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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2019-12-09 20:30:49 +0000 (Mon, 09 Dec 2019) $
5# $Author: toby $
6# $Revision: 4198 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 4198 2019-12-09 20:30:49Z toby $
9########### SVN repository information ###################
10
11'''
12*GSASIIobj: Data objects*
13=========================
14
15This module defines and/or documents the data structures used in GSAS-II, as well
16as provides misc. support routines.
17
18.. _Constraints_table:
19
20.. index::
21   single: Constraints object description
22   single: Data object descriptions; Constraints
23
24Constraints Tree Item
25----------------------
26
27Constraints are stored in a dict, separated into groups.
28Note that parameter are named in the following pattern,
29p:h:<var>:n, where p is the phase number, h is the histogram number
30<var> is a variable name and n is the parameter number.
31If a parameter does not depend on a histogram or phase or is unnumbered, that
32number is omitted.
33Note that the contents of each dict item is a List where each element in the
34list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
35The constraints in this form are converted in
36:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
37
38The keys in the Constraints dict are:
39
40.. tabularcolumns:: |l|p{4.5in}|
41
42==========  ====================================================
43  key         explanation
44==========  ====================================================
45Hist        This specifies a list of constraints on
46            histogram-related parameters,
47            which will be of form :h:<var>:n.
48HAP         This specifies a list of constraints on parameters
49            that are defined for every histogram in each phase
50            and are of form p:h:<var>:n.
51Phase       This specifies a list of constraints on phase
52            parameters,
53            which will be of form p::<var>:n.
54Global      This specifies a list of constraints on parameters
55            that are not tied to a histogram or phase and
56            are of form ::<var>:n
57==========  ====================================================
58
59.. _Constraint_definitions_table:
60
61.. index::
62   single: Constraint definition object description
63   single: Data object descriptions; Constraint Definition
64
65Each constraint is defined as an item in a list. Each constraint is of form::
66
67[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
68
69Where the variable pair list item containing two values [<mult>, <var>], where:
70
71  * <mult> is a multiplier for the constraint (float)
72  * <var> a :class:`G2VarObj` object (previously a str variable name of form
73      'p:h:name[:at]')
74
75Note that the last three items in the list play a special role:
76
77 * <fixedval> is the fixed value for a `constant equation` (``constype=c``)
78   constraint or is None. For a `New variable` (``constype=f``) constraint,
79   a variable name can be specified as a str (used for externally
80   generated constraints)
81 * <varyflag> is True or False for `New variable` (``constype=f``) constraints
82   or is None. This indicates if this variable should be refined.
83 * <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:
84
85    * 'e' defines a set of equivalent variables. Only the first variable is refined (if the
86      appropriate refine flag is set) and and all other equivalent variables in the list
87      are generated from that variable, using the appropriate multipliers.
88    * 'c' defines a constraint equation of form,
89      :math:`m_1 \\times var_1 + m_2 \\times var_2 + ... = c`
90    * 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
91      even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
92      constraint and the mult value is ignored.
93      This is of particular value when needing to hold one or more variables where a
94      single flag controls a set of variables such as, coordinates,
95      the reciprocal metric tensor or anisotropic displacement parameter.
96    * 'f' defines a new variable (function) according to relationship
97      :math:`newvar = m_1 \\times var_1 + m_2 \\times var_2 + ...`
98
99.. _Covariance_table:
100
101.. index::
102   single: Covariance description
103   single: Data object descriptions; Covariance
104
105Covariance Tree Item
106--------------------
107
108The Covariance tree item has results from the last least-squares run. They
109are stored in a dict with these keys:
110
111.. tabularcolumns:: |l|l|p{4in}|
112
113=============  ===============  ====================================================
114  key            sub-key        explanation
115=============  ===============  ====================================================
116newCellDict    \                dict with lattice parameters computed by
117                                :func:`GSASIIstrMath.GetNewCellParms` (dict)
118title          \                Name of gpx file(?) (str)
119variables      \                Values for all N refined variables
120                                (list of float values, length N,
121                                ordered to match varyList)
122sig            \                Uncertainty values for all N refined variables
123                                (list of float values, length N,
124                                ordered to match varyList)
125varyList       \                List of directly refined variables
126                                (list of str values, length N)
127newAtomDict    \                dict with atom position values computed in
128                                :func:`GSASIIstrMath.ApplyXYZshifts` (dict)
129Rvals          \                R-factors, GOF, Marquardt value for last
130                                refinement cycle (dict)
131\              Nobs             Number of observed data points (int)
132\              Rwp              overall weighted profile R-factor (%, float)
133\              chisq            sum[w*(Iobs-Icalc)**2] for all data
134                                note this is not the reduced chi squared (float)
135\              lamMax           Marquardt value applied to Hessian diagonal
136                                (float)
137\              GOF              The goodness-of-fit, aka square root of
138                                the reduced chi squared. (float)
139covMatrix      \                The (NxN) covVariance matrix (np.array)
140=============  ===============  ====================================================
141
142.. _Phase_table:
143
144.. index::
145   single: Phase object description
146   single: Data object descriptions; Phase
147
148Phase Tree Items
149----------------
150
151Phase information is stored in the GSAS-II data tree as children of the
152Phases item in a dict with keys:
153
154.. tabularcolumns:: |l|l|p{4in}|
155
156==========  ===============  ====================================================
157  key         sub-key        explanation
158==========  ===============  ====================================================
159General         \            Overall information for the phase (dict)
160  \         AtomPtrs         list of four locations to use to pull info
161                             from the atom records (list)
162  \         F000X            x-ray F(000) intensity (float)
163  \         F000N            neutron F(000) intensity (float)
164  \         Mydir            directory of current .gpx file (str)
165  \         MCSA controls    Monte Carlo-Simulated Annealing controls (dict)
166  \         Cell             List with 8 items: cell refinement flag (bool)
167                             a, b, c, (Angstrom, float)
168                             alpha, beta & gamma (degrees, float)
169                             volume (A^3, float)
170  \         Type             'nuclear' or 'macromolecular' for now (str)
171  \         Map              dict of map parameters
172  \         SH Texture       dict of spherical harmonic preferred orientation
173                             parameters
174  \         Isotope          dict of isotopes for each atom type
175  \         Isotopes         dict of scattering lengths for each isotope
176                             combination for each element in phase
177  \         Name             phase name (str)
178  \         SGData           Space group details as a :ref:`space group (SGData) object <SGData_table>`
179                             as defined in :func:`GSASIIspc.SpcGroup`.
180  \         Pawley neg wt    Restraint value for negative Pawley intensities
181                             (float)
182  \         Flip             dict of Charge flip controls
183  \         Data plot type   data plot type ('Mustrain', 'Size' or
184                             'Preferred orientation') for powder data (str)
185  \         Mass             Mass of unit cell contents in g/mol
186  \         POhkl            March-Dollase preferred orientation direction
187  \         Z                dict of atomic numbers for each atom type
188  \         vdWRadii         dict of van der Waals radii for each atom type
189  \         Color            Colors for atoms (list of (r,b,g) triplets)
190  \         AtomTypes        List of atom types
191  \         AtomMass         List of masses for atoms
192  \         doPawley         Flag for Pawley intensity extraction (bool)
193  \         NoAtoms          Number of atoms per unit cell of each type (dict)
194  \         Pawley dmin      maximum Q (as d-space) to use for Pawley
195                             extraction (float)
196  \         BondRadii        Default radius for each atom used to compute
197                             interatomic distances (list of floats)
198  \         AngleRadii       Default radius for each atom used to compute
199                             interatomic angles (list of floats)
200  \         DisAglCtls       Dict with distance/angle search controls,
201                             which has keys 'Name', 'AtomTypes',
202                             'BondRadii', 'AngleRadii' which are as above
203                             except are possibly edited. Also contains
204                             'Factors', which is a 2 element list with
205                             a multiplier for bond and angle search range
206                             [typically (0.85,0.85)].
207ranId           \            unique random number Id for phase (int)
208pId             \            Phase Id number for current project (int).
209Atoms           \            Atoms in phase as a list of lists. The outer list
210                             is for each atom, the inner list contains varying
211                             items depending on the type of phase, see
212                             the :ref:`Atom Records <Atoms_table>` description.
213                             (list of lists)
214Drawing         \            Display parameters (dict)
215\           ballScale        Size of spheres in ball-and-stick display (float)
216\           bondList         dict with bonds
217\           contourLevel     map contour level in e/A^3 (float)
218\           showABC          Flag to show view point triplet (bool). True=show.
219\           viewDir          cartesian viewing direction (np.array with three
220                             elements)
221\           Zclip            clipping distance in A (float)
222\           backColor        background for plot as and R,G,B triplet
223                             (default = [0, 0, 0], black).
224                             (list with three atoms)
225\           selectedAtoms    List of selected atoms (list of int values)
226\           showRigidBodies  Flag to highlight rigid body placement
227\           sizeH            Size ratio for H atoms (float)
228\           bondRadius       Size of binds in A (float)
229\           atomPtrs         positions of x, type, site sym, ADP flag in Draw Atoms (list)
230\           viewPoint        list of lists. First item in list is [x,y,z]
231                             in fractional coordinates for the center of
232                             the plot. Second item list of previous & current
233                             atom number viewed (may be [0,0])
234\           showHydrogen     Flag to control plotting of H atoms.
235\           unitCellBox      Flag to control display of the unit cell.
236\           ellipseProb      Probability limit for display of thermal
237                             ellipsoids in % (float).
238\           vdwScale         Multiplier of van der Waals radius for
239                             display of vdW spheres.
240\           Atoms            A list of lists with an entry for each atom
241                             that is plotted.
242\           Zstep            Step to de/increase Z-clip (float)
243\           Quaternion       Viewing quaternion (4 element np.array)
244\           radiusFactor     Distance ratio for searching for bonds. ? Bonds
245                             are located that are within r(Ra+Rb) and (Ra+Rb)/r
246                             where Ra and Rb are the atomic radii.
247\           oldxy            previous view point (list with two floats)
248\           cameraPos        Viewing position in A for plot (float)
249\           depthFog         True if use depthFog on plot - set currently as False (bool)
250RBModels        \            Rigid body assignments (note Rigid body definitions
251                             are stored in their own main top-level tree entry.)
252Pawley ref      \            Pawley reflections
253Histograms      \            A dict of dicts. The key for the outer dict is
254                             the histograms tied to this phase. The inner
255                             dict contains the combined phase/histogram
256                             parameters for items such as scale factors,
257                             size and strain parameters. The following are the
258                             keys to the inner dict. (dict)
259\           Babinet          For protein crystallography. Dictionary with two
260                             entries, 'BabA', 'BabU'
261\           Extinction       Extinction parameter (list of float, bool)
262\           HStrain          Hydrostatic strain. List of two lists. The first is
263                             a list of the HStrain parameters (1, 2, 3, 4, or 6
264                             depending on unit cell), the second is a list of boolean
265                             refinement parameters (same length)
266\           Histogram        The name of the associated histogram (str)
267\           LeBail           Flag for LeBail extraction (bool)
268\           Mustrain         List of microstrain parameters, in order:
269
270                               0. Type, one of u'generalized', u'isotropic',
271                                  u'uniaxial'
272                               1. Isotropic/uniaxial parameters - list of 3 floats
273                               2. Refinement flags - list of 3 bools
274                               3. Microstrain axis - list of 3 ints, [h, k, l]
275                               4. Generalized mustrain parameters - list of 2-6
276                                  floats, depending on space group
277                               5. Generalized refinement flags - list of bools,
278                                  corresponding to the parameters of (4)
279\           Pref.Ori.        Preferred Orientation. List of eight parameters.
280                             Items marked SH are only used for Spherical Harmonics.
281
282                               0. Type, 'MD' for March-Dollase or 'SH' for
283                                  Spherical Harmonics
284                               1. Value, float
285                               2. Refinement flag, bool
286                               3. Preferred direction, list of ints, [h, k, l]
287                               4. SH - number of terms, int
288                               5. SH - dict
289                               6. SH - list
290                               7. SH - float
291\           Scale            Phase fraction, list of [float, bool].
292\           Show             bool
293\           Use              bool
294\           newLeBail        Whether to perform a new LeBail extraction
295MCSA            \            Monte-Carlo simulated annealing parameters (dict)
296\
297==========  ===============  ====================================================
298
299.. _RBData_table:
300
301.. index::
302   single: Rigid Body Data description
303   single: Data object descriptions; Rigid Body Data
304
305Rigid Body Objects
306------------------
307
308Rigid body descriptions are available for two types of rigid bodies: 'Vector'
309and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
310with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
311with defined refinable torsion angles.
312
313.. tabularcolumns:: |l|l|p{4in}|
314
315==========  ===============  ====================================================
316  key         sub-key        explanation
317==========  ===============  ====================================================
318Vector      RBId             vector rigid bodies (dict of dict)
319\           AtInfo           Drad, Color: atom drawing radius & color for each atom type (dict)
320\           RBname           Name assigned by user to rigid body (str)
321\           VectMag          vector magnitudes in A (list)
322\           rbXYZ            Cartesian coordinates for Vector rigid body (list of 3 float)
323\           rbRef            3 assigned reference atom nos. in rigid body for origin
324                             definition, use center of atoms flag (list of 3 int & 1 bool)
325\           VectRef          refinement flags for VectMag values (list of bool)
326\           rbTypes          Atom types for each atom in rigid body (list of str)
327\           rbVect           Cartesian vectors for each translation used to build rigid body (list of lists)
328\           useCount         Number of times rigid body is used in any structure (int)
329Residue     RBId             residue rigid bodies (dict of dict)
330\           AtInfo           Drad, Color: atom drawing radius & color for each atom type(dict)
331\           RBname           Name assigned by user to rigid body (str)
332\           rbXYZ            Cartesian coordinates for Residue rigid body (list of 3 float)
333\           rbTypes          Atom types for each atom in rigid body (list of str)
334\           atNames          Names of each atom in rigid body (e.g. C1,N2...) (list of str)
335\           rbRef            3 assigned reference atom nos. in rigid body for origin
336                             definition, use center of atoms flag (list of 3 int & 1 bool)
337\           rbSeq            Orig,Piv,angle,Riding (list): definition of internal rigid body
338                             torsion; origin atom (int), pivot atom (int), torsion angle (float),
339                             riding atoms (list of int)
340\           SelSeq           [int,int] used by SeqSizer to identify objects
341\           useCount         Number of times rigid body is used in any structure (int)
342RBIds           \            unique Ids generated upon creation of each rigid body (dict)
343\           Vector           Ids for each Vector rigid body (list)
344\           Residue          Ids for each Residue rigid body (list)
345==========  ===============  ====================================================
346
347.. _SGData_table:
348
349.. index::
350   single: Space Group Data description
351   single: Data object descriptions; Space Group Data
352
353Space Group Objects
354-------------------
355
356Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
357and the information is placed in a SGdata object
358which is a dict with these keys:
359
360.. tabularcolumns:: |l|p{4.5in}|
361
362==========  ====================================================
363  key         explanation
364==========  ====================================================
365SpGrp       space group symbol (str)
366Laue        one of the following 14 Laue classes:
367            -1, 2/m, mmm, 4/m, 4/mmm, 3R,
368            3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m (str)
369SGInv       True if centrosymmetric, False if not (bool)
370SGLatt      Lattice centering type. Will be one of
371            P, A, B, C, I, F, R (str)
372SGUniq      unique axis if monoclinic. Will be
373            a, b, or c for monoclinic space groups.
374            Will be blank for non-monoclinic. (str)
375SGCen       Symmetry cell centering vectors. A (n,3) np.array
376            of centers. Will always have at least one row:
377            ``np.array([[0, 0, 0]])``
378SGOps       symmetry operations as a list of form
379            ``[[M1,T1], [M2,T2],...]``
380            where :math:`M_n` is a 3x3 np.array
381            and :math:`T_n` is a length 3 np.array.
382            Atom coordinates are transformed where the
383            Asymmetric unit coordinates [X is (x,y,z)]
384            are transformed using
385            :math:`X^\prime = M_n*X+T_n`
386SGSys       symmetry unit cell: type one of
387            'triclinic', 'monoclinic', 'orthorhombic',
388            'tetragonal', 'rhombohedral', 'trigonal',
389            'hexagonal', 'cubic' (str)
390SGPolax     Axes for space group polarity. Will be one of
391            '', 'x', 'y', 'x y', 'z', 'x z', 'y z',
392            'xyz'. In the case where axes are arbitrary
393            '111' is used (P 1, and ?).
394==========  ====================================================
395
396.. _SSGData_table:
397
398.. index::
399   single: Superspace Group Data description
400   single: Data object descriptions; Superspace Group Data
401
402Superspace groups [3+1] are interpreted by :func:`GSASIIspc.SSpcGroup`
403and the information is placed in a SSGdata object
404which is a dict with these keys:
405
406.. tabularcolumns:: |l|p{4.5in}|
407
408==========  ====================================================
409  key         explanation
410==========  ====================================================
411SSpGrp      superspace group symbol extension to space group
412            symbol, accidental spaces removed
413SSGCen      4D cell centering vectors [0,0,0,0] at least
414SSGOps      4D symmetry operations as [M,T] so that M*x+T = x'
415==========  ====================================================
416
417
418.. _Atoms_table:
419
420.. index::
421   single: Atoms record description
422   single: Data object descriptions; Atoms record
423
424Atom Records
425------------
426
427If ``phasedict`` points to the phase information in the data tree, then
428atoms are contained in a list of atom records (list) in
429``phasedict['Atoms']``. Also needed to read atom information
430are four pointers, ``cx,ct,cs,cia = phasedict['General']['AtomPtrs']``,
431which define locations in the atom record, as shown below. Items shown are
432always present; additional ones for macromolecular phases are marked 'mm'
433
434.. tabularcolumns:: |l|p{4.5in}|
435
436==============   ====================================================
437location         explanation
438==============   ====================================================
439ct-4              mm - residue number (str)
440ct-3              mm - residue name (e.g. ALA) (str)
441ct-2              mm - chain label (str)
442ct-1              atom label (str)
443ct                atom type (str)
444ct+1              refinement flags; combination of 'F', 'X', 'U' (str)
445cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
446cx+3              site occupancy (float)
447cs                site symmetry (str)
448cs+1              site multiplicity (int)
449cia               ADP flag: Isotropic ('I') or Anisotropic ('A')
450cia+1             Uiso (float)
451cia+2...cia+7     U11, U22, U33, U12, U13, U23 (6 floats)
452atom[cia+8]       unique atom identifier (int)
453
454==============   ====================================================
455
456.. _Drawing_atoms_table:
457
458.. index::
459   single: Drawing atoms record description
460   single: Data object descriptions; Drawing atoms record
461
462Drawing Atom Records
463--------------------
464
465If ``phasedict`` points to the phase information in the data tree, then
466drawing atoms are contained in a list of drawing atom records (list) in
467``phasedict['Drawing']['Atoms']``. Also needed to read atom information
468are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
469which define locations in the atom record, as shown below. Items shown are
470always present; additional ones for macromolecular phases are marked 'mm'
471
472.. tabularcolumns:: |l|p{4.5in}|
473
474==============   ====================================================
475location         explanation
476==============   ====================================================
477ct-4              mm - residue number (str)
478ct-3              mm - residue name (e.g. ALA) (str)
479ct-2              mm - chain label (str)
480ct-1              atom label (str)
481ct                atom type (str)
482cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
483cs-1              Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
484cs                atom drawing style; e.g. 'balls & sticks' (str)
485cs+1              atom label style (e.g. 'name') (str)
486cs+2              atom color (RBG triplet) (int)
487cs+3              ADP flag: Isotropic ('I') or Anisotropic ('A')
488cs+4              Uiso (float)
489cs+5...cs+11      U11, U22, U33, U12, U13, U23 (6 floats)
490ci                unique atom identifier; matches source atom Id in Atom Records (int)
491==============   ====================================================
492
493.. _Powder_table:
494
495.. index::
496   single: Powder data object description
497   single: Data object descriptions; Powder Data
498
499Powder Diffraction Tree Items
500-----------------------------
501
502Every powder diffraction histogram is stored in the GSAS-II data tree
503with a top-level entry named beginning with the string "PWDR ". The
504diffraction data for that information are directly associated with
505that tree item and there are a series of children to that item. The
506routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
507and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
508load this information into a dictionary where the child tree name is
509used as a key, and the information in the main entry is assigned
510a key of ``Data``, as outlined below.
511
512.. tabularcolumns:: |p{1in}|p{1in}|p{4in}|
513
514======================  ===============  ====================================================
515  key                      sub-key        explanation
516======================  ===============  ====================================================
517Comments                      \           Text strings extracted from the original powder
518                                          data header. These cannot be changed by the user;
519                                          it may be empty.
520Limits                       \            A list of two two element lists, as [[Ld,Hd],[L,H]]
521                                          where L and Ld are the current and default lowest
522                                          two-theta value to be used and
523                                          where H and Hd are the current and default highest
524                                          two-theta value to be used.
525Reflection Lists              \           A dict with an entry for each phase in the
526                                          histogram. The contents of each dict item
527                                          is a dict containing reflections, as described in
528                                          the :ref:`Powder Reflections <PowderRefl_table>`
529                                          description.
530Instrument Parameters         \           A list containing two dicts where the possible
531                                          keys in each dict are listed below. The value
532                                          for each item is a list containing three values:
533                                          the initial value, the current value and a
534                                          refinement flag which can have a value of
535                                          True, False or 0 where 0 indicates a value that
536                                          cannot be refined. The first and second
537                                          values are floats unless otherwise noted.
538                                          Items in the first dict are noted as [1]
539\                         Lam             Specifies a wavelength in Angstroms [1]
540\                         Lam1            Specifies the primary wavelength in
541                                          Angstrom, when an alpha1, alpha2
542                                          source is used [1]
543\                         Lam2            Specifies the secondary wavelength in
544                                          Angstrom, when an alpha1, alpha2
545                                          source is used [1]
546                          I(L2)/I(L1)     Ratio of Lam2 to Lam1 [1]
547\                         Type            Histogram type (str) [1]:
548                                           * 'PXC' for constant wavelength x-ray
549                                           * 'PNC' for constant wavelength neutron
550                                           * 'PNT' for time of flight neutron
551\                         Zero            Two-theta zero correction in *degrees* [1]
552\                         Azimuth         Azimuthal setting angle for data recorded
553                                          with differing setting angles [1]
554\                         U, V, W         Cagliotti profile coefficients
555                                          for Gaussian instrumental broadening, where the
556                                          FWHM goes as
557                                          :math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
558\                         X, Y            Cauchy (Lorentzian) instrumental broadening
559                                          coefficients [1]
560\                         SH/L            Variant of the Finger-Cox-Jephcoat asymmetric
561                                          peak broadening ratio. Note that this is the
562                                          average between S/L and H/L where S is
563                                          sample height, H is the slit height and
564                                          L is the goniometer diameter. [1]
565\                         Polariz.        Polarization coefficient. [1]
566wtFactor                      \           A weighting factor to increase or decrease
567                                          the leverage of data in the histogram (float).
568                                          A value of 1.0 weights the data with their
569                                          standard uncertainties and a larger value
570                                          increases the weighting of the data (equivalent
571                                          to decreasing the uncertainties).
572Sample Parameters             \           Specifies a dict with parameters that describe how
573                                          the data were collected, as listed
574                                          below. Refinable parameters are a list containing
575                                          a float and a bool, where the second value
576                                          specifies if the value is refined, otherwise
577                                          the value is a float unless otherwise noted.
578\                         Scale           The histogram scale factor (refinable)
579\                         Absorption      The sample absorption coefficient as
580                                          :math:`\\mu r` where r is the radius
581                                          (refinable). Only valid for Debye-Scherrer geometry.
582\                         SurfaceRoughA   Surface roughness parameter A as defined by
583                                          Surotti,J. Appl. Cryst, 5,325-331, 1972.(refinable -
584                                          only valid for Bragg-Brentano geometry)
585\                         SurfaceRoughB   Surface roughness parameter B (refinable -
586                                          only valid for Bragg-Brentano geometry)
587\                         DisplaceX,      Sample displacement from goniometer center
588                          DisplaceY       where Y is along the beam direction and
589                                          X is perpendicular. Units are :math:`\\mu m`
590                                          (refinable).
591\                         Phi, Chi,       Goniometer sample setting angles, in degrees.
592                          Omega
593\                         Gonio. radius   Radius of the diffractometer in mm
594\                         InstrName       A name for the instrument, used in preparing
595                                          a CIF (str).
596\                         Force,          Variables that describe how the measurement
597                          Temperature,    was performed. Not used directly in
598                          Humidity,       any computations.
599                          Pressure,
600                          Voltage
601\                         ranId           The random-number Id for the histogram
602                                          (same value as where top-level key is ranId)
603\                         Type            Type of diffraction data, may be 'Debye-Scherrer'
604                                          or 'Bragg-Brentano' (str).
605\                         Diffuse         not in use?
606hId                           \           The number assigned to the histogram when
607                                          the project is loaded or edited (can change)
608ranId                         \           A random number id for the histogram
609                                          that does not change
610Background                    \           The background is stored as a list with where
611                                          the first item in the list is list and the second
612                                          item is a dict. The list contains the background
613                                          function and its coefficients; the dict contains
614                                          Debye diffuse terms and background peaks.
615                                          (TODO: this needs to be expanded.)
616Data                          \           The data consist of a list of 6 np.arrays
617                                          containing in order:
618
619                                           0. the x-postions (two-theta in degrees),
620                                           1. the intensity values (Yobs),
621                                           2. the weights for each Yobs value
622                                           3. the computed intensity values (Ycalc)
623                                           4. the background values
624                                           5. Yobs-Ycalc
625======================  ===============  ====================================================
626
627.. _PowderRefl_table:
628
629.. index::
630   single: Powder reflection object description
631   single: Data object descriptions; Powder Reflections
632
633Powder Reflection Data Structure
634--------------------------------
635
636For every phase in a histogram, the ``Reflection Lists`` value is a dict
637one element of which is `'RefList'`, which is a np.array containing
638reflections. The columns in that array are documented below.
639
640==========  ====================================================
641  index         explanation
642==========  ====================================================
643 0,1,2       h,k,l (float)
644 3           multiplicity
645 4           d-space, Angstrom
646 5           pos, two-theta
647 6           sig, Gaussian width
648 7           gam, Lorenzian width
649 8           :math:`F_{obs}^2`
650 9           :math:`F_{calc}^2`
651 10          reflection phase, in degrees
652 11          intensity correction for reflection, this times
653             :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
654==========  ====================================================
655
656.. _Xtal_table:
657
658.. index::
659   single: Single Crystal data object description
660   single: Data object descriptions; Single crystal data
661
662Single Crystal Tree Items
663-------------------------
664
665Every single crystal diffraction histogram is stored in the GSAS-II data tree
666with a top-level entry named beginning with the string "HKLF ". The
667diffraction data for that information are directly associated with
668that tree item and there are a series of children to that item. The
669routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
670and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
671load this information into a dictionary where the child tree name is
672used as a key, and the information in the main entry is assigned
673a key of ``Data``, as outlined below.
674
675.. tabularcolumns:: |l|l|p{4in}|
676
677======================  ===============  ====================================================
678  key                      sub-key        explanation
679======================  ===============  ====================================================
680Data                          \           A dict that contains the
681                                          reflection table,
682                                          as described in the
683                                          :ref:`Single Crystal Reflections
684                                          <XtalRefl_table>`
685                                          description.
686
687Instrument Parameters         \           A list containing two dicts where the possible
688                                          keys in each dict are listed below. The value
689                                          for most items is a list containing two values:
690                                          the initial value, the current value.
691                                          The first and second
692                                          values are floats unless otherwise noted.
693\                         Lam             Specifies a wavelength in Angstroms (two floats)
694\                         Type            Histogram type (two str values):
695                                           * 'SXC' for constant wavelength x-ray
696                                           * 'SNC' for constant wavelength neutron
697                                           * 'SNT' for time of flight neutron
698\                         InstrName       A name for the instrument, used in preparing
699                                          a CIF (str).
700
701wtFactor                      \           A weighting factor to increase or decrease
702                                          the leverage of data in the histogram (float).
703                                          A value of 1.0 weights the data with their
704                                          standard uncertainties and a larger value
705                                          increases the weighting of the data (equivalent
706                                          to decreasing the uncertainties).
707
708hId                           \           The number assigned to the histogram when
709                                          the project is loaded or edited (can change)
710ranId                         \           A random number id for the histogram
711                                          that does not change
712======================  ===============  ====================================================
713
714.. _XtalRefl_table:
715
716.. index::
717   single: Single Crystal reflection object description
718   single: Data object descriptions; Single Crystal Reflections
719
720Single Crystal Reflection Data Structure
721----------------------------------------
722
723For every single crystal a histogram, the ``'Data'`` item contains
724the structure factors as an np.array in item `'RefList'`.
725The columns in that array are documented below.
726
727==========  ====================================================
728  index         explanation
729==========  ====================================================
730 0,1,2       h,k,l (float)
731 3           multiplicity
732 4           d-space, Angstrom
733 5           :math:`F_{obs}^2`
734 6           :math:`\sigma(F_{obs}^2)`
735 7           :math:`F_{calc}^2`
736 8           :math:`F_{obs}^2T`
737 9           :math:`F_{calc}^2T`
738 10          reflection phase, in degrees
739 11          intensity correction for reflection, this times
740             :math:`F_{obs}^2` or :math:`F_{calc}^2`
741             gives Iobs or Icalc
742==========  ====================================================
743
744.. _Image_table:
745
746.. index::
747   image: Image data object description
748   image: Image object descriptions
749
750Image Data Structure
751--------------------
752
753Every 2-dimensional image is stored in the GSAS-II data tree
754with a top-level entry named beginning with the string "IMG ". The
755image data are directly associated with that tree item and there
756are a series of children to that item. The routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
757and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
758load this information into a dictionary where the child tree name is
759used as a key, and the information in the main entry is assigned
760a key of ``Data``, as outlined below.
761
762.. tabularcolumns:: |l|l|p{4in}|
763
764======================  ======================  ====================================================
765  key                      sub-key              explanation
766======================  ======================  ====================================================
767Comments                       \                Text strings extracted from the original image data
768                                                header or a metafile. These cannot be changed by
769                                                the user; it may be empty.
770Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
771                                                value. Accomodates
772                                                detector orientations other than with the detector
773                                                X-axis
774                                                horizontal.
775\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
776                                                during image integration multiplied by value. It must have the same size/shape as
777                                                the integrated image. NB: value < 0 for subtraction.
778\                           calibrant           (str) The material used for determining the position/orientation
779                                                of the image. The data is obtained from :func:`ImageCalibrants`
780                                                and UserCalibrants.py (supplied by user).
781\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
782\                           calibskip           (int) The number of expected diffraction lines skipped during the last
783                                                calibration run.
784\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
785                                                strikes the detector plane as determined by calibration. This point
786                                                does not have to be within the limits of the detector boundaries.
787\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
788                                                of the image is at the center line otherwise it is at the leading edge.
789\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
790\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
791                                                calibration calculations. See pixLimit for details as how point is found.
792\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
793                                                ring offset at higher angles. Optionally determined by calibration.
794\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
795\                           distance            (float) The distance (mm) from sample to detector plane.
796\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
797                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
798                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
799                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
800                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
801\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
802\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
803\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
804                                                Required for texture calculations.
805\                           invert_x            (bool) If True display the image with the x-axis inverted.
806\                           invert_y            (bool) If True display the image with the y-axis inverted.
807\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
808\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
809\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
810                                                intensities obtained during integration.
811\                           outAzimuths         (int) The number of azimuth pie slices.
812\                           outChannels         (int) The number of 2-theta steps.
813\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
814\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
815                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
816                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
817                                                Locations are used to construct rings of points for calibration calcualtions.
818\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
819                                                integration using value.
820\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
821                                                diffraction ring with the same d-spacing (dsp)
822\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
823                                                selected by the user,
824\                           Range               (list) The minimum & maximum values of the image
825\                           rotation            (float) The angle between the x-axis and the vector about which the
826                                                detector is tilted. Constrained to -180 to 180 deg.
827\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
828                                                calculations.
829\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
830                                                to cause correction to be applied.
831\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
832\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.
833\                           showLines           (bool) If True then isplay the integration limits to be used.
834\                           size                (list:int) The number of pixels on the image x & y axes
835\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
836\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
837\                           wavelength          (float) Tha radiation wavelength (Angstroms) as entered by the user (or someday obtained from the image header).
838
839Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
840                                                to be excluded from integration
841\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
842                                                of which is excluded from recalibration and integration. Only one frame is allowed.
843\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
844                                                from integration.
845\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
846                                                to be excluded from integration.
847\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
848                                                to be excluded from integration.
849\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
850                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.
851
852Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
853\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
854                                                These will be restricted by space group symmetry; result of strain fit refinement.
855\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
856\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
857                                                and are used to determine the strain tensor.
858                                                The dictionary items are:
859                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
860                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
861                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
862                                                'Esig': (list: float) Esds for Emat from fitting.
863                                                'pixLimit': (int) Search range to find highest point on ring for each data point
864                                                'cutoff': (float) I/Ib cutoff for searching.
865                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
866                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
867                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
868
869======================  ======================  ====================================================
870
871.. _parmDict_table:
872
873.. index::
874   single: Parameter dictionary
875
876Parameter Dictionary
877-------------------------
878
879The parameter dictionary contains all of the variable parameters for the refinement.
880The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
881It is prepared in two ways. When loaded from the tree
882(in :meth:`GSASIIdataGUI.GSASII.MakeLSParmDict` and
883:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
884the values are lists with two elements: ``[value, refine flag]``
885
886When loaded from the GPX file (in
887:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
888dict is the actual parameter value (usually a float, but sometimes a
889letter or string flag value (such as I or A for iso/anisotropic).
890
891
892*Classes and routines*
893----------------------
894
895'''
896from __future__ import division, print_function
897import platform
898import re
899import imp
900import random as ran
901import sys
902import os.path as ospath
903if '2' in platform.python_version_tuple()[0]:
904    import cPickle
905else:
906    import pickle as cPickle
907import GSASIIpath
908import GSASIImath as G2mth
909import GSASIIspc as G2spc
910import numpy as np
911
912GSASIIpath.SetVersionNumber("$Revision: 4198 $")
913
914DefaultControls = {
915    'deriv type':'analytic Hessian',
916    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
917    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
918    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
919    'Author':'no name',
920    'FreePrm1':'Sample humidity (%)',
921    'FreePrm2':'Sample voltage (V)',
922    'FreePrm3':'Applied load (MN)',
923    'ShowCell':False,
924    }
925'''Values to be used as defaults for the initial contents of the ``Controls``
926data tree item.
927'''
928def StripUnicode(string,subs='.'):
929    '''Strip non-ASCII characters from strings
930
931    :param str string: string to strip Unicode characters from
932    :param str subs: character(s) to place into string in place of each
933      Unicode character. Defaults to '.'
934
935    :returns: a new string with only ASCII characters
936    '''
937    s = ''
938    for c in string:
939        if ord(c) < 128:
940            s += c
941        else:
942            s += subs
943    return s
944#    return s.encode('ascii','replace')
945
946def MakeUniqueLabel(lbl,labellist):
947    '''Make sure that every a label is unique against a list by adding
948    digits at the end until it is not found in list.
949
950    :param str lbl: the input label
951    :param list labellist: the labels that have already been encountered
952    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
953      ``_10-99``, etc.) appended at the end
954    '''
955    lbl = StripUnicode(lbl.strip(),'_')
956    if not lbl: # deal with a blank label
957        lbl = '_1'
958    if lbl not in labellist:
959        labellist.append(lbl)
960        return lbl
961    i = 1
962    prefix = lbl
963    if '_' in lbl:
964        prefix = lbl[:lbl.rfind('_')]
965        suffix = lbl[lbl.rfind('_')+1:]
966        try:
967            i = int(suffix)+1
968        except: # suffix could not be parsed
969            i = 1
970            prefix = lbl
971    while prefix+'_'+str(i) in labellist:
972        i += 1
973    else:
974        lbl = prefix+'_'+str(i)
975        labellist.append(lbl)
976    return lbl
977
978PhaseIdLookup = {}
979'''dict listing phase name and random Id keyed by sequential phase index as a str;
980best to access this using :func:`LookupPhaseName`
981'''
982PhaseRanIdLookup = {}
983'''dict listing phase sequential index keyed by phase random Id;
984best to access this using :func:`LookupPhaseId`
985'''
986HistIdLookup = {}
987'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
988best to access this using :func:`LookupHistName`
989'''
990HistRanIdLookup = {}
991'''dict listing histogram sequential index keyed by histogram random Id;
992best to access this using :func:`LookupHistId`
993'''
994AtomIdLookup = {}
995'''dict listing for each phase index as a str, the atom label and atom random Id,
996keyed by atom sequential index as a str;
997best to access this using :func:`LookupAtomLabel`
998'''
999AtomRanIdLookup = {}
1000'''dict listing for each phase the atom sequential index keyed by atom random Id;
1001best to access this using :func:`LookupAtomId`
1002'''
1003ShortPhaseNames = {}
1004'''a dict containing a possibly shortened and when non-unique numbered
1005version of the phase name. Keyed by the phase sequential index.
1006'''
1007ShortHistNames = {}
1008'''a dict containing a possibly shortened and when non-unique numbered
1009version of the histogram name. Keyed by the histogram sequential index.
1010'''
1011
1012#VarDesc = {}  # removed 1/30/19 BHT as no longer needed (I think)
1013#''' This dictionary lists descriptions for GSAS-II variables,
1014#as set in :func:`CompileVarDesc`. See that function for a description
1015#for how keys and values are written.
1016#'''
1017
1018reVarDesc = {}
1019''' This dictionary lists descriptions for GSAS-II variables where
1020keys are compiled regular expressions that will match the name portion
1021of a parameter name. Initialized in :func:`CompileVarDesc`.
1022'''
1023
1024reVarStep = {}
1025''' This dictionary lists the preferred step size for numerical
1026derivative computation w/r to a GSAS-II variable. Keys are compiled
1027regular expressions and values are the step size for that parameter.
1028Initialized in :func:`CompileVarDesc`.
1029'''
1030# create a default space group object for P1; N.B. fails when building documentation
1031try:
1032    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
1033except:
1034    pass
1035
1036def GetPhaseNames(fl):
1037    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
1038    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename
1039
1040    :param file fl: opened .gpx file
1041    :return: list of phase names
1042    '''
1043    PhaseNames = []
1044    while True:
1045        try:
1046            data = cPickle.load(fl)
1047        except EOFError:
1048            break
1049        datum = data[0]
1050        if 'Phases' == datum[0]:
1051            for datus in data[1:]:
1052                PhaseNames.append(datus[0])
1053    fl.seek(0)          #reposition file
1054    return PhaseNames
1055
1056def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
1057    '''Create a new phase dict with default values for various parameters
1058
1059    :param str Name: Name for new Phase
1060
1061    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
1062      defaults to data for P 1
1063
1064    :param list cell: unit cell parameter list; defaults to
1065      [1.0,1.0,1.0,90.,90,90.,1.]
1066
1067    '''
1068    if SGData is None: SGData = P1SGData
1069    if cell is None: cell=[1.0,1.0,1.0,90.,90.,90.,1.]
1070    phaseData = {
1071        'ranId':ran.randint(0,sys.maxsize),
1072        'General':{
1073            'Name':Name,
1074            'Type':'nuclear',
1075            'Modulated':False,
1076            'AtomPtrs':[3,1,7,9],
1077            'SGData':SGData,
1078            'Cell':[False,]+cell,
1079            'Pawley dmin':1.0,
1080            'Data plot type':'None',
1081            'SH Texture':{
1082                'Order':0,
1083                'Model':'cylindrical',
1084                'Sample omega':[False,0.0],
1085                'Sample chi':[False,0.0],
1086                'Sample phi':[False,0.0],
1087                'SH Coeff':[False,{}],
1088                'SHShow':False,
1089                'PFhkl':[0,0,1],
1090                'PFxyz':[0,0,1],
1091                'PlotType':'Pole figure',
1092                'Penalty':[['',],0.1,False,1.0]}},
1093        'Atoms':[],
1094        'Drawing':{},
1095        'Histograms':{},
1096        'Pawley ref':[],
1097        'RBModels':{},
1098        }
1099    if Super and Super.get('Use',False):
1100        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
1101        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
1102        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]
1103
1104    return phaseData
1105
1106def ReadCIF(URLorFile):
1107    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
1108    (from James Hester).
1109    The open routine gets confused with DOS names that begin with a letter and colon
1110    "C:\dir\" so this routine will try to open the passed name as a file and if that
1111    fails, try it as a URL
1112
1113    :param str URLorFile: string containing a URL or a file name. Code will try first
1114      to open it as a file and then as a URL.
1115
1116    :returns: a PyCifRW CIF object.
1117    '''
1118    import CifFile as cif # PyCifRW from James Hester
1119
1120    # alternate approach:
1121    #import urllib
1122    #ciffile = 'file:'+urllib.pathname2url(filename)
1123
1124    try:
1125        fp = open(URLorFile,'r')
1126        cf = cif.ReadCif(fp)
1127        fp.close()
1128        return cf
1129    except IOError:
1130        return cif.ReadCif(URLorFile)
1131
1132def IndexAllIds(Histograms,Phases):
1133    '''Scan through the used phases & histograms and create an index
1134    to the random numbers of phases, histograms and atoms. While doing this,
1135    confirm that assigned random numbers are unique -- just in case lightning
1136    strikes twice in the same place.
1137
1138    Note: this code assumes that the atom random Id (ranId) is the last
1139    element each atom record.
1140
1141    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
1142    (which loads the histograms and phases from a GPX file),
1143    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
1144    (which loads the histograms and phases from the data tree.) and
1145    :meth:`GSASIIconstrGUI.UpdateConstraints`
1146    (which displays & edits the constraints in a GUI)
1147
1148    TODO: do we need a lookup for rigid body variables?
1149    '''
1150    # process phases and atoms
1151    PhaseIdLookup.clear()
1152    PhaseRanIdLookup.clear()
1153    AtomIdLookup.clear()
1154    AtomRanIdLookup.clear()
1155    ShortPhaseNames.clear()
1156    for ph in Phases:
1157        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
1158        ranId = Phases[ph]['ranId']
1159        while ranId in PhaseRanIdLookup:
1160            # Found duplicate random Id! note and reassign
1161            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
1162            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1163        pId = str(Phases[ph]['pId'])
1164        PhaseIdLookup[pId] = (ph,ranId)
1165        PhaseRanIdLookup[ranId] = pId
1166        shortname = ph  #[:10]
1167        while shortname in ShortPhaseNames.values():
1168            shortname = ph[:8] + ' ('+ pId + ')'
1169        ShortPhaseNames[pId] = shortname
1170        AtomIdLookup[pId] = {}
1171        AtomRanIdLookup[pId] = {}
1172        for iatm,at in enumerate(Phases[ph]['Atoms']):
1173            ranId = at[cia+8]
1174            while ranId in AtomRanIdLookup[pId]: # check for dups
1175                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
1176                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
1177            AtomRanIdLookup[pId][ranId] = str(iatm)
1178            if Phases[ph]['General']['Type'] == 'macromolecular':
1179                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
1180            else:
1181                label = at[ct-1]
1182            AtomIdLookup[pId][str(iatm)] = (label,ranId)
1183    # process histograms
1184    HistIdLookup.clear()
1185    HistRanIdLookup.clear()
1186    ShortHistNames.clear()
1187    for hist in Histograms:
1188        ranId = Histograms[hist]['ranId']
1189        while ranId in HistRanIdLookup:
1190            # Found duplicate random Id! note and reassign
1191            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1192            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1193        hId = str(Histograms[hist]['hId'])
1194        HistIdLookup[hId] = (hist,ranId)
1195        HistRanIdLookup[ranId] = hId
1196        shortname = hist[:15]
1197        while shortname in ShortHistNames.values():
1198            shortname = hist[:11] + ' ('+ hId + ')'
1199        ShortHistNames[hId] = shortname
1200
1201def LookupAtomId(pId,ranId):
1202    '''Get the atom number from a phase and atom random Id
1203
1204    :param int/str pId: the sequential number of the phase
1205    :param int ranId: the random Id assigned to an atom
1206
1207    :returns: the index number of the atom (str)
1208    '''
1209    if not AtomRanIdLookup:
1210        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
1211    if pId is None or pId == '':
1212        raise KeyError('Error: phase is invalid (None or blank)')
1213    pId = str(pId)
1214    if pId not in AtomRanIdLookup:
1215        raise KeyError('Error: LookupAtomId does not have phase '+pId)
1216    if ranId not in AtomRanIdLookup[pId]:
1217        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
1218    return AtomRanIdLookup[pId][ranId]
1219
1220def LookupAtomLabel(pId,index):
1221    '''Get the atom label from a phase and atom index number
1222
1223    :param int/str pId: the sequential number of the phase
1224    :param int index: the index of the atom in the list of atoms
1225
1226    :returns: the label for the atom (str) and the random Id of the atom (int)
1227    '''
1228    if not AtomIdLookup:
1229        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
1230    if pId is None or pId == '':
1231        raise KeyError('Error: phase is invalid (None or blank)')
1232    pId = str(pId)
1233    if pId not in AtomIdLookup:
1234        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
1235    if index not in AtomIdLookup[pId]:
1236        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
1237    return AtomIdLookup[pId][index]
1238
1239def LookupPhaseId(ranId):
1240    '''Get the phase number and name from a phase random Id
1241
1242    :param int ranId: the random Id assigned to a phase
1243    :returns: the sequential Id (pId) number for the phase (str)
1244    '''
1245    if not PhaseRanIdLookup:
1246        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
1247    if ranId not in PhaseRanIdLookup:
1248        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
1249    return PhaseRanIdLookup[ranId]
1250
1251def LookupPhaseName(pId):
1252    '''Get the phase number and name from a phase Id
1253
1254    :param int/str pId: the sequential assigned to a phase
1255    :returns:  (phase,ranId) where phase is the name of the phase (str)
1256      and ranId is the random # id for the phase (int)
1257    '''
1258    if not PhaseIdLookup:
1259        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
1260    if pId is None or pId == '':
1261        raise KeyError('Error: phase is invalid (None or blank)')
1262    pId = str(pId)
1263    if pId not in PhaseIdLookup:
1264        raise KeyError('Error: LookupPhaseName does not have index '+pId)
1265    return PhaseIdLookup[pId]
1266
1267def LookupHistId(ranId):
1268    '''Get the histogram number and name from a histogram random Id
1269
1270    :param int ranId: the random Id assigned to a histogram
1271    :returns: the sequential Id (hId) number for the histogram (str)
1272    '''
1273    if not HistRanIdLookup:
1274        raise Exception('Error: LookupHistId called before IndexAllIds was run')
1275    if ranId not in HistRanIdLookup:
1276        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
1277    return HistRanIdLookup[ranId]
1278
1279def LookupHistName(hId):
1280    '''Get the histogram number and name from a histogram Id
1281
1282    :param int/str hId: the sequential assigned to a histogram
1283    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1284      and ranId is the random # id for the histogram (int)
1285    '''
1286    if not HistIdLookup:
1287        raise Exception('Error: LookupHistName called before IndexAllIds was run')
1288    if hId is None or hId == '':
1289        raise KeyError('Error: histogram is invalid (None or blank)')
1290    hId = str(hId)
1291    if hId not in HistIdLookup:
1292        raise KeyError('Error: LookupHistName does not have index '+hId)
1293    return HistIdLookup[hId]
1294
1295def fmtVarDescr(varname):
1296    '''Return a string with a more complete description for a GSAS-II variable
1297
1298    :param str varname: A full G2 variable name with 2 or 3 or 4
1299       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1300
1301    :returns: a string with the description
1302    '''
1303    s,l = VarDescr(varname)
1304    return s+": "+l
1305
1306def VarDescr(varname):
1307    '''Return two strings with a more complete description for a GSAS-II variable
1308
1309    :param str name: A full G2 variable name with 2 or 3 or 4
1310       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1311
1312    :returns: (loc,meaning) where loc describes what item the variable is mapped
1313      (phase, histogram, etc.) and meaning describes what the variable does.
1314    '''
1315
1316    # special handling for parameter names without a colon
1317    # for now, assume self-defining
1318    if varname.find(':') == -1:
1319        return "Global",varname
1320
1321    l = getVarDescr(varname)
1322    if not l:
1323        return ("invalid variable name ("+str(varname)+")!"),""
1324#        return "invalid variable name!",""
1325
1326    if not l[-1]:
1327        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1328
1329    if len(l) == 3:         #SASD variable name!
1330        s = 'component:'+l[1]
1331        return s,l[-1]
1332    s = ""
1333    if l[0] is not None and l[1] is not None: # HAP: keep short
1334        if l[2] == "Scale": # fix up ambigous name
1335            l[5] = "Phase fraction"
1336        if l[0] == '*':
1337            lbl = 'Seq. ref.'
1338        else:
1339            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1340        if l[1] == '*':
1341            hlbl = 'Seq. ref.'
1342        else:
1343            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1344        if hlbl[:4] == 'HKLF':
1345            hlbl = 'Xtl='+hlbl[5:]
1346        elif hlbl[:4] == 'PWDR':
1347            hlbl = 'Pwd='+hlbl[5:]
1348        else:
1349            hlbl = 'Hist='+hlbl
1350        s = "Ph="+str(lbl)+" * "+str(hlbl)
1351    else:
1352        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1353            l[5] = "Scale factor"
1354        if l[2] == 'Back': # background parameters are "special", alas
1355            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1356            l[-1] += ' #'+str(l[3])
1357        elif l[4] is not None: # rigid body parameter or modulation parm
1358            lbl = ShortPhaseNames.get(l[0],'phase?')
1359            if 'RB' in l[2]:    #rigid body parm
1360                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1361            else: #modulation parm
1362                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
1363        elif l[3] is not None: # atom parameter,
1364            lbl = ShortPhaseNames.get(l[0],'phase?')
1365            try:
1366                albl = LookupAtomLabel(l[0],l[3])[0]
1367            except KeyError:
1368                albl = 'Atom?'
1369            s = "Atom "+str(albl)+" in "+str(lbl)
1370        elif l[0] == '*':
1371            s = "All phases "
1372        elif l[0] is not None:
1373            lbl = ShortPhaseNames.get(l[0],'phase?')
1374            s = "Phase "+str(lbl)
1375        elif l[1] == '*':
1376            s = 'All hists'
1377        elif l[1] is not None:
1378            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1379            if hlbl[:4] == 'HKLF':
1380                hlbl = 'Xtl='+hlbl[5:]
1381            elif hlbl[:4] == 'PWDR':
1382                hlbl = 'Pwd='+hlbl[5:]
1383            else:
1384                hlbl = 'Hist='+hlbl
1385            s = str(hlbl)
1386    if not s:
1387        s = 'Global'
1388    return s,l[-1]
1389
1390def getVarDescr(varname):
1391    '''Return a short description for a GSAS-II variable
1392
1393    :param str name: A full G2 variable name with 2 or 3 or 4
1394       colons (<p>:<h>:name[:<a1>][:<a2>])
1395
1396    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1397      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1398      the histogram number and the atom number; `name` will always be
1399      a str; and `description` is str or `None`.
1400      If the variable name is incorrectly formed (for example, wrong
1401      number of colons), `None` is returned instead of a list.
1402    '''
1403    l = varname.split(':')
1404    if len(l) == 2:     #SASD parameter name
1405        return varname,l[0],getDescr(l[1])
1406    if len(l) == 3:
1407        l += [None,None]
1408    elif len(l) == 4:
1409        l += [None]
1410    elif len(l) != 5:
1411        return None
1412    for i in (0,1,3,4):
1413        if l[i] == "":
1414            l[i] = None
1415    l += [getDescr(l[2])]
1416    return l
1417
1418def CompileVarDesc():
1419    '''Set the values in the variable lookup tables
1420    (:attr:`reVarDesc` and :attr:`reVarStep`).
1421    This is called in :func:`getDescr` and :func:`getVarStep` so this
1422    initialization is always done before use.
1423
1424    Note that keys may contain regular expressions, where '[xyz]'
1425    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range
1426    of values). '.*' matches any string. For example::
1427
1428    'AUiso':'Atomic isotropic displacement parameter',
1429
1430    will match variable ``'p::AUiso:a'``.
1431    If parentheses are used in the key, the contents of those parentheses can be
1432    used in the value, such as::
1433
1434    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1435
1436    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1437    in the value when used.
1438
1439    '''
1440    if reVarDesc: return # already done
1441    for key,value in {
1442        # derived or other sequential vars
1443        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1444        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1445        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1446        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1447        # ambiguous, alas:
1448        'Scale' : 'Phase or Histogram scale factor',
1449        # Phase vars (p::<var>)
1450        'A([0-5])' : ('Reciprocal metric tensor component \\1',1e-5),
1451        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
1452        # Atom vars (p::<var>:a)
1453        'dA([xyz])$' : ('change to atomic coordinate, \\1',1e-6),
1454        'A([xyz])$' : '\\1 fractional atomic coordinate',
1455        'AUiso':('Atomic isotropic displacement parameter',1e-4),
1456        'AU([123][123])':('Atomic anisotropic displacement parameter U\\1',1e-4),
1457        'Afrac': ('Atomic site fraction parameter',1e-5),
1458        'Amul': 'Atomic site multiplicity value',
1459        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
1460        # Hist & Phase (HAP) vars (p:h:<var>)
1461        'Back': 'Background term',
1462        'BkPkint;(.*)':'Background peak #\\1 intensity',
1463        'BkPkpos;(.*)':'Background peak #\\1 position',
1464        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1465        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1466        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1467        'D([123][123])' : 'Anisotropic strain coef. \\1',
1468        'Extinction' : 'Extinction coef.',
1469        'MD' : 'March-Dollase coef.',
1470        'Mustrain;.*' : 'Microstrain coef.',
1471        'Size;.*' : 'Crystallite size value',
1472        'eA$' : 'Cubic mustrain value',
1473        'Ep$' : 'Primary extinction',
1474        'Es$' : 'Secondary type II extinction',
1475        'Eg$' : 'Secondary type I extinction',
1476        'Flack' : 'Flack parameter',
1477        'TwinFr' : 'Twin fraction',
1478        #Histogram vars (:h:<var>)
1479        'Absorption' : 'Absorption coef.',
1480        'Displace([XY])' : ('Debye-Scherrer sample displacement \\1',0.1),
1481        'Lam' : ('Wavelength',1e-6),
1482        'I\(L2\)\/I\(L1\)' : ('Ka2/Ka1 intensity ratio',0.001),
1483        'Polariz\.' : ('Polarization correction',1e-3),
1484        'SH/L' : ('FCJ peak asymmetry correction',1e-4),
1485        '([UVW])$' : ('Gaussian instrument broadening \\1',1e-5),
1486        '([XYZ])$' : ('Cauchy instrument broadening \\1',1e-5),
1487        'Zero' : 'Debye-Scherrer zero correction',
1488        'Shift' : 'Bragg-Brentano sample displ.',
1489        'SurfRoughA' : 'Bragg-Brenano surface roughness A',
1490        'SurfRoughB' : 'Bragg-Brenano surface roughness B',
1491        'Transparency' : 'Bragg-Brentano sample tranparency',
1492        'DebyeA' : 'Debye model amplitude',
1493        'DebyeR' : 'Debye model radius',
1494        'DebyeU' : 'Debye model Uiso',
1495        'RBV.*' : 'Vector rigid body parameter',
1496        'RBR.*' : 'Residue rigid body parameter',
1497        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1498        'RBRP([xyz])' : 'Residue rigid body position parameter',
1499        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1500        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1501        'constr([0-9]*)' : 'Parameter from constraint',
1502        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1503        'mV([0-2])$' : 'Modulation vector component \\1',
1504        'Fsin'  :   'Sin site fraction modulation',
1505        'Fcos'  :   'Cos site fraction modulation',
1506        'Fzero'  :   'Crenel function offset',      #may go away
1507        'Fwid'   :   'Crenel function width',
1508        'Tmin'   :   'ZigZag/Block min location',
1509        'Tmax'   :   'ZigZag/Block max location',
1510        '([XYZ])max': 'ZigZag/Block max value for \\1',
1511        '([XYZ])sin'  : 'Sin position wave for \\1',
1512        '([XYZ])cos'  : 'Cos position wave for \\1',
1513        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1514        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1515        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1516        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1517        # PDF peak parms (l:<var>;l = peak no.)
1518        'PDFpos'  : 'PDF peak position',
1519        'PDFmag'  : 'PDF peak magnitude',
1520        'PDFsig'  : 'PDF peak std. dev.',
1521        # SASD vars (l:<var>;l = component)
1522        'Aspect ratio' : 'Particle aspect ratio',
1523        'Length' : 'Cylinder length',
1524        'Diameter' : 'Cylinder/disk diameter',
1525        'Thickness' : 'Disk thickness',
1526        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
1527        'Dist' : 'Interparticle distance',
1528        'VolFr' : 'Dense scatterer volume fraction',
1529        'epis' : 'Sticky sphere epsilon',
1530        'Sticky' : 'Stickyness',
1531        'Depth' : 'Well depth',
1532        'Width' : 'Well width',
1533        'Volume' : 'Particle volume',
1534        'Radius' : 'Sphere/cylinder/disk radius',
1535        'Mean' : 'Particle mean radius',
1536        'StdDev' : 'Standard deviation in Mean',
1537        'G$': 'Guinier prefactor',
1538        'Rg$': 'Guinier radius of gyration',
1539        'B$': 'Porod prefactor',
1540        'P$': 'Porod power',
1541        'Cutoff': 'Porod cutoff',
1542        'PkInt': 'Bragg peak intensity',
1543        'PkPos': 'Bragg peak position',
1544        'PkSig': 'Bragg peak sigma',
1545        'PkGam': 'Bragg peak gamma',
1546        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1547        'Dcalc': 'Calc. d-spacing',
1548        'Back$': 'background parameter',
1549        'pos$': 'peak position',
1550        'int$': 'peak intensity',
1551        'WgtFrac':'phase weight fraction',
1552        'alpha':'TOF profile term',
1553        'beta-[01q]':'TOF profile term',
1554        'sig-[012q]':'TOF profile term',
1555        'dif[ABC]':'TOF to d-space calibration',
1556        'C\([0-9]*,[0-9]*\)' : 'spherical harmonics preferred orientation coef.',
1557        }.items():
1558        if len(value) == 2:
1559            #VarDesc[key] = value[0]
1560            reVarDesc[re.compile(key)] = value[0]
1561            reVarStep[re.compile(key)] = value[1]
1562        else:
1563            #VarDesc[key] = value
1564            reVarDesc[re.compile(key)] = value
1565
1566def removeNonRefined(parmList):
1567    '''Remove items from variable list that are not refined and should not
1568    appear as options for constraints
1569
1570    :param list parmList: a list of strings of form "p:h:VAR:a" where
1571      VAR is the variable name
1572
1573    :returns: a list after removing variables where VAR matches a
1574      entry in local variable NonRefinedList
1575    '''
1576    NonRefinedList = ['Omega','Type','Chi','Phi', 'Azimuth','Gonio. radius',
1577                          'Lam1','Lam2','Back','Temperature','Pressure',
1578                          'FreePrm1','FreePrm2','FreePrm3',
1579                          'Source','nPeaks','LeBail','newLeBail','Bank',
1580                          'nDebye', #'',
1581                    ]
1582    return [prm for prm in parmList if prm.split(':')[2] not in NonRefinedList]
1583       
1584def getDescr(name):
1585    '''Return a short description for a GSAS-II variable
1586
1587    :param str name: The descriptive part of the variable name without colons (:)
1588
1589    :returns: a short description or None if not found
1590    '''
1591
1592    CompileVarDesc() # compile the regular expressions, if needed
1593    for key in reVarDesc:
1594        m = key.match(name)
1595        if m:
1596            reVarDesc[key]
1597            return m.expand(reVarDesc[key])
1598    return None
1599
1600def getVarStep(name,parmDict=None):
1601    '''Return a step size for computing the derivative of a GSAS-II variable
1602
1603    :param str name: A complete variable name (with colons, :)
1604    :param dict parmDict: A dict with parameter values or None (default)
1605
1606    :returns: a float that should be an appropriate step size, either from
1607      the value supplied in :func:`CompileVarDesc` or based on the value for
1608      name in parmDict, if supplied. If not found or the value is zero,
1609      a default value of 1e-5 is used. If parmDict is None (default) and
1610      no value is provided in :func:`CompileVarDesc`, then None is returned.
1611    '''
1612    CompileVarDesc() # compile the regular expressions, if needed
1613    for key in reVarStep:
1614        m = key.match(name)
1615        if m:
1616            return reVarStep[key]
1617    if parmDict is None: return None
1618    val = parmDict.get(key,0.0)
1619    if abs(val) > 0.05:
1620        return abs(val)/1000.
1621    else:
1622        return 1e-5
1623
1624def GenWildCard(varlist):
1625    '''Generate wildcard versions of G2 variables. These introduce '*'
1626    for a phase, histogram or atom number (but only for one of these
1627    fields) but only when there is more than one matching variable in the
1628    input variable list. So if the input is this::
1629
1630      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1631
1632    then the output will be this::
1633
1634       wildList = ['*::AUiso:0', '0::AUiso:*']
1635
1636    :param list varlist: an input list of GSAS-II variable names
1637      (such as 0::AUiso:0)
1638
1639    :returns: wildList, the generated list of wild card variable names.
1640    '''
1641    wild = []
1642    for i in (0,1,3):
1643        currentL = varlist[:]
1644        while currentL:
1645            item1 = currentL.pop(0)
1646            i1splt = item1.split(':')
1647            if i >= len(i1splt): continue
1648            if i1splt[i]:
1649                nextL = []
1650                i1splt[i] = '[0-9]+'
1651                rexp = re.compile(':'.join(i1splt))
1652                matchlist = [item1]
1653                for nxtitem in currentL:
1654                    if rexp.match(nxtitem):
1655                        matchlist += [nxtitem]
1656                    else:
1657                        nextL.append(nxtitem)
1658                if len(matchlist) > 1:
1659                    i1splt[i] = '*'
1660                    wild.append(':'.join(i1splt))
1661                currentL = nextL
1662    return wild
1663
1664def LookupWildCard(varname,varlist):
1665    '''returns a list of variable names from list varname
1666    that match wildcard name in varname
1667
1668    :param str varname: a G2 variable name containing a wildcard
1669      (such as \*::var)
1670    :param list varlist: the list of all variable names used in
1671      the current project
1672    :returns: a list of matching GSAS-II variables (may be empty)
1673    '''
1674    rexp = re.compile(varname.replace('*','[0-9]+'))
1675    return sorted([var for var in varlist if rexp.match(var)])
1676
1677
1678def _lookup(dic,key):
1679    '''Lookup a key in a dictionary, where None returns an empty string
1680    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1681    '''
1682    if key is None:
1683        return ""
1684    elif key == "*":
1685        return "*"
1686    else:
1687        return dic.get(key,'?')
1688
1689def SortVariables(varlist):
1690    '''Sorts variable names in a sensible manner
1691    '''
1692    def cvnnums(var):
1693        v = []
1694        for i in var.split(':'):
1695            if i == '':
1696                v.append(-1)
1697                continue
1698            try:
1699                v.append(int(i))
1700            except:
1701                v.append(i)
1702        return v
1703    return sorted(varlist,key=cvnnums)
1704
1705class G2VarObj(object):
1706    '''Defines a GSAS-II variable either using the phase/atom/histogram
1707    unique Id numbers or using a character string that specifies
1708    variables by phase/atom/histogram number (which can change).
1709    Note that :func:`LoadID` should be used to (re)load the current Ids
1710    before creating or later using the G2VarObj object.
1711
1712    This can store rigid body variables, but does not translate the residue # and
1713    body # to/from random Ids
1714
1715    A :class:`G2VarObj` object can be created with a single parameter:
1716
1717    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1718      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1719
1720     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
1721     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1722     * a is the atom number (which may be left blank in which case the third colon is omitted).
1723       The atom number can be specified as '*' if a phase number is specified (not as '*').
1724       For rigid body variables, specify a will be a string of form "residue:body#"
1725
1726      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1727      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1728      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1729      For a rigid body variables, AtomID is a string of form "residue:body#".
1730
1731    If four positional arguments are supplied, they are:
1732
1733    :param str/int phasenum: The number for the phase (or None or '*')
1734    :param str/int histnum: The number for the histogram (or None or '*')
1735    :param str varname: a single value can be used to create a :class:`G2VarObj`
1736    :param str/int atomnum: The number for the atom (or None or '*')
1737
1738    '''
1739    IDdict = {}
1740    IDdict['phases'] = {}
1741    IDdict['hists'] = {}
1742    IDdict['atoms'] = {}
1743    def __init__(self,*args):
1744        self.phase = None
1745        self.histogram = None
1746        self.name = ''
1747        self.atom = None
1748        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1749            # single arg with 4 values
1750            self.phase,self.histogram,self.name,self.atom = args[0]
1751        elif len(args) == 1 and ':' in args[0]:
1752            #parse a string
1753            lst = args[0].split(':')
1754            if lst[0] == '*':
1755                self.phase = '*'
1756                if len(lst) > 3:
1757                    self.atom = lst[3]
1758                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1759            elif lst[1] == '*':
1760                self.histogram = '*'
1761                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1762            else:
1763                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1764                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1765                if len(lst) == 4:
1766                    if lst[3] == '*':
1767                        self.atom = '*'
1768                    else:
1769                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1770                elif len(lst) == 5:
1771                    self.atom = lst[3]+":"+lst[4]
1772                elif len(lst) == 3:
1773                    pass
1774                else:
1775                    raise Exception("Too many colons in var name "+str(args[0]))
1776            self.name = lst[2]
1777        elif len(args) == 4:
1778            if args[0] == '*':
1779                self.phase = '*'
1780                self.atom = args[3]
1781            else:
1782                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1783                if args[3] == '*':
1784                    self.atom = '*'
1785                elif args[0] is not None:
1786                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1787            if args[1] == '*':
1788                self.histogram = '*'
1789            else:
1790                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1791            self.name = args[2]
1792        else:
1793            raise Exception("Incorrectly called GSAS-II parameter name")
1794
1795        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1796
1797    def __str__(self):
1798        return self.varname()
1799
1800    def varname(self):
1801        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1802        string (p:h:<var>:a) or (p:h:<var>)
1803
1804        :returns: the variable name as a str
1805        '''
1806        a = ""
1807        if self.phase == "*":
1808            ph = "*"
1809            if self.atom:
1810                a = ":" + str(self.atom)
1811        else:
1812            ph = _lookup(PhaseRanIdLookup,self.phase)
1813            if self.atom == '*':
1814                a = ':*'
1815            elif self.atom:
1816                if ":" in str(self.atom):
1817                    a = ":" + str(self.atom)
1818                elif ph in AtomRanIdLookup:
1819                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1820                else:
1821                    a = ":?"
1822        if self.histogram == "*":
1823            hist = "*"
1824        else:
1825            hist = _lookup(HistRanIdLookup,self.histogram)
1826        s = (ph + ":" + hist + ":" + str(self.name)) + a
1827        return s
1828
1829    def __repr__(self):
1830        '''Return the detailed contents of the object
1831        '''
1832        s = "<"
1833        if self.phase == '*':
1834            s += "Phases: all; "
1835            if self.atom is not None:
1836                if ":" in str(self.atom):
1837                    s += "Rigid body" + str(self.atom) + "; "
1838                else:
1839                    s += "Atom #" + str(self.atom) + "; "
1840        elif self.phase is not None:
1841            ph =  _lookup(PhaseRanIdLookup,self.phase)
1842            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1843            if self.atom == '*':
1844                s += "Atoms: all; "
1845            elif ":" in str(self.atom):
1846                s += "Rigid body" + str(self.atom) + "; "
1847            elif self.atom is not None:
1848                s += "Atom rId=" + str(self.atom)
1849                if ph in AtomRanIdLookup:
1850                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1851                else:
1852                    s += " (#? -- not found!); "
1853        if self.histogram == '*':
1854            s += "Histograms: all; "
1855        elif self.histogram is not None:
1856            hist = _lookup(HistRanIdLookup,self.histogram)
1857            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1858        s += 'Variable name="' + str(self.name) + '">'
1859        return s+" ("+self.varname()+")"
1860
1861    def __eq__(self, other):
1862        if type(other) is type(self):
1863            return (self.phase == other.phase and
1864                    self.histogram == other.histogram and
1865                    self.name == other.name and
1866                    self.atom == other.atom)
1867        return False
1868
1869    def _show(self):
1870        'For testing, shows the current lookup table'
1871        print ('phases'+ self.IDdict['phases'])
1872        print ('hists'+ self.IDdict['hists'])
1873        print ('atomDict'+ self.IDdict['atoms'])
1874
1875#==========================================================================
1876def SetDefaultSample():
1877    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
1878    return {
1879        'InstrName':'',
1880        'ranId':ran.randint(0,sys.maxsize),
1881        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
1882        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],'Diffuse':[],
1883        'Temperature':300.,'Pressure':0.1,'Time':0.0,
1884        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
1885        'Gonio. radius':200.0,
1886        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
1887#SASD items
1888        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
1889        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
1890        'Trans':1.0,                            #measured transmission
1891        'SlitLen':0.0,                          #Slit length - in Q(A-1)
1892        }
1893######################################################################
1894class ImportBaseclass(object):
1895    '''Defines a base class for the reading of input files (diffraction
1896    data, coordinates,...). See :ref:`Writing a Import Routine<import_routines>`
1897    for an explanation on how to use a subclass of this class.
1898    '''
1899    class ImportException(Exception):
1900        '''Defines an Exception that is used when an import routine hits an expected error,
1901        usually in .Reader.
1902
1903        Good practice is that the Reader should define a value in self.errors that
1904        tells the user some information about what is wrong with their file.
1905        '''
1906        pass
1907
1908    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
1909    def __init__(self,formatName,longFormatName=None,
1910                 extensionlist=[],strictExtension=False,):
1911        self.formatName = formatName # short string naming file type
1912        if longFormatName: # longer string naming file type
1913            self.longFormatName = longFormatName
1914        else:
1915            self.longFormatName = formatName
1916        # define extensions that are allowed for the file type
1917        # for windows, remove any extensions that are duplicate, as case is ignored
1918        if sys.platform == 'windows' and extensionlist:
1919            extensionlist = list(set([s.lower() for s in extensionlist]))
1920        self.extensionlist = extensionlist
1921        # If strictExtension is True, the file will not be read, unless
1922        # the extension matches one in the extensionlist
1923        self.strictExtension = strictExtension
1924        self.errors = ''
1925        self.warnings = ''
1926        self.SciPy = False          #image reader needed scipy
1927        # used for readers that will use multiple passes to read
1928        # more than one data block
1929        self.repeat = False
1930        self.selections = []
1931        self.repeatcount = 0
1932        self.readfilename = '?'
1933        self.scriptable = False
1934        #print 'created',self.__class__
1935
1936    def ReInitialize(self):
1937        'Reinitialize the Reader to initial settings'
1938        self.errors = ''
1939        self.warnings = ''
1940        self.SciPy = False          #image reader needed scipy
1941        self.repeat = False
1942        self.repeatcount = 0
1943        self.readfilename = '?'
1944
1945
1946#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
1947#        '''This method must be supplied in the child class to read the file.
1948#        if the read fails either return False or raise an Exception
1949#        preferably of type ImportException.
1950#        '''
1951#        #start reading
1952#        raise ImportException("Error occurred while...")
1953#        self.errors += "Hint for user on why the error occur
1954#        return False # if an error occurs
1955#        return True # if read OK
1956
1957    def ExtensionValidator(self, filename):
1958        '''This methods checks if the file has the correct extension
1959       
1960        :returns:
1961       
1962          * False if this filename will not be supported by this reader (only
1963            when strictExtension is True)
1964          * True if the extension matches the list supplied by the reader
1965          * None if the reader allows un-registered extensions
1966         
1967        '''
1968        if filename:
1969            ext = ospath.splitext(filename)[1]
1970            if not ext and self.strictExtension: return False
1971            for ext in self.extensionlist:               
1972                if sys.platform == 'windows':
1973                    if filename.lower().endswith(ext): return True
1974                else:
1975                    if filename.endswith(ext): return True
1976        if self.strictExtension:
1977            return False
1978        else:
1979            return None
1980
1981    def ContentsValidator(self, filename):
1982        '''This routine will attempt to determine if the file can be read
1983        with the current format.
1984        This will typically be overridden with a method that
1985        takes a quick scan of [some of]
1986        the file contents to do a "sanity" check if the file
1987        appears to match the selected format.
1988        the file must be opened here with the correct format (binary/text)
1989        '''
1990        #filepointer.seek(0) # rewind the file pointer
1991        return True
1992
1993    def CIFValidator(self, filepointer):
1994        '''A :meth:`ContentsValidator` for use to validate CIF files.
1995        '''
1996        filepointer.seek(0)
1997        for i,l in enumerate(filepointer):
1998            if i >= 1000: return True
1999            '''Encountered only blank lines or comments in first 1000
2000            lines. This is unlikely, but assume it is CIF anyway, since we are
2001            even less likely to find a file with nothing but hashes and
2002            blank lines'''
2003            line = l.strip()
2004            if len(line) == 0: # ignore blank lines
2005                continue
2006            elif line.startswith('#'): # ignore comments
2007                continue
2008            elif line.startswith('data_'): # on the right track, accept this file
2009                return True
2010            else: # found something invalid
2011                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
2012                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
2013                    self.errors += '  '+str(l)
2014                else:
2015                    self.errors += '  (binary)'
2016                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
2017                self.errors += '\n        a data_ statement begins a block.'
2018                return False
2019
2020######################################################################
2021class ImportPhase(ImportBaseclass):
2022    '''Defines a base class for the reading of files with coordinates
2023
2024    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
2025    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` and in
2026    :func:`GSASIIscriptable.import_generic`.
2027    See :ref:`Writing a Import Routine<import_routines>`
2028    for an explanation on how to use this class.
2029
2030    '''
2031    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2032        strictExtension=False,):
2033        # call parent __init__
2034        ImportBaseclass.__init__(self,formatName,longFormatName,
2035            extensionlist,strictExtension)
2036        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
2037        self.Constraints = None
2038
2039######################################################################
2040class ImportStructFactor(ImportBaseclass):
2041    '''Defines a base class for the reading of files with tables
2042    of structure factors.
2043
2044    Structure factors are read with a call to :meth:`GSASIIdataGUI.GSASII.OnImportSfact`
2045    which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`, which calls
2046    methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2047    :meth:`Reader`.
2048
2049    See :ref:`Writing a Import Routine<import_routines>`
2050    for an explanation on how to use import classes in general. The specifics
2051    for reading a structure factor histogram require that
2052    the ``Reader()`` routine in the import
2053    class need to do only a few things: It
2054    should load :attr:`RefDict` item ``'RefList'`` with the reflection list,
2055    and set :attr:`Parameters` with the instrument parameters
2056    (initialized with :meth:`InitParameters` and set with :meth:`UpdateParameters`).
2057    '''
2058    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2059        strictExtension=False,):
2060        ImportBaseclass.__init__(self,formatName,longFormatName,
2061            extensionlist,strictExtension)
2062
2063        # define contents of Structure Factor entry
2064        self.Parameters = []
2065        'self.Parameters is a list with two dicts for data parameter settings'
2066        self.InitParameters()
2067        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2068        self.Banks = []             #for multi bank data (usually TOF)
2069        '''self.RefDict is a dict containing the reflection information, as read from the file.
2070        Item 'RefList' contains the reflection information. See the
2071        :ref:`Single Crystal Reflection Data Structure<XtalRefl_table>`
2072        for the contents of each row. Dict element 'FF'
2073        contains the form factor values for each element type; if this entry
2074        is left as initialized (an empty list) it will be initialized as needed later.
2075        '''
2076    def ReInitialize(self):
2077        'Reinitialize the Reader to initial settings'
2078        ImportBaseclass.ReInitialize(self)
2079        self.InitParameters()
2080        self.Banks = []             #for multi bank data (usually TOF)
2081        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2082
2083    def InitParameters(self):
2084        'initialize the instrument parameters structure'
2085        Lambda = 0.70926
2086        HistType = 'SXC'
2087        self.Parameters = [{'Type':[HistType,HistType], # create the structure
2088                            'Lam':[Lambda,Lambda]
2089                            }, {}]
2090        'Parameters is a list with two dicts for data parameter settings'
2091
2092    def UpdateParameters(self,Type=None,Wave=None):
2093        'Revise the instrument parameters'
2094        if Type is not None:
2095            self.Parameters[0]['Type'] = [Type,Type]
2096        if Wave is not None:
2097            self.Parameters[0]['Lam'] = [Wave,Wave]
2098
2099######################################################################
2100class ImportPowderData(ImportBaseclass):
2101    '''Defines a base class for the reading of files with powder data.
2102
2103    Objects constructed that subclass this (in import/G2pwd_*.py etc.) will be used
2104    in :meth:`GSASIIdataGUI.GSASII.OnImportPowder` and in
2105    :func:`GSASIIscriptable.import_generic`.
2106    See :ref:`Writing a Import Routine<import_routines>`
2107    for an explanation on how to use this class.
2108    '''
2109    def __init__(self,formatName,longFormatName=None,
2110        extensionlist=[],strictExtension=False,):
2111        ImportBaseclass.__init__(self,formatName,longFormatName,
2112            extensionlist,strictExtension)
2113        self.clockWd = None  # used in TOF
2114        self.ReInitialize()
2115
2116    def ReInitialize(self):
2117        'Reinitialize the Reader to initial settings'
2118        ImportBaseclass.ReInitialize(self)
2119        self.powderentry = ['',None,None] #  (filename,Pos,Bank)
2120        self.powderdata = [] # Powder dataset
2121        '''A powder data set is a list with items [x,y,w,yc,yb,yd]:
2122                np.array(x), # x-axis values
2123                np.array(y), # powder pattern intensities
2124                np.array(w), # 1/sig(intensity)^2 values (weights)
2125                np.array(yc), # calc. intensities (zero)
2126                np.array(yb), # calc. background (zero)
2127                np.array(yd), # obs-calc profiles
2128        '''
2129        self.comments = []
2130        self.idstring = ''
2131        self.Sample = SetDefaultSample() # default sample parameters
2132        self.Controls = {}  # items to be placed in top-level Controls
2133        self.GSAS = None     # used in TOF
2134        self.repeat_instparm = True # Should a parm file be
2135        #                             used for multiple histograms?
2136        self.instparm = None # name hint from file of instparm to use
2137        self.instfile = '' # full path name to instrument parameter file
2138        self.instbank = '' # inst parm bank number
2139        self.instmsg = ''  # a label that gets printed to show
2140                           # where instrument parameters are from
2141        self.numbanks = 1
2142        self.instdict = {} # place items here that will be transferred to the instrument parameters
2143        self.pwdparms = {} # place parameters that are transferred directly to the tree
2144                           # here (typically from an existing GPX file)
2145######################################################################
2146class ImportSmallAngleData(ImportBaseclass):
2147    '''Defines a base class for the reading of files with small angle data.
2148    See :ref:`Writing a Import Routine<import_routines>`
2149    for an explanation on how to use this class.
2150    '''
2151    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2152        strictExtension=False,):
2153
2154        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2155            strictExtension)
2156        self.ReInitialize()
2157
2158    def ReInitialize(self):
2159        'Reinitialize the Reader to initial settings'
2160        ImportBaseclass.ReInitialize(self)
2161        self.smallangleentry = ['',None,None] #  (filename,Pos,Bank)
2162        self.smallangledata = [] # SASD dataset
2163        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2164                np.array(x), # x-axis values
2165                np.array(y), # powder pattern intensities
2166                np.array(w), # 1/sig(intensity)^2 values (weights)
2167                np.array(yc), # calc. intensities (zero)
2168                np.array(yd), # obs-calc profiles
2169                np.array(yb), # preset bkg
2170        '''
2171        self.comments = []
2172        self.idstring = ''
2173        self.Sample = SetDefaultSample()
2174        self.GSAS = None     # used in TOF
2175        self.clockWd = None  # used in TOF
2176        self.numbanks = 1
2177        self.instdict = {} # place items here that will be transferred to the instrument parameters
2178
2179######################################################################
2180class ImportReflectometryData(ImportBaseclass):
2181    '''Defines a base class for the reading of files with reflectometry data.
2182    See :ref:`Writing a Import Routine<import_routines>`
2183    for an explanation on how to use this class.
2184    '''
2185    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2186        strictExtension=False,):
2187
2188        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2189            strictExtension)
2190        self.ReInitialize()
2191
2192    def ReInitialize(self):
2193        'Reinitialize the Reader to initial settings'
2194        ImportBaseclass.ReInitialize(self)
2195        self.reflectometryentry = ['',None,None] #  (filename,Pos,Bank)
2196        self.reflectometrydata = [] # SASD dataset
2197        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2198                np.array(x), # x-axis values
2199                np.array(y), # powder pattern intensities
2200                np.array(w), # 1/sig(intensity)^2 values (weights)
2201                np.array(yc), # calc. intensities (zero)
2202                np.array(yd), # obs-calc profiles
2203                np.array(yb), # preset bkg
2204        '''
2205        self.comments = []
2206        self.idstring = ''
2207        self.Sample = SetDefaultSample()
2208        self.GSAS = None     # used in TOF
2209        self.clockWd = None  # used in TOF
2210        self.numbanks = 1
2211        self.instdict = {} # place items here that will be transferred to the instrument parameters
2212
2213######################################################################
2214class ImportPDFData(ImportBaseclass):
2215    '''Defines a base class for the reading of files with PDF G(R) data.
2216    See :ref:`Writing a Import Routine<import_routines>`
2217    for an explanation on how to use this class.
2218    '''
2219    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2220        strictExtension=False,):
2221
2222        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2223            strictExtension)
2224        self.ReInitialize()
2225
2226    def ReInitialize(self):
2227        'Reinitialize the Reader to initial settings'
2228        ImportBaseclass.ReInitialize(self)
2229        self.pdfentry = ['',None,None] #  (filename,Pos,Bank)
2230        self.pdfdata = [] # PDF G(R) dataset
2231        '''A pdf g(r) data set is a list with items [x,y]:
2232                np.array(x), # r-axis values
2233                np.array(y), # pdf g(r)
2234        '''
2235        self.comments = []
2236        self.idstring = ''
2237        self.numbanks = 1
2238
2239######################################################################
2240class ImportImage(ImportBaseclass):
2241    '''Defines a base class for the reading of images
2242
2243    Images are read in only these places:
2244
2245      * Initial reading is typically done from a menu item
2246        with a call to :meth:`GSASIIdataGUI.GSASII.OnImportImage`
2247        which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`. That calls
2248        methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2249        :meth:`Reader`. This returns a list of reader objects for each read image.
2250        Also used in :func:`GSASIIscriptable.import_generic`.
2251
2252      * Images are read alternatively in :func:`GSASIIIO.ReadImages`, which puts image info
2253        directly into the data tree.
2254
2255      * Images are reloaded with :func:`GSASIIIO.GetImageData`.
2256
2257    When reading an image, the ``Reader()`` routine in the ImportImage class
2258    should set:
2259
2260      * :attr:`Comments`: a list of strings (str),
2261      * :attr:`Npix`: the number of pixels in the image (int),
2262      * :attr:`Image`: the actual image as a numpy array (np.array)
2263      * :attr:`Data`: a dict defining image parameters (dict). Within this dict the following
2264        data items are needed:
2265
2266         * 'pixelSize': size of each pixel in microns (such as ``[200.,200.]``.
2267         * 'wavelength': wavelength in Angstoms.
2268         * 'distance': distance of detector from sample in cm.
2269         * 'center': uncalibrated center of beam on detector (such as ``[204.8,204.8]``.
2270         * 'size': size of image (such as ``[2048,2048]``).
2271         * 'ImageTag': image number or other keyword used to retrieve image from
2272           a multi-image data file (defaults to ``1`` if not specified).
2273         * 'sumfile': holds sum image file name if a sum was produced from a multi image file
2274
2275    optional data items:
2276
2277      * :attr:`repeat`: set to True if there are additional images to
2278        read in the file, False otherwise
2279      * :attr:`repeatcount`: set to the number of the image.
2280
2281    Note that the above is initialized with :meth:`InitParameters`.
2282    (Also see :ref:`Writing a Import Routine<import_routines>`
2283    for an explanation on how to use import classes in general.)
2284    '''
2285    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2286        strictExtension=False,):
2287        ImportBaseclass.__init__(self,formatName,longFormatName,
2288            extensionlist,strictExtension)
2289        self.InitParameters()
2290
2291    def ReInitialize(self):
2292        'Reinitialize the Reader to initial settings -- not used at present'
2293        ImportBaseclass.ReInitialize(self)
2294        self.InitParameters()
2295
2296    def InitParameters(self):
2297        'initialize the instrument parameters structure'
2298        self.Comments = ['No comments']
2299        self.Data = {}
2300        self.Npix = 0
2301        self.Image = None
2302        self.repeat = False
2303        self.repeatcount = 1
2304        self.sumfile = ''
2305
2306    def LoadImage(self,ParentFrame,imagefile,imagetag=None):
2307        '''Optionally, call this after reading in an image to load it into the tree.
2308        This saves time by preventing a reread of the same information.
2309        '''
2310        if ParentFrame:
2311            ParentFrame.ImageZ = self.Image   # store the image for plotting
2312            ParentFrame.oldImagefile = imagefile # save the name of the last image file read
2313            ParentFrame.oldImageTag = imagetag   # save the tag of the last image file read
2314
2315#################################################################################################
2316# shortcut routines
2317exp = np.exp
2318sind = sin = s = lambda x: np.sin(x*np.pi/180.)
2319cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
2320tand = tan = t = lambda x: np.tan(x*np.pi/180.)
2321sqrt = sq = lambda x: np.sqrt(x)
2322pi = lambda: np.pi
2323class ExpressionObj(object):
2324    '''Defines an object with a user-defined expression, to be used for
2325    secondary fits or restraints. Object is created null, but is changed
2326    using :meth:`LoadExpression`. This contains only the minimum
2327    information that needs to be stored to save and load the expression
2328    and how it is mapped to GSAS-II variables.
2329    '''
2330    def __init__(self):
2331        self.expression = ''
2332        'The expression as a text string'
2333        self.assgnVars = {}
2334        '''A dict where keys are label names in the expression mapping to a GSAS-II
2335        variable. The value a G2 variable name.
2336        Note that the G2 variable name may contain a wild-card and correspond to
2337        multiple values.
2338        '''
2339        self.freeVars = {}
2340        '''A dict where keys are label names in the expression mapping to a free
2341        parameter. The value is a list with:
2342
2343         * a name assigned to the parameter
2344         * a value for to the parameter and
2345         * a flag to determine if the variable is refined.
2346        '''
2347        self.depVar = None
2348
2349        self.lastError = ('','')
2350        '''Shows last encountered error in processing expression
2351        (list of 1-3 str values)'''
2352
2353        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
2354        self.distance_atoms = None  # to be used for defining atom distances
2355
2356    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
2357        '''Load the expression and associated settings into the object. Raises
2358        an exception if the expression is not parsed, if not all functions
2359        are defined or if not all needed parameter labels in the expression
2360        are defined.
2361
2362        This will not test if the variable referenced in these definitions
2363        are actually in the parameter dictionary. This is checked when the
2364        computation for the expression is done in :meth:`SetupCalc`.
2365
2366        :param str expr: the expression
2367        :param list exprVarLst: parameter labels found in the expression
2368        :param dict varSelect: this will be 0 for Free parameters
2369          and non-zero for expression labels linked to G2 variables.
2370        :param dict varName: Defines a name (str) associated with each free parameter
2371        :param dict varValue: Defines a value (float) associated with each free parameter
2372        :param dict varRefflag: Defines a refinement flag (bool)
2373          associated with each free parameter
2374        '''
2375        self.expression = expr
2376        self.compiledExpr = None
2377        self.freeVars = {}
2378        self.assgnVars = {}
2379        for v in exprVarLst:
2380            if varSelect[v] == 0:
2381                self.freeVars[v] = [
2382                    varName.get(v),
2383                    varValue.get(v),
2384                    varRefflag.get(v),
2385                    ]
2386            else:
2387                self.assgnVars[v] = varName[v]
2388        self.CheckVars()
2389
2390    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
2391        '''Load the expression and associated settings from the object into
2392        arrays used for editing.
2393
2394        :param list exprVarLst: parameter labels found in the expression
2395        :param dict varSelect: this will be 0 for Free parameters
2396          and non-zero for expression labels linked to G2 variables.
2397        :param dict varName: Defines a name (str) associated with each free parameter
2398        :param dict varValue: Defines a value (float) associated with each free parameter
2399        :param dict varRefflag: Defines a refinement flag (bool)
2400          associated with each free parameter
2401
2402        :returns: the expression as a str
2403        '''
2404        for v in self.freeVars:
2405            varSelect[v] = 0
2406            varName[v] = self.freeVars[v][0]
2407            varValue[v] = self.freeVars[v][1]
2408            varRefflag[v] = self.freeVars[v][2]
2409        for v in self.assgnVars:
2410            varSelect[v] = 1
2411            varName[v] = self.assgnVars[v]
2412        return self.expression
2413
2414    def GetVaried(self):
2415        'Returns the names of the free parameters that will be refined'
2416        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
2417
2418    def GetVariedVarVal(self):
2419        'Returns the names and values of the free parameters that will be refined'
2420        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
2421
2422    def UpdateVariedVars(self,varyList,values):
2423        'Updates values for the free parameters (after a refinement); only updates refined vars'
2424        for v in self.freeVars:
2425            if not self.freeVars[v][2]: continue
2426            if "::"+self.freeVars[v][0] not in varyList: continue
2427            indx = list(varyList).index("::"+self.freeVars[v][0])
2428            self.freeVars[v][1] = values[indx]
2429
2430    def GetIndependentVars(self):
2431        'Returns the names of the required independent parameters used in expression'
2432        return [self.assgnVars[v] for v in self.assgnVars]
2433
2434    def CheckVars(self):
2435        '''Check that the expression can be parsed, all functions are
2436        defined and that input loaded into the object is internally
2437        consistent. If not an Exception is raised.
2438
2439        :returns: a dict with references to packages needed to
2440          find functions referenced in the expression.
2441        '''
2442        ret = self.ParseExpression(self.expression)
2443        if not ret:
2444            raise Exception("Expression parse error")
2445        exprLblList,fxnpkgdict = ret
2446        # check each var used in expression is defined
2447        defined = list(self.assgnVars.keys()) + list(self.freeVars.keys())
2448        notfound = []
2449        for var in exprLblList:
2450            if var not in defined:
2451                notfound.append(var)
2452        if notfound:
2453            msg = 'Not all variables defined'
2454            msg1 = 'The following variables were not defined: '
2455            msg2 = ''
2456            for var in notfound:
2457                if msg: msg += ', '
2458                msg += var
2459            self.lastError = (msg1,'  '+msg2)
2460            raise Exception(msg)
2461        return fxnpkgdict
2462
2463    def ParseExpression(self,expr):
2464        '''Parse an expression and return a dict of called functions and
2465        the variables used in the expression. Returns None in case an error
2466        is encountered. If packages are referenced in functions, they are loaded
2467        and the functions are looked up into the modules global
2468        workspace.
2469
2470        Note that no changes are made to the object other than
2471        saving an error message, so that this can be used for testing prior
2472        to the save.
2473
2474        :returns: a list of used variables
2475        '''
2476        self.lastError = ('','')
2477        import ast
2478        def FindFunction(f):
2479            '''Find the object corresponding to function f
2480            :param str f: a function name such as 'numpy.exp'
2481            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
2482              that defines the package location(s) and where pkgobj
2483              defines the object associated with the function.
2484              If the function is not found, pkgobj is None.
2485            '''
2486            df = f.split('.')
2487            pkgdict = {}
2488            # no listed package, try in current namespace
2489            if len(df) == 1:
2490                try:
2491                    fxnobj = eval(f)
2492                    return pkgdict,fxnobj
2493                except (AttributeError, NameError):
2494                    return None,None
2495            else:
2496                try:
2497                    fxnobj = eval(f)
2498                    pkgdict[df[0]] = eval(df[0])
2499                    return pkgdict,fxnobj
2500                except (AttributeError, NameError):
2501                    pass
2502            # includes a package, lets try to load the packages
2503            pkgname = ''
2504            path = sys.path+['./',]
2505            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
2506                if pkgname:
2507                    pkgname += '.' + pkg
2508                else:
2509                    pkgname = pkg
2510                fp = None
2511                try:
2512                    fp, fppath,desc = imp.find_module(pkg,path)
2513                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
2514                    pkgdict[pkgname] = pkgobj
2515                    path = [fppath]
2516                except Exception as msg:
2517                    print('load of '+pkgname+' failed with error='+str(msg))
2518                    return {},None
2519                finally:
2520                    if fp: fp.close()
2521                try:
2522                    #print 'before',pkgdict.keys()
2523                    fxnobj = eval(f,globals(),pkgdict)
2524                    #print 'after 1',pkgdict.keys()
2525                    #fxnobj = eval(f,pkgdict)
2526                    #print 'after 2',pkgdict.keys()
2527                    return pkgdict,fxnobj
2528                except:
2529                    continue
2530            return None # not found
2531        def ASTtransverse(node,fxn=False):
2532            '''Transverse a AST-parsed expresson, compiling a list of variables
2533            referenced in the expression. This routine is used recursively.
2534
2535            :returns: varlist,fxnlist where
2536              varlist is a list of referenced variable names and
2537              fxnlist is a list of used functions
2538            '''
2539            varlist = []
2540            fxnlist = []
2541            if isinstance(node, list):
2542                for b in node:
2543                    v,f = ASTtransverse(b,fxn)
2544                    varlist += v
2545                    fxnlist += f
2546            elif isinstance(node, ast.AST):
2547                for a, b in ast.iter_fields(node):
2548                    if isinstance(b, ast.AST):
2549                        if a == 'func':
2550                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
2551                            continue
2552                        v,f = ASTtransverse(b,fxn)
2553                        varlist += v
2554                        fxnlist += f
2555                    elif isinstance(b, list):
2556                        v,f = ASTtransverse(b,fxn)
2557                        varlist += v
2558                        fxnlist += f
2559                    elif node.__class__.__name__ == "Name":
2560                        varlist += [b]
2561                    elif fxn and node.__class__.__name__ == "Attribute":
2562                        varlist += [b]
2563            return varlist,fxnlist
2564        try:
2565            exprast = ast.parse(expr)
2566        except SyntaxError:
2567            s = ''
2568            import traceback
2569            for i in traceback.format_exc().splitlines()[-3:-1]:
2570                if s: s += "\n"
2571                s += str(i)
2572            self.lastError = ("Error parsing expression:",s)
2573            return
2574        # find the variables & functions
2575        v,f = ASTtransverse(exprast)
2576        varlist = sorted(list(set(v)))
2577        fxnlist = list(set(f))
2578        pkgdict = {}
2579        # check the functions are defined
2580        for fxn in fxnlist:
2581            fxndict,fxnobj = FindFunction(fxn)
2582            if not fxnobj:
2583                self.lastError = ("Error: Invalid function",fxn,
2584                                  "is not defined")
2585                return
2586            if not hasattr(fxnobj,'__call__'):
2587                self.lastError = ("Error: Not a function.",fxn,
2588                                  "cannot be called as a function")
2589                return
2590            pkgdict.update(fxndict)
2591        return varlist,pkgdict
2592
2593    def GetDepVar(self):
2594        'return the dependent variable, or None'
2595        return self.depVar
2596
2597    def SetDepVar(self,var):
2598        'Set the dependent variable, if used'
2599        self.depVar = var
2600#==========================================================================
2601class ExpressionCalcObj(object):
2602    '''An object used to evaluate an expression from a :class:`ExpressionObj`
2603    object.
2604
2605    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
2606      an expression string and mappings for the parameter labels in that object.
2607    '''
2608    def __init__(self,exprObj):
2609        self.eObj = exprObj
2610        'The expression and mappings; a :class:`ExpressionObj` object'
2611        self.compiledExpr = None
2612        'The expression as compiled byte-code'
2613        self.exprDict = {}
2614        '''dict that defines values for labels used in expression and packages
2615        referenced by functions
2616        '''
2617        self.lblLookup = {}
2618        '''Lookup table that specifies the expression label name that is
2619        tied to a particular GSAS-II parameters in the parmDict.
2620        '''
2621        self.fxnpkgdict = {}
2622        '''a dict with references to packages needed to
2623        find functions referenced in the expression.
2624        '''
2625        self.varLookup = {}
2626        '''Lookup table that specifies the GSAS-II variable(s)
2627        indexed by the expression label name. (Used for only for diagnostics
2628        not evaluation of expression.)
2629        '''
2630        self.su = None
2631        '''Standard error evaluation where supplied by the evaluator
2632        '''
2633        # Patch: for old-style expressions with a (now removed step size)
2634        if '2' in platform.python_version_tuple()[0]: 
2635            basestr = basestring
2636        else:
2637            basestr = str
2638        for v in self.eObj.assgnVars:
2639            if not isinstance(self.eObj.assgnVars[v], basestr):
2640                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
2641        self.parmDict = {}
2642        '''A copy of the parameter dictionary, for distance and angle computation
2643        '''
2644
2645    def SetupCalc(self,parmDict):
2646        '''Do all preparations to use the expression for computation.
2647        Adds the free parameter values to the parameter dict (parmDict).
2648        '''
2649        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2650            return
2651        self.fxnpkgdict = self.eObj.CheckVars()
2652        # all is OK, compile the expression
2653        self.compiledExpr = compile(self.eObj.expression,'','eval')
2654
2655        # look at first value in parmDict to determine its type
2656        parmsInList = True
2657        if '2' in platform.python_version_tuple()[0]: 
2658            basestr = basestring
2659        else:
2660            basestr = str
2661        for key in parmDict:
2662            val = parmDict[key]
2663            if isinstance(val, basestr):
2664                parmsInList = False
2665                break
2666            try: # check if values are in lists
2667                val = parmDict[key][0]
2668            except (TypeError,IndexError):
2669                parmsInList = False
2670            break
2671
2672        # set up the dicts needed to speed computations
2673        self.exprDict = {}
2674        self.lblLookup = {}
2675        self.varLookup = {}
2676        for v in self.eObj.freeVars:
2677            varname = self.eObj.freeVars[v][0]
2678            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
2679            self.lblLookup[varname] = v
2680            self.varLookup[v] = varname
2681            if parmsInList:
2682                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
2683            else:
2684                parmDict[varname] = self.eObj.freeVars[v][1]
2685            self.exprDict[v] = self.eObj.freeVars[v][1]
2686        for v in self.eObj.assgnVars:
2687            varname = self.eObj.assgnVars[v]
2688            if varname in parmDict:
2689                self.lblLookup[varname] = v
2690                self.varLookup[v] = varname
2691                if parmsInList:
2692                    self.exprDict[v] = parmDict[varname][0]
2693                else:
2694                    self.exprDict[v] = parmDict[varname]
2695            elif '*' in varname:
2696                varlist = LookupWildCard(varname,list(parmDict.keys()))
2697                if len(varlist) == 0:
2698                    raise Exception("No variables match "+str(v))
2699                for var in varlist:
2700                    self.lblLookup[var] = v
2701                if parmsInList:
2702                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
2703                else:
2704                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
2705                self.varLookup[v] = [var for var in varlist]
2706            else:
2707                self.exprDict[v] = None
2708#                raise Exception,"No value for variable "+str(v)
2709        self.exprDict.update(self.fxnpkgdict)
2710
2711    def UpdateVars(self,varList,valList):
2712        '''Update the dict for the expression with a set of values
2713        :param list varList: a list of variable names
2714        :param list valList: a list of corresponding values
2715        '''
2716        for var,val in zip(varList,valList):
2717            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
2718
2719    def UpdateDict(self,parmDict):
2720        '''Update the dict for the expression with values in a dict
2721        :param dict parmDict: a dict of values, items not in use are ignored
2722        '''
2723        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2724            self.parmDict = parmDict
2725            return
2726        for var in parmDict:
2727            if var in self.lblLookup:
2728                self.exprDict[self.lblLookup[var]] = parmDict[var]
2729
2730    def EvalExpression(self):
2731        '''Evaluate an expression. Note that the expression
2732        and mapping are taken from the :class:`ExpressionObj` expression object
2733        and the parameter values were specified in :meth:`SetupCalc`.
2734        :returns: a single value for the expression. If parameter
2735        values are arrays (for example, from wild-carded variable names),
2736        the sum of the resulting expression is returned.
2737
2738        For example, if the expression is ``'A*B'``,
2739        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
2740
2741        [0.5, 1, 0.5]
2742
2743        then the result will be ``4.0``.
2744        '''
2745        self.su = None
2746        if self.eObj.expression.startswith('Dist'):
2747#            GSASIIpath.IPyBreak()
2748            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
2749            return dist
2750        elif self.eObj.expression.startswith('Angle'):
2751            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
2752            return angle
2753        if self.compiledExpr is None:
2754            raise Exception("EvalExpression called before SetupCalc")
2755        try:
2756            val = eval(self.compiledExpr,globals(),self.exprDict)
2757        except TypeError:
2758            val = None
2759        if not np.isscalar(val):
2760            val = np.sum(val)
2761        return val
2762
2763class G2Exception(Exception):
2764    'A generic GSAS-II exception class'
2765    def __init__(self,msg):
2766        self.msg = msg
2767    def __str__(self):
2768        return repr(self.msg)
2769
2770class G2RefineCancel(Exception):
2771    'Raised when Cancel is pressed in a refinement dialog'
2772    def __init__(self,msg):
2773        self.msg = msg
2774    def __str__(self):
2775        return repr(self.msg)
2776   
2777def HowDidIgetHere(wherecalledonly=False):
2778    '''Show a traceback with calls that brought us to the current location.
2779    Used for debugging.
2780    '''
2781    import traceback
2782    if wherecalledonly:
2783        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
2784        print(i.strip().rstrip())
2785    else:
2786        print (70*'*')
2787        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
2788        print (70*'*')
2789
2790# Note that this is GUI code and should be moved at somepoint
2791def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
2792    '''Create and initialize a new set of PDF tree entries
2793
2794    :param Frame G2frame: main GSAS-II tree frame object
2795    :param str PWDRtree: name of PWDR to be used to create PDF item
2796    :param dict ElList: data structure with composition
2797    :param list Qlimits: Q limits to be used for computing the PDF
2798    :param float numAtm: no. atom in chemical formula
2799    :param float FltBkg: flat background value
2800    :param list PDFnames: previously used PDF names
2801
2802    :returns: the Id of the newly created PDF entry
2803    '''
2804    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
2805    if PDFname in PDFnames:
2806        print('Skipping, entry already exists: '+PDFname)
2807        return None
2808    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
2809    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
2810    Data = {
2811        'Sample':{'Name':PWDRtree,'Mult':1.0},
2812        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
2813        'Container':{'Name':'','Mult':-1.0,'Refine':False},
2814        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
2815        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
2816        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
2817        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
2818        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
2819    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
2820    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
2821        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
2822    return Id
2823#%%
2824class ShowTiming(object):
2825    '''An object to use for timing repeated sections of code.
2826
2827    Create the object with::
2828       tim0 = ShowTiming()
2829
2830    Tag sections of code to be timed with::
2831       tim0.start('start')
2832       tim0.start('in section 1')
2833       tim0.start('in section 2')
2834       
2835    etc. (Note that each section should have a unique label.)
2836
2837    After the last section, end timing with::
2838       tim0.end()
2839
2840    Show timing results with::
2841       tim0.show()
2842       
2843    '''
2844    def __init__(self):
2845        self.timeSum =  []
2846        self.timeStart = []
2847        self.label = []
2848        self.prev = None
2849    def start(self,label):
2850        import time
2851        if label in self.label:
2852            i = self.label.index(label)
2853            self.timeStart[i] = time.time()
2854        else:
2855            i = len(self.label)
2856            self.timeSum.append(0.0)
2857            self.timeStart.append(time.time())
2858            self.label.append(label)
2859        if self.prev is not None:
2860            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
2861        self.prev = i
2862    def end(self):
2863        import time
2864        if self.prev is not None:
2865            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
2866        self.prev = None
2867    def show(self):
2868        sumT = sum(self.timeSum)
2869        print('Timing results (total={:.2f} sec)'.format(sumT))
2870        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
2871            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
2872#%%
2873
2874if __name__ == "__main__":
2875    # test variable descriptions
2876    for var in '0::Afrac:*',':1:Scale','1::dAx:0','::undefined':
2877        v = var.split(':')[2]
2878        print(var+':\t', getDescr(v),getVarStep(v))
2879    import sys; sys.exit()
2880    # test equation evaluation
2881    def showEQ(calcobj):
2882        print (50*'=')
2883        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
2884        for v in sorted(calcobj.varLookup):
2885            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
2886        # print '  Derivatives'
2887        # for v in calcobj.derivStep.keys():
2888        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2889
2890    obj = ExpressionObj()
2891
2892    obj.expression = "A*np.exp(B)"
2893    obj.assgnVars =  {'B': '0::Afrac:1'}
2894    obj.freeVars =  {'A': [u'A', 0.5, True]}
2895    #obj.CheckVars()
2896    calcobj = ExpressionCalcObj(obj)
2897
2898    obj1 = ExpressionObj()
2899    obj1.expression = "A*np.exp(B)"
2900    obj1.assgnVars =  {'B': '0::Afrac:*'}
2901    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
2902    #obj.CheckVars()
2903    calcobj1 = ExpressionCalcObj(obj1)
2904
2905    obj2 = ExpressionObj()
2906    obj2.distance_stuff = np.array([[0,1],[1,-1]])
2907    obj2.expression = "Dist(1,2)"
2908    GSASIIpath.InvokeDebugOpts()
2909    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2910    calcobj2 = ExpressionCalcObj(obj2)
2911    calcobj2.SetupCalc(parmDict2)
2912    showEQ(calcobj2)
2913
2914    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2915    print ('\nDict = '+parmDict1)
2916    calcobj.SetupCalc(parmDict1)
2917    showEQ(calcobj)
2918    calcobj1.SetupCalc(parmDict1)
2919    showEQ(calcobj1)
2920
2921    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2922    print ('Dict = '+parmDict2)
2923    calcobj.SetupCalc(parmDict2)
2924    showEQ(calcobj)
2925    calcobj1.SetupCalc(parmDict2)
2926    showEQ(calcobj1)
2927    calcobj2.SetupCalc(parmDict2)
2928    showEQ(calcobj2)
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