BayMEM - A computer program for application of the Maximum
Contents
1. M ied ostia s GiMeENSiON eru tmu vd EE SP datus s electrons xw Creme Enea Rs ua p Se EX exira endextrg ui oe d oben RR edd oes fbegin endf eom hy RU RU E AA Ne A nde Etats ebegin ends aaepe ia eae ee ea E99 Peppe qt LER orn Ne atate imiialdensity 4 x se REX a Ae 9 E initialfie uu os LM EU cus s uud memcheck Se Ya des Yu A aus dr RE Oe a ep CDS SCR RUE outp tlormab doe eq ud oU SH RI HERE Eu ve eee weak A AA ee ee eens ee le ok a qvectors endqvectors 2e realdimension 4 reg larwidth Space group wu OE EAE EA CONTENTS 5 3 27 name symmetry endsymmetry 5 8 28 name symtable 5 3 29 name title 5 3 30 name 5 4 Examples of typical input fi les Example dl ceo es 5 4 3 Example2 6 Description of the output 6 1 Electron density 6 1 1 Format BMascii 6 1 3 Format BMbinary 6 1 3 Format jana janapl 6 2 File jobname BMout 6 3 File jobname BMlog 6 4 File jobname BMhst 6 5 File jobname BMcheck 6 6 File jobname BMsymtb 7 Ru2. 90 0 105 781 90 0 voxel 64 32 128 Spacegroup P21 n CHAPTER 5 SPECIFICATION OF THE INPUT centro yes electrons 132 symmetry xi x2 x3 1 2 x1 1 2 2 1 2 x3 x1 x2 x3 1 2 1 1 2 x2 1 2 x3 endsymmetry fbegin 2 0 0 25 3459292 0 4 0 0 10 4668808 0 5 4 1 4 1934419 0 1 4 1 9409568 0 2 5 1 0 6319270 0 endf 5 4 2 Example 2 0000000 0000000 0000000 0000000 0000000 2727374 1478727 1320773 1921479 5103144 20 The following input file can be used for determination of accurate charge density of a 4D structure It uses prior density and prior derived F constraints keyword priorsf The generalized F constraint of order 4 is used The input and output formats are BMascii This format allows easy transfer of the densities between different platforms title Example 2 dimension 4 initialfile prior density asc initialdensity BMasci i outputfile example2 asc outputformat BMascii algorithm MEMSys 4 1 1 1 conorder 4 priorsf 0 89 1 5 0 01 cell 7 5281 5 8851 10 437 90 90 voxel 128 100 162 32 Spacegroup Pnma a00 0 electrons 248 qvectors 0 4794 0 0 endqvectors centro yes centers the0000c 0 0 0 0 0 0 0 0 endcenters symmetry x1 x2 x3 x1 1 2 x2 x3 1 2 x1 x2 1 2 x3 1 2 x1 1 2 x2 1 2 x3 x1 x2 x3 x1 1 2 x2 x3 1 2 x1 x2 1 2 x3 1 2 x1 1 2 x2 1 2 x3 endsymmetry fbegin o 2 0 0 0 4 0 0 0 endf 1 ss 0 05 x4 1 2 x4
3. THE OUTPUT 24 Error Statement either missing or doubled cell Error Statement either missing or doubled voxel Info Statement not included or doubled expandedlog Info Statement not included or doubled file Info Statement not included or doubled conorder 2 errors found in the input file There are 3 infos If a missing or doubled compulsory keywords are encountered BAYMEM terminates with an error message written to the standard output It is recommended to always check this part of the BMlog file Even non fatal infos can indicate a problem in the input file e Summary of the input data This part is almost identical with the corresponding part of the BMout file Subsection 6 2 e List of all input reflection with components of the structure factor or square root of the intensity of the G constraints amplitude of the structure factor sigma assignment to a g group zero for F constraints see keyword gbegin endg multiplicity of each reflection and some other diagnostic information e Information about the total number of voxels and number of voxels in asymmetric unit Voxels in unitcell 66355200 Voxels in asymmetric unit 8294402 e A list of reflections is produced that contains all reflections that are equivalent by symmetry to other reflections in the input file If such equivalent reflections are found the program terminates with an error message written to the standard output and to the BMlog file e I
4. convergence is still slow consider increas ing the standard uncertainty of the F 000 structure factor keyword fbegin endf But do not increase it too much or you end up with a problem described below CHAPTER 8 TROUBLESHOOTING 32 e Problem The Cambridge algorithm converges but the value of Test is high Solution The two most probable reasons for this problem are too large value of RATE or too large value of o F 000 Try to decrease them and repeat the calcu lation Under special circumstances with very informative prior and or inaccurate data the condition on the value of the constraint is reached sooner than the proper MEM path is found This can be sometimes also solved by decreasing RATE or by decreasing the internal accuracy keyword settings e Problem The Sakata Sato algorithm converges very slowly virtually stops converg ing Solution The convergence of Sakata Sato algorithm is not guaranteed However slow convergence can be caused by various errors in the input file It is recommended to try calculation with the Cambridge algorithm if possible If the Cambridge algorithm converges the problem is in the Sakata Sato algorithm If none of the two algorithms converge the problem is in the data In that case or if the Cambridge algorithm is not available try to see solutions of previous problems Bibliography De Vries R Y Briels W J amp Feil D 1994 Novel treatment of the experimental data in t
5. example the difference electron densities 5 3 2 name algorithm e value S S MEMSys optional algorithm specific settings e default compulsory keyword no default e description This keyword selects one of the two algorithms presently available in BAYMEM 5 5 selects the Sakata Sato algorithm MemSys selects the Cambridge algorithm implemented in the MEMSys5 package Each algorithm has its own specific settings For algorithm MEMSys the settings are method Integer 4 for the historical maximum entropy x N 1 2 and 3 for different variants of the Bayesian maximum entropy Gull amp Skilling 19996 All choices are possible but only method 4 has been extensively tested and the other methods did not prove to be useful in crystallographic problems NRAND Integer Number of random vectors used in the calculation of conjugate gradient in the MEMSys package NRAND 1 is safe for the vast majority of cases For more details see Gull amp Skilling 19990 aim Real number The stopping criterion aim where C is the value of constraint Usually 1 0 Lower values mean closer fit of the MEM density to the experimental structure factors RATE Real number Sets the user definable factor that influences the sizes of the steps along the conjugate gradient vector For more details see Gull amp Skilling 19990 Usually between 1 0 and 5 0 at the beginning of the iteration RATE can be increased interactively during the i
6. line denotes the center of each interval The next number in line gives the number of normalized residuals falling into that interval The number of crosses X in each line corresponds to number of residuals in each interval rescaled by a factor given in the header of the histogram if the number of normalized residuals in any interval exceeds 100 Three types of slashes outline the ideal Gaussian distribution After the main body of the histogram a list of moments of the distribution is printed separated into contribution of F constraints and G constraints The even moments are normalized so that the expected value of the ideal Gaussian distribution is 1 Ideal Gaussian value of the odd moments is zero 6 5 File jobname BMcheck This file allows the user to graphically check the quality of the MaxEnt solution The file is produced only if the keyword memcheck is present in the input file For closer description of the underlying mathematics see description of the keyword memcheck The file has this format Algorithm MEMSys direct space gradient number dS drho dC drho multiplicity 686 0 10099E 01 0 26331 03 8 1372 0 10160E 01 0 17682E 03 2058 0 10429E 01 0 45650E 03 2744 0 10190E 01 0 53921 03 3430 0 10327E 01 0 22974E 03 4116 0 10345E 01 0 21474E 04 4802 0 10134E 01 0 34958E 04 5488 0 96380E 00 0 14663E 03 6174 0 99438E 00 0 11397E 03 OO OO OO OO reciprocal space gradient dS dF
7. symmetry of the pixel grid is analyzed and the asymmetric unit is found And finally the set of unique reflections given in the input file is expanded into the whole sphere to facilitate Fast Fourier Transform performed later during the iteration 3 The iteration The heart of the program More about the iteration process will be described in following subsections BAYMEM can work with two different MEM algorithms The Sakata Sato algorithm Sakata amp Sato 1990 has been implemented as a part of the code of BAYMEM The MEMSys5 set of subroutines that implements the Cambridge algorithm Skilling amp Bryan 1984 is commercial and must be purchased separately Gull amp Skilling 19990 BAYMEM provides interface with the MEMSys5 package Following chapter discusses issues specific for the two algorithms 4 Writing the output After the iteration has been finished BAYMEM writes out the electron density and other files containing information about the MEM calculation The output is described in Chapter 6 These four steps are performed automatically by the program The task of the user is just to prepare the input file Chapter 3 Algorithms 3 1 Sakata Sato algorithm The Sakata Sato algorithm is based on an approximate solution of the MEM equation Sakata amp Sato 1990 Kumazawa et al 1995 The crucial point in the performance of the algorithm is selection of the value of the Lagrange multiplier In the zeroth order
8. the program 7 1 Program to user communication Almost all messages from the program are written into the BMlog file Section 6 3 This is because the MaxEnt runs might take very long time and the terminal BAYMEM has been run from might have been closed before the MaxEnt run has finished Therefore user should always check the BMlog file for possible warnings and error messages especially in the initial stages of the runs There are few exceptions when an error message is written both to the BMlog file and to the standard output These exceptions concern problems encountered during the reading of data e g at the very beginning of the run 7 2 User to program communication All information necessary to run BAYMEM is given in the input file However there is a limited set of commands that can be passed to the program during its run time The commands must be written in the file jobname BMcom This file is checked by the program and if some known command is found it is performed and the file is deleted No multiple commands are allowed in the BMcom file The commands are case sensitive The most convenient way to pass a command to BAYMEM is to use command echo echo command 2 jobname BMcom The allowed commands are e DENSITY filename If this command is found the current is written to the file specified in the command and the iteration continues e STOP If this command is found the iteration is stopped like if the maxima
9. 0 500 0 0 0 0 1 0 0 0 0 000 0 0 0 0 1 0 0 0 0 000 0 0 0 0 0 0 1 0 0 000 0 0 0 0 0 0 1 0 0 000 0 0 0 0 0 0 1 0 0 500 Symmetry operations 7 through 8 1 0 0 0 0 0 0 0 0 500 1 0 0 0 0 0 0 0 0 500 0 0 1 0 0 0 0 0 0 000 0 0 1 0 0 0 0 0 0 500 0 0 0 0 1 0 0 0 0 500 0 0 0 0 1 0 0 0 0 500 0 0 0 0 0 0 1 0 0 500 0 0 0 0 0 0 1 0 0 000 F Constraints input expanded 3970 30045 P Constraints input expanded 15270 118968 G Constraints input expanded 0 0 e Information about initial and final status of the iteration Contains starting and ending time of the iteration initial and final R values and related quantities Part of the CHAPTER 6 DESCRIPTION OF THE OUTPUT 23 BMout file corresponding to Example 2 is show here The lines beginning with are comments and are not present in the file Date of iteration start 30 01 2003 Time 14 03 58 Initial state Non weighted and weighted R value for all reflections F constraints and G constraints R 0 9725 Rw 0 7779 RF 0 9725 RwF 0 7779 RG 0 0000 RwG 0 0000 Entropy 0 0000000E 00 Sum of calculated mem and observed obs amplitudes of F and G constraints Sum Fmem 2 480E 02 Sum Gmem 0 000E 00 Sum Fobs 9 031E 03 Sum Gobs 0 000E 00 Sum all F and G mem 2 480E 02 F Constraint 2 373E 03 G Constraint 0 000E 00 Date of iteration end 01 02 2003 Time 09 41 56 After 38 Cycles of iteration Elapsed CPU time 2628 min 28 sec Final state R 0 0137 Rw 0 0159 RF 0 0137 RwF 0
10. 0159 RG 0 0000 RwG 0 0000 Entropy 3 0085513 02 Sum Fmem 8 914E 03 Sum Gmem 0 000E 00 Sum Fobs 9 031E 03 Sum Gobs 0 000E 00 Sum all F and G mem 8 914 03 F Constraint 9 964E 01 G Constraint 0 000E 00 F Constraints input expanded 3970 30045 P constraints denote the F constraints calculated from the prior density see keyword priorsf P Constraints input expanded 15270 118968 G Constraints input expanded 0 0 e List of the reflections The list contains information about all input reflections and optional extra reflection see keyword extra endextra F Constraints ho es A Gobs B A Gmem B DeltaF Sigma DeltaF Sigma sinth 1 1 2 0 0 0 37 4445880 0 0000000 37 7395357 0 0000000 0 2949477 NN 0 2325634 1 2682464 0 132835 2 4 0 0 0 8 2858164 0 0000000 8 1621250 0 0000000 0 1236914 NN 0 0570781 2 1670549 0 265671 All input F constraints are listed DeltaF Fobs Feaic sinth 1 denotes sin 0 A reflections with DeltaF gt 3sigma and DeltaF gt 6sigma are marked with and at the end of the line 6 3 File jobname BMlog This is the log file for all messages and informations produced by BAYMEM during its run time The file can be separated into several parts e report from the reading of the input file This part contains error messages about missing or doubled compulsory keywords and information about missing or doubled optional keywords The part has form CHAPTER 6 DESCRIPTION OF
11. 1 2 x4 x4 x4 1 2 x4 1 2 x4 248 3T 2858164 x4 0000000 4445880 1344953 1234955 9918284 90 oo 0000000 0000000 0000000 0000000 0000000 0000000 oo o entering vector can be omitted here it is given just for illustration 1000000 2325634 0570781 2110144 2823512 0583801 Chapter 6 Description of the output The most important output of the MEM calculation is the optimized electron density Apart from this output there are several other files containing information about the input data data processing symmetry iteration and results All files except for the density file have names of the form jobname BM If several runs are performed with the same jobname all the jobname BM files except for BMsymtb are appended not overwritten 6 1 Electron density 6 1 1 Format BMascii In this format the electron density of all pixels in the unit cell is written with six values per line in exponential format preceded by a four line header The pixels are sorted first by increasing first coordinate then second then third etc The file has this form dimension real_dimension pixel_division lattice parameters a b c alpha beta gama volume minimum and maximum of the map density values six numbers per line multiple occurrence For example 4 3 128 100 162 32 5 41530 12 33200 6 78930 90 00000 90 00000 90 00000 453 40 1 041386E 02 4 063997E 01 2 348115E 02 2 38075
12. 5 2 x Det Fat e 5 2 The weighted G constraints can be defined analogically Weighting factor is defined as w 1 or w F depending on the value of the keyword conweight is the length of the diffraction vector and F is the amplitude of the structure factor of every reflection The power n can be any number but numbers between 2 and 5 proved to be the most efficient The weighting on F is not applicable to G constraints because the separate intensities of reflections in one group are not known 5 3 8 name correction e value none normalize cut flat raise e default none e description The prior density used in BAYMEM must bepositive everywhere with exception of the two channel entropy method If the prior density does not fulfil this requirement BAYMEM offers several possibilities to make the prior density positive everywhere The meaning of the values is none No correction normalize The density is normalized to the number of electrons given in the input file corr N UNCOTT gS cut If the minimum of the density is negative then all pixels with p lt abs pPmin are assigned the value of flat Values less than zero are set to value corresponding to an equally distributed NaVuc density 2 raise If the minimum of the density is negative then the whole density is raised by 1 5 abs Pmin The charge of the prior density must be equal to the total ch
13. 6 1 The file must not exist BAYMEM will never overwrite an existing density file Instead of that the output density is written to a file named bmmapXX ert where XX is a serial number starting from 00 A warning 15 written to the logfile jobname BMlog If all hundred files bmmap00 ext bmmap99 ext exist the program will try to ask the user for the filename on the terminal If the ter minal which BAYMEM has been started from does not exist anymore the program will stop without writing any output density file 5 3 21 name outputformat e value jana janapl1 BMascii BMbinary e default compulsory keyword no default e description Supported formats of the output density files are jana and single precision m81 format of the program package JANA2000 BMascii double precision ascii format of BAYMEM transferable between platforms BMbinary dou ble precision binary format of BAYMEM usually non transferable between different platforms The files written with format jana contain pixels with coordinates 0 N 1 in each direction i Format janapl contains all pixels with coordinates 0 N in each direction e g with the redundant border of the unit cell For more description of the formats of the output density see Section 6 1 5 3 22 name priorsf e value three real numbers optional positive integer e default no adding of prior structure factors e description This keyword provides a possibility to include struc
14. 6E 02 2 477587E 02 2 641150E 02 2 877340E 02 3 185024E 02 3 561728E 02 4 012891E 02 4 537618E 02 5 122452E 02 5 765039E 02 6 476191E 02 7 245219E 02 8 037046E 02 8 832136E 02 9 632531E 02 1 042432E 01 1 116911E 01 6 1 2 Format BMbinary This is a double precision binary format of BAYMEM The order of numbers is the same as in the ascii format only the minimum and maximum of the map is omitted in the binary format Dimension real dimension and pixel division is written as integers all following numbers are written as double precision floating point numbers 21 CHAPTER 6 DESCRIPTION OF THE OUTPUT 22 6 1 3 Format jana 1 This is the format of the crystallographic software package Jana Its standard extension is m81 It stores the electron density in single precision direct access binary format It is beyond the scope of this manual to fully describe this format The density file written in the format jana contains only the pixels in one unit cell 0 N 1 in each direction N is the pixel division in the direction i format janap1 contains also the border of the unit cell e g pixels with coordinates 0 N in each direction i 6 2 File jobname BMout This file contains all important information about the input data data processing and results of the MEM run It consist of three parts e Summary of the input data This part contains the most important information col lected by the program from the input file Its c
15. BAYMEM A computer program for application of the Maximum Entropy Method in reconstructions of electron densities in arbitrary dimension User Manual Lukas Palatinus Sander van Smaalen version 05 01 2005 Contents 1 Introduction 2 Basic operation of BAYMEM 3 Algorithms 3 1 Sakata Sato algorithm eA 3 2 MemSys5 package eere 4 Technical details 4 1 Programming language and system requirements 4 2 Execution s a xenon Rae uu RG e py vsus trs 5 Specification of the input bull types Of input ele Gia gaa a Gracie Seb ee e RR ERA 5 2 Format of the ASCII input file 53 Specification of keywords eA 5 3 1 5 3 2 5 3 3 5 3 4 5 3 5 5 3 6 5 3 7 5 3 8 5 3 9 5 3 10 5 3 11 5 3 12 5 3 13 5 3 14 5 3 15 5 3 16 5 3 17 5 3 18 5 3 19 5 3 20 5 3 21 5 3 22 5 3 23 5 3 24 5 3 25 5 3 26 name name name name name name name name name name name name name name name name name name name name name name name name name name 2ch nrnel there ceo ve eu dae be a algoribhin eye Gy Gee x P Rae Ded RW Tek Bad Gellt rne udo Rodi ee eB cote io dedos e dees He toe centers endcenters CENEO eee ete be ELA Poe eat ora p rM ge HER Go ordero lu s were xx Sere dM ANM beta Sh e ret utendo s COLTECHION
16. ENGTH ENDIF ENDIF should be replaced by KCORE KB J LENGTH KL J e file vector for lines 567 589 the original code between lines 567 and 589 If using dynamic block sizes instead of fixed LBLOCK IF MORE EQ 1 THEN Calculate block size and set up stack LBLOCK KL J IF NBUF GT 0 THEN LBLOCK MIN LBLOCK LWORK NBUF if held on disc IF ACTION CALL USTORE ST KCORE KB J IOFF LENGTH CALL VSTACK 1 KCORE ENDIF ENDIF Any more elements IF IOFF LENGTH GE KL J MORE 0 should be completely removed Operation of MemSys5 is extensively described in the MemSys5 user manual cite The Cambridge algorithm guaranties convergence to the proper MaxEnt solution under normal circumstances If the computation with Cambridge algorithm does not converge the reason is usually in the input data and the data should be checked for errors see Section 8 However the MemSys5 set of subroutines is complex and relatively rigid and therefore difficult to adapt to non standard problems For this reason some variations of the constraints are not implemented in BAYMEM with the Cambridge algorithm This concerns G constraints and the generalized F constraints These constraints work only with the Sakata Sato algorithm Important MemSys5 version 1 2 does not have a built in option for normalization of the MEM distribution although this option is described in the user manual Therefore the normalization must be
17. ST DEF S GS SUM One block of standard entropy without normalization IMPLICIT CHARACTER A Z DOUBLE PRECISION ST 0 DEF S GS SUM DOUBLE PRECISION ZERO EPS A C INTEGER I PARAMETER ZERO 0 0D0 EPS 1 0D 13 IF DEF GT ZERO THEN CALL MFILL ST 2 DEF LL MMUL ST 2 4 2 LL MSUM ST 2 A LL MDIV ST 1 4 2 LL MEXP ST 2 2 LL MSMUL ST 2 DEF 2 CA CA CA CA CA ELSE CA CA CA CA CA ENDI LL MMUL ST 3 4 2 LL MSUM ST 2 A LL MDIV ST 1 4 2 LL MEXP ST 2 2 LL MMUL ST 2 3 2 F CALL MDOT ST 2 4 SUM CALL MDOT ST 2 1 C S SUM A C CALL CALL CALL CALL CALL CALL END MMUL ST 1 1 1 MDIV ST 2 4 2 MSUM ST 2 SUM MDOT ST 2 1 GS MSQRT ST 2 1 ST 2 4 2 file memsys5 for lines 3661 3663 Replace code 5 with code 5 CALL CALL CALL CALL CALL CALL CALL MSUB ST 21 25 24 MMUL ST 24 22 24 MDOT ST 24 24 PLHOOD MSUB ST 21 25 24 MMUL ST 24 22 24 MMUL ST 24 31 28 MDOT ST 28 28 PLHOOD Following changes are not necessary for proper performance of the program but they remove some unnecessary operations on the data and thus speed up the operation of the program CHAPTER 3 ALGORITHMS 8 e file vector for lines 540 563 the original code between lines 540 and 563 IF MORE EQ 0 THEN Initialise and count disc buffers if using dynamic block sizes MORE 1 NBUF 0 held on disc CALL VSTACK 1 KCORE IF ACTION CALL UFETCH ST KCORE KB J IOFF L
18. XXXXXX 1 2 27 XXXXXXXXXXXXXXXXXXXXXXXXXX 1 4 31 1 6 17 XXXXXXXXXXXXXXXX 1 8 24 XXXXXXXXXXXXXXXX XXXXXX 2 0 8 XXXXXXXX 2 2 8 XXXXXXX 2 4 4 XXXX 2 6 3 XX 2 8 2 X 3 0 1 1 3 2 0 1 3 4 01 3 6 2 XX 3 8 01 4 0 01 4 2 01 4 4 o l 4 6 1 IX 4 8 1 IX 5 0 1 IX 5 2 01 5 4 o l 5 6 0 5 8 o 6 0 1 IX 6 2 01 6 4 o l 6 6 0 6 8 o 40 o 52 o 7 4 0 7 6 01 7 8 o l 8 0 0 8 2 o 8 4 o 8 6 0 8 8 1 IX Statistics F G Combined 1 7 397E 01 0 000 00 7 397E 01 2 1 007E 00 0 000E 00 1 007 00 3 2 443E 00 0 000E 00 2 443E 00 4 3 552E 00 0 000E 00 3 552E 00 5 6 807 01 0 000E 00 6 807 01 6 3 451E 01 0 000E 00 3 451E 01 7 4 244E 03 0 000 00 4 244 03 8 3 434E 02 0 000E 00 3 434E 02 End of histogram CHAPTER 6 DESCRIPTION OF THE OUTPUT 28 The header contains basic information about the MEM run The time refers to the time of writing of the histogram and is almost equal to the time of writing the output electron density Weighting and Constrained moment refer to the static weighting keyword conweight and to the order of the generalized F constraint keyword conorder respectively The main body of the histogram consists of a representation of the distribution of nor malized residuals The interval between the minimum and maximum normalized residue is divided into intervals of 0 2 The number at the beginning of each
19. achieved by adding the F 000 structure factor to the dataset with value equal to the number of electron given in the input file For details on handling the F 000 see description of the keyword fbegin endf Section 5 3 Chapter 4 Technical details 4 1 Programming language and system requirements The program BAYMEM is written in the programming language Fortran 90 It has been compiled and tested on two computers e Compaq AlphaStation ES40 with 500MHz 64 bit Alpha EV6 RISC processor and with Compaq Fortran Compiler V5 5 1877 48BBF e Silicon Graphics Fuel with 500MHz IP35 MIPS R14000 processor and with MIPSPro Fortran compiler V7 4 The program obeys Fortran 90 standards and should therefore be compilable with any F90 compiler The program does not have any special system requirements It does not use graphical interface and the input can be edited with any plain text editor such as vi nedit or emacs However it should be noted that the requirements for the RAM are quite high in order of GB for large problems 4 2 Execution The program is executed with command BayMEM input filebase ncycles where input filebase is the name of the ASCII file containing input parameters see sections 5 2 5 3 and 5 4 without the extension BayMEM The extension BayMEM is automat ically added by the program every input file must have this extension If the input filebase is omitted the program will prompt for it interactively The opti
20. arge of the resulting Pmem Therefore the prior densities obtained by the corrections cut flat or raise are subsequently normalized to the number of electrons given in the input file 5 3 9 name dimension e value positive integer e default compulsory keyword no default e description This keyword defines the dimension of the structure Dimension must be larger or equal to the value of realdimension Apart from this restriction the dimension is arbitrary However for dimensions larger that the parameter MAXDIM in the module Globaldefinitions the parameter MAXDIM must be changed and the program recompiled The current value of MAXDIM is 8 CHAPTER 5 SPECIFICATION OF THE INPUT 14 5 3 10 name electrons e value real number e default compulsory keyword no default e description Gives the number of electrons in the unit cell The resulting electron density will be normalized to this number of electrons It the value F 000 is given in the list of structure factors see keyword fbegin endf it must be equal to the value of electrons Zero or negative value of the number of electrons is possible only with two channel entropy see keyword 2 1 5 3 11 name expandedlog e value yes no e default no e description If the value is yes the log file will contain the full list of all symmetry expanded reflections If the value is no only the symmetry independent reflections are listed 5 3 12 name extra endext
21. be reported as doubled reflection The standard deviation of F 000 will be set to one third of the smallest standard uncertainty found in the input data F 000 is not included in calculation of the starting and final R values and values of the F constraint but it is included in the value of x reported by MEMSys CHAPTER 5 SPECIFICATION OF THE INPUT 15 5 3 14 name file e value valid specification of filename without extension e default The first command line argument to BAYMEM at start e description The user can change the base of all output files generated by BAYMEM The default base is the base of the input file filename without the extension Bay MEM 5 3 15 name gbegin endg e value one or more groups of intensities see keyword ggroup e default no G group e description The so called G groups are groups of two or more reflections where only sum of their intensities in known Several such groups can be placed between the keywords gbegin and gend Each group starts with keyword ggroup 5 3 16 name ggroup e value first line ggroup G o G where G is the group amplitude and o G is the standard uncertainty of G following lines ndim integers representing the indices of reflections in the G group default no ggroups description ggroup defines one G group The group amplitude is defined as 5 3 Ng is the number of reflections in the G group m is the multiplicity of the reflection j Fj is the a
22. charge of the new pygw and of the previous cycle before the new density is normalized Large values of this factor indicate too large change between the two cycles If the automatic lambda control is enabled the last cycle will automatically be repeated with a decreased value of lambda if the charge increase factor exceeds 100 If the automatic lambda control is disabled only a warning is printed to the BMlog file Entropy The total entropy of the unit cell Pi ila 1 L The total maximized Lagrangian L S AC 6 2 Constrained moment number Order of the generalized constraint see keyword conorder Combined FG constraint Constraint calculated only from the experimental data present in the input file If this value becomes smaller than aim keyword settings the iteration is considered to be converged Combined FPG constraint Constraint calculated from all data including the prior derived F constraints keyword priorsf This quantity is the measure of the con vergence of the algorithm If the constraint shift between the FPG constraints of successive cycles is negative the calculation is considered to diverge This line occurs only if the prior derived F constraints are used FCon i GCon i Values of the ith moments of the distribution of the normalized residuals The odd values should remain close to zero the even values should converge CHAPTER 6 DESCRIPTION OF THE OUTPUT 26 to one These value
23. cine Acta Crystal logr A 52 397 407 Sakata M amp Sato M 1990 Accurate structure analysis by the maximum entropy method Acta Crystallogr A 46 263 270 Schneider M 2001 Ph D thesis University of Bayreuth Bayreuth Germany Skilling J amp Bryan R K 1984 Maximum entropy image reconstruction general algo rithm Mon Not R Astr Soc 211 111 124 van Smaalen S Palatinus L amp Schneider M 2003 Maximum entropy method in su perspace Acta Crystallogr A von der Linden W Dose V Fisher R amp Preuss R eds 1998 Maximum Entropy and Bayesian Methods Kluwer Academic Publishers Dordrecht 33
24. f the prior derived F constraints are used this list will contain also the structure factors calculated from prior density The format is identical with the format of ex perimental F constraints e f setting expandedlog yes is present in the input file then the BMlog file will contain a full list of all reflections expanded by the symmetry operators from the input file This listing is suppressed by default In the default case only this summary is printed Listing of expanded reflections suppressed summary follows Totals of expanded reflections F Constraints 30045 P Constraints 118968 G Constraints 0 Alltogether 149013 e Record of the progress of the iteration The style of this part depends of the type of algorithm in use Sakata Sato algorithm A record identical to the record in the BMout file is written to the BMlog file at the beginning of the iteration If automatic determination of the starting A is allowed keyword settings following information occurs in the BMlog file Automatic calculation of starting lambda the value set to 0 3144E 02 Following statistics is written into the log file after each cycle CHAPTER 6 DESCRIPTION OF THE OUTPUT 25 Cycle 392 Lambda 0 1308E 01 Test 0 2313 R 7 596E 03 Charge increase factor 1 0002 Rw 6 674E 03 RF 7 596E 03 RwF 6 674E 03 RG 0 000E 00 RwG 0 000E 00 Entropy 3 5944897E 01 Entropy shift 4 512E 04 L 3 6019225E 01 Constrained moment numbe
25. flat 10 06 2003 Time 09 31 08 Weighting No Constrained moment 2 Rescaled by 100 105 CHAPTER 6 DESCRIPTION OF THE OUTPUT 27 D F sigma D of appearances graphical representation 4 6 1 IX 4 4 o 4 2 01 4 0 01 3 8 o l 3 6 01 3 4 o l 3 2 0 N 3 0 i JN 2 8 2 XN 2 6 1 2 4 3 XXX N 2 2 2 XX X 2 0 9 XXXXXXXXX 1 8 7 XXXXXXX N 1 6 20 XXXXXXXXXXXXXXXXXXX N 1 4 34 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1 2 39 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1 0 49 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 0 8 75 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXX 0 6 87 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXX 0 4 96 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXX 0 2 104 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXX 0 0 105 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXX 0 2 101 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXX 0 4 98 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXX 0 6 79 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XK 0 8 69 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XX 1 0 45 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
26. haracters any text exceeding this length is ignored 5 3 Specification of keywords There are two basic types of keywords The first type is followed by one or more values on the same line keyword valuel value2 value3 The second type has the form initial keyword line 1 line 2 final keyword Each line may contain one or more values The name of the keyword of the first type is a single word without spaces The name of the keyword of the second type is a pair of initial and final word separated by a hyphen in the following text 10 CHAPTER 5 SPECIFICATION OF THE INPUT 11 Each value can be a constant of type real integer or character The type of the parame ters and their allowed values are specified Alternative values are separated by slashes The keywords are either compulsory or optional The compulsory keywords must be specified for the analysis to proceed The optional keywords can be omitted If an op tional keyword is omitted the default value is used Compulsory keywords are indicated by compulsory keyword no default value in the item default The item description describes the function of the keyword its influence on the output and relations to other keywords 5 3 1 name 2channel e value yes no e default no e description Activates or deactivates the two channel entropy formalism Papoular et al 1996 That allows to reconstruct the maps with both positive and negative densities for
27. he application of the maximum entropy method to the determination of the electron density distribution from x ray experiments Acta Crystallogr A 50 383 391 Gilmore C J 1996 Maximum entropy and bayesian statistics in crystallography a review of practical applications Acta Crystallogr A 52 561 589 Gull S amp Skilling J 19994 MEMSys5 v1 2 program package September 6 1999 Maximum Entropy Data Consultants Ltd Suffolk U K Gull S amp Skilling J 19990 Quatified Maximum Entropy MEMSyYs5 Users Manual Maximum Entropy Data Consultants Ltd Suffolk U K Jaynes E T 1996 Probability theory The Logic of Science http www bayes wustl edu etj postscript Fragmentary Edition Kumazawa S Takata M amp Sakata M 1995 On the single pixel aprroximation in maximum entropy analysis Acta Crystallogr A 51 47 53 Palatinus L 2003 Ph D thesis University of Bayreuth Bayreuth Germany Palatinus L amp van Smaalen S 2002 The generalized f constraint in the maximum entropy method a study on simulated data Acta Crystallogr A accepted Palatinus L amp van Smaalen S 2003 The prior derived f constraint Suppressing the artefacting in the maximum entropy method Acta Crystallogr A in preparation Papoular R J Vekhter Y amp Coppens P 1996 The two channel maximum entropy method applied to the charge density of a molecular crystal a gly
28. hy If the symmetry operator 15 R r then the format of each entry is Tj Ri1xl Ryox2 Rinxn Ra1x1 R22X2 Ronxn Example n glide perpendicular to b 1 2 1 x2 1 2 x3 The translation components can be given either as fractions or decimal numbers 5 3 28 name symtable e value yes no e default no CHAPTER 5 SPECIFICATION OF THE INPUT 19 e description BAYMEM calculates so called symmetry table at the beginning of each run This symmetry table contains all information about the symmetry of the pixel grid This calculation is quite time consuming 10 save computer time in subsequent calculations with the same grid and symmetry the symmetry table can be written out in a file called jobname BMsymtb BAYMEM will write the file jobname BMsymtb only if setting symtable yes is present in the input file If the file jobname BMsymtb exists BAYMEM reads the symmetry information from that file instead of calculating it Generally this option is useful only if many calculations with the same symmetry setting are planned Note that the BMsymtb file can be very large up to several GB for large grids Once the file jobname BMsymtb exists BAYMEM will read it regardless of the value of symtable This setting influences only writing of the file 5 3 29 name title e value text shorter or equal to 132 characters e default compulsory keyword no default e description The title of the job It is used in the outpu
29. j dC dF j multiplicity 0 98691E 02 0 26485E 01 1 0 19613E 01 0 32598E 02 0 93420E 02 0 21646E 02 0 45182E 02 0 10621E 02 0 10662E 02 0 14466E 01 0 21129E 02 0 18777E 01 0 30789E 03 0 14683E 01 0 46036E 02 0 11276E 02 9 0 42390E 02 0 78690E 01 10 0 44431E 03 0 10764E 01 11 0 11022E 02 0 37930E 01 12 0 28685E 03 0 82155E 00 NON OIN IN OIN IN OIN 0 INS IND IND The pixels in the direct space gradient are sampled so that the total number of samples corresponds to the number given by the keyword memcheck The list of reflections in the reciprocal space part is complete If a chart of second vs third columns is plotted the points should form a straight line in case of an ideal MaxEnt solution CHAPTER 6 DESCRIPTION OF THE OUTPUT 29 6 6 File jobname BMsymtb This is a binary file containing the information about the symmetry of the discrete unit cell It is intended for internal use in BAYMEM This file is written only if enabled in the input file keyword symtable If the file jobname BMsymtb exists the symmetry information is read from the file and the time consuming calculation of the symmetry information is not performed Having this file can be useful if many runs with identical symmetry settings are planned However note that the BMsymtb file can be very large several GB for more dimensional unit cells The file is never deleted by BAYMEM Chapter 7 Run time interaction with
30. l allowed number of cycles were exceeded The output density and all output files are written e RATE value This command applies only to the algorithm MEMSys It allows the user to change the value of parameter RATE specified originally in the keyword settings Higher values of RATE speed up the convergence but too high values can cause failure of the algorithm For more information on this problem see Section 8 The information about the change of RATE is written in the BMlog file 30 Chapter 8 Troubleshooting e Problem BAYMEM terminates very quickly without writing any output density Solution Check the jobname BMlog file for possible reports on errors in the data like some missing or mistyped keywords or non unique set of reflections e Problem The input data check in the file jobname BMlog returns too large value Solution This indicates some inconsistency in the input parameters or data Most probable reason is that the symmetry operators do not form a space group Check also whether the keyword centro is consistent with the symmetry operators All symmetry operators of the space group must be listed including those related by the center of symmetry Another possibility is that the list of reflections in the input file contains reflections that are systematically extinct Such reflections must not be present in the input list Such a situation can occur if the reflections have been indexed in other symmetry or only othe
31. ler than or equal to dim see keyword dimension e default 3 e description Defines the dimension of the real space Normally this is 3 For some special applications two dimensional diffraction on surfaces other values than 3 can be chosen 5 3 25 name regularwidth e value dim positive real numbers e default regularization function not used e description BAYMEM has the capability of introducing a correlation between the neighboring pixels The correlation is introduced by convolution of the density with a nD normalized Gaussian distribution More about this topic can be found in cite Schneider The Gaussian can have different widths in different directions The widths w are given as argument to regularwidth The units of w are dmin where 1 Hmaz Hmaz is the longest reciprocal vector present in the input dataset 5 3 26 name spacegroup e value text shorter or equal to 132 characters e default empty e description Symbol of the super space group Currently not used in the program 5 3 27 symmetry endsymmetry e value each line contains definition of one symmetry operator e default compulsory keyword no default e description This keyword contains the complete definition of the symmetry with ex ception of the centering vectors Each line contains one symmetry operator The format of the symmetry operators corresponds to the conventions used in the Interna tional Tables for Crystallograp
32. mplitude of the structure factor of reflection j Each line following the line with ggroup contains indices of one reflection in the G group The format of the whole ggroup is gbegin first ggroup ggroup g amplitude g sigma hkl hkl hkl second ggroup ggroup g amplitude g sigma endg CHAPTER 5 SPECIFICATION OF THE INPUT 16 5 3 17 name initialdensity e value flat jana BMascii BMbinary e default compulsory keyword no default e description initialdensity defines the type of the prior density 7 If initialdensity is set to flat the prior density is assigned a uniform value of electrons NPix NPix being the total number of pixels in the unit cell see keywords electrons and voxel Any other initialdensity has to be accompanied by specification of the prior density file see keyword initialfile Formats are jana single precision m81 format of the program package JANA2000 BMascii ascii format of BAYMEM transferable between platforms BMbinary double precision binary format of BAYMEM usually non transferable between different platforms 5 3 18 name initialfile e value valid filename shorter or equal in length to 132 characters e default compulsory keyword no default if initialdensity is other than flat e description Specifies the file containing the input electron density map See keyword initaldensity 5 3 19 name memcheck e value positive integer e default no memcheck output e de
33. n time interaction with the program 7 1 Program to user communication 7 2 User to program communication 8 Troubleshooting 18 18 19 19 19 19 20 21 21 21 22 22 23 26 28 29 30 30 30 31 Chapter 1 Introduction The Maximum Entropy Method MEM is a versatile statistical method for reconstruction of images of virtually any type One of its applications is the reconstruction of the electron density distributions from the X ray diffraction data As a special case combination of the MEM and superspace approach offers new possibilities for studies of the modulation functions of modulated structures BAYMEM is a computer program that has been developed for applications of the MEM in charge density reconstructions of both ordinary and modulated crystal structures This manual is intended to provide practical guide to the usage of BAYMEM it will not focus on the theory of the MEM and on details of different algorithms and types of MEM available in the program The reader can find the theoretical information in special liter ature The basic foundations of the MEM are described in Jaynes 1996 A collection of articles encompassing the wide variety of applications of the MEM in science was is compiled in von der Linden et al 1998 The various applications of the MEM to the crystallograph ical problems are described in a review article by Gilmore 1996 The description of the Sakata Sato algorithm is given in Saka
34. onal parameter ncycles defines the maximal number of MEM iterations After BAYMEM performs ncycles iter ations it stops regardless of the degree of convergence of the job If ncycles is omitted the value MAXCYCLES from the module GlobalDefinitions in file Variables mod f90 is used currently MAXCYCLES 100000 Chapter 5 Specification of the input 5 1 Types of input There are two types of input The basic input is the ASCII input file it contains all the necessary parameters of the BAYMEM run In following sections the expression input file means always the ASCII input file The second type is a file containing the reference electron density prior This input is used only if the keyword inputdensity has another value than flat Currently BAYMEM supports electron density files in three different formats see section 6 1 The file with the reference electron density is referred to as a prior density file or prior density in following text 5 2 Format of the ASCII input file The input file is a free format file based on keywords Each keyword represents a specific parameter of the MEM calculation and must be given a value Multiple spaces anywhere in the file are handled as a single space If the sign or I occurs anywhere in the line the rest of the line after this sign is treated as comment and not interpreted Blank lines anywhere in the input file are ignored The length of the interpreted part of the line is 132 c
35. ontent is self explainatory Following BMout file was produced by the input file in Example 2 Section 5 4 2 Title Example 2 Input example2 BayMEM Dimension of superspace 4 Real dimensions Cellparameters a b c alpha beta gamma Volume 7 52810 5 88510 10 43700 NN 90 00000 90 00000 90 00000 462 40 Reciprocal cellparameters a b c alpha beta gamma Volume 0 1328356 0 1699206 0 0958130 NN 90 00000 290 00000 290 00000 2 162644E 03 Pixel a b c 128 100 162 32 Electrons per unit cell 248 0000 Type of initial density file BMascii Initial density filename prior density asc Initial density correction type none Algorithm type is set to MEMSys The settings are Method 4 NRand 1 Aim 10000D 01 Rate 10000D 01 Utol 50000D 01 Constrained moment order 2 Spacegroup Pnma a00 0ss Centrosymmetric structure No Friedel pairs are computed while expanding reflections q vectors 1 1 0 4794000 0 0000000 0 0000000 Symmetry operations 8 Symmetry operations 1 through 3 1 0 0 0 0 0 0 0 0 000 1 0 0 0 0 0 0 0 0 000 1 0 0 0 0 0 0 0 0 500 0 0 1 0 0 0 0 0 0 000 0 0 1 0 0 0 0 0 0 500 0 0 1 0 0 0 0 0 0 000 0 0 0 0 1 0 0 0 0 000 0 0 0 1 0 0 0 0 000 0 0 0 0 1 0 0 0 0 500 0 0 0 0 0 0 1 0 0 000 0 0 0 0 0 0 1 0 0 500 0 0 0 0 0 0 1 0 0 500 Symmetry operations 4 through 6 1 0 0 0 0 0 0 0 0 500 1 0 0 0 0 0 0 0 000 1 0 0 0 0 0 0 0 0 000 0 0 1 0 0 0 0 0 0 500 0 0 1 0 0 0 0 0 0 000 0 0 1 0 0 0 0 0 0 500 0 0 0 0 1 0 0 0
36. r 4 Sum Fmem 4 799E 03 Sum Gmem 0 000E 00 Sum Fobs 4 801E 03 Sum Gobs 0 000E 00 Sum all F and G calc 4 799E 03 F constrained moment 5 246E 02 G constrained moment 0 000E 00 Combined FG Constraint 0 998 Constraint shift 5 136E 03 Combined FPG Constraint 0 057 Constraint shift 2 891E 04 Aim 1 000 FCon 1 5 231E 02 FCon 3 1 688E 01 FCon 5 1 635E 00 FCon 7 2 806E 01 FCon 2 7 993E 02 FCon 4 5 246E 02 FCon 6 2 888E 02 FCon 8 1 153E 02 GCon 1 0 000E 00 GCon 3 0 000E 00 GCon 5 0 000E 00 GCon 7 0 000E 00 GCon 2 0 000E 00 GCon 4 0 000E 00 GCon 6 0 000E 00 GCon 8 0 000E 00 The majority of the text is self explanatory or has been explained in Section 6 2 The meaning of the remaining statements is given here Lambda The Lagrange multiplier For more description see chapter 3 1 Test Test 1 cos VS VC VC VS i e one minus the cosine of the angle between the gradients of the entropy and of the constraint The angle is zero for the ideal MaxEnt solution and consequently the test should be close to zero too However there is no guarantee that the Sakata Sato algorithm leads to an ideal MaxEnt solution Therefore a larger deviation of test from zero does not necessarily indicate a problem in the computation and or input data The higher value of test may be caused by the inadequacy of the approximations used in the Sakata Sato algorithm Charge increase factor Ratio of total
37. r setting of the space group that the symmetry operators refer to e Problem The Cambridge algorithm MemSys5 package converges smoothly up to certain value of omega but then oscillates around that value without reaching the final value omega 1 Solution This usually indicates inconsistency in the number of electrons given in various places The total number of electrons given by the keyword electrons must be consistent with the value of F 000 in the input reflection list and if applicable with the number of electrons in the prior electron density BAYMEM does not automatically normalize the prior electron density to the expected number of electron it is user s responsibility to supply consistent prior density e Problem The Cambridge algorithm converges very slowly the change in Omega between cycles is very small Solution If none of the previously described problems applies you may have chosen too low value of RATE Try to increase it either in the input file keyword settings or during the iteration recommended see Section 7 2 In general more symmetrical structures can have higher RATE up to 15 or 20 in extreme cases Important Do not increase RATE too much better increase it by small amount several times Watch the value of Test If Test starts to increase do not increase Rate further Increasing Rate too much can and probably will lead to serious problems with convergence If the value of RATE is already high and the
38. r the ideal MaxEnt solution In the MEMSys algorithm this value is a crucial indicator of the quality of the MaxEnt solution The value should be low at the end of the iteration say less than 0 1 Omega is an indicator of the progress of the iteration Iteration is stopped only if Omega is equal to 1 4 internal accuracy see keyword settings Code is a string of ones and zeroes Iteration will not stop before all digits in Code are zero For the meaning of individual positions in Code please refer to the MEMSys 5 user manual Note that one cycle of MEMSys iteration is not comparable with one cycle of iteration of Sakata Sato algorithm In each iteration cycle of MEMSys several subcycles are performed The number of total direct and inverse Fourier transforms performed during one iteration cycle is given as Ntrans in the last line of the output of each cycle 6 4 File jobname BMhst One of the basic assumptions underlying the principle of the F and G constraints is that the noise in the data is distributed randomly with a Gaussian distribution Thus the proper solution should produce normalized residuals Fobs Feate o Foos that have a Gaussian distribution The file jobname BMcheck contains a representation of the histogram of normalized residuals for an easy assessment of the quality of the distribution of the normalized residuals This is an example of the histogram Start of histogram Title Sample histogram Prior type
39. ra e value each line contains indices of one reflection with optional expected value of the structure factors of that reflection e default no extra reflection e description The maximum entropy method is able to estimate the values of the struc ture factors that have not been used in the MaxEnt optimization The estimated values of the structure factors of reflections given in the extra endextra list are written to the output file jobname BMout at the end of the calculation If an expected value of structure factor is given this value is also written in the output file and the expected and estimated values can be directly compared 5 3 13 name fbegin endf e value each line contains the indices real and imaginary part of the structure factor and ats estimated standard uncertainty of one reflection from the input dataset e default compulsory keyword no default e description This keyword serves for definition of the input data The format of each line is free the order is indices B o F A and B are the real and imaginary components of the structure factor Number of indices must be consistent with the dimension of the structure defined in keyword dimension F 000 must be present in the data set Section 3 2 If F 000 is present as the first structure factor in the input data its value and sigma are read by BAYMEM otherwise BAYMEM adds this structure factor automatically and any later occurrence of F 000 will
40. rent A modes The Sakata Sato algorithm works well in most cases However its convergence is not guaranteed Sometimes the speed of the convergence becomes so low that the calculation must be stopped before the final value is reached If the difference between the current value of the constraint and the desired stopping value is not large the problem is usually not dramatic because the electron density changes only very little in the last stages of the iteration Note also the some problems with convergence are not due to the algorithm but due to inconsistencies in the input data See Chapter 8 for description of possible problems 3 2 MemSys5 package MemSys5 package is a general MEM system applicable to any MEM problem not only crystallographic The package is commercial and must be purchased separately Gull amp Skilling 1999a The interface with MemSys5 is provided as a part of BAYMEM The interface is written so as to avoid modifications to the code of MemSys5 package as much as possible However modifications changes could not be avoided entirely These changes CHAPTER 3 ALGORITHMS 6 have to be made in the source code of the MemSys5 package without them BAYMEM will not work with MemSys5 properly The changes are listed here The line numbers refer to the version 1 2 of MemSys5 package released on September 6 1999 e All declarations of the floating point numbers should be changed from REAL to DOU BLE PRECISION Thi
41. s allow the user to estimate the quality of the distribution of the normalized residuals before the end of the iteration MEMSys package Prior to beginning of the iteration check of consistency of the transformation routines is performed Output of this check is a real number If the check is successful the number is very small comparable to the numerical accuracy of the calculation For double precision calculations the value of check should not exceed 10714 The result of the check is written to the BMlog file Result of input data check 0 3803E 17 Important It is strongly recommended to check this number at the beginning of the calculation especially if a completely new dataset is used If this check fails the calculation will not lead to correct results For more information see Section 8 The information logged at each cycle is produced by the MEMSys5 package User should refer to MEMSys5 manual for description of the output Gull amp Skilling 19995 Here only the description of the most important values will be given The standard form of the output is Iteration 5 Entropy 1 4524 01 Test 0 0214 Chisq 7 6539E 03 Omega 0 260387 dist 0 2746 Alpha 7 3870E 03 Ntrans 74 Code 001010 The most important indicators are Test Omega and Code Test is defined as Test 1 cos VS VC VC V S i e one minus the cosine of the angle between the gradients of entropy and constraints Test is zero fo
42. s can be done by replacing all occurrences of text REAL with text DOUBLE PRECISION note the ending spaces in files memsys5 for vector for and memsys inc e file memsys5 for line 896 replace code IF METHDi LT 1 0R 4 LT METHD1 STOP Illegal METHOD 1 value by code IF METHD1 LT 1 0R 5 LT METHD1 STOP Illegal METHOD 1 value e file memsys5 for line 3409 Between lines 3409 and 3410 CALL MENT4 ST DEF PS PGRADS PSUM END IF this code must be inserted ELSEIF METHD1 EQ 5 THEN CALL MENT5 ST DEF PS PGRADS PSUM e file memsys5 for subroutine MENTI Replace the code of subroutine MENTI be tween lines 3418 and 3440 by this code SUBROUTINE MENT1 ST DEF S GS SUM One block of standard entropy IMPLICIT CHARACTER A Z DOUBLE PRECISION ST 0 DEF S GS SUM DOUBLE PRECISION ZERO A C PARAMETER ZERO 0 0DO IF DEF GT ZERO THEN CALL MFILL ST 2 DEF CALL MMUL ST 2 4 2 CALL MSUM ST 2 A CALL MDIV ST 1 4 2 CALL MEXP ST 2 2 CALL MSMUL ST 2 DEF 2 ELSE CALL MMUL ST 3 4 2 CALL MSUM ST 2 A CALL MDIV ST 1 4 2 CALL MEXP ST 2 2 CALL MMUL ST 2 3 2 ENDIF CALL MDOT ST 2 4 SUM C A SUM CALL MSMUL ST 2 C 2 CALL MDOT ST 2 1 C S SUM A C CALL MMUL ST 1 1 1 CALL MDIV ST 2 4 2 CALL MSUM ST 2 SUM CHAPTER 3 ALGORITHMS CALL MDOT ST 2 1 GS CALL MSQRT ST 2 1 CALL MMUL ST 2 4 2 END e file memsys5 for line 3441 Insert code of subroutine MENTS5 here SUBROUTINE MENTS
43. scription The correctness of the MaxEnt solution can be checked by testing the set of equations 05 oC Agoma C Lors 5 4 or its equivalent in reciprocal space oS OC uen cdita 5 5 FMEM FMEM OF OF where 5 is the entropy of the MEM density and C is the constraint If the pairs ap vs dd or vs are plotted they should be aligned on straight line The keyword memcheck can be used to produce a file jobname BMcheck that contains list of the pairs aor This file be used to plot the the corresponding graphs The list of every pixel of the asymmetric unit eq 5 4 could be extremely long Therefore only some pixels are selected The number of selected pixels is given by the value of the keyword memcheck The pairs corresponding to the equation in reciprocal space eq 5 5 are listed completely 5 3 20 name outputfile e value a valid filename of a non existing file e default jobname ezt where ext is a format specific extension CHAPTER 5 SPECIFICATION OF THE INPUT 17 e description Specifies the filename of the output electron density If the keyword is omitted then the name of the output file is created from the jobbase see keyword file and format specific extension which is asc for outputformat BMascii raw for outputformat BMbinary and m81 for outputformat jana janap1 for descrip tion of the formats see Section
44. single pixel approximation used by the Sakata Sato algorithm the value of A is not critical for the convergence of the algorithm unless it is too large Too large values lead to diver gence of the algorithm On the other hand too small values of only decrease the speed of convergence Selection of the value of A is user s responsibility and does not follow from the theory BAYMEM offer two modes of handling The first mode is the fixed A mode The user selects the value of A at the beginning of the iteration and the value is fixed during the iteration If divergence is encountered in this mode BAYMEM terminates The second mode is called the automatic A control The starting value of is increased by an arbitrary factor f every cycle currently f 1 1 If divergence is encountered A is decreased by a factor fa currently fa 0 75 and the cycle is repeated At the same time the factor f is lowered currently 1 2 so that the increments of lambda are not so large in following cycles In the majority of cases the automatic A control gives the best possible performance of the Sakata Sato algorithm However in some exceptional cases the automatic A control fails and divergence occurs that cannot be avoided by any decreasing of In those cases the only solution is to turn off the automatic A control and set A to a fixed value See description of the keyword settings Section 5 3 for information on how to select diffe
45. t files to identify the individual calculations It is recommended but not necessary to change the title with every new calculation 5 3 30 name voxel e value dim positive integers e default compulsory keyword no default e description Defines the division of the unit cell Each number corresponds to the number of pixels along one axis of the superspace unit cell The division must obey the symmetry of the unit cell ie a center of any pixel must be mapped by the symmetry operators onto itself or onto a center some other pixel This means that for example the numbers of pixels along the directions of the screw axes 21 31 41 62 and 6 must be multiples of 2 3 4 3 and 6 respectively Numbers with small prime factors should be preferred to take the full advantage of the speed of the Fast Fourier Transform Combinations of powers of two or three are especially favorable The largest prime factor of all divisions must be smaller than 23 5 4 Examples of typical input files 5 4 1 Example 1 This is an example of a simple input file for the calculation of a 3D electron density of a monoclinic crystal using a flat prior density The Sakata Sato algorithm is selected while the alternative setting for the MEMSys algorithm is commented out by hashes 72 title oxalic acid dimension 3 initialdensity flat outputfile examplei m81 outputformat jana algorithm S S AUTO 1 0 algorithm MEMSys 4 1 1 0 1 0 0 05 cell 6 1005 3 4999 11 9554
46. ta amp Sato 1990 The Cambridge algorithm was first published by Skilling amp Bryan 1984 The commercial set of subroutines MEMSys5 that implements the Cambridge algorithm and that BAYMEM provides interface with has its own extensive user manual Gull amp Skilling 19995 The first version of BAYMEM has been described in a PhD thesis by Schneider 2001 Further developments of BAYMEM are described in a PhD thesis by Palatinus 2003 An article on the theory of MEM in superspace with description of BAYMEM and examples of application was published by van Smaalen et al 2003 A variety of methods exist that can enhance the performance of the MEM Many of them are available in BAYMEM Among them is the concept of static weighting De Vries et al 1994 the generalized F constraints Palatinus amp van Smaalen 2002 the two channel entropy formalism Papoular et al 1996 and the prior derived F constraints Palatinus amp van Smaalen 2003 Chapter 2 Basic operation of BAYMEM The operation of BAYMEM can be considered to be split into following steps 1 Reading the data The data from the input file is read and checked for consistency Dynamic arrays for holding the data are allocated The format of the input file is described in Chapter 5 2 Initializing the MEM iteration Before start of the iteration three essential steps are necessary First the prior density is created or read from an external file Second the
47. teration see Section 7 2 internal accuracy Real number Defines the internal accuracy in the calculation of the conjugate gradient The recommended value is 0 05 The precise value is not crucial for the performance of the algorithm Too small values do not improve the accuracy but slow down the iteration For algorithm S S the settings are lambda Real The initial estimate of the lagrange multiplier is always positive If the parameter lambda is given negative the absolute value is taken and fixed e g BAYMEM will operate in the fixed mode Section 3 1 If the string AUTO case CHAPTER 5 SPECIFICATION OF THE INPUT 12 sensitive occurs instead of a number BAYMEM will estimate the starting value of A automatically aim Real The stopping criterion aim where C is the value of constraint Usually 1 0 Lower values mean closer fit of the MEM density to the experimental structure factors The settings after the specification of the algorithm can be omitted In that case the default settings are used The defaults are algorithm 5 5 algorithm S S AUTO 1 0algorithm MEMSys algorithm MEMSys 4 1 1 0 1 0 0 05 5 3 3 name cell e value a b c o D e default compulsory keyword no default e description Lattice parameters of the structure 5 3 4 name centers endcenters e value Each line contains one centering vector e default no centering vectors e description Defines the centering vectors of
48. the super space group The dimension of the centering vectors must correspond to the dimension of the structure defined by the keyword dimension The components can be given both as fractions and as fractional number 5 3 5 name centro e value yes no e default compulsory keyword no default e description The value yes corresponds to a centrosymmetric structure The value of centro must be consistent with the symmetry operators given in keyword symmetry endsymmetry 5 3 6 name conorder e value even positive integer e default 2 e description Defines the order of the generalized F constraint Palatinus amp van Smaalen 2002 The generalized F constraint of order n is defined as Np 1 Ds Cr 1 Ng x ma Gauss is the value of the nt central moment of the Gaussian distribution The generalized F constraint is implemented only in the 5 5 algorithm n 2 corresponds to the standard x constraint If conorder other than 2 is combined with the MEMSys algorithm the program terminates with an error message CHAPTER 5 SPECIFICATION OF THE INPUT 13 5 3 7 name conweight e value Hn or Fn n is a number between 50 and 50 e default n 0 no weighting e description Static weighting according to De Vries et al 1994 The F constraint with the static weighting is defined as Nr Lum 1 F H FUIT 5 Cy w Foos X
49. ture factors calculated from the prior density in the input data set Palatinus amp van Smaalen 2003 The format of the keyword is priorsf sin6 A in sin Almar sigma maxindex All structure factors between sin0 A min and sin0 A maz that are not present in the input data are calculated from the prior density and added to the data set as so called P constraints These P constraints behave exactly like the F constraints in the MEM iteration but they are not included in the calculation of x and therefore do not influence the stopping point of the convergence The optional parameter maxindex tells the program that only the reflections with the maximal satellite index smaller or equal to the value of maxindex will be added to the dataset Default value of maxindex is 0 Currently maxindex works correctly only for ordinary modulated structures and not for composites because the definition of a satellite reflection is slightly different in the two cases 5 3 23 name qvectors endqvectors e value Each line contains the components of one q vector There must be dim rdim q vectors between the start and end keyword rdim is the number of real space dimensions keyword realdimension e default compulsory keyword no default not applicable if dim rdim e description This keyword contains coordinates of the q vectors CHAPTER 5 SPECIFICATION OF THE INPUT 18 5 3 24 name realdimension e value positive integer smal
Download Pdf Manuals
Related Search