2 TOTAL NUMBER OF REFLECTIONS=17346
        CHKSUM  3 TOTAL NUMBER OF REFLECTION RECORDS=8673
        CHKSUM  4 SUM OF FOBS=0.235499E+07
          0   0   3     60      9    16           0   0   4    106    307    25
          0   0   5    166     23    20           0   0   6    239    657    52
          0   0   7    326      0    38           0   0   8    425    511    40
        . . . . . . . . . . . . . . . . . . . . . .

        C. Example of a simple formatted file of structure factor amplitudes 
           which is assumed to contain H,K,L,F,sig(F):
                    
             2  3   4    12.3   1.2
            -2 -3  -4    11.4   1.1
            . . . . . . . . . . . . .

            or without sig(F):

             2  3   4    12.3  
            -2 -3  -4    11.4  
            . . . . . . . . . 

       The length of file records must not exceed 80 characters.
       The format of the records is free, e.g. data must be separated by
       blancs. ( be careful - some PDB files do not satisfy this rule)  
       The program uses the information about cell parameters and space
       group from the coordinate file and ignores such information in
       the structure factor file.

Memory control

      Memory control parameters ( in main_sfcheck_ccp4.f ):
                       
C 
          MEMORY - memory for densities, gradients, coordinates, ...
          PARAMETER ( MEMORY=5000000)
          REAL      POOL(MEMORY)
C
          NCRDMAX - maximal number of coordinates
          PARAMETER ( NCRDMAX=200000)
C
          IPRSYM - maximal number of symmetry operators
          PARAMETER ( IPRSYM=96    )
          INTEGER*2 ISYM(5,3,IPRSYM)
C 
          ISYM    - integer*2 array for cryst.symmetry operators 
          IPRSYM  - dimension of integer*2 array ISYM(5,3,IPRSYM)
                    maximal number of cryst.symmetry operators.
C
          MEMORY  - dimension array POOL. 
C
                 MEMORY = MAPMAX + (NCRDMAX/2)*5 , where MAPMAX - maximal
                                                   size of XY-section (NX*NY)

Appendix


  Estimation of the width of atomic peak by the Patterson origin peak.

  Fourier transform of atomic Gaussian:

            1
         ---------------      exp( -r2/(2 sigma_four2) )
         (2pi sigma_four)2/3
   
             where sigma_four is standard deviation of Gaussian.

 is also Gaussian:

                 B s2
          exp( - ----- )     where B = 8pi2 sigma_four2  
                  4

Patterson function which calculated as Fourier transform of reciprocal 
space Gaussian in square:

                 2 B s2
          exp( - ------- )     
                  4

 is also Gaussian with standard deviation (for infinite fourie series) 

                            2B
          sigma_patt_02 = ----  = 2 sigma_four2
                           8pi2 

 Effect of series termination of Fourier transform can be considered
 as the product in the reciprocal space infinite number of 
 Fourier coefficients and the sphere with radius 1/d_min, where
 d_min is minimum d-spacing. The product in the reciprocal space 
 corresponds to the convolution in the Patterson space.
 Fourie image of sphere is the sherical interference 
 function T(r) (Int.Tables,1993,vol B,p247):
 
           3 ( sin(x) - x cos(x) )
   T(r) = -------------------------  where x = 2pi r (1/d_min)
                     x3
    
 Using Taylor's expansion the origin peak of function T(r)
 can be approximated by Gaussian:

                      r2
          exp( - ------------- )    
                 2 sigma_res2

                    where sigma_res is standard deviation of Gaussian.   

                          sigma_res = ( d_min *sqrt(5) )/ 2pi = 0.356 * d_min  
  
 This result is identical to the optical definition of resolution
 (Blandell,1976), (James,1948)
 as twice the distance from maximim to the first zero of image 
 of a point source. In 3-dimentional case the coordinate of the first
 zero is 0.715 d_min ~ 2 sigma_res.

 Standard deviation 'sigma' of Gaussian which is product of two Gaussians with
 standard deviations sigma_1 and sigma_2 is

    sigma2 = sigma_12 + sigma_22

Therefore the standard deviation of Patterson origin peak with finite
Fourier series is

    sigma_patt2 = sigma_patt_02 + sigma_res2

Standard deviation of expected atomic peak for finite Fourier series is

    sigma_four2 = sigma_patt_02/2 + sigma_res2 =

                 = sigma_patt2/2  + sigma_res2/2
      
 Finally, expected width of atomic peak is:

  W = 2 sigma_four = sqrt ( 2 ( sigma_patt2 + sigma_res2) )