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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2020-04-25 02:52:46 +0000 (Sat, 25 Apr 2020) $
5# $Author: toby $
6# $Revision: 4413 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 4413 2020-04-25 02:52:46Z 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*Classes and routines*
1144----------------------
1145
1146'''
1147from __future__ import division, print_function
1148import platform
1149import re
1150import imp
1151import random as ran
1152import sys
1153import os.path as ospath
1154if '2' in platform.python_version_tuple()[0]:
1155    import cPickle
1156else:
1157    import pickle as cPickle
1158import GSASIIpath
1159import GSASIImath as G2mth
1160import GSASIIspc as G2spc
1161import numpy as np
1162
1163GSASIIpath.SetVersionNumber("$Revision: 4413 $")
1164
1165DefaultControls = {
1166    'deriv type':'analytic Hessian',
1167    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
1168    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
1169    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
1170    'Author':'no name',
1171    'FreePrm1':'Sample humidity (%)',
1172    'FreePrm2':'Sample voltage (V)',
1173    'FreePrm3':'Applied load (MN)',
1174    'ShowCell':False,
1175    }
1176'''Values to be used as defaults for the initial contents of the ``Controls``
1177data tree item.
1178'''
1179def StripUnicode(string,subs='.'):
1180    '''Strip non-ASCII characters from strings
1181
1182    :param str string: string to strip Unicode characters from
1183    :param str subs: character(s) to place into string in place of each
1184      Unicode character. Defaults to '.'
1185
1186    :returns: a new string with only ASCII characters
1187    '''
1188    s = ''
1189    for c in string:
1190        if ord(c) < 128:
1191            s += c
1192        else:
1193            s += subs
1194    return s
1195#    return s.encode('ascii','replace')
1196
1197def MakeUniqueLabel(lbl,labellist):
1198    '''Make sure that every a label is unique against a list by adding
1199    digits at the end until it is not found in list.
1200
1201    :param str lbl: the input label
1202    :param list labellist: the labels that have already been encountered
1203    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
1204      ``_10-99``, etc.) appended at the end
1205    '''
1206    lbl = StripUnicode(lbl.strip(),'_')
1207    if not lbl: # deal with a blank label
1208        lbl = '_1'
1209    if lbl not in labellist:
1210        labellist.append(lbl)
1211        return lbl
1212    i = 1
1213    prefix = lbl
1214    if '_' in lbl:
1215        prefix = lbl[:lbl.rfind('_')]
1216        suffix = lbl[lbl.rfind('_')+1:]
1217        try:
1218            i = int(suffix)+1
1219        except: # suffix could not be parsed
1220            i = 1
1221            prefix = lbl
1222    while prefix+'_'+str(i) in labellist:
1223        i += 1
1224    else:
1225        lbl = prefix+'_'+str(i)
1226        labellist.append(lbl)
1227    return lbl
1228
1229PhaseIdLookup = {}
1230'''dict listing phase name and random Id keyed by sequential phase index as a str;
1231best to access this using :func:`LookupPhaseName`
1232'''
1233PhaseRanIdLookup = {}
1234'''dict listing phase sequential index keyed by phase random Id;
1235best to access this using :func:`LookupPhaseId`
1236'''
1237HistIdLookup = {}
1238'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
1239best to access this using :func:`LookupHistName`
1240'''
1241HistRanIdLookup = {}
1242'''dict listing histogram sequential index keyed by histogram random Id;
1243best to access this using :func:`LookupHistId`
1244'''
1245AtomIdLookup = {}
1246'''dict listing for each phase index as a str, the atom label and atom random Id,
1247keyed by atom sequential index as a str;
1248best to access this using :func:`LookupAtomLabel`
1249'''
1250AtomRanIdLookup = {}
1251'''dict listing for each phase the atom sequential index keyed by atom random Id;
1252best to access this using :func:`LookupAtomId`
1253'''
1254ShortPhaseNames = {}
1255'''a dict containing a possibly shortened and when non-unique numbered
1256version of the phase name. Keyed by the phase sequential index.
1257'''
1258ShortHistNames = {}
1259'''a dict containing a possibly shortened and when non-unique numbered
1260version of the histogram name. Keyed by the histogram sequential index.
1261'''
1262
1263#VarDesc = {}  # removed 1/30/19 BHT as no longer needed (I think)
1264#''' This dictionary lists descriptions for GSAS-II variables,
1265#as set in :func:`CompileVarDesc`. See that function for a description
1266#for how keys and values are written.
1267#'''
1268
1269reVarDesc = {}
1270''' This dictionary lists descriptions for GSAS-II variables where
1271keys are compiled regular expressions that will match the name portion
1272of a parameter name. Initialized in :func:`CompileVarDesc`.
1273'''
1274
1275reVarStep = {}
1276''' This dictionary lists the preferred step size for numerical
1277derivative computation w/r to a GSAS-II variable. Keys are compiled
1278regular expressions and values are the step size for that parameter.
1279Initialized in :func:`CompileVarDesc`.
1280'''
1281# create a default space group object for P1; N.B. fails when building documentation
1282try:
1283    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
1284except:
1285    pass
1286
1287def GetPhaseNames(fl):
1288    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
1289    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename
1290
1291    :param file fl: opened .gpx file
1292    :return: list of phase names
1293    '''
1294    PhaseNames = []
1295    while True:
1296        try:
1297            data = cPickle.load(fl)
1298        except EOFError:
1299            break
1300        datum = data[0]
1301        if 'Phases' == datum[0]:
1302            for datus in data[1:]:
1303                PhaseNames.append(datus[0])
1304    fl.seek(0)          #reposition file
1305    return PhaseNames
1306
1307def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
1308    '''Create a new phase dict with default values for various parameters
1309
1310    :param str Name: Name for new Phase
1311
1312    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
1313      defaults to data for P 1
1314
1315    :param list cell: unit cell parameter list; defaults to
1316      [1.0,1.0,1.0,90.,90,90.,1.]
1317
1318    '''
1319    if SGData is None: SGData = P1SGData
1320    if cell is None: cell=[1.0,1.0,1.0,90.,90.,90.,1.]
1321    phaseData = {
1322        'ranId':ran.randint(0,sys.maxsize),
1323        'General':{
1324            'Name':Name,
1325            'Type':'nuclear',
1326            'Modulated':False,
1327            'AtomPtrs':[3,1,7,9],
1328            'SGData':SGData,
1329            'Cell':[False,]+cell,
1330            'Pawley dmin':1.0,
1331            'Data plot type':'None',
1332            'SH Texture':{
1333                'Order':0,
1334                'Model':'cylindrical',
1335                'Sample omega':[False,0.0],
1336                'Sample chi':[False,0.0],
1337                'Sample phi':[False,0.0],
1338                'SH Coeff':[False,{}],
1339                'SHShow':False,
1340                'PFhkl':[0,0,1],
1341                'PFxyz':[0,0,1],
1342                'PlotType':'Pole figure',
1343                'Penalty':[['',],0.1,False,1.0]}},
1344        'Atoms':[],
1345        'Drawing':{},
1346        'Histograms':{},
1347        'Pawley ref':[],
1348        'RBModels':{},
1349        }
1350    if Super and Super.get('Use',False):
1351        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
1352        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
1353        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]
1354
1355    return phaseData
1356
1357def ReadCIF(URLorFile):
1358    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
1359    (from James Hester).
1360    The open routine gets confused with DOS names that begin with a letter and colon
1361    "C:\dir\" so this routine will try to open the passed name as a file and if that
1362    fails, try it as a URL
1363
1364    :param str URLorFile: string containing a URL or a file name. Code will try first
1365      to open it as a file and then as a URL.
1366
1367    :returns: a PyCifRW CIF object.
1368    '''
1369    import CifFile as cif # PyCifRW from James Hester
1370
1371    # alternate approach:
1372    #import urllib
1373    #ciffile = 'file:'+urllib.pathname2url(filename)
1374
1375    try:
1376        fp = open(URLorFile,'r')
1377        cf = cif.ReadCif(fp)
1378        fp.close()
1379        return cf
1380    except IOError:
1381        return cif.ReadCif(URLorFile)
1382
1383def IndexAllIds(Histograms,Phases):
1384    '''Scan through the used phases & histograms and create an index
1385    to the random numbers of phases, histograms and atoms. While doing this,
1386    confirm that assigned random numbers are unique -- just in case lightning
1387    strikes twice in the same place.
1388
1389    Note: this code assumes that the atom random Id (ranId) is the last
1390    element each atom record.
1391
1392    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
1393    (which loads the histograms and phases from a GPX file),
1394    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
1395    (which loads the histograms and phases from the data tree.) and
1396    :meth:`GSASIIconstrGUI.UpdateConstraints`
1397    (which displays & edits the constraints in a GUI)
1398
1399    TODO: do we need a lookup for rigid body variables?
1400    '''
1401    # process phases and atoms
1402    PhaseIdLookup.clear()
1403    PhaseRanIdLookup.clear()
1404    AtomIdLookup.clear()
1405    AtomRanIdLookup.clear()
1406    ShortPhaseNames.clear()
1407    for ph in Phases:
1408        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
1409        ranId = Phases[ph]['ranId']
1410        while ranId in PhaseRanIdLookup:
1411            # Found duplicate random Id! note and reassign
1412            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
1413            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1414        pId = str(Phases[ph]['pId'])
1415        PhaseIdLookup[pId] = (ph,ranId)
1416        PhaseRanIdLookup[ranId] = pId
1417        shortname = ph  #[:10]
1418        while shortname in ShortPhaseNames.values():
1419            shortname = ph[:8] + ' ('+ pId + ')'
1420        ShortPhaseNames[pId] = shortname
1421        AtomIdLookup[pId] = {}
1422        AtomRanIdLookup[pId] = {}
1423        for iatm,at in enumerate(Phases[ph]['Atoms']):
1424            ranId = at[cia+8]
1425            while ranId in AtomRanIdLookup[pId]: # check for dups
1426                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
1427                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
1428            AtomRanIdLookup[pId][ranId] = str(iatm)
1429            if Phases[ph]['General']['Type'] == 'macromolecular':
1430                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
1431            else:
1432                label = at[ct-1]
1433            AtomIdLookup[pId][str(iatm)] = (label,ranId)
1434    # process histograms
1435    HistIdLookup.clear()
1436    HistRanIdLookup.clear()
1437    ShortHistNames.clear()
1438    for hist in Histograms:
1439        ranId = Histograms[hist]['ranId']
1440        while ranId in HistRanIdLookup:
1441            # Found duplicate random Id! note and reassign
1442            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1443            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1444        hId = str(Histograms[hist]['hId'])
1445        HistIdLookup[hId] = (hist,ranId)
1446        HistRanIdLookup[ranId] = hId
1447        shortname = hist[:15]
1448        while shortname in ShortHistNames.values():
1449            shortname = hist[:11] + ' ('+ hId + ')'
1450        ShortHistNames[hId] = shortname
1451
1452def LookupAtomId(pId,ranId):
1453    '''Get the atom number from a phase and atom random Id
1454
1455    :param int/str pId: the sequential number of the phase
1456    :param int ranId: the random Id assigned to an atom
1457
1458    :returns: the index number of the atom (str)
1459    '''
1460    if not AtomRanIdLookup:
1461        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
1462    if pId is None or pId == '':
1463        raise KeyError('Error: phase is invalid (None or blank)')
1464    pId = str(pId)
1465    if pId not in AtomRanIdLookup:
1466        raise KeyError('Error: LookupAtomId does not have phase '+pId)
1467    if ranId not in AtomRanIdLookup[pId]:
1468        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
1469    return AtomRanIdLookup[pId][ranId]
1470
1471def LookupAtomLabel(pId,index):
1472    '''Get the atom label from a phase and atom index number
1473
1474    :param int/str pId: the sequential number of the phase
1475    :param int index: the index of the atom in the list of atoms
1476
1477    :returns: the label for the atom (str) and the random Id of the atom (int)
1478    '''
1479    if not AtomIdLookup:
1480        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
1481    if pId is None or pId == '':
1482        raise KeyError('Error: phase is invalid (None or blank)')
1483    pId = str(pId)
1484    if pId not in AtomIdLookup:
1485        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
1486    if index not in AtomIdLookup[pId]:
1487        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
1488    return AtomIdLookup[pId][index]
1489
1490def LookupPhaseId(ranId):
1491    '''Get the phase number and name from a phase random Id
1492
1493    :param int ranId: the random Id assigned to a phase
1494    :returns: the sequential Id (pId) number for the phase (str)
1495    '''
1496    if not PhaseRanIdLookup:
1497        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
1498    if ranId not in PhaseRanIdLookup:
1499        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
1500    return PhaseRanIdLookup[ranId]
1501
1502def LookupPhaseName(pId):
1503    '''Get the phase number and name from a phase Id
1504
1505    :param int/str pId: the sequential assigned to a phase
1506    :returns:  (phase,ranId) where phase is the name of the phase (str)
1507      and ranId is the random # id for the phase (int)
1508    '''
1509    if not PhaseIdLookup:
1510        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
1511    if pId is None or pId == '':
1512        raise KeyError('Error: phase is invalid (None or blank)')
1513    pId = str(pId)
1514    if pId not in PhaseIdLookup:
1515        raise KeyError('Error: LookupPhaseName does not have index '+pId)
1516    return PhaseIdLookup[pId]
1517
1518def LookupHistId(ranId):
1519    '''Get the histogram number and name from a histogram random Id
1520
1521    :param int ranId: the random Id assigned to a histogram
1522    :returns: the sequential Id (hId) number for the histogram (str)
1523    '''
1524    if not HistRanIdLookup:
1525        raise Exception('Error: LookupHistId called before IndexAllIds was run')
1526    if ranId not in HistRanIdLookup:
1527        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
1528    return HistRanIdLookup[ranId]
1529
1530def LookupHistName(hId):
1531    '''Get the histogram number and name from a histogram Id
1532
1533    :param int/str hId: the sequential assigned to a histogram
1534    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1535      and ranId is the random # id for the histogram (int)
1536    '''
1537    if not HistIdLookup:
1538        raise Exception('Error: LookupHistName called before IndexAllIds was run')
1539    if hId is None or hId == '':
1540        raise KeyError('Error: histogram is invalid (None or blank)')
1541    hId = str(hId)
1542    if hId not in HistIdLookup:
1543        raise KeyError('Error: LookupHistName does not have index '+hId)
1544    return HistIdLookup[hId]
1545
1546def fmtVarDescr(varname):
1547    '''Return a string with a more complete description for a GSAS-II variable
1548
1549    :param str varname: A full G2 variable name with 2 or 3 or 4
1550       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1551
1552    :returns: a string with the description
1553    '''
1554    s,l = VarDescr(varname)
1555    return s+": "+l
1556
1557def VarDescr(varname):
1558    '''Return two strings with a more complete description for a GSAS-II variable
1559
1560    :param str name: A full G2 variable name with 2 or 3 or 4
1561       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1562
1563    :returns: (loc,meaning) where loc describes what item the variable is mapped
1564      (phase, histogram, etc.) and meaning describes what the variable does.
1565    '''
1566
1567    # special handling for parameter names without a colon
1568    # for now, assume self-defining
1569    if varname.find(':') == -1:
1570        return "Global",varname
1571
1572    l = getVarDescr(varname)
1573    if not l:
1574        return ("invalid variable name ("+str(varname)+")!"),""
1575#        return "invalid variable name!",""
1576
1577    if not l[-1]:
1578        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1579
1580    if len(l) == 3:         #SASD variable name!
1581        s = 'component:'+l[1]
1582        return s,l[-1]
1583    s = ""
1584    if l[0] is not None and l[1] is not None: # HAP: keep short
1585        if l[2] == "Scale": # fix up ambigous name
1586            l[5] = "Phase fraction"
1587        if l[0] == '*':
1588            lbl = 'Seq. ref.'
1589        else:
1590            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1591        if l[1] == '*':
1592            hlbl = 'Seq. ref.'
1593        else:
1594            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1595        if hlbl[:4] == 'HKLF':
1596            hlbl = 'Xtl='+hlbl[5:]
1597        elif hlbl[:4] == 'PWDR':
1598            hlbl = 'Pwd='+hlbl[5:]
1599        else:
1600            hlbl = 'Hist='+hlbl
1601        s = "Ph="+str(lbl)+" * "+str(hlbl)
1602    else:
1603        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1604            l[5] = "Scale factor"
1605        if l[2] == 'Back': # background parameters are "special", alas
1606            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1607            l[-1] += ' #'+str(l[3])
1608        elif l[4] is not None: # rigid body parameter or modulation parm
1609            lbl = ShortPhaseNames.get(l[0],'phase?')
1610            if 'RB' in l[2]:    #rigid body parm
1611                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1612            else: #modulation parm
1613                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
1614        elif l[3] is not None: # atom parameter,
1615            lbl = ShortPhaseNames.get(l[0],'phase?')
1616            try:
1617                albl = LookupAtomLabel(l[0],l[3])[0]
1618            except KeyError:
1619                albl = 'Atom?'
1620            s = "Atom "+str(albl)+" in "+str(lbl)
1621        elif l[0] == '*':
1622            s = "All phases "
1623        elif l[0] is not None:
1624            lbl = ShortPhaseNames.get(l[0],'phase?')
1625            s = "Phase "+str(lbl)
1626        elif l[1] == '*':
1627            s = 'All hists'
1628        elif l[1] is not None:
1629            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1630            if hlbl[:4] == 'HKLF':
1631                hlbl = 'Xtl='+hlbl[5:]
1632            elif hlbl[:4] == 'PWDR':
1633                hlbl = 'Pwd='+hlbl[5:]
1634            else:
1635                hlbl = 'Hist='+hlbl
1636            s = str(hlbl)
1637    if not s:
1638        s = 'Global'
1639    return s,l[-1]
1640
1641def getVarDescr(varname):
1642    '''Return a short description for a GSAS-II variable
1643
1644    :param str name: A full G2 variable name with 2 or 3 or 4
1645       colons (<p>:<h>:name[:<a1>][:<a2>])
1646
1647    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1648      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1649      the histogram number and the atom number; `name` will always be
1650      a str; and `description` is str or `None`.
1651      If the variable name is incorrectly formed (for example, wrong
1652      number of colons), `None` is returned instead of a list.
1653    '''
1654    l = varname.split(':')
1655    if len(l) == 2:     #SASD parameter name
1656        return varname,l[0],getDescr(l[1])
1657    if len(l) == 3:
1658        l += [None,None]
1659    elif len(l) == 4:
1660        l += [None]
1661    elif len(l) != 5:
1662        return None
1663    for i in (0,1,3,4):
1664        if l[i] == "":
1665            l[i] = None
1666    l += [getDescr(l[2])]
1667    return l
1668
1669def CompileVarDesc():
1670    '''Set the values in the variable lookup tables
1671    (:attr:`reVarDesc` and :attr:`reVarStep`).
1672    This is called in :func:`getDescr` and :func:`getVarStep` so this
1673    initialization is always done before use.
1674
1675    Note that keys may contain regular expressions, where '[xyz]'
1676    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range
1677    of values). '.*' matches any string. For example::
1678
1679    'AUiso':'Atomic isotropic displacement parameter',
1680
1681    will match variable ``'p::AUiso:a'``.
1682    If parentheses are used in the key, the contents of those parentheses can be
1683    used in the value, such as::
1684
1685    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1686
1687    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1688    in the value when used.
1689
1690    '''
1691    if reVarDesc: return # already done
1692    for key,value in {
1693        # derived or other sequential vars
1694        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1695        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1696        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1697        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1698        # ambiguous, alas:
1699        'Scale' : 'Phase or Histogram scale factor',
1700        # Phase vars (p::<var>)
1701        'A([0-5])' : ('Reciprocal metric tensor component \\1',1e-5),
1702        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
1703        # Atom vars (p::<var>:a)
1704        'dA([xyz])$' : ('change to atomic coordinate, \\1',1e-6),
1705        'A([xyz])$' : '\\1 fractional atomic coordinate',
1706        'AUiso':('Atomic isotropic displacement parameter',1e-4),
1707        'AU([123][123])':('Atomic anisotropic displacement parameter U\\1',1e-4),
1708        'Afrac': ('Atomic site fraction parameter',1e-5),
1709        'Amul': 'Atomic site multiplicity value',
1710        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
1711        # Hist & Phase (HAP) vars (p:h:<var>)
1712        'Back': 'Background term',
1713        'BkPkint;(.*)':'Background peak #\\1 intensity',
1714        'BkPkpos;(.*)':'Background peak #\\1 position',
1715        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1716        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1717        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1718        'D([123][123])' : 'Anisotropic strain coef. \\1',
1719        'Extinction' : 'Extinction coef.',
1720        'MD' : 'March-Dollase coef.',
1721        'Mustrain;.*' : 'Microstrain coef.',
1722        'Size;.*' : 'Crystallite size value',
1723        'eA$' : 'Cubic mustrain value',
1724        'Ep$' : 'Primary extinction',
1725        'Es$' : 'Secondary type II extinction',
1726        'Eg$' : 'Secondary type I extinction',
1727        'Flack' : 'Flack parameter',
1728        'TwinFr' : 'Twin fraction',
1729        'Layer Disp'  : 'Layer displacement along beam',
1730        #Histogram vars (:h:<var>)
1731        'Absorption' : 'Absorption coef.',
1732        'Displace([XY])' : ('Debye-Scherrer sample displacement \\1',0.1),
1733        'Lam' : ('Wavelength',1e-6),
1734        'I\(L2\)\/I\(L1\)' : ('Ka2/Ka1 intensity ratio',0.001),
1735        'Polariz\.' : ('Polarization correction',1e-3),
1736        'SH/L' : ('FCJ peak asymmetry correction',1e-4),
1737        '([UVW])$' : ('Gaussian instrument broadening \\1',1e-5),
1738        '([XYZ])$' : ('Cauchy instrument broadening \\1',1e-5),
1739        'Zero' : 'Debye-Scherrer zero correction',
1740        'Shift' : 'Bragg-Brentano sample displ.',
1741        'SurfRoughA' : 'Bragg-Brenano surface roughness A',
1742        'SurfRoughB' : 'Bragg-Brenano surface roughness B',
1743        'Transparency' : 'Bragg-Brentano sample tranparency',
1744        'DebyeA' : 'Debye model amplitude',
1745        'DebyeR' : 'Debye model radius',
1746        'DebyeU' : 'Debye model Uiso',
1747        'RBV.*' : 'Vector rigid body parameter',
1748        'RBR.*' : 'Residue rigid body parameter',
1749        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1750        'RBRP([xyz])' : 'Residue rigid body position parameter',
1751        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1752        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1753        'constr([0-9]*)' : 'Parameter from constraint',
1754        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1755        'mV([0-2])$' : 'Modulation vector component \\1',
1756        'Fsin'  :   'Sin site fraction modulation',
1757        'Fcos'  :   'Cos site fraction modulation',
1758        'Fzero'  :   'Crenel function offset',      #may go away
1759        'Fwid'   :   'Crenel function width',
1760        'Tmin'   :   'ZigZag/Block min location',
1761        'Tmax'   :   'ZigZag/Block max location',
1762        '([XYZ])max': 'ZigZag/Block max value for \\1',
1763        '([XYZ])sin'  : 'Sin position wave for \\1',
1764        '([XYZ])cos'  : 'Cos position wave for \\1',
1765        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1766        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1767        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1768        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1769        # PDF peak parms (l:<var>;l = peak no.)
1770        'PDFpos'  : 'PDF peak position',
1771        'PDFmag'  : 'PDF peak magnitude',
1772        'PDFsig'  : 'PDF peak std. dev.',
1773        # SASD vars (l:<var>;l = component)
1774        'Aspect ratio' : 'Particle aspect ratio',
1775        'Length' : 'Cylinder length',
1776        'Diameter' : 'Cylinder/disk diameter',
1777        'Thickness' : 'Disk thickness',
1778        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
1779        'Dist' : 'Interparticle distance',
1780        'VolFr' : 'Dense scatterer volume fraction',
1781        'epis' : 'Sticky sphere epsilon',
1782        'Sticky' : 'Stickyness',
1783        'Depth' : 'Well depth',
1784        'Width' : 'Well width',
1785        'Volume' : 'Particle volume',
1786        'Radius' : 'Sphere/cylinder/disk radius',
1787        'Mean' : 'Particle mean radius',
1788        'StdDev' : 'Standard deviation in Mean',
1789        'G$': 'Guinier prefactor',
1790        'Rg$': 'Guinier radius of gyration',
1791        'B$': 'Porod prefactor',
1792        'P$': 'Porod power',
1793        'Cutoff': 'Porod cutoff',
1794        'PkInt': 'Bragg peak intensity',
1795        'PkPos': 'Bragg peak position',
1796        'PkSig': 'Bragg peak sigma',
1797        'PkGam': 'Bragg peak gamma',
1798        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1799        'Dcalc': 'Calc. d-spacing',
1800        'Back$': 'background parameter',
1801        'pos$': 'peak position',
1802        'int$': 'peak intensity',
1803        'WgtFrac':'phase weight fraction',
1804        'alpha':'TOF profile term',
1805        'beta-[01q]':'TOF profile term',
1806        'sig-[012q]':'TOF profile term',
1807        'dif[ABC]':'TOF to d-space calibration',
1808        'C\([0-9]*,[0-9]*\)' : 'spherical harmonics preferred orientation coef.',
1809        }.items():
1810        if len(value) == 2:
1811            #VarDesc[key] = value[0]
1812            reVarDesc[re.compile(key)] = value[0]
1813            reVarStep[re.compile(key)] = value[1]
1814        else:
1815            #VarDesc[key] = value
1816            reVarDesc[re.compile(key)] = value
1817
1818def removeNonRefined(parmList):
1819    '''Remove items from variable list that are not refined and should not
1820    appear as options for constraints
1821
1822    :param list parmList: a list of strings of form "p:h:VAR:a" where
1823      VAR is the variable name
1824
1825    :returns: a list after removing variables where VAR matches a
1826      entry in local variable NonRefinedList
1827    '''
1828    NonRefinedList = ['Omega','Type','Chi','Phi', 'Azimuth','Gonio. radius',
1829                          'Lam1','Lam2','Back','Temperature','Pressure',
1830                          'FreePrm1','FreePrm2','FreePrm3',
1831                          'Source','nPeaks','LeBail','newLeBail','Bank',
1832                          'nDebye', #'',
1833                    ]
1834    return [prm for prm in parmList if prm.split(':')[2] not in NonRefinedList]
1835       
1836def getDescr(name):
1837    '''Return a short description for a GSAS-II variable
1838
1839    :param str name: The descriptive part of the variable name without colons (:)
1840
1841    :returns: a short description or None if not found
1842    '''
1843
1844    CompileVarDesc() # compile the regular expressions, if needed
1845    for key in reVarDesc:
1846        m = key.match(name)
1847        if m:
1848            reVarDesc[key]
1849            return m.expand(reVarDesc[key])
1850    return None
1851
1852def getVarStep(name,parmDict=None):
1853    '''Return a step size for computing the derivative of a GSAS-II variable
1854
1855    :param str name: A complete variable name (with colons, :)
1856    :param dict parmDict: A dict with parameter values or None (default)
1857
1858    :returns: a float that should be an appropriate step size, either from
1859      the value supplied in :func:`CompileVarDesc` or based on the value for
1860      name in parmDict, if supplied. If not found or the value is zero,
1861      a default value of 1e-5 is used. If parmDict is None (default) and
1862      no value is provided in :func:`CompileVarDesc`, then None is returned.
1863    '''
1864    CompileVarDesc() # compile the regular expressions, if needed
1865    for key in reVarStep:
1866        m = key.match(name)
1867        if m:
1868            return reVarStep[key]
1869    if parmDict is None: return None
1870    val = parmDict.get(key,0.0)
1871    if abs(val) > 0.05:
1872        return abs(val)/1000.
1873    else:
1874        return 1e-5
1875
1876def GenWildCard(varlist):
1877    '''Generate wildcard versions of G2 variables. These introduce '*'
1878    for a phase, histogram or atom number (but only for one of these
1879    fields) but only when there is more than one matching variable in the
1880    input variable list. So if the input is this::
1881
1882      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1883
1884    then the output will be this::
1885
1886       wildList = ['*::AUiso:0', '0::AUiso:*']
1887
1888    :param list varlist: an input list of GSAS-II variable names
1889      (such as 0::AUiso:0)
1890
1891    :returns: wildList, the generated list of wild card variable names.
1892    '''
1893    wild = []
1894    for i in (0,1,3):
1895        currentL = varlist[:]
1896        while currentL:
1897            item1 = currentL.pop(0)
1898            i1splt = item1.split(':')
1899            if i >= len(i1splt): continue
1900            if i1splt[i]:
1901                nextL = []
1902                i1splt[i] = '[0-9]+'
1903                rexp = re.compile(':'.join(i1splt))
1904                matchlist = [item1]
1905                for nxtitem in currentL:
1906                    if rexp.match(nxtitem):
1907                        matchlist += [nxtitem]
1908                    else:
1909                        nextL.append(nxtitem)
1910                if len(matchlist) > 1:
1911                    i1splt[i] = '*'
1912                    wild.append(':'.join(i1splt))
1913                currentL = nextL
1914    return wild
1915
1916def LookupWildCard(varname,varlist):
1917    '''returns a list of variable names from list varname
1918    that match wildcard name in varname
1919
1920    :param str varname: a G2 variable name containing a wildcard
1921      (such as \*::var)
1922    :param list varlist: the list of all variable names used in
1923      the current project
1924    :returns: a list of matching GSAS-II variables (may be empty)
1925    '''
1926    rexp = re.compile(varname.replace('*','[0-9]+'))
1927    return sorted([var for var in varlist if rexp.match(var)])
1928
1929
1930def _lookup(dic,key):
1931    '''Lookup a key in a dictionary, where None returns an empty string
1932    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1933    '''
1934    if key is None:
1935        return ""
1936    elif key == "*":
1937        return "*"
1938    else:
1939        return dic.get(key,'?')
1940
1941def SortVariables(varlist):
1942    '''Sorts variable names in a sensible manner
1943    '''
1944    def cvnnums(var):
1945        v = []
1946        for i in var.split(':'):
1947            if i == '':
1948                v.append(-1)
1949                continue
1950            try:
1951                v.append(int(i))
1952            except:
1953                v.append(i)
1954        return v
1955    return sorted(varlist,key=cvnnums)
1956
1957class G2VarObj(object):
1958    '''Defines a GSAS-II variable either using the phase/atom/histogram
1959    unique Id numbers or using a character string that specifies
1960    variables by phase/atom/histogram number (which can change).
1961    Note that :func:`LoadID` should be used to (re)load the current Ids
1962    before creating or later using the G2VarObj object.
1963
1964    This can store rigid body variables, but does not translate the residue # and
1965    body # to/from random Ids
1966
1967    A :class:`G2VarObj` object can be created with a single parameter:
1968
1969    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1970      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1971
1972     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
1973     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1974     * a is the atom number (which may be left blank in which case the third colon is omitted).
1975       The atom number can be specified as '*' if a phase number is specified (not as '*').
1976       For rigid body variables, specify a will be a string of form "residue:body#"
1977
1978      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1979      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1980      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1981      For a rigid body variables, AtomID is a string of form "residue:body#".
1982
1983    If four positional arguments are supplied, they are:
1984
1985    :param str/int phasenum: The number for the phase (or None or '*')
1986    :param str/int histnum: The number for the histogram (or None or '*')
1987    :param str varname: a single value can be used to create a :class:`G2VarObj`
1988    :param str/int atomnum: The number for the atom (or None or '*')
1989
1990    '''
1991    IDdict = {}
1992    IDdict['phases'] = {}
1993    IDdict['hists'] = {}
1994    IDdict['atoms'] = {}
1995    def __init__(self,*args):
1996        self.phase = None
1997        self.histogram = None
1998        self.name = ''
1999        self.atom = None
2000        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
2001            # single arg with 4 values
2002            self.phase,self.histogram,self.name,self.atom = args[0]
2003        elif len(args) == 1 and ':' in args[0]:
2004            #parse a string
2005            lst = args[0].split(':')
2006            if lst[0] == '*':
2007                self.phase = '*'
2008                if len(lst) > 3:
2009                    self.atom = lst[3]
2010                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2011            elif lst[1] == '*':
2012                self.histogram = '*'
2013                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2014            else:
2015                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
2016                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
2017                if len(lst) == 4:
2018                    if lst[3] == '*':
2019                        self.atom = '*'
2020                    else:
2021                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
2022                elif len(lst) == 5:
2023                    self.atom = lst[3]+":"+lst[4]
2024                elif len(lst) == 3:
2025                    pass
2026                else:
2027                    raise Exception("Too many colons in var name "+str(args[0]))
2028            self.name = lst[2]
2029        elif len(args) == 4:
2030            if args[0] == '*':
2031                self.phase = '*'
2032                self.atom = args[3]
2033            else:
2034                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
2035                if args[3] == '*':
2036                    self.atom = '*'
2037                elif args[0] is not None:
2038                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
2039            if args[1] == '*':
2040                self.histogram = '*'
2041            else:
2042                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
2043            self.name = args[2]
2044        else:
2045            raise Exception("Incorrectly called GSAS-II parameter name")
2046
2047        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
2048
2049    def __str__(self):
2050        return self.varname()
2051
2052    def varname(self):
2053        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
2054        string (p:h:<var>:a) or (p:h:<var>)
2055
2056        :returns: the variable name as a str
2057        '''
2058        a = ""
2059        if self.phase == "*":
2060            ph = "*"
2061            if self.atom:
2062                a = ":" + str(self.atom)
2063        else:
2064            ph = _lookup(PhaseRanIdLookup,self.phase)
2065            if self.atom == '*':
2066                a = ':*'
2067            elif self.atom:
2068                if ":" in str(self.atom):
2069                    a = ":" + str(self.atom)
2070                elif ph in AtomRanIdLookup:
2071                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
2072                else:
2073                    a = ":?"
2074        if self.histogram == "*":
2075            hist = "*"
2076        else:
2077            hist = _lookup(HistRanIdLookup,self.histogram)
2078        s = (ph + ":" + hist + ":" + str(self.name)) + a
2079        return s
2080
2081    def __repr__(self):
2082        '''Return the detailed contents of the object
2083        '''
2084        s = "<"
2085        if self.phase == '*':
2086            s += "Phases: all; "
2087            if self.atom is not None:
2088                if ":" in str(self.atom):
2089                    s += "Rigid body" + str(self.atom) + "; "
2090                else:
2091                    s += "Atom #" + str(self.atom) + "; "
2092        elif self.phase is not None:
2093            ph =  _lookup(PhaseRanIdLookup,self.phase)
2094            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
2095            if self.atom == '*':
2096                s += "Atoms: all; "
2097            elif ":" in str(self.atom):
2098                s += "Rigid body" + str(self.atom) + "; "
2099            elif self.atom is not None:
2100                s += "Atom rId=" + str(self.atom)
2101                if ph in AtomRanIdLookup:
2102                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
2103                else:
2104                    s += " (#? -- not found!); "
2105        if self.histogram == '*':
2106            s += "Histograms: all; "
2107        elif self.histogram is not None:
2108            hist = _lookup(HistRanIdLookup,self.histogram)
2109            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
2110        s += 'Variable name="' + str(self.name) + '">'
2111        return s+" ("+self.varname()+")"
2112
2113    def __eq__(self, other):
2114        if type(other) is type(self):
2115            return (self.phase == other.phase and
2116                    self.histogram == other.histogram and
2117                    self.name == other.name and
2118                    self.atom == other.atom)
2119        return False
2120
2121    def _show(self):
2122        'For testing, shows the current lookup table'
2123        print ('phases'+ self.IDdict['phases'])
2124        print ('hists'+ self.IDdict['hists'])
2125        print ('atomDict'+ self.IDdict['atoms'])
2126
2127#==========================================================================
2128def SetDefaultSample():
2129    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
2130    return {
2131        'InstrName':'',
2132        'ranId':ran.randint(0,sys.maxsize),
2133        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
2134        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],
2135        'Temperature':300.,'Pressure':0.1,'Time':0.0,
2136        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
2137        'Gonio. radius':200.0,
2138        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
2139#SASD items
2140        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
2141        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
2142        'Trans':1.0,                            #measured transmission
2143        'SlitLen':0.0,                          #Slit length - in Q(A-1)
2144        }
2145######################################################################
2146class ImportBaseclass(object):
2147    '''Defines a base class for the reading of input files (diffraction
2148    data, coordinates,...). See :ref:`Writing a Import Routine<import_routines>`
2149    for an explanation on how to use a subclass of this class.
2150    '''
2151    class ImportException(Exception):
2152        '''Defines an Exception that is used when an import routine hits an expected error,
2153        usually in .Reader.
2154
2155        Good practice is that the Reader should define a value in self.errors that
2156        tells the user some information about what is wrong with their file.
2157        '''
2158        pass
2159
2160    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
2161    def __init__(self,formatName,longFormatName=None,
2162                 extensionlist=[],strictExtension=False,):
2163        self.formatName = formatName # short string naming file type
2164        if longFormatName: # longer string naming file type
2165            self.longFormatName = longFormatName
2166        else:
2167            self.longFormatName = formatName
2168        # define extensions that are allowed for the file type
2169        # for windows, remove any extensions that are duplicate, as case is ignored
2170        if sys.platform == 'windows' and extensionlist:
2171            extensionlist = list(set([s.lower() for s in extensionlist]))
2172        self.extensionlist = extensionlist
2173        # If strictExtension is True, the file will not be read, unless
2174        # the extension matches one in the extensionlist
2175        self.strictExtension = strictExtension
2176        self.errors = ''
2177        self.warnings = ''
2178        self.SciPy = False          #image reader needed scipy
2179        # used for readers that will use multiple passes to read
2180        # more than one data block
2181        self.repeat = False
2182        self.selections = []
2183        self.repeatcount = 0
2184        self.readfilename = '?'
2185        self.scriptable = False
2186        #print 'created',self.__class__
2187
2188    def ReInitialize(self):
2189        'Reinitialize the Reader to initial settings'
2190        self.errors = ''
2191        self.warnings = ''
2192        self.SciPy = False          #image reader needed scipy
2193        self.repeat = False
2194        self.repeatcount = 0
2195        self.readfilename = '?'
2196
2197
2198#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
2199#        '''This method must be supplied in the child class to read the file.
2200#        if the read fails either return False or raise an Exception
2201#        preferably of type ImportException.
2202#        '''
2203#        #start reading
2204#        raise ImportException("Error occurred while...")
2205#        self.errors += "Hint for user on why the error occur
2206#        return False # if an error occurs
2207#        return True # if read OK
2208
2209    def ExtensionValidator(self, filename):
2210        '''This methods checks if the file has the correct extension
2211       
2212        :returns:
2213       
2214          * False if this filename will not be supported by this reader (only
2215            when strictExtension is True)
2216          * True if the extension matches the list supplied by the reader
2217          * None if the reader allows un-registered extensions
2218         
2219        '''
2220        if filename:
2221            ext = ospath.splitext(filename)[1]
2222            if not ext and self.strictExtension: return False
2223            for ext in self.extensionlist:               
2224                if sys.platform == 'windows':
2225                    if filename.lower().endswith(ext): return True
2226                else:
2227                    if filename.endswith(ext): return True
2228        if self.strictExtension:
2229            return False
2230        else:
2231            return None
2232
2233    def ContentsValidator(self, filename):
2234        '''This routine will attempt to determine if the file can be read
2235        with the current format.
2236        This will typically be overridden with a method that
2237        takes a quick scan of [some of]
2238        the file contents to do a "sanity" check if the file
2239        appears to match the selected format.
2240        the file must be opened here with the correct format (binary/text)
2241        '''
2242        #filepointer.seek(0) # rewind the file pointer
2243        return True
2244
2245    def CIFValidator(self, filepointer):
2246        '''A :meth:`ContentsValidator` for use to validate CIF files.
2247        '''
2248        filepointer.seek(0)
2249        for i,l in enumerate(filepointer):
2250            if i >= 1000: return True
2251            '''Encountered only blank lines or comments in first 1000
2252            lines. This is unlikely, but assume it is CIF anyway, since we are
2253            even less likely to find a file with nothing but hashes and
2254            blank lines'''
2255            line = l.strip()
2256            if len(line) == 0: # ignore blank lines
2257                continue
2258            elif line.startswith('#'): # ignore comments
2259                continue
2260            elif line.startswith('data_'): # on the right track, accept this file
2261                return True
2262            else: # found something invalid
2263                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
2264                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
2265                    self.errors += '  '+str(l)
2266                else:
2267                    self.errors += '  (binary)'
2268                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
2269                self.errors += '\n        a data_ statement begins a block.'
2270                return False
2271
2272######################################################################
2273class ImportPhase(ImportBaseclass):
2274    '''Defines a base class for the reading of files with coordinates
2275
2276    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
2277    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` and in
2278    :func:`GSASIIscriptable.import_generic`.
2279    See :ref:`Writing a Import Routine<import_routines>`
2280    for an explanation on how to use this class.
2281
2282    '''
2283    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2284        strictExtension=False,):
2285        # call parent __init__
2286        ImportBaseclass.__init__(self,formatName,longFormatName,
2287            extensionlist,strictExtension)
2288        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
2289        self.Constraints = None
2290
2291######################################################################
2292class ImportStructFactor(ImportBaseclass):
2293    '''Defines a base class for the reading of files with tables
2294    of structure factors.
2295
2296    Structure factors are read with a call to :meth:`GSASIIdataGUI.GSASII.OnImportSfact`
2297    which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`, which calls
2298    methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2299    :meth:`Reader`.
2300
2301    See :ref:`Writing a Import Routine<import_routines>`
2302    for an explanation on how to use import classes in general. The specifics
2303    for reading a structure factor histogram require that
2304    the ``Reader()`` routine in the import
2305    class need to do only a few things: It
2306    should load :attr:`RefDict` item ``'RefList'`` with the reflection list,
2307    and set :attr:`Parameters` with the instrument parameters
2308    (initialized with :meth:`InitParameters` and set with :meth:`UpdateParameters`).
2309    '''
2310    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2311        strictExtension=False,):
2312        ImportBaseclass.__init__(self,formatName,longFormatName,
2313            extensionlist,strictExtension)
2314
2315        # define contents of Structure Factor entry
2316        self.Parameters = []
2317        'self.Parameters is a list with two dicts for data parameter settings'
2318        self.InitParameters()
2319        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2320        self.Banks = []             #for multi bank data (usually TOF)
2321        '''self.RefDict is a dict containing the reflection information, as read from the file.
2322        Item 'RefList' contains the reflection information. See the
2323        :ref:`Single Crystal Reflection Data Structure<XtalRefl_table>`
2324        for the contents of each row. Dict element 'FF'
2325        contains the form factor values for each element type; if this entry
2326        is left as initialized (an empty list) it will be initialized as needed later.
2327        '''
2328    def ReInitialize(self):
2329        'Reinitialize the Reader to initial settings'
2330        ImportBaseclass.ReInitialize(self)
2331        self.InitParameters()
2332        self.Banks = []             #for multi bank data (usually TOF)
2333        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2334
2335    def InitParameters(self):
2336        'initialize the instrument parameters structure'
2337        Lambda = 0.70926
2338        HistType = 'SXC'
2339        self.Parameters = [{'Type':[HistType,HistType], # create the structure
2340                            'Lam':[Lambda,Lambda]
2341                            }, {}]
2342        'Parameters is a list with two dicts for data parameter settings'
2343
2344    def UpdateParameters(self,Type=None,Wave=None):
2345        'Revise the instrument parameters'
2346        if Type is not None:
2347            self.Parameters[0]['Type'] = [Type,Type]
2348        if Wave is not None:
2349            self.Parameters[0]['Lam'] = [Wave,Wave]
2350
2351######################################################################
2352class ImportPowderData(ImportBaseclass):
2353    '''Defines a base class for the reading of files with powder data.
2354
2355    Objects constructed that subclass this (in import/G2pwd_*.py etc.) will be used
2356    in :meth:`GSASIIdataGUI.GSASII.OnImportPowder` and in
2357    :func:`GSASIIscriptable.import_generic`.
2358    See :ref:`Writing a Import Routine<import_routines>`
2359    for an explanation on how to use this class.
2360    '''
2361    def __init__(self,formatName,longFormatName=None,
2362        extensionlist=[],strictExtension=False,):
2363        ImportBaseclass.__init__(self,formatName,longFormatName,
2364            extensionlist,strictExtension)
2365        self.clockWd = None  # used in TOF
2366        self.ReInitialize()
2367
2368    def ReInitialize(self):
2369        'Reinitialize the Reader to initial settings'
2370        ImportBaseclass.ReInitialize(self)
2371        self.powderentry = ['',None,None] #  (filename,Pos,Bank)
2372        self.powderdata = [] # Powder dataset
2373        '''A powder data set is a list with items [x,y,w,yc,yb,yd]:
2374                np.array(x), # x-axis values
2375                np.array(y), # powder pattern intensities
2376                np.array(w), # 1/sig(intensity)^2 values (weights)
2377                np.array(yc), # calc. intensities (zero)
2378                np.array(yb), # calc. background (zero)
2379                np.array(yd), # obs-calc profiles
2380        '''
2381        self.comments = []
2382        self.idstring = ''
2383        self.Sample = SetDefaultSample() # default sample parameters
2384        self.Controls = {}  # items to be placed in top-level Controls
2385        self.GSAS = None     # used in TOF
2386        self.repeat_instparm = True # Should a parm file be
2387        #                             used for multiple histograms?
2388        self.instparm = None # name hint from file of instparm to use
2389        self.instfile = '' # full path name to instrument parameter file
2390        self.instbank = '' # inst parm bank number
2391        self.instmsg = ''  # a label that gets printed to show
2392                           # where instrument parameters are from
2393        self.numbanks = 1
2394        self.instdict = {} # place items here that will be transferred to the instrument parameters
2395        self.pwdparms = {} # place parameters that are transferred directly to the tree
2396                           # here (typically from an existing GPX file)
2397######################################################################
2398class ImportSmallAngleData(ImportBaseclass):
2399    '''Defines a base class for the reading of files with small angle data.
2400    See :ref:`Writing a Import Routine<import_routines>`
2401    for an explanation on how to use this class.
2402    '''
2403    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2404        strictExtension=False,):
2405
2406        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2407            strictExtension)
2408        self.ReInitialize()
2409
2410    def ReInitialize(self):
2411        'Reinitialize the Reader to initial settings'
2412        ImportBaseclass.ReInitialize(self)
2413        self.smallangleentry = ['',None,None] #  (filename,Pos,Bank)
2414        self.smallangledata = [] # SASD dataset
2415        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2416                np.array(x), # x-axis values
2417                np.array(y), # powder pattern intensities
2418                np.array(w), # 1/sig(intensity)^2 values (weights)
2419                np.array(yc), # calc. intensities (zero)
2420                np.array(yd), # obs-calc profiles
2421                np.array(yb), # preset bkg
2422        '''
2423        self.comments = []
2424        self.idstring = ''
2425        self.Sample = SetDefaultSample()
2426        self.GSAS = None     # used in TOF
2427        self.clockWd = None  # used in TOF
2428        self.numbanks = 1
2429        self.instdict = {} # place items here that will be transferred to the instrument parameters
2430
2431######################################################################
2432class ImportReflectometryData(ImportBaseclass):
2433    '''Defines a base class for the reading of files with reflectometry data.
2434    See :ref:`Writing a Import Routine<import_routines>`
2435    for an explanation on how to use this class.
2436    '''
2437    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2438        strictExtension=False,):
2439
2440        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2441            strictExtension)
2442        self.ReInitialize()
2443
2444    def ReInitialize(self):
2445        'Reinitialize the Reader to initial settings'
2446        ImportBaseclass.ReInitialize(self)
2447        self.reflectometryentry = ['',None,None] #  (filename,Pos,Bank)
2448        self.reflectometrydata = [] # SASD dataset
2449        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2450                np.array(x), # x-axis values
2451                np.array(y), # powder pattern intensities
2452                np.array(w), # 1/sig(intensity)^2 values (weights)
2453                np.array(yc), # calc. intensities (zero)
2454                np.array(yd), # obs-calc profiles
2455                np.array(yb), # preset bkg
2456        '''
2457        self.comments = []
2458        self.idstring = ''
2459        self.Sample = SetDefaultSample()
2460        self.GSAS = None     # used in TOF
2461        self.clockWd = None  # used in TOF
2462        self.numbanks = 1
2463        self.instdict = {} # place items here that will be transferred to the instrument parameters
2464
2465######################################################################
2466class ImportPDFData(ImportBaseclass):
2467    '''Defines a base class for the reading of files with PDF G(R) data.
2468    See :ref:`Writing a Import Routine<import_routines>`
2469    for an explanation on how to use this class.
2470    '''
2471    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2472        strictExtension=False,):
2473
2474        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2475            strictExtension)
2476        self.ReInitialize()
2477
2478    def ReInitialize(self):
2479        'Reinitialize the Reader to initial settings'
2480        ImportBaseclass.ReInitialize(self)
2481        self.pdfentry = ['',None,None] #  (filename,Pos,Bank)
2482        self.pdfdata = [] # PDF G(R) dataset
2483        '''A pdf g(r) data set is a list with items [x,y]:
2484                np.array(x), # r-axis values
2485                np.array(y), # pdf g(r)
2486        '''
2487        self.comments = []
2488        self.idstring = ''
2489        self.numbanks = 1
2490
2491######################################################################
2492class ImportImage(ImportBaseclass):
2493    '''Defines a base class for the reading of images
2494
2495    Images are read in only these places:
2496
2497      * Initial reading is typically done from a menu item
2498        with a call to :meth:`GSASIIdataGUI.GSASII.OnImportImage`
2499        which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`. That calls
2500        methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2501        :meth:`Reader`. This returns a list of reader objects for each read image.
2502        Also used in :func:`GSASIIscriptable.import_generic`.
2503
2504      * Images are read alternatively in :func:`GSASIIIO.ReadImages`, which puts image info
2505        directly into the data tree.
2506
2507      * Images are reloaded with :func:`GSASIIIO.GetImageData`.
2508
2509    When reading an image, the ``Reader()`` routine in the ImportImage class
2510    should set:
2511
2512      * :attr:`Comments`: a list of strings (str),
2513      * :attr:`Npix`: the number of pixels in the image (int),
2514      * :attr:`Image`: the actual image as a numpy array (np.array)
2515      * :attr:`Data`: a dict defining image parameters (dict). Within this dict the following
2516        data items are needed:
2517
2518         * 'pixelSize': size of each pixel in microns (such as ``[200.,200.]``.
2519         * 'wavelength': wavelength in :math:`\\AA`.
2520         * 'distance': distance of detector from sample in cm.
2521         * 'center': uncalibrated center of beam on detector (such as ``[204.8,204.8]``.
2522         * 'size': size of image (such as ``[2048,2048]``).
2523         * 'ImageTag': image number or other keyword used to retrieve image from
2524           a multi-image data file (defaults to ``1`` if not specified).
2525         * 'sumfile': holds sum image file name if a sum was produced from a multi image file
2526
2527    optional data items:
2528
2529      * :attr:`repeat`: set to True if there are additional images to
2530        read in the file, False otherwise
2531      * :attr:`repeatcount`: set to the number of the image.
2532
2533    Note that the above is initialized with :meth:`InitParameters`.
2534    (Also see :ref:`Writing a Import Routine<import_routines>`
2535    for an explanation on how to use import classes in general.)
2536    '''
2537    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2538        strictExtension=False,):
2539        ImportBaseclass.__init__(self,formatName,longFormatName,
2540            extensionlist,strictExtension)
2541        self.InitParameters()
2542
2543    def ReInitialize(self):
2544        'Reinitialize the Reader to initial settings -- not used at present'
2545        ImportBaseclass.ReInitialize(self)
2546        self.InitParameters()
2547
2548    def InitParameters(self):
2549        'initialize the instrument parameters structure'
2550        self.Comments = ['No comments']
2551        self.Data = {}
2552        self.Npix = 0
2553        self.Image = None
2554        self.repeat = False
2555        self.repeatcount = 1
2556        self.sumfile = ''
2557
2558    def LoadImage(self,ParentFrame,imagefile,imagetag=None):
2559        '''Optionally, call this after reading in an image to load it into the tree.
2560        This saves time by preventing a reread of the same information.
2561        '''
2562        if ParentFrame:
2563            ParentFrame.ImageZ = self.Image   # store the image for plotting
2564            ParentFrame.oldImagefile = imagefile # save the name of the last image file read
2565            ParentFrame.oldImageTag = imagetag   # save the tag of the last image file read
2566
2567#################################################################################################
2568# shortcut routines
2569exp = np.exp
2570sind = sin = s = lambda x: np.sin(x*np.pi/180.)
2571cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
2572tand = tan = t = lambda x: np.tan(x*np.pi/180.)
2573sqrt = sq = lambda x: np.sqrt(x)
2574pi = lambda: np.pi
2575class ExpressionObj(object):
2576    '''Defines an object with a user-defined expression, to be used for
2577    secondary fits or restraints. Object is created null, but is changed
2578    using :meth:`LoadExpression`. This contains only the minimum
2579    information that needs to be stored to save and load the expression
2580    and how it is mapped to GSAS-II variables.
2581    '''
2582    def __init__(self):
2583        self.expression = ''
2584        'The expression as a text string'
2585        self.assgnVars = {}
2586        '''A dict where keys are label names in the expression mapping to a GSAS-II
2587        variable. The value a G2 variable name.
2588        Note that the G2 variable name may contain a wild-card and correspond to
2589        multiple values.
2590        '''
2591        self.freeVars = {}
2592        '''A dict where keys are label names in the expression mapping to a free
2593        parameter. The value is a list with:
2594
2595         * a name assigned to the parameter
2596         * a value for to the parameter and
2597         * a flag to determine if the variable is refined.
2598        '''
2599        self.depVar = None
2600
2601        self.lastError = ('','')
2602        '''Shows last encountered error in processing expression
2603        (list of 1-3 str values)'''
2604
2605        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
2606        self.distance_atoms = None  # to be used for defining atom distances
2607
2608    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
2609        '''Load the expression and associated settings into the object. Raises
2610        an exception if the expression is not parsed, if not all functions
2611        are defined or if not all needed parameter labels in the expression
2612        are defined.
2613
2614        This will not test if the variable referenced in these definitions
2615        are actually in the parameter dictionary. This is checked when the
2616        computation for the expression is done in :meth:`SetupCalc`.
2617
2618        :param str expr: the expression
2619        :param list exprVarLst: parameter labels found in the expression
2620        :param dict varSelect: this will be 0 for Free parameters
2621          and non-zero for expression labels linked to G2 variables.
2622        :param dict varName: Defines a name (str) associated with each free parameter
2623        :param dict varValue: Defines a value (float) associated with each free parameter
2624        :param dict varRefflag: Defines a refinement flag (bool)
2625          associated with each free parameter
2626        '''
2627        self.expression = expr
2628        self.compiledExpr = None
2629        self.freeVars = {}
2630        self.assgnVars = {}
2631        for v in exprVarLst:
2632            if varSelect[v] == 0:
2633                self.freeVars[v] = [
2634                    varName.get(v),
2635                    varValue.get(v),
2636                    varRefflag.get(v),
2637                    ]
2638            else:
2639                self.assgnVars[v] = varName[v]
2640        self.CheckVars()
2641
2642    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
2643        '''Load the expression and associated settings from the object into
2644        arrays used for editing.
2645
2646        :param list exprVarLst: parameter labels found in the expression
2647        :param dict varSelect: this will be 0 for Free parameters
2648          and non-zero for expression labels linked to G2 variables.
2649        :param dict varName: Defines a name (str) associated with each free parameter
2650        :param dict varValue: Defines a value (float) associated with each free parameter
2651        :param dict varRefflag: Defines a refinement flag (bool)
2652          associated with each free parameter
2653
2654        :returns: the expression as a str
2655        '''
2656        for v in self.freeVars:
2657            varSelect[v] = 0
2658            varName[v] = self.freeVars[v][0]
2659            varValue[v] = self.freeVars[v][1]
2660            varRefflag[v] = self.freeVars[v][2]
2661        for v in self.assgnVars:
2662            varSelect[v] = 1
2663            varName[v] = self.assgnVars[v]
2664        return self.expression
2665
2666    def GetVaried(self):
2667        'Returns the names of the free parameters that will be refined'
2668        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
2669
2670    def GetVariedVarVal(self):
2671        'Returns the names and values of the free parameters that will be refined'
2672        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
2673
2674    def UpdateVariedVars(self,varyList,values):
2675        'Updates values for the free parameters (after a refinement); only updates refined vars'
2676        for v in self.freeVars:
2677            if not self.freeVars[v][2]: continue
2678            if "::"+self.freeVars[v][0] not in varyList: continue
2679            indx = list(varyList).index("::"+self.freeVars[v][0])
2680            self.freeVars[v][1] = values[indx]
2681
2682    def GetIndependentVars(self):
2683        'Returns the names of the required independent parameters used in expression'
2684        return [self.assgnVars[v] for v in self.assgnVars]
2685
2686    def CheckVars(self):
2687        '''Check that the expression can be parsed, all functions are
2688        defined and that input loaded into the object is internally
2689        consistent. If not an Exception is raised.
2690
2691        :returns: a dict with references to packages needed to
2692          find functions referenced in the expression.
2693        '''
2694        ret = self.ParseExpression(self.expression)
2695        if not ret:
2696            raise Exception("Expression parse error")
2697        exprLblList,fxnpkgdict = ret
2698        # check each var used in expression is defined
2699        defined = list(self.assgnVars.keys()) + list(self.freeVars.keys())
2700        notfound = []
2701        for var in exprLblList:
2702            if var not in defined:
2703                notfound.append(var)
2704        if notfound:
2705            msg = 'Not all variables defined'
2706            msg1 = 'The following variables were not defined: '
2707            msg2 = ''
2708            for var in notfound:
2709                if msg: msg += ', '
2710                msg += var
2711            self.lastError = (msg1,'  '+msg2)
2712            raise Exception(msg)
2713        return fxnpkgdict
2714
2715    def ParseExpression(self,expr):
2716        '''Parse an expression and return a dict of called functions and
2717        the variables used in the expression. Returns None in case an error
2718        is encountered. If packages are referenced in functions, they are loaded
2719        and the functions are looked up into the modules global
2720        workspace.
2721
2722        Note that no changes are made to the object other than
2723        saving an error message, so that this can be used for testing prior
2724        to the save.
2725
2726        :returns: a list of used variables
2727        '''
2728        self.lastError = ('','')
2729        import ast
2730        def FindFunction(f):
2731            '''Find the object corresponding to function f
2732            :param str f: a function name such as 'numpy.exp'
2733            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
2734              that defines the package location(s) and where pkgobj
2735              defines the object associated with the function.
2736              If the function is not found, pkgobj is None.
2737            '''
2738            df = f.split('.')
2739            pkgdict = {}
2740            # no listed package, try in current namespace
2741            if len(df) == 1:
2742                try:
2743                    fxnobj = eval(f)
2744                    return pkgdict,fxnobj
2745                except (AttributeError, NameError):
2746                    return None,None
2747            else:
2748                try:
2749                    fxnobj = eval(f)
2750                    pkgdict[df[0]] = eval(df[0])
2751                    return pkgdict,fxnobj
2752                except (AttributeError, NameError):
2753                    pass
2754            # includes a package, lets try to load the packages
2755            pkgname = ''
2756            path = sys.path+['./',]
2757            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
2758                if pkgname:
2759                    pkgname += '.' + pkg
2760                else:
2761                    pkgname = pkg
2762                fp = None
2763                try:
2764                    fp, fppath,desc = imp.find_module(pkg,path)
2765                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
2766                    pkgdict[pkgname] = pkgobj
2767                    path = [fppath]
2768                except Exception as msg:
2769                    print('load of '+pkgname+' failed with error='+str(msg))
2770                    return {},None
2771                finally:
2772                    if fp: fp.close()
2773                try:
2774                    #print 'before',pkgdict.keys()
2775                    fxnobj = eval(f,globals(),pkgdict)
2776                    #print 'after 1',pkgdict.keys()
2777                    #fxnobj = eval(f,pkgdict)
2778                    #print 'after 2',pkgdict.keys()
2779                    return pkgdict,fxnobj
2780                except:
2781                    continue
2782            return None # not found
2783        def ASTtransverse(node,fxn=False):
2784            '''Transverse a AST-parsed expresson, compiling a list of variables
2785            referenced in the expression. This routine is used recursively.
2786
2787            :returns: varlist,fxnlist where
2788              varlist is a list of referenced variable names and
2789              fxnlist is a list of used functions
2790            '''
2791            varlist = []
2792            fxnlist = []
2793            if isinstance(node, list):
2794                for b in node:
2795                    v,f = ASTtransverse(b,fxn)
2796                    varlist += v
2797                    fxnlist += f
2798            elif isinstance(node, ast.AST):
2799                for a, b in ast.iter_fields(node):
2800                    if isinstance(b, ast.AST):
2801                        if a == 'func':
2802                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
2803                            continue
2804                        v,f = ASTtransverse(b,fxn)
2805                        varlist += v
2806                        fxnlist += f
2807                    elif isinstance(b, list):
2808                        v,f = ASTtransverse(b,fxn)
2809                        varlist += v
2810                        fxnlist += f
2811                    elif node.__class__.__name__ == "Name":
2812                        varlist += [b]
2813                    elif fxn and node.__class__.__name__ == "Attribute":
2814                        varlist += [b]
2815            return varlist,fxnlist
2816        try:
2817            exprast = ast.parse(expr)
2818        except SyntaxError:
2819            s = ''
2820            import traceback
2821            for i in traceback.format_exc().splitlines()[-3:-1]:
2822                if s: s += "\n"
2823                s += str(i)
2824            self.lastError = ("Error parsing expression:",s)
2825            return
2826        # find the variables & functions
2827        v,f = ASTtransverse(exprast)
2828        varlist = sorted(list(set(v)))
2829        fxnlist = list(set(f))
2830        pkgdict = {}
2831        # check the functions are defined
2832        for fxn in fxnlist:
2833            fxndict,fxnobj = FindFunction(fxn)
2834            if not fxnobj:
2835                self.lastError = ("Error: Invalid function",fxn,
2836                                  "is not defined")
2837                return
2838            if not hasattr(fxnobj,'__call__'):
2839                self.lastError = ("Error: Not a function.",fxn,
2840                                  "cannot be called as a function")
2841                return
2842            pkgdict.update(fxndict)
2843        return varlist,pkgdict
2844
2845    def GetDepVar(self):
2846        'return the dependent variable, or None'
2847        return self.depVar
2848
2849    def SetDepVar(self,var):
2850        'Set the dependent variable, if used'
2851        self.depVar = var
2852#==========================================================================
2853class ExpressionCalcObj(object):
2854    '''An object used to evaluate an expression from a :class:`ExpressionObj`
2855    object.
2856
2857    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
2858      an expression string and mappings for the parameter labels in that object.
2859    '''
2860    def __init__(self,exprObj):
2861        self.eObj = exprObj
2862        'The expression and mappings; a :class:`ExpressionObj` object'
2863        self.compiledExpr = None
2864        'The expression as compiled byte-code'
2865        self.exprDict = {}
2866        '''dict that defines values for labels used in expression and packages
2867        referenced by functions
2868        '''
2869        self.lblLookup = {}
2870        '''Lookup table that specifies the expression label name that is
2871        tied to a particular GSAS-II parameters in the parmDict.
2872        '''
2873        self.fxnpkgdict = {}
2874        '''a dict with references to packages needed to
2875        find functions referenced in the expression.
2876        '''
2877        self.varLookup = {}
2878        '''Lookup table that specifies the GSAS-II variable(s)
2879        indexed by the expression label name. (Used for only for diagnostics
2880        not evaluation of expression.)
2881        '''
2882        self.su = None
2883        '''Standard error evaluation where supplied by the evaluator
2884        '''
2885        # Patch: for old-style expressions with a (now removed step size)
2886        if '2' in platform.python_version_tuple()[0]: 
2887            basestr = basestring
2888        else:
2889            basestr = str
2890        for v in self.eObj.assgnVars:
2891            if not isinstance(self.eObj.assgnVars[v], basestr):
2892                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
2893        self.parmDict = {}
2894        '''A copy of the parameter dictionary, for distance and angle computation
2895        '''
2896
2897    def SetupCalc(self,parmDict):
2898        '''Do all preparations to use the expression for computation.
2899        Adds the free parameter values to the parameter dict (parmDict).
2900        '''
2901        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2902            return
2903        self.fxnpkgdict = self.eObj.CheckVars()
2904        # all is OK, compile the expression
2905        self.compiledExpr = compile(self.eObj.expression,'','eval')
2906
2907        # look at first value in parmDict to determine its type
2908        parmsInList = True
2909        if '2' in platform.python_version_tuple()[0]: 
2910            basestr = basestring
2911        else:
2912            basestr = str
2913        for key in parmDict:
2914            val = parmDict[key]
2915            if isinstance(val, basestr):
2916                parmsInList = False
2917                break
2918            try: # check if values are in lists
2919                val = parmDict[key][0]
2920            except (TypeError,IndexError):
2921                parmsInList = False
2922            break
2923
2924        # set up the dicts needed to speed computations
2925        self.exprDict = {}
2926        self.lblLookup = {}
2927        self.varLookup = {}
2928        for v in self.eObj.freeVars:
2929            varname = self.eObj.freeVars[v][0]
2930            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
2931            self.lblLookup[varname] = v
2932            self.varLookup[v] = varname
2933            if parmsInList:
2934                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
2935            else:
2936                parmDict[varname] = self.eObj.freeVars[v][1]
2937            self.exprDict[v] = self.eObj.freeVars[v][1]
2938        for v in self.eObj.assgnVars:
2939            varname = self.eObj.assgnVars[v]
2940            if varname in parmDict:
2941                self.lblLookup[varname] = v
2942                self.varLookup[v] = varname
2943                if parmsInList:
2944                    self.exprDict[v] = parmDict[varname][0]
2945                else:
2946                    self.exprDict[v] = parmDict[varname]
2947            elif '*' in varname:
2948                varlist = LookupWildCard(varname,list(parmDict.keys()))
2949                if len(varlist) == 0:
2950                    raise Exception("No variables match "+str(v))
2951                for var in varlist:
2952                    self.lblLookup[var] = v
2953                if parmsInList:
2954                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
2955                else:
2956                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
2957                self.varLookup[v] = [var for var in varlist]
2958            else:
2959                self.exprDict[v] = None
2960#                raise Exception,"No value for variable "+str(v)
2961        self.exprDict.update(self.fxnpkgdict)
2962
2963    def UpdateVars(self,varList,valList):
2964        '''Update the dict for the expression with a set of values
2965        :param list varList: a list of variable names
2966        :param list valList: a list of corresponding values
2967        '''
2968        for var,val in zip(varList,valList):
2969            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
2970
2971    def UpdateDict(self,parmDict):
2972        '''Update the dict for the expression with values in a dict
2973        :param dict parmDict: a dict of values, items not in use are ignored
2974        '''
2975        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2976            self.parmDict = parmDict
2977            return
2978        for var in parmDict:
2979            if var in self.lblLookup:
2980                self.exprDict[self.lblLookup[var]] = parmDict[var]
2981
2982    def EvalExpression(self):
2983        '''Evaluate an expression. Note that the expression
2984        and mapping are taken from the :class:`ExpressionObj` expression object
2985        and the parameter values were specified in :meth:`SetupCalc`.
2986        :returns: a single value for the expression. If parameter
2987        values are arrays (for example, from wild-carded variable names),
2988        the sum of the resulting expression is returned.
2989
2990        For example, if the expression is ``'A*B'``,
2991        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
2992
2993        [0.5, 1, 0.5]
2994
2995        then the result will be ``4.0``.
2996        '''
2997        self.su = None
2998        if self.eObj.expression.startswith('Dist'):
2999#            GSASIIpath.IPyBreak()
3000            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
3001            return dist
3002        elif self.eObj.expression.startswith('Angle'):
3003            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
3004            return angle
3005        if self.compiledExpr is None:
3006            raise Exception("EvalExpression called before SetupCalc")
3007        try:
3008            val = eval(self.compiledExpr,globals(),self.exprDict)
3009        except TypeError:
3010            val = None
3011        if not np.isscalar(val):
3012            val = np.sum(val)
3013        return val
3014
3015class G2Exception(Exception):
3016    'A generic GSAS-II exception class'
3017    def __init__(self,msg):
3018        self.msg = msg
3019    def __str__(self):
3020        return repr(self.msg)
3021
3022class G2RefineCancel(Exception):
3023    'Raised when Cancel is pressed in a refinement dialog'
3024    def __init__(self,msg):
3025        self.msg = msg
3026    def __str__(self):
3027        return repr(self.msg)
3028   
3029def HowDidIgetHere(wherecalledonly=False):
3030    '''Show a traceback with calls that brought us to the current location.
3031    Used for debugging.
3032    '''
3033    import traceback
3034    if wherecalledonly:
3035        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
3036        print(i.strip().rstrip())
3037    else:
3038        print (70*'*')
3039        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
3040        print (70*'*')
3041
3042# Note that this is GUI code and should be moved at somepoint
3043def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
3044    '''Create and initialize a new set of PDF tree entries
3045
3046    :param Frame G2frame: main GSAS-II tree frame object
3047    :param str PWDRtree: name of PWDR to be used to create PDF item
3048    :param dict ElList: data structure with composition
3049    :param list Qlimits: Q limits to be used for computing the PDF
3050    :param float numAtm: no. atom in chemical formula
3051    :param float FltBkg: flat background value
3052    :param list PDFnames: previously used PDF names
3053
3054    :returns: the Id of the newly created PDF entry
3055    '''
3056    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
3057    if PDFname in PDFnames:
3058        print('Skipping, entry already exists: '+PDFname)
3059        return None
3060    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
3061    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
3062    Data = {
3063        'Sample':{'Name':PWDRtree,'Mult':1.0},
3064        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
3065        'Container':{'Name':'','Mult':-1.0,'Refine':False},
3066        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
3067        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
3068        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
3069        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
3070        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
3071    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
3072    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
3073        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
3074    return Id
3075#%%
3076class ShowTiming(object):
3077    '''An object to use for timing repeated sections of code.
3078
3079    Create the object with::
3080       tim0 = ShowTiming()
3081
3082    Tag sections of code to be timed with::
3083       tim0.start('start')
3084       tim0.start('in section 1')
3085       tim0.start('in section 2')
3086       
3087    etc. (Note that each section should have a unique label.)
3088
3089    After the last section, end timing with::
3090       tim0.end()
3091
3092    Show timing results with::
3093       tim0.show()
3094       
3095    '''
3096    def __init__(self):
3097        self.timeSum =  []
3098        self.timeStart = []
3099        self.label = []
3100        self.prev = None
3101    def start(self,label):
3102        import time
3103        if label in self.label:
3104            i = self.label.index(label)
3105            self.timeStart[i] = time.time()
3106        else:
3107            i = len(self.label)
3108            self.timeSum.append(0.0)
3109            self.timeStart.append(time.time())
3110            self.label.append(label)
3111        if self.prev is not None:
3112            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
3113        self.prev = i
3114    def end(self):
3115        import time
3116        if self.prev is not None:
3117            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
3118        self.prev = None
3119    def show(self):
3120        sumT = sum(self.timeSum)
3121        print('Timing results (total={:.2f} sec)'.format(sumT))
3122        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
3123            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
3124#%%
3125
3126if __name__ == "__main__":
3127    # test variable descriptions
3128    for var in '0::Afrac:*',':1:Scale','1::dAx:0','::undefined':
3129        v = var.split(':')[2]
3130        print(var+':\t', getDescr(v),getVarStep(v))
3131    import sys; sys.exit()
3132    # test equation evaluation
3133    def showEQ(calcobj):
3134        print (50*'=')
3135        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
3136        for v in sorted(calcobj.varLookup):
3137            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
3138        # print '  Derivatives'
3139        # for v in calcobj.derivStep.keys():
3140        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
3141
3142    obj = ExpressionObj()
3143
3144    obj.expression = "A*np.exp(B)"
3145    obj.assgnVars =  {'B': '0::Afrac:1'}
3146    obj.freeVars =  {'A': [u'A', 0.5, True]}
3147    #obj.CheckVars()
3148    calcobj = ExpressionCalcObj(obj)
3149
3150    obj1 = ExpressionObj()
3151    obj1.expression = "A*np.exp(B)"
3152    obj1.assgnVars =  {'B': '0::Afrac:*'}
3153    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
3154    #obj.CheckVars()
3155    calcobj1 = ExpressionCalcObj(obj1)
3156
3157    obj2 = ExpressionObj()
3158    obj2.distance_stuff = np.array([[0,1],[1,-1]])
3159    obj2.expression = "Dist(1,2)"
3160    GSASIIpath.InvokeDebugOpts()
3161    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3162    calcobj2 = ExpressionCalcObj(obj2)
3163    calcobj2.SetupCalc(parmDict2)
3164    showEQ(calcobj2)
3165
3166    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
3167    print ('\nDict = '+parmDict1)
3168    calcobj.SetupCalc(parmDict1)
3169    showEQ(calcobj)
3170    calcobj1.SetupCalc(parmDict1)
3171    showEQ(calcobj1)
3172
3173    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
3174    print ('Dict = '+parmDict2)
3175    calcobj.SetupCalc(parmDict2)
3176    showEQ(calcobj)
3177    calcobj1.SetupCalc(parmDict2)
3178    showEQ(calcobj1)
3179    calcobj2.SetupCalc(parmDict2)
3180    showEQ(calcobj2)
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