source: trunk/GSASIIobj.py @ 4578

Last change on this file since 4578 was 4578, checked in by toby, 2 years ago

docs for freezing parameters started + docs cleanup; start scriptable for freezing params; record initial chi2; Show more post refinement info; noted but unfixed bkg GUI bug

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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2020-09-28 18:23:10 +0000 (Mon, 28 Sep 2020) $
5# $Author: toby $
6# $Revision: 4578 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 4578 2020-09-28 18:23:10Z 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 named using the standard GSAS-II variable
1190(see :func:`getVarDescr` and :func:`CompileVarDesc`) or with a variable name, where a
1191wildcard ('*') is used for histogram number or atom number (phase number is intentionally not
1192allowed as a wildcard as it makes little sense to group together different phases). Note
1193that func:`prmLookup` is used to see if a name matches a wildcard. The upper or lower limit
1194is placed into these dicts as a float value. These values can be edited using the window
1195created by the Calculate/"View LS parms" menu command or in scripting with the
1196:meth:`GSASIIscriptable.G2Project.set_Controls` function.
1197In the GUI, a checkbox labeled "match all histograms/atoms" is used to insert a wildcard
1198into the appropriate part of the variable name.
1199
1200When a refinement is conducted, routine :func:`GSASIIstrMain.dropOOBvars` is used to
1201find parameters that have refined to values outside their limits. If this occurs, the parameter
1202is set to the limiting value and the variable name is added to a list of frozen variables kept in the
1203``Controls['parmFrozen']`` dict. In a sequential refinement, this is kept as a list in
1204``Controls['parmFrozen'][histogram]`` (where the key is the histogram name) or in
1205``Controls['parmFrozen']['FrozenList']`` for a non-sequential fit.
1206This allows different variables
1207to be frozen in each section of a sequential fit.
1208Frozen parameters are not included in refinements through removal from the
1209list of parameters to be refined (``varyList``) in :func:`GSASIIstrMain.Refine` or
1210:func:`GSASIIstrMain.SeqRefine`. Once a variable is frozen, it will not be refined in any
1211future refinements unless the the variable is removed (manually) from the list. This can also
1212be done with the Calculate/"View LS parms" menu window or ...
1213
1214*Classes and routines*
1215----------------------
1216
1217'''
1218from __future__ import division, print_function
1219import platform
1220import re
1221import imp
1222import random as ran
1223import sys
1224import os.path as ospath
1225if '2' in platform.python_version_tuple()[0]:
1226    import cPickle
1227else:
1228    import pickle as cPickle
1229import GSASIIpath
1230import GSASIImath as G2mth
1231import GSASIIspc as G2spc
1232import numpy as np
1233
1234GSASIIpath.SetVersionNumber("$Revision: 4578 $")
1235
1236DefaultControls = {
1237    'deriv type':'analytic Hessian',
1238    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
1239    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
1240    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
1241    'Author':'no name',
1242    'FreePrm1':'Sample humidity (%)',
1243    'FreePrm2':'Sample voltage (V)',
1244    'FreePrm3':'Applied load (MN)',
1245    'ShowCell':False,
1246    }
1247'''Values to be used as defaults for the initial contents of the ``Controls``
1248data tree item.
1249'''
1250def StripUnicode(string,subs='.'):
1251    '''Strip non-ASCII characters from strings
1252
1253    :param str string: string to strip Unicode characters from
1254    :param str subs: character(s) to place into string in place of each
1255      Unicode character. Defaults to '.'
1256
1257    :returns: a new string with only ASCII characters
1258    '''
1259    s = ''
1260    for c in string:
1261        if ord(c) < 128:
1262            s += c
1263        else:
1264            s += subs
1265    return s
1266#    return s.encode('ascii','replace')
1267
1268def MakeUniqueLabel(lbl,labellist):
1269    '''Make sure that every a label is unique against a list by adding
1270    digits at the end until it is not found in list.
1271
1272    :param str lbl: the input label
1273    :param list labellist: the labels that have already been encountered
1274    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
1275      ``_10-99``, etc.) appended at the end
1276    '''
1277    lbl = StripUnicode(lbl.strip(),'_')
1278    if not lbl: # deal with a blank label
1279        lbl = '_1'
1280    if lbl not in labellist:
1281        labellist.append(lbl)
1282        return lbl
1283    i = 1
1284    prefix = lbl
1285    if '_' in lbl:
1286        prefix = lbl[:lbl.rfind('_')]
1287        suffix = lbl[lbl.rfind('_')+1:]
1288        try:
1289            i = int(suffix)+1
1290        except: # suffix could not be parsed
1291            i = 1
1292            prefix = lbl
1293    while prefix+'_'+str(i) in labellist:
1294        i += 1
1295    else:
1296        lbl = prefix+'_'+str(i)
1297        labellist.append(lbl)
1298    return lbl
1299
1300PhaseIdLookup = {}
1301'''dict listing phase name and random Id keyed by sequential phase index as a str;
1302best to access this using :func:`LookupPhaseName`
1303'''
1304PhaseRanIdLookup = {}
1305'''dict listing phase sequential index keyed by phase random Id;
1306best to access this using :func:`LookupPhaseId`
1307'''
1308HistIdLookup = {}
1309'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
1310best to access this using :func:`LookupHistName`
1311'''
1312HistRanIdLookup = {}
1313'''dict listing histogram sequential index keyed by histogram random Id;
1314best to access this using :func:`LookupHistId`
1315'''
1316AtomIdLookup = {}
1317'''dict listing for each phase index as a str, the atom label and atom random Id,
1318keyed by atom sequential index as a str;
1319best to access this using :func:`LookupAtomLabel`
1320'''
1321AtomRanIdLookup = {}
1322'''dict listing for each phase the atom sequential index keyed by atom random Id;
1323best to access this using :func:`LookupAtomId`
1324'''
1325ShortPhaseNames = {}
1326'''a dict containing a possibly shortened and when non-unique numbered
1327version of the phase name. Keyed by the phase sequential index.
1328'''
1329ShortHistNames = {}
1330'''a dict containing a possibly shortened and when non-unique numbered
1331version of the histogram name. Keyed by the histogram sequential index.
1332'''
1333
1334#VarDesc = {}  # removed 1/30/19 BHT as no longer needed (I think)
1335#''' This dictionary lists descriptions for GSAS-II variables,
1336#as set in :func:`CompileVarDesc`. See that function for a description
1337#for how keys and values are written.
1338#'''
1339
1340reVarDesc = {}
1341''' This dictionary lists descriptions for GSAS-II variables where
1342keys are compiled regular expressions that will match the name portion
1343of a parameter name. Initialized in :func:`CompileVarDesc`.
1344'''
1345
1346reVarStep = {}
1347''' This dictionary lists the preferred step size for numerical
1348derivative computation w/r to a GSAS-II variable. Keys are compiled
1349regular expressions and values are the step size for that parameter.
1350Initialized in :func:`CompileVarDesc`.
1351'''
1352# create a default space group object for P1; N.B. fails when building documentation
1353try:
1354    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
1355except:
1356    pass
1357
1358def GetPhaseNames(fl):
1359    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
1360    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename
1361
1362    :param file fl: opened .gpx file
1363    :return: list of phase names
1364    '''
1365    PhaseNames = []
1366    while True:
1367        try:
1368            data = cPickle.load(fl)
1369        except EOFError:
1370            break
1371        datum = data[0]
1372        if 'Phases' == datum[0]:
1373            for datus in data[1:]:
1374                PhaseNames.append(datus[0])
1375    fl.seek(0)          #reposition file
1376    return PhaseNames
1377
1378def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
1379    '''Create a new phase dict with default values for various parameters
1380
1381    :param str Name: Name for new Phase
1382
1383    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
1384      defaults to data for P 1
1385
1386    :param list cell: unit cell parameter list; defaults to
1387      [1.0,1.0,1.0,90.,90,90.,1.]
1388
1389    '''
1390    if SGData is None: SGData = P1SGData
1391    if cell is None: cell=[1.0,1.0,1.0,90.,90.,90.,1.]
1392    phaseData = {
1393        'ranId':ran.randint(0,sys.maxsize),
1394        'General':{
1395            'Name':Name,
1396            'Type':'nuclear',
1397            'Modulated':False,
1398            'AtomPtrs':[3,1,7,9],
1399            'SGData':SGData,
1400            'Cell':[False,]+cell,
1401            'Pawley dmin':1.0,
1402            'Data plot type':'None',
1403            'SH Texture':{
1404                'Order':0,
1405                'Model':'cylindrical',
1406                'Sample omega':[False,0.0],
1407                'Sample chi':[False,0.0],
1408                'Sample phi':[False,0.0],
1409                'SH Coeff':[False,{}],
1410                'SHShow':False,
1411                'PFhkl':[0,0,1],
1412                'PFxyz':[0,0,1],
1413                'PlotType':'Pole figure',
1414                'Penalty':[['',],0.1,False,1.0]}},
1415        'Atoms':[],
1416        'Drawing':{},
1417        'Histograms':{},
1418        'Pawley ref':[],
1419        'RBModels':{},
1420        }
1421    if Super and Super.get('Use',False):
1422        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
1423        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
1424        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]
1425
1426    return phaseData
1427
1428def ReadCIF(URLorFile):
1429    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
1430    (from James Hester).
1431    The open routine gets confused with DOS names that begin with a letter and colon
1432    "C:\dir\" so this routine will try to open the passed name as a file and if that
1433    fails, try it as a URL
1434
1435    :param str URLorFile: string containing a URL or a file name. Code will try first
1436      to open it as a file and then as a URL.
1437
1438    :returns: a PyCifRW CIF object.
1439    '''
1440    import CifFile as cif # PyCifRW from James Hester
1441
1442    # alternate approach:
1443    #import urllib
1444    #ciffile = 'file:'+urllib.pathname2url(filename)
1445
1446    try:
1447        fp = open(URLorFile,'r')
1448        cf = cif.ReadCif(fp)
1449        fp.close()
1450        return cf
1451    except IOError:
1452        return cif.ReadCif(URLorFile)
1453
1454def IndexAllIds(Histograms,Phases):
1455    '''Scan through the used phases & histograms and create an index
1456    to the random numbers of phases, histograms and atoms. While doing this,
1457    confirm that assigned random numbers are unique -- just in case lightning
1458    strikes twice in the same place.
1459
1460    Note: this code assumes that the atom random Id (ranId) is the last
1461    element each atom record.
1462
1463    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
1464    (which loads the histograms and phases from a GPX file),
1465    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
1466    (which loads the histograms and phases from the data tree.) and
1467    :meth:`GSASIIconstrGUI.UpdateConstraints`
1468    (which displays & edits the constraints in a GUI)
1469
1470    TODO: do we need a lookup for rigid body variables?
1471    '''
1472    # process phases and atoms
1473    PhaseIdLookup.clear()
1474    PhaseRanIdLookup.clear()
1475    AtomIdLookup.clear()
1476    AtomRanIdLookup.clear()
1477    ShortPhaseNames.clear()
1478    for ph in Phases:
1479        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
1480        ranId = Phases[ph]['ranId']
1481        while ranId in PhaseRanIdLookup:
1482            # Found duplicate random Id! note and reassign
1483            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
1484            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1485        pId = str(Phases[ph]['pId'])
1486        PhaseIdLookup[pId] = (ph,ranId)
1487        PhaseRanIdLookup[ranId] = pId
1488        shortname = ph  #[:10]
1489        while shortname in ShortPhaseNames.values():
1490            shortname = ph[:8] + ' ('+ pId + ')'
1491        ShortPhaseNames[pId] = shortname
1492        AtomIdLookup[pId] = {}
1493        AtomRanIdLookup[pId] = {}
1494        for iatm,at in enumerate(Phases[ph]['Atoms']):
1495            ranId = at[cia+8]
1496            while ranId in AtomRanIdLookup[pId]: # check for dups
1497                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
1498                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
1499            AtomRanIdLookup[pId][ranId] = str(iatm)
1500            if Phases[ph]['General']['Type'] == 'macromolecular':
1501                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
1502            else:
1503                label = at[ct-1]
1504            AtomIdLookup[pId][str(iatm)] = (label,ranId)
1505    # process histograms
1506    HistIdLookup.clear()
1507    HistRanIdLookup.clear()
1508    ShortHistNames.clear()
1509    for hist in Histograms:
1510        ranId = Histograms[hist]['ranId']
1511        while ranId in HistRanIdLookup:
1512            # Found duplicate random Id! note and reassign
1513            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1514            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1515        hId = str(Histograms[hist]['hId'])
1516        HistIdLookup[hId] = (hist,ranId)
1517        HistRanIdLookup[ranId] = hId
1518        shortname = hist[:15]
1519        while shortname in ShortHistNames.values():
1520            shortname = hist[:11] + ' ('+ hId + ')'
1521        ShortHistNames[hId] = shortname
1522
1523def LookupAtomId(pId,ranId):
1524    '''Get the atom number from a phase and atom random Id
1525
1526    :param int/str pId: the sequential number of the phase
1527    :param int ranId: the random Id assigned to an atom
1528
1529    :returns: the index number of the atom (str)
1530    '''
1531    if not AtomRanIdLookup:
1532        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
1533    if pId is None or pId == '':
1534        raise KeyError('Error: phase is invalid (None or blank)')
1535    pId = str(pId)
1536    if pId not in AtomRanIdLookup:
1537        raise KeyError('Error: LookupAtomId does not have phase '+pId)
1538    if ranId not in AtomRanIdLookup[pId]:
1539        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
1540    return AtomRanIdLookup[pId][ranId]
1541
1542def LookupAtomLabel(pId,index):
1543    '''Get the atom label from a phase and atom index number
1544
1545    :param int/str pId: the sequential number of the phase
1546    :param int index: the index of the atom in the list of atoms
1547
1548    :returns: the label for the atom (str) and the random Id of the atom (int)
1549    '''
1550    if not AtomIdLookup:
1551        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
1552    if pId is None or pId == '':
1553        raise KeyError('Error: phase is invalid (None or blank)')
1554    pId = str(pId)
1555    if pId not in AtomIdLookup:
1556        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
1557    if index not in AtomIdLookup[pId]:
1558        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
1559    return AtomIdLookup[pId][index]
1560
1561def LookupPhaseId(ranId):
1562    '''Get the phase number and name from a phase random Id
1563
1564    :param int ranId: the random Id assigned to a phase
1565    :returns: the sequential Id (pId) number for the phase (str)
1566    '''
1567    if not PhaseRanIdLookup:
1568        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
1569    if ranId not in PhaseRanIdLookup:
1570        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
1571    return PhaseRanIdLookup[ranId]
1572
1573def LookupPhaseName(pId):
1574    '''Get the phase number and name from a phase Id
1575
1576    :param int/str pId: the sequential assigned to a phase
1577    :returns:  (phase,ranId) where phase is the name of the phase (str)
1578      and ranId is the random # id for the phase (int)
1579    '''
1580    if not PhaseIdLookup:
1581        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
1582    if pId is None or pId == '':
1583        raise KeyError('Error: phase is invalid (None or blank)')
1584    pId = str(pId)
1585    if pId not in PhaseIdLookup:
1586        raise KeyError('Error: LookupPhaseName does not have index '+pId)
1587    return PhaseIdLookup[pId]
1588
1589def LookupHistId(ranId):
1590    '''Get the histogram number and name from a histogram random Id
1591
1592    :param int ranId: the random Id assigned to a histogram
1593    :returns: the sequential Id (hId) number for the histogram (str)
1594    '''
1595    if not HistRanIdLookup:
1596        raise Exception('Error: LookupHistId called before IndexAllIds was run')
1597    if ranId not in HistRanIdLookup:
1598        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
1599    return HistRanIdLookup[ranId]
1600
1601def LookupHistName(hId):
1602    '''Get the histogram number and name from a histogram Id
1603
1604    :param int/str hId: the sequential assigned to a histogram
1605    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1606      and ranId is the random # id for the histogram (int)
1607    '''
1608    if not HistIdLookup:
1609        raise Exception('Error: LookupHistName called before IndexAllIds was run')
1610    if hId is None or hId == '':
1611        raise KeyError('Error: histogram is invalid (None or blank)')
1612    hId = str(hId)
1613    if hId not in HistIdLookup:
1614        raise KeyError('Error: LookupHistName does not have index '+hId)
1615    return HistIdLookup[hId]
1616
1617def fmtVarDescr(varname):
1618    '''Return a string with a more complete description for a GSAS-II variable
1619
1620    :param str varname: A full G2 variable name with 2 or 3 or 4
1621       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1622
1623    :returns: a string with the description
1624    '''
1625    s,l = VarDescr(varname)
1626    return s+": "+l
1627
1628def VarDescr(varname):
1629    '''Return two strings with a more complete description for a GSAS-II variable
1630
1631    :param str name: A full G2 variable name with 2 or 3 or 4
1632       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1633
1634    :returns: (loc,meaning) where loc describes what item the variable is mapped
1635      (phase, histogram, etc.) and meaning describes what the variable does.
1636    '''
1637
1638    # special handling for parameter names without a colon
1639    # for now, assume self-defining
1640    if varname.find(':') == -1:
1641        return "Global",varname
1642
1643    l = getVarDescr(varname)
1644    if not l:
1645        return ("invalid variable name ("+str(varname)+")!"),""
1646#        return "invalid variable name!",""
1647
1648    if not l[-1]:
1649        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1650
1651    if len(l) == 3:         #SASD variable name!
1652        s = 'component:'+l[1]
1653        return s,l[-1]
1654    s = ""
1655    if l[0] is not None and l[1] is not None: # HAP: keep short
1656        if l[2] == "Scale": # fix up ambigous name
1657            l[5] = "Phase fraction"
1658        if l[0] == '*':
1659            lbl = 'Seq. ref.'
1660        else:
1661            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1662        if l[1] == '*':
1663            hlbl = 'Seq. ref.'
1664        else:
1665            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1666        if hlbl[:4] == 'HKLF':
1667            hlbl = 'Xtl='+hlbl[5:]
1668        elif hlbl[:4] == 'PWDR':
1669            hlbl = 'Pwd='+hlbl[5:]
1670        else:
1671            hlbl = 'Hist='+hlbl
1672        s = "Ph="+str(lbl)+" * "+str(hlbl)
1673    else:
1674        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1675            l[5] = "Scale factor"
1676        if l[2] == 'Back': # background parameters are "special", alas
1677            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1678            l[-1] += ' #'+str(l[3])
1679        elif l[4] is not None: # rigid body parameter or modulation parm
1680            lbl = ShortPhaseNames.get(l[0],'phase?')
1681            if 'RB' in l[2]:    #rigid body parm
1682                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1683            else: #modulation parm
1684                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
1685        elif l[3] is not None: # atom parameter,
1686            lbl = ShortPhaseNames.get(l[0],'phase?')
1687            try:
1688                albl = LookupAtomLabel(l[0],l[3])[0]
1689            except KeyError:
1690                albl = 'Atom?'
1691            s = "Atom "+str(albl)+" in "+str(lbl)
1692        elif l[0] == '*':
1693            s = "All phases "
1694        elif l[0] is not None:
1695            lbl = ShortPhaseNames.get(l[0],'phase?')
1696            s = "Phase "+str(lbl)
1697        elif l[1] == '*':
1698            s = 'All hists'
1699        elif l[1] is not None:
1700            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1701            if hlbl[:4] == 'HKLF':
1702                hlbl = 'Xtl='+hlbl[5:]
1703            elif hlbl[:4] == 'PWDR':
1704                hlbl = 'Pwd='+hlbl[5:]
1705            else:
1706                hlbl = 'Hist='+hlbl
1707            s = str(hlbl)
1708    if not s:
1709        s = 'Global'
1710    return s,l[-1]
1711
1712def getVarDescr(varname):
1713    '''Return a short description for a GSAS-II variable
1714
1715    :param str name: A full G2 variable name with 2 or 3 or 4
1716       colons (<p>:<h>:name[:<a1>][:<a2>])
1717
1718    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1719      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1720      the histogram number and the atom number; `name` will always be
1721      a str; and `description` is str or `None`.
1722      If the variable name is incorrectly formed (for example, wrong
1723      number of colons), `None` is returned instead of a list.
1724    '''
1725    l = varname.split(':')
1726    if len(l) == 2:     #SASD parameter name
1727        return varname,l[0],getDescr(l[1])
1728    if len(l) == 3:
1729        l += [None,None]
1730    elif len(l) == 4:
1731        l += [None]
1732    elif len(l) != 5:
1733        return None
1734    for i in (0,1,3,4):
1735        if l[i] == "":
1736            l[i] = None
1737    l += [getDescr(l[2])]
1738    return l
1739
1740def CompileVarDesc():
1741    '''Set the values in the variable lookup tables
1742    (:attr:`reVarDesc` and :attr:`reVarStep`).
1743    This is called in :func:`getDescr` and :func:`getVarStep` so this
1744    initialization is always done before use.
1745
1746    Note that keys may contain regular expressions, where '[xyz]'
1747    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range
1748    of values). '.*' matches any string. For example::
1749
1750    'AUiso':'Atomic isotropic displacement parameter',
1751
1752    will match variable ``'p::AUiso:a'``.
1753    If parentheses are used in the key, the contents of those parentheses can be
1754    used in the value, such as::
1755
1756    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1757
1758    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1759    in the value when used.
1760
1761    '''
1762    if reVarDesc: return # already done
1763    for key,value in {
1764        # derived or other sequential vars
1765        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1766        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1767        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1768        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1769        # ambiguous, alas:
1770        'Scale' : 'Phase or Histogram scale factor',
1771        # Phase vars (p::<var>)
1772        'A([0-5])' : ('Reciprocal metric tensor component \\1',1e-5),
1773        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
1774        # Atom vars (p::<var>:a)
1775        'dA([xyz])$' : ('change to atomic coordinate, \\1',1e-6),
1776        'A([xyz])$' : '\\1 fractional atomic coordinate',
1777        'AUiso':('Atomic isotropic displacement parameter',1e-4),
1778        'AU([123][123])':('Atomic anisotropic displacement parameter U\\1',1e-4),
1779        'Afrac': ('Atomic site fraction parameter',1e-5),
1780        'Amul': 'Atomic site multiplicity value',
1781        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
1782        # Hist & Phase (HAP) vars (p:h:<var>)
1783        'Back': 'Background term',
1784        'BkPkint;(.*)':'Background peak #\\1 intensity',
1785        'BkPkpos;(.*)':'Background peak #\\1 position',
1786        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1787        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1788        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1789        'D([123][123])' : 'Anisotropic strain coef. \\1',
1790        'Extinction' : 'Extinction coef.',
1791        'MD' : 'March-Dollase coef.',
1792        'Mustrain;.*' : 'Microstrain coef.',
1793        'Size;.*' : 'Crystallite size value',
1794        'eA$' : 'Cubic mustrain value',
1795        'Ep$' : 'Primary extinction',
1796        'Es$' : 'Secondary type II extinction',
1797        'Eg$' : 'Secondary type I extinction',
1798        'Flack' : 'Flack parameter',
1799        'TwinFr' : 'Twin fraction',
1800        'Layer Disp'  : 'Layer displacement along beam',
1801        #Histogram vars (:h:<var>)
1802        'Absorption' : 'Absorption coef.',
1803        'Displace([XY])' : ('Debye-Scherrer sample displacement \\1',0.1),
1804        'Lam' : ('Wavelength',1e-6),
1805        'I\(L2\)\/I\(L1\)' : ('Ka2/Ka1 intensity ratio',0.001),
1806        'Polariz\.' : ('Polarization correction',1e-3),
1807        'SH/L' : ('FCJ peak asymmetry correction',1e-4),
1808        '([UVW])$' : ('Gaussian instrument broadening \\1',1e-5),
1809        '([XYZ])$' : ('Cauchy instrument broadening \\1',1e-5),
1810        'Zero' : 'Debye-Scherrer zero correction',
1811        'Shift' : 'Bragg-Brentano sample displ.',
1812        'SurfRoughA' : 'Bragg-Brenano surface roughness A',
1813        'SurfRoughB' : 'Bragg-Brenano surface roughness B',
1814        'Transparency' : 'Bragg-Brentano sample tranparency',
1815        'DebyeA' : 'Debye model amplitude',
1816        'DebyeR' : 'Debye model radius',
1817        'DebyeU' : 'Debye model Uiso',
1818        'RBV.*' : 'Vector rigid body parameter',
1819        'RBR.*' : 'Residue rigid body parameter',
1820        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1821        'RBRP([xyz])' : 'Residue rigid body position parameter',
1822        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1823        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1824        'constr([0-9]*)' : 'Parameter from constraint',
1825        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1826        'mV([0-2])$' : 'Modulation vector component \\1',
1827        'Fsin'  :   'Sin site fraction modulation',
1828        'Fcos'  :   'Cos site fraction modulation',
1829        'Fzero'  :   'Crenel function offset',      #may go away
1830        'Fwid'   :   'Crenel function width',
1831        'Tmin'   :   'ZigZag/Block min location',
1832        'Tmax'   :   'ZigZag/Block max location',
1833        '([XYZ])max': 'ZigZag/Block max value for \\1',
1834        '([XYZ])sin'  : 'Sin position wave for \\1',
1835        '([XYZ])cos'  : 'Cos position wave for \\1',
1836        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1837        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1838        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1839        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1840        # PDF peak parms (l:<var>;l = peak no.)
1841        'PDFpos'  : 'PDF peak position',
1842        'PDFmag'  : 'PDF peak magnitude',
1843        'PDFsig'  : 'PDF peak std. dev.',
1844        # SASD vars (l:<var>;l = component)
1845        'Aspect ratio' : 'Particle aspect ratio',
1846        'Length' : 'Cylinder length',
1847        'Diameter' : 'Cylinder/disk diameter',
1848        'Thickness' : 'Disk thickness',
1849        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
1850        'Dist' : 'Interparticle distance',
1851        'VolFr' : 'Dense scatterer volume fraction',
1852        'epis' : 'Sticky sphere epsilon',
1853        'Sticky' : 'Stickyness',
1854        'Depth' : 'Well depth',
1855        'Width' : 'Well width',
1856        'Volume' : 'Particle volume',
1857        'Radius' : 'Sphere/cylinder/disk radius',
1858        'Mean' : 'Particle mean radius',
1859        'StdDev' : 'Standard deviation in Mean',
1860        'G$': 'Guinier prefactor',
1861        'Rg$': 'Guinier radius of gyration',
1862        'B$': 'Porod prefactor',
1863        'P$': 'Porod power',
1864        'Cutoff': 'Porod cutoff',
1865        'PkInt': 'Bragg peak intensity',
1866        'PkPos': 'Bragg peak position',
1867        'PkSig': 'Bragg peak sigma',
1868        'PkGam': 'Bragg peak gamma',
1869        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1870        'Dcalc': 'Calc. d-spacing',
1871        'Back$': 'background parameter',
1872        'pos$': 'peak position',
1873        'int$': 'peak intensity',
1874        'WgtFrac':'phase weight fraction',
1875        'alpha':'TOF profile term',
1876        'alpha-[01]':'Pink profile term',
1877        'beta-[01q]':'TOF/Pink profile term',
1878        'sig-[012q]':'TOF profile term',
1879        'dif[ABC]':'TOF to d-space calibration',
1880        'C\([0-9]*,[0-9]*\)' : 'spherical harmonics preferred orientation coef.',
1881        }.items():
1882        if len(value) == 2:
1883            #VarDesc[key] = value[0]
1884            reVarDesc[re.compile(key)] = value[0]
1885            reVarStep[re.compile(key)] = value[1]
1886        else:
1887            #VarDesc[key] = value
1888            reVarDesc[re.compile(key)] = value
1889
1890def removeNonRefined(parmList):
1891    '''Remove items from variable list that are not refined and should not
1892    appear as options for constraints
1893
1894    :param list parmList: a list of strings of form "p:h:VAR:a" where
1895      VAR is the variable name
1896
1897    :returns: a list after removing variables where VAR matches a
1898      entry in local variable NonRefinedList
1899    '''
1900    NonRefinedList = ['Omega','Type','Chi','Phi', 'Azimuth','Gonio. radius',
1901                          'Lam1','Lam2','Back','Temperature','Pressure',
1902                          'FreePrm1','FreePrm2','FreePrm3',
1903                          'Source','nPeaks','LeBail','newLeBail','Bank',
1904                          'nDebye', #'',
1905                    ]
1906    return [prm for prm in parmList if prm.split(':')[2] not in NonRefinedList]
1907       
1908def getDescr(name):
1909    '''Return a short description for a GSAS-II variable
1910
1911    :param str name: The descriptive part of the variable name without colons (:)
1912
1913    :returns: a short description or None if not found
1914    '''
1915
1916    CompileVarDesc() # compile the regular expressions, if needed
1917    for key in reVarDesc:
1918        m = key.match(name)
1919        if m:
1920            reVarDesc[key]
1921            return m.expand(reVarDesc[key])
1922    return None
1923
1924def getVarStep(name,parmDict=None):
1925    '''Return a step size for computing the derivative of a GSAS-II variable
1926
1927    :param str name: A complete variable name (with colons, :)
1928    :param dict parmDict: A dict with parameter values or None (default)
1929
1930    :returns: a float that should be an appropriate step size, either from
1931      the value supplied in :func:`CompileVarDesc` or based on the value for
1932      name in parmDict, if supplied. If not found or the value is zero,
1933      a default value of 1e-5 is used. If parmDict is None (default) and
1934      no value is provided in :func:`CompileVarDesc`, then None is returned.
1935    '''
1936    CompileVarDesc() # compile the regular expressions, if needed
1937    for key in reVarStep:
1938        m = key.match(name)
1939        if m:
1940            return reVarStep[key]
1941    if parmDict is None: return None
1942    val = parmDict.get(key,0.0)
1943    if abs(val) > 0.05:
1944        return abs(val)/1000.
1945    else:
1946        return 1e-5
1947
1948def GenWildCard(varlist):
1949    '''Generate wildcard versions of G2 variables. These introduce '*'
1950    for a phase, histogram or atom number (but only for one of these
1951    fields) but only when there is more than one matching variable in the
1952    input variable list. So if the input is this::
1953
1954      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1955
1956    then the output will be this::
1957
1958       wildList = ['*::AUiso:0', '0::AUiso:*']
1959
1960    :param list varlist: an input list of GSAS-II variable names
1961      (such as 0::AUiso:0)
1962
1963    :returns: wildList, the generated list of wild card variable names.
1964    '''
1965    wild = []
1966    for i in (0,1,3):
1967        currentL = varlist[:]
1968        while currentL:
1969            item1 = currentL.pop(0)
1970            i1splt = item1.split(':')
1971            if i >= len(i1splt): continue
1972            if i1splt[i]:
1973                nextL = []
1974                i1splt[i] = '[0-9]+'
1975                rexp = re.compile(':'.join(i1splt))
1976                matchlist = [item1]
1977                for nxtitem in currentL:
1978                    if rexp.match(nxtitem):
1979                        matchlist += [nxtitem]
1980                    else:
1981                        nextL.append(nxtitem)
1982                if len(matchlist) > 1:
1983                    i1splt[i] = '*'
1984                    wild.append(':'.join(i1splt))
1985                currentL = nextL
1986    return wild
1987
1988def LookupWildCard(varname,varlist):
1989    '''returns a list of variable names from list varname
1990    that match wildcard name in varname
1991
1992    :param str varname: a G2 variable name containing a wildcard
1993      (such as \*::var)
1994    :param list varlist: the list of all variable names used in
1995      the current project
1996    :returns: a list of matching GSAS-II variables (may be empty)
1997    '''
1998    rexp = re.compile(varname.replace('*','[0-9]+'))
1999    return sorted([var for var in varlist if rexp.match(var)])
2000
2001def prmLookup(name,prmDict):
2002    '''looks for a parameter in a min/max dictionary, optionally
2003    considering a wild card for histogram & atom number
2004    '''
2005    sn = name.split(':')
2006    if sn[1] != '': sn[1] = '*'
2007    if len(sn) >= 4 and sn[3] != '': sn[3] = '*'
2008    wname = ':'.join(sn)
2009    if wname in prmDict:
2010        return wname,prmDict[wname]
2011    elif name in prmDict:
2012        return name,prmDict[name]
2013    else:
2014        return None,None
2015       
2016
2017def _lookup(dic,key):
2018    '''Lookup a key in a dictionary, where None returns an empty string
2019    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
2020    '''
2021    if key is None:
2022        return ""
2023    elif key == "*":
2024        return "*"
2025    else:
2026        return dic.get(key,'?')
2027
2028def SortVariables(varlist):
2029    '''Sorts variable names in a sensible manner
2030    '''
2031    def cvnnums(var):
2032        v = []
2033        for i in var.split(':'):
2034            if i == '':
2035                v.append(-1)
2036                continue
2037            try:
2038                v.append(int(i))
2039            except:
2040                v.append(i)
2041        return v
2042    return sorted(varlist,key=cvnnums)
2043
2044class G2VarObj(object):
2045    '''Defines a GSAS-II variable either using the phase/atom/histogram
2046    unique Id numbers or using a character string that specifies
2047    variables by phase/atom/histogram number (which can change).
2048    Note that :func:`LoadID` should be used to (re)load the current Ids
2049    before creating or later using the G2VarObj object.
2050
2051    This can store rigid body variables, but does not translate the residue # and
2052    body # to/from random Ids
2053
2054    A :class:`G2VarObj` object can be created with a single parameter:
2055
2056    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
2057      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
2058
2059     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
2060     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
2061     * a is the atom number (which may be left blank in which case the third colon is omitted).
2062       The atom number can be specified as '*' if a phase number is specified (not as '*').
2063       For rigid body variables, specify a will be a string of form "residue:body#"
2064
2065      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
2066      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
2067      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
2068      For a rigid body variables, AtomID is a string of form "residue:body#".
2069
2070    If four positional arguments are supplied, they are:
2071
2072    :param str/int phasenum: The number for the phase (or None or '*')
2073    :param str/int histnum: The number for the histogram (or None or '*')
2074    :param str varname: a single value can be used to create a :class:`G2VarObj`
2075    :param str/int atomnum: The number for the atom (or None or '*')
2076
2077    '''
2078    IDdict = {}
2079    IDdict['phases'] = {}
2080    IDdict['hists'] = {}
2081    IDdict['atoms'] = {}
2082    def __init__(self,*args):
2083        self.phase = None
2084        self.histogram = None
2085        self.name = ''
2086        self.atom = None
2087        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
2088            # single arg with 4 values
2089            self.phase,self.histogram,self.name,self.atom = args[0]
2090        elif len(args) == 1 and ':' in args[0]:
2091            #parse a string
2092            lst = args[0].split(':')
2093            if lst[0] == '*':
2094                self.phase = '*'
2095                if len(lst) > 3:
2096                    self.atom = lst[3]
2097                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2098            elif lst[1] == '*':
2099                self.histogram = '*'
2100                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2101            else:
2102                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2103                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2104                if len(lst) == 4:
2105                    if lst[3] == '*':
2106                        self.atom = '*'
2107                    else:
2108                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
2109                elif len(lst) == 5:
2110                    self.atom = lst[3]+":"+lst[4]
2111                elif len(lst) == 3:
2112                    pass
2113                else:
2114                    raise Exception("Too many colons in var name "+str(args[0]))
2115            self.name = lst[2]
2116        elif len(args) == 4:
2117            if args[0] == '*':
2118                self.phase = '*'
2119                self.atom = args[3]
2120            else:
2121                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
2122                if args[3] == '*':
2123                    self.atom = '*'
2124                elif args[0] is not None:
2125                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
2126            if args[1] == '*':
2127                self.histogram = '*'
2128            else:
2129                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
2130            self.name = args[2]
2131        else:
2132            raise Exception("Incorrectly called GSAS-II parameter name")
2133
2134        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
2135
2136    def __str__(self):
2137        return self.varname()
2138
2139    def varname(self):
2140        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
2141        string (p:h:<var>:a) or (p:h:<var>)
2142
2143        :returns: the variable name as a str
2144        '''
2145        a = ""
2146        if self.phase == "*":
2147            ph = "*"
2148            if self.atom:
2149                a = ":" + str(self.atom)
2150        else:
2151            ph = _lookup(PhaseRanIdLookup,self.phase)
2152            if self.atom == '*':
2153                a = ':*'
2154            elif self.atom:
2155                if ":" in str(self.atom):
2156                    a = ":" + str(self.atom)
2157                elif ph in AtomRanIdLookup:
2158                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
2159                else:
2160                    a = ":?"
2161        if self.histogram == "*":
2162            hist = "*"
2163        else:
2164            hist = _lookup(HistRanIdLookup,self.histogram)
2165        s = (ph + ":" + hist + ":" + str(self.name)) + a
2166        return s
2167
2168    def __repr__(self):
2169        '''Return the detailed contents of the object
2170        '''
2171        s = "<"
2172        if self.phase == '*':
2173            s += "Phases: all; "
2174            if self.atom is not None:
2175                if ":" in str(self.atom):
2176                    s += "Rigid body" + str(self.atom) + "; "
2177                else:
2178                    s += "Atom #" + str(self.atom) + "; "
2179        elif self.phase is not None:
2180            ph =  _lookup(PhaseRanIdLookup,self.phase)
2181            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
2182            if self.atom == '*':
2183                s += "Atoms: all; "
2184            elif ":" in str(self.atom):
2185                s += "Rigid body" + str(self.atom) + "; "
2186            elif self.atom is not None:
2187                s += "Atom rId=" + str(self.atom)
2188                if ph in AtomRanIdLookup:
2189                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
2190                else:
2191                    s += " (#? -- not found!); "
2192        if self.histogram == '*':
2193            s += "Histograms: all; "
2194        elif self.histogram is not None:
2195            hist = _lookup(HistRanIdLookup,self.histogram)
2196            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
2197        s += 'Variable name="' + str(self.name) + '">'
2198        return s+" ("+self.varname()+")"
2199
2200    def __eq__(self, other):
2201        if type(other) is type(self):
2202            return (self.phase == other.phase and
2203                    self.histogram == other.histogram and
2204                    self.name == other.name and
2205                    self.atom == other.atom)
2206        return False
2207
2208    def _show(self):
2209        'For testing, shows the current lookup table'
2210        print ('phases'+ self.IDdict['phases'])
2211        print ('hists'+ self.IDdict['hists'])
2212        print ('atomDict'+ self.IDdict['atoms'])
2213
2214#==========================================================================
2215def SetDefaultSample():
2216    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
2217    return {
2218        'InstrName':'',
2219        'ranId':ran.randint(0,sys.maxsize),
2220        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
2221        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],
2222        'Temperature':300.,'Pressure':0.1,'Time':0.0,
2223        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
2224        'Gonio. radius':200.0,
2225        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
2226#SASD items
2227        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
2228        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
2229        'Trans':1.0,                            #measured transmission
2230        'SlitLen':0.0,                          #Slit length - in Q(A-1)
2231        }
2232######################################################################
2233class ImportBaseclass(object):
2234    '''Defines a base class for the reading of input files (diffraction
2235    data, coordinates,...). See :ref:`Writing a Import Routine<import_routines>`
2236    for an explanation on how to use a subclass of this class.
2237    '''
2238    class ImportException(Exception):
2239        '''Defines an Exception that is used when an import routine hits an expected error,
2240        usually in .Reader.
2241
2242        Good practice is that the Reader should define a value in self.errors that
2243        tells the user some information about what is wrong with their file.
2244        '''
2245        pass
2246
2247    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
2248    def __init__(self,formatName,longFormatName=None,
2249                 extensionlist=[],strictExtension=False,):
2250        self.formatName = formatName # short string naming file type
2251        if longFormatName: # longer string naming file type
2252            self.longFormatName = longFormatName
2253        else:
2254            self.longFormatName = formatName
2255        # define extensions that are allowed for the file type
2256        # for windows, remove any extensions that are duplicate, as case is ignored
2257        if sys.platform == 'windows' and extensionlist:
2258            extensionlist = list(set([s.lower() for s in extensionlist]))
2259        self.extensionlist = extensionlist
2260        # If strictExtension is True, the file will not be read, unless
2261        # the extension matches one in the extensionlist
2262        self.strictExtension = strictExtension
2263        self.errors = ''
2264        self.warnings = ''
2265        self.SciPy = False          #image reader needed scipy
2266        # used for readers that will use multiple passes to read
2267        # more than one data block
2268        self.repeat = False
2269        self.selections = []
2270        self.repeatcount = 0
2271        self.readfilename = '?'
2272        self.scriptable = False
2273        #print 'created',self.__class__
2274
2275    def ReInitialize(self):
2276        'Reinitialize the Reader to initial settings'
2277        self.errors = ''
2278        self.warnings = ''
2279        self.SciPy = False          #image reader needed scipy
2280        self.repeat = False
2281        self.repeatcount = 0
2282        self.readfilename = '?'
2283
2284
2285#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
2286#        '''This method must be supplied in the child class to read the file.
2287#        if the read fails either return False or raise an Exception
2288#        preferably of type ImportException.
2289#        '''
2290#        #start reading
2291#        raise ImportException("Error occurred while...")
2292#        self.errors += "Hint for user on why the error occur
2293#        return False # if an error occurs
2294#        return True # if read OK
2295
2296    def ExtensionValidator(self, filename):
2297        '''This methods checks if the file has the correct extension
2298       
2299        :returns:
2300       
2301          * False if this filename will not be supported by this reader (only
2302            when strictExtension is True)
2303          * True if the extension matches the list supplied by the reader
2304          * None if the reader allows un-registered extensions
2305         
2306        '''
2307        if filename:
2308            ext = ospath.splitext(filename)[1]
2309            if not ext and self.strictExtension: return False
2310            for ext in self.extensionlist:               
2311                if sys.platform == 'windows':
2312                    if filename.lower().endswith(ext): return True
2313                else:
2314                    if filename.endswith(ext): return True
2315        if self.strictExtension:
2316            return False
2317        else:
2318            return None
2319
2320    def ContentsValidator(self, filename):
2321        '''This routine will attempt to determine if the file can be read
2322        with the current format.
2323        This will typically be overridden with a method that
2324        takes a quick scan of [some of]
2325        the file contents to do a "sanity" check if the file
2326        appears to match the selected format.
2327        the file must be opened here with the correct format (binary/text)
2328        '''
2329        #filepointer.seek(0) # rewind the file pointer
2330        return True
2331
2332    def CIFValidator(self, filepointer):
2333        '''A :meth:`ContentsValidator` for use to validate CIF files.
2334        '''
2335        filepointer.seek(0)
2336        for i,l in enumerate(filepointer):
2337            if i >= 1000: return True
2338            '''Encountered only blank lines or comments in first 1000
2339            lines. This is unlikely, but assume it is CIF anyway, since we are
2340            even less likely to find a file with nothing but hashes and
2341            blank lines'''
2342            line = l.strip()
2343            if len(line) == 0: # ignore blank lines
2344                continue
2345            elif line.startswith('#'): # ignore comments
2346                continue
2347            elif line.startswith('data_'): # on the right track, accept this file
2348                return True
2349            else: # found something invalid
2350                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
2351                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
2352                    self.errors += '  '+str(l)
2353                else:
2354                    self.errors += '  (binary)'
2355                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
2356                self.errors += '\n        a data_ statement begins a block.'
2357                return False
2358
2359######################################################################
2360class ImportPhase(ImportBaseclass):
2361    '''Defines a base class for the reading of files with coordinates
2362
2363    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
2364    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` and in
2365    :func:`GSASIIscriptable.import_generic`.
2366    See :ref:`Writing a Import Routine<import_routines>`
2367    for an explanation on how to use this class.
2368
2369    '''
2370    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2371        strictExtension=False,):
2372        # call parent __init__
2373        ImportBaseclass.__init__(self,formatName,longFormatName,
2374            extensionlist,strictExtension)
2375        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
2376        self.Constraints = None
2377
2378######################################################################
2379class ImportStructFactor(ImportBaseclass):
2380    '''Defines a base class for the reading of files with tables
2381    of structure factors.
2382
2383    Structure factors are read with a call to :meth:`GSASIIdataGUI.GSASII.OnImportSfact`
2384    which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`, which calls
2385    methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2386    :meth:`Reader`.
2387
2388    See :ref:`Writing a Import Routine<import_routines>`
2389    for an explanation on how to use import classes in general. The specifics
2390    for reading a structure factor histogram require that
2391    the ``Reader()`` routine in the import
2392    class need to do only a few things: It
2393    should load :attr:`RefDict` item ``'RefList'`` with the reflection list,
2394    and set :attr:`Parameters` with the instrument parameters
2395    (initialized with :meth:`InitParameters` and set with :meth:`UpdateParameters`).
2396    '''
2397    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2398        strictExtension=False,):
2399        ImportBaseclass.__init__(self,formatName,longFormatName,
2400            extensionlist,strictExtension)
2401
2402        # define contents of Structure Factor entry
2403        self.Parameters = []
2404        'self.Parameters is a list with two dicts for data parameter settings'
2405        self.InitParameters()
2406        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2407        self.Banks = []             #for multi bank data (usually TOF)
2408        '''self.RefDict is a dict containing the reflection information, as read from the file.
2409        Item 'RefList' contains the reflection information. See the
2410        :ref:`Single Crystal Reflection Data Structure<XtalRefl_table>`
2411        for the contents of each row. Dict element 'FF'
2412        contains the form factor values for each element type; if this entry
2413        is left as initialized (an empty list) it will be initialized as needed later.
2414        '''
2415    def ReInitialize(self):
2416        'Reinitialize the Reader to initial settings'
2417        ImportBaseclass.ReInitialize(self)
2418        self.InitParameters()
2419        self.Banks = []             #for multi bank data (usually TOF)
2420        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2421
2422    def InitParameters(self):
2423        'initialize the instrument parameters structure'
2424        Lambda = 0.70926
2425        HistType = 'SXC'
2426        self.Parameters = [{'Type':[HistType,HistType], # create the structure
2427                            'Lam':[Lambda,Lambda]
2428                            }, {}]
2429        'Parameters is a list with two dicts for data parameter settings'
2430
2431    def UpdateParameters(self,Type=None,Wave=None):
2432        'Revise the instrument parameters'
2433        if Type is not None:
2434            self.Parameters[0]['Type'] = [Type,Type]
2435        if Wave is not None:
2436            self.Parameters[0]['Lam'] = [Wave,Wave]
2437
2438######################################################################
2439class ImportPowderData(ImportBaseclass):
2440    '''Defines a base class for the reading of files with powder data.
2441
2442    Objects constructed that subclass this (in import/G2pwd_*.py etc.) will be used
2443    in :meth:`GSASIIdataGUI.GSASII.OnImportPowder` and in
2444    :func:`GSASIIscriptable.import_generic`.
2445    See :ref:`Writing a Import Routine<import_routines>`
2446    for an explanation on how to use this class.
2447    '''
2448    def __init__(self,formatName,longFormatName=None,
2449        extensionlist=[],strictExtension=False,):
2450        ImportBaseclass.__init__(self,formatName,longFormatName,
2451            extensionlist,strictExtension)
2452        self.clockWd = None  # used in TOF
2453        self.ReInitialize()
2454
2455    def ReInitialize(self):
2456        'Reinitialize the Reader to initial settings'
2457        ImportBaseclass.ReInitialize(self)
2458        self.powderentry = ['',None,None] #  (filename,Pos,Bank)
2459        self.powderdata = [] # Powder dataset
2460        '''A powder data set is a list with items [x,y,w,yc,yb,yd]:
2461                np.array(x), # x-axis values
2462                np.array(y), # powder pattern intensities
2463                np.array(w), # 1/sig(intensity)^2 values (weights)
2464                np.array(yc), # calc. intensities (zero)
2465                np.array(yb), # calc. background (zero)
2466                np.array(yd), # obs-calc profiles
2467        '''
2468        self.comments = []
2469        self.idstring = ''
2470        self.Sample = SetDefaultSample() # default sample parameters
2471        self.Controls = {}  # items to be placed in top-level Controls
2472        self.GSAS = None     # used in TOF
2473        self.repeat_instparm = True # Should a parm file be
2474        #                             used for multiple histograms?
2475        self.instparm = None # name hint from file of instparm to use
2476        self.instfile = '' # full path name to instrument parameter file
2477        self.instbank = '' # inst parm bank number
2478        self.instmsg = ''  # a label that gets printed to show
2479                           # where instrument parameters are from
2480        self.numbanks = 1
2481        self.instdict = {} # place items here that will be transferred to the instrument parameters
2482        self.pwdparms = {} # place parameters that are transferred directly to the tree
2483                           # here (typically from an existing GPX file)
2484######################################################################
2485class ImportSmallAngleData(ImportBaseclass):
2486    '''Defines a base class for the reading of files with small angle data.
2487    See :ref:`Writing a Import Routine<import_routines>`
2488    for an explanation on how to use this class.
2489    '''
2490    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2491        strictExtension=False,):
2492
2493        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2494            strictExtension)
2495        self.ReInitialize()
2496
2497    def ReInitialize(self):
2498        'Reinitialize the Reader to initial settings'
2499        ImportBaseclass.ReInitialize(self)
2500        self.smallangleentry = ['',None,None] #  (filename,Pos,Bank)
2501        self.smallangledata = [] # SASD dataset
2502        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2503                np.array(x), # x-axis values
2504                np.array(y), # powder pattern intensities
2505                np.array(w), # 1/sig(intensity)^2 values (weights)
2506                np.array(yc), # calc. intensities (zero)
2507                np.array(yd), # obs-calc profiles
2508                np.array(yb), # preset bkg
2509        '''
2510        self.comments = []
2511        self.idstring = ''
2512        self.Sample = SetDefaultSample()
2513        self.GSAS = None     # used in TOF
2514        self.clockWd = None  # used in TOF
2515        self.numbanks = 1
2516        self.instdict = {} # place items here that will be transferred to the instrument parameters
2517
2518######################################################################
2519class ImportReflectometryData(ImportBaseclass):
2520    '''Defines a base class for the reading of files with reflectometry data.
2521    See :ref:`Writing a Import Routine<import_routines>`
2522    for an explanation on how to use this class.
2523    '''
2524    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2525        strictExtension=False,):
2526
2527        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2528            strictExtension)
2529        self.ReInitialize()
2530
2531    def ReInitialize(self):
2532        'Reinitialize the Reader to initial settings'
2533        ImportBaseclass.ReInitialize(self)
2534        self.reflectometryentry = ['',None,None] #  (filename,Pos,Bank)
2535        self.reflectometrydata = [] # SASD dataset
2536        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2537                np.array(x), # x-axis values
2538                np.array(y), # powder pattern intensities
2539                np.array(w), # 1/sig(intensity)^2 values (weights)
2540                np.array(yc), # calc. intensities (zero)
2541                np.array(yd), # obs-calc profiles
2542                np.array(yb), # preset bkg
2543        '''
2544        self.comments = []
2545        self.idstring = ''
2546        self.Sample = SetDefaultSample()
2547        self.GSAS = None     # used in TOF
2548        self.clockWd = None  # used in TOF
2549        self.numbanks = 1
2550        self.instdict = {} # place items here that will be transferred to the instrument parameters
2551
2552######################################################################
2553class ImportPDFData(ImportBaseclass):
2554    '''Defines a base class for the reading of files with PDF G(R) data.
2555    See :ref:`Writing a Import Routine<import_routines>`
2556    for an explanation on how to use this class.
2557    '''
2558    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2559        strictExtension=False,):
2560
2561        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2562            strictExtension)
2563        self.ReInitialize()
2564
2565    def ReInitialize(self):
2566        'Reinitialize the Reader to initial settings'
2567        ImportBaseclass.ReInitialize(self)
2568        self.pdfentry = ['',None,None] #  (filename,Pos,Bank)
2569        self.pdfdata = [] # PDF G(R) dataset
2570        '''A pdf g(r) data set is a list with items [x,y]:
2571                np.array(x), # r-axis values
2572                np.array(y), # pdf g(r)
2573        '''
2574        self.comments = []
2575        self.idstring = ''
2576        self.numbanks = 1
2577
2578######################################################################
2579class ImportImage(ImportBaseclass):
2580    '''Defines a base class for the reading of images
2581
2582    Images are read in only these places:
2583
2584      * Initial reading is typically done from a menu item
2585        with a call to :meth:`GSASIIdataGUI.GSASII.OnImportImage`
2586        which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`. That calls
2587        methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2588        :meth:`Reader`. This returns a list of reader objects for each read image.
2589        Also used in :func:`GSASIIscriptable.import_generic`.
2590
2591      * Images are read alternatively in :func:`GSASIIIO.ReadImages`, which puts image info
2592        directly into the data tree.
2593
2594      * Images are reloaded with :func:`GSASIIIO.GetImageData`.
2595
2596    When reading an image, the ``Reader()`` routine in the ImportImage class
2597    should set:
2598
2599      * :attr:`Comments`: a list of strings (str),
2600      * :attr:`Npix`: the number of pixels in the image (int),
2601      * :attr:`Image`: the actual image as a numpy array (np.array)
2602      * :attr:`Data`: a dict defining image parameters (dict). Within this dict the following
2603        data items are needed:
2604
2605         * 'pixelSize': size of each pixel in microns (such as ``[200.,200.]``.
2606         * 'wavelength': wavelength in :math:`\\AA`.
2607         * 'distance': distance of detector from sample in cm.
2608         * 'center': uncalibrated center of beam on detector (such as ``[204.8,204.8]``.
2609         * 'size': size of image (such as ``[2048,2048]``).
2610         * 'ImageTag': image number or other keyword used to retrieve image from
2611           a multi-image data file (defaults to ``1`` if not specified).
2612         * 'sumfile': holds sum image file name if a sum was produced from a multi image file
2613
2614    optional data items:
2615
2616      * :attr:`repeat`: set to True if there are additional images to
2617        read in the file, False otherwise
2618      * :attr:`repeatcount`: set to the number of the image.
2619
2620    Note that the above is initialized with :meth:`InitParameters`.
2621    (Also see :ref:`Writing a Import Routine<import_routines>`
2622    for an explanation on how to use import classes in general.)
2623    '''
2624    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2625        strictExtension=False,):
2626        ImportBaseclass.__init__(self,formatName,longFormatName,
2627            extensionlist,strictExtension)
2628        self.InitParameters()
2629
2630    def ReInitialize(self):
2631        'Reinitialize the Reader to initial settings -- not used at present'
2632        ImportBaseclass.ReInitialize(self)
2633        self.InitParameters()
2634
2635    def InitParameters(self):
2636        'initialize the instrument parameters structure'
2637        self.Comments = ['No comments']
2638        self.Data = {}
2639        self.Npix = 0
2640        self.Image = None
2641        self.repeat = False
2642        self.repeatcount = 1
2643        self.sumfile = ''
2644
2645    def LoadImage(self,ParentFrame,imagefile,imagetag=None):
2646        '''Optionally, call this after reading in an image to load it into the tree.
2647        This saves time by preventing a reread of the same information.
2648        '''
2649        if ParentFrame:
2650            ParentFrame.ImageZ = self.Image   # store the image for plotting
2651            ParentFrame.oldImagefile = imagefile # save the name of the last image file read
2652            ParentFrame.oldImageTag = imagetag   # save the tag of the last image file read
2653
2654#################################################################################################
2655# shortcut routines
2656exp = np.exp
2657sind = sin = s = lambda x: np.sin(x*np.pi/180.)
2658cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
2659tand = tan = t = lambda x: np.tan(x*np.pi/180.)
2660sqrt = sq = lambda x: np.sqrt(x)
2661pi = lambda: np.pi
2662class ExpressionObj(object):
2663    '''Defines an object with a user-defined expression, to be used for
2664    secondary fits or restraints. Object is created null, but is changed
2665    using :meth:`LoadExpression`. This contains only the minimum
2666    information that needs to be stored to save and load the expression
2667    and how it is mapped to GSAS-II variables.
2668    '''
2669    def __init__(self):
2670        self.expression = ''
2671        'The expression as a text string'
2672        self.assgnVars = {}
2673        '''A dict where keys are label names in the expression mapping to a GSAS-II
2674        variable. The value a G2 variable name.
2675        Note that the G2 variable name may contain a wild-card and correspond to
2676        multiple values.
2677        '''
2678        self.freeVars = {}
2679        '''A dict where keys are label names in the expression mapping to a free
2680        parameter. The value is a list with:
2681
2682         * a name assigned to the parameter
2683         * a value for to the parameter and
2684         * a flag to determine if the variable is refined.
2685        '''
2686        self.depVar = None
2687
2688        self.lastError = ('','')
2689        '''Shows last encountered error in processing expression
2690        (list of 1-3 str values)'''
2691
2692        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
2693        self.distance_atoms = None  # to be used for defining atom distances
2694
2695    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
2696        '''Load the expression and associated settings into the object. Raises
2697        an exception if the expression is not parsed, if not all functions
2698        are defined or if not all needed parameter labels in the expression
2699        are defined.
2700
2701        This will not test if the variable referenced in these definitions
2702        are actually in the parameter dictionary. This is checked when the
2703        computation for the expression is done in :meth:`SetupCalc`.
2704
2705        :param str expr: the expression
2706        :param list exprVarLst: parameter labels found in the expression
2707        :param dict varSelect: this will be 0 for Free parameters
2708          and non-zero for expression labels linked to G2 variables.
2709        :param dict varName: Defines a name (str) associated with each free parameter
2710        :param dict varValue: Defines a value (float) associated with each free parameter
2711        :param dict varRefflag: Defines a refinement flag (bool)
2712          associated with each free parameter
2713        '''
2714        self.expression = expr
2715        self.compiledExpr = None
2716        self.freeVars = {}
2717        self.assgnVars = {}
2718        for v in exprVarLst:
2719            if varSelect[v] == 0:
2720                self.freeVars[v] = [
2721                    varName.get(v),
2722                    varValue.get(v),
2723                    varRefflag.get(v),
2724                    ]
2725            else:
2726                self.assgnVars[v] = varName[v]
2727        self.CheckVars()
2728
2729    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
2730        '''Load the expression and associated settings from the object into
2731        arrays used for editing.
2732
2733        :param list exprVarLst: parameter labels found in the expression
2734        :param dict varSelect: this will be 0 for Free parameters
2735          and non-zero for expression labels linked to G2 variables.
2736        :param dict varName: Defines a name (str) associated with each free parameter
2737        :param dict varValue: Defines a value (float) associated with each free parameter
2738        :param dict varRefflag: Defines a refinement flag (bool)
2739          associated with each free parameter
2740
2741        :returns: the expression as a str
2742        '''
2743        for v in self.freeVars:
2744            varSelect[v] = 0
2745            varName[v] = self.freeVars[v][0]
2746            varValue[v] = self.freeVars[v][1]
2747            varRefflag[v] = self.freeVars[v][2]
2748        for v in self.assgnVars:
2749            varSelect[v] = 1
2750            varName[v] = self.assgnVars[v]
2751        return self.expression
2752
2753    def GetVaried(self):
2754        'Returns the names of the free parameters that will be refined'
2755        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
2756
2757    def GetVariedVarVal(self):
2758        'Returns the names and values of the free parameters that will be refined'
2759        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
2760
2761    def UpdateVariedVars(self,varyList,values):
2762        'Updates values for the free parameters (after a refinement); only updates refined vars'
2763        for v in self.freeVars:
2764            if not self.freeVars[v][2]: continue
2765            if "::"+self.freeVars[v][0] not in varyList: continue
2766            indx = list(varyList).index("::"+self.freeVars[v][0])
2767            self.freeVars[v][1] = values[indx]
2768
2769    def GetIndependentVars(self):
2770        'Returns the names of the required independent parameters used in expression'
2771        return [self.assgnVars[v] for v in self.assgnVars]
2772
2773    def CheckVars(self):
2774        '''Check that the expression can be parsed, all functions are
2775        defined and that input loaded into the object is internally
2776        consistent. If not an Exception is raised.
2777
2778        :returns: a dict with references to packages needed to
2779          find functions referenced in the expression.
2780        '''
2781        ret = self.ParseExpression(self.expression)
2782        if not ret:
2783            raise Exception("Expression parse error")
2784        exprLblList,fxnpkgdict = ret
2785        # check each var used in expression is defined
2786        defined = list(self.assgnVars.keys()) + list(self.freeVars.keys())
2787        notfound = []
2788        for var in exprLblList:
2789            if var not in defined:
2790                notfound.append(var)
2791        if notfound:
2792            msg = 'Not all variables defined'
2793            msg1 = 'The following variables were not defined: '
2794            msg2 = ''
2795            for var in notfound:
2796                if msg: msg += ', '
2797                msg += var
2798            self.lastError = (msg1,'  '+msg2)
2799            raise Exception(msg)
2800        return fxnpkgdict
2801
2802    def ParseExpression(self,expr):
2803        '''Parse an expression and return a dict of called functions and
2804        the variables used in the expression. Returns None in case an error
2805        is encountered. If packages are referenced in functions, they are loaded
2806        and the functions are looked up into the modules global
2807        workspace.
2808
2809        Note that no changes are made to the object other than
2810        saving an error message, so that this can be used for testing prior
2811        to the save.
2812
2813        :returns: a list of used variables
2814        '''
2815        self.lastError = ('','')
2816        import ast
2817        def FindFunction(f):
2818            '''Find the object corresponding to function f
2819            :param str f: a function name such as 'numpy.exp'
2820            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
2821              that defines the package location(s) and where pkgobj
2822              defines the object associated with the function.
2823              If the function is not found, pkgobj is None.
2824            '''
2825            df = f.split('.')
2826            pkgdict = {}
2827            # no listed package, try in current namespace
2828            if len(df) == 1:
2829                try:
2830                    fxnobj = eval(f)
2831                    return pkgdict,fxnobj
2832                except (AttributeError, NameError):
2833                    return None,None
2834            else:
2835                try:
2836                    fxnobj = eval(f)
2837                    pkgdict[df[0]] = eval(df[0])
2838                    return pkgdict,fxnobj
2839                except (AttributeError, NameError):
2840                    pass
2841            # includes a package, lets try to load the packages
2842            pkgname = ''
2843            path = sys.path+['./',]
2844            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
2845                if pkgname:
2846                    pkgname += '.' + pkg
2847                else:
2848                    pkgname = pkg
2849                fp = None
2850                try:
2851                    fp, fppath,desc = imp.find_module(pkg,path)
2852                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
2853                    pkgdict[pkgname] = pkgobj
2854                    path = [fppath]
2855                except Exception as msg:
2856                    print('load of '+pkgname+' failed with error='+str(msg))
2857                    return {},None
2858                finally:
2859                    if fp: fp.close()
2860                try:
2861                    #print 'before',pkgdict.keys()
2862                    fxnobj = eval(f,globals(),pkgdict)
2863                    #print 'after 1',pkgdict.keys()
2864                    #fxnobj = eval(f,pkgdict)
2865                    #print 'after 2',pkgdict.keys()
2866                    return pkgdict,fxnobj
2867                except:
2868                    continue
2869            return None # not found
2870        def ASTtransverse(node,fxn=False):
2871            '''Transverse a AST-parsed expresson, compiling a list of variables
2872            referenced in the expression. This routine is used recursively.
2873
2874            :returns: varlist,fxnlist where
2875              varlist is a list of referenced variable names and
2876              fxnlist is a list of used functions
2877            '''
2878            varlist = []
2879            fxnlist = []
2880            if isinstance(node, list):
2881                for b in node:
2882                    v,f = ASTtransverse(b,fxn)
2883                    varlist += v
2884                    fxnlist += f
2885            elif isinstance(node, ast.AST):
2886                for a, b in ast.iter_fields(node):
2887                    if isinstance(b, ast.AST):
2888                        if a == 'func':
2889                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
2890                            continue
2891                        v,f = ASTtransverse(b,fxn)
2892                        varlist += v
2893                        fxnlist += f
2894                    elif isinstance(b, list):
2895                        v,f = ASTtransverse(b,fxn)
2896                        varlist += v
2897                        fxnlist += f
2898                    elif node.__class__.__name__ == "Name":
2899                        varlist += [b]
2900                    elif fxn and node.__class__.__name__ == "Attribute":
2901                        varlist += [b]
2902            return varlist,fxnlist
2903        try:
2904            exprast = ast.parse(expr)
2905        except SyntaxError:
2906            s = ''
2907            import traceback
2908            for i in traceback.format_exc().splitlines()[-3:-1]:
2909                if s: s += "\n"
2910                s += str(i)
2911            self.lastError = ("Error parsing expression:",s)
2912            return
2913        # find the variables & functions
2914        v,f = ASTtransverse(exprast)
2915        varlist = sorted(list(set(v)))
2916        fxnlist = list(set(f))
2917        pkgdict = {}
2918        # check the functions are defined
2919        for fxn in fxnlist:
2920            fxndict,fxnobj = FindFunction(fxn)
2921            if not fxnobj:
2922                self.lastError = ("Error: Invalid function",fxn,
2923                                  "is not defined")
2924                return
2925            if not hasattr(fxnobj,'__call__'):
2926                self.lastError = ("Error: Not a function.",fxn,
2927                                  "cannot be called as a function")
2928                return
2929            pkgdict.update(fxndict)
2930        return varlist,pkgdict
2931
2932    def GetDepVar(self):
2933        'return the dependent variable, or None'
2934        return self.depVar
2935
2936    def SetDepVar(self,var):
2937        'Set the dependent variable, if used'
2938        self.depVar = var
2939#==========================================================================
2940class ExpressionCalcObj(object):
2941    '''An object used to evaluate an expression from a :class:`ExpressionObj`
2942    object.
2943
2944    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
2945      an expression string and mappings for the parameter labels in that object.
2946    '''
2947    def __init__(self,exprObj):
2948        self.eObj = exprObj
2949        'The expression and mappings; a :class:`ExpressionObj` object'
2950        self.compiledExpr = None
2951        'The expression as compiled byte-code'
2952        self.exprDict = {}
2953        '''dict that defines values for labels used in expression and packages
2954        referenced by functions
2955        '''
2956        self.lblLookup = {}
2957        '''Lookup table that specifies the expression label name that is
2958        tied to a particular GSAS-II parameters in the parmDict.
2959        '''
2960        self.fxnpkgdict = {}
2961        '''a dict with references to packages needed to
2962        find functions referenced in the expression.
2963        '''
2964        self.varLookup = {}
2965        '''Lookup table that specifies the GSAS-II variable(s)
2966        indexed by the expression label name. (Used for only for diagnostics
2967        not evaluation of expression.)
2968        '''
2969        self.su = None
2970        '''Standard error evaluation where supplied by the evaluator
2971        '''
2972        # Patch: for old-style expressions with a (now removed step size)
2973        if '2' in platform.python_version_tuple()[0]: 
2974            basestr = basestring
2975        else:
2976            basestr = str
2977        for v in self.eObj.assgnVars:
2978            if not isinstance(self.eObj.assgnVars[v], basestr):
2979                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
2980        self.parmDict = {}
2981        '''A copy of the parameter dictionary, for distance and angle computation
2982        '''
2983
2984    def SetupCalc(self,parmDict):
2985        '''Do all preparations to use the expression for computation.
2986        Adds the free parameter values to the parameter dict (parmDict).
2987        '''
2988        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2989            return
2990        self.fxnpkgdict = self.eObj.CheckVars()
2991        # all is OK, compile the expression
2992        self.compiledExpr = compile(self.eObj.expression,'','eval')
2993
2994        # look at first value in parmDict to determine its type
2995        parmsInList = True
2996        if '2' in platform.python_version_tuple()[0]: 
2997            basestr = basestring
2998        else:
2999            basestr = str
3000        for key in parmDict:
3001            val = parmDict[key]
3002            if isinstance(val, basestr):
3003                parmsInList = False
3004                break
3005            try: # check if values are in lists
3006                val = parmDict[key][0]
3007            except (TypeError,IndexError):
3008                parmsInList = False
3009            break
3010
3011        # set up the dicts needed to speed computations
3012        self.exprDict = {}
3013        self.lblLookup = {}
3014        self.varLookup = {}
3015        for v in self.eObj.freeVars:
3016            varname = self.eObj.freeVars[v][0]
3017            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
3018            self.lblLookup[varname] = v
3019            self.varLookup[v] = varname
3020            if parmsInList:
3021                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
3022            else:
3023                parmDict[varname] = self.eObj.freeVars[v][1]
3024            self.exprDict[v] = self.eObj.freeVars[v][1]
3025        for v in self.eObj.assgnVars:
3026            varname = self.eObj.assgnVars[v]
3027            if varname in parmDict:
3028                self.lblLookup[varname] = v
3029                self.varLookup[v] = varname
3030                if parmsInList:
3031                    self.exprDict[v] = parmDict[varname][0]
3032                else:
3033                    self.exprDict[v] = parmDict[varname]
3034            elif '*' in varname:
3035                varlist = LookupWildCard(varname,list(parmDict.keys()))
3036                if len(varlist) == 0:
3037                    raise Exception("No variables match "+str(v))
3038                for var in varlist:
3039                    self.lblLookup[var] = v
3040                if parmsInList:
3041                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
3042                else:
3043                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
3044                self.varLookup[v] = [var for var in varlist]
3045            else:
3046                self.exprDict[v] = None
3047#                raise Exception,"No value for variable "+str(v)
3048        self.exprDict.update(self.fxnpkgdict)
3049
3050    def UpdateVars(self,varList,valList):
3051        '''Update the dict for the expression with a set of values
3052        :param list varList: a list of variable names
3053        :param list valList: a list of corresponding values
3054        '''
3055        for var,val in zip(varList,valList):
3056            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
3057
3058    def UpdateDict(self,parmDict):
3059        '''Update the dict for the expression with values in a dict
3060        :param dict parmDict: a dict of values, items not in use are ignored
3061        '''
3062        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
3063            self.parmDict = parmDict
3064            return
3065        for var in parmDict:
3066            if var in self.lblLookup:
3067                self.exprDict[self.lblLookup[var]] = parmDict[var]
3068
3069    def EvalExpression(self):
3070        '''Evaluate an expression. Note that the expression
3071        and mapping are taken from the :class:`ExpressionObj` expression object
3072        and the parameter values were specified in :meth:`SetupCalc`.
3073        :returns: a single value for the expression. If parameter
3074        values are arrays (for example, from wild-carded variable names),
3075        the sum of the resulting expression is returned.
3076
3077        For example, if the expression is ``'A*B'``,
3078        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
3079
3080        [0.5, 1, 0.5]
3081
3082        then the result will be ``4.0``.
3083        '''
3084        self.su = None
3085        if self.eObj.expression.startswith('Dist'):
3086#            GSASIIpath.IPyBreak()
3087            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
3088            return dist
3089        elif self.eObj.expression.startswith('Angle'):
3090            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
3091            return angle
3092        if self.compiledExpr is None:
3093            raise Exception("EvalExpression called before SetupCalc")
3094        try:
3095            val = eval(self.compiledExpr,globals(),self.exprDict)
3096        except TypeError:
3097            val = None
3098        if not np.isscalar(val):
3099            val = np.sum(val)
3100        return val
3101
3102class G2Exception(Exception):
3103    'A generic GSAS-II exception class'
3104    def __init__(self,msg):
3105        self.msg = msg
3106    def __str__(self):
3107        return repr(self.msg)
3108
3109class G2RefineCancel(Exception):
3110    'Raised when Cancel is pressed in a refinement dialog'
3111    def __init__(self,msg):
3112        self.msg = msg
3113    def __str__(self):
3114        return repr(self.msg)
3115   
3116def HowDidIgetHere(wherecalledonly=False):
3117    '''Show a traceback with calls that brought us to the current location.
3118    Used for debugging.
3119    '''
3120    import traceback
3121    if wherecalledonly:
3122        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
3123        print(i.strip().rstrip())
3124    else:
3125        print (70*'*')
3126        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
3127        print (70*'*')
3128
3129# Note that this is GUI code and should be moved at somepoint
3130def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
3131    '''Create and initialize a new set of PDF tree entries
3132
3133    :param Frame G2frame: main GSAS-II tree frame object
3134    :param str PWDRtree: name of PWDR to be used to create PDF item
3135    :param dict ElList: data structure with composition
3136    :param list Qlimits: Q limits to be used for computing the PDF
3137    :param float numAtm: no. atom in chemical formula
3138    :param float FltBkg: flat background value
3139    :param list PDFnames: previously used PDF names
3140
3141    :returns: the Id of the newly created PDF entry
3142    '''
3143    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
3144    if PDFname in PDFnames:
3145        print('Skipping, entry already exists: '+PDFname)
3146        return None
3147    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
3148    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
3149    Data = {
3150        'Sample':{'Name':PWDRtree,'Mult':1.0},
3151        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
3152        'Container':{'Name':'','Mult':-1.0,'Refine':False},
3153        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
3154        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
3155        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
3156        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
3157        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
3158    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
3159    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
3160        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
3161    return Id
3162#%%
3163class ShowTiming(object):
3164    '''An object to use for timing repeated sections of code.
3165
3166    Create the object with::
3167       tim0 = ShowTiming()
3168
3169    Tag sections of code to be timed with::
3170       tim0.start('start')
3171       tim0.start('in section 1')
3172       tim0.start('in section 2')
3173       
3174    etc. (Note that each section should have a unique label.)
3175
3176    After the last section, end timing with::
3177       tim0.end()
3178
3179    Show timing results with::
3180       tim0.show()
3181       
3182    '''
3183    def __init__(self):
3184        self.timeSum =  []
3185        self.timeStart = []
3186        self.label = []
3187        self.prev = None
3188    def start(self,label):
3189        import time
3190        if label in self.label:
3191            i = self.label.index(label)
3192            self.timeStart[i] = time.time()
3193        else:
3194            i = len(self.label)
3195            self.timeSum.append(0.0)
3196            self.timeStart.append(time.time())
3197            self.label.append(label)
3198        if self.prev is not None:
3199            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
3200        self.prev = i
3201    def end(self):
3202        import time
3203        if self.prev is not None:
3204            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
3205        self.prev = None
3206    def show(self):
3207        sumT = sum(self.timeSum)
3208        print('Timing results (total={:.2f} sec)'.format(sumT))
3209        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
3210            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
3211#%%
3212
3213if __name__ == "__main__":
3214    # test variable descriptions
3215    for var in '0::Afrac:*',':1:Scale','1::dAx:0','::undefined':
3216        v = var.split(':')[2]
3217        print(var+':\t', getDescr(v),getVarStep(v))
3218    import sys; sys.exit()
3219    # test equation evaluation
3220    def showEQ(calcobj):
3221        print (50*'=')
3222        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
3223        for v in sorted(calcobj.varLookup):
3224            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
3225        # print '  Derivatives'
3226        # for v in calcobj.derivStep.keys():
3227        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
3228
3229    obj = ExpressionObj()
3230
3231    obj.expression = "A*np.exp(B)"
3232    obj.assgnVars =  {'B': '0::Afrac:1'}
3233    obj.freeVars =  {'A': [u'A', 0.5, True]}
3234    #obj.CheckVars()
3235    calcobj = ExpressionCalcObj(obj)
3236
3237    obj1 = ExpressionObj()
3238    obj1.expression = "A*np.exp(B)"
3239    obj1.assgnVars =  {'B': '0::Afrac:*'}
3240    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
3241    #obj.CheckVars()
3242    calcobj1 = ExpressionCalcObj(obj1)
3243
3244    obj2 = ExpressionObj()
3245    obj2.distance_stuff = np.array([[0,1],[1,-1]])
3246    obj2.expression = "Dist(1,2)"
3247    GSASIIpath.InvokeDebugOpts()
3248    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3249    calcobj2 = ExpressionCalcObj(obj2)
3250    calcobj2.SetupCalc(parmDict2)
3251    showEQ(calcobj2)
3252
3253    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
3254    print ('\nDict = '+parmDict1)
3255    calcobj.SetupCalc(parmDict1)
3256    showEQ(calcobj)
3257    calcobj1.SetupCalc(parmDict1)
3258    showEQ(calcobj1)
3259
3260    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3261    print ('Dict = '+parmDict2)
3262    calcobj.SetupCalc(parmDict2)
3263    showEQ(calcobj)
3264    calcobj1.SetupCalc(parmDict2)
3265    showEQ(calcobj1)
3266    calcobj2.SetupCalc(parmDict2)
3267    showEQ(calcobj2)
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