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************************* * PROGRAM PACKAGE GNOM * ************************* Small-Angle Scattering Data Processing by Means of the Regularization Technique ----- Version E4.3 21/08/99 16:50 ----- ----- for IBM-PC and UNIX ----- GNOM is written by D.Svergun & A.Semenyuk EMBL c/o DESY Notkestrasse 85 D-22603 Hamburg, GERMANY and Institute of Crystallography Academy of Sciences of Russia 117333 Leninsky pr.,59 Mocsow, RUSSIA Version 4.3 released by D.Svergun Tel. (+49) (0)40 89902 125 Fax. (+49) (0)40 89902 149 E-mail Svergun@EMBL-Hamburg.DE URL http://www.embl-hamburg.de/ExternalInfo/Research/Sax/ ------------------------------------------------------------ CONTENT Introduction What is new in version 4.3 Structure of input data file Output file Standard deviations Integral kernel and job type Experimental conditions Regularization parameter Perceptual criteria Error estimates Graphics Next job On-line help Configuration file Practical advises Hardware and software requirements References ----------------------------------------------------------- Introduction ============ GNOM is an indirect transform program for small-angle scattering data processing. It reads in one-dimensional scattering curves (possibly smeared with instrumental distortions) and evaluates the particle distance distribution function p(r) (for monodisperse systems) or the size distribution function D(R) (for polydisperse systems). The main equations relating the scattering intensity to the distribution functions and describing the smearing effects one can find in the text-books (e.g. ). GNOM is similar to the known programs of Glatter , Moore  and Provencher . There are, however, some points, which make GNOM more convenient in application. GNOM is a dialogue program; the user instructions presented here explain how to answer the questions properly. The versions E4.0 and higher make use of the "configuration file", where some or all the parameters can be pre-defined; this allows to work with GNOM in different modes, ranging from fully interactive to batch mode. The names of the parameters in the following description refer to the configuration file names. The algorithms used in the program are described elsewhere [4-6]. They are based on the Tikhonov's regularization technique ; several subroutines published in  are modified and used in GNOM. The value of the regularization parameter is estimated by the program automatically using the perceptual criteria . What is new in version 4.3 ========================== 1. Version 4.3 WILL NOT run under DOS or Win3.x on IBM PC, it requires Win95/98 or WinNT. 2. Version 4.3 is a double precision version. 3. Maximum numbers of experimental points in the input data file, of the data points after joining and of the points in the characteristic function are increased to 2048, 512 and 101, respectively. 4. Version 4.3 searches for the input of the data stream in a smarter way. When reading in the input data, GNOM searches for THREE valid lines containing increasing s and positive I(s). Due to this, GNOM is able to read e.g. files in sasCIF format or those in the ILL or LOQ format without editing. 5. A possibility is added to omit data points in the beginning and at the end of the input file(s). 6. The angular scale can optionally be reduced to the units of 4*pi*sin(theta)/lambda [Angstrom]. 7. An option AH (or LH ) < 0 is added to emulate the case of infinite slit coliimation (e.g. Kratky camera geometry) 8. Both IBM-PC and UNIX versions of GNOM4.3 use now the GNUPLOT graphics and support several printer formats for hardcopy output. Structure of input data file ============================ Input file (parameter INPUT1) is a sequential ASCII file containing the experimental data. First line is always treated as a problem title (comment). Then the program searches for the first data line. Valid data line should contain momentum transfer, non-zero intensity, and, optionally, standard deviation in a free format (that is, separated by blanks or commas). After this all valid lines are treated as data; invalid line or end-of-file are considered as the end of the input stream. Maximum number of data points is 1024. This way to read data is rather flexible, allowing to skip additional headers and to use the data with or without the standard deviations. However, long files will take some time to read (especially on VAX'es). With modern devices one can measure lots of data points with tiny angular step. This is not always good, and sometimes might become harmful when using indirect methods, because each angular point gives rise to a separate equation, which are, in fact, linear dependent. Note that the angular step Delta(s) = Dsamp / 6, where Dsamp=(pi)/Dmax is a sampling distance, is claimed to be optimum. To optimize the performance, GNOM joins neighbouring data points when it finds the number of points to be unreasonably high. The program can handle simultaneously two data sets corresponding to the same sample but recorded with different conditions (see below). The second input file (parameter INPUT2) should have the same structure. Default answer to the question 'Input file name, second run' is NO second run. Note, that the momentum transfer is assumed to be s = 4 (pi) sin (theta) / (average wavelength), where theta is a half of the scattering angle. Example of the input file : .......................................................................... PROBLEM #13 This line is skipped because of error, the next because of zero intensity : 0.0001 0.0 17.1 This is again skipped: the next is the first valid data line: 0.05564 , 1.2323e10 111111111. 0.05574 1.1323e10 0.05584 18303353, 1e10 , This is the text which does not change anything! 1.e-1 1.0323e10, 8E8 It is just not read. 0.07 0.0 17.1 The previous line indicates the end of the data set .......................................................................... Output file =========== This is a sequential disk file where all the information from GNOM will be printed in ASCII form (parameter OUTPUT, default file name is gnom.out) Standard deviations =================== If some standard deviations (or all of them) are not specified, negative or equal to zero, the user will be prompted for their estimation (parameter DEVIAT). A positive number means constant relative deviation per point. If the user enters zero (default answer), the program will estimate the errors automatically with the help of a polynomial smoothing procedure. Example .......................................................................... 3 means that for each point with a non-positive standard deviation a relative deviation 0.03*A is assumed, where A is the intensity in this point .......................................................................... Integral kernel and job type ============================ The program searches for a distribution function in real space (characteristic function for monodisperse systems or size distribution function for polydisperse systems). These functions are related to the experimental intensity by corresponding Fourier transform followed by some convolutions representing smearing effects (if the latter exist). The integral equation is represented in a form of a linear system and solved with respect to the distribution function. The matrix of the system is called "design matrix". To evaluate it, the user must specify several parameters: *** JOBTYP 0 - calculation of distance distribution function for a monodisperse system (default job). The function p(r) = gamma(r)*r**2 is evaluated, where gamma(r) is the characteristic function of the particle. 1 - calculation of volume distribution function D(R)=(4*pi/3)*R**3 N(R) for polydisperse system of solid spheres (R is the sphere radius, N(R) relative number of particles with this radius in the system) 2 - calculation of size distribution function of particles with the user-supplied form factor (parameter FORFAC). In this case the form factor of particles should be supplied in a separate file. The first line of this file should contain three values in free format: NFORM - number of points in the formfactor NDIM - number of dimensions (NDIM=1 long particles, NDIM=2 plane particles, NDIM=3 globular particles) DELSR - increment in the s*R units (s scattering vector, R characteristic particle size). The form factor is to be given in the points 0., DELSR, 2DELSR,... ...(NFORM-1)*DELSR. This should be followed by the form factor values (NFORM values in 8E10.3 format, NFORM <2500) The function D(R) = N(R)*R**NDIM is evaluated; R is a user-defined characteristic size (e.g. radius of gyration) 3 - calculation of the distance distribution function of thickness assuming monodisperse system of flattened particles. The function p(r) = gammat(r) is evaluated, where gammat(r) is the characteristic function of thickness. In this case the experimental intensity as well the errors are multiplied by s**2 which corresponds to the thickness scattering factor. 4 - calculation of the distance distribution function of the cross-section assuming monodisperse system of rod-like particles. The function p(r) = gammac(r)*r is evaluated, where gammac(r) is the characteristic function of thickness. In this case the experimental intensity as well as the errors are multiplied by s, which corresponds to the cross-section scattering factor. 5 - calculation of the length distribution function p(r) for a polydisperse system of long cylinders p(r) = H N(H), where H is the length of the cylinder, N(H) number of rods of the lengths H. Radius of the cylinder is assumed to be a constant (see parameter RAD56 below). 6 - calculation of the surface distribution function p(r) for a polydisperse system of spherical shells p(r) = 4*pi*R**2*N(R), where R is the outer radius of the shell, N(R) number of the shells of the outer radius R. The shells are assumed to have the same relative thickness (see parameter RAD56 below). *** RMIN (for JOB=1,2,5,6), RMAX Maximum diameter of the particle (for JOB=0) Minimum and maximum radii of spheres (for JOB=1) Minimum and maximum characteristic particle sizes (for JOB=2) Maximum diameter of the particle thickness (for JOB=3) Maximum diameter of the particle cross-section (for JOB=4) Minimum and maximum heights of cylinders (for JOB=5) Minimum and maximum outer radii of shells (for JOB=6) - define the interval in real space, where the distribution function is assumed to be non-zero *** For JOB=5 or 6, the parameter RAD56 is to be specified: JOB=5: RAD56 means the radius of a cylinder (RAD56=0 means infinitely thin rods) JOB=6: RAD56 means the relative thickness of a shell (its inner radius is RAD56*(outer radius). RAD56=0 means infinitely thin shells. *** Number of real space points (parameter NREAL) - number of points, in which the disiribution function will be specified (less than 72). Default number of NR is evaluated by GNOM in order to have reasonable ratio (number-of-data-points)/(number-of-parameters-to-be-found). *** Boundary conditions (parameters LZRMIN, LZRMAX) - it is possible to fix the values of the distribution function to zero at the ends of the interval by answering "Yes". *** Kernel-storage file name (parameter KERNEL) - name of the file, where the design matrix is saved Experimental conditions ======================= *** Type of experimental set-up (parameter IDET) The user must define which type of experimental set-up is used. IDET=0 means no smearing, IDET=1 means 1D-detector (slit geometry with rectangular slits is assumed), IDET=2 means 2D-detector (the data is obtained by a circular average). *** Wavelength smearing (parameters FWHM1 and FWHM2, valid for IDET=1 or 2) are the Full-Width-at-Half-Maximum of the wavelength distribution function for the first (second) data set. FWHM=0 means monochromatic radiation. If IDET=2 (2D-detector), a possibility of submitting an arbitrary wavelength profile is forseen. To this end, one should specify FWHM=0, and the program will try to read the wavelength profile from the beam profile file (SPOT1 and/or SPOT2), assuming that it follows the beam profile. If the wavelength profile is not present monochromatic radiation is assumed. *** Beam divergency in 1D-case (parameters AH1, AH2, AW1, AW2, LH1, LH2, LW1, LW2, valid for IDET=2 ) In 1D-case, a rectangular slit geometry is assumed, with the slit-height parameters AH - projection of the beam height in the detector plane, and AL - heigth of the detector slit, and similar slit-width parameters AW and LW. Therefore, the beam profile is assumed to be a trapezoidal function < ----- (A-L) ----- > * * * * * * * * * * * * * * * * * * * *-----------------------------* < ---------- (A+L) -----------> both in the direction perpendicular and parallel to the alignment of the detector. In the former case (slit-height effect) A=AH, L=LH; in the latter case (slit-width effect) A=AW, L=LW. The units of AH, LH, AW, LW are to be the same as for the momentum transfer. *** Beam profile files (parameters SPOT1 and SPOT2, valid for IDET=2) To describe the beam divergency in the 2D-case the used should specify the file containing the "spot function", i.e. distribution of the primary beam intensity in the 2D-detector plane (without sample), measured with the given geometry. The function is assumed to be a square matrix, stored in a separate file. The file structure: 1st line :NB - number of rows (and columns) in the beam profile; TRANS - the factor relating the resolution of the beam profile (detector step, DetSt) and the angular step in the experimental curve (DeltaS), TRANS=DetSt/DeltaS. By default, TRANS=1, i.e. it is assumed that the angular step is equal to the distance between two channels in the beam profile. NB and TRANS can be written in the free format separated by blanks or commas (NB is compulsory parameter, TRANS - auxiliary). A comment can be added after TRANS (of NBEAM if TRANS is not specified). 2nd-(NB+1)st lines : each containing NB numbers, separated by blanks or commas - beam profile. The beam profile is used to evaluate the smearing due to beam divergency assuming that the curve is obtained by a circular average. Circularly averaged and normalized profile is used to this end. Additional smearing due to the radial average of the 2D-data is assumed to be one unit in the detector profile. If FWHM = 0 (see above), then an arbitrary wavelength profile could be specified after the beam profile in the following way: (NB+2)nd line : :comment (NB+3)rd line : :NW - number of points in the wavelength profile; WL1 - starting wavelength; DLAM - wavelength increment (all the three parameters are compulsory) (NB+4)th etc :wavelength profile (NW values in arbitrary format). If FWHM = 0 and the wavelength profile is not submitted (or improperly specified), no wavelength smearing is included. Example .......................................................................... 7 1.5 Beam profile: Detector step=1.5*Delta(s) in the input file 0. 1. 4. 5. 4. 1. 0. 1. 45. 143. 211. 143. 45. 1. 4. 143. 460. 678. 460. 143. 4. 5. 211. 678. 1000. 678. 211. 5. 4. 143. 460. 678. 460. 143. 4. 1. 45. 143. 211. 143. 45. 1. 0. 1. 4. 5. 4. 1. 0. Wavelength profile (will be read in if FWHM=0 has been specified) 27, 4.59, 0.01106 0.00, 30.36, 68.16, 175.4, 236.1, 240.3, 200.3, 174.7, 139.2, 113.9, 112.4, 115.9, 109.3, 87.42, 65.51, 76.43, 116.7, 125.7, 128.0, 106.9, 80.50, 62.44, 48.11, 49.16, 43.41, 28.76, 0. .......................................................................... If instrumental distortions (especially all of them) present, the evaluation of the design matrix may become a time-consuming procedure. When making successive computations with the same experimental conditions and real space limitations, one can use the same integral kernel, if it has been already calculated. For this, one should answer 'Y' when prompted 'Is the kernel already evaluated [N]?' (parameter LKERN), and enter after it the kernel-storage file name. The program can handle simultaneously two runs recorded at different (or the same) experimental conditions. The user should then supply two separate experimental data files (first - with lower s range; however, the ranges may overlap) and specify explicitly two sets of experimental conditions. The scale factor for the second run (parameter COEF) is evaluated by the program automatically . Regularization parameter ======================== The main question, typical for solving ill-posed problems is how to stabilize the solution properly (here: how to find a positive regularization parameter ALPHA, which demands smoothness of the solution). The larger ALPHA, the more attention is paid to the smoothness of the distribution function and the less attention - to fitting the experimental data. This search was done in the earlier GNOM versions by the generalized discrepancy method  using sucsessive calculations with different ALPHA values. The ALPHA was chosen so as to fulfil the well-known Chi-square criterion: the sum of deviations of the smeared intensity, corresponding to the given ALPHA, from the experimantal values, weighted with the standard deviations, should be equal to 1 + AN1. Here the value of AN1 is calculated by the program and represents the degree of unconformity of the problem (it equals to zero if NS=NR and increases with the ratio NS/NR). If AN1 is too large (AN1 > 1) the warning is printed. This warning, in princilpe, means that the input data/parameters are to be checked; however, it does not hinder followins calculations. The discrepancy criterion alone, however, in many cases can not ensure the correctness of the solution. Standart deviations may not be known or may be wrong. Another criterion which can also be used is the stability of the solution with respect to changing ALPHA. It can serve for manual , or automatic  search, but sometimes fails as well. Perceptual criteria ==================== In the EN.N versions the computer is instructed to get a plausible solution basing on several criteria, like its smoothness, stability, absence of systematic deviations, etc. Some of them are to be fulfilled by increasing ALPHA, the others - by its decreasing. A compromise is to be found. It is done as follows. Each criterion is expressed mathematically. For a given solution one calculates the value of the criterion and compares with its "ideal" value. All estimates of the parameters have the form of Gaussians P(i) = EXP ( - [(A(i) - B(i))/SIGMA(i)]**2 ) where A(i) - expected ("ideal") value of the criterion B(i) - its actual value, SIGMA(i) - width of the distribution (FWHM/1.665) (values A(i) and SIGMA(i) are specified a priori). Then the total estimate is calculated as TOTAL = P = SUM ( P(i) * W(i) ) / SUM (W(i)) where W(i) - weight of the given criterion (also fixed). Therefore, all P(i) and P are between 0 and 1. The program searches for a maximum of the total estimate P. The following criteria are used for estimates: DISCRP --- CHI-square test in reciprocal space (using the specified standard deviations. If they are correct, should be slightly less than 1 (ideal value is taken as 0.7). Increases with ALPHA. OSCILL --- shows the smoothness of the solution. Evaluated as the ratio ||dp/dr|| / ||p|| related to this ratio for a monomodal sine function. Decreases with ALPHA. Ideal value 1.1 (for a characteristic function of a uniform sphere). Here || || denotes the function norm. STABIL --- shows stability of the solution with respect to the change of ALPHA. Calculated as d(ln||p||)/d(ln(ALPHA)) Ideal value 0. SYSDEV --- indicates the presence of systematic deviations of the restored (smeared) curve Ires(s) from the experimetnal data Iexp(s). Calculated as N1 / (N/2), where N is the number of experimental points, N1 - number of changing sign of the difference (Iexp - Ires). Ideal value 1. Important parameter (unless you suspect your data contain systematic deviations). Increases with ALPHA. POSITV --- relative norm of positive part of p(r). Ideal value, of course, 1. VALCEN --- indicates validity of the chosen interval in real space (relative norm of the central part of p(r) ). Ideal value tends to 1 (0.95 for a sphere). Much less than 1 if your interval is too wide. The user is asked to enter the ALPHA value. If this value is already known to the user (e.g., from previous calculations with similar data), he can type the negative ALPHA, then the solution with -(ALPHA) will be evaluated. A positive ALPHA means automatic search of ALPHA by maximizing the total estimate as described below; no further manual refinement is possible (this is convenient for using GNOM in the batch mode). Default case (ALPHA=0) means automatic search accompanied by a graphic representation (plot lg(ALPHA) vs TOTAL). This plot would help the user to correct ALPHA manually in the cases when the automatic search breaks down (see Practical advises). The search of ALPHA works as follows. First the program finds the theoretical maximum (Highest) ALPHA value for the given problem  (in graphic representation the Y-axis is drawn through this value). Then it tries to maximze the total estimate with the given set of A(i), SIGMA(i) and W(i). The default set is Parameter DISCRP OSCILL STABIL SYSDEV POSITV VALCEN Weight 1.000 3.000 3.000 3.000 1.000 1.000 Sigma .300 .600 .120 .120 .120 .120 Ideal .700 1.100 .000 1.000 1.000 .950 (here parameters OSCILL, STABIL and SYSDEV are considered to be most important). The program evaluates first the grid of the TOTAL values for ALPHA < 1000*Highest ALPHA (indicated as open circles in the plot). Then the golden section search is performed to maximize the estimate (characters '+' on the plot). NOTE: when OSCILL is too large while SYSDEV already reasonable (here: OSCILL>13, SYSDEV>0.5), the value of TOTAL is put to zero. If zero value is encountered, the program stops evaluating the grid. This is made in order to avoid useless computations for too small ALPHA values. After the solution is found, the user may either accept it, or change the weight/width of distribution for any criterion, or try to get a new maximum estimate, or change the ALPHA manually. When you increase the distribution width for a given parameter, larger deviations from the expected values are allowed for this parameter. When you increase the weight of a parameter, it plays a more significaht role in the estimate, therefore the solution maximizing the estimate will be shifted to fulfil the corresponding criterion. The changed set of parameters can be stored onto an ASCII disk file and then used again for a similar object by entering its name when prompted 'File containing expert parameters' (parameter EXPERT). In this file user may also edit all the values (including "ideal" estimations). The solution can also be plotted on the screen. The intensity plot presents together the experimental data (astericks), the desmeared (solid) curve and the corresponding smeared (dotted) curve. Note that for the cases JOB = 3, 4 and 5 the experimental curves are modified. Namely, for JOB=3, I(s) is multiplied by s**2, for JOB=4 by s, for JOB=5 divided by (2*J1(s*RAD56)/s*RAD56)**2 (the latter is the cross-section factor of a cylinder, J1(x) Bessel function of the 1-st order). These modified curves are are plotted and printed onto the output file. The distribution plot shows the obtained correlation or size distribution function. Radius of gyration and zero angle intensity are also evaluated in real space using the p(r) function. Note that for the case JOB=2 the values in real and reciprocal space may not coincide, because I(0) will be evaluated as the NDIM-th moment of D(R), and Rg as sqrt((NDIM+2)th moment)/2I(0)) Error estimates ================= After the soluton is accepted by the user, the errors propagation can be estimated. This is made via a series of Monte-Carlo simulations. The standard deviations in the p(r) function as well as in the radius of gyration and zero-angle intensity are evaluated. The random sequence is initiated by the four-digit value of current time (min:sec), so that slightly different values of error estimates are obtained on exactly the same data set (the number of Monte-Carlo generations is 100). Note: the Monte-Carlo routines were rewritten for the versions E3.3 and then 4.1 therefore some differences may also exist between the results of different versions. Graphics ========== Graphic routines in the program use GKS or GHOST-80 (VMS or UNIX versions), MS-Fortran 5.1 graphic package (MS-DOS version). The possibility to use the public domain Gnuplot package also exists for UNIX version. --- GKS graphics --- If you use DEC GKS assign your used workstation to the logical GKS$CONID and the workstation type to GKS$WSTYPE. (See HELP GKS) If you want to use GNOM with other than DEC GKS implementation you have to specify some or all of the elements of an configuration matrix stored in a configuration file. The users of a GKS implementation are free to chose LUNs, CONIDs, and WSTYPEs. Some implementations make a difference between the LUN of a FORTRAN open statement and the CONID of a GKS open workstation statement. Empty matrix elements are not used. LUN - logical unit number CONID - connection identifier WSTYPE - workstation type | LUN | CONID | WSTYPE ------------------------+----------+----------+--------- Error log file | cfg(1,1) | | ------------------------+----------+----------+--------- Workstation independent | | | segment storage | | cfg(2,2) | cfg(3,2) ------------------------+----------+----------+--------- Used workstation | | cfg(2,3) | cfg(3,3) ------------------------+----------+----------+--------- GKS metafile output | | | workstation | cfg(1,4) | cfg(2,4) | cfg(3,4) ------------------------+----------+----------+--------- TEKTRONIX 4010/4014 | | | workstation | | | cfg(3,5) ------------------------+----------+----------+--------- Example for GTS-GRAL GKS on VXDSY.DESY.DE (VT220 with TEKTRONIX emulation). | LUN | CONID | WSTYPE ------------------------+----------+----------+--------- Error log file | 6 *) | 0 | 0 ------------------------+----------+----------+--------- Workstation independend | | | segment storage | 0 | 0 | 3 ------------------------+----------+----------+--------- Used workstation | 0 | 6 *) | -101 **) ------------------------+----------+----------+--------- GKS metafile output | | | workstation | 100 | 100 | 4 ------------------------+----------+----------+--------- TEKTRONIX 4010/4014 | | | workstation | 0 | 0 | 101 ------------------------+----------+----------+--------- *) standard FORTRAN output unit **) or assign -101 to logical GKS$WSTYPE. If you use a TEKTRONIX terminal with VT220 compatible mode or vice versa the program switches automatically between both modes by specifying the minus sign. Assign the configuration file specification to the logical GO_CONFIGURATION. Separate the fifteen integers in this file at least by one blank. For example, the GTS-GRAL GO_CONFIGURATION file is: 6 0 0 0 0 3 0 6 -101 100 100 4 0 0 101 Optionally, the plots can be saved in the device-independent form and then reproduced on other terminal or device. To this end, user should enter a non-blank file name when prompted "Metafile name [none]:". This metafile has the default extension .GKSM and can afterwards be processed by the dialogue GKSM interpreter (file GMI.EXE), which either shows the metafile on the screen, or prepares device-dependent file with extension .LIS to be printed on an output device (line printer, laser printer, plotter). If you use the GKS metafile interpreter with a DEC GKS implementation assign .FALSE. to the logical GMI_CONFIGURATION otherwise .TRUE. The low-level graphic calls to GKS and the GKSM-interpreter are written by O.Kuehnholz (GKSS Research Center, Geesthacht, Germany). --- GHOST-80 graphics --- It uses the pure Tektronix emulation (linked with T4010 and GRIDPLUS). The output to the grid file is similar the metafile output for GKS. The default extenstion for the grid file is .GRD. --- MS-Fortran graphics --- CGA, EGA, VGA, Olivetti and Hercules adapters are suppotred (for the latter case, one should first run the file MSHERC.COM ). The font file COURB.FON from the MS-Fortran distribution package is assumed to be either in the working directory, or in the c:\, or in c:\fortran\lib\ directory. If the file is not found, no text will appear in graphic mode. The build-in PrintScreen facility does NOT require preliminary loading of the DOS GRAPHICS. It supports 9-pin and 24-pin Epson-compatible dot matrix printers, as well as any HP-compatible printer recognizing HP PCL commands (HP Laser Jet, Desk Jet, etc ). The use of the dump screen routines is regulated by the parameter PRINTER (valid printers are EPSON09, EPSON24 and HPPCL). If your printer is NOT compatible with either Epson or HP, use standard DOS PrintScreen (then GRAPHICS is necessary). Note: after PrintScreen, no command "Eject" is send. The page is to be ejected manually. This allows in some cases, e.g. when printing with HP printers on DIN A4 paper, to have two plots on one page. --- Gnuplot graphics (UNIX version) --- On UNIX machines, a possibility exists to use the public domain Gnuplot graphic package. It is used not as a separate interactive program, but as a graphic library. GNOM creates a sequence of data/command files in the /tmp directory which are then executed by Gnuplot. To use Gnuplot version of GNOM, the following is required: i) Gnuplot version 3.0 and higher must be installed and the gnuplot executables should be in the PATH variable. ii) Environment vagiable GNUTERM has to be defined according to the Gnuplot conventions. If GNUTERM is not defined, no graphic output is produced. iii) If the environment variable GNUPRINT is defined, GNOM captures each plot in the format of this printer onto a fixed disk file named /tmp/gnu-capture. This is made after the plot is viewed and CR is pressed. Note that this file will be OVERWRITTEN by the next screen capture, therefore, if the user wishes to have a hardcopy, the file has to be sent to the printer or renamed BEFORE pressing CR after viewing the NEXT plot. After GNOM finishes, the file /tmp/gnu-capture contains the LAST plot. Note also that the GNOM variable PRINTER is yet dummy in the UNIX version. If GNUPRINT is not defined, GNOM produces no screen captures. Examples: Specify %setenv GNUTERM x11 %setenv GNUPRINT postscript if you run GNOM in a X-window environment and want an output for the postscript printer. Specify %setenv GNUTERM vttek %setenv GNUPRINT hpljii if you run GNOM on a VT-Tektronix emulation and want an output for the HP-Laserjet series II. For a detailed description of the supported terminals and printers, type 'set term' inside Gnuplot. Next job ======== After the job is finished, the user is asked whether to run the program again (parameter NEXTJOB). Answering "No" stops the program. "Yes" means new job. "Same" means that the new data set will be calculated under the same conditions as the previous one (with the same integral kernel). On-line help ============ Answering a question mark '?' followed by 'Enter' to each question allows to get a short help on the parameter. Configuration file ================== Some or all of the parameters used by the program can be specified in the configuration file named 'gnom.cfg'. The first line of the file is always treated as a comment. The structure of a valid information line is shown below: 1-7 9 Between brackets Comment NAME Type Value PRINTER C [ HPPCL ] Printer type Here NAME is the name of the parameter (all names are fixed), the letter in the 9-th column shows the type of the parameter: (C - character, I - integer, R - real). The value of the parameter is to be put between the square brackets (not more than 35 characters). If the line is not valid (e.g., ] is missing, or the parameter name is wrong), it is skipped and the warning is printed. When GNOM is started, it first tries to find and read the configuration file in the current directory. If the local file named 'gnom.cfg' does not exist, it tries to read the global configuration file : On IBM-PC, it is always the file 'c:\gnom\gnom.cfg' On VAX, it is 'GNOCFG:gnom.cfg', where the logical GNOCFG defines the directory. Example: if the command $DEFINE GNOCFG SYS$LOGIN is issued, the global file will be searched in the user's login directory. On UNIX machines, it is 'GNOCFGgnom.cfg', where GNOCFG is an environment variable. Example: if the command %setenv GNOCFG /usr/local/include/ is given , the global configuration file is '/usr/local/include/gnom.cfg' If GNOM finds a non-blank value between the square brackets for a parameter in the configuration file, this parameter is assumed to be already defined, therefore, it will NOT be prompted interactively (the other parameters will be asked as usual). The read-in configuration table is printed on the screen ( ... means that the variable is not defined). The user can either accept the values or switch to the interactive mode. GNOM assumes the interactive mode also when neither local nor global configuration file has been found. Specific values for some parameters : Zero values of the parameters NREAL and COEF mean that the values evaluated by the program will be accepted. For the EXPERT and INPUT2, 'none' means NO file. As UNIX is case-sensitive, be careful with the file names in the configuration file for the UNIX version. For IDET=2, if FWHM1/FWHM2 are equal to zero, GNOM will try to find the wavelength distribution function after the beam profile in the corresponding SPOT1/SPOT2 file. The example of the global configuration file is shown below. In this file only a few variables are fixed, and the program will not ask for them. More specific configuration files can be put in the local working directories. They can be configured in such a way, that the program will ask only a few questions or even run in the batch mode. Examples of the local configuration files can be found in the distribution package. General configuration file PRINTER C [ HPPCL ] Printer type FORFAC C [ ] Form factor file (valid for JOB=2) EXPERT C [ none ] File containing expert parameters INPUT1 C [ ] Input file name (first file) INPUT2 C [ ] Input file name (second file) OUTPUT C [ ] Output file PLOINP C [ y ] Plotting flag: input data (Y/N) PLORES C [ y ] Plotting flag: results (Y/N) EVAERR C [ ] Error flags: calculate errors (Y/N) PLOERR C [ y ] Plotting flag: p(r) with errors (Y/N) LKERN C [ ] Kernel file status (Y/N) JOBTYP I [ ] Type of system (0/1/2/3/4/5/6) RMIN R [ ] Rmin for evaluating p(r) RMAX R [ ] Rmax for evaluating p(r) LZRMIN C [ ] Zero condition at r=rmin (Y/N) LZRMAX C [ ] Zero condition at r=rmax (Y/N) KERNEL C [ ] Kernel-storage file DEVIAT R [ 0.0 ] Default input errors level IDET I [ ] Experimental set up (0/1/2) FWHM1 R [ ] FWHM for 1st run FWHM2 R [ ] FWHM for 2nd run AH1 R [ ] Slit-height parameter AH (first run) LH1 R [ ] Slit-height parameter LH (first run) AW1 R [ ] Slit-width parameter AW (first run) LW1 R [ ] Slit-width parameter LW (first run) AH2 R [ ] Slit-height parameter AH (second run) LH2 R [ ] Slit-height parameter LH (second run) AW2 R [ ] Slit-width parameter AW (second run) LW2 R [ ] Slit-width parameter LW (second run) SPOT1 C [ ] Beam profile file (first run) SPOT2 C [ ] Beam profile file (second run) ALPHA R [ 0.0 ] Initial ALPHA NREAL R [ 0 ] Number of points in real space COEF R [ ] RAD56 R [ ] Radius/thickness (valid for JOB=5,6) NEXTJOB C [ ] The configuration file may contain arbitrary number of parameters. Not all of them have to appear in the file: the missing parameters will be treated as non-defined. It is advisable, however, to end the configuration file with the NEXTJOB parameter. If NEXTJOB is 'Y' or 'S', the next lines will describe the parameters for the new job, and so on. The last line in this case should be: NEXTJOB C [ N ] Ends the program If you run the NEXTJOB, GNOM keeps the values which were used in the previous job as program defaults (for character variables it is true if the number of characters does not exceed 12). Example: using the general configuration file shown above, the default output file will be 'gnom.out' (program default); if you enter another name, say,'mygnom.out' and then answer "Y" to the NEXTJOB question, default output file will be 'mygnom.out'. Practical advises ================= This chapter has arisen as a result of practical applications of GNOM and is based mainly on the typical user questions. GNOM is intended to be as user-friendly as possible, that is, it normally runs OK using the default answers. In particular, default value of the number of real space points is highly recommended to use. The units in real and reciprocal space must be reciprocal to each other. Thus, if the momentum transfer is given in reciprocal angstroms (lambda in angstroms), the particle sizes in real space are to be specified also in angstroms. If you want particle sizes in miles, the input file has to contain momentum transfer in reciprocal miles. The units of the parameters describing beam divergency should be the same as for the momentum transfer. All the weighting functions are normalized so that the desmeared curve is on the same scale as the smeared one. In parcitular, as the wavelength effects are always relative, the wavelength distribution gets reduced to Lambda=1. This does not mean that the program works only for this wavelength, because the wavelength information is already contained in the s-units. One more thing about the wavelength effects: in X-ray experiments with the conventional sources (X-ray tubes) they are normally negligible. The rectangular slit geometry assumed for the 1D-detectors is normally a good approximation for practical applications. It is valid, of course, both for linear multi-channel detectors and single channel moving detectors. Note that the slit-height function, if non-symmetric, can be symmetriezed, because of the properties of the slit-smearing integral. Asymmetries in the slit-width function, if exist, can be neglected, as the slit-width effects are normally small. The case of "infinitely long slit" can be covered, e.g., by putting AH=Smax, LH=0, where Smax is the momentum transfer of the last data point. For a more detailed description of the smearing effects see, e.g. Ref, Ch.9. If you specify the maximum size so that Dmax*Smin (Smin the momentum transfer of the first data point) is greater than Pi=3.1416926, a warning is printed. This means that the first data point is beyond the first sampling point and the information content may be not sufficient to obtain a reliable solution. However, the warning does not hinder the progran continuation. Default settings of the Expert parameters are also valid for the most of "normal" systems. However, in some cases it is advisable to change the default set in order to ensure reliable automatic search of ALPHA. Typical examples are: -- If you do not know standard deviations in the experimental data, put the weight of DISCRP to zero. -- If you suspect that your distribution function is non-monomodal, put the ideal value of OSCILL to M, where M is the number of modes. For example, if you expect to have a bimodal size distribution function (JOB=1), put OSCILL=2. -- If the distribution function can show negative peaks (say, X-ray scattering from lipoproteins in water, JOB=0), put the weight of POSITV to zero (and OSCILL is better to put to 2 or 3, as in previous example). The program may fail to evaluate the constant for the second run in the trivial case with no smearing because of poor stability of the design matrix in this case. The users are kindly asked to correct the value manually. The program explores the range (10**3 * Hightest ALPHA) > ALPHA > (10**(-18) * Highest ALPHA) to maximize the estimate. If the total estimate is monotonous in this range, the warning is printed. In such cases the user can perform manual search, or restart the maximization from the current point. Important: normally, the plausible range of ALPHAs is approximately 10E-6 * (Hihgest ALPHA). If the solution found by the program is by far not acceptable, this just means that the maximization procedure (golden section search in logarithmic ALPHA scale) is trapped by a local minimum. One can restart the maximization from an ALPHA in a "plausible" range. Another reason of getting a non-acceptable solution could be a non-consistency of the data and the assumptions. In this case the user will get the warning about AN1 and, normally, rather low value of the maximum estimate. By default, the program puts p(rmin)=0, p(rmax)=0. If these conditions are not applied, non-zero p(r)'s can exist at the ends of the real space interval. Sometimes by p(0) one can take a constant background into account (note that for JOB=3 p(0) is normally non-zero). If you do not know Dmax, it is better first not to fix p(rmax), because this value will help to judge whether the chosen interval is correct (if, for example, rmax is too small, p(r) is systematically higher than zero in the vicinity of rmax). Model calculations show that the evaluation of the size distribution function of cylinders (JOB=5) is a very ill-posed problem, because the scattering curves from long cylinders are rather flat and it is not so easy to distinguish between them in the scattering curve, as e.g. for polydisperse system of spheres. Therefore for JOB=5 it is very important to have good measurements in the beginning of the scattering curve where scattering from cylinders of different length differs significantly from each other. Hardware and software requirements ================================== --- IBM-PC --- MS-DOS version 2.1 and higher (DOS 5.0 is recommended). Minimum 468Kbytes RAM and 512KBytes free disk space. CGA, EGA, VGA, GVGA, ATT or Hercules graphic board. A 8087/287/387/487 mathematical co-processor. --- VAX-VMS --- GKS implemebtation level not less than 2b, or GHOST graphics with Tektronix emulation --- UNIX --- GKS implemebtation level not less than 2b, or GHOST graphics with Tektronix emulation, or Gnuplot public domain graphic package version 3.0 and higher. References ========== 0. Feigin L.A. & Svergun D.I. (1987). Structure Analysis by Small-Angle X-Ray and Neutron Scattering. NY: Plenum Press. 1. Glatter O. (1977). J.Appl.Cryst., 10, 415-421 2. Moore P.B. (1980). J.Appl.Cryst., 13, 168-175 3. Provencher S.W. (1982). Computer Phys.Commun., 27, 213-227, 229-242 4. Svergun D.I., Semenyuk A.V. (1987). Doklady AN SSSR, 297, 1373-1377 (in Russian) 5. Svergun D.I., Semenyuk A.V., Feigin L.A. (1988). Acta Cryst., A44, 244-250 6. Svergun D.I. (1991). J.Appl.Cryst., 24, 485-492 7. Tikhonov A.N., Arsenin V.Ya. (1977). Solution of Ill-Posed Problems. NY: Wiley 8. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. (1983). Regularizing Algorithms and a priory Information. Moscow: Nauka, (in Russian) 9. Svergun D.I. (1992). J. Appl. Cryst., 25, 495-503.