source: trunk/GSASIIobj.py @ 4661

Last change on this file since 4661 was 4661, checked in by toby, 13 months ago

update CIF export: add rigid body, fix bug in single xtal ref tbl; picker bug on single xtal plot

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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2020-11-28 02:48:26 +0000 (Sat, 28 Nov 2020) $
5# $Author: toby $
6# $Revision: 4661 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 4661 2020-11-28 02:48:26Z 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`.
1214The data window for the Controls tree item shows the number of Frozen variables and
1215the individual variables can be viewed with the Calculate/"View LS parms" menu window or
1216obtained with :meth:`GSASIIscriptable.G2Project.get_Frozen`.
1217Once a variable is frozen, it will not be refined in any
1218future refinements unless the the variable is removed (manually) from the list. This can also
1219be done with the Calculate/"View LS parms" menu window or
1220:meth:`GSASIIscriptable.G2Project.set_Frozen`.
1221
1222
1223.. seealso::
1224  :class:`G2VarObj`
1225  :func:`getVarDescr`
1226  :func:`CompileVarDesc`
1227  :func:`prmLookup`
1228  :class:`GSASIIctrlGUI.ShowLSParms`
1229  :class:`GSASIIctrlGUI.VirtualVarBox`
1230  :func:`GSASIIstrIO.SetUsedHistogramsAndPhases`
1231  :func:`GSASIIstrIO.SaveUpdatedHistogramsAndPhases`
1232  :func:`GSASIIstrIO.SetSeqResult`
1233  :func:`GSASIIstrMain.dropOOBvars`
1234  :meth:`GSASIIscriptable.G2Project.set_Controls`
1235  :meth:`GSASIIscriptable.G2Project.get_Frozen`
1236  :meth:`GSASIIscriptable.G2Project.set_Frozen`
1237
1238*Classes and routines*
1239----------------------
1240
1241'''
1242from __future__ import division, print_function
1243import platform
1244import re
1245import random as ran
1246import sys
1247import os.path as ospath
1248if '2' in platform.python_version_tuple()[0]:
1249    import cPickle
1250else:
1251    import pickle as cPickle
1252import GSASIIpath
1253import GSASIImath as G2mth
1254import GSASIIspc as G2spc
1255import numpy as np
1256
1257GSASIIpath.SetVersionNumber("$Revision: 4661 $")
1258
1259DefaultControls = {
1260    'deriv type':'analytic Hessian',
1261    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
1262    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
1263    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
1264    'Author':'no name',
1265    'FreePrm1':'Sample humidity (%)',
1266    'FreePrm2':'Sample voltage (V)',
1267    'FreePrm3':'Applied load (MN)',
1268    'ShowCell':False,
1269    }
1270'''Values to be used as defaults for the initial contents of the ``Controls``
1271data tree item.
1272'''
1273def StripUnicode(string,subs='.'):
1274    '''Strip non-ASCII characters from strings
1275
1276    :param str string: string to strip Unicode characters from
1277    :param str subs: character(s) to place into string in place of each
1278      Unicode character. Defaults to '.'
1279
1280    :returns: a new string with only ASCII characters
1281    '''
1282    s = ''
1283    for c in string:
1284        if ord(c) < 128:
1285            s += c
1286        else:
1287            s += subs
1288    return s
1289#    return s.encode('ascii','replace')
1290
1291def MakeUniqueLabel(lbl,labellist):
1292    '''Make sure that every a label is unique against a list by adding
1293    digits at the end until it is not found in list.
1294
1295    :param str lbl: the input label
1296    :param list labellist: the labels that have already been encountered
1297    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
1298      ``_10-99``, etc.) appended at the end
1299    '''
1300    lbl = StripUnicode(lbl.strip(),'_')
1301    if not lbl: # deal with a blank label
1302        lbl = '_1'
1303    if lbl not in labellist:
1304        labellist.append(lbl)
1305        return lbl
1306    i = 1
1307    prefix = lbl
1308    if '_' in lbl:
1309        prefix = lbl[:lbl.rfind('_')]
1310        suffix = lbl[lbl.rfind('_')+1:]
1311        try:
1312            i = int(suffix)+1
1313        except: # suffix could not be parsed
1314            i = 1
1315            prefix = lbl
1316    while prefix+'_'+str(i) in labellist:
1317        i += 1
1318    else:
1319        lbl = prefix+'_'+str(i)
1320        labellist.append(lbl)
1321    return lbl
1322
1323PhaseIdLookup = {}
1324'''dict listing phase name and random Id keyed by sequential phase index as a str;
1325best to access this using :func:`LookupPhaseName`
1326'''
1327PhaseRanIdLookup = {}
1328'''dict listing phase sequential index keyed by phase random Id;
1329best to access this using :func:`LookupPhaseId`
1330'''
1331HistIdLookup = {}
1332'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
1333best to access this using :func:`LookupHistName`
1334'''
1335HistRanIdLookup = {}
1336'''dict listing histogram sequential index keyed by histogram random Id;
1337best to access this using :func:`LookupHistId`
1338'''
1339AtomIdLookup = {}
1340'''dict listing for each phase index as a str, the atom label and atom random Id,
1341keyed by atom sequential index as a str;
1342best to access this using :func:`LookupAtomLabel`
1343'''
1344AtomRanIdLookup = {}
1345'''dict listing for each phase the atom sequential index keyed by atom random Id;
1346best to access this using :func:`LookupAtomId`
1347'''
1348ShortPhaseNames = {}
1349'''a dict containing a possibly shortened and when non-unique numbered
1350version of the phase name. Keyed by the phase sequential index.
1351'''
1352ShortHistNames = {}
1353'''a dict containing a possibly shortened and when non-unique numbered
1354version of the histogram name. Keyed by the histogram sequential index.
1355'''
1356
1357#VarDesc = {}  # removed 1/30/19 BHT as no longer needed (I think)
1358#''' This dictionary lists descriptions for GSAS-II variables,
1359#as set in :func:`CompileVarDesc`. See that function for a description
1360#for how keys and values are written.
1361#'''
1362
1363reVarDesc = {}
1364''' This dictionary lists descriptions for GSAS-II variables where
1365keys are compiled regular expressions that will match the name portion
1366of a parameter name. Initialized in :func:`CompileVarDesc`.
1367'''
1368
1369reVarStep = {}
1370''' This dictionary lists the preferred step size for numerical
1371derivative computation w/r to a GSAS-II variable. Keys are compiled
1372regular expressions and values are the step size for that parameter.
1373Initialized in :func:`CompileVarDesc`.
1374'''
1375# create a default space group object for P1; N.B. fails when building documentation
1376try:
1377    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
1378except:
1379    pass
1380
1381def GetPhaseNames(fl):
1382    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
1383    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename
1384
1385    :param file fl: opened .gpx file
1386    :return: list of phase names
1387    '''
1388    PhaseNames = []
1389    while True:
1390        try:
1391            data = cPickle.load(fl)
1392        except EOFError:
1393            break
1394        datum = data[0]
1395        if 'Phases' == datum[0]:
1396            for datus in data[1:]:
1397                PhaseNames.append(datus[0])
1398    fl.seek(0)          #reposition file
1399    return PhaseNames
1400
1401def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
1402    '''Create a new phase dict with default values for various parameters
1403
1404    :param str Name: Name for new Phase
1405
1406    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
1407      defaults to data for P 1
1408
1409    :param list cell: unit cell parameter list; defaults to
1410      [1.0,1.0,1.0,90.,90,90.,1.]
1411
1412    '''
1413    if SGData is None: SGData = P1SGData
1414    if cell is None: cell=[1.0,1.0,1.0,90.,90.,90.,1.]
1415    phaseData = {
1416        'ranId':ran.randint(0,sys.maxsize),
1417        'General':{
1418            'Name':Name,
1419            'Type':'nuclear',
1420            'Modulated':False,
1421            'AtomPtrs':[3,1,7,9],
1422            'SGData':SGData,
1423            'Cell':[False,]+cell,
1424            'Pawley dmin':1.0,
1425            'Data plot type':'None',
1426            'SH Texture':{
1427                'Order':0,
1428                'Model':'cylindrical',
1429                'Sample omega':[False,0.0],
1430                'Sample chi':[False,0.0],
1431                'Sample phi':[False,0.0],
1432                'SH Coeff':[False,{}],
1433                'SHShow':False,
1434                'PFhkl':[0,0,1],
1435                'PFxyz':[0,0,1],
1436                'PlotType':'Pole figure',
1437                'Penalty':[['',],0.1,False,1.0]}},
1438        'Atoms':[],
1439        'Drawing':{},
1440        'Histograms':{},
1441        'Pawley ref':[],
1442        'RBModels':{},
1443        }
1444    if Super and Super.get('Use',False):
1445        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
1446        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
1447        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]
1448
1449    return phaseData
1450
1451def ReadCIF(URLorFile):
1452    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
1453    (from James Hester).
1454    The open routine gets confused with DOS names that begin with a letter and colon
1455    "C:\\dir\" so this routine will try to open the passed name as a file and if that
1456    fails, try it as a URL
1457
1458    :param str URLorFile: string containing a URL or a file name. Code will try first
1459      to open it as a file and then as a URL.
1460
1461    :returns: a PyCifRW CIF object.
1462    '''
1463    import CifFile as cif # PyCifRW from James Hester
1464
1465    # alternate approach:
1466    #import urllib
1467    #ciffile = 'file:'+urllib.pathname2url(filename)
1468
1469    try:
1470        fp = open(URLorFile,'r')
1471        cf = cif.ReadCif(fp)
1472        fp.close()
1473        return cf
1474    except IOError:
1475        return cif.ReadCif(URLorFile)
1476
1477def TestIndexAll():
1478    '''Test if :func:`IndexAllIds` has been called to index all phases and
1479    histograms (this is needed before :func:`G2VarObj` can be used.
1480
1481    :returns: Returns True if indexing is needed.
1482    '''
1483    if PhaseIdLookup or AtomIdLookup or HistIdLookup:
1484        return False
1485    return True
1486       
1487def IndexAllIds(Histograms,Phases):
1488    '''Scan through the used phases & histograms and create an index
1489    to the random numbers of phases, histograms and atoms. While doing this,
1490    confirm that assigned random numbers are unique -- just in case lightning
1491    strikes twice in the same place.
1492
1493    Note: this code assumes that the atom random Id (ranId) is the last
1494    element each atom record.
1495
1496    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
1497    (which loads the histograms and phases from a GPX file),
1498    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
1499    (which loads the histograms and phases from the data tree.) and
1500    :meth:`GSASIIconstrGUI.UpdateConstraints`
1501    (which displays & edits the constraints in a GUI)
1502
1503    TODO: do we need a lookup for rigid body variables?
1504    '''
1505    # process phases and atoms
1506    PhaseIdLookup.clear()
1507    PhaseRanIdLookup.clear()
1508    AtomIdLookup.clear()
1509    AtomRanIdLookup.clear()
1510    ShortPhaseNames.clear()
1511    for ph in Phases:
1512        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
1513        ranId = Phases[ph]['ranId']
1514        while ranId in PhaseRanIdLookup:
1515            # Found duplicate random Id! note and reassign
1516            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
1517            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1518        pId = str(Phases[ph]['pId'])
1519        PhaseIdLookup[pId] = (ph,ranId)
1520        PhaseRanIdLookup[ranId] = pId
1521        shortname = ph  #[:10]
1522        while shortname in ShortPhaseNames.values():
1523            shortname = ph[:8] + ' ('+ pId + ')'
1524        ShortPhaseNames[pId] = shortname
1525        AtomIdLookup[pId] = {}
1526        AtomRanIdLookup[pId] = {}
1527        for iatm,at in enumerate(Phases[ph]['Atoms']):
1528            ranId = at[cia+8]
1529            while ranId in AtomRanIdLookup[pId]: # check for dups
1530                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
1531                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
1532            AtomRanIdLookup[pId][ranId] = str(iatm)
1533            if Phases[ph]['General']['Type'] == 'macromolecular':
1534                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
1535            else:
1536                label = at[ct-1]
1537            AtomIdLookup[pId][str(iatm)] = (label,ranId)
1538    # process histograms
1539    HistIdLookup.clear()
1540    HistRanIdLookup.clear()
1541    ShortHistNames.clear()
1542    for hist in Histograms:
1543        ranId = Histograms[hist]['ranId']
1544        while ranId in HistRanIdLookup:
1545            # Found duplicate random Id! note and reassign
1546            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1547            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1548        hId = str(Histograms[hist]['hId'])
1549        HistIdLookup[hId] = (hist,ranId)
1550        HistRanIdLookup[ranId] = hId
1551        shortname = hist[:15]
1552        while shortname in ShortHistNames.values():
1553            shortname = hist[:11] + ' ('+ hId + ')'
1554        ShortHistNames[hId] = shortname
1555
1556def LookupAtomId(pId,ranId):
1557    '''Get the atom number from a phase and atom random Id
1558
1559    :param int/str pId: the sequential number of the phase
1560    :param int ranId: the random Id assigned to an atom
1561
1562    :returns: the index number of the atom (str)
1563    '''
1564    if not AtomRanIdLookup:
1565        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
1566    if pId is None or pId == '':
1567        raise KeyError('Error: phase is invalid (None or blank)')
1568    pId = str(pId)
1569    if pId not in AtomRanIdLookup:
1570        raise KeyError('Error: LookupAtomId does not have phase '+pId)
1571    if ranId not in AtomRanIdLookup[pId]:
1572        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
1573    return AtomRanIdLookup[pId][ranId]
1574
1575def LookupAtomLabel(pId,index):
1576    '''Get the atom label from a phase and atom index number
1577
1578    :param int/str pId: the sequential number of the phase
1579    :param int index: the index of the atom in the list of atoms
1580
1581    :returns: the label for the atom (str) and the random Id of the atom (int)
1582    '''
1583    if not AtomIdLookup:
1584        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
1585    if pId is None or pId == '':
1586        raise KeyError('Error: phase is invalid (None or blank)')
1587    pId = str(pId)
1588    if pId not in AtomIdLookup:
1589        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
1590    if index not in AtomIdLookup[pId]:
1591        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
1592    return AtomIdLookup[pId][index]
1593
1594def LookupPhaseId(ranId):
1595    '''Get the phase number and name from a phase random Id
1596
1597    :param int ranId: the random Id assigned to a phase
1598    :returns: the sequential Id (pId) number for the phase (str)
1599    '''
1600    if not PhaseRanIdLookup:
1601        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
1602    if ranId not in PhaseRanIdLookup:
1603        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
1604    return PhaseRanIdLookup[ranId]
1605
1606def LookupPhaseName(pId):
1607    '''Get the phase number and name from a phase Id
1608
1609    :param int/str pId: the sequential assigned to a phase
1610    :returns:  (phase,ranId) where phase is the name of the phase (str)
1611      and ranId is the random # id for the phase (int)
1612    '''
1613    if not PhaseIdLookup:
1614        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
1615    if pId is None or pId == '':
1616        raise KeyError('Error: phase is invalid (None or blank)')
1617    pId = str(pId)
1618    if pId not in PhaseIdLookup:
1619        raise KeyError('Error: LookupPhaseName does not have index '+pId)
1620    return PhaseIdLookup[pId]
1621
1622def LookupHistId(ranId):
1623    '''Get the histogram number and name from a histogram random Id
1624
1625    :param int ranId: the random Id assigned to a histogram
1626    :returns: the sequential Id (hId) number for the histogram (str)
1627    '''
1628    if not HistRanIdLookup:
1629        raise Exception('Error: LookupHistId called before IndexAllIds was run')
1630    if ranId not in HistRanIdLookup:
1631        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
1632    return HistRanIdLookup[ranId]
1633
1634def LookupHistName(hId):
1635    '''Get the histogram number and name from a histogram Id
1636
1637    :param int/str hId: the sequential assigned to a histogram
1638    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1639      and ranId is the random # id for the histogram (int)
1640    '''
1641    if not HistIdLookup:
1642        raise Exception('Error: LookupHistName called before IndexAllIds was run')
1643    if hId is None or hId == '':
1644        raise KeyError('Error: histogram is invalid (None or blank)')
1645    hId = str(hId)
1646    if hId not in HistIdLookup:
1647        raise KeyError('Error: LookupHistName does not have index '+hId)
1648    return HistIdLookup[hId]
1649
1650def fmtVarDescr(varname):
1651    '''Return a string with a more complete description for a GSAS-II variable
1652
1653    :param str varname: A full G2 variable name with 2 or 3 or 4
1654       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1655
1656    :returns: a string with the description
1657    '''
1658    s,l = VarDescr(varname)
1659    return s+": "+l
1660
1661def VarDescr(varname):
1662    '''Return two strings with a more complete description for a GSAS-II variable
1663
1664    :param str name: A full G2 variable name with 2 or 3 or 4
1665       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1666
1667    :returns: (loc,meaning) where loc describes what item the variable is mapped
1668      (phase, histogram, etc.) and meaning describes what the variable does.
1669    '''
1670
1671    # special handling for parameter names without a colon
1672    # for now, assume self-defining
1673    if varname.find(':') == -1:
1674        return "Global",varname
1675
1676    l = getVarDescr(varname)
1677    if not l:
1678        return ("invalid variable name ("+str(varname)+")!"),""
1679#        return "invalid variable name!",""
1680
1681    if not l[-1]:
1682        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1683
1684    if len(l) == 3:         #SASD variable name!
1685        s = 'component:'+l[1]
1686        return s,l[-1]
1687    s = ""
1688    if l[0] is not None and l[1] is not None: # HAP: keep short
1689        if l[2] == "Scale": # fix up ambigous name
1690            l[5] = "Phase fraction"
1691        if l[0] == '*':
1692            lbl = 'Seq. ref.'
1693        else:
1694            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1695        if l[1] == '*':
1696            hlbl = 'Seq. ref.'
1697        else:
1698            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1699        if hlbl[:4] == 'HKLF':
1700            hlbl = 'Xtl='+hlbl[5:]
1701        elif hlbl[:4] == 'PWDR':
1702            hlbl = 'Pwd='+hlbl[5:]
1703        else:
1704            hlbl = 'Hist='+hlbl
1705        s = "Ph="+str(lbl)+" * "+str(hlbl)
1706    else:
1707        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1708            l[5] = "Scale factor"
1709        if l[2] == 'Back': # background parameters are "special", alas
1710            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1711            l[-1] += ' #'+str(l[3])
1712        elif l[4] is not None: # rigid body parameter or modulation parm
1713            lbl = ShortPhaseNames.get(l[0],'phase?')
1714            if 'RB' in l[2]:    #rigid body parm
1715                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1716            else: #modulation parm
1717                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
1718        elif l[3] is not None: # atom parameter,
1719            lbl = ShortPhaseNames.get(l[0],'phase?')
1720            try:
1721                albl = LookupAtomLabel(l[0],l[3])[0]
1722            except KeyError:
1723                albl = 'Atom?'
1724            s = "Atom "+str(albl)+" in "+str(lbl)
1725        elif l[0] == '*':
1726            s = "All phases "
1727        elif l[0] is not None:
1728            lbl = ShortPhaseNames.get(l[0],'phase?')
1729            s = "Phase "+str(lbl)
1730        elif l[1] == '*':
1731            s = 'All hists'
1732        elif l[1] is not None:
1733            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1734            if hlbl[:4] == 'HKLF':
1735                hlbl = 'Xtl='+hlbl[5:]
1736            elif hlbl[:4] == 'PWDR':
1737                hlbl = 'Pwd='+hlbl[5:]
1738            else:
1739                hlbl = 'Hist='+hlbl
1740            s = str(hlbl)
1741    if not s:
1742        s = 'Global'
1743    return s,l[-1]
1744
1745def getVarDescr(varname):
1746    '''Return a short description for a GSAS-II variable
1747
1748    :param str name: A full G2 variable name with 2 or 3 or 4
1749       colons (<p>:<h>:name[:<a1>][:<a2>])
1750
1751    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1752      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1753      the histogram number and the atom number; `name` will always be
1754      a str; and `description` is str or `None`.
1755      If the variable name is incorrectly formed (for example, wrong
1756      number of colons), `None` is returned instead of a list.
1757    '''
1758    l = varname.split(':')
1759    if len(l) == 2:     #SASD parameter name
1760        return varname,l[0],getDescr(l[1])
1761    if len(l) == 3:
1762        l += [None,None]
1763    elif len(l) == 4:
1764        l += [None]
1765    elif len(l) != 5:
1766        return None
1767    for i in (0,1,3,4):
1768        if l[i] == "":
1769            l[i] = None
1770    l += [getDescr(l[2])]
1771    return l
1772
1773def CompileVarDesc():
1774    '''Set the values in the variable lookup tables
1775    (:attr:`reVarDesc` and :attr:`reVarStep`).
1776    This is called in :func:`getDescr` and :func:`getVarStep` so this
1777    initialization is always done before use.
1778
1779    Note that keys may contain regular expressions, where '[xyz]'
1780    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range
1781    of values). '.*' matches any string. For example::
1782
1783    'AUiso':'Atomic isotropic displacement parameter',
1784
1785    will match variable ``'p::AUiso:a'``.
1786    If parentheses are used in the key, the contents of those parentheses can be
1787    used in the value, such as::
1788
1789    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1790
1791    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1792    in the value when used.
1793
1794    '''
1795    if reVarDesc: return # already done
1796    for key,value in {
1797        # derived or other sequential vars
1798        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1799        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1800        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1801        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1802        # ambiguous, alas:
1803        'Scale' : 'Phase or Histogram scale factor',
1804        # Phase vars (p::<var>)
1805        'A([0-5])' : ('Reciprocal metric tensor component \\1',1e-5),
1806        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
1807        # Atom vars (p::<var>:a)
1808        'dA([xyz])$' : ('change to atomic coordinate, \\1',1e-6),
1809        'A([xyz])$' : '\\1 fractional atomic coordinate',
1810        'AUiso':('Atomic isotropic displacement parameter',1e-4),
1811        'AU([123][123])':('Atomic anisotropic displacement parameter U\\1',1e-4),
1812        'Afrac': ('Atomic site fraction parameter',1e-5),
1813        'Amul': 'Atomic site multiplicity value',
1814        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
1815        # Hist & Phase (HAP) vars (p:h:<var>)
1816        'Back': 'Background term',
1817        'BkPkint;(.*)':'Background peak #\\1 intensity',
1818        'BkPkpos;(.*)':'Background peak #\\1 position',
1819        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1820        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1821        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1822        'D([123][123])' : 'Anisotropic strain coef. \\1',
1823        'Extinction' : 'Extinction coef.',
1824        'MD' : 'March-Dollase coef.',
1825        'Mustrain;.*' : 'Microstrain coef.',
1826        'Size;.*' : 'Crystallite size value',
1827        'eA$' : 'Cubic mustrain value',
1828        'Ep$' : 'Primary extinction',
1829        'Es$' : 'Secondary type II extinction',
1830        'Eg$' : 'Secondary type I extinction',
1831        'Flack' : 'Flack parameter',
1832        'TwinFr' : 'Twin fraction',
1833        'Layer Disp'  : 'Layer displacement along beam',
1834        #Histogram vars (:h:<var>)
1835        'Absorption' : 'Absorption coef.',
1836        'Displace([XY])' : ('Debye-Scherrer sample displacement \\1',0.1),
1837        'Lam' : ('Wavelength',1e-6),
1838        'I\\(L2\\)\\/I\\(L1\\)' : ('Ka2/Ka1 intensity ratio',0.001),
1839        'Polariz\\.' : ('Polarization correction',1e-3),
1840        'SH/L' : ('FCJ peak asymmetry correction',1e-4),
1841        '([UVW])$' : ('Gaussian instrument broadening \\1',1e-5),
1842        '([XYZ])$' : ('Cauchy instrument broadening \\1',1e-5),
1843        'Zero' : 'Debye-Scherrer zero correction',
1844        'Shift' : 'Bragg-Brentano sample displ.',
1845        'SurfRoughA' : 'Bragg-Brenano surface roughness A',
1846        'SurfRoughB' : 'Bragg-Brenano surface roughness B',
1847        'Transparency' : 'Bragg-Brentano sample tranparency',
1848        'DebyeA' : 'Debye model amplitude',
1849        'DebyeR' : 'Debye model radius',
1850        'DebyeU' : 'Debye model Uiso',
1851        'RBV.*' : 'Vector rigid body parameter',
1852        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1853        'RBRP([xyz])' : 'Residue rigid body position parameter',
1854        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1855        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1856        'RBRU' : 'Residue rigid body group Uiso param.',
1857        'constr([0-9]*)' : 'Parameter from constraint',
1858        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1859        'mV([0-2])$' : 'Modulation vector component \\1',
1860        'Fsin'  :   'Sin site fraction modulation',
1861        'Fcos'  :   'Cos site fraction modulation',
1862        'Fzero'  :   'Crenel function offset',      #may go away
1863        'Fwid'   :   'Crenel function width',
1864        'Tmin'   :   'ZigZag/Block min location',
1865        'Tmax'   :   'ZigZag/Block max location',
1866        '([XYZ])max': 'ZigZag/Block max value for \\1',
1867        '([XYZ])sin'  : 'Sin position wave for \\1',
1868        '([XYZ])cos'  : 'Cos position wave for \\1',
1869        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1870        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1871        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1872        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1873        # PDF peak parms (l:<var>;l = peak no.)
1874        'PDFpos'  : 'PDF peak position',
1875        'PDFmag'  : 'PDF peak magnitude',
1876        'PDFsig'  : 'PDF peak std. dev.',
1877        # SASD vars (l:<var>;l = component)
1878        'Aspect ratio' : 'Particle aspect ratio',
1879        'Length' : 'Cylinder length',
1880        'Diameter' : 'Cylinder/disk diameter',
1881        'Thickness' : 'Disk thickness',
1882        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
1883        'Dist' : 'Interparticle distance',
1884        'VolFr' : 'Dense scatterer volume fraction',
1885        'epis' : 'Sticky sphere epsilon',
1886        'Sticky' : 'Stickyness',
1887        'Depth' : 'Well depth',
1888        'Width' : 'Well width',
1889        'Volume' : 'Particle volume',
1890        'Radius' : 'Sphere/cylinder/disk radius',
1891        'Mean' : 'Particle mean radius',
1892        'StdDev' : 'Standard deviation in Mean',
1893        'G$': 'Guinier prefactor',
1894        'Rg$': 'Guinier radius of gyration',
1895        'B$': 'Porod prefactor',
1896        'P$': 'Porod power',
1897        'Cutoff': 'Porod cutoff',
1898        'PkInt': 'Bragg peak intensity',
1899        'PkPos': 'Bragg peak position',
1900        'PkSig': 'Bragg peak sigma',
1901        'PkGam': 'Bragg peak gamma',
1902        'e([12][12])' : 'strain tensor e\\1',   # strain vars e11, e22, e12
1903        'Dcalc': 'Calc. d-spacing',
1904        'Back$': 'background parameter',
1905        'pos$': 'peak position',
1906        'int$': 'peak intensity',
1907        'WgtFrac':'phase weight fraction',
1908        'alpha':'TOF profile term',
1909        'alpha-[01]':'Pink profile term',
1910        'beta-[01q]':'TOF/Pink profile term',
1911        'sig-[012q]':'TOF profile term',
1912        'dif[ABC]':'TOF to d-space calibration',
1913        'C\\([0-9]*,[0-9]*\\)' : 'spherical harmonics preferred orientation coef.',
1914        'Pressure': 'Pressure level for measurement in MPa',
1915        'Temperature': 'T value for measurement, K',
1916        'FreePrm([123])': 'User defined measurement parameter \\1',
1917        'Gonio. radius': 'Distance from sample to detector, mm',
1918        }.items():
1919        # Needs documentation: HAP: LayerDisp, LeBail, newLeBail
1920        # hist: Azimuth, Chi, Omega, Phi, Bank, nDebye, nPeaks
1921       
1922        if len(value) == 2:
1923            #VarDesc[key] = value[0]
1924            reVarDesc[re.compile(key)] = value[0]
1925            reVarStep[re.compile(key)] = value[1]
1926        else:
1927            #VarDesc[key] = value
1928            reVarDesc[re.compile(key)] = value
1929
1930def removeNonRefined(parmList):
1931    '''Remove items from variable list that are not refined and should not
1932    appear as options for constraints
1933
1934    :param list parmList: a list of strings of form "p:h:VAR:a" where
1935      VAR is the variable name
1936
1937    :returns: a list after removing variables where VAR matches a
1938      entry in local variable NonRefinedList
1939    '''
1940    NonRefinedList = ['Omega','Type','Chi','Phi', 'Azimuth','Gonio. radius',
1941                          'Lam1','Lam2','Back','Temperature','Pressure',
1942                          'FreePrm1','FreePrm2','FreePrm3',
1943                          'Source','nPeaks','LeBail','newLeBail','Bank',
1944                          'nDebye', #'',
1945                    ]
1946    return [prm for prm in parmList if prm.split(':')[2] not in NonRefinedList]
1947       
1948def getDescr(name):
1949    '''Return a short description for a GSAS-II variable
1950
1951    :param str name: The descriptive part of the variable name without colons (:)
1952
1953    :returns: a short description or None if not found
1954    '''
1955
1956    CompileVarDesc() # compile the regular expressions, if needed
1957    for key in reVarDesc:
1958        m = key.match(name)
1959        if m:
1960            reVarDesc[key]
1961            return m.expand(reVarDesc[key])
1962    return None
1963
1964def getVarStep(name,parmDict=None):
1965    '''Return a step size for computing the derivative of a GSAS-II variable
1966
1967    :param str name: A complete variable name (with colons, :)
1968    :param dict parmDict: A dict with parameter values or None (default)
1969
1970    :returns: a float that should be an appropriate step size, either from
1971      the value supplied in :func:`CompileVarDesc` or based on the value for
1972      name in parmDict, if supplied. If not found or the value is zero,
1973      a default value of 1e-5 is used. If parmDict is None (default) and
1974      no value is provided in :func:`CompileVarDesc`, then None is returned.
1975    '''
1976    CompileVarDesc() # compile the regular expressions, if needed
1977    for key in reVarStep:
1978        m = key.match(name)
1979        if m:
1980            return reVarStep[key]
1981    if parmDict is None: return None
1982    val = parmDict.get(key,0.0)
1983    if abs(val) > 0.05:
1984        return abs(val)/1000.
1985    else:
1986        return 1e-5
1987
1988def GenWildCard(varlist):
1989    '''Generate wildcard versions of G2 variables. These introduce '*'
1990    for a phase, histogram or atom number (but only for one of these
1991    fields) but only when there is more than one matching variable in the
1992    input variable list. So if the input is this::
1993
1994      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1995
1996    then the output will be this::
1997
1998       wildList = ['*::AUiso:0', '0::AUiso:*']
1999
2000    :param list varlist: an input list of GSAS-II variable names
2001      (such as 0::AUiso:0)
2002
2003    :returns: wildList, the generated list of wild card variable names.
2004    '''
2005    wild = []
2006    for i in (0,1,3):
2007        currentL = varlist[:]
2008        while currentL:
2009            item1 = currentL.pop(0)
2010            i1splt = item1.split(':')
2011            if i >= len(i1splt): continue
2012            if i1splt[i]:
2013                nextL = []
2014                i1splt[i] = '[0-9]+'
2015                rexp = re.compile(':'.join(i1splt))
2016                matchlist = [item1]
2017                for nxtitem in currentL:
2018                    if rexp.match(nxtitem):
2019                        matchlist += [nxtitem]
2020                    else:
2021                        nextL.append(nxtitem)
2022                if len(matchlist) > 1:
2023                    i1splt[i] = '*'
2024                    wild.append(':'.join(i1splt))
2025                currentL = nextL
2026    return wild
2027
2028def LookupWildCard(varname,varlist):
2029    '''returns a list of variable names from list varname
2030    that match wildcard name in varname
2031
2032    :param str varname: a G2 variable name containing a wildcard
2033      (such as \\*::var)
2034    :param list varlist: the list of all variable names used in
2035      the current project
2036    :returns: a list of matching GSAS-II variables (may be empty)
2037    '''
2038    rexp = re.compile(varname.replace('*','[0-9]+'))
2039    return sorted([var for var in varlist if rexp.match(var)])
2040
2041def prmLookup(name,prmDict):
2042    '''Looks for a parameter in a min/max dictionary, optionally
2043    considering a wild card for histogram or atom number (use of
2044    both will never occur at the same time).
2045
2046    :param name: a GSAS-II parameter name (str, see :func:`getVarDescr`
2047      and :func:`CompileVarDesc`) or a :class:`G2VarObj` object.
2048    :param dict prmDict: a min/max dictionary, (parmMinDict
2049      or parmMaxDict in Controls) where keys are :class:`G2VarObj`
2050      objects.
2051    :returns: Two values, (**matchname**, **value**), are returned where:
2052
2053       * **matchname** *(str)* is the :class:`G2VarObj` object
2054         corresponding to the actual matched name,
2055         which could contain a wildcard even if **name** does not; and
2056       * **value** *(float)* which contains the parameter limit.
2057    '''
2058    for key,value in prmDict.items():
2059        if str(key) == str(name): return key,value
2060        if key == name: return key,value
2061    return None,None
2062       
2063
2064def _lookup(dic,key):
2065    '''Lookup a key in a dictionary, where None returns an empty string
2066    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
2067    '''
2068    if key is None:
2069        return ""
2070    elif key == "*":
2071        return "*"
2072    else:
2073        return dic.get(key,'?')
2074
2075def SortVariables(varlist):
2076    '''Sorts variable names in a sensible manner
2077    '''
2078    def cvnnums(var):
2079        v = []
2080        for i in var.split(':'):
2081            if i == '':
2082                v.append(-1)
2083                continue
2084            try:
2085                v.append(int(i))
2086            except:
2087                v.append(i)
2088        return v
2089    return sorted(varlist,key=cvnnums)
2090
2091class G2VarObj(object):
2092    '''Defines a GSAS-II variable either using the phase/atom/histogram
2093    unique Id numbers or using a character string that specifies
2094    variables by phase/atom/histogram number (which can change).
2095    Note that :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`,
2096    which calls :func:`IndexAllIds` (or
2097    :func:`GSASIIscriptable.G2Project.index_ids`) should be used to
2098    (re)load the current Ids
2099    before creating or later using the G2VarObj object.
2100
2101    This can store rigid body variables, but does not translate the residue # and
2102    body # to/from random Ids
2103
2104    A :class:`G2VarObj` object can be created with a single parameter:
2105
2106    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
2107      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
2108
2109     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
2110     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
2111     * a is the atom number (which may be left blank in which case the third colon is omitted).
2112       The atom number can be specified as '*' if a phase number is specified (not as '*').
2113       For rigid body variables, specify a will be a string of form "residue:body#"
2114
2115      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
2116      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
2117      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
2118      For a rigid body variables, AtomID is a string of form "residue:body#".
2119
2120    If four positional arguments are supplied, they are:
2121
2122    :param str/int phasenum: The number for the phase (or None or '*')
2123    :param str/int histnum: The number for the histogram (or None or '*')
2124    :param str varname: a single value can be used to create a :class:`G2VarObj`
2125    :param str/int atomnum: The number for the atom (or None or '*')
2126
2127    '''
2128    IDdict = {}
2129    IDdict['phases'] = {}
2130    IDdict['hists'] = {}
2131    IDdict['atoms'] = {}
2132    def __init__(self,*args):
2133        self.phase = None
2134        self.histogram = None
2135        self.name = ''
2136        self.atom = None
2137        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
2138            # single arg with 4 values
2139            self.phase,self.histogram,self.name,self.atom = args[0]
2140        elif len(args) == 1 and ':' in args[0]:
2141            #parse a string
2142            lst = args[0].split(':')
2143            if lst[0] == '*':
2144                self.phase = '*'
2145                if len(lst) > 3:
2146                    self.atom = lst[3]
2147                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2148            elif lst[1] == '*':
2149                self.histogram = '*'
2150                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2151            else:
2152                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2153                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2154                if len(lst) == 4:
2155                    if lst[3] == '*':
2156                        self.atom = '*'
2157                    else:
2158                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
2159                elif len(lst) == 5:
2160                    self.atom = lst[3]+":"+lst[4]
2161                elif len(lst) == 3:
2162                    pass
2163                else:
2164                    raise Exception("Too many colons in var name "+str(args[0]))
2165            self.name = lst[2]
2166        elif len(args) == 4:
2167            if args[0] == '*':
2168                self.phase = '*'
2169                self.atom = args[3]
2170            else:
2171                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
2172                if args[3] == '*':
2173                    self.atom = '*'
2174                elif args[0] is not None:
2175                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
2176            if args[1] == '*':
2177                self.histogram = '*'
2178            else:
2179                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
2180            self.name = args[2]
2181        else:
2182            raise Exception("Incorrectly called GSAS-II parameter name")
2183
2184        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
2185
2186    def __str__(self):
2187        return self.varname()
2188
2189    def __hash__(self):
2190        'Allow G2VarObj to be a dict key by implementing hashing'
2191        return hash(self.varname())
2192
2193    def varname(self):
2194        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
2195        string (p:h:<var>:a) or (p:h:<var>)
2196
2197        :returns: the variable name as a str
2198        '''
2199        a = ""
2200        if self.phase == "*":
2201            ph = "*"
2202            if self.atom:
2203                a = ":" + str(self.atom)
2204        else:
2205            ph = _lookup(PhaseRanIdLookup,self.phase)
2206            if self.atom == '*':
2207                a = ':*'
2208            elif self.atom:
2209                if ":" in str(self.atom):
2210                    a = ":" + str(self.atom)
2211                elif ph in AtomRanIdLookup:
2212                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
2213                else:
2214                    a = ":?"
2215        if self.histogram == "*":
2216            hist = "*"
2217        else:
2218            hist = _lookup(HistRanIdLookup,self.histogram)
2219        s = (ph + ":" + hist + ":" + str(self.name)) + a
2220        return s
2221
2222    def __repr__(self):
2223        '''Return the detailed contents of the object
2224        '''
2225        s = "<"
2226        if self.phase == '*':
2227            s += "Phases: all; "
2228            if self.atom is not None:
2229                if ":" in str(self.atom):
2230                    s += "Rigid body" + str(self.atom) + "; "
2231                else:
2232                    s += "Atom #" + str(self.atom) + "; "
2233        elif self.phase is not None:
2234            ph =  _lookup(PhaseRanIdLookup,self.phase)
2235            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
2236            if self.atom == '*':
2237                s += "Atoms: all; "
2238            elif ":" in str(self.atom):
2239                s += "Rigid body" + str(self.atom) + "; "
2240            elif self.atom is not None:
2241                s += "Atom rId=" + str(self.atom)
2242                if ph in AtomRanIdLookup:
2243                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
2244                else:
2245                    s += " (#? -- not found!); "
2246        if self.histogram == '*':
2247            s += "Histograms: all; "
2248        elif self.histogram is not None:
2249            hist = _lookup(HistRanIdLookup,self.histogram)
2250            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
2251        s += 'Variable name="' + str(self.name) + '">'
2252        return s+" ("+self.varname()+")"
2253
2254    def __eq__(self, other):
2255        '''Allow comparison of G2VarObj to other G2VarObj objects or strings.
2256        If any field is a wildcard ('*') that field matches.
2257        '''
2258        if type(other) is str:
2259            other = G2VarObj(other)
2260        elif type(other) is not G2VarObj:
2261            raise Exception("Invalid type ({}) for G2VarObj comparison with {}"
2262                            .format(type(other),other))
2263        if self.phase != other.phase and self.phase != '*' and other.phase != '*':
2264            return False
2265        if self.histogram != other.histogram and self.histogram != '*' and other.histogram != '*':
2266            return False
2267        if self.atom != other.atom and self.atom != '*' and other.atom != '*':
2268            return False
2269        if self.name != other.name:
2270            return False
2271        return True
2272
2273    def _show(self):
2274        'For testing, shows the current lookup table'
2275        print ('phases'+ self.IDdict['phases'])
2276        print ('hists'+ self.IDdict['hists'])
2277        print ('atomDict'+ self.IDdict['atoms'])
2278
2279#==========================================================================
2280def SetDefaultSample():
2281    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
2282    return {
2283        'InstrName':'',
2284        'ranId':ran.randint(0,sys.maxsize),
2285        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
2286        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],
2287        'Temperature':300.,'Pressure':0.1,'Time':0.0,
2288        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
2289        'Gonio. radius':200.0,
2290        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
2291#SASD items
2292        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
2293        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
2294        'Trans':1.0,                            #measured transmission
2295        'SlitLen':0.0,                          #Slit length - in Q(A-1)
2296        }
2297######################################################################
2298class ImportBaseclass(object):
2299    '''Defines a base class for the reading of input files (diffraction
2300    data, coordinates,...). See :ref:`Writing a Import Routine<import_routines>`
2301    for an explanation on how to use a subclass of this class.
2302    '''
2303    class ImportException(Exception):
2304        '''Defines an Exception that is used when an import routine hits an expected error,
2305        usually in .Reader.
2306
2307        Good practice is that the Reader should define a value in self.errors that
2308        tells the user some information about what is wrong with their file.
2309        '''
2310        pass
2311
2312    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
2313    def __init__(self,formatName,longFormatName=None,
2314                 extensionlist=[],strictExtension=False,):
2315        self.formatName = formatName # short string naming file type
2316        if longFormatName: # longer string naming file type
2317            self.longFormatName = longFormatName
2318        else:
2319            self.longFormatName = formatName
2320        # define extensions that are allowed for the file type
2321        # for windows, remove any extensions that are duplicate, as case is ignored
2322        if sys.platform == 'windows' and extensionlist:
2323            extensionlist = list(set([s.lower() for s in extensionlist]))
2324        self.extensionlist = extensionlist
2325        # If strictExtension is True, the file will not be read, unless
2326        # the extension matches one in the extensionlist
2327        self.strictExtension = strictExtension
2328        self.errors = ''
2329        self.warnings = ''
2330        self.SciPy = False          #image reader needed scipy
2331        # used for readers that will use multiple passes to read
2332        # more than one data block
2333        self.repeat = False
2334        self.selections = []
2335        self.repeatcount = 0
2336        self.readfilename = '?'
2337        self.scriptable = False
2338        #print 'created',self.__class__
2339
2340    def ReInitialize(self):
2341        'Reinitialize the Reader to initial settings'
2342        self.errors = ''
2343        self.warnings = ''
2344        self.SciPy = False          #image reader needed scipy
2345        self.repeat = False
2346        self.repeatcount = 0
2347        self.readfilename = '?'
2348
2349
2350#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
2351#        '''This method must be supplied in the child class to read the file.
2352#        if the read fails either return False or raise an Exception
2353#        preferably of type ImportException.
2354#        '''
2355#        #start reading
2356#        raise ImportException("Error occurred while...")
2357#        self.errors += "Hint for user on why the error occur
2358#        return False # if an error occurs
2359#        return True # if read OK
2360
2361    def ExtensionValidator(self, filename):
2362        '''This methods checks if the file has the correct extension
2363       
2364        :returns:
2365       
2366          * False if this filename will not be supported by this reader (only
2367            when strictExtension is True)
2368          * True if the extension matches the list supplied by the reader
2369          * None if the reader allows un-registered extensions
2370         
2371        '''
2372        if filename:
2373            ext = ospath.splitext(filename)[1]
2374            if not ext and self.strictExtension: return False
2375            for ext in self.extensionlist:               
2376                if sys.platform == 'windows':
2377                    if filename.lower().endswith(ext): return True
2378                else:
2379                    if filename.endswith(ext): return True
2380        if self.strictExtension:
2381            return False
2382        else:
2383            return None
2384
2385    def ContentsValidator(self, filename):
2386        '''This routine will attempt to determine if the file can be read
2387        with the current format.
2388        This will typically be overridden with a method that
2389        takes a quick scan of [some of]
2390        the file contents to do a "sanity" check if the file
2391        appears to match the selected format.
2392        the file must be opened here with the correct format (binary/text)
2393        '''
2394        #filepointer.seek(0) # rewind the file pointer
2395        return True
2396
2397    def CIFValidator(self, filepointer):
2398        '''A :meth:`ContentsValidator` for use to validate CIF files.
2399        '''
2400        filepointer.seek(0)
2401        for i,l in enumerate(filepointer):
2402            if i >= 1000: return True
2403            '''Encountered only blank lines or comments in first 1000
2404            lines. This is unlikely, but assume it is CIF anyway, since we are
2405            even less likely to find a file with nothing but hashes and
2406            blank lines'''
2407            line = l.strip()
2408            if len(line) == 0: # ignore blank lines
2409                continue
2410            elif line.startswith('#'): # ignore comments
2411                continue
2412            elif line.startswith('data_'): # on the right track, accept this file
2413                return True
2414            else: # found something invalid
2415                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
2416                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
2417                    self.errors += '  '+str(l)
2418                else:
2419                    self.errors += '  (binary)'
2420                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
2421                self.errors += '\n        a data_ statement begins a block.'
2422                return False
2423
2424######################################################################
2425class ImportPhase(ImportBaseclass):
2426    '''Defines a base class for the reading of files with coordinates
2427
2428    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
2429    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` and in
2430    :func:`GSASIIscriptable.import_generic`.
2431    See :ref:`Writing a Import Routine<import_routines>`
2432    for an explanation on how to use this class.
2433
2434    '''
2435    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2436        strictExtension=False,):
2437        # call parent __init__
2438        ImportBaseclass.__init__(self,formatName,longFormatName,
2439            extensionlist,strictExtension)
2440        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
2441        self.SymOps = {} # specified when symmetry ops are in file (e.g. CIF)
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
2728
2729def FindFunction(f):
2730    '''Find the object corresponding to function f
2731
2732    :param str f: a function name such as 'numpy.exp'
2733    :returns: (pkgdict,pkgobj) where pkgdict contains a dict
2734      that defines the package location(s) and where pkgobj
2735      defines the object associated with the function.
2736      If the function is not found, pkgobj is None.
2737    '''
2738    df = f.split('.')
2739    pkgdict = {}
2740    # no listed module name, try in current namespace
2741    if len(df) == 1:
2742        try:
2743            fxnobj = eval(f)
2744            return pkgdict,fxnobj
2745        except (AttributeError, NameError):
2746            return None,None
2747
2748    # includes a package, see if package is already imported
2749    pkgnam = '.'.join(df[:-1])
2750    try:
2751        fxnobj = eval(f)
2752        pkgdict[pkgnam] = eval(pkgnam)
2753        return pkgdict,fxnobj
2754    except (AttributeError, NameError):
2755        pass
2756    # package not yet imported, so let's try
2757    if '.' not in sys.path: sys.path.append('.')
2758    pkgnam = '.'.join(df[:-1])
2759    #for pkg in f.split('.')[:-1]: # if needed, descend down the tree
2760    #    if pkgname:
2761    #        pkgname += '.' + pkg
2762    #    else:
2763    #        pkgname = pkg
2764    try:
2765        exec('import '+pkgnam)
2766        pkgdict[pkgnam] = eval(pkgnam)
2767        fxnobj = eval(f)
2768    except Exception as msg:
2769        print('load of '+pkgnam+' failed with error='+str(msg))
2770        return {},None
2771    # can we access the function? I am not exactly sure what
2772    #    I intended this to test originally (BHT)
2773    try:
2774        fxnobj = eval(f,globals(),pkgdict)
2775        return pkgdict,fxnobj
2776    except Exception as msg:
2777        print('call to',f,' failed with error=',str(msg))
2778        return None,None # not found
2779               
2780class ExpressionObj(object):
2781    '''Defines an object with a user-defined expression, to be used for
2782    secondary fits or restraints. Object is created null, but is changed
2783    using :meth:`LoadExpression`. This contains only the minimum
2784    information that needs to be stored to save and load the expression
2785    and how it is mapped to GSAS-II variables.
2786    '''
2787    def __init__(self):
2788        self.expression = ''
2789        'The expression as a text string'
2790        self.assgnVars = {}
2791        '''A dict where keys are label names in the expression mapping to a GSAS-II
2792        variable. The value a G2 variable name.
2793        Note that the G2 variable name may contain a wild-card and correspond to
2794        multiple values.
2795        '''
2796        self.freeVars = {}
2797        '''A dict where keys are label names in the expression mapping to a free
2798        parameter. The value is a list with:
2799
2800         * a name assigned to the parameter
2801         * a value for to the parameter and
2802         * a flag to determine if the variable is refined.
2803        '''
2804        self.depVar = None
2805
2806        self.lastError = ('','')
2807        '''Shows last encountered error in processing expression
2808        (list of 1-3 str values)'''
2809
2810        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
2811        self.distance_atoms = None  # to be used for defining atom distances
2812
2813    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
2814        '''Load the expression and associated settings into the object. Raises
2815        an exception if the expression is not parsed, if not all functions
2816        are defined or if not all needed parameter labels in the expression
2817        are defined.
2818
2819        This will not test if the variable referenced in these definitions
2820        are actually in the parameter dictionary. This is checked when the
2821        computation for the expression is done in :meth:`SetupCalc`.
2822
2823        :param str expr: the expression
2824        :param list exprVarLst: parameter labels found in the expression
2825        :param dict varSelect: this will be 0 for Free parameters
2826          and non-zero for expression labels linked to G2 variables.
2827        :param dict varName: Defines a name (str) associated with each free parameter
2828        :param dict varValue: Defines a value (float) associated with each free parameter
2829        :param dict varRefflag: Defines a refinement flag (bool)
2830          associated with each free parameter
2831        '''
2832        self.expression = expr
2833        self.compiledExpr = None
2834        self.freeVars = {}
2835        self.assgnVars = {}
2836        for v in exprVarLst:
2837            if varSelect[v] == 0:
2838                self.freeVars[v] = [
2839                    varName.get(v),
2840                    varValue.get(v),
2841                    varRefflag.get(v),
2842                    ]
2843            else:
2844                self.assgnVars[v] = varName[v]
2845        self.CheckVars()
2846
2847    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
2848        '''Load the expression and associated settings from the object into
2849        arrays used for editing.
2850
2851        :param list exprVarLst: parameter labels found in the expression
2852        :param dict varSelect: this will be 0 for Free parameters
2853          and non-zero for expression labels linked to G2 variables.
2854        :param dict varName: Defines a name (str) associated with each free parameter
2855        :param dict varValue: Defines a value (float) associated with each free parameter
2856        :param dict varRefflag: Defines a refinement flag (bool)
2857          associated with each free parameter
2858
2859        :returns: the expression as a str
2860        '''
2861        for v in self.freeVars:
2862            varSelect[v] = 0
2863            varName[v] = self.freeVars[v][0]
2864            varValue[v] = self.freeVars[v][1]
2865            varRefflag[v] = self.freeVars[v][2]
2866        for v in self.assgnVars:
2867            varSelect[v] = 1
2868            varName[v] = self.assgnVars[v]
2869        return self.expression
2870
2871    def GetVaried(self):
2872        'Returns the names of the free parameters that will be refined'
2873        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
2874
2875    def GetVariedVarVal(self):
2876        'Returns the names and values of the free parameters that will be refined'
2877        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
2878
2879    def UpdateVariedVars(self,varyList,values):
2880        'Updates values for the free parameters (after a refinement); only updates refined vars'
2881        for v in self.freeVars:
2882            if not self.freeVars[v][2]: continue
2883            if "::"+self.freeVars[v][0] not in varyList: continue
2884            indx = list(varyList).index("::"+self.freeVars[v][0])
2885            self.freeVars[v][1] = values[indx]
2886
2887    def GetIndependentVars(self):
2888        'Returns the names of the required independent parameters used in expression'
2889        return [self.assgnVars[v] for v in self.assgnVars]
2890
2891    def CheckVars(self):
2892        '''Check that the expression can be parsed, all functions are
2893        defined and that input loaded into the object is internally
2894        consistent. If not an Exception is raised.
2895
2896        :returns: a dict with references to packages needed to
2897          find functions referenced in the expression.
2898        '''
2899        ret = self.ParseExpression(self.expression)
2900        if not ret:
2901            raise Exception("Expression parse error")
2902        exprLblList,fxnpkgdict = ret
2903        # check each var used in expression is defined
2904        defined = list(self.assgnVars.keys()) + list(self.freeVars.keys())
2905        notfound = []
2906        for var in exprLblList:
2907            if var not in defined:
2908                notfound.append(var)
2909        if notfound:
2910            msg = 'Not all variables defined'
2911            msg1 = 'The following variables were not defined: '
2912            msg2 = ''
2913            for var in notfound:
2914                if msg: msg += ', '
2915                msg += var
2916            self.lastError = (msg1,'  '+msg2)
2917            raise Exception(msg)
2918        return fxnpkgdict
2919
2920    def ParseExpression(self,expr):
2921        '''Parse an expression and return a dict of called functions and
2922        the variables used in the expression. Returns None in case an error
2923        is encountered. If packages are referenced in functions, they are loaded
2924        and the functions are looked up into the modules global
2925        workspace.
2926
2927        Note that no changes are made to the object other than
2928        saving an error message, so that this can be used for testing prior
2929        to the save.
2930
2931        :returns: a list of used variables
2932        '''
2933        self.lastError = ('','')
2934        import ast
2935        def ASTtransverse(node,fxn=False):
2936            '''Transverse a AST-parsed expresson, compiling a list of variables
2937            referenced in the expression. This routine is used recursively.
2938
2939            :returns: varlist,fxnlist where
2940              varlist is a list of referenced variable names and
2941              fxnlist is a list of used functions
2942            '''
2943            varlist = []
2944            fxnlist = []
2945            if isinstance(node, list):
2946                for b in node:
2947                    v,f = ASTtransverse(b,fxn)
2948                    varlist += v
2949                    fxnlist += f
2950            elif isinstance(node, ast.AST):
2951                for a, b in ast.iter_fields(node):
2952                    if isinstance(b, ast.AST):
2953                        if a == 'func':
2954                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
2955                            continue
2956                        v,f = ASTtransverse(b,fxn)
2957                        varlist += v
2958                        fxnlist += f
2959                    elif isinstance(b, list):
2960                        v,f = ASTtransverse(b,fxn)
2961                        varlist += v
2962                        fxnlist += f
2963                    elif node.__class__.__name__ == "Name":
2964                        varlist += [b]
2965                    elif fxn and node.__class__.__name__ == "Attribute":
2966                        varlist += [b]
2967            return varlist,fxnlist
2968        try:
2969            exprast = ast.parse(expr)
2970        except SyntaxError:
2971            s = ''
2972            import traceback
2973            for i in traceback.format_exc().splitlines()[-3:-1]:
2974                if s: s += "\n"
2975                s += str(i)
2976            self.lastError = ("Error parsing expression:",s)
2977            return
2978        # find the variables & functions
2979        v,f = ASTtransverse(exprast)
2980        varlist = sorted(list(set(v)))
2981        fxnlist = list(set(f))
2982        pkgdict = {}
2983        # check the functions are defined
2984        for fxn in fxnlist:
2985            fxndict,fxnobj = FindFunction(fxn)
2986            if not fxnobj:
2987                self.lastError = ("Error: Invalid function",fxn,
2988                                  "is not defined")
2989                return
2990            if not hasattr(fxnobj,'__call__'):
2991                self.lastError = ("Error: Not a function.",fxn,
2992                                  "cannot be called as a function")
2993                return
2994            pkgdict.update(fxndict)
2995        return varlist,pkgdict
2996
2997    def GetDepVar(self):
2998        'return the dependent variable, or None'
2999        return self.depVar
3000
3001    def SetDepVar(self,var):
3002        'Set the dependent variable, if used'
3003        self.depVar = var
3004#==========================================================================
3005class ExpressionCalcObj(object):
3006    '''An object used to evaluate an expression from a :class:`ExpressionObj`
3007    object.
3008
3009    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
3010      an expression string and mappings for the parameter labels in that object.
3011    '''
3012    def __init__(self,exprObj):
3013        self.eObj = exprObj
3014        'The expression and mappings; a :class:`ExpressionObj` object'
3015        self.compiledExpr = None
3016        'The expression as compiled byte-code'
3017        self.exprDict = {}
3018        '''dict that defines values for labels used in expression and packages
3019        referenced by functions
3020        '''
3021        self.lblLookup = {}
3022        '''Lookup table that specifies the expression label name that is
3023        tied to a particular GSAS-II parameters in the parmDict.
3024        '''
3025        self.fxnpkgdict = {}
3026        '''a dict with references to packages needed to
3027        find functions referenced in the expression.
3028        '''
3029        self.varLookup = {}
3030        '''Lookup table that specifies the GSAS-II variable(s)
3031        indexed by the expression label name. (Used for only for diagnostics
3032        not evaluation of expression.)
3033        '''
3034        self.su = None
3035        '''Standard error evaluation where supplied by the evaluator
3036        '''
3037        # Patch: for old-style expressions with a (now removed step size)
3038        if '2' in platform.python_version_tuple()[0]: 
3039            basestr = basestring
3040        else:
3041            basestr = str
3042        for v in self.eObj.assgnVars:
3043            if not isinstance(self.eObj.assgnVars[v], basestr):
3044                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
3045        self.parmDict = {}
3046        '''A copy of the parameter dictionary, for distance and angle computation
3047        '''
3048
3049    def SetupCalc(self,parmDict):
3050        '''Do all preparations to use the expression for computation.
3051        Adds the free parameter values to the parameter dict (parmDict).
3052        '''
3053        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
3054            return
3055        self.fxnpkgdict = self.eObj.CheckVars()
3056        # all is OK, compile the expression
3057        self.compiledExpr = compile(self.eObj.expression,'','eval')
3058
3059        # look at first value in parmDict to determine its type
3060        parmsInList = True
3061        if '2' in platform.python_version_tuple()[0]: 
3062            basestr = basestring
3063        else:
3064            basestr = str
3065        for key in parmDict:
3066            val = parmDict[key]
3067            if isinstance(val, basestr):
3068                parmsInList = False
3069                break
3070            try: # check if values are in lists
3071                val = parmDict[key][0]
3072            except (TypeError,IndexError):
3073                parmsInList = False
3074            break
3075
3076        # set up the dicts needed to speed computations
3077        self.exprDict = {}
3078        self.lblLookup = {}
3079        self.varLookup = {}
3080        for v in self.eObj.freeVars:
3081            varname = self.eObj.freeVars[v][0]
3082            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
3083            self.lblLookup[varname] = v
3084            self.varLookup[v] = varname
3085            if parmsInList:
3086                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
3087            else:
3088                parmDict[varname] = self.eObj.freeVars[v][1]
3089            self.exprDict[v] = self.eObj.freeVars[v][1]
3090        for v in self.eObj.assgnVars:
3091            varname = self.eObj.assgnVars[v]
3092            if varname in parmDict:
3093                self.lblLookup[varname] = v
3094                self.varLookup[v] = varname
3095                if parmsInList:
3096                    self.exprDict[v] = parmDict[varname][0]
3097                else:
3098                    self.exprDict[v] = parmDict[varname]
3099            elif '*' in varname:
3100                varlist = LookupWildCard(varname,list(parmDict.keys()))
3101                if len(varlist) == 0:
3102                    raise Exception("No variables match "+str(v))
3103                for var in varlist:
3104                    self.lblLookup[var] = v
3105                if parmsInList:
3106                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
3107                else:
3108                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
3109                self.varLookup[v] = [var for var in varlist]
3110            else:
3111                self.exprDict[v] = None
3112#                raise Exception,"No value for variable "+str(v)
3113        self.exprDict.update(self.fxnpkgdict)
3114
3115    def UpdateVars(self,varList,valList):
3116        '''Update the dict for the expression with a set of values
3117        :param list varList: a list of variable names
3118        :param list valList: a list of corresponding values
3119        '''
3120        for var,val in zip(varList,valList):
3121            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
3122
3123    def UpdateDict(self,parmDict):
3124        '''Update the dict for the expression with values in a dict
3125        :param dict parmDict: a dict of values, items not in use are ignored
3126        '''
3127        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
3128            self.parmDict = parmDict
3129            return
3130        for var in parmDict:
3131            if var in self.lblLookup:
3132                self.exprDict[self.lblLookup[var]] = parmDict[var]
3133
3134    def EvalExpression(self):
3135        '''Evaluate an expression. Note that the expression
3136        and mapping are taken from the :class:`ExpressionObj` expression object
3137        and the parameter values were specified in :meth:`SetupCalc`.
3138        :returns: a single value for the expression. If parameter
3139        values are arrays (for example, from wild-carded variable names),
3140        the sum of the resulting expression is returned.
3141
3142        For example, if the expression is ``'A*B'``,
3143        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
3144
3145        [0.5, 1, 0.5]
3146
3147        then the result will be ``4.0``.
3148        '''
3149        self.su = None
3150        if self.eObj.expression.startswith('Dist'):
3151#            GSASIIpath.IPyBreak()
3152            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
3153            return dist
3154        elif self.eObj.expression.startswith('Angle'):
3155            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
3156            return angle
3157        if self.compiledExpr is None:
3158            raise Exception("EvalExpression called before SetupCalc")
3159        try:
3160            val = eval(self.compiledExpr,globals(),self.exprDict)
3161        except TypeError:
3162            val = None
3163        if not np.isscalar(val):
3164            val = np.sum(val)
3165        return val
3166
3167class G2Exception(Exception):
3168    'A generic GSAS-II exception class'
3169    def __init__(self,msg):
3170        self.msg = msg
3171    def __str__(self):
3172        return repr(self.msg)
3173
3174class G2RefineCancel(Exception):
3175    'Raised when Cancel is pressed in a refinement dialog'
3176    def __init__(self,msg):
3177        self.msg = msg
3178    def __str__(self):
3179        return repr(self.msg)
3180   
3181def HowDidIgetHere(wherecalledonly=False):
3182    '''Show a traceback with calls that brought us to the current location.
3183    Used for debugging.
3184    '''
3185    import traceback
3186    if wherecalledonly:
3187        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
3188        print(i.strip().rstrip())
3189    else:
3190        print (70*'*')
3191        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
3192        print (70*'*')
3193
3194# Note that this is GUI code and should be moved at somepoint
3195def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
3196    '''Create and initialize a new set of PDF tree entries
3197
3198    :param Frame G2frame: main GSAS-II tree frame object
3199    :param str PWDRtree: name of PWDR to be used to create PDF item
3200    :param dict ElList: data structure with composition
3201    :param list Qlimits: Q limits to be used for computing the PDF
3202    :param float numAtm: no. atom in chemical formula
3203    :param float FltBkg: flat background value
3204    :param list PDFnames: previously used PDF names
3205
3206    :returns: the Id of the newly created PDF entry
3207    '''
3208    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
3209    if PDFname in PDFnames:
3210        print('Skipping, entry already exists: '+PDFname)
3211        return None
3212    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
3213    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
3214    Data = {
3215        'Sample':{'Name':PWDRtree,'Mult':1.0},
3216        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
3217        'Container':{'Name':'','Mult':-1.0,'Refine':False},
3218        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
3219        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
3220        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
3221        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
3222        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
3223    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
3224    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
3225        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
3226    return Id
3227#%%
3228class ShowTiming(object):
3229    '''An object to use for timing repeated sections of code.
3230
3231    Create the object with::
3232       tim0 = ShowTiming()
3233
3234    Tag sections of code to be timed with::
3235       tim0.start('start')
3236       tim0.start('in section 1')
3237       tim0.start('in section 2')
3238       
3239    etc. (Note that each section should have a unique label.)
3240
3241    After the last section, end timing with::
3242       tim0.end()
3243
3244    Show timing results with::
3245       tim0.show()
3246       
3247    '''
3248    def __init__(self):
3249        self.timeSum =  []
3250        self.timeStart = []
3251        self.label = []
3252        self.prev = None
3253    def start(self,label):
3254        import time
3255        if label in self.label:
3256            i = self.label.index(label)
3257            self.timeStart[i] = time.time()
3258        else:
3259            i = len(self.label)
3260            self.timeSum.append(0.0)
3261            self.timeStart.append(time.time())
3262            self.label.append(label)
3263        if self.prev is not None:
3264            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
3265        self.prev = i
3266    def end(self):
3267        import time
3268        if self.prev is not None:
3269            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
3270        self.prev = None
3271    def show(self):
3272        sumT = sum(self.timeSum)
3273        print('Timing results (total={:.2f} sec)'.format(sumT))
3274        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
3275            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
3276#%%
3277
3278def validateAtomDrawType(typ,generalData={}):
3279    '''Confirm that the selected Atom drawing type is valid for the current
3280    phase. If not, use 'vdW balls'. This is currently used only for setting a
3281    default when atoms are added to the atoms draw list.
3282    '''
3283    if typ in ('lines','vdW balls','sticks','balls & sticks','ellipsoids'):
3284        return typ
3285    # elif generalData.get('Type','') == 'macromolecular':
3286    #     if typ in ('backbone',):
3287    #         return typ
3288    return 'vdW balls'
3289
3290if __name__ == "__main__":
3291    # test variable descriptions
3292    for var in '0::Afrac:*',':1:Scale','1::dAx:0','::undefined':
3293        v = var.split(':')[2]
3294        print(var+':\t', getDescr(v),getVarStep(v))
3295    import sys; sys.exit()
3296    # test equation evaluation
3297    def showEQ(calcobj):
3298        print (50*'=')
3299        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
3300        for v in sorted(calcobj.varLookup):
3301            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
3302        # print '  Derivatives'
3303        # for v in calcobj.derivStep.keys():
3304        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
3305
3306    obj = ExpressionObj()
3307
3308    obj.expression = "A*np.exp(B)"
3309    obj.assgnVars =  {'B': '0::Afrac:1'}
3310    obj.freeVars =  {'A': [u'A', 0.5, True]}
3311    #obj.CheckVars()
3312    calcobj = ExpressionCalcObj(obj)
3313
3314    obj1 = ExpressionObj()
3315    obj1.expression = "A*np.exp(B)"
3316    obj1.assgnVars =  {'B': '0::Afrac:*'}
3317    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
3318    #obj.CheckVars()
3319    calcobj1 = ExpressionCalcObj(obj1)
3320
3321    obj2 = ExpressionObj()
3322    obj2.distance_stuff = np.array([[0,1],[1,-1]])
3323    obj2.expression = "Dist(1,2)"
3324    GSASIIpath.InvokeDebugOpts()
3325    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3326    calcobj2 = ExpressionCalcObj(obj2)
3327    calcobj2.SetupCalc(parmDict2)
3328    showEQ(calcobj2)
3329
3330    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
3331    print ('\nDict = '+parmDict1)
3332    calcobj.SetupCalc(parmDict1)
3333    showEQ(calcobj)
3334    calcobj1.SetupCalc(parmDict1)
3335    showEQ(calcobj1)
3336
3337    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3338    print ('Dict = '+parmDict2)
3339    calcobj.SetupCalc(parmDict2)
3340    showEQ(calcobj)
3341    calcobj1.SetupCalc(parmDict2)
3342    showEQ(calcobj1)
3343    calcobj2.SetupCalc(parmDict2)
3344    showEQ(calcobj2)
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