source: trunk/GSASIIobj.py @ 4588

Last change on this file since 4588 was 4588, checked in by toby, 2 years ago

use G2VarObj for param limits; add more info to seq. ref. done dialog; show Frozen in show LS parameters

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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2020-10-11 17:07:42 +0000 (Sun, 11 Oct 2020) $
5# $Author: toby $
6# $Revision: 4588 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 4588 2020-10-11 17:07:42Z 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.. Next command allows \AA to be used in HTML
19
20.. only:: html
21
22   :math:`\\require{mediawiki-texvc}`
23
24.. _Constraints_table:
25
26.. index::
27   single: Constraints object description
28   single: Data object descriptions; Constraints
29
30Constraints Tree Item
31----------------------
32
33Constraints are stored in a dict, separated into groups.
34Note that parameter are named in the following pattern,
35p:h:<var>:n, where p is the phase number, h is the histogram number
36<var> is a variable name and n is the parameter number.
37If a parameter does not depend on a histogram or phase or is unnumbered, that
38number is omitted.
39Note that the contents of each dict item is a List where each element in the
40list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
41The constraints in this form are converted in
42:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
43
44The keys in the Constraints dict are:
45
46.. tabularcolumns:: |l|p{4.5in}|
47
48==========  ====================================================
49  key         explanation
50==========  ====================================================
51Hist        This specifies a list of constraints on
52            histogram-related parameters,
53            which will be of form :h:<var>:n.
54HAP         This specifies a list of constraints on parameters
55            that are defined for every histogram in each phase
56            and are of form p:h:<var>:n.
57Phase       This specifies a list of constraints on phase
58            parameters,
59            which will be of form p::<var>:n.
60Global      This specifies a list of constraints on parameters
61            that are not tied to a histogram or phase and
62            are of form ::<var>:n
63==========  ====================================================
64
65.. _Constraint_definitions_table:
66
67.. index::
68   single: Constraint definition object description
69   single: Data object descriptions; Constraint Definition
70
71Each constraint is defined as an item in a list. Each constraint is of form::
72
73[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
74
75Where the variable pair list item containing two values [<mult>, <var>], where:
76
77  * <mult> is a multiplier for the constraint (float)
78  * <var> a :class:`G2VarObj` object (previously a str variable name of form
79      'p:h:name[:at]')
80
81Note that the last three items in the list play a special role:
82
83 * <fixedval> is the fixed value for a `constant equation` (``constype=c``)
84   constraint or is None. For a `New variable` (``constype=f``) constraint,
85   a variable name can be specified as a str (used for externally
86   generated constraints)
87 * <varyflag> is True or False for `New variable` (``constype=f``) constraints
88   or is None. This indicates if this variable should be refined.
89 * <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:
90
91    * 'e' defines a set of equivalent variables. Only the first variable is refined (if the
92      appropriate refine flag is set) and and all other equivalent variables in the list
93      are generated from that variable, using the appropriate multipliers.
94    * 'c' defines a constraint equation of form,
95      :math:`m_1 \\times var_1 + m_2 \\times var_2 + ... = c`
96    * 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
97      even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
98      constraint and the mult value is ignored.
99      This is of particular value when needing to hold one or more variables where a
100      single flag controls a set of variables such as, coordinates,
101      the reciprocal metric tensor or anisotropic displacement parameter.
102    * 'f' defines a new variable (function) according to relationship
103      :math:`newvar = m_1 \\times var_1 + m_2 \\times var_2 + ...`
104
105.. _Covariance_table:
106
107.. index::
108   single: Covariance description
109   single: Data object descriptions; Covariance
110
111Covariance Tree Item
112--------------------
113
114The Covariance tree item has results from the last least-squares run. They
115are stored in a dict with these keys:
116
117.. tabularcolumns:: |l|l|p{4in}|
118
119=============  ===============  ====================================================
120  key            sub-key        explanation
121=============  ===============  ====================================================
122newCellDict    \                (dict) ith lattice parameters computed by
123                                :func:`GSASIIstrMath.GetNewCellParms`
124title          \                (str) Name of gpx file(?)
125variables      \                (list) Values for all N refined variables
126                                (list of float values, length N,
127                                ordered to match varyList)
128sig            \                (list) Uncertainty values for all N refined variables
129                                (list of float values, length N,
130                                ordered to match varyList)
131varyList       \                (list of str values, length N) List of directly refined variables
132                               
133newAtomDict    \                (dict) atom position values computed in
134                                :func:`GSASIIstrMath.ApplyXYZshifts`
135Rvals          \                (dict) R-factors, GOF, Marquardt value for last
136                                refinement cycle
137\              Nobs             (int) Number of observed data points
138\              Rwp              (float) overall weighted profile R-factor (%)
139\              chisq            (float) :math:`\sum w*(I_{obs}-I_{calc})^2`                               
140                                for all data.
141                                Note: this is not the reduced :math:`\chi^2`.
142\              lamMax           (float) Marquardt value applied to Hessian diagonal
143\              GOF              (float) The goodness-of-fit, aka square root of
144                                the reduced chi squared.
145covMatrix      \                (np.array) The (NxN) covVariance matrix
146=============  ===============  ====================================================
147
148.. _Phase_table:
149
150.. index::
151   single: Phase object description
152   single: Data object descriptions; Phase
153
154Phase Tree Items
155----------------
156
157Phase information is stored in the GSAS-II data tree as children of the
158Phases item in a dict with keys:
159
160.. tabularcolumns:: |l|l|p{4in}|
161
162==========  ===============     =====================================================================================================
163  key         sub-key           explanation
164==========  ===============     =====================================================================================================
165General         \               (dict) Overall information for the phase
166  \         3Dproj              (list of str) projections for 3D pole distribution plots
167  \         AngleRadii          (list of floats) Default radius for each atom used to compute
168                                interatomic angles
169  \         AtomMass            (list of floats) Masses for atoms
170  \         AtomPtrs            (list of int) four locations (cx,ct,cs & cu) to use to pull info
171                                from the atom records
172  \         AtomTypes           (llist of str) Atom types
173  \         BondRadii           (list of floats) Default radius for each atom used to compute
174                                interatomic distances
175  \         Cell                Unit cell parameters & ref. flag
176                                (list with 8 items. All but first item are float.)
177
178                                 0: cell refinement flag (True/False),
179                                 1-3: a, b, c, (:math:`\\AA`)
180                                 4-6: alpha, beta & gamma, (degrees)
181                                 7: volume (:math:`\\AA^3`)
182  \         Color               (list of (r,b,g) triplets) Colors for atoms
183  \         Compare             (dict) Polygon comparison parameters
184  \         Data plot type      (str) data plot type ('Mustrain', 'Size' or
185                                'Preferred orientation') for powder data
186  \         DisAglCtls          (dDict) with distance/angle search controls,
187                                which has keys 'Name', 'AtomTypes',
188                                'BondRadii', 'AngleRadii' which are as above
189                                except are possibly edited. Also contains
190                                'Factors', which is a 2 element list with
191                                a multiplier for bond and angle search range
192                                [typically (0.85,0.85)].
193  \         F000X               (float) x-ray F(000) intensity
194  \         F000N               (float) neutron F(000) intensity
195  \         Flip                (dict) Charge flip controls
196  \         HydIds              (dict) geometrically generated hydrogen atoms
197  \         Isotope             (dict) Isotopes for each atom type
198  \         Isotopes            (dict) Scattering lengths for each isotope
199                                combination for each element in phase
200  \         MCSA controls       (dict) Monte Carlo-Simulated Annealing controls
201  \         Map                 (dict) Map parameters
202  \         Mass                (float) Mass of unit cell contents in g/mol
203  \         Modulated           (bool) True if phase modulated
204  \         Mydir               (str) Directory of current .gpx file
205  \         Name                (str) Phase name
206  \         NoAtoms             (dict) Number of atoms per unit cell of each type
207  \         POhkl               (list) March-Dollase preferred orientation direction
208  \         Pawley dmin         (float) maximum Q (as d-space) to use for Pawley extraction
209  \         Pawley dmax         (float) minimum Q (as d-space) to use for Pawley extraction
210  \         Pawley neg wt       (float) Restraint value for negative Pawley intensities
211  \         SGData              (object) Space group details as a
212                                :ref:`space group (SGData) <SGData_table>`
213                                object, as defined in :func:`GSASIIspc.SpcGroup`.
214  \         SH Texture          (dict) Spherical harmonic preferred orientation parameters
215  \         Super               (int) dimension of super group (0,1 only)
216  \         Type                (str) phase type (e.g. 'nuclear')
217  \         Z                   (dict) Atomic numbers for each atom type
218  \         doDysnomia          (bool) flag for max ent map modification via Dysnomia
219  \         doPawley            (bool) Flag for Pawley intensity extraction
220  \         vdWRadii            (dict) Van der Waals radii for each atom type
221ranId           \               (int) unique random number Id for phase
222pId             \               (int) Phase Id number for current project.
223Atoms           \               (list of lists) Atoms in phase as a list of lists. The outer list
224                                is for each atom, the inner list contains varying
225                                items depending on the type of phase, see
226                                the :ref:`Atom Records <Atoms_table>` description.
227Drawing         \               (dict) Display parameters
228\           Atoms               (list of lists) with an entry for each atom that is drawn
229\           Plane               (list) Controls for contour density plane display
230\           Quaternion          (4 element np.array) Viewing quaternion
231\           Zclip               (float) clipping distance in :math:`\\AA`
232\           Zstep               (float) Step to de/increase Z-clip
233\           atomPtrs            (list) positions of x, type, site sym, ADP flag in Draw Atoms
234\           backColor           (list) background for plot as and R,G,B triplet
235                                (default = [0, 0, 0], black).
236\           ballScale           (float) Radius of spheres in ball-and-stick display
237\           bondList            (dict) Bonds
238\           bondRadius          (float) Radius of binds in :math:`\\AA`
239\           cameraPos           (float) Viewing position in :math:`\\AA` for plot
240\           contourLevel        (float) map contour level in :math:`e/\\AA^3`
241\           contourMax          (float) map contour maximum
242\           depthFog            (bool) True if use depthFog on plot - set currently as False
243\           ellipseProb         (float) Probability limit for display of thermal
244                                ellipsoids in % .
245\           magMult             (float) multiplier for magnetic moment arrows
246\           mapSize             (float) x & y dimensions of contourmap (fixed internally)
247\           modelView           (4,4 array) from openGL drawing transofmation matrix
248\           oldxy               (list with two floats) previous view point
249\           radiusFactor        (float) Distance ratio for searching for bonds. Bonds
250                                are located that are within r(Ra+Rb) and (Ra+Rb)/r
251                                where Ra and Rb are the atomic radii.
252\           selectedAtoms       (list of int values) List of selected atoms
253\           showABC             (bool) Flag to show view point triplet. True=show.
254\           showHydrogen        (bool) Flag to control plotting of H atoms.
255\           showRigidBodies     (bool) Flag to highlight rigid body placement
256\           showSlice           (bool) flag to show contour map
257\           sizeH               (float) Size ratio for H atoms
258\           unitCellBox         (bool) Flag to control display of the unit cell.
259\           vdwScale            (float) Multiplier of van der Waals radius for display of vdW spheres.
260\           viewDir             (np.array with three floats) cartesian viewing direction
261\           viewPoint           (list of lists) First item in list is [x,y,z]
262                                in fractional coordinates for the center of
263                                the plot. Second item list of previous & current
264                                atom number viewed (may be [0,0])
265RBModels        \               Rigid body assignments (note Rigid body definitions
266                                are stored in their own main top-level tree entry.)
267RMC             \               (dict) RMCProfile & rmcfull controls
268Pawley ref      \               (list) Pawley reflections
269Histograms      \               (dict of dicts) The key for the outer dict is
270                                the histograms tied to this phase. The inner
271                                dict contains the combined phase/histogram
272                                parameters for items such as scale factors,
273                                size and strain parameters. The following are the
274                                keys to the inner dict. (dict)
275\           Babinet             (dict) For protein crystallography. Dictionary with two
276                                entries, 'BabA', 'BabU'
277\           Extinction          (list of float, bool) Extinction parameter
278\           Flack               (list of [float, bool]) Flack parameter & refine flag
279\           HStrain             (list of two lists) Hydrostatic strain. The first is
280                                a list of the HStrain parameters (1, 2, 3, 4, or 6
281                                depending on unit cell), the second is a list of boolean
282                                refinement parameters (same length)
283\           Histogram           (str) The name of the associated histogram
284\           Layer Disp          (list of [float, bool]) Layer displacement in beam direction & refine flag
285\           LeBail              (bool) Flag for LeBail extraction
286\           Mustrain            (list) Microstrain parameters, in order:
287   
288                                0. Type, one of  u'isotropic', u'uniaxial', u'generalized'
289                                1. Isotropic/uniaxial parameters - list of 3 floats
290                                2. Refinement flags - list of 3 bools
291                                3. Microstrain axis - list of 3 ints, [h, k, l]
292                                4. Generalized mustrain parameters - list of 2-6 floats, depending on space group
293                                5. Generalized refinement flags - list of bools, corresponding to the parameters of (4)
294\           Pref.Ori.           (list) Preferred Orientation. List of eight parameters.
295                                Items marked SH are only used for Spherical Harmonics.
296                               
297                                0. (str) Type, 'MD' for March-Dollase or 'SH' for Spherical Harmonics
298                                1. (float) Value
299                                2. (bool) Refinement flag
300                                3. (list) Preferred direction, list of ints, [h, k, l]
301                                4. (int) SH - number of terms
302                                5. (dict) SH - 
303                                6. (list) SH
304                                7. (float) SH
305\           Scale               (list of [float, bool]) Phase fraction & refine flag
306\           Size                List of crystallite size parameters, in order:
307
308                                0. (str) Type, one of  u'isotropic', u'uniaxial', u'ellipsoidal'
309                                1. (list) Isotropic/uniaxial parameters - list of 3 floats
310                                2. (list) Refinement flags - list of 3 bools
311                                3. (list) Size axis - list of 3 ints, [h, k, l]
312                                4. (list) Ellipsoidal size parameters - list of 6 floats
313                                5. (list) Ellipsoidal refinement flags - list of bools, corresponding to the parameters of (4)
314\           Use                 (bool) True if this histogram is to be used in refinement
315\           newLeBail           (bool) Whether to perform a new LeBail extraction
316MCSA            \               (dict) Monte-Carlo simulated annealing parameters
317==========  ===============     =====================================================================================================
318
319.. _RBData_table:
320
321.. index::
322   single: Rigid Body Data description
323   single: Data object descriptions; Rigid Body Data
324
325Rigid Body Objects
326------------------
327
328Rigid body descriptions are available for two types of rigid bodies: 'Vector'
329and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
330with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
331with defined refinable torsion angles.
332
333.. tabularcolumns:: |l|l|p{4in}|
334
335==========  ===============     ====================================================
336  key         sub-key           explanation
337==========  ===============     ====================================================
338Vector      RBId                (dict of dict) vector rigid bodies
339\           AtInfo              (dict) Drad, Color: atom drawing radius & color for each atom type
340\           RBname              (str) Name assigned by user to rigid body
341\           VectMag             (list) vector magnitudes in :math:`\\AA`
342\           rbXYZ               (list of 3 float Cartesian coordinates for Vector rigid body )
343\           rbRef               (list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin
344                                definition, use center of atoms flag
345\           VectRef             (list of bool refinement flags for VectMag values )
346\           rbTypes             (list of str) Atom types for each atom in rigid body
347\           rbVect              (list of lists) Cartesian vectors for each translation used to build rigid body
348\           useCount            (int) Number of times rigid body is used in any structure
349Residue     RBId                (dict of dict) residue rigid bodies
350\           AtInfo              (dict) Drad, Color: atom drawing radius & color for each atom type
351\           RBname              (str) Name assigned by user to rigid body
352\           rbXYZ               (list of 3 float) Cartesian coordinates for Residue rigid body
353\           rbTypes             (list of str) Atom types for each atom in rigid body
354\           atNames             (list of str) Names of each atom in rigid body (e.g. C1,N2...)
355\           rbRef               (list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin
356                                definition, use center of atoms flag
357\           rbSeq               (list) Orig,Piv,angle,Riding : definition of internal rigid body
358                                torsion; origin atom (int), pivot atom (int), torsion angle (float),
359                                riding atoms (list of int)
360\           SelSeq              (int,int) used by SeqSizer to identify objects
361\           useCount            (int)Number of times rigid body is used in any structure
362RBIds           \               (dict) unique Ids generated upon creation of each rigid body
363\           Vector              (list) Ids for each Vector rigid body
364\           Residue             (list) Ids for each Residue rigid body
365==========  ===============     ====================================================
366
367.. _SGData_table:
368
369.. index::
370   single: Space Group Data description
371   single: Data object descriptions; Space Group Data
372
373Space Group Objects
374-------------------
375
376Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
377and the information is placed in a SGdata object
378which is a dict with these keys. Magnetic ones are marked "mag"
379
380.. tabularcolumns:: |l|p{4.5in}|
381
382==========  ========================================================================================
383  key         explanation
384==========  ========================================================================================
385BNSlattsym  mag - (str) BNS magnetic space group symbol and centering vector
386GenFlg      mag - (list) symmetry generators indices
387GenSym      mag - (list) names for each generator
388MagMom      mag - (list) "time reversals" for each magnetic operator
389MagPtGp     mag - (str) Magnetic point group symbol
390MagSpGrp    mag - (str) Magnetic space group symbol
391OprNames    mag - (list) names for each space group operation
392SGCen       (np.array) Symmetry cell centering vectors. A (n,3) np.array
393            of centers. Will always have at least one row: ``np.array([[0, 0, 0]])``
394SGFixed     (bool) Only True if phase mported from a magnetic cif file
395            then the space group can not be changed by the user because
396            operator set from cif may be nonstandard
397SGGen       (list) generators
398SGGray      (bool) True if space group is a gray group (incommensurate magnetic structures)
399SGInv       (bool) True if centrosymmetric, False if not
400SGLatt      (str)Lattice centering type. Will be one of
401            P, A, B, C, I, F, R
402SGLaue      (str) one of the following 14 Laue classes:
403            -1, 2/m, mmm, 4/m, 4/mmm, 3R,
404            3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m
405SGOps       (list) symmetry operations as a list of form
406            ``[[M1,T1], [M2,T2],...]``
407            where :math:`M_n` is a 3x3 np.array
408            and :math:`T_n` is a length 3 np.array.
409            Atom coordinates are transformed where the
410            Asymmetric unit coordinates [X is (x,y,z)]
411            are transformed using
412            :math:`X^\prime = M_n*X+T_n`
413SGPolax     (str) Axes for space group polarity. Will be one of
414            '', 'x', 'y', 'x y', 'z', 'x z', 'y z',
415            'xyz'. In the case where axes are arbitrary
416            '111' is used (P 1, and ?).
417SGPtGrp     (str) Point group of the space group
418SGUniq      unique axis if monoclinic. Will be
419            a, b, or c for monoclinic space groups.
420            Will be blank for non-monoclinic.
421SGSpin      mag - (list) of spin flip operatiors (+1 or -1) for the space group operations
422SGSys       (str) symmetry unit cell: type one of
423            'triclinic', 'monoclinic', 'orthorhombic',
424            'tetragonal', 'rhombohedral', 'trigonal',
425            'hexagonal', 'cubic'
426SSGK1       (list) Superspace multipliers
427SpGrp       (str) space group symbol
428SpnFlp      mag - (list) Magnetic spin flips for every magnetic space group operator
429==========  ========================================================================================
430
431.. _SSGData_table:
432
433.. index::
434   single: Superspace Group Data description
435   single: Data object descriptions; Superspace Group Data
436
437Superspace groups [3+1] are interpreted by :func:`GSASIIspc.SSpcGroup`
438and the information is placed in a SSGdata object
439which is a dict with these keys:
440
441.. tabularcolumns:: |l|p{4.5in}|
442
443==========  ====================================================
444  key         explanation
445==========  ====================================================
446SSGCen      (list) 4D cell centering vectors [0,0,0,0] at least
447SSGK1       (list) Superspace multipliers
448SSGOps      (list) 4D symmetry operations as [M,T] so that M*x+T = x'
449SSpGrp      (str) superspace group symbol extension to space group
450            symbol, accidental spaces removed
451modQ        (list) modulation/propagation vector
452modSymb     (list of str) Modulation symbols
453==========  ====================================================
454
455
456.. _Atoms_table:
457
458.. index::
459   single: Atoms record description
460   single: Data object descriptions; Atoms record
461
462Atom Records
463------------
464
465If ``phasedict`` points to the phase information in the data tree, then
466atoms are contained in a list of atom records (list) in
467``phasedict['Atoms']``. Also needed to read atom information
468are four pointers, ``cx,ct,cs,cia = phasedict['General']['AtomPtrs']``,
469which define locations in the atom record, as shown below. Items shown are
470always present; additional ones for macromolecular phases are marked 'mm',
471and those for magnetic structures are marked 'mg'
472
473.. tabularcolumns:: |l|p{4.5in}|
474
475==============      ====================================================
476location            explanation
477==============      ====================================================
478ct-4                mm - (str) residue number
479ct-3                mm - (str) residue name (e.g. ALA)
480ct-2                mm - (str) chain label
481ct-1                (str) atom label
482ct                  (str) atom type
483ct+1                (str) refinement flags; combination of 'F', 'X', 'U', 'M'
484cx,cx+1,cx+2        (3 floats) the x,y and z coordinates
485cx+3                (float) site occupancy
486cx+4,cx+5,cx+6      mg - (list) atom magnetic moment along a,b,c in Bohr magnetons
487cs                  (str) site symmetry
488cs+1                (int) site multiplicity
489cia                 (str) ADP flag: Isotropic ('I') or Anisotropic ('A')
490cia+1               (float) Uiso
491cia+2...cia+7       (6 floats) U11, U22, U33, U12, U13, U23
492atom[cia+8]         (int) unique atom identifier
493
494==============      ====================================================
495
496.. _Drawing_atoms_table:
497
498.. index::
499   single: Drawing atoms record description
500   single: Data object descriptions; Drawing atoms record
501
502Drawing Atom Records
503--------------------
504
505If ``phasedict`` points to the phase information in the data tree, then
506drawing atoms are contained in a list of drawing atom records (list) in
507``phasedict['Drawing']['Atoms']``. Also needed to read atom information
508are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
509which define locations in the atom record, as shown below. Items shown are
510always present; additional ones for macromolecular phases are marked 'mm',
511and those for magnetic structures are marked 'mg'
512
513.. tabularcolumns:: |l|p{4.5in}|
514
515==============   ===================================================================================
516location            explanation
517==============   ===================================================================================
518ct-4                mm - (str) residue number
519ct-3                mm - (str) residue name (e.g. ALA)
520ct-2                mm - (str) chain label
521ct-1                (str) atom label
522ct                  (str) atom type
523cx,cx+1,cx+2        (3 floats) the x,y and z coordinates
524cx+3,cx+4,cx+5      mg - (3 floats) atom magnetic moment along a,b,c in Bohr magnetons
525cs-1                (str) Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1')
526cs                  (str) atom drawing style; e.g. 'balls & sticks'
527cs+1                (str) atom label style (e.g. 'name')
528cs+2                (int) atom color (RBG triplet)
529cs+3                (str) ADP flag: Isotropic ('I') or Anisotropic ('A')
530cs+4                (float) Uiso
531cs+5...cs+11        (6 floats) U11, U22, U33, U12, U13, U23
532ci                  (int) unique atom identifier; matches source atom Id in Atom Records
533==============   ===================================================================================
534
535.. _Powder_table:
536
537.. index::
538   single: Powder data object description
539   single: Data object descriptions; Powder Data
540
541Powder Diffraction Tree Items
542-----------------------------
543
544Every powder diffraction histogram is stored in the GSAS-II data tree
545with a top-level entry named beginning with the string "PWDR ". The
546diffraction data for that information are directly associated with
547that tree item and there are a series of children to that item. The
548routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
549and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
550load this information into a dictionary where the child tree name is
551used as a key, and the information in the main entry is assigned
552a key of ``Data``, as outlined below.
553
554.. tabularcolumns:: |p{1in}|p{1in}|p{4in}|
555
556======================     ===============  ===========================================================
557  key                       sub-key          explanation
558======================     ===============  ===========================================================
559Comments                    \               (list of str) Text strings extracted from the original powder
560                                            data header. These cannot be changed by the user;
561                                            it may be empty.
562Limits                      \               (list) two two element lists, as [[Ld,Hd],[L,H]]
563                                            where L and Ld are the current and default lowest
564                                            two-theta value to be used and
565                                            where H and Hd are the current and default highest
566                                            two-theta value to be used.
567Reflection Lists            \               (dict of dicts) with an entry for each phase in the
568                                            histogram. The contents of each dict item
569                                            is a dict containing reflections, as described in
570                                            the :ref:`Powder Reflections <PowderRefl_table>`
571                                            description.
572Instrument Parameters       \               (dict) The instrument parameters uses different dicts
573                                            for the constant wavelength (CW) and time-of-flight (TOF)
574                                            cases. See below for the descriptions of each.
575wtFactor                    \               (float) A weighting factor to increase or decrease
576                                            the leverage of data in the histogram .
577                                            A value of 1.0 weights the data with their
578                                            standard uncertainties and a larger value
579                                            increases the weighting of the data (equivalent
580                                            to decreasing the uncertainties).
581Sample Parameters           \               (dict) Parameters that describe how
582                                            the data were collected, as listed
583                                            below. Refinable parameters are a list containing
584                                            a float and a bool, where the second value
585                                            specifies if the value is refined, otherwise
586                                            the value is a float unless otherwise noted.
587\                           Scale           The histogram scale factor (refinable)
588\                           Absorption      The sample absorption coefficient as
589                                            :math:`\\mu r` where r is the radius
590                                            (refinable). Only valid for Debye-Scherrer geometry.
591\                           SurfaceRoughA   Surface roughness parameter A as defined by
592                                            Surotti, *J. Appl. Cryst*, **5**, 325-331, 1972.
593                                            (refinable - only valid for Bragg-Brentano geometry)
594\                           SurfaceRoughB   Surface roughness parameter B (refinable -
595                                            only valid for Bragg-Brentano geometry)
596\                           DisplaceX,      Sample displacement from goniometer center
597                            DisplaceY       where Y is along the beam direction and
598                                            X is perpendicular. Units are :math:`\\mu m`
599                                            (refinable).
600\                           Phi, Chi,       Goniometer sample setting angles, in degrees.
601                            Omega
602\                           Gonio. radius   Radius of the diffractometer in mm
603\                           InstrName       (str) A name for the instrument, used in preparing
604                                            a CIF .
605\                           Force,          Variables that describe how the measurement
606                            Temperature,    was performed. Not used directly in
607                            Humidity,       any computations.
608                            Pressure,
609                            Voltage
610\                           ranId           (int) The random-number Id for the histogram
611                                            (same value as where top-level key is ranId)
612\                           Type            (str) Type of diffraction data, may be 'Debye-Scherrer'
613                                            or 'Bragg-Brentano' .
614hId                         \               (int) The number assigned to the histogram when
615                                            the project is loaded or edited (can change)
616ranId                       \               (int) A random number id for the histogram
617                                            that does not change
618Background                  \               (list) The background is stored as a list with where
619                                            the first item in the list is list and the second
620                                            item is a dict. The list contains the background
621                                            function and its coefficients; the dict contains
622                                            Debye diffuse terms and background peaks.
623                                            (TODO: this needs to be expanded.)
624Data                        \               (list) The data consist of a list of 6 np.arrays
625                                            containing in order:
626
627                                            0. the x-postions (two-theta in degrees),
628                                            1. the intensity values (Yobs),
629                                            2. the weights for each Yobs value
630                                            3. the computed intensity values (Ycalc)
631                                            4. the background values
632                                            5. Yobs-Ycalc
633======================     ===============  ===========================================================
634
635.. _CWPowder_table:
636
637.. index::
638   single: Powder data CW Instrument Parameters
639
640-----------------------------
641CW Instrument Parameters
642-----------------------------
643
644Instrument Parameters are placed in a list of two dicts,
645where the keys in the first dict are listed below. Note that the dict contents are different for
646constant wavelength (CW) vs. time-of-flight (TOF) histograms.
647The value for each item is a list containing three values: the initial value, the current value
648and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that
649cannot be refined. The first and second values are floats unless otherwise noted.
650Items not refined are noted as [*]
651
652.. tabularcolumns:: |l|p{1in}|p{4in}|
653
654========================    ===============  ===========================================================
655  key                       sub-key           explanation
656========================    ===============  ===========================================================
657Instrument Parameters[0]    Type [*]            (str) Histogram type:
658                                                * 'PXC' for constant wavelength x-ray
659                                                * 'PNC' for constant wavelength neutron
660\                           Bank [*]            (int) Data set number in a multidata file (usually 1)
661\                           Lam                 (float) Specifies a wavelength in :math:`\\AA`
662\                           Lam1 [*]            (float) Specifies the primary wavelength in
663                                                :math:`\\AA`, used in place of Lam
664                                                when an :math:`\\alpha_1, \\alpha_2`
665                                                source is used.
666\                           Lam2 [*]            (float) Specifies the secondary wavelength in
667                                                :math:`\\AA`, used with Lam1
668\                           I(L2)/I(L1)         (float) Ratio of Lam2 to Lam1, used with Lam1
669\                           Zero                (float) Two-theta zero correction in *degrees*
670\                           Azimuth [*]         (float) Azimuthal setting angle for data recorded with differing setting angles
671\                           U, V, W             (float) Cagliotti profile coefficients
672                                                for Gaussian instrumental broadening, where the
673                                                FWHM goes as
674                                                :math:`U \\tan^2\\theta + V \\tan\\theta + W`
675\                           X, Y, Z             (float) Cauchy (Lorentzian) instrumental broadening coefficients
676\                           SH/L                (float) Variant of the Finger-Cox-Jephcoat asymmetric
677                                                peak broadening ratio. Note that this is the
678                                                sum of S/L and H/L where S is
679                                                sample height, H is the slit height and
680                                                L is the goniometer diameter.
681\                           Polariz.            (float) Polarization coefficient.
682Instrument Parameters[1]                        (empty dict)
683========================    ===============  ===========================================================
684
685.. _TOFPowder_table:
686
687.. index::
688   single: Powder data TOF Instrument Parameters
689
690-----------------------------
691TOF Instrument Parameters
692-----------------------------
693
694Instrument Parameters are also placed in a list of two dicts,
695where the keys in each dict listed below, but here for
696time-of-flight (TOF) histograms.
697The value for each item is a list containing three values: the initial value, the current value
698and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that
699cannot be refined. The first and second values are floats unless otherwise noted.
700Items not refined are noted as [*]
701
702.. tabularcolumns:: |l|p{1.5in}|p{4in}|
703
704========================    ===============  ===========================================================
705  key                        sub-key          explanation
706========================    ===============  ===========================================================
707Instrument Parameters[0]    Type [*]            (str) Histogram type:
708                                                * 'PNT' for time of flight neutron
709\                           Bank                (int) Data set number in a multidata file
710\                           2-theta [*]         (float) Nominal scattering angle for the detector
711\                           fltPath [*]         (float) Total flight path source-sample-detector
712\                           Azimuth [*]         (float) Azimuth angle for detector right hand rotation
713                                                from horizontal away from source
714\                           difC,difA,          (float) Diffractometer constants for conversion of d-spacing to TOF
715                            difB                in microseconds
716\                           Zero                (float) Zero point offset (microseconds)
717\                           alpha               (float) Exponential rise profile coefficients
718\                           beta-0              (float) Exponential decay profile coefficients
719                            beta-1
720                            beta-q
721\                           sig-0               (float) Gaussian profile coefficients
722                            sig-1
723                            sig-2
724                            sig-q   
725\                           X,Y,Z               (float) Lorentzian profile coefficients
726Instrument Parameters[1]    Pdabc               (list of 4 float lists) Originally created for use in gsas as optional tables
727                                                of d, alp, bet, d-true; for a reflection alpha & beta are obtained via interpolation
728                                                from the d-spacing and these tables. The d-true column is apparently unused.
729========================    ===============  ===========================================================
730
731
732.. _PowderRefl_table:
733
734.. index::
735   single: Powder reflection object description
736   single: Data object descriptions; Powder Reflections
737
738Powder Reflection Data Structure
739--------------------------------
740
741For every phase in a histogram, the ``Reflection Lists`` value is a dict
742one element of which is `'RefList'`, which is a np.array containing
743reflections. The columns in that array are documented below.
744
745==========  ====================================================
746  index         explanation
747==========  ====================================================
748 0,1,2          h,k,l (float)
749 3              (int) multiplicity
750 4              (float) d-space, :math:`\\AA`
751 5              (float) pos, two-theta
752 6              (float) sig, Gaussian width
753 7              (float) gam, Lorenzian width
754 8              (float) :math:`F_{obs}^2`
755 9              (float) :math:`F_{calc}^2`
756 10             (float) reflection phase, in degrees
757 11             (float) intensity correction for reflection, this times
758                :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
759 12             (float) Preferred orientation correction
760 13             (float) Transmission (absorption correction)
761 14             (float) Extinction correction
762==========  ====================================================
763
764.. _Xtal_table:
765
766.. index::
767   single: Single Crystal data object description
768   single: Data object descriptions; Single crystal data
769
770Single Crystal Tree Items
771-------------------------
772
773Every single crystal diffraction histogram is stored in the GSAS-II data tree
774with a top-level entry named beginning with the string "HKLF ". The
775diffraction data for that information are directly associated with
776that tree item and there are a series of children to that item. The
777routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
778and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
779load this information into a dictionary where the child tree name is
780used as a key, and the information in the main entry is assigned
781a key of ``Data``, as outlined below.
782
783.. tabularcolumns:: |l|l|p{4in}|
784
785======================  ===============     ====================================================
786  key                      sub-key          explanation
787======================  ===============     ====================================================
788Data                        \               (dict) that contains the
789                                            reflection table,
790                                            as described in the
791                                            :ref:`Single Crystal Reflections
792                                            <XtalRefl_table>`
793                                            description.
794
795Instrument Parameters       \               (list) containing two dicts where the possible
796                                            keys in each dict are listed below. The value
797                                            for most items is a list containing two values:
798                                            the initial value, the current value.
799                                            The first and second
800                                            values are floats unless otherwise noted.
801\                           Lam             (two floats) Specifies a wavelength in :math:`\\AA`
802\                           Type            (two str values) Histogram type :
803                                            * 'SXC' for constant wavelength x-ray
804                                            * 'SNC' for constant wavelength neutron
805                                            * 'SNT' for time of flight neutron
806\                           InstrName       (str) A name for the instrument, used in preparing a CIF
807wtFactor                    \               (float) A weighting factor to increase or decrease
808                                            the leverage of data in the histogram.
809                                            A value of 1.0 weights the data with their
810                                            standard uncertainties and a larger value
811                                            increases the weighting of the data (equivalent
812                                            to decreasing the uncertainties).
813
814hId                         \               (int) The number assigned to the histogram when
815                                            the project is loaded or edited (can change)
816ranId                       \               (int) A random number id for the histogram
817                                            that does not change
818======================  ===============     ====================================================
819
820.. _XtalRefl_table:
821
822.. index::
823   single: Single Crystal reflection object description
824   single: Data object descriptions; Single Crystal Reflections
825
826Single Crystal Reflection Data Structure
827----------------------------------------
828
829For every single crystal a histogram, the ``'Data'`` item contains
830the structure factors as an np.array in item `'RefList'`.
831The columns in that array are documented below.
832
833.. tabularcolumns:: |l|p{4in}|
834
835==========  ====================================================
836  index         explanation
837==========  ====================================================
838 0,1,2          (float) h,k,l
839 3              (int) multiplicity
840 4              (float) d-space, :math:`\\AA`
841 5              (float) :math:`F_{obs}^2`
842 6              (float) :math:`\sigma(F_{obs}^2)`
843 7              (float) :math:`F_{calc}^2`
844 8              (float) :math:`F_{obs}^2T`
845 9              (float) :math:`F_{calc}^2T`
846 10             (float) reflection phase, in degrees
847 11             (float) intensity correction for reflection, this times
848                :math:`F_{obs}^2` or :math:`F_{calc}^2`
849                gives Iobs or Icalc
850==========  ====================================================
851
852.. _Image_table:
853
854.. index::
855   image: Image data object description
856   image: Image object descriptions
857
858Image Data Structure
859--------------------
860
861Every 2-dimensional image is stored in the GSAS-II data tree
862with a top-level entry named beginning with the string "IMG ". The
863image data are directly associated with that tree item and there
864are a series of children to that item. The routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
865and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
866load this information into a dictionary where the child tree name is
867used as a key, and the information in the main entry is assigned
868a key of ``Data``, as outlined below.
869
870.. tabularcolumns:: |l|l|p{4in}|
871
872======================  ======================  ====================================================
873  key                      sub-key              explanation
874======================  ======================  ====================================================
875Comments                    \                   (list of str) Text strings extracted from the original image data
876                                                header or a metafile. These cannot be changed by
877                                                the user; it may be empty.
878Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
879                                                value. Accomodates
880                                                detector orientations other than with the detector
881                                                X-axis
882                                                horizontal.
883\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
884                                                during image integration multiplied by value. It must have the same size/shape as
885                                                the integrated image. NB: value < 0 for subtraction.
886\                           calibrant           (str) The material used for determining the position/orientation
887                                                of the image. The data is obtained from :func:`ImageCalibrants`
888                                                and UserCalibrants.py (supplied by user).
889\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
890\                           calibskip           (int) The number of expected diffraction lines skipped during the last
891                                                calibration run.
892\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
893                                                strikes the detector plane as determined by calibration. This point
894                                                does not have to be within the limits of the detector boundaries.
895\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
896                                                of the image is at the center line otherwise it is at the leading edge.
897\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
898\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
899                                                calibration calculations. See pixLimit for details as how point is found.
900\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
901                                                ring offset at higher angles. Optionally determined by calibration.
902\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
903\                           distance            (float) The distance (mm) from sample to detector plane.
904\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
905                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
906                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
907                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
908                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
909\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
910\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
911\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
912                                                Required for texture calculations.
913\                           invert_x            (bool) If True display the image with the x-axis inverted.
914\                           invert_y            (bool) If True display the image with the y-axis inverted.
915\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
916\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
917\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
918                                                intensities obtained during integration.
919\                           outAzimuths         (int) The number of azimuth pie slices.
920\                           outChannels         (int) The number of 2-theta steps.
921\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
922\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
923                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
924                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
925                                                Locations are used to construct rings of points for calibration calcualtions.
926\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
927                                                integration using value.
928\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
929                                                diffraction ring with the same d-spacing (dsp)
930\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
931                                                selected by the user,
932\                           Range               (list) The minimum & maximum values of the image
933\                           rotation            (float) The angle between the x-axis and the vector about which the
934                                                detector is tilted. Constrained to -180 to 180 deg.
935\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
936                                                calculations.
937\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
938                                                to cause correction to be applied.
939\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
940\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.
941\                           showLines           (bool) If True then isplay the integration limits to be used.
942\                           size                (list:int) The number of pixels on the image x & y axes
943\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
944\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
945\                           wavelength          (float) The radiation wavelength (:math:`\\AA`) as entered by the user
946                                                (or someday obtained from the image header).
947Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
948                                                to be excluded from integration
949\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
950                                                of which is excluded from recalibration and integration. Only one frame is allowed.
951\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
952                                                from integration.
953\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
954                                                to be excluded from integration.
955\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
956                                                to be excluded from integration.
957\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
958                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.
959\                           SpotMask            (dict: int & array)
960                                                'esdMul'(int) number of standard deviations above mean ring intensity to mask
961                                                'spotMask' (bool array) the spot mask for every pixel in image         
962
963Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
964\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
965                                                These will be restricted by space group symmetry; result of strain fit refinement.
966\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
967\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
968                                                and are used to determine the strain tensor.
969                                                The dictionary items are:
970                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
971                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
972                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
973                                                'Esig': (list: float) Esds for Emat from fitting.
974                                                'pixLimit': (int) Search range to find highest point on ring for each data point
975                                                'cutoff': (float) I/Ib cutoff for searching.
976                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
977                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
978                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
979
980======================  ======================  ====================================================
981
982.. _parmDict_table:
983
984.. index::
985   single: Parameter dictionary
986
987Parameter Dictionary
988-------------------------
989
990The parameter dictionary contains all of the variable parameters for the refinement.
991The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
992It is prepared in two ways. When loaded from the tree
993(in :meth:`GSASIIdataGUI.GSASII.MakeLSParmDict` and
994:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
995the values are lists with two elements: ``[value, refine flag]``
996
997When loaded from the GPX file (in
998:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
999dict is the actual parameter value (usually a float, but sometimes a
1000letter or string flag value (such as I or A for iso/anisotropic).
1001
1002Texture implementation
1003------------------------------
1004
1005There are two different places where texture can be treated in GSAS-II.
1006One is for mitigating the effects of texture in a structural refinement.
1007The other is for texture characterization.
1008
1009For reducing the effect of texture in a structural refinement
1010there are entries labeled preferred orientation in each phase's
1011data tab. Two different
1012approaches can be used for this, the March-Dollase model and
1013spherical harmonics.
1014For the March-Dollase model, one axis in reciprocal space is designated as
1015unique (defaulting to the 001 axis) and reflections are corrected
1016according to the angle they make with this axis depending on
1017the March-Dollase ratio. (If unity, no correction is made).
1018The ratio can be greater than one or less than one depending on if
1019crystallites oriented along the designated axis are
1020overrepresented or underrepresented. For most crystal systems there is an
1021obvious choice for the direction of the unique axis and then only a single
1022term needs to be refined. If the number is close to 1, then the correction
1023is not needed.
1024
1025The second method for reducing the effect of texture in a structural
1026refinement is to create a probability surface as an expansion in
1027terms spherical harmonic functions. Only functions consistent with
1028cylindrical diffraction suymmetry and having texture symmetry
1029consistent with the Laue class of phase are used and are allowed,
1030so the higher the symmetry
1031the fewer terms that are available for a given spherical harmonics order.
1032For use of this correction, select the lowest order that provides
1033refinable terms and perform a refinement. If the texture index remains close to
1034one, then the correction is not needed. If a significant improvement is
1035noted in the profile Rwp, one may wish to see if a higher order expansion
1036gives an even larger improvement.
1037
1038To characterize texture in a material, one needs data collected with the
1039sample at multiple orientations or, for TOF, with detectors at multiple
1040locations around the sample. In this case the detector orientation is given in
1041each histogram's Sample Parameters and the sample's orientation is described
1042with the Euler angles specifed on the phase's Texture tab, which is also
1043where the texture type (cylindrical, rolling,...) and the sherical
1044harmonic order is selected. This should not be used with a single dataset and
1045should not be used if the preferred orientations corrections are used.
1046
1047The coordinate system used for texture characterization is defined where
1048the sample coordinates (Psi, gamma) are defined with an instrument coordinate
1049system (I, J, K) such that I is normal to the diffraction plane and J is coincident with the
1050direction of the incident radiation beam pointing away from the source. We further define
1051a standard set of right-handed goniometer eulerian angles (Omega, Chi, Phi) so that Omega and Phi are
1052rotations about I and Chi is a rotation about J when Omega, Chi, Phi = 0. Finally, as the sample
1053may be mounted so that the sample coordinate system (Is, Js, Ks) does not coincide with
1054the instrument coordinate system (I, J, K), we define three eulerian sample rotation angles
1055(Omega-s, Chi-s, Phi-s) that describe the rotation from (I, J, K) to (Is, Js, Ks). The sample rotation
1056angles are defined so that with the goniometer angles at zero Omega-s and Phi-s are rotations
1057about I and Chi-s is a rotation about J.
1058
1059ISODISTORT implementation
1060------------------------------
1061
1062CIFs prepared with the ISODISTORT web site
1063https://stokes.byu.edu/iso/isodistort_version5.6.1/isodistort.php
1064[B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, "ISODISPLACE: An Internet Tool for Exploring Structural Distortions." J. Appl. Cryst. 39, 607-614 (2006).]
1065can be read into GSAS-II using import CIF. This will cause constraints to be established for structural distortion modes read from the CIF.
1066At present, of the five types of modes  only displacive(``_iso_displacivemode``...) and occupancy (``_iso_occupancymode``...) are processed. Not yet processed: ``_iso_magneticmode``..., ``_iso_rotationalmode``... & ``_iso_strainmode``...
1067
1068The CIF importer :mod:`G2phase_CIF` implements class :class:`G2phase_CIF.CIFPhaseReader` which offers two methods associated with ISODISTORT (ID) input. Method :meth:`G2phase_CIF.CIFPhaseReader.ISODISTORT_test`
1069checks to see if a CIF block contains the loops with ``_iso_displacivemode_label`` or  ``_iso_occupancymode_label`` items.
1070If so, method :meth:`G2phase_CIF.CIFPhaseReader.ISODISTORT_proc` is called to read and interpret them.
1071The results are placed into the reader object's ``.Phase`` class variable as a dict item with key ``'ISODISTORT'``.
1072
1073Note that each mode ID has a long label with a name such as  Pm-3m[1/2,1/2,1/2]R5+(a,a,0)[La:b:dsp]T1u(a). Function :func:`G2phase_CIF.ISODISTORT_shortLbl` is used to create a short name for this,
1074such as R5_T1u(a) which is made unique by addition of _n if the short name is duplicated.
1075As each mode is processed, a constraint corresponding to that mode is
1076created and is added to list in the reader object's ``.Constraints`` class variable. Items placed into that list can either be a list, which corresponds to a function (new var) type :ref:`constraint definition <Constraints_table>` entry, or an item can be a dict, which provides help information for each constraint.
1077
1078------------------------------
1079Displacive modes
1080------------------------------
1081
1082The coordinate variables, as named by ISODISTORT, are placed in
1083``.Phase['ISODISTORT']['IsoVarList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2VarList']``. The mode variables,
1084as named by ISODISTORT, are placed in ``.Phase['ISODISTORT']['IsoModeList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2ModeList']``.
1085[Use ``str(G2VarObj)`` to get the variable name from the G2VarObj object, but note that the phase number, *n*, for the prefix "*n*::" cannot be determined as the phase number is not yet assigned.]
1086
1087Displacive modes are a bit complex in that they relate to delta displacements, relative to an offset value for each coordinate, and because the modes are normalized, while GSAS-II also uses displacements, but these are added to the coordinates after each refinement cycle and the delta values are set to zero. ISODISTORT uses fixed offsets (subtracted from the actual position to obtain the delta values) that are taken from ``_iso_coordinate_formula`` and these are placed in ``.Phase['ISODISTORT']['ParentStructure]`` (keyed by atom label). The normalization factors (which the delta values are divided by) are taken from ``_iso_displacivemodenorm_value`` and are placed in ``.Phase['ISODISTORT']['NormList']`` in the same order as as ``...['IsoModeList']`` and
1088``...['G2ModeList']``.
1089
1090The CIF contains a sparse matrix, from the ``loop_`` containing
1091``_iso_displacivemodematrix_value`` which provides the equations for determining the mode values from the coordinates, that matrix is placed in ``.Phase['ISODISTORT']['Mode2VarMatrix']``. The matrix is inverted to produce
1092``.Phase['ISODISTORT']['Var2ModeMatrix']``, which determines how to compute the
1093mode values from the delta coordinate values. These values are used for the
1094in :func:`GSASIIconstrGUI.ShowIsoDistortCalc` which shows coordinate and mode
1095values, the latter with s.u. values.
1096
1097
1098------------------------------
1099Occupancy modes
1100------------------------------
1101
1102
1103The delta occupancy variables, as named by ISODISTORT, are placed in
1104``.Phase['ISODISTORT']['OccVarList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2OccVarList']``. The mode variables, as named by ISODISTORT, are placed in ``.Phase['ISODISTORT']['OccModeList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2OccModeList']``.
1105
1106Occupancy modes, like Displacive modes, are also refined as delta values.  However, GSAS-II directly refines the fractional occupancies.
1107Offset values for each atom, are taken from ``_iso_occupancy_formula`` and are placed in
1108``.Phase['ISODISTORT']['ParentOcc]``.
1109(Offset values are subtracted from the actual position to obtain the delta values.)
1110Modes are normalized (where the mode values are divided by the normalization factor)
1111are taken from ``_iso_occupancymodenorm_value`` and are placed in ``.Phase['ISODISTORT']['OccNormList']`` in the same order as as ``...['OccModeList']`` and
1112``...['G2OccModeList']``.
1113
1114The CIF contains a sparse matrix, from the ``loop_`` containing
1115``_iso_occupancymodematrix_value``, which provides the equations for determining the mode values from the coordinates. That matrix is placed in ``.Phase['ISODISTORT']['Occ2VarMatrix']``. The matrix is inverted to produce
1116``.Phase['ISODISTORT']['Var2OccMatrix']``, which determines how to compute the
1117mode values from the delta coordinate values.
1118
1119
1120------------------------------
1121Mode Computations
1122------------------------------
1123
1124Constraints are processed after the CIF has been read in
1125:meth:`GSASIIdataGUI.GSASII.OnImportPhase` or 
1126:meth:`GSASIIscriptable.G2Project.add_phase` by moving them from the reader
1127object's ``.Constraints`` class variable to
1128the Constraints tree entry's ['Phase'] list (for list items defining constraints) or
1129the Constraints tree entry's ['_Explain'] dict (for dict items defining constraint help information)
1130
1131The information in ``.Phase['ISODISTORT']`` is used
1132in :func:`GSASIIconstrGUI.ShowIsoDistortCalc` which shows coordinate and mode
1133values, the latter with s.u. values. This can be called from the Constraints and Phase/Atoms tree items.
1134
1135Before each refinement, constraints are processed as
1136:ref:`described elsewhere <Constraints_processing>`. After a refinement
1137is complete, :func:`GSASIImapvars.PrintIndependentVars` shows the
1138shifts and s.u.'s on the refined modes, using GSAS-II values, but
1139:func:`GSASIIstrIO.PrintISOmodes` prints the ISODISTORT modes as computed
1140in the web site.
1141
1142
1143.. _ParameterLimits:
1144
1145.. index::
1146   single: Parameter limits
1147
1148Parameter Limits
1149------------------------------
1150
1151One of the most often requested "enhancements" for GSAS-II would be the inclusion
1152of constraints to force parameters such as occupancies or Uiso values to stay within
1153expected ranges. While it is possible for users to supply their own restraints that would
1154perform this by supplying an appropriate expression with the "General" restraints, the
1155GSAS-II authors do not feel that use of restraints or constraints are a good solution for
1156this common problem where parameters refine to non-physical values. This is because when
1157this occurs, most likely one of the following cases is occurring:
1158
1159#. there is a significant problem
1160   with the model, for example for an x-ray fit if an O atom is placed where a S is actually
1161   present, the Uiso will refine artificially small or the occupancy much larger than unity
1162   to try to compensate for the missing electrons; or
1163 
1164#. the data are simply insensitive
1165   to the parameter or combination of parameters, for example unless very high-Q data
1166   are included, the effects of a occupancy and Uiso value can have compensating effects,
1167   so an assumption must be made; likewise, with neutron data natural-abundance V atoms
1168   are nearly invisible due to weak coherent scattering. No parameters can be fit for a
1169   V atom with neutrons.
1170
1171#. the parameter is non-physical (such as a negative Uiso value) but within
1172   two sigma (sigma = standard uncertainty, aka e.s.d.) of a reasonable value,
1173   in which case the
1174   value is not problematic as it is experimentally indistinguishable from an
1175   expected value. 
1176
1177#. there is a systematic problem with the data (experimental error)
1178
1179In all these cases, this situation needs to be reviewed by a crystallographer to decide
1180how to best determine a structural model for these data. An implementation with a constraint
1181or restraint is likely to simply hide the problem from the user, making it more probable
1182that a poor model choice is obtained.
1183
1184What GSAS-II does implement is to allow users to specify ranges for parameters
1185that works by disabling
1186refinement of parameters that refine beyond either a lower limit or an upper limit, where
1187either or both may be optionally specified. Parameters limits are specified in the Controls
1188tree entry in dicts named as ``Controls['parmMaxDict']`` and ``Controls['parmMinDict']``, where
1189the keys are :class:`G2VarObj` objects corresponding to standard GSAS-II variable
1190(see :func:`getVarDescr` and :func:`CompileVarDesc`) names, where a
1191wildcard ('*') may optionally be used for histogram number or atom number
1192(phase number is intentionally not  allowed as a wildcard as it makes little sense
1193to group the same parameter together different phases). Note
1194that :func:`prmLookup` is used to see if a name matches a wildcard. The upper or lower limit
1195is placed into these dicts as a float value. These values can be edited using the window
1196created by the Calculate/"View LS parms" menu command or in scripting with the
1197:meth:`GSASIIscriptable.G2Project.set_Controls` function.
1198In the GUI, a checkbox labeled "match all histograms/atoms" is used to insert a wildcard
1199into the appropriate part of the variable name.
1200
1201When a refinement is conducted, routine :func:`GSASIIstrMain.dropOOBvars` is used to
1202find parameters that have refined to values outside their limits. If this occurs, the parameter
1203is set to the limiting value and the variable name is added to a list of frozen variables
1204(as a :class:`G2VarObj` objects) kept in a list in the
1205``Controls['parmFrozen']`` dict. In a sequential refinement, this is kept separate for
1206each histogram as a list in
1207``Controls['parmFrozen'][histogram]`` (where the key is the histogram name) or as a list in
1208``Controls['parmFrozen']['FrozenList']`` for a non-sequential fit.
1209This allows different variables
1210to be frozen in each section of a sequential fit.
1211Frozen parameters are not included in refinements through removal from the
1212list of parameters to be refined (``varyList``) in :func:`GSASIIstrMain.Refine` or
1213:func:`GSASIIstrMain.SeqRefine`. Once a variable is frozen, it will not be refined in any
1214future refinements unless the the variable is removed (manually) from the list. This can also
1215be done with the Calculate/"View LS parms" menu window or ...
1216
1217.. seealso::
1218  :class:`G2VarObj`
1219  :func:`getVarDescr`
1220  :func:`CompileVarDesc`
1221  :func:`prmLookup`
1222  :class:`GSASIIctrlGUI.ShowLSParms`
1223  :class:`GSASIIctrlGUI.VirtualVarBox`
1224  :func:`GSASIIstrIO.SetUsedHistogramsAndPhases`
1225  :func:`GSASIIstrIO.SaveUpdatedHistogramsAndPhases`
1226  :func:`GSASIIstrIO.SetSeqResult`
1227  :func:`GSASIIstrMain.dropOOBvars`
1228  :meth:`GSASIIscriptable.G2Project.set_Controls`
1229
1230*Classes and routines*
1231----------------------
1232
1233'''
1234from __future__ import division, print_function
1235import platform
1236import re
1237import imp
1238import random as ran
1239import sys
1240import os.path as ospath
1241if '2' in platform.python_version_tuple()[0]:
1242    import cPickle
1243else:
1244    import pickle as cPickle
1245import GSASIIpath
1246import GSASIImath as G2mth
1247import GSASIIspc as G2spc
1248import numpy as np
1249
1250GSASIIpath.SetVersionNumber("$Revision: 4588 $")
1251
1252DefaultControls = {
1253    'deriv type':'analytic Hessian',
1254    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
1255    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
1256    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
1257    'Author':'no name',
1258    'FreePrm1':'Sample humidity (%)',
1259    'FreePrm2':'Sample voltage (V)',
1260    'FreePrm3':'Applied load (MN)',
1261    'ShowCell':False,
1262    }
1263'''Values to be used as defaults for the initial contents of the ``Controls``
1264data tree item.
1265'''
1266def StripUnicode(string,subs='.'):
1267    '''Strip non-ASCII characters from strings
1268
1269    :param str string: string to strip Unicode characters from
1270    :param str subs: character(s) to place into string in place of each
1271      Unicode character. Defaults to '.'
1272
1273    :returns: a new string with only ASCII characters
1274    '''
1275    s = ''
1276    for c in string:
1277        if ord(c) < 128:
1278            s += c
1279        else:
1280            s += subs
1281    return s
1282#    return s.encode('ascii','replace')
1283
1284def MakeUniqueLabel(lbl,labellist):
1285    '''Make sure that every a label is unique against a list by adding
1286    digits at the end until it is not found in list.
1287
1288    :param str lbl: the input label
1289    :param list labellist: the labels that have already been encountered
1290    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
1291      ``_10-99``, etc.) appended at the end
1292    '''
1293    lbl = StripUnicode(lbl.strip(),'_')
1294    if not lbl: # deal with a blank label
1295        lbl = '_1'
1296    if lbl not in labellist:
1297        labellist.append(lbl)
1298        return lbl
1299    i = 1
1300    prefix = lbl
1301    if '_' in lbl:
1302        prefix = lbl[:lbl.rfind('_')]
1303        suffix = lbl[lbl.rfind('_')+1:]
1304        try:
1305            i = int(suffix)+1
1306        except: # suffix could not be parsed
1307            i = 1
1308            prefix = lbl
1309    while prefix+'_'+str(i) in labellist:
1310        i += 1
1311    else:
1312        lbl = prefix+'_'+str(i)
1313        labellist.append(lbl)
1314    return lbl
1315
1316PhaseIdLookup = {}
1317'''dict listing phase name and random Id keyed by sequential phase index as a str;
1318best to access this using :func:`LookupPhaseName`
1319'''
1320PhaseRanIdLookup = {}
1321'''dict listing phase sequential index keyed by phase random Id;
1322best to access this using :func:`LookupPhaseId`
1323'''
1324HistIdLookup = {}
1325'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
1326best to access this using :func:`LookupHistName`
1327'''
1328HistRanIdLookup = {}
1329'''dict listing histogram sequential index keyed by histogram random Id;
1330best to access this using :func:`LookupHistId`
1331'''
1332AtomIdLookup = {}
1333'''dict listing for each phase index as a str, the atom label and atom random Id,
1334keyed by atom sequential index as a str;
1335best to access this using :func:`LookupAtomLabel`
1336'''
1337AtomRanIdLookup = {}
1338'''dict listing for each phase the atom sequential index keyed by atom random Id;
1339best to access this using :func:`LookupAtomId`
1340'''
1341ShortPhaseNames = {}
1342'''a dict containing a possibly shortened and when non-unique numbered
1343version of the phase name. Keyed by the phase sequential index.
1344'''
1345ShortHistNames = {}
1346'''a dict containing a possibly shortened and when non-unique numbered
1347version of the histogram name. Keyed by the histogram sequential index.
1348'''
1349
1350#VarDesc = {}  # removed 1/30/19 BHT as no longer needed (I think)
1351#''' This dictionary lists descriptions for GSAS-II variables,
1352#as set in :func:`CompileVarDesc`. See that function for a description
1353#for how keys and values are written.
1354#'''
1355
1356reVarDesc = {}
1357''' This dictionary lists descriptions for GSAS-II variables where
1358keys are compiled regular expressions that will match the name portion
1359of a parameter name. Initialized in :func:`CompileVarDesc`.
1360'''
1361
1362reVarStep = {}
1363''' This dictionary lists the preferred step size for numerical
1364derivative computation w/r to a GSAS-II variable. Keys are compiled
1365regular expressions and values are the step size for that parameter.
1366Initialized in :func:`CompileVarDesc`.
1367'''
1368# create a default space group object for P1; N.B. fails when building documentation
1369try:
1370    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
1371except:
1372    pass
1373
1374def GetPhaseNames(fl):
1375    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
1376    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename
1377
1378    :param file fl: opened .gpx file
1379    :return: list of phase names
1380    '''
1381    PhaseNames = []
1382    while True:
1383        try:
1384            data = cPickle.load(fl)
1385        except EOFError:
1386            break
1387        datum = data[0]
1388        if 'Phases' == datum[0]:
1389            for datus in data[1:]:
1390                PhaseNames.append(datus[0])
1391    fl.seek(0)          #reposition file
1392    return PhaseNames
1393
1394def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
1395    '''Create a new phase dict with default values for various parameters
1396
1397    :param str Name: Name for new Phase
1398
1399    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
1400      defaults to data for P 1
1401
1402    :param list cell: unit cell parameter list; defaults to
1403      [1.0,1.0,1.0,90.,90,90.,1.]
1404
1405    '''
1406    if SGData is None: SGData = P1SGData
1407    if cell is None: cell=[1.0,1.0,1.0,90.,90.,90.,1.]
1408    phaseData = {
1409        'ranId':ran.randint(0,sys.maxsize),
1410        'General':{
1411            'Name':Name,
1412            'Type':'nuclear',
1413            'Modulated':False,
1414            'AtomPtrs':[3,1,7,9],
1415            'SGData':SGData,
1416            'Cell':[False,]+cell,
1417            'Pawley dmin':1.0,
1418            'Data plot type':'None',
1419            'SH Texture':{
1420                'Order':0,
1421                'Model':'cylindrical',
1422                'Sample omega':[False,0.0],
1423                'Sample chi':[False,0.0],
1424                'Sample phi':[False,0.0],
1425                'SH Coeff':[False,{}],
1426                'SHShow':False,
1427                'PFhkl':[0,0,1],
1428                'PFxyz':[0,0,1],
1429                'PlotType':'Pole figure',
1430                'Penalty':[['',],0.1,False,1.0]}},
1431        'Atoms':[],
1432        'Drawing':{},
1433        'Histograms':{},
1434        'Pawley ref':[],
1435        'RBModels':{},
1436        }
1437    if Super and Super.get('Use',False):
1438        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
1439        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
1440        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]
1441
1442    return phaseData
1443
1444def ReadCIF(URLorFile):
1445    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
1446    (from James Hester).
1447    The open routine gets confused with DOS names that begin with a letter and colon
1448    "C:\dir\" so this routine will try to open the passed name as a file and if that
1449    fails, try it as a URL
1450
1451    :param str URLorFile: string containing a URL or a file name. Code will try first
1452      to open it as a file and then as a URL.
1453
1454    :returns: a PyCifRW CIF object.
1455    '''
1456    import CifFile as cif # PyCifRW from James Hester
1457
1458    # alternate approach:
1459    #import urllib
1460    #ciffile = 'file:'+urllib.pathname2url(filename)
1461
1462    try:
1463        fp = open(URLorFile,'r')
1464        cf = cif.ReadCif(fp)
1465        fp.close()
1466        return cf
1467    except IOError:
1468        return cif.ReadCif(URLorFile)
1469
1470def TestIndexAll():
1471    '''Test if :func:`IndexAllIds` has been called to index all phases and
1472    histograms (this is needed before :func:`G2VarObj` can be used.
1473
1474    :returns: Returns True if indexing is needed.
1475    '''
1476    if PhaseIdLookup or AtomIdLookup or HistIdLookup:
1477        return False
1478    return True
1479       
1480def IndexAllIds(Histograms,Phases):
1481    '''Scan through the used phases & histograms and create an index
1482    to the random numbers of phases, histograms and atoms. While doing this,
1483    confirm that assigned random numbers are unique -- just in case lightning
1484    strikes twice in the same place.
1485
1486    Note: this code assumes that the atom random Id (ranId) is the last
1487    element each atom record.
1488
1489    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
1490    (which loads the histograms and phases from a GPX file),
1491    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
1492    (which loads the histograms and phases from the data tree.) and
1493    :meth:`GSASIIconstrGUI.UpdateConstraints`
1494    (which displays & edits the constraints in a GUI)
1495
1496    TODO: do we need a lookup for rigid body variables?
1497    '''
1498    # process phases and atoms
1499    PhaseIdLookup.clear()
1500    PhaseRanIdLookup.clear()
1501    AtomIdLookup.clear()
1502    AtomRanIdLookup.clear()
1503    ShortPhaseNames.clear()
1504    for ph in Phases:
1505        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
1506        ranId = Phases[ph]['ranId']
1507        while ranId in PhaseRanIdLookup:
1508            # Found duplicate random Id! note and reassign
1509            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
1510            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1511        pId = str(Phases[ph]['pId'])
1512        PhaseIdLookup[pId] = (ph,ranId)
1513        PhaseRanIdLookup[ranId] = pId
1514        shortname = ph  #[:10]
1515        while shortname in ShortPhaseNames.values():
1516            shortname = ph[:8] + ' ('+ pId + ')'
1517        ShortPhaseNames[pId] = shortname
1518        AtomIdLookup[pId] = {}
1519        AtomRanIdLookup[pId] = {}
1520        for iatm,at in enumerate(Phases[ph]['Atoms']):
1521            ranId = at[cia+8]
1522            while ranId in AtomRanIdLookup[pId]: # check for dups
1523                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
1524                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
1525            AtomRanIdLookup[pId][ranId] = str(iatm)
1526            if Phases[ph]['General']['Type'] == 'macromolecular':
1527                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
1528            else:
1529                label = at[ct-1]
1530            AtomIdLookup[pId][str(iatm)] = (label,ranId)
1531    # process histograms
1532    HistIdLookup.clear()
1533    HistRanIdLookup.clear()
1534    ShortHistNames.clear()
1535    for hist in Histograms:
1536        ranId = Histograms[hist]['ranId']
1537        while ranId in HistRanIdLookup:
1538            # Found duplicate random Id! note and reassign
1539            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1540            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1541        hId = str(Histograms[hist]['hId'])
1542        HistIdLookup[hId] = (hist,ranId)
1543        HistRanIdLookup[ranId] = hId
1544        shortname = hist[:15]
1545        while shortname in ShortHistNames.values():
1546            shortname = hist[:11] + ' ('+ hId + ')'
1547        ShortHistNames[hId] = shortname
1548
1549def LookupAtomId(pId,ranId):
1550    '''Get the atom number from a phase and atom random Id
1551
1552    :param int/str pId: the sequential number of the phase
1553    :param int ranId: the random Id assigned to an atom
1554
1555    :returns: the index number of the atom (str)
1556    '''
1557    if not AtomRanIdLookup:
1558        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
1559    if pId is None or pId == '':
1560        raise KeyError('Error: phase is invalid (None or blank)')
1561    pId = str(pId)
1562    if pId not in AtomRanIdLookup:
1563        raise KeyError('Error: LookupAtomId does not have phase '+pId)
1564    if ranId not in AtomRanIdLookup[pId]:
1565        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
1566    return AtomRanIdLookup[pId][ranId]
1567
1568def LookupAtomLabel(pId,index):
1569    '''Get the atom label from a phase and atom index number
1570
1571    :param int/str pId: the sequential number of the phase
1572    :param int index: the index of the atom in the list of atoms
1573
1574    :returns: the label for the atom (str) and the random Id of the atom (int)
1575    '''
1576    if not AtomIdLookup:
1577        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
1578    if pId is None or pId == '':
1579        raise KeyError('Error: phase is invalid (None or blank)')
1580    pId = str(pId)
1581    if pId not in AtomIdLookup:
1582        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
1583    if index not in AtomIdLookup[pId]:
1584        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
1585    return AtomIdLookup[pId][index]
1586
1587def LookupPhaseId(ranId):
1588    '''Get the phase number and name from a phase random Id
1589
1590    :param int ranId: the random Id assigned to a phase
1591    :returns: the sequential Id (pId) number for the phase (str)
1592    '''
1593    if not PhaseRanIdLookup:
1594        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
1595    if ranId not in PhaseRanIdLookup:
1596        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
1597    return PhaseRanIdLookup[ranId]
1598
1599def LookupPhaseName(pId):
1600    '''Get the phase number and name from a phase Id
1601
1602    :param int/str pId: the sequential assigned to a phase
1603    :returns:  (phase,ranId) where phase is the name of the phase (str)
1604      and ranId is the random # id for the phase (int)
1605    '''
1606    if not PhaseIdLookup:
1607        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
1608    if pId is None or pId == '':
1609        raise KeyError('Error: phase is invalid (None or blank)')
1610    pId = str(pId)
1611    if pId not in PhaseIdLookup:
1612        raise KeyError('Error: LookupPhaseName does not have index '+pId)
1613    return PhaseIdLookup[pId]
1614
1615def LookupHistId(ranId):
1616    '''Get the histogram number and name from a histogram random Id
1617
1618    :param int ranId: the random Id assigned to a histogram
1619    :returns: the sequential Id (hId) number for the histogram (str)
1620    '''
1621    if not HistRanIdLookup:
1622        raise Exception('Error: LookupHistId called before IndexAllIds was run')
1623    if ranId not in HistRanIdLookup:
1624        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
1625    return HistRanIdLookup[ranId]
1626
1627def LookupHistName(hId):
1628    '''Get the histogram number and name from a histogram Id
1629
1630    :param int/str hId: the sequential assigned to a histogram
1631    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1632      and ranId is the random # id for the histogram (int)
1633    '''
1634    if not HistIdLookup:
1635        raise Exception('Error: LookupHistName called before IndexAllIds was run')
1636    if hId is None or hId == '':
1637        raise KeyError('Error: histogram is invalid (None or blank)')
1638    hId = str(hId)
1639    if hId not in HistIdLookup:
1640        raise KeyError('Error: LookupHistName does not have index '+hId)
1641    return HistIdLookup[hId]
1642
1643def fmtVarDescr(varname):
1644    '''Return a string with a more complete description for a GSAS-II variable
1645
1646    :param str varname: A full G2 variable name with 2 or 3 or 4
1647       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1648
1649    :returns: a string with the description
1650    '''
1651    s,l = VarDescr(varname)
1652    return s+": "+l
1653
1654def VarDescr(varname):
1655    '''Return two strings with a more complete description for a GSAS-II variable
1656
1657    :param str name: A full G2 variable name with 2 or 3 or 4
1658       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1659
1660    :returns: (loc,meaning) where loc describes what item the variable is mapped
1661      (phase, histogram, etc.) and meaning describes what the variable does.
1662    '''
1663
1664    # special handling for parameter names without a colon
1665    # for now, assume self-defining
1666    if varname.find(':') == -1:
1667        return "Global",varname
1668
1669    l = getVarDescr(varname)
1670    if not l:
1671        return ("invalid variable name ("+str(varname)+")!"),""
1672#        return "invalid variable name!",""
1673
1674    if not l[-1]:
1675        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1676
1677    if len(l) == 3:         #SASD variable name!
1678        s = 'component:'+l[1]
1679        return s,l[-1]
1680    s = ""
1681    if l[0] is not None and l[1] is not None: # HAP: keep short
1682        if l[2] == "Scale": # fix up ambigous name
1683            l[5] = "Phase fraction"
1684        if l[0] == '*':
1685            lbl = 'Seq. ref.'
1686        else:
1687            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1688        if l[1] == '*':
1689            hlbl = 'Seq. ref.'
1690        else:
1691            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1692        if hlbl[:4] == 'HKLF':
1693            hlbl = 'Xtl='+hlbl[5:]
1694        elif hlbl[:4] == 'PWDR':
1695            hlbl = 'Pwd='+hlbl[5:]
1696        else:
1697            hlbl = 'Hist='+hlbl
1698        s = "Ph="+str(lbl)+" * "+str(hlbl)
1699    else:
1700        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1701            l[5] = "Scale factor"
1702        if l[2] == 'Back': # background parameters are "special", alas
1703            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1704            l[-1] += ' #'+str(l[3])
1705        elif l[4] is not None: # rigid body parameter or modulation parm
1706            lbl = ShortPhaseNames.get(l[0],'phase?')
1707            if 'RB' in l[2]:    #rigid body parm
1708                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1709            else: #modulation parm
1710                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
1711        elif l[3] is not None: # atom parameter,
1712            lbl = ShortPhaseNames.get(l[0],'phase?')
1713            try:
1714                albl = LookupAtomLabel(l[0],l[3])[0]
1715            except KeyError:
1716                albl = 'Atom?'
1717            s = "Atom "+str(albl)+" in "+str(lbl)
1718        elif l[0] == '*':
1719            s = "All phases "
1720        elif l[0] is not None:
1721            lbl = ShortPhaseNames.get(l[0],'phase?')
1722            s = "Phase "+str(lbl)
1723        elif l[1] == '*':
1724            s = 'All hists'
1725        elif l[1] is not None:
1726            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1727            if hlbl[:4] == 'HKLF':
1728                hlbl = 'Xtl='+hlbl[5:]
1729            elif hlbl[:4] == 'PWDR':
1730                hlbl = 'Pwd='+hlbl[5:]
1731            else:
1732                hlbl = 'Hist='+hlbl
1733            s = str(hlbl)
1734    if not s:
1735        s = 'Global'
1736    return s,l[-1]
1737
1738def getVarDescr(varname):
1739    '''Return a short description for a GSAS-II variable
1740
1741    :param str name: A full G2 variable name with 2 or 3 or 4
1742       colons (<p>:<h>:name[:<a1>][:<a2>])
1743
1744    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1745      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1746      the histogram number and the atom number; `name` will always be
1747      a str; and `description` is str or `None`.
1748      If the variable name is incorrectly formed (for example, wrong
1749      number of colons), `None` is returned instead of a list.
1750    '''
1751    l = varname.split(':')
1752    if len(l) == 2:     #SASD parameter name
1753        return varname,l[0],getDescr(l[1])
1754    if len(l) == 3:
1755        l += [None,None]
1756    elif len(l) == 4:
1757        l += [None]
1758    elif len(l) != 5:
1759        return None
1760    for i in (0,1,3,4):
1761        if l[i] == "":
1762            l[i] = None
1763    l += [getDescr(l[2])]
1764    return l
1765
1766def CompileVarDesc():
1767    '''Set the values in the variable lookup tables
1768    (:attr:`reVarDesc` and :attr:`reVarStep`).
1769    This is called in :func:`getDescr` and :func:`getVarStep` so this
1770    initialization is always done before use.
1771
1772    Note that keys may contain regular expressions, where '[xyz]'
1773    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range
1774    of values). '.*' matches any string. For example::
1775
1776    'AUiso':'Atomic isotropic displacement parameter',
1777
1778    will match variable ``'p::AUiso:a'``.
1779    If parentheses are used in the key, the contents of those parentheses can be
1780    used in the value, such as::
1781
1782    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1783
1784    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1785    in the value when used.
1786
1787    '''
1788    if reVarDesc: return # already done
1789    for key,value in {
1790        # derived or other sequential vars
1791        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1792        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1793        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1794        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1795        # ambiguous, alas:
1796        'Scale' : 'Phase or Histogram scale factor',
1797        # Phase vars (p::<var>)
1798        'A([0-5])' : ('Reciprocal metric tensor component \\1',1e-5),
1799        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
1800        # Atom vars (p::<var>:a)
1801        'dA([xyz])$' : ('change to atomic coordinate, \\1',1e-6),
1802        'A([xyz])$' : '\\1 fractional atomic coordinate',
1803        'AUiso':('Atomic isotropic displacement parameter',1e-4),
1804        'AU([123][123])':('Atomic anisotropic displacement parameter U\\1',1e-4),
1805        'Afrac': ('Atomic site fraction parameter',1e-5),
1806        'Amul': 'Atomic site multiplicity value',
1807        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
1808        # Hist & Phase (HAP) vars (p:h:<var>)
1809        'Back': 'Background term',
1810        'BkPkint;(.*)':'Background peak #\\1 intensity',
1811        'BkPkpos;(.*)':'Background peak #\\1 position',
1812        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1813        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1814        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1815        'D([123][123])' : 'Anisotropic strain coef. \\1',
1816        'Extinction' : 'Extinction coef.',
1817        'MD' : 'March-Dollase coef.',
1818        'Mustrain;.*' : 'Microstrain coef.',
1819        'Size;.*' : 'Crystallite size value',
1820        'eA$' : 'Cubic mustrain value',
1821        'Ep$' : 'Primary extinction',
1822        'Es$' : 'Secondary type II extinction',
1823        'Eg$' : 'Secondary type I extinction',
1824        'Flack' : 'Flack parameter',
1825        'TwinFr' : 'Twin fraction',
1826        'Layer Disp'  : 'Layer displacement along beam',
1827        #Histogram vars (:h:<var>)
1828        'Absorption' : 'Absorption coef.',
1829        'Displace([XY])' : ('Debye-Scherrer sample displacement \\1',0.1),
1830        'Lam' : ('Wavelength',1e-6),
1831        'I\(L2\)\/I\(L1\)' : ('Ka2/Ka1 intensity ratio',0.001),
1832        'Polariz\.' : ('Polarization correction',1e-3),
1833        'SH/L' : ('FCJ peak asymmetry correction',1e-4),
1834        '([UVW])$' : ('Gaussian instrument broadening \\1',1e-5),
1835        '([XYZ])$' : ('Cauchy instrument broadening \\1',1e-5),
1836        'Zero' : 'Debye-Scherrer zero correction',
1837        'Shift' : 'Bragg-Brentano sample displ.',
1838        'SurfRoughA' : 'Bragg-Brenano surface roughness A',
1839        'SurfRoughB' : 'Bragg-Brenano surface roughness B',
1840        'Transparency' : 'Bragg-Brentano sample tranparency',
1841        'DebyeA' : 'Debye model amplitude',
1842        'DebyeR' : 'Debye model radius',
1843        'DebyeU' : 'Debye model Uiso',
1844        'RBV.*' : 'Vector rigid body parameter',
1845        'RBR.*' : 'Residue rigid body parameter',
1846        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1847        'RBRP([xyz])' : 'Residue rigid body position parameter',
1848        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1849        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1850        'constr([0-9]*)' : 'Parameter from constraint',
1851        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1852        'mV([0-2])$' : 'Modulation vector component \\1',
1853        'Fsin'  :   'Sin site fraction modulation',
1854        'Fcos'  :   'Cos site fraction modulation',
1855        'Fzero'  :   'Crenel function offset',      #may go away
1856        'Fwid'   :   'Crenel function width',
1857        'Tmin'   :   'ZigZag/Block min location',
1858        'Tmax'   :   'ZigZag/Block max location',
1859        '([XYZ])max': 'ZigZag/Block max value for \\1',
1860        '([XYZ])sin'  : 'Sin position wave for \\1',
1861        '([XYZ])cos'  : 'Cos position wave for \\1',
1862        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1863        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1864        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1865        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1866        # PDF peak parms (l:<var>;l = peak no.)
1867        'PDFpos'  : 'PDF peak position',
1868        'PDFmag'  : 'PDF peak magnitude',
1869        'PDFsig'  : 'PDF peak std. dev.',
1870        # SASD vars (l:<var>;l = component)
1871        'Aspect ratio' : 'Particle aspect ratio',
1872        'Length' : 'Cylinder length',
1873        'Diameter' : 'Cylinder/disk diameter',
1874        'Thickness' : 'Disk thickness',
1875        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
1876        'Dist' : 'Interparticle distance',
1877        'VolFr' : 'Dense scatterer volume fraction',
1878        'epis' : 'Sticky sphere epsilon',
1879        'Sticky' : 'Stickyness',
1880        'Depth' : 'Well depth',
1881        'Width' : 'Well width',
1882        'Volume' : 'Particle volume',
1883        'Radius' : 'Sphere/cylinder/disk radius',
1884        'Mean' : 'Particle mean radius',
1885        'StdDev' : 'Standard deviation in Mean',
1886        'G$': 'Guinier prefactor',
1887        'Rg$': 'Guinier radius of gyration',
1888        'B$': 'Porod prefactor',
1889        'P$': 'Porod power',
1890        'Cutoff': 'Porod cutoff',
1891        'PkInt': 'Bragg peak intensity',
1892        'PkPos': 'Bragg peak position',
1893        'PkSig': 'Bragg peak sigma',
1894        'PkGam': 'Bragg peak gamma',
1895        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1896        'Dcalc': 'Calc. d-spacing',
1897        'Back$': 'background parameter',
1898        'pos$': 'peak position',
1899        'int$': 'peak intensity',
1900        'WgtFrac':'phase weight fraction',
1901        'alpha':'TOF profile term',
1902        'alpha-[01]':'Pink profile term',
1903        'beta-[01q]':'TOF/Pink profile term',
1904        'sig-[012q]':'TOF profile term',
1905        'dif[ABC]':'TOF to d-space calibration',
1906        'C\([0-9]*,[0-9]*\)' : 'spherical harmonics preferred orientation coef.',
1907        }.items():
1908        if len(value) == 2:
1909            #VarDesc[key] = value[0]
1910            reVarDesc[re.compile(key)] = value[0]
1911            reVarStep[re.compile(key)] = value[1]
1912        else:
1913            #VarDesc[key] = value
1914            reVarDesc[re.compile(key)] = value
1915
1916def removeNonRefined(parmList):
1917    '''Remove items from variable list that are not refined and should not
1918    appear as options for constraints
1919
1920    :param list parmList: a list of strings of form "p:h:VAR:a" where
1921      VAR is the variable name
1922
1923    :returns: a list after removing variables where VAR matches a
1924      entry in local variable NonRefinedList
1925    '''
1926    NonRefinedList = ['Omega','Type','Chi','Phi', 'Azimuth','Gonio. radius',
1927                          'Lam1','Lam2','Back','Temperature','Pressure',
1928                          'FreePrm1','FreePrm2','FreePrm3',
1929                          'Source','nPeaks','LeBail','newLeBail','Bank',
1930                          'nDebye', #'',
1931                    ]
1932    return [prm for prm in parmList if prm.split(':')[2] not in NonRefinedList]
1933       
1934def getDescr(name):
1935    '''Return a short description for a GSAS-II variable
1936
1937    :param str name: The descriptive part of the variable name without colons (:)
1938
1939    :returns: a short description or None if not found
1940    '''
1941
1942    CompileVarDesc() # compile the regular expressions, if needed
1943    for key in reVarDesc:
1944        m = key.match(name)
1945        if m:
1946            reVarDesc[key]
1947            return m.expand(reVarDesc[key])
1948    return None
1949
1950def getVarStep(name,parmDict=None):
1951    '''Return a step size for computing the derivative of a GSAS-II variable
1952
1953    :param str name: A complete variable name (with colons, :)
1954    :param dict parmDict: A dict with parameter values or None (default)
1955
1956    :returns: a float that should be an appropriate step size, either from
1957      the value supplied in :func:`CompileVarDesc` or based on the value for
1958      name in parmDict, if supplied. If not found or the value is zero,
1959      a default value of 1e-5 is used. If parmDict is None (default) and
1960      no value is provided in :func:`CompileVarDesc`, then None is returned.
1961    '''
1962    CompileVarDesc() # compile the regular expressions, if needed
1963    for key in reVarStep:
1964        m = key.match(name)
1965        if m:
1966            return reVarStep[key]
1967    if parmDict is None: return None
1968    val = parmDict.get(key,0.0)
1969    if abs(val) > 0.05:
1970        return abs(val)/1000.
1971    else:
1972        return 1e-5
1973
1974def GenWildCard(varlist):
1975    '''Generate wildcard versions of G2 variables. These introduce '*'
1976    for a phase, histogram or atom number (but only for one of these
1977    fields) but only when there is more than one matching variable in the
1978    input variable list. So if the input is this::
1979
1980      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1981
1982    then the output will be this::
1983
1984       wildList = ['*::AUiso:0', '0::AUiso:*']
1985
1986    :param list varlist: an input list of GSAS-II variable names
1987      (such as 0::AUiso:0)
1988
1989    :returns: wildList, the generated list of wild card variable names.
1990    '''
1991    wild = []
1992    for i in (0,1,3):
1993        currentL = varlist[:]
1994        while currentL:
1995            item1 = currentL.pop(0)
1996            i1splt = item1.split(':')
1997            if i >= len(i1splt): continue
1998            if i1splt[i]:
1999                nextL = []
2000                i1splt[i] = '[0-9]+'
2001                rexp = re.compile(':'.join(i1splt))
2002                matchlist = [item1]
2003                for nxtitem in currentL:
2004                    if rexp.match(nxtitem):
2005                        matchlist += [nxtitem]
2006                    else:
2007                        nextL.append(nxtitem)
2008                if len(matchlist) > 1:
2009                    i1splt[i] = '*'
2010                    wild.append(':'.join(i1splt))
2011                currentL = nextL
2012    return wild
2013
2014def LookupWildCard(varname,varlist):
2015    '''returns a list of variable names from list varname
2016    that match wildcard name in varname
2017
2018    :param str varname: a G2 variable name containing a wildcard
2019      (such as \*::var)
2020    :param list varlist: the list of all variable names used in
2021      the current project
2022    :returns: a list of matching GSAS-II variables (may be empty)
2023    '''
2024    rexp = re.compile(varname.replace('*','[0-9]+'))
2025    return sorted([var for var in varlist if rexp.match(var)])
2026
2027def prmLookup(name,prmDict):
2028    '''Looks for a parameter in a min/max dictionary, optionally
2029    considering a wild card for histogram or atom number (use of
2030    both will never occur at the same time).
2031
2032    :param name: a GSAS-II parameter name (str, see :func:`getVarDescr`
2033      and :func:`CompileVarDesc`) or a :class:`G2VarObj` object.
2034      If this contains a wildcard (* for
2035      histogram or atom number) only the exact same name (with
2036      that wildcard) will be matched in parmDict
2037    :param dict prmDict: a min/max dictionary, (parmMinDict
2038      or parmMaxDict in Controls) where keys are :class:`G2VarObj`
2039      objects.
2040    :returns: Two values, (**matchname**, **value**), are returned where:
2041
2042       * **matchname** *(str)* is the :class:`G2VarObj` object
2043         corresponding to the actual matched name,
2044         which could contain a wildcard even if **name** does not; and
2045       * **value** *(float)* which contains the parameter limit.
2046    '''
2047    keyLookup = {str(key):key for key in prmDict}
2048    sn = str(name).split(':')
2049    if str(name) in keyLookup:
2050        return keyLookup[str(name)],prmDict[keyLookup[str(name)]]
2051    elif sn[1] != '':
2052        sn[1] = '*'
2053        wname = ':'.join(sn)
2054    elif len(sn) >= 4 and sn[3] != '':
2055        sn[3] = '*'
2056        wname = ':'.join(sn)
2057    else:
2058        return None,None
2059    if wname in keyLookup:
2060        return keyLookup[wname],prmDict[keyLookup[wname]]
2061    else:
2062        return None,None
2063       
2064
2065def _lookup(dic,key):
2066    '''Lookup a key in a dictionary, where None returns an empty string
2067    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
2068    '''
2069    if key is None:
2070        return ""
2071    elif key == "*":
2072        return "*"
2073    else:
2074        return dic.get(key,'?')
2075
2076def SortVariables(varlist):
2077    '''Sorts variable names in a sensible manner
2078    '''
2079    def cvnnums(var):
2080        v = []
2081        for i in var.split(':'):
2082            if i == '':
2083                v.append(-1)
2084                continue
2085            try:
2086                v.append(int(i))
2087            except:
2088                v.append(i)
2089        return v
2090    return sorted(varlist,key=cvnnums)
2091
2092class G2VarObj(object):
2093    '''Defines a GSAS-II variable either using the phase/atom/histogram
2094    unique Id numbers or using a character string that specifies
2095    variables by phase/atom/histogram number (which can change).
2096    Note that :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`,
2097    which calls :func:`IndexAllIds` (or
2098    :func:`GSASIIscriptable.G2Project.index_ids`) should be used to
2099    (re)load the current Ids
2100    before creating or later using the G2VarObj object.
2101
2102    This can store rigid body variables, but does not translate the residue # and
2103    body # to/from random Ids
2104
2105    A :class:`G2VarObj` object can be created with a single parameter:
2106
2107    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
2108      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
2109
2110     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
2111     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
2112     * a is the atom number (which may be left blank in which case the third colon is omitted).
2113       The atom number can be specified as '*' if a phase number is specified (not as '*').
2114       For rigid body variables, specify a will be a string of form "residue:body#"
2115
2116      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
2117      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
2118      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
2119      For a rigid body variables, AtomID is a string of form "residue:body#".
2120
2121    If four positional arguments are supplied, they are:
2122
2123    :param str/int phasenum: The number for the phase (or None or '*')
2124    :param str/int histnum: The number for the histogram (or None or '*')
2125    :param str varname: a single value can be used to create a :class:`G2VarObj`
2126    :param str/int atomnum: The number for the atom (or None or '*')
2127
2128    '''
2129    IDdict = {}
2130    IDdict['phases'] = {}
2131    IDdict['hists'] = {}
2132    IDdict['atoms'] = {}
2133    def __init__(self,*args):
2134        self.phase = None
2135        self.histogram = None
2136        self.name = ''
2137        self.atom = None
2138        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
2139            # single arg with 4 values
2140            self.phase,self.histogram,self.name,self.atom = args[0]
2141        elif len(args) == 1 and ':' in args[0]:
2142            #parse a string
2143            lst = args[0].split(':')
2144            if lst[0] == '*':
2145                self.phase = '*'
2146                if len(lst) > 3:
2147                    self.atom = lst[3]
2148                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2149            elif lst[1] == '*':
2150                self.histogram = '*'
2151                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2152            else:
2153                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2154                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2155                if len(lst) == 4:
2156                    if lst[3] == '*':
2157                        self.atom = '*'
2158                    else:
2159                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
2160                elif len(lst) == 5:
2161                    self.atom = lst[3]+":"+lst[4]
2162                elif len(lst) == 3:
2163                    pass
2164                else:
2165                    raise Exception("Too many colons in var name "+str(args[0]))
2166            self.name = lst[2]
2167        elif len(args) == 4:
2168            if args[0] == '*':
2169                self.phase = '*'
2170                self.atom = args[3]
2171            else:
2172                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
2173                if args[3] == '*':
2174                    self.atom = '*'
2175                elif args[0] is not None:
2176                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
2177            if args[1] == '*':
2178                self.histogram = '*'
2179            else:
2180                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
2181            self.name = args[2]
2182        else:
2183            raise Exception("Incorrectly called GSAS-II parameter name")
2184
2185        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
2186
2187    def __str__(self):
2188        return self.varname()
2189
2190    def __hash__(self):
2191        'Allow G2VarObj to be a dict key by implementing hashing'
2192        return hash(self.varname())
2193
2194    def varname(self):
2195        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
2196        string (p:h:<var>:a) or (p:h:<var>)
2197
2198        :returns: the variable name as a str
2199        '''
2200        a = ""
2201        if self.phase == "*":
2202            ph = "*"
2203            if self.atom:
2204                a = ":" + str(self.atom)
2205        else:
2206            ph = _lookup(PhaseRanIdLookup,self.phase)
2207            if self.atom == '*':
2208                a = ':*'
2209            elif self.atom:
2210                if ":" in str(self.atom):
2211                    a = ":" + str(self.atom)
2212                elif ph in AtomRanIdLookup:
2213                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
2214                else:
2215                    a = ":?"
2216        if self.histogram == "*":
2217            hist = "*"
2218        else:
2219            hist = _lookup(HistRanIdLookup,self.histogram)
2220        s = (ph + ":" + hist + ":" + str(self.name)) + a
2221        return s
2222
2223    def __repr__(self):
2224        '''Return the detailed contents of the object
2225        '''
2226        s = "<"
2227        if self.phase == '*':
2228            s += "Phases: all; "
2229            if self.atom is not None:
2230                if ":" in str(self.atom):
2231                    s += "Rigid body" + str(self.atom) + "; "
2232                else:
2233                    s += "Atom #" + str(self.atom) + "; "
2234        elif self.phase is not None:
2235            ph =  _lookup(PhaseRanIdLookup,self.phase)
2236            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
2237            if self.atom == '*':
2238                s += "Atoms: all; "
2239            elif ":" in str(self.atom):
2240                s += "Rigid body" + str(self.atom) + "; "
2241            elif self.atom is not None:
2242                s += "Atom rId=" + str(self.atom)
2243                if ph in AtomRanIdLookup:
2244                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
2245                else:
2246                    s += " (#? -- not found!); "
2247        if self.histogram == '*':
2248            s += "Histograms: all; "
2249        elif self.histogram is not None:
2250            hist = _lookup(HistRanIdLookup,self.histogram)
2251            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
2252        s += 'Variable name="' + str(self.name) + '">'
2253        return s+" ("+self.varname()+")"
2254
2255    def __eq__(self, other):
2256        '''Allow comparison of G2VarObj to other G2VarObj objects or strings.
2257        If any field is a wildcard ('*') that field matches.
2258        '''
2259        if type(other) is str:
2260            other = G2VarObj(other)
2261        elif type(other) is not G2VarObj:
2262            raise Exception("Invalid type ({}) for G2VarObj comparison with {}"
2263                            .format(type(other),other))
2264        if self.phase != other.phase and self.phase != '*' and other.phase != '*':
2265            return False
2266        if self.histogram != other.histogram and self.histogram != '*' and other.histogram != '*':
2267            return False
2268        if self.atom != other.atom and self.atom != '*' and other.atom != '*':
2269            return False
2270        if self.name != other.name:
2271            return False
2272        return True
2273
2274    def _show(self):
2275        'For testing, shows the current lookup table'
2276        print ('phases'+ self.IDdict['phases'])
2277        print ('hists'+ self.IDdict['hists'])
2278        print ('atomDict'+ self.IDdict['atoms'])
2279
2280#==========================================================================
2281def SetDefaultSample():
2282    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
2283    return {
2284        'InstrName':'',
2285        'ranId':ran.randint(0,sys.maxsize),
2286        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
2287        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],
2288        'Temperature':300.,'Pressure':0.1,'Time':0.0,
2289        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
2290        'Gonio. radius':200.0,
2291        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
2292#SASD items
2293        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
2294        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
2295        'Trans':1.0,                            #measured transmission
2296        'SlitLen':0.0,                          #Slit length - in Q(A-1)
2297        }
2298######################################################################
2299class ImportBaseclass(object):
2300    '''Defines a base class for the reading of input files (diffraction
2301    data, coordinates,...). See :ref:`Writing a Import Routine<import_routines>`
2302    for an explanation on how to use a subclass of this class.
2303    '''
2304    class ImportException(Exception):
2305        '''Defines an Exception that is used when an import routine hits an expected error,
2306        usually in .Reader.
2307
2308        Good practice is that the Reader should define a value in self.errors that
2309        tells the user some information about what is wrong with their file.
2310        '''
2311        pass
2312
2313    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
2314    def __init__(self,formatName,longFormatName=None,
2315                 extensionlist=[],strictExtension=False,):
2316        self.formatName = formatName # short string naming file type
2317        if longFormatName: # longer string naming file type
2318            self.longFormatName = longFormatName
2319        else:
2320            self.longFormatName = formatName
2321        # define extensions that are allowed for the file type
2322        # for windows, remove any extensions that are duplicate, as case is ignored
2323        if sys.platform == 'windows' and extensionlist:
2324            extensionlist = list(set([s.lower() for s in extensionlist]))
2325        self.extensionlist = extensionlist
2326        # If strictExtension is True, the file will not be read, unless
2327        # the extension matches one in the extensionlist
2328        self.strictExtension = strictExtension
2329        self.errors = ''
2330        self.warnings = ''
2331        self.SciPy = False          #image reader needed scipy
2332        # used for readers that will use multiple passes to read
2333        # more than one data block
2334        self.repeat = False
2335        self.selections = []
2336        self.repeatcount = 0
2337        self.readfilename = '?'
2338        self.scriptable = False
2339        #print 'created',self.__class__
2340
2341    def ReInitialize(self):
2342        'Reinitialize the Reader to initial settings'
2343        self.errors = ''
2344        self.warnings = ''
2345        self.SciPy = False          #image reader needed scipy
2346        self.repeat = False
2347        self.repeatcount = 0
2348        self.readfilename = '?'
2349
2350
2351#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
2352#        '''This method must be supplied in the child class to read the file.
2353#        if the read fails either return False or raise an Exception
2354#        preferably of type ImportException.
2355#        '''
2356#        #start reading
2357#        raise ImportException("Error occurred while...")
2358#        self.errors += "Hint for user on why the error occur
2359#        return False # if an error occurs
2360#        return True # if read OK
2361
2362    def ExtensionValidator(self, filename):
2363        '''This methods checks if the file has the correct extension
2364       
2365        :returns:
2366       
2367          * False if this filename will not be supported by this reader (only
2368            when strictExtension is True)
2369          * True if the extension matches the list supplied by the reader
2370          * None if the reader allows un-registered extensions
2371         
2372        '''
2373        if filename:
2374            ext = ospath.splitext(filename)[1]
2375            if not ext and self.strictExtension: return False
2376            for ext in self.extensionlist:               
2377                if sys.platform == 'windows':
2378                    if filename.lower().endswith(ext): return True
2379                else:
2380                    if filename.endswith(ext): return True
2381        if self.strictExtension:
2382            return False
2383        else:
2384            return None
2385
2386    def ContentsValidator(self, filename):
2387        '''This routine will attempt to determine if the file can be read
2388        with the current format.
2389        This will typically be overridden with a method that
2390        takes a quick scan of [some of]
2391        the file contents to do a "sanity" check if the file
2392        appears to match the selected format.
2393        the file must be opened here with the correct format (binary/text)
2394        '''
2395        #filepointer.seek(0) # rewind the file pointer
2396        return True
2397
2398    def CIFValidator(self, filepointer):
2399        '''A :meth:`ContentsValidator` for use to validate CIF files.
2400        '''
2401        filepointer.seek(0)
2402        for i,l in enumerate(filepointer):
2403            if i >= 1000: return True
2404            '''Encountered only blank lines or comments in first 1000
2405            lines. This is unlikely, but assume it is CIF anyway, since we are
2406            even less likely to find a file with nothing but hashes and
2407            blank lines'''
2408            line = l.strip()
2409            if len(line) == 0: # ignore blank lines
2410                continue
2411            elif line.startswith('#'): # ignore comments
2412                continue
2413            elif line.startswith('data_'): # on the right track, accept this file
2414                return True
2415            else: # found something invalid
2416                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
2417                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
2418                    self.errors += '  '+str(l)
2419                else:
2420                    self.errors += '  (binary)'
2421                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
2422                self.errors += '\n        a data_ statement begins a block.'
2423                return False
2424
2425######################################################################
2426class ImportPhase(ImportBaseclass):
2427    '''Defines a base class for the reading of files with coordinates
2428
2429    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
2430    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` and in
2431    :func:`GSASIIscriptable.import_generic`.
2432    See :ref:`Writing a Import Routine<import_routines>`
2433    for an explanation on how to use this class.
2434
2435    '''
2436    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2437        strictExtension=False,):
2438        # call parent __init__
2439        ImportBaseclass.__init__(self,formatName,longFormatName,
2440            extensionlist,strictExtension)
2441        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
2442        self.Constraints = None
2443
2444######################################################################
2445class ImportStructFactor(ImportBaseclass):
2446    '''Defines a base class for the reading of files with tables
2447    of structure factors.
2448
2449    Structure factors are read with a call to :meth:`GSASIIdataGUI.GSASII.OnImportSfact`
2450    which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`, which calls
2451    methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2452    :meth:`Reader`.
2453
2454    See :ref:`Writing a Import Routine<import_routines>`
2455    for an explanation on how to use import classes in general. The specifics
2456    for reading a structure factor histogram require that
2457    the ``Reader()`` routine in the import
2458    class need to do only a few things: It
2459    should load :attr:`RefDict` item ``'RefList'`` with the reflection list,
2460    and set :attr:`Parameters` with the instrument parameters
2461    (initialized with :meth:`InitParameters` and set with :meth:`UpdateParameters`).
2462    '''
2463    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2464        strictExtension=False,):
2465        ImportBaseclass.__init__(self,formatName,longFormatName,
2466            extensionlist,strictExtension)
2467
2468        # define contents of Structure Factor entry
2469        self.Parameters = []
2470        'self.Parameters is a list with two dicts for data parameter settings'
2471        self.InitParameters()
2472        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2473        self.Banks = []             #for multi bank data (usually TOF)
2474        '''self.RefDict is a dict containing the reflection information, as read from the file.
2475        Item 'RefList' contains the reflection information. See the
2476        :ref:`Single Crystal Reflection Data Structure<XtalRefl_table>`
2477        for the contents of each row. Dict element 'FF'
2478        contains the form factor values for each element type; if this entry
2479        is left as initialized (an empty list) it will be initialized as needed later.
2480        '''
2481    def ReInitialize(self):
2482        'Reinitialize the Reader to initial settings'
2483        ImportBaseclass.ReInitialize(self)
2484        self.InitParameters()
2485        self.Banks = []             #for multi bank data (usually TOF)
2486        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2487
2488    def InitParameters(self):
2489        'initialize the instrument parameters structure'
2490        Lambda = 0.70926
2491        HistType = 'SXC'
2492        self.Parameters = [{'Type':[HistType,HistType], # create the structure
2493                            'Lam':[Lambda,Lambda]
2494                            }, {}]
2495        'Parameters is a list with two dicts for data parameter settings'
2496
2497    def UpdateParameters(self,Type=None,Wave=None):
2498        'Revise the instrument parameters'
2499        if Type is not None:
2500            self.Parameters[0]['Type'] = [Type,Type]
2501        if Wave is not None:
2502            self.Parameters[0]['Lam'] = [Wave,Wave]
2503
2504######################################################################
2505class ImportPowderData(ImportBaseclass):
2506    '''Defines a base class for the reading of files with powder data.
2507
2508    Objects constructed that subclass this (in import/G2pwd_*.py etc.) will be used
2509    in :meth:`GSASIIdataGUI.GSASII.OnImportPowder` and in
2510    :func:`GSASIIscriptable.import_generic`.
2511    See :ref:`Writing a Import Routine<import_routines>`
2512    for an explanation on how to use this class.
2513    '''
2514    def __init__(self,formatName,longFormatName=None,
2515        extensionlist=[],strictExtension=False,):
2516        ImportBaseclass.__init__(self,formatName,longFormatName,
2517            extensionlist,strictExtension)
2518        self.clockWd = None  # used in TOF
2519        self.ReInitialize()
2520
2521    def ReInitialize(self):
2522        'Reinitialize the Reader to initial settings'
2523        ImportBaseclass.ReInitialize(self)
2524        self.powderentry = ['',None,None] #  (filename,Pos,Bank)
2525        self.powderdata = [] # Powder dataset
2526        '''A powder data set is a list with items [x,y,w,yc,yb,yd]:
2527                np.array(x), # x-axis values
2528                np.array(y), # powder pattern intensities
2529                np.array(w), # 1/sig(intensity)^2 values (weights)
2530                np.array(yc), # calc. intensities (zero)
2531                np.array(yb), # calc. background (zero)
2532                np.array(yd), # obs-calc profiles
2533        '''
2534        self.comments = []
2535        self.idstring = ''
2536        self.Sample = SetDefaultSample() # default sample parameters
2537        self.Controls = {}  # items to be placed in top-level Controls
2538        self.GSAS = None     # used in TOF
2539        self.repeat_instparm = True # Should a parm file be
2540        #                             used for multiple histograms?
2541        self.instparm = None # name hint from file of instparm to use
2542        self.instfile = '' # full path name to instrument parameter file
2543        self.instbank = '' # inst parm bank number
2544        self.instmsg = ''  # a label that gets printed to show
2545                           # where instrument parameters are from
2546        self.numbanks = 1
2547        self.instdict = {} # place items here that will be transferred to the instrument parameters
2548        self.pwdparms = {} # place parameters that are transferred directly to the tree
2549                           # here (typically from an existing GPX file)
2550######################################################################
2551class ImportSmallAngleData(ImportBaseclass):
2552    '''Defines a base class for the reading of files with small angle data.
2553    See :ref:`Writing a Import Routine<import_routines>`
2554    for an explanation on how to use this class.
2555    '''
2556    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2557        strictExtension=False,):
2558
2559        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2560            strictExtension)
2561        self.ReInitialize()
2562
2563    def ReInitialize(self):
2564        'Reinitialize the Reader to initial settings'
2565        ImportBaseclass.ReInitialize(self)
2566        self.smallangleentry = ['',None,None] #  (filename,Pos,Bank)
2567        self.smallangledata = [] # SASD dataset
2568        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2569                np.array(x), # x-axis values
2570                np.array(y), # powder pattern intensities
2571                np.array(w), # 1/sig(intensity)^2 values (weights)
2572                np.array(yc), # calc. intensities (zero)
2573                np.array(yd), # obs-calc profiles
2574                np.array(yb), # preset bkg
2575        '''
2576        self.comments = []
2577        self.idstring = ''
2578        self.Sample = SetDefaultSample()
2579        self.GSAS = None     # used in TOF
2580        self.clockWd = None  # used in TOF
2581        self.numbanks = 1
2582        self.instdict = {} # place items here that will be transferred to the instrument parameters
2583
2584######################################################################
2585class ImportReflectometryData(ImportBaseclass):
2586    '''Defines a base class for the reading of files with reflectometry data.
2587    See :ref:`Writing a Import Routine<import_routines>`
2588    for an explanation on how to use this class.
2589    '''
2590    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2591        strictExtension=False,):
2592
2593        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2594            strictExtension)
2595        self.ReInitialize()
2596
2597    def ReInitialize(self):
2598        'Reinitialize the Reader to initial settings'
2599        ImportBaseclass.ReInitialize(self)
2600        self.reflectometryentry = ['',None,None] #  (filename,Pos,Bank)
2601        self.reflectometrydata = [] # SASD dataset
2602        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2603                np.array(x), # x-axis values
2604                np.array(y), # powder pattern intensities
2605                np.array(w), # 1/sig(intensity)^2 values (weights)
2606                np.array(yc), # calc. intensities (zero)
2607                np.array(yd), # obs-calc profiles
2608                np.array(yb), # preset bkg
2609        '''
2610        self.comments = []
2611        self.idstring = ''
2612        self.Sample = SetDefaultSample()
2613        self.GSAS = None     # used in TOF
2614        self.clockWd = None  # used in TOF
2615        self.numbanks = 1
2616        self.instdict = {} # place items here that will be transferred to the instrument parameters
2617
2618######################################################################
2619class ImportPDFData(ImportBaseclass):
2620    '''Defines a base class for the reading of files with PDF G(R) data.
2621    See :ref:`Writing a Import Routine<import_routines>`
2622    for an explanation on how to use this class.
2623    '''
2624    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2625        strictExtension=False,):
2626
2627        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2628            strictExtension)
2629        self.ReInitialize()
2630
2631    def ReInitialize(self):
2632        'Reinitialize the Reader to initial settings'
2633        ImportBaseclass.ReInitialize(self)
2634        self.pdfentry = ['',None,None] #  (filename,Pos,Bank)
2635        self.pdfdata = [] # PDF G(R) dataset
2636        '''A pdf g(r) data set is a list with items [x,y]:
2637                np.array(x), # r-axis values
2638                np.array(y), # pdf g(r)
2639        '''
2640        self.comments = []
2641        self.idstring = ''
2642        self.numbanks = 1
2643
2644######################################################################
2645class ImportImage(ImportBaseclass):
2646    '''Defines a base class for the reading of images
2647
2648    Images are read in only these places:
2649
2650      * Initial reading is typically done from a menu item
2651        with a call to :meth:`GSASIIdataGUI.GSASII.OnImportImage`
2652        which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`. That calls
2653        methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2654        :meth:`Reader`. This returns a list of reader objects for each read image.
2655        Also used in :func:`GSASIIscriptable.import_generic`.
2656
2657      * Images are read alternatively in :func:`GSASIIIO.ReadImages`, which puts image info
2658        directly into the data tree.
2659
2660      * Images are reloaded with :func:`GSASIIIO.GetImageData`.
2661
2662    When reading an image, the ``Reader()`` routine in the ImportImage class
2663    should set:
2664
2665      * :attr:`Comments`: a list of strings (str),
2666      * :attr:`Npix`: the number of pixels in the image (int),
2667      * :attr:`Image`: the actual image as a numpy array (np.array)
2668      * :attr:`Data`: a dict defining image parameters (dict). Within this dict the following
2669        data items are needed:
2670
2671         * 'pixelSize': size of each pixel in microns (such as ``[200.,200.]``.
2672         * 'wavelength': wavelength in :math:`\\AA`.
2673         * 'distance': distance of detector from sample in cm.
2674         * 'center': uncalibrated center of beam on detector (such as ``[204.8,204.8]``.
2675         * 'size': size of image (such as ``[2048,2048]``).
2676         * 'ImageTag': image number or other keyword used to retrieve image from
2677           a multi-image data file (defaults to ``1`` if not specified).
2678         * 'sumfile': holds sum image file name if a sum was produced from a multi image file
2679
2680    optional data items:
2681
2682      * :attr:`repeat`: set to True if there are additional images to
2683        read in the file, False otherwise
2684      * :attr:`repeatcount`: set to the number of the image.
2685
2686    Note that the above is initialized with :meth:`InitParameters`.
2687    (Also see :ref:`Writing a Import Routine<import_routines>`
2688    for an explanation on how to use import classes in general.)
2689    '''
2690    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2691        strictExtension=False,):
2692        ImportBaseclass.__init__(self,formatName,longFormatName,
2693            extensionlist,strictExtension)
2694        self.InitParameters()
2695
2696    def ReInitialize(self):
2697        'Reinitialize the Reader to initial settings -- not used at present'
2698        ImportBaseclass.ReInitialize(self)
2699        self.InitParameters()
2700
2701    def InitParameters(self):
2702        'initialize the instrument parameters structure'
2703        self.Comments = ['No comments']
2704        self.Data = {}
2705        self.Npix = 0
2706        self.Image = None
2707        self.repeat = False
2708        self.repeatcount = 1
2709        self.sumfile = ''
2710
2711    def LoadImage(self,ParentFrame,imagefile,imagetag=None):
2712        '''Optionally, call this after reading in an image to load it into the tree.
2713        This saves time by preventing a reread of the same information.
2714        '''
2715        if ParentFrame:
2716            ParentFrame.ImageZ = self.Image   # store the image for plotting
2717            ParentFrame.oldImagefile = imagefile # save the name of the last image file read
2718            ParentFrame.oldImageTag = imagetag   # save the tag of the last image file read
2719
2720#################################################################################################
2721# shortcut routines
2722exp = np.exp
2723sind = sin = s = lambda x: np.sin(x*np.pi/180.)
2724cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
2725tand = tan = t = lambda x: np.tan(x*np.pi/180.)
2726sqrt = sq = lambda x: np.sqrt(x)
2727pi = lambda: np.pi
2728class ExpressionObj(object):
2729    '''Defines an object with a user-defined expression, to be used for
2730    secondary fits or restraints. Object is created null, but is changed
2731    using :meth:`LoadExpression`. This contains only the minimum
2732    information that needs to be stored to save and load the expression
2733    and how it is mapped to GSAS-II variables.
2734    '''
2735    def __init__(self):
2736        self.expression = ''
2737        'The expression as a text string'
2738        self.assgnVars = {}
2739        '''A dict where keys are label names in the expression mapping to a GSAS-II
2740        variable. The value a G2 variable name.
2741        Note that the G2 variable name may contain a wild-card and correspond to
2742        multiple values.
2743        '''
2744        self.freeVars = {}
2745        '''A dict where keys are label names in the expression mapping to a free
2746        parameter. The value is a list with:
2747
2748         * a name assigned to the parameter
2749         * a value for to the parameter and
2750         * a flag to determine if the variable is refined.
2751        '''
2752        self.depVar = None
2753
2754        self.lastError = ('','')
2755        '''Shows last encountered error in processing expression
2756        (list of 1-3 str values)'''
2757
2758        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
2759        self.distance_atoms = None  # to be used for defining atom distances
2760
2761    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
2762        '''Load the expression and associated settings into the object. Raises
2763        an exception if the expression is not parsed, if not all functions
2764        are defined or if not all needed parameter labels in the expression
2765        are defined.
2766
2767        This will not test if the variable referenced in these definitions
2768        are actually in the parameter dictionary. This is checked when the
2769        computation for the expression is done in :meth:`SetupCalc`.
2770
2771        :param str expr: the expression
2772        :param list exprVarLst: parameter labels found in the expression
2773        :param dict varSelect: this will be 0 for Free parameters
2774          and non-zero for expression labels linked to G2 variables.
2775        :param dict varName: Defines a name (str) associated with each free parameter
2776        :param dict varValue: Defines a value (float) associated with each free parameter
2777        :param dict varRefflag: Defines a refinement flag (bool)
2778          associated with each free parameter
2779        '''
2780        self.expression = expr
2781        self.compiledExpr = None
2782        self.freeVars = {}
2783        self.assgnVars = {}
2784        for v in exprVarLst:
2785            if varSelect[v] == 0:
2786                self.freeVars[v] = [
2787                    varName.get(v),
2788                    varValue.get(v),
2789                    varRefflag.get(v),
2790                    ]
2791            else:
2792                self.assgnVars[v] = varName[v]
2793        self.CheckVars()
2794
2795    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
2796        '''Load the expression and associated settings from the object into
2797        arrays used for editing.
2798
2799        :param list exprVarLst: parameter labels found in the expression
2800        :param dict varSelect: this will be 0 for Free parameters
2801          and non-zero for expression labels linked to G2 variables.
2802        :param dict varName: Defines a name (str) associated with each free parameter
2803        :param dict varValue: Defines a value (float) associated with each free parameter
2804        :param dict varRefflag: Defines a refinement flag (bool)
2805          associated with each free parameter
2806
2807        :returns: the expression as a str
2808        '''
2809        for v in self.freeVars:
2810            varSelect[v] = 0
2811            varName[v] = self.freeVars[v][0]
2812            varValue[v] = self.freeVars[v][1]
2813            varRefflag[v] = self.freeVars[v][2]
2814        for v in self.assgnVars:
2815            varSelect[v] = 1
2816            varName[v] = self.assgnVars[v]
2817        return self.expression
2818
2819    def GetVaried(self):
2820        'Returns the names of the free parameters that will be refined'
2821        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
2822
2823    def GetVariedVarVal(self):
2824        'Returns the names and values of the free parameters that will be refined'
2825        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
2826
2827    def UpdateVariedVars(self,varyList,values):
2828        'Updates values for the free parameters (after a refinement); only updates refined vars'
2829        for v in self.freeVars:
2830            if not self.freeVars[v][2]: continue
2831            if "::"+self.freeVars[v][0] not in varyList: continue
2832            indx = list(varyList).index("::"+self.freeVars[v][0])
2833            self.freeVars[v][1] = values[indx]
2834
2835    def GetIndependentVars(self):
2836        'Returns the names of the required independent parameters used in expression'
2837        return [self.assgnVars[v] for v in self.assgnVars]
2838
2839    def CheckVars(self):
2840        '''Check that the expression can be parsed, all functions are
2841        defined and that input loaded into the object is internally
2842        consistent. If not an Exception is raised.
2843
2844        :returns: a dict with references to packages needed to
2845          find functions referenced in the expression.
2846        '''
2847        ret = self.ParseExpression(self.expression)
2848        if not ret:
2849            raise Exception("Expression parse error")
2850        exprLblList,fxnpkgdict = ret
2851        # check each var used in expression is defined
2852        defined = list(self.assgnVars.keys()) + list(self.freeVars.keys())
2853        notfound = []
2854        for var in exprLblList:
2855            if var not in defined:
2856                notfound.append(var)
2857        if notfound:
2858            msg = 'Not all variables defined'
2859            msg1 = 'The following variables were not defined: '
2860            msg2 = ''
2861            for var in notfound:
2862                if msg: msg += ', '
2863                msg += var
2864            self.lastError = (msg1,'  '+msg2)
2865            raise Exception(msg)
2866        return fxnpkgdict
2867
2868    def ParseExpression(self,expr):
2869        '''Parse an expression and return a dict of called functions and
2870        the variables used in the expression. Returns None in case an error
2871        is encountered. If packages are referenced in functions, they are loaded
2872        and the functions are looked up into the modules global
2873        workspace.
2874
2875        Note that no changes are made to the object other than
2876        saving an error message, so that this can be used for testing prior
2877        to the save.
2878
2879        :returns: a list of used variables
2880        '''
2881        self.lastError = ('','')
2882        import ast
2883        def FindFunction(f):
2884            '''Find the object corresponding to function f
2885            :param str f: a function name such as 'numpy.exp'
2886            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
2887              that defines the package location(s) and where pkgobj
2888              defines the object associated with the function.
2889              If the function is not found, pkgobj is None.
2890            '''
2891            df = f.split('.')
2892            pkgdict = {}
2893            # no listed package, try in current namespace
2894            if len(df) == 1:
2895                try:
2896                    fxnobj = eval(f)
2897                    return pkgdict,fxnobj
2898                except (AttributeError, NameError):
2899                    return None,None
2900            else:
2901                try:
2902                    fxnobj = eval(f)
2903                    pkgdict[df[0]] = eval(df[0])
2904                    return pkgdict,fxnobj
2905                except (AttributeError, NameError):
2906                    pass
2907            # includes a package, lets try to load the packages
2908            pkgname = ''
2909            path = sys.path+['./',]
2910            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
2911                if pkgname:
2912                    pkgname += '.' + pkg
2913                else:
2914                    pkgname = pkg
2915                fp = None
2916                try:
2917                    fp, fppath,desc = imp.find_module(pkg,path)
2918                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
2919                    pkgdict[pkgname] = pkgobj
2920                    path = [fppath]
2921                except Exception as msg:
2922                    print('load of '+pkgname+' failed with error='+str(msg))
2923                    return {},None
2924                finally:
2925                    if fp: fp.close()
2926                try:
2927                    #print 'before',pkgdict.keys()
2928                    fxnobj = eval(f,globals(),pkgdict)
2929                    #print 'after 1',pkgdict.keys()
2930                    #fxnobj = eval(f,pkgdict)
2931                    #print 'after 2',pkgdict.keys()
2932                    return pkgdict,fxnobj
2933                except:
2934                    continue
2935            return None # not found
2936        def ASTtransverse(node,fxn=False):
2937            '''Transverse a AST-parsed expresson, compiling a list of variables
2938            referenced in the expression. This routine is used recursively.
2939
2940            :returns: varlist,fxnlist where
2941              varlist is a list of referenced variable names and
2942              fxnlist is a list of used functions
2943            '''
2944            varlist = []
2945            fxnlist = []
2946            if isinstance(node, list):
2947                for b in node:
2948                    v,f = ASTtransverse(b,fxn)
2949                    varlist += v
2950                    fxnlist += f
2951            elif isinstance(node, ast.AST):
2952                for a, b in ast.iter_fields(node):
2953                    if isinstance(b, ast.AST):
2954                        if a == 'func':
2955                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
2956                            continue
2957                        v,f = ASTtransverse(b,fxn)
2958                        varlist += v
2959                        fxnlist += f
2960                    elif isinstance(b, list):
2961                        v,f = ASTtransverse(b,fxn)
2962                        varlist += v
2963                        fxnlist += f
2964                    elif node.__class__.__name__ == "Name":
2965                        varlist += [b]
2966                    elif fxn and node.__class__.__name__ == "Attribute":
2967                        varlist += [b]
2968            return varlist,fxnlist
2969        try:
2970            exprast = ast.parse(expr)
2971        except SyntaxError:
2972            s = ''
2973            import traceback
2974            for i in traceback.format_exc().splitlines()[-3:-1]:
2975                if s: s += "\n"
2976                s += str(i)
2977            self.lastError = ("Error parsing expression:",s)
2978            return
2979        # find the variables & functions
2980        v,f = ASTtransverse(exprast)
2981        varlist = sorted(list(set(v)))
2982        fxnlist = list(set(f))
2983        pkgdict = {}
2984        # check the functions are defined
2985        for fxn in fxnlist:
2986            fxndict,fxnobj = FindFunction(fxn)
2987            if not fxnobj:
2988                self.lastError = ("Error: Invalid function",fxn,
2989                                  "is not defined")
2990                return
2991            if not hasattr(fxnobj,'__call__'):
2992                self.lastError = ("Error: Not a function.",fxn,
2993                                  "cannot be called as a function")
2994                return
2995            pkgdict.update(fxndict)
2996        return varlist,pkgdict
2997
2998    def GetDepVar(self):
2999        'return the dependent variable, or None'
3000        return self.depVar
3001
3002    def SetDepVar(self,var):
3003        'Set the dependent variable, if used'
3004        self.depVar = var
3005#==========================================================================
3006class ExpressionCalcObj(object):
3007    '''An object used to evaluate an expression from a :class:`ExpressionObj`
3008    object.
3009
3010    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
3011      an expression string and mappings for the parameter labels in that object.
3012    '''
3013    def __init__(self,exprObj):
3014        self.eObj = exprObj
3015        'The expression and mappings; a :class:`ExpressionObj` object'
3016        self.compiledExpr = None
3017        'The expression as compiled byte-code'
3018        self.exprDict = {}
3019        '''dict that defines values for labels used in expression and packages
3020        referenced by functions
3021        '''
3022        self.lblLookup = {}
3023        '''Lookup table that specifies the expression label name that is
3024        tied to a particular GSAS-II parameters in the parmDict.
3025        '''
3026        self.fxnpkgdict = {}
3027        '''a dict with references to packages needed to
3028        find functions referenced in the expression.
3029        '''
3030        self.varLookup = {}
3031        '''Lookup table that specifies the GSAS-II variable(s)
3032        indexed by the expression label name. (Used for only for diagnostics
3033        not evaluation of expression.)
3034        '''
3035        self.su = None
3036        '''Standard error evaluation where supplied by the evaluator
3037        '''
3038        # Patch: for old-style expressions with a (now removed step size)
3039        if '2' in platform.python_version_tuple()[0]: 
3040            basestr = basestring
3041        else:
3042            basestr = str
3043        for v in self.eObj.assgnVars:
3044            if not isinstance(self.eObj.assgnVars[v], basestr):
3045                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
3046        self.parmDict = {}
3047        '''A copy of the parameter dictionary, for distance and angle computation
3048        '''
3049
3050    def SetupCalc(self,parmDict):
3051        '''Do all preparations to use the expression for computation.
3052        Adds the free parameter values to the parameter dict (parmDict).
3053        '''
3054        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
3055            return
3056        self.fxnpkgdict = self.eObj.CheckVars()
3057        # all is OK, compile the expression
3058        self.compiledExpr = compile(self.eObj.expression,'','eval')
3059
3060        # look at first value in parmDict to determine its type
3061        parmsInList = True
3062        if '2' in platform.python_version_tuple()[0]: 
3063            basestr = basestring
3064        else:
3065            basestr = str
3066        for key in parmDict:
3067            val = parmDict[key]
3068            if isinstance(val, basestr):
3069                parmsInList = False
3070                break
3071            try: # check if values are in lists
3072                val = parmDict[key][0]
3073            except (TypeError,IndexError):
3074                parmsInList = False
3075            break
3076
3077        # set up the dicts needed to speed computations
3078        self.exprDict = {}
3079        self.lblLookup = {}
3080        self.varLookup = {}
3081        for v in self.eObj.freeVars:
3082            varname = self.eObj.freeVars[v][0]
3083            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
3084            self.lblLookup[varname] = v
3085            self.varLookup[v] = varname
3086            if parmsInList:
3087                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
3088            else:
3089                parmDict[varname] = self.eObj.freeVars[v][1]
3090            self.exprDict[v] = self.eObj.freeVars[v][1]
3091        for v in self.eObj.assgnVars:
3092            varname = self.eObj.assgnVars[v]
3093            if varname in parmDict:
3094                self.lblLookup[varname] = v
3095                self.varLookup[v] = varname
3096                if parmsInList:
3097                    self.exprDict[v] = parmDict[varname][0]
3098                else:
3099                    self.exprDict[v] = parmDict[varname]
3100            elif '*' in varname:
3101                varlist = LookupWildCard(varname,list(parmDict.keys()))
3102                if len(varlist) == 0:
3103                    raise Exception("No variables match "+str(v))
3104                for var in varlist:
3105                    self.lblLookup[var] = v
3106                if parmsInList:
3107                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
3108                else:
3109                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
3110                self.varLookup[v] = [var for var in varlist]
3111            else:
3112                self.exprDict[v] = None
3113#                raise Exception,"No value for variable "+str(v)
3114        self.exprDict.update(self.fxnpkgdict)
3115
3116    def UpdateVars(self,varList,valList):
3117        '''Update the dict for the expression with a set of values
3118        :param list varList: a list of variable names
3119        :param list valList: a list of corresponding values
3120        '''
3121        for var,val in zip(varList,valList):
3122            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
3123
3124    def UpdateDict(self,parmDict):
3125        '''Update the dict for the expression with values in a dict
3126        :param dict parmDict: a dict of values, items not in use are ignored
3127        '''
3128        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
3129            self.parmDict = parmDict
3130            return
3131        for var in parmDict:
3132            if var in self.lblLookup:
3133                self.exprDict[self.lblLookup[var]] = parmDict[var]
3134
3135    def EvalExpression(self):
3136        '''Evaluate an expression. Note that the expression
3137        and mapping are taken from the :class:`ExpressionObj` expression object
3138        and the parameter values were specified in :meth:`SetupCalc`.
3139        :returns: a single value for the expression. If parameter
3140        values are arrays (for example, from wild-carded variable names),
3141        the sum of the resulting expression is returned.
3142
3143        For example, if the expression is ``'A*B'``,
3144        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
3145
3146        [0.5, 1, 0.5]
3147
3148        then the result will be ``4.0``.
3149        '''
3150        self.su = None
3151        if self.eObj.expression.startswith('Dist'):
3152#            GSASIIpath.IPyBreak()
3153            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
3154            return dist
3155        elif self.eObj.expression.startswith('Angle'):
3156            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
3157            return angle
3158        if self.compiledExpr is None:
3159            raise Exception("EvalExpression called before SetupCalc")
3160        try:
3161            val = eval(self.compiledExpr,globals(),self.exprDict)
3162        except TypeError:
3163            val = None
3164        if not np.isscalar(val):
3165            val = np.sum(val)
3166        return val
3167
3168class G2Exception(Exception):
3169    'A generic GSAS-II exception class'
3170    def __init__(self,msg):
3171        self.msg = msg
3172    def __str__(self):
3173        return repr(self.msg)
3174
3175class G2RefineCancel(Exception):
3176    'Raised when Cancel is pressed in a refinement dialog'
3177    def __init__(self,msg):
3178        self.msg = msg
3179    def __str__(self):
3180        return repr(self.msg)
3181   
3182def HowDidIgetHere(wherecalledonly=False):
3183    '''Show a traceback with calls that brought us to the current location.
3184    Used for debugging.
3185    '''
3186    import traceback
3187    if wherecalledonly:
3188        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
3189        print(i.strip().rstrip())
3190    else:
3191        print (70*'*')
3192        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
3193        print (70*'*')
3194
3195# Note that this is GUI code and should be moved at somepoint
3196def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
3197    '''Create and initialize a new set of PDF tree entries
3198
3199    :param Frame G2frame: main GSAS-II tree frame object
3200    :param str PWDRtree: name of PWDR to be used to create PDF item
3201    :param dict ElList: data structure with composition
3202    :param list Qlimits: Q limits to be used for computing the PDF
3203    :param float numAtm: no. atom in chemical formula
3204    :param float FltBkg: flat background value
3205    :param list PDFnames: previously used PDF names
3206
3207    :returns: the Id of the newly created PDF entry
3208    '''
3209    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
3210    if PDFname in PDFnames:
3211        print('Skipping, entry already exists: '+PDFname)
3212        return None
3213    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
3214    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
3215    Data = {
3216        'Sample':{'Name':PWDRtree,'Mult':1.0},
3217        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
3218        'Container':{'Name':'','Mult':-1.0,'Refine':False},
3219        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
3220        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
3221        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
3222        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
3223        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
3224    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
3225    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
3226        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
3227    return Id
3228#%%
3229class ShowTiming(object):
3230    '''An object to use for timing repeated sections of code.
3231
3232    Create the object with::
3233       tim0 = ShowTiming()
3234
3235    Tag sections of code to be timed with::
3236       tim0.start('start')
3237       tim0.start('in section 1')
3238       tim0.start('in section 2')
3239       
3240    etc. (Note that each section should have a unique label.)
3241
3242    After the last section, end timing with::
3243       tim0.end()
3244
3245    Show timing results with::
3246       tim0.show()
3247       
3248    '''
3249    def __init__(self):
3250        self.timeSum =  []
3251        self.timeStart = []
3252        self.label = []
3253        self.prev = None
3254    def start(self,label):
3255        import time
3256        if label in self.label:
3257            i = self.label.index(label)
3258            self.timeStart[i] = time.time()
3259        else:
3260            i = len(self.label)
3261            self.timeSum.append(0.0)
3262            self.timeStart.append(time.time())
3263            self.label.append(label)
3264        if self.prev is not None:
3265            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
3266        self.prev = i
3267    def end(self):
3268        import time
3269        if self.prev is not None:
3270            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
3271        self.prev = None
3272    def show(self):
3273        sumT = sum(self.timeSum)
3274        print('Timing results (total={:.2f} sec)'.format(sumT))
3275        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
3276            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
3277#%%
3278
3279if __name__ == "__main__":
3280    # test variable descriptions
3281    for var in '0::Afrac:*',':1:Scale','1::dAx:0','::undefined':
3282        v = var.split(':')[2]
3283        print(var+':\t', getDescr(v),getVarStep(v))
3284    import sys; sys.exit()
3285    # test equation evaluation
3286    def showEQ(calcobj):
3287        print (50*'=')
3288        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
3289        for v in sorted(calcobj.varLookup):
3290            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
3291        # print '  Derivatives'
3292        # for v in calcobj.derivStep.keys():
3293        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
3294
3295    obj = ExpressionObj()
3296
3297    obj.expression = "A*np.exp(B)"
3298    obj.assgnVars =  {'B': '0::Afrac:1'}
3299    obj.freeVars =  {'A': [u'A', 0.5, True]}
3300    #obj.CheckVars()
3301    calcobj = ExpressionCalcObj(obj)
3302
3303    obj1 = ExpressionObj()
3304    obj1.expression = "A*np.exp(B)"
3305    obj1.assgnVars =  {'B': '0::Afrac:*'}
3306    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
3307    #obj.CheckVars()
3308    calcobj1 = ExpressionCalcObj(obj1)
3309
3310    obj2 = ExpressionObj()
3311    obj2.distance_stuff = np.array([[0,1],[1,-1]])
3312    obj2.expression = "Dist(1,2)"
3313    GSASIIpath.InvokeDebugOpts()
3314    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3315    calcobj2 = ExpressionCalcObj(obj2)
3316    calcobj2.SetupCalc(parmDict2)
3317    showEQ(calcobj2)
3318
3319    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
3320    print ('\nDict = '+parmDict1)
3321    calcobj.SetupCalc(parmDict1)
3322    showEQ(calcobj)
3323    calcobj1.SetupCalc(parmDict1)
3324    showEQ(calcobj1)
3325
3326    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3327    print ('Dict = '+parmDict2)
3328    calcobj.SetupCalc(parmDict2)
3329    showEQ(calcobj)
3330    calcobj1.SetupCalc(parmDict2)
3331    showEQ(calcobj1)
3332    calcobj2.SetupCalc(parmDict2)
3333    showEQ(calcobj2)
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