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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2018-06-28 21:50:46 +0000 (Thu, 28 Jun 2018) $
5# $Author: toby $
6# $Revision: 3458 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 3458 2018-06-28 21:50:46Z 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
18Constraints Tree Item
19----------------------
20
21.. _Constraints_table:
22
23.. index::
24   single: Constraints object description
25   single: Data object descriptions; Constraints
26
27Constraints are stored in a dict, separated into groups.
28Note that parameter are named in the following pattern,
29p:h:<var>:n, where p is the phase number, h is the histogram number
30<var> is a variable name and n is the parameter number.
31If a parameter does not depend on a histogram or phase or is unnumbered, that
32number is omitted.
33Note that the contents of each dict item is a List where each element in the
34list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
35The constraints in this form are converted in
36:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
37
38The keys in the Constraints dict are:
39
40.. tabularcolumns:: |l|p{4.5in}|
41
42==========  ====================================================
43  key         explanation
44==========  ====================================================
45Hist        This specifies a list of constraints on
46            histogram-related parameters,
47            which will be of form :h:<var>:n.
48HAP         This specifies a list of constraints on parameters
49            that are defined for every histogram in each phase
50            and are of form p:h:<var>:n.
51Phase       This specifies a list of constraints on phase
52            parameters,
53            which will be of form p::<var>:n.
54Global      This specifies a list of constraints on parameters
55            that are not tied to a histogram or phase and
56            are of form ::<var>:n
57==========  ====================================================
58
59.. _Constraint_definitions_table:
60
61.. index::
62   single: Constraint definition object description
63   single: Data object descriptions; Constraint Definition
64
65Each constraint is defined as an item in a list. Each constraint is of form::
66
67[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
68
69Where the variable pair list item containing two values [<mult>, <var>], where:
70
71  * <mult> is a multiplier for the constraint (float)
72  * <var> a :class:`G2VarObj` object (previously a str variable name of form
73      'p:h:name[:at]')
74
75Note that the last three items in the list play a special role:
76
77 * <fixedval> is the fixed value for a `constant equation` (``constype=c``)
78   constraint or is None. For a `New variable` (``constype=f``) constraint,
79   a variable name can be specified as a str (used for externally
80   generated constraints)
81 * <varyflag> is True or False for `New variable` (``constype=f``) constraints
82   or is None. This will be implemented in the future to indicate if these variables
83   should be refined.
84 * <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:
85
86    * 'e' defines a set of equivalent variables. Only the first variable is refined (if the
87      appropriate refine flag is set) and and all other equivalent variables in the list
88      are generated from that variable, using the appropriate multipliers.
89    * 'c' defines a constraint equation of form,
90      :math:`m_1 \\times var_1 + m_2 \\times var_2 + ... = c`
91    * 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
92      even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
93      constraint and the mult value is ignored.
94      This is of particular value when needing to hold one or more variables where a
95      single flag controls a set of variables such as, coordinates,
96      the reciprocal metric tensor or anisotropic displacement parameter.
97    * 'f' defines a new variable (function) according to relationship
98      :math:`newvar = m_1 \\times var_1 + m_2 \\times var_2 + ...`
99
100Covariance Tree Item
101--------------------
102
103.. _Covariance_table:
104
105.. index::
106   single: Covariance description
107   single: Data object descriptions; Covariance
108
109The Covariance tree item has results from the last least-squares run. They
110are stored in a dict with these keys:
111
112.. tabularcolumns:: |l|l|p{4in}|
113
114=============  ===============  ====================================================
115  key            sub-key        explanation
116=============  ===============  ====================================================
117newCellDict    \                dict with lattice parameters computed by
118                                :func:`GSASIIstrMath.GetNewCellParms` (dict)
119title          \                Name of gpx file(?) (str)
120variables      \                Values for all N refined variables
121                                (list of float values, length N,
122                                ordered to match varyList)
123sig            \                Uncertainty values for all N refined variables
124                                (list of float values, length N,
125                                ordered to match varyList)
126varyList       \                List of directly refined variables
127                                (list of str values, length N)
128newAtomDict    \                dict with atom position values computed in
129                                :func:`GSASIIstrMath.ApplyXYZshifts` (dict)
130Rvals          \                R-factors, GOF, Marquardt value for last
131                                refinement cycle (dict)
132\              Nobs             Number of observed data points (int)
133\              Rwp              overall weighted profile R-factor (%, float)
134\              chisq            sum[w*(Iobs-Icalc)**2] for all data
135                                note this is not the reduced chi squared (float)
136\              lamMax           Marquardt value applied to Hessian diagonal
137                                (float)
138\              GOF              The goodness-of-fit, aka square root of
139                                the reduced chi squared. (float)
140covMatrix      \                The (NxN) covVariance matrix (np.array)
141=============  ===============  ====================================================
142
143Phase Tree Items
144----------------
145
146.. _Phase_table:
147
148.. index::
149   single: Phase object description
150   single: Data object descriptions; Phase
151
152Phase information is stored in the GSAS-II data tree as children of the
153Phases item in a dict with keys:
154
155.. tabularcolumns:: |l|l|p{4in}|
156
157==========  ===============  ====================================================
158  key         sub-key        explanation
159==========  ===============  ====================================================
160General         \            Overall information for the phase (dict)
161  \         AtomPtrs         list of four locations to use to pull info
162                             from the atom records (list)
163  \         F000X            x-ray F(000) intensity (float)
164  \         F000N            neutron F(000) intensity (float)
165  \         Mydir            directory of current .gpx file (str)
166  \         MCSA controls    Monte Carlo-Simulated Annealing controls (dict)
167  \         Cell             List with 8 items: cell refinement flag (bool)
168                             a, b, c, (Angstrom, float)
169                             alpha, beta & gamma (degrees, float)
170                             volume (A^3, float)
171  \         Type             'nuclear' or 'macromolecular' for now (str)
172  \         Map              dict of map parameters
173  \         SH Texture       dict of spherical harmonic preferred orientation
174                             parameters
175  \         Isotope          dict of isotopes for each atom type
176  \         Isotopes         dict of scattering lengths for each isotope
177                             combination for each element in phase
178  \         Name             phase name (str)
179  \         SGData           Space group details as a :ref:`space group (SGData) object <SGData_table>`
180                             as defined in :func:`GSASIIspc.SpcGroup`.
181  \         Pawley neg wt    Restraint value for negative Pawley intensities
182                             (float)
183  \         Flip             dict of Charge flip controls
184  \         Data plot type   data plot type ('Mustrain', 'Size' or
185                             'Preferred orientation') for powder data (str)
186  \         Mass             Mass of unit cell contents in g/mol
187  \         POhkl            March-Dollase preferred orientation direction
188  \         Z                dict of atomic numbers for each atom type
189  \         vdWRadii         dict of van der Waals radii for each atom type
190  \         Color            Colors for atoms (list of (r,b,g) triplets)
191  \         AtomTypes        List of atom types
192  \         AtomMass         List of masses for atoms
193  \         doPawley         Flag for Pawley intensity extraction (bool)
194  \         NoAtoms          Number of atoms per unit cell of each type (dict)
195  \         Pawley dmin      maximum Q (as d-space) to use for Pawley
196                             extraction (float)
197  \         BondRadii        Default radius for each atom used to compute
198                             interatomic distances (list of floats)
199  \         AngleRadii       Default radius for each atom used to compute
200                             interatomic angles (list of floats)
201  \         DisAglCtls       Dict with distance/angle search controls,
202                             which has keys 'Name', 'AtomTypes',
203                             'BondRadii', 'AngleRadii' which are as above
204                             except are possibly edited. Also contains
205                             'Factors', which is a 2 element list with
206                             a multiplier for bond and angle search range
207                             [typically (0.85,0.85)].
208ranId           \            unique random number Id for phase (int)
209pId             \            Phase Id number for current project (int).
210Atoms           \            Atoms in phase as a list of lists. The outer list
211                             is for each atom, the inner list contains varying
212                             items depending on the type of phase, see
213                             the :ref:`Atom Records <Atoms_table>` description.
214                             (list of lists)
215Drawing         \            Display parameters (dict)
216\           ballScale        Size of spheres in ball-and-stick display (float)
217\           bondList         dict with bonds
218\           contourLevel     map contour level in e/A^3 (float)
219\           showABC          Flag to show view point triplet (bool). True=show.
220\           viewDir          cartesian viewing direction (np.array with three
221                             elements)
222\           Zclip            clipping distance in A (float)
223\           backColor        background for plot as and R,G,B triplet
224                             (default = [0, 0, 0], black).
225                             (list with three atoms)
226\           selectedAtoms    List of selected atoms (list of int values)
227\           showRigidBodies  Flag to highlight rigid body placement
228\           sizeH            Size ratio for H atoms (float)
229\           bondRadius       Size of binds in A (float)
230\           atomPtrs         positions of x, type, site sym, ADP flag in Draw Atoms (list)
231\           viewPoint        list of lists. First item in list is [x,y,z]
232                             in fractional coordinates for the center of
233                             the plot. Second item list of previous & current
234                             atom number viewed (may be [0,0])
235\           showHydrogen     Flag to control plotting of H atoms.
236\           unitCellBox      Flag to control display of the unit cell.
237\           ellipseProb      Probability limit for display of thermal
238                             ellipsoids in % (float).
239\           vdwScale         Multiplier of van der Waals radius for
240                             display of vdW spheres.
241\           Atoms            A list of lists with an entry for each atom
242                             that is plotted.
243\           Zstep            Step to de/increase Z-clip (float)
244\           Quaternion       Viewing quaternion (4 element np.array)
245\           radiusFactor     Distance ratio for searching for bonds. ? Bonds
246                             are located that are within r(Ra+Rb) and (Ra+Rb)/r
247                             where Ra and Rb are the atomic radii.
248\           oldxy            previous view point (list with two floats)
249\           cameraPos        Viewing position in A for plot (float)
250\           depthFog         True if use depthFog on plot - set currently as False (bool)
251RBModels        \            Rigid body assignments (note Rigid body definitions
252                             are stored in their own main top-level tree entry.)
253Pawley ref      \            Pawley reflections
254Histograms      \            A dict of dicts. The key for the outer dict is
255                             the histograms tied to this phase. The inner
256                             dict contains the combined phase/histogram
257                             parameters for items such as scale factors,
258                             size and strain parameters. The following are the
259                             keys to the inner dict. (dict)
260\           Babinet          For protein crystallography. Dictionary with two
261                             entries, 'BabA', 'BabU'
262\           Extinction       Extinction parameter (list of float, bool)
263\           HStrain          Hydrostatic strain. List of two lists. The first is
264                             a list of the HStrain parameters (1, 2, 3, 4, or 6
265                             depending on unit cell), the second is a list of boolean
266                             refinement parameters (same length)
267\           Histogram        The name of the associated histogram (str)
268\           LeBail           Flag for LeBail extraction (bool)
269\           Mustrain         List of microstrain parameters, in order:
270
271                               0. Type, one of u'generalized', u'isotropic',
272                                  u'uniaxial'
273                               1. Isotropic/uniaxial parameters - list of 3 floats
274                               2. Refinement flags - list of 3 bools
275                               3. Microstrain axis - list of 3 ints, [h, k, l]
276                               4. Generalized mustrain parameters - list of 2-6
277                                  floats, depending on space group
278                               5. Generalized refinement flags - list of bools,
279                                  corresponding to the parameters of (4)
280\           Pref.Ori.        Preferred Orientation. List of eight parameters.
281                             Items marked SH are only used for Spherical Harmonics.
282
283                               0. Type, 'MD' for March-Dollase or 'SH' for
284                                  Spherical Harmonics
285                               1. Value, float
286                               2. Refinement flag, bool
287                               3. Preferred direction, list of ints, [h, k, l]
288                               4. SH - number of terms, int
289                               5. SH - dict
290                               6. SH - list
291                               7. SH - float
292\           Scale            Phase fraction, list of [float, bool].
293\           Show             bool
294\           Use              bool
295\           newLeBail        Whether to perform a new LeBail extraction
296MCSA            \            Monte-Carlo simulated annealing parameters (dict)
297\
298==========  ===============  ====================================================
299
300Rigid Body Objects
301------------------
302
303.. _RBData_table:
304
305.. index::
306   single: Rigid Body Data description
307   single: Data object descriptions; Rigid Body Data
308
309Rigid body descriptions are available for two types of rigid bodies: 'Vector'
310and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
311with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
312with defined refinable torsion angles.
313
314.. tabularcolumns:: |l|l|p{4in}|
315
316==========  ===============  ====================================================
317  key         sub-key        explanation
318==========  ===============  ====================================================
319Vector      RBId             vector rigid bodies (dict of dict)
320\           AtInfo           Drad, Color: atom drawing radius & color for each atom type (dict)
321\           RBname           Name assigned by user to rigid body (str)
322\           VectMag          vector magnitudes in A (list)
323\           rbXYZ            Cartesian coordinates for Vector rigid body (list of 3 float)
324\           rbRef            3 assigned reference atom nos. in rigid body for origin
325                             definition, use center of atoms flag (list of 3 int & 1 bool)
326\           VectRef          refinement flags for VectMag values (list of bool)
327\           rbTypes          Atom types for each atom in rigid body (list of str)
328\           rbVect           Cartesian vectors for each translation used to build rigid body (list of lists)
329\           useCount         Number of times rigid body is used in any structure (int)
330Residue     RBId             residue rigid bodies (dict of dict)
331\           AtInfo           Drad, Color: atom drawing radius & color for each atom type(dict)
332\           RBname           Name assigned by user to rigid body (str)
333\           rbXYZ            Cartesian coordinates for Residue rigid body (list of 3 float)
334\           rbTypes          Atom types for each atom in rigid body (list of str)
335\           atNames          Names of each atom in rigid body (e.g. C1,N2...) (list of str)
336\           rbRef            3 assigned reference atom nos. in rigid body for origin
337                             definition, use center of atoms flag (list of 3 int & 1 bool)
338\           rbSeq            Orig,Piv,angle,Riding (list): definition of internal rigid body
339                             torsion; origin atom (int), pivot atom (int), torsion angle (float),
340                             riding atoms (list of int)
341\           SelSeq           [int,int] used by SeqSizer to identify objects
342\           useCount         Number of times rigid body is used in any structure (int)
343RBIds           \            unique Ids generated upon creation of each rigid body (dict)
344\           Vector           Ids for each Vector rigid body (list)
345\           Residue          Ids for each Residue rigid body (list)
346==========  ===============  ====================================================
347
348Space Group Objects
349-------------------
350
351.. _SGData_table:
352
353.. index::
354   single: Space Group Data description
355   single: Data object descriptions; Space Group Data
356
357Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
358and the information is placed in a SGdata object
359which is a dict with these keys:
360
361.. tabularcolumns:: |l|p{4.5in}|
362
363==========  ====================================================
364  key         explanation
365==========  ====================================================
366SpGrp       space group symbol (str)
367Laue        one of the following 14 Laue classes:
368            -1, 2/m, mmm, 4/m, 4/mmm, 3R,
369            3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m (str)
370SGInv       True if centrosymmetric, False if not (bool)
371SGLatt      Lattice centering type. Will be one of
372            P, A, B, C, I, F, R (str)
373SGUniq      unique axis if monoclinic. Will be
374            a, b, or c for monoclinic space groups.
375            Will be blank for non-monoclinic. (str)
376SGCen       Symmetry cell centering vectors. A (n,3) np.array
377            of centers. Will always have at least one row:
378            ``np.array([[0, 0, 0]])``
379SGOps       symmetry operations as a list of form
380            ``[[M1,T1], [M2,T2],...]``
381            where :math:`M_n` is a 3x3 np.array
382            and :math:`T_n` is a length 3 np.array.
383            Atom coordinates are transformed where the
384            Asymmetric unit coordinates [X is (x,y,z)]
385            are transformed using
386            :math:`X^\prime = M_n*X+T_n`
387SGSys       symmetry unit cell: type one of
388            'triclinic', 'monoclinic', 'orthorhombic',
389            'tetragonal', 'rhombohedral', 'trigonal',
390            'hexagonal', 'cubic' (str)
391SGPolax     Axes for space group polarity. Will be one of
392            '', 'x', 'y', 'x y', 'z', 'x z', 'y z',
393            'xyz'. In the case where axes are arbitrary
394            '111' is used (P 1, and ?).
395==========  ====================================================
396
397.. _SSGData_table:
398
399.. index::
400   single: Superspace Group Data description
401   single: Data object descriptions; Superspace Group Data
402
403Superspace groups [3+1] are interpreted by :func:`GSASIIspc.SSpcGroup`
404and the information is placed in a SSGdata object
405which is a dict with these keys:
406
407.. tabularcolumns:: |l|p{4.5in}|
408
409==========  ====================================================
410  key         explanation
411==========  ====================================================
412SSpGrp      superspace group symbol extension to space group
413            symbol, accidental spaces removed
414SSGCen      4D cell centering vectors [0,0,0,0] at least
415SSGOps      4D symmetry operations as [M,T] so that M*x+T = x'
416==========  ====================================================
417
418
419Atom Records
420------------
421
422.. _Atoms_table:
423
424.. index::
425   single: Atoms record description
426   single: Data object descriptions; Atoms record
427
428
429If ``phasedict`` points to the phase information in the data tree, then
430atoms are contained in a list of atom records (list) in
431``phasedict['Atoms']``. Also needed to read atom information
432are four pointers, ``cx,ct,cs,cia = phasedict['General']['AtomPtrs']``,
433which define locations in the atom record, as shown below. Items shown are
434always present; additional ones for macromolecular phases are marked 'mm'
435
436.. tabularcolumns:: |l|p{4.5in}|
437
438==============   ====================================================
439location         explanation
440==============   ====================================================
441ct-4              mm - residue number (str)
442ct-3              mm - residue name (e.g. ALA) (str)
443ct-2              mm - chain label (str)
444ct-1              atom label (str)
445ct                atom type (str)
446ct+1              refinement flags; combination of 'F', 'X', 'U' (str)
447cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
448cx+3              site occupancy (float)
449cs                site symmetry (str)
450cs+1              site multiplicity (int)
451cia               ADP flag: Isotropic ('I') or Anisotropic ('A')
452cia+1             Uiso (float)
453cia+2...cia+7     U11, U22, U33, U12, U13, U23 (6 floats)
454atom[cia+8]       unique atom identifier (int)
455
456==============   ====================================================
457
458Drawing Atom Records
459--------------------
460
461.. _Drawing_atoms_table:
462
463.. index::
464   single: Drawing atoms record description
465   single: Data object descriptions; Drawing atoms record
466
467
468If ``phasedict`` points to the phase information in the data tree, then
469drawing atoms are contained in a list of drawing atom records (list) in
470``phasedict['Drawing']['Atoms']``. Also needed to read atom information
471are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
472which define locations in the atom record, as shown below. Items shown are
473always present; additional ones for macromolecular phases are marked 'mm'
474
475.. tabularcolumns:: |l|p{4.5in}|
476
477==============   ====================================================
478location         explanation
479==============   ====================================================
480ct-4              mm - residue number (str)
481ct-3              mm - residue name (e.g. ALA) (str)
482ct-2              mm - chain label (str)
483ct-1              atom label (str)
484ct                atom type (str)
485cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
486cs-1              Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
487cs                atom drawing style; e.g. 'balls & sticks' (str)
488cs+1              atom label style (e.g. 'name') (str)
489cs+2              atom color (RBG triplet) (int)
490cs+3              ADP flag: Isotropic ('I') or Anisotropic ('A')
491cs+4              Uiso (float)
492cs+5...cs+11      U11, U22, U33, U12, U13, U23 (6 floats)
493ci                unique atom identifier; matches source atom Id in Atom Records (int)
494==============   ====================================================
495
496Powder Diffraction Tree Items
497-----------------------------
498
499.. _Powder_table:
500
501.. index::
502   single: Powder data object description
503   single: Data object descriptions; Powder Data
504
505Every powder diffraction histogram is stored in the GSAS-II data tree
506with a top-level entry named beginning with the string "PWDR ". The
507diffraction data for that information are directly associated with
508that tree item and there are a series of children to that item. The
509routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
510and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
511load this information into a dictionary where the child tree name is
512used as a key, and the information in the main entry is assigned
513a key of ``Data``, as outlined below.
514
515.. tabularcolumns:: |p{1in}|p{1in}|p{4in}|
516
517======================  ===============  ====================================================
518  key                      sub-key        explanation
519======================  ===============  ====================================================
520Comments                      \           Text strings extracted from the original powder
521                                          data header. These cannot be changed by the user;
522                                          it may be empty.
523Limits                       \            A list of two two element lists, as [[Ld,Hd],[L,H]]
524                                          where L and Ld are the current and default lowest
525                                          two-theta value to be used and
526                                          where H and Hd are the current and default highest
527                                          two-theta value to be used.
528Reflection Lists              \           A dict with an entry for each phase in the
529                                          histogram. The contents of each dict item
530                                          is a dict containing reflections, as described in
531                                          the :ref:`Powder Reflections <PowderRefl_table>`
532                                          description.
533Instrument Parameters         \           A list containing two dicts where the possible
534                                          keys in each dict are listed below. The value
535                                          for each item is a list containing three values:
536                                          the initial value, the current value and a
537                                          refinement flag which can have a value of
538                                          True, False or 0 where 0 indicates a value that
539                                          cannot be refined. The first and second
540                                          values are floats unless otherwise noted.
541                                          Items in the first dict are noted as [1]
542\                         Lam             Specifies a wavelength in Angstroms [1]
543\                         Lam1            Specifies the primary wavelength in
544                                          Angstrom, when an alpha1, alpha2
545                                          source is used [1]
546\                         Lam2            Specifies the secondary wavelength in
547                                          Angstrom, when an alpha1, alpha2
548                                          source is used [1]
549                          I(L2)/I(L1)     Ratio of Lam2 to Lam1 [1]
550\                         Type            Histogram type (str) [1]:
551                                           * 'PXC' for constant wavelength x-ray
552                                           * 'PNC' for constant wavelength neutron
553                                           * 'PNT' for time of flight neutron
554\                         Zero            Two-theta zero correction in *degrees* [1]
555\                         Azimuth         Azimuthal setting angle for data recorded
556                                          with differing setting angles [1]
557\                         U, V, W         Cagliotti profile coefficients
558                                          for Gaussian instrumental broadening, where the
559                                          FWHM goes as
560                                          :math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
561\                         X, Y            Cauchy (Lorentzian) instrumental broadening
562                                          coefficients [1]
563\                         SH/L            Variant of the Finger-Cox-Jephcoat asymmetric
564                                          peak broadening ratio. Note that this is the
565                                          average between S/L and H/L where S is
566                                          sample height, H is the slit height and
567                                          L is the goniometer diameter. [1]
568\                         Polariz.        Polarization coefficient. [1]
569wtFactor                      \           A weighting factor to increase or decrease
570                                          the leverage of data in the histogram (float).
571                                          A value of 1.0 weights the data with their
572                                          standard uncertainties and a larger value
573                                          increases the weighting of the data (equivalent
574                                          to decreasing the uncertainties).
575Sample Parameters             \           Specifies a dict with parameters that describe how
576                                          the data were collected, as listed
577                                          below. Refinable parameters are a list containing
578                                          a float and a bool, where the second value
579                                          specifies if the value is refined, otherwise
580                                          the value is a float unless otherwise noted.
581\                         Scale           The histogram scale factor (refinable)
582\                         Absorption      The sample absorption coefficient as
583                                          :math:`\\mu r` where r is the radius
584                                          (refinable). Only valid for Debye-Scherrer geometry.
585\                         SurfaceRoughA   Surface roughness parameter A as defined by
586                                          Surotti,J. Appl. Cryst, 5,325-331, 1972.(refinable -
587                                          only valid for Bragg-Brentano geometry)
588\                         SurfaceRoughB   Surface roughness parameter B (refinable -
589                                          only valid for Bragg-Brentano geometry)
590\                         DisplaceX,      Sample displacement from goniometer center
591                          DisplaceY       where Y is along the beam direction and
592                                          X is perpendicular. Units are :math:`\\mu m`
593                                          (refinable).
594\                         Phi, Chi,       Goniometer sample setting angles, in degrees.
595                          Omega
596\                         Gonio. radius   Radius of the diffractometer in mm
597\                         InstrName       A name for the instrument, used in preparing
598                                          a CIF (str).
599\                         Force,          Variables that describe how the measurement
600                          Temperature,    was performed. Not used directly in
601                          Humidity,       any computations.
602                          Pressure,
603                          Voltage
604\                         ranId           The random-number Id for the histogram
605                                          (same value as where top-level key is ranId)
606\                         Type            Type of diffraction data, may be 'Debye-Scherrer'
607                                          or 'Bragg-Brentano' (str).
608\                         Diffuse         not in use?
609hId                           \           The number assigned to the histogram when
610                                          the project is loaded or edited (can change)
611ranId                         \           A random number id for the histogram
612                                          that does not change
613Background                    \           The background is stored as a list with where
614                                          the first item in the list is list and the second
615                                          item is a dict. The list contains the background
616                                          function and its coefficients; the dict contains
617                                          Debye diffuse terms and background peaks.
618                                          (TODO: this needs to be expanded.)
619Data                          \           The data consist of a list of 6 np.arrays
620                                          containing in order:
621
622                                           0. the x-postions (two-theta in degrees),
623                                           1. the intensity values (Yobs),
624                                           2. the weights for each Yobs value
625                                           3. the computed intensity values (Ycalc)
626                                           4. the background values
627                                           5. Yobs-Ycalc
628======================  ===============  ====================================================
629
630Powder Reflection Data Structure
631--------------------------------
632
633.. _PowderRefl_table:
634
635.. index::
636   single: Powder reflection object description
637   single: Data object descriptions; Powder Reflections
638
639For every phase in a histogram, the ``Reflection Lists`` value is a dict
640one element of which is `'RefList'`, which is a np.array containing
641reflections. The columns in that array are documented below.
642
643==========  ====================================================
644  index         explanation
645==========  ====================================================
646 0,1,2       h,k,l (float)
647 3           multiplicity
648 4           d-space, Angstrom
649 5           pos, two-theta
650 6           sig, Gaussian width
651 7           gam, Lorenzian width
652 8           :math:`F_{obs}^2`
653 9           :math:`F_{calc}^2`
654 10          reflection phase, in degrees
655 11          intensity correction for reflection, this times
656             :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
657==========  ====================================================
658
659Single Crystal Tree Items
660-------------------------
661
662.. _Xtal_table:
663
664.. index::
665   single: Single Crystal data object description
666   single: Data object descriptions; Single crystal data
667
668Every single crystal diffraction histogram is stored in the GSAS-II data tree
669with a top-level entry named beginning with the string "HKLF ". The
670diffraction data for that information are directly associated with
671that tree item and there are a series of children to that item. The
672routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
673and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
674load this information into a dictionary where the child tree name is
675used as a key, and the information in the main entry is assigned
676a key of ``Data``, as outlined below.
677
678.. tabularcolumns:: |l|l|p{4in}|
679
680======================  ===============  ====================================================
681  key                      sub-key        explanation
682======================  ===============  ====================================================
683Data                          \           A dict that contains the
684                                          reflection table,
685                                          as described in the
686                                          :ref:`Single Crystal Reflections
687                                          <XtalRefl_table>`
688                                          description.
689
690Instrument Parameters         \           A list containing two dicts where the possible
691                                          keys in each dict are listed below. The value
692                                          for most items is a list containing two values:
693                                          the initial value, the current value.
694                                          The first and second
695                                          values are floats unless otherwise noted.
696\                         Lam             Specifies a wavelength in Angstroms (two floats)
697\                         Type            Histogram type (two str values):
698                                           * 'SXC' for constant wavelength x-ray
699                                           * 'SNC' for constant wavelength neutron
700                                           * 'SNT' for time of flight neutron
701\                         InstrName       A name for the instrument, used in preparing
702                                          a CIF (str).
703
704wtFactor                      \           A weighting factor to increase or decrease
705                                          the leverage of data in the histogram (float).
706                                          A value of 1.0 weights the data with their
707                                          standard uncertainties and a larger value
708                                          increases the weighting of the data (equivalent
709                                          to decreasing the uncertainties).
710
711hId                           \           The number assigned to the histogram when
712                                          the project is loaded or edited (can change)
713ranId                         \           A random number id for the histogram
714                                          that does not change
715======================  ===============  ====================================================
716
717Single Crystal Reflection Data Structure
718----------------------------------------
719
720.. _XtalRefl_table:
721
722.. index::
723   single: Single Crystal reflection object description
724   single: Data object descriptions; Single Crystal Reflections
725
726For every single crystal a histogram, the ``'Data'`` item contains
727the structure factors as an np.array in item `'RefList'`.
728The columns in that array are documented below.
729
730==========  ====================================================
731  index         explanation
732==========  ====================================================
733 0,1,2       h,k,l (float)
734 3           multiplicity
735 4           d-space, Angstrom
736 5           :math:`F_{obs}^2`
737 6           :math:`\sigma(F_{obs}^2)`
738 7           :math:`F_{calc}^2`
739 8           :math:`F_{obs}^2T`
740 9           :math:`F_{calc}^2T`
741 10          reflection phase, in degrees
742 11          intensity correction for reflection, this times
743             :math:`F_{obs}^2` or :math:`F_{calc}^2`
744             gives Iobs or Icalc
745==========  ====================================================
746
747Image Data Structure
748--------------------
749
750.. _Image_table:
751
752.. index::
753   image: Image data object description
754   image: Image object descriptions
755
756Every 2-dimensional image is stored in the GSAS-II data tree
757with a top-level entry named beginning with the string "IMG ". The
758image data are directly associated with that tree item and there
759are a series of children to that item. The routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
760and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
761load this information into a dictionary where the child tree name is
762used as a key, and the information in the main entry is assigned
763a key of ``Data``, as outlined below.
764
765.. tabularcolumns:: |l|l|p{4in}|
766
767======================  ======================  ====================================================
768  key                      sub-key              explanation
769======================  ======================  ====================================================
770Comments                       \                Text strings extracted from the original image data
771                                                header or a metafile. These cannot be changed by
772                                                the user; it may be empty.
773Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
774                                                value. Accomodates
775                                                detector orientations other than with the detector
776                                                X-axis
777                                                horizontal.
778\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
779                                                during image integration multiplied by value. It must have the same size/shape as
780                                                the integrated image. NB: value < 0 for subtraction.
781\                           calibrant           (str) The material used for determining the position/orientation
782                                                of the image. The data is obtained from :func:`ImageCalibrants`
783                                                and UserCalibrants.py (supplied by user).
784\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
785\                           calibskip           (int) The number of expected diffraction lines skipped during the last
786                                                calibration run.
787\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
788                                                strikes the detector plane as determined by calibration. This point
789                                                does not have to be within the limits of the detector boundaries.
790\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
791                                                of the image is at the center line otherwise it is at the leading edge.
792\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
793\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
794                                                calibration calculations. See pixLimit for details as how point is found.
795\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
796                                                ring offset at higher angles. Optionally determined by calibration.
797\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
798\                           distance            (float) The distance (mm) from sample to detector plane.
799\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
800                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
801                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
802                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
803                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
804\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
805\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
806\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
807                                                Required for texture calculations.
808\                           invert_x            (bool) If True display the image with the x-axis inverted.
809\                           invert_y            (bool) If True display the image with the y-axis inverted.
810\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
811\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
812\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
813                                                intensities obtained during integration.
814\                           outAzimuths         (int) The number of azimuth pie slices.
815\                           outChannels         (int) The number of 2-theta steps.
816\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
817\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
818                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
819                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
820                                                Locations are used to construct rings of points for calibration calcualtions.
821\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
822                                                integration using value.
823\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
824                                                diffraction ring with the same d-spacing (dsp)
825\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
826                                                selected by the user,
827\                           Range               (list) The minimum & maximum values of the image
828\                           rotation            (float) The angle between the x-axis and the vector about which the
829                                                detector is tilted. Constrained to -180 to 180 deg.
830\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
831                                                calculations.
832\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
833                                                to cause correction to be applied.
834\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
835\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.
836\                           showLines           (bool) If True then isplay the integration limits to be used.
837\                           size                (list:int) The number of pixels on the image x & y axes
838\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
839\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
840\                           wavelength          (float) Tha radiation wavelength (Angstroms) as entered by the user (or someday obtained from the image header).
841
842Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
843                                                to be excluded from integration
844\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
845                                                of which is excluded from recalibration and integration. Only one frame is allowed.
846\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
847                                                from integration.
848\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
849                                                to be excluded from integration.
850\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
851                                                to be excluded from integration.
852\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
853                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.
854
855Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
856\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
857                                                These will be restricted by space group symmetry; result of strain fit refinement.
858\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
859\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
860                                                and are used to determine the strain tensor.
861                                                The dictionary items are:
862                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
863                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
864                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
865                                                'Esig': (list: float) Esds for Emat from fitting.
866                                                'pixLimit': (int) Search range to find highest point on ring for each data point
867                                                'cutoff': (float) I/Ib cutoff for searching.
868                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
869                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
870                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
871
872======================  ======================  ====================================================
873
874Parameter Dictionary
875-------------------------
876
877.. _parmDict_table:
878
879.. index::
880   single: Parameter dictionary
881
882The parameter dictionary contains all of the variable parameters for the refinement.
883The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
884It is prepared in two ways. When loaded from the tree
885(in :meth:`GSASIIdataGUI.GSASII.MakeLSParmDict` and
886:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
887the values are lists with two elements: ``[value, refine flag]``
888
889When loaded from the GPX file (in
890:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
891dict is the actual parameter value (usually a float, but sometimes a
892letter or string flag value (such as I or A for iso/anisotropic).
893
894
895*Classes and routines*
896----------------------
897
898'''
899from __future__ import division, print_function
900import platform
901import re
902import imp
903import random as ran
904import sys
905import os.path as ospath
906if '2' in platform.python_version_tuple()[0]:
907    import cPickle
908else:
909    import pickle as cPickle
910import GSASIIpath
911import GSASIImath as G2mth
912import GSASIIspc as G2spc
913import numpy as np
914
915GSASIIpath.SetVersionNumber("$Revision: 3458 $")
916
917DefaultControls = {
918    'deriv type':'analytic Hessian',
919    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
920    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
921    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
922    'Author':'no name',
923    'FreePrm1':'Sample humidity (%)',
924    'FreePrm2':'Sample voltage (V)',
925    'FreePrm3':'Applied load (MN)',
926    'ShowCell':False,
927    }
928'''Values to be used as defaults for the initial contents of the ``Controls``
929data tree item.
930'''
931def StripUnicode(string,subs='.'):
932    '''Strip non-ASCII characters from strings
933
934    :param str string: string to strip Unicode characters from
935    :param str subs: character(s) to place into string in place of each
936      Unicode character. Defaults to '.'
937
938    :returns: a new string with only ASCII characters
939    '''
940    s = ''
941    for c in string:
942        if ord(c) < 128:
943            s += c
944        else:
945            s += subs
946    return s
947#    return s.encode('ascii','replace')
948
949def MakeUniqueLabel(lbl,labellist):
950    '''Make sure that every a label is unique against a list by adding
951    digits at the end until it is not found in list.
952
953    :param str lbl: the input label
954    :param list labellist: the labels that have already been encountered
955    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
956      ``_10-99``, etc.) appended at the end
957    '''
958    lbl = StripUnicode(lbl.strip(),'_')
959    if not lbl: # deal with a blank label
960        lbl = '_1'
961    if lbl not in labellist:
962        labellist.append(lbl)
963        return lbl
964    i = 1
965    prefix = lbl
966    if '_' in lbl:
967        prefix = lbl[:lbl.rfind('_')]
968        suffix = lbl[lbl.rfind('_')+1:]
969        try:
970            i = int(suffix)+1
971        except: # suffix could not be parsed
972            i = 1
973            prefix = lbl
974    while prefix+'_'+str(i) in labellist:
975        i += 1
976    else:
977        lbl = prefix+'_'+str(i)
978        labellist.append(lbl)
979    return lbl
980
981PhaseIdLookup = {}
982'''dict listing phase name and random Id keyed by sequential phase index as a str;
983best to access this using :func:`LookupPhaseName`
984'''
985PhaseRanIdLookup = {}
986'''dict listing phase sequential index keyed by phase random Id;
987best to access this using :func:`LookupPhaseId`
988'''
989HistIdLookup = {}
990'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
991best to access this using :func:`LookupHistName`
992'''
993HistRanIdLookup = {}
994'''dict listing histogram sequential index keyed by histogram random Id;
995best to access this using :func:`LookupHistId`
996'''
997AtomIdLookup = {}
998'''dict listing for each phase index as a str, the atom label and atom random Id,
999keyed by atom sequential index as a str;
1000best to access this using :func:`LookupAtomLabel`
1001'''
1002AtomRanIdLookup = {}
1003'''dict listing for each phase the atom sequential index keyed by atom random Id;
1004best to access this using :func:`LookupAtomId`
1005'''
1006ShortPhaseNames = {}
1007'''a dict containing a possibly shortened and when non-unique numbered
1008version of the phase name. Keyed by the phase sequential index.
1009'''
1010ShortHistNames = {}
1011'''a dict containing a possibly shortened and when non-unique numbered
1012version of the histogram name. Keyed by the histogram sequential index.
1013'''
1014
1015VarDesc = {}
1016''' This dictionary lists descriptions for GSAS-II variables,
1017as set in :func:`CompileVarDesc`. See that function for a description
1018for how keys and values are written.
1019'''
1020
1021reVarDesc = {}
1022''' This dictionary lists descriptions for GSAS-II variables with
1023the same values as :attr:`VarDesc` except that keys have been compiled as
1024regular expressions. Initialized in :func:`CompileVarDesc`.
1025'''
1026# create a default space group object for P1; N.B. fails when building documentation
1027try:
1028    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
1029except:
1030    pass
1031
1032def GetPhaseNames(fl):
1033    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
1034    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename
1035
1036    :param file fl: opened .gpx file
1037    :return: list of phase names
1038    '''
1039    PhaseNames = []
1040    while True:
1041        try:
1042            data = cPickle.load(fl)
1043        except EOFError:
1044            break
1045        datum = data[0]
1046        if 'Phases' == datum[0]:
1047            for datus in data[1:]:
1048                PhaseNames.append(datus[0])
1049    fl.seek(0)          #reposition file
1050    return PhaseNames
1051
1052def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
1053    '''Create a new phase dict with default values for various parameters
1054
1055    :param str Name: Name for new Phase
1056
1057    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
1058      defaults to data for P 1
1059
1060    :param list cell: unit cell parameter list; defaults to
1061      [1.0,1.0,1.0,90.,90,90.,1.]
1062
1063    '''
1064    if SGData is None: SGData = P1SGData
1065    if cell is None: cell=[1.0,1.0,1.0,90.,90,90.,1.]
1066    phaseData = {
1067        'ranId':ran.randint(0,sys.maxsize),
1068        'General':{
1069            'Name':Name,
1070            'Type':'nuclear',
1071            'Modulated':False,
1072            'AtomPtrs':[3,1,7,9],
1073            'SGData':SGData,
1074            'Cell':[False,]+cell,
1075            'Pawley dmin':1.0,
1076            'Data plot type':'None',
1077            'SH Texture':{
1078                'Order':0,
1079                'Model':'cylindrical',
1080                'Sample omega':[False,0.0],
1081                'Sample chi':[False,0.0],
1082                'Sample phi':[False,0.0],
1083                'SH Coeff':[False,{}],
1084                'SHShow':False,
1085                'PFhkl':[0,0,1],
1086                'PFxyz':[0,0,1],
1087                'PlotType':'Pole figure',
1088                'Penalty':[['',],0.1,False,1.0]}},
1089        'Atoms':[],
1090        'Drawing':{},
1091        'Histograms':{},
1092        'Pawley ref':[],
1093        'RBModels':{},
1094        }
1095    if Super and Super.get('Use',False):
1096        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
1097        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
1098        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]
1099
1100    return phaseData
1101
1102def ReadCIF(URLorFile):
1103    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
1104    (from James Hester).
1105    The open routine gets confused with DOS names that begin with a letter and colon
1106    "C:\dir\" so this routine will try to open the passed name as a file and if that
1107    fails, try it as a URL
1108
1109    :param str URLorFile: string containing a URL or a file name. Code will try first
1110      to open it as a file and then as a URL.
1111
1112    :returns: a PyCifRW CIF object.
1113    '''
1114    import CifFile as cif # PyCifRW from James Hester
1115
1116    # alternate approach:
1117    #import urllib
1118    #ciffile = 'file:'+urllib.pathname2url(filename)
1119
1120    try:
1121        fp = open(URLorFile,'r')
1122        cf = cif.ReadCif(fp)
1123        fp.close()
1124        return cf
1125    except IOError:
1126        return cif.ReadCif(URLorFile)
1127
1128def IndexAllIds(Histograms,Phases):
1129    '''Scan through the used phases & histograms and create an index
1130    to the random numbers of phases, histograms and atoms. While doing this,
1131    confirm that assigned random numbers are unique -- just in case lightning
1132    strikes twice in the same place.
1133
1134    Note: this code assumes that the atom random Id (ranId) is the last
1135    element each atom record.
1136
1137    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
1138    (which loads the histograms and phases from a GPX file),
1139    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
1140    (which loads the histograms and phases from the data tree.) and
1141    :meth:`GSASIIconstrGUI.UpdateConstraints`
1142    (which displays & edits the constraints in a GUI)
1143
1144    TODO: do we need a lookup for rigid body variables?
1145    '''
1146    # process phases and atoms
1147    PhaseIdLookup.clear()
1148    PhaseRanIdLookup.clear()
1149    AtomIdLookup.clear()
1150    AtomRanIdLookup.clear()
1151    ShortPhaseNames.clear()
1152    for ph in Phases:
1153        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
1154        ranId = Phases[ph]['ranId']
1155        while ranId in PhaseRanIdLookup:
1156            # Found duplicate random Id! note and reassign
1157            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
1158            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1159        pId = str(Phases[ph]['pId'])
1160        PhaseIdLookup[pId] = (ph,ranId)
1161        PhaseRanIdLookup[ranId] = pId
1162        shortname = ph  #[:10]
1163        while shortname in ShortPhaseNames.values():
1164            shortname = ph[:8] + ' ('+ pId + ')'
1165        ShortPhaseNames[pId] = shortname
1166        AtomIdLookup[pId] = {}
1167        AtomRanIdLookup[pId] = {}
1168        for iatm,at in enumerate(Phases[ph]['Atoms']):
1169            ranId = at[cia+8]
1170            while ranId in AtomRanIdLookup[pId]: # check for dups
1171                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
1172                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
1173            AtomRanIdLookup[pId][ranId] = str(iatm)
1174            if Phases[ph]['General']['Type'] == 'macromolecular':
1175                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
1176            else:
1177                label = at[ct-1]
1178            AtomIdLookup[pId][str(iatm)] = (label,ranId)
1179    # process histograms
1180    HistIdLookup.clear()
1181    HistRanIdLookup.clear()
1182    ShortHistNames.clear()
1183    for hist in Histograms:
1184        ranId = Histograms[hist]['ranId']
1185        while ranId in HistRanIdLookup:
1186            # Found duplicate random Id! note and reassign
1187            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1188            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
1189        hId = str(Histograms[hist]['hId'])
1190        HistIdLookup[hId] = (hist,ranId)
1191        HistRanIdLookup[ranId] = hId
1192        shortname = hist[:15]
1193        while shortname in ShortHistNames.values():
1194            shortname = hist[:11] + ' ('+ hId + ')'
1195        ShortHistNames[hId] = shortname
1196
1197def LookupAtomId(pId,ranId):
1198    '''Get the atom number from a phase and atom random Id
1199
1200    :param int/str pId: the sequential number of the phase
1201    :param int ranId: the random Id assigned to an atom
1202
1203    :returns: the index number of the atom (str)
1204    '''
1205    if not AtomRanIdLookup:
1206        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
1207    if pId is None or pId == '':
1208        raise KeyError('Error: phase is invalid (None or blank)')
1209    pId = str(pId)
1210    if pId not in AtomRanIdLookup:
1211        raise KeyError('Error: LookupAtomId does not have phase '+pId)
1212    if ranId not in AtomRanIdLookup[pId]:
1213        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
1214    return AtomRanIdLookup[pId][ranId]
1215
1216def LookupAtomLabel(pId,index):
1217    '''Get the atom label from a phase and atom index number
1218
1219    :param int/str pId: the sequential number of the phase
1220    :param int index: the index of the atom in the list of atoms
1221
1222    :returns: the label for the atom (str) and the random Id of the atom (int)
1223    '''
1224    if not AtomIdLookup:
1225        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
1226    if pId is None or pId == '':
1227        raise KeyError('Error: phase is invalid (None or blank)')
1228    pId = str(pId)
1229    if pId not in AtomIdLookup:
1230        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
1231    if index not in AtomIdLookup[pId]:
1232        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
1233    return AtomIdLookup[pId][index]
1234
1235def LookupPhaseId(ranId):
1236    '''Get the phase number and name from a phase random Id
1237
1238    :param int ranId: the random Id assigned to a phase
1239    :returns: the sequential Id (pId) number for the phase (str)
1240    '''
1241    if not PhaseRanIdLookup:
1242        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
1243    if ranId not in PhaseRanIdLookup:
1244        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
1245    return PhaseRanIdLookup[ranId]
1246
1247def LookupPhaseName(pId):
1248    '''Get the phase number and name from a phase Id
1249
1250    :param int/str pId: the sequential assigned to a phase
1251    :returns:  (phase,ranId) where phase is the name of the phase (str)
1252      and ranId is the random # id for the phase (int)
1253    '''
1254    if not PhaseIdLookup:
1255        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
1256    if pId is None or pId == '':
1257        raise KeyError('Error: phase is invalid (None or blank)')
1258    pId = str(pId)
1259    if pId not in PhaseIdLookup:
1260        raise KeyError('Error: LookupPhaseName does not have index '+pId)
1261    return PhaseIdLookup[pId]
1262
1263def LookupHistId(ranId):
1264    '''Get the histogram number and name from a histogram random Id
1265
1266    :param int ranId: the random Id assigned to a histogram
1267    :returns: the sequential Id (hId) number for the histogram (str)
1268    '''
1269    if not HistRanIdLookup:
1270        raise Exception('Error: LookupHistId called before IndexAllIds was run')
1271    if ranId not in HistRanIdLookup:
1272        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
1273    return HistRanIdLookup[ranId]
1274
1275def LookupHistName(hId):
1276    '''Get the histogram number and name from a histogram Id
1277
1278    :param int/str hId: the sequential assigned to a histogram
1279    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1280      and ranId is the random # id for the histogram (int)
1281    '''
1282    if not HistIdLookup:
1283        raise Exception('Error: LookupHistName called before IndexAllIds was run')
1284    if hId is None or hId == '':
1285        raise KeyError('Error: histogram is invalid (None or blank)')
1286    hId = str(hId)
1287    if hId not in HistIdLookup:
1288        raise KeyError('Error: LookupHistName does not have index '+hId)
1289    return HistIdLookup[hId]
1290
1291def fmtVarDescr(varname):
1292    '''Return a string with a more complete description for a GSAS-II variable
1293
1294    :param str varname: A full G2 variable name with 2 or 3 or 4
1295       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1296
1297    :returns: a string with the description
1298    '''
1299    s,l = VarDescr(varname)
1300    return s+": "+l
1301
1302def VarDescr(varname):
1303    '''Return two strings with a more complete description for a GSAS-II variable
1304
1305    :param str name: A full G2 variable name with 2 or 3 or 4
1306       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1307
1308    :returns: (loc,meaning) where loc describes what item the variable is mapped
1309      (phase, histogram, etc.) and meaning describes what the variable does.
1310    '''
1311
1312    # special handling for parameter names without a colons
1313    # for now, assume self-defining
1314    if varname.find(':') == -1:
1315        return "Global",varname
1316
1317    l = getVarDescr(varname)
1318    if not l:
1319        return ("invalid variable name ("+str(varname)+")!"),""
1320#        return "invalid variable name!",""
1321
1322    if not l[-1]:
1323        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1324
1325    if len(l) == 3:         #SASD variable name!
1326        s = 'component:'+l[1]
1327        return s,l[-1]
1328    s = ""
1329    if l[0] is not None and l[1] is not None: # HAP: keep short
1330        if l[2] == "Scale": # fix up ambigous name
1331            l[5] = "Phase fraction"
1332        if l[0] == '*':
1333            lbl = 'Seq. ref.'
1334        else:
1335            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1336        if l[1] == '*':
1337            hlbl = 'Seq. ref.'
1338        else:
1339            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1340        if hlbl[:4] == 'HKLF':
1341            hlbl = 'Xtl='+hlbl[5:]
1342        elif hlbl[:4] == 'PWDR':
1343            hlbl = 'Pwd='+hlbl[5:]
1344        else:
1345            hlbl = 'Hist='+hlbl
1346        s = "Ph="+str(lbl)+" * "+str(hlbl)
1347    else:
1348        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1349            l[5] = "Scale factor"
1350        if l[2] == 'Back': # background parameters are "special", alas
1351            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1352            l[-1] += ' #'+str(l[3])
1353        elif l[4] is not None: # rigid body parameter or modulation parm
1354            lbl = ShortPhaseNames.get(l[0],'phase?')
1355            if 'RB' in l[2]:    #rigid body parm
1356                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1357            else: #modulation parm
1358                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
1359        elif l[3] is not None: # atom parameter,
1360            lbl = ShortPhaseNames.get(l[0],'phase?')
1361            try:
1362                albl = LookupAtomLabel(l[0],l[3])[0]
1363            except KeyError:
1364                albl = 'Atom?'
1365            s = "Atom "+str(albl)+" in "+str(lbl)
1366        elif l[0] == '*':
1367            s = "All phases "
1368        elif l[0] is not None:
1369            lbl = ShortPhaseNames.get(l[0],'phase?')
1370            s = "Phase "+str(lbl)
1371        elif l[1] == '*':
1372            s = 'All hists'
1373        elif l[1] is not None:
1374            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1375            if hlbl[:4] == 'HKLF':
1376                hlbl = 'Xtl='+hlbl[5:]
1377            elif hlbl[:4] == 'PWDR':
1378                hlbl = 'Pwd='+hlbl[5:]
1379            else:
1380                hlbl = 'Hist='+hlbl
1381            s = str(hlbl)
1382    if not s:
1383        s = 'Global'
1384    return s,l[-1]
1385
1386def getVarDescr(varname):
1387    '''Return a short description for a GSAS-II variable
1388
1389    :param str name: A full G2 variable name with 2 or 3 or 4
1390       colons (<p>:<h>:name[:<a1>][:<a2>])
1391
1392    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1393      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1394      the histogram number and the atom number; `name` will always be
1395      a str; and `description` is str or `None`.
1396      If the variable name is incorrectly formed (for example, wrong
1397      number of colons), `None` is returned instead of a list.
1398    '''
1399    l = varname.split(':')
1400    if len(l) == 2:     #SASD parameter name
1401        return varname,l[0],getDescr(l[1])
1402    if len(l) == 3:
1403        l += [None,None]
1404    elif len(l) == 4:
1405        l += [None]
1406    elif len(l) != 5:
1407        return None
1408    for i in (0,1,3,4):
1409        if l[i] == "":
1410            l[i] = None
1411    l += [getDescr(l[2])]
1412    return l
1413
1414def CompileVarDesc():
1415    '''Set the values in the variable description lookup table (:attr:`VarDesc`)
1416    into :attr:`reVarDesc`. This is called in :func:`getDescr` so the initialization
1417    is always done before use.
1418
1419    Note that keys may contain regular expressions, where '[xyz]'
1420    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range of values).
1421    '.*' matches any string. For example::
1422
1423    'AUiso':'Atomic isotropic displacement parameter',
1424
1425    will match variable ``'p::AUiso:a'``.
1426    If parentheses are used in the key, the contents of those parentheses can be
1427    used in the value, such as::
1428
1429    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1430
1431    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1432    in the value when used.
1433
1434    '''
1435    if reVarDesc: return # already done
1436    for key,value in {
1437        # derived or other sequential vars
1438        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1439        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1440        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1441        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1442        # ambiguous, alas:
1443        'Scale' : 'Phase or Histogram scale factor',
1444        # Phase vars (p::<var>)
1445        'A([0-5])' : 'Reciprocal metric tensor component \\1',
1446        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
1447        # Atom vars (p::<var>:a)
1448        'dA([xyz])$' : 'change to atomic coordinate, \\1',
1449        'A([xyz])$' : '\\1 fractional atomic coordinate',
1450        'AUiso':'Atomic isotropic displacement parameter',
1451        'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1452        'Afrac': 'Atomic site fraction parameter',
1453        'Amul': 'Atomic site multiplicity value',
1454        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
1455        # Hist & Phase (HAP) vars (p:h:<var>)
1456        'Back': 'Background term',
1457        'BkPkint;(.*)':'Background peak #\\1 intensity',
1458        'BkPkpos;(.*)':'Background peak #\\1 position',
1459        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1460        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1461        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1462        'D([123][123])' : 'Anisotropic strain coef. \\1',
1463        'Extinction' : 'Extinction coef.',
1464        'MD' : 'March-Dollase coef.',
1465        'Mustrain;.*' : 'Microstrain coef.',
1466        'Size;.*' : 'Crystallite size value',
1467        'eA$' : 'Cubic mustrain value',
1468        'Ep$' : 'Primary extinction',
1469        'Es$' : 'Secondary type II extinction',
1470        'Eg$' : 'Secondary type I extinction',
1471        'Flack' : 'Flack parameter',
1472        'TwinFr' : 'Twin fraction',
1473        #Histogram vars (:h:<var>)
1474        'Absorption' : 'Absorption coef.',
1475        'Displace([XY])' : 'Debye-Scherrer sample displacement \\1',
1476        'Lam' : 'Wavelength',
1477        'Polariz\.' : 'Polarization correction',
1478        'SH/L' : 'FCJ peak asymmetry correction',
1479        '([UVW])$' : 'Gaussian instrument broadening \\1',
1480        '([XYZ])$' : 'Cauchy instrument broadening \\1',
1481        'Zero' : 'Debye-Scherrer zero correction',
1482        'nDebye' : 'Debye model background corr. terms',
1483        'nPeaks' : 'Fixed peak background corr. terms',
1484        'RBV.*' : 'Vector rigid body parameter',
1485        'RBR.*' : 'Residue rigid body parameter',
1486        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1487        'RBRP([xyz])' : 'Residue rigid body position parameter',
1488        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1489        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1490        'constr([0-9]*)' : 'Parameter from constraint',
1491        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1492        'mV([0-2])$' : 'Modulation vector component \\1',
1493        'Fsin'  :   'Sin site fraction modulation',
1494        'Fcos'  :   'Cos site fraction modulation',
1495        'Fzero'  :   'Crenel function offset',      #may go away
1496        'Fwid'   :   'Crenel function width',
1497        'Tmin'   :   'ZigZag/Block min location',
1498        'Tmax'   :   'ZigZag/Block max location',
1499        '([XYZ])max': 'ZigZag/Block max value for \\1',
1500        '([XYZ])sin'  : 'Sin position wave for \\1',
1501        '([XYZ])cos'  : 'Cos position wave for \\1',
1502        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1503        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1504        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1505        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1506        # PDF peak parms (l:<var>;l = peak no.)
1507        'PDFpos'  : 'PDF peak position',
1508        'PDFmag'  : 'PDF peak magnitude',
1509        'PDFsig'  : 'PDF peak std. dev.',
1510        # SASD vars (l:<var>;l = component)
1511        'Aspect ratio' : 'Particle aspect ratio',
1512        'Length' : 'Cylinder length',
1513        'Diameter' : 'Cylinder/disk diameter',
1514        'Thickness' : 'Disk thickness',
1515        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
1516        'Dist' : 'Interparticle distance',
1517        'VolFr' : 'Dense scatterer volume fraction',
1518        'epis' : 'Sticky sphere epsilon',
1519        'Sticky' : 'Stickyness',
1520        'Depth' : 'Well depth',
1521        'Width' : 'Well width',
1522        'Volume' : 'Particle volume',
1523        'Radius' : 'Sphere/cylinder/disk radius',
1524        'Mean' : 'Particle mean radius',
1525        'StdDev' : 'Standard deviation in Mean',
1526        'G$': 'Guinier prefactor',
1527        'Rg$': 'Guinier radius of gyration',
1528        'B$': 'Porod prefactor',
1529        'P$': 'Porod power',
1530        'Cutoff': 'Porod cutoff',
1531        'PkInt': 'Bragg peak intensity',
1532        'PkPos': 'Bragg peak position',
1533        'PkSig': 'Bragg peak sigma',
1534        'PkGam': 'Bragg peak gamma',
1535        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1536        'Dcalc': 'Calc. d-spacing',
1537        'Back$': 'background parameter',
1538        'pos$': 'peak position',
1539        'int$': 'peak intensity',
1540        'WgtFrac':'phase weight fraction',
1541        'alpha':'TOF profile term',
1542        'beta-[01q]':'TOF profile term',
1543        'sig-[012q]':'TOF profile term',
1544        'dif[ABC]':'TOF to d-space calibration',
1545        'C\([0-9]*,[0-9]*\)' : 'spherical harmonics preferred orientation coef.',
1546        }.items():
1547        VarDesc[key] = value
1548        reVarDesc[re.compile(key)] = value
1549
1550def getDescr(name):
1551    '''Return a short description for a GSAS-II variable
1552
1553    :param str name: The descriptive part of the variable name without colons (:)
1554
1555    :returns: a short description or None if not found
1556    '''
1557
1558    CompileVarDesc() # compile the regular expressions, if needed
1559    for key in reVarDesc:
1560        m = key.match(name)
1561        if m:
1562            reVarDesc[key]
1563            return m.expand(reVarDesc[key])
1564    return None
1565
1566def GenWildCard(varlist):
1567    '''Generate wildcard versions of G2 variables. These introduce '*'
1568    for a phase, histogram or atom number (but only for one of these
1569    fields) but only when there is more than one matching variable in the
1570    input variable list. So if the input is this::
1571
1572      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1573
1574    then the output will be this::
1575
1576       wildList = ['*::AUiso:0', '0::AUiso:*']
1577
1578    :param list varlist: an input list of GSAS-II variable names
1579      (such as 0::AUiso:0)
1580
1581    :returns: wildList, the generated list of wild card variable names.
1582    '''
1583    wild = []
1584    for i in (0,1,3):
1585        currentL = varlist[:]
1586        while currentL:
1587            item1 = currentL.pop(0)
1588            i1splt = item1.split(':')
1589            if i >= len(i1splt): continue
1590            if i1splt[i]:
1591                nextL = []
1592                i1splt[i] = '[0-9]+'
1593                rexp = re.compile(':'.join(i1splt))
1594                matchlist = [item1]
1595                for nxtitem in currentL:
1596                    if rexp.match(nxtitem):
1597                        matchlist += [nxtitem]
1598                    else:
1599                        nextL.append(nxtitem)
1600                if len(matchlist) > 1:
1601                    i1splt[i] = '*'
1602                    wild.append(':'.join(i1splt))
1603                currentL = nextL
1604    return wild
1605
1606def LookupWildCard(varname,varlist):
1607    '''returns a list of variable names from list varname
1608    that match wildcard name in varname
1609
1610    :param str varname: a G2 variable name containing a wildcard
1611      (such as \*::var)
1612    :param list varlist: the list of all variable names used in
1613      the current project
1614    :returns: a list of matching GSAS-II variables (may be empty)
1615    '''
1616    rexp = re.compile(varname.replace('*','[0-9]+'))
1617    return sorted([var for var in varlist if rexp.match(var)])
1618
1619
1620def _lookup(dic,key):
1621    '''Lookup a key in a dictionary, where None returns an empty string
1622    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1623    '''
1624    if key is None:
1625        return ""
1626    elif key == "*":
1627        return "*"
1628    else:
1629        return dic.get(key,'?')
1630
1631def SortVariables(varlist):
1632    '''Sorts variable names in a sensible manner
1633    '''
1634    def cvnnums(var):
1635        v = []
1636        for i in var.split(':'):
1637            if i == '':
1638                v.append(-1)
1639                continue
1640            try:
1641                v.append(int(i))
1642            except:
1643                v.append(i)
1644        return v
1645    return sorted(varlist,key=cvnnums)
1646
1647class G2VarObj(object):
1648    '''Defines a GSAS-II variable either using the phase/atom/histogram
1649    unique Id numbers or using a character string that specifies
1650    variables by phase/atom/histogram number (which can change).
1651    Note that :func:`LoadID` should be used to (re)load the current Ids
1652    before creating or later using the G2VarObj object.
1653
1654    This can store rigid body variables, but does not translate the residue # and
1655    body # to/from random Ids
1656
1657    A :class:`G2VarObj` object can be created with a single parameter:
1658
1659    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1660      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1661
1662     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
1663     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1664     * a is the atom number (which may be left blank in which case the third colon is omitted).
1665       The atom number can be specified as '*' if a phase number is specified (not as '*').
1666       For rigid body variables, specify a will be a string of form "residue:body#"
1667
1668      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1669      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1670      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1671      For a rigid body variables, AtomID is a string of form "residue:body#".
1672
1673    If four positional arguments are supplied, they are:
1674
1675    :param str/int phasenum: The number for the phase (or None or '*')
1676    :param str/int histnum: The number for the histogram (or None or '*')
1677    :param str varname: a single value can be used to create a :class:`G2VarObj`
1678    :param str/int atomnum: The number for the atom (or None or '*')
1679
1680    '''
1681    IDdict = {}
1682    IDdict['phases'] = {}
1683    IDdict['hists'] = {}
1684    IDdict['atoms'] = {}
1685    def __init__(self,*args):
1686        self.phase = None
1687        self.histogram = None
1688        self.name = ''
1689        self.atom = None
1690        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1691            # single arg with 4 values
1692            self.phase,self.histogram,self.name,self.atom = args[0]
1693        elif len(args) == 1 and ':' in args[0]:
1694            #parse a string
1695            lst = args[0].split(':')
1696            if lst[0] == '*':
1697                self.phase = '*'
1698                if len(lst) > 3:
1699                    self.atom = lst[3]
1700                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1701            elif lst[1] == '*':
1702                self.histogram = '*'
1703                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1704            else:
1705                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1706                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1707                if len(lst) == 4:
1708                    if lst[3] == '*':
1709                        self.atom = '*'
1710                    else:
1711                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1712                elif len(lst) == 5:
1713                    self.atom = lst[3]+":"+lst[4]
1714                elif len(lst) == 3:
1715                    pass
1716                else:
1717                    raise Exception("Too many colons in var name "+str(args[0]))
1718            self.name = lst[2]
1719        elif len(args) == 4:
1720            if args[0] == '*':
1721                self.phase = '*'
1722                self.atom = args[3]
1723            else:
1724                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1725                if args[3] == '*':
1726                    self.atom = '*'
1727                elif args[0] is not None:
1728                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1729            if args[1] == '*':
1730                self.histogram = '*'
1731            else:
1732                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1733            self.name = args[2]
1734        else:
1735            raise Exception("Incorrectly called GSAS-II parameter name")
1736
1737        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1738
1739    def __str__(self):
1740        return self.varname()
1741
1742    def varname(self):
1743        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1744        string (p:h:<var>:a) or (p:h:<var>)
1745
1746        :returns: the variable name as a str
1747        '''
1748        a = ""
1749        if self.phase == "*":
1750            ph = "*"
1751            if self.atom:
1752                a = ":" + str(self.atom)
1753        else:
1754            ph = _lookup(PhaseRanIdLookup,self.phase)
1755            if self.atom == '*':
1756                a = ':*'
1757            elif self.atom:
1758                if ":" in str(self.atom):
1759                    a = ":" + str(self.atom)
1760                elif ph in AtomRanIdLookup:
1761                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1762                else:
1763                    a = ":?"
1764        if self.histogram == "*":
1765            hist = "*"
1766        else:
1767            hist = _lookup(HistRanIdLookup,self.histogram)
1768        s = (ph + ":" + hist + ":" + str(self.name)) + a
1769        return s
1770
1771    def __repr__(self):
1772        '''Return the detailed contents of the object
1773        '''
1774        s = "<"
1775        if self.phase == '*':
1776            s += "Phases: all; "
1777            if self.atom is not None:
1778                if ":" in str(self.atom):
1779                    s += "Rigid body" + str(self.atom) + "; "
1780                else:
1781                    s += "Atom #" + str(self.atom) + "; "
1782        elif self.phase is not None:
1783            ph =  _lookup(PhaseRanIdLookup,self.phase)
1784            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1785            if self.atom == '*':
1786                s += "Atoms: all; "
1787            elif ":" in str(self.atom):
1788                s += "Rigid body" + str(self.atom) + "; "
1789            elif self.atom is not None:
1790                s += "Atom rId=" + str(self.atom)
1791                if ph in AtomRanIdLookup:
1792                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1793                else:
1794                    s += " (#? -- not found!); "
1795        if self.histogram == '*':
1796            s += "Histograms: all; "
1797        elif self.histogram is not None:
1798            hist = _lookup(HistRanIdLookup,self.histogram)
1799            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1800        s += 'Variable name="' + str(self.name) + '">'
1801        return s+" ("+self.varname()+")"
1802
1803    def __eq__(self, other):
1804        if type(other) is type(self):
1805            return (self.phase == other.phase and
1806                    self.histogram == other.histogram and
1807                    self.name == other.name and
1808                    self.atom == other.atom)
1809        return False
1810
1811    def _show(self):
1812        'For testing, shows the current lookup table'
1813        print ('phases'+ self.IDdict['phases'])
1814        print ('hists'+ self.IDdict['hists'])
1815        print ('atomDict'+ self.IDdict['atoms'])
1816
1817#==========================================================================
1818def SetDefaultSample():
1819    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
1820    return {
1821        'InstrName':'',
1822        'ranId':ran.randint(0,sys.maxsize),
1823        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
1824        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],'Diffuse':[],
1825        'Temperature':300.,'Pressure':0.1,'Time':0.0,
1826        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
1827        'Gonio. radius':200.0,
1828        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
1829#SASD items
1830        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
1831        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
1832        'Trans':1.0,                            #measured transmission
1833        'SlitLen':0.0,                          #Slit length - in Q(A-1)
1834        }
1835######################################################################
1836class ImportBaseclass(object):
1837    '''Defines a base class for the reading of input files (diffraction
1838    data, coordinates,...). See :ref:`Writing a Import Routine<Import_routines>`
1839    for an explanation on how to use a subclass of this class.
1840    '''
1841    class ImportException(Exception):
1842        '''Defines an Exception that is used when an import routine hits an expected error,
1843        usually in .Reader.
1844
1845        Good practice is that the Reader should define a value in self.errors that
1846        tells the user some information about what is wrong with their file.
1847        '''
1848        pass
1849
1850    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
1851    def __init__(self,formatName,longFormatName=None,
1852                 extensionlist=[],strictExtension=False,):
1853        self.formatName = formatName # short string naming file type
1854        if longFormatName: # longer string naming file type
1855            self.longFormatName = longFormatName
1856        else:
1857            self.longFormatName = formatName
1858        # define extensions that are allowed for the file type
1859        # for windows, remove any extensions that are duplicate, as case is ignored
1860        if sys.platform == 'windows' and extensionlist:
1861            extensionlist = list(set([s.lower() for s in extensionlist]))
1862        self.extensionlist = extensionlist
1863        # If strictExtension is True, the file will not be read, unless
1864        # the extension matches one in the extensionlist
1865        self.strictExtension = strictExtension
1866        self.errors = ''
1867        self.warnings = ''
1868        self.SciPy = False          #image reader needed scipy
1869        # used for readers that will use multiple passes to read
1870        # more than one data block
1871        self.repeat = False
1872        self.selections = []
1873        self.repeatcount = 0
1874        self.readfilename = '?'
1875        self.scriptable = False
1876        #print 'created',self.__class__
1877
1878    def ReInitialize(self):
1879        'Reinitialize the Reader to initial settings'
1880        self.errors = ''
1881        self.warnings = ''
1882        self.SciPy = False          #image reader needed scipy
1883        self.repeat = False
1884        self.repeatcount = 0
1885        self.readfilename = '?'
1886
1887
1888#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
1889#        '''This method must be supplied in the child class to read the file.
1890#        if the read fails either return False or raise an Exception
1891#        preferably of type ImportException.
1892#        '''
1893#        #start reading
1894#        raise ImportException("Error occurred while...")
1895#        self.errors += "Hint for user on why the error occur
1896#        return False # if an error occurs
1897#        return True # if read OK
1898
1899    def ExtensionValidator(self, filename):
1900        '''This methods checks if the file has the correct extension
1901        Return False if this filename will not be supported by this reader
1902        Return True if the extension matches the list supplied by the reader
1903        Return None if the reader allows un-registered extensions
1904        '''
1905        if filename:
1906            ext = ospath.splitext(filename)[1]
1907            if sys.platform == 'windows': ext = ext.lower()
1908            if ext in self.extensionlist: return True
1909            if self.strictExtension: return False
1910        return 
1911
1912    def ContentsValidator(self, filename):
1913        '''This routine will attempt to determine if the file can be read
1914        with the current format.
1915        This will typically be overridden with a method that
1916        takes a quick scan of [some of]
1917        the file contents to do a "sanity" check if the file
1918        appears to match the selected format.
1919        the file must be opened here with the correct format (binary/text)
1920        '''
1921        #filepointer.seek(0) # rewind the file pointer
1922        return True
1923
1924    def CIFValidator(self, filepointer):
1925        '''A :meth:`ContentsValidator` for use to validate CIF files.
1926        '''
1927        filepointer.seek(0)
1928        for i,l in enumerate(filepointer):
1929            if i >= 1000: return True
1930            '''Encountered only blank lines or comments in first 1000
1931            lines. This is unlikely, but assume it is CIF anyway, since we are
1932            even less likely to find a file with nothing but hashes and
1933            blank lines'''
1934            line = l.strip()
1935            if len(line) == 0: # ignore blank lines
1936                continue
1937            elif line.startswith('#'): # ignore comments
1938                continue
1939            elif line.startswith('data_'): # on the right track, accept this file
1940                return True
1941            else: # found something invalid
1942                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
1943                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
1944                    self.errors += '  '+str(l)
1945                else:
1946                    self.errors += '  (binary)'
1947                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
1948                self.errors += '\n        a data_ statement begins a block.'
1949                return False
1950
1951######################################################################
1952class ImportPhase(ImportBaseclass):
1953    '''Defines a base class for the reading of files with coordinates
1954
1955    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
1956    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase`.
1957    See :ref:`Writing a Import Routine<Import_Routines>`
1958    for an explanation on how to use this class.
1959
1960    '''
1961    def __init__(self,formatName,longFormatName=None,extensionlist=[],
1962        strictExtension=False,):
1963        # call parent __init__
1964        ImportBaseclass.__init__(self,formatName,longFormatName,
1965            extensionlist,strictExtension)
1966        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
1967        self.Constraints = None
1968
1969######################################################################
1970class ImportStructFactor(ImportBaseclass):
1971    '''Defines a base class for the reading of files with tables
1972    of structure factors.
1973
1974    Structure factors are read with a call to :meth:`GSASIIdataGUI.GSASII.OnImportSfact`
1975    which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`, which calls
1976    methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
1977    :meth:`Reader`.
1978
1979    See :ref:`Writing a Import Routine<Import_Routines>`
1980    for an explanation on how to use import classes in general. The specifics
1981    for reading a structure factor histogram require that
1982    the ``Reader()`` routine in the import
1983    class need to do only a few things: It
1984    should load :attr:`RefDict` item ``'RefList'`` with the reflection list,
1985    and set :attr:`Parameters` with the instrument parameters
1986    (initialized with :meth:`InitParameters` and set with :meth:`UpdateParameters`).
1987    '''
1988    def __init__(self,formatName,longFormatName=None,extensionlist=[],
1989        strictExtension=False,):
1990        ImportBaseclass.__init__(self,formatName,longFormatName,
1991            extensionlist,strictExtension)
1992
1993        # define contents of Structure Factor entry
1994        self.Parameters = []
1995        'self.Parameters is a list with two dicts for data parameter settings'
1996        self.InitParameters()
1997        self.RefDict = {'RefList':[],'FF':{},'Super':0}
1998        self.Banks = []             #for multi bank data (usually TOF)
1999        '''self.RefDict is a dict containing the reflection information, as read from the file.
2000        Item 'RefList' contains the reflection information. See the
2001        :ref:`Single Crystal Reflection Data Structure<XtalRefl_table>`
2002        for the contents of each row. Dict element 'FF'
2003        contains the form factor values for each element type; if this entry
2004        is left as initialized (an empty list) it will be initialized as needed later.
2005        '''
2006    def ReInitialize(self):
2007        'Reinitialize the Reader to initial settings'
2008        ImportBaseclass.ReInitialize(self)
2009        self.InitParameters()
2010        self.Banks = []             #for multi bank data (usually TOF)
2011        self.RefDict = {'RefList':[],'FF':{},'Super':0}
2012
2013    def InitParameters(self):
2014        'initialize the instrument parameters structure'
2015        Lambda = 0.70926
2016        HistType = 'SXC'
2017        self.Parameters = [{'Type':[HistType,HistType], # create the structure
2018                            'Lam':[Lambda,Lambda]
2019                            }, {}]
2020        'Parameters is a list with two dicts for data parameter settings'
2021
2022    def UpdateParameters(self,Type=None,Wave=None):
2023        'Revise the instrument parameters'
2024        if Type is not None:
2025            self.Parameters[0]['Type'] = [Type,Type]
2026        if Wave is not None:
2027            self.Parameters[0]['Lam'] = [Wave,Wave]
2028
2029######################################################################
2030class ImportPowderData(ImportBaseclass):
2031    '''Defines a base class for the reading of files with powder data.
2032
2033    Objects constructed that subclass this (in import/G2pwd_*.py etc.) will be used
2034    in :meth:`GSASIIdataGUI.GSASII.OnImportPowder`.
2035    See :ref:`Writing a Import Routine<Import_Routines>`
2036    for an explanation on how to use this class.
2037    '''
2038    def __init__(self,formatName,longFormatName=None,
2039        extensionlist=[],strictExtension=False,):
2040        ImportBaseclass.__init__(self,formatName,longFormatName,
2041            extensionlist,strictExtension)
2042        self.clockWd = None  # used in TOF
2043        self.ReInitialize()
2044
2045    def ReInitialize(self):
2046        'Reinitialize the Reader to initial settings'
2047        ImportBaseclass.ReInitialize(self)
2048        self.powderentry = ['',None,None] #  (filename,Pos,Bank)
2049        self.powderdata = [] # Powder dataset
2050        '''A powder data set is a list with items [x,y,w,yc,yb,yd]:
2051                np.array(x), # x-axis values
2052                np.array(y), # powder pattern intensities
2053                np.array(w), # 1/sig(intensity)^2 values (weights)
2054                np.array(yc), # calc. intensities (zero)
2055                np.array(yb), # calc. background (zero)
2056                np.array(yd), # obs-calc profiles
2057        '''
2058        self.comments = []
2059        self.idstring = ''
2060        self.Sample = SetDefaultSample() # default sample parameters
2061        self.Controls = {}  # items to be placed in top-level Controls
2062        self.GSAS = None     # used in TOF
2063        self.repeat_instparm = True # Should a parm file be
2064        #                             used for multiple histograms?
2065        self.instparm = None # name hint from file of instparm to use
2066        self.instfile = '' # full path name to instrument parameter file
2067        self.instbank = '' # inst parm bank number
2068        self.instmsg = ''  # a label that gets printed to show
2069                           # where instrument parameters are from
2070        self.numbanks = 1
2071        self.instdict = {} # place items here that will be transferred to the instrument parameters
2072        self.pwdparms = {} # place parameters that are transferred directly to the tree
2073                           # here (typically from an existing GPX file)
2074######################################################################
2075class ImportSmallAngleData(ImportBaseclass):
2076    '''Defines a base class for the reading of files with small angle data.
2077    See :ref:`Writing a Import Routine<Import_Routines>`
2078    for an explanation on how to use this class.
2079    '''
2080    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2081        strictExtension=False,):
2082
2083        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2084            strictExtension)
2085        self.ReInitialize()
2086
2087    def ReInitialize(self):
2088        'Reinitialize the Reader to initial settings'
2089        ImportBaseclass.ReInitialize(self)
2090        self.smallangleentry = ['',None,None] #  (filename,Pos,Bank)
2091        self.smallangledata = [] # SASD dataset
2092        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2093                np.array(x), # x-axis values
2094                np.array(y), # powder pattern intensities
2095                np.array(w), # 1/sig(intensity)^2 values (weights)
2096                np.array(yc), # calc. intensities (zero)
2097                np.array(yd), # obs-calc profiles
2098                np.array(yb), # preset bkg
2099        '''
2100        self.comments = []
2101        self.idstring = ''
2102        self.Sample = SetDefaultSample()
2103        self.GSAS = None     # used in TOF
2104        self.clockWd = None  # used in TOF
2105        self.numbanks = 1
2106        self.instdict = {} # place items here that will be transferred to the instrument parameters
2107
2108######################################################################
2109class ImportReflectometryData(ImportBaseclass):
2110    '''Defines a base class for the reading of files with reflectometry data.
2111    See :ref:`Writing a Import Routine<Import_Routines>`
2112    for an explanation on how to use this class.
2113    '''
2114    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2115        strictExtension=False,):
2116
2117        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2118            strictExtension)
2119        self.ReInitialize()
2120
2121    def ReInitialize(self):
2122        'Reinitialize the Reader to initial settings'
2123        ImportBaseclass.ReInitialize(self)
2124        self.reflectometryentry = ['',None,None] #  (filename,Pos,Bank)
2125        self.reflectometrydata = [] # SASD dataset
2126        '''A small angle data set is a list with items [x,y,w,yc,yd]:
2127                np.array(x), # x-axis values
2128                np.array(y), # powder pattern intensities
2129                np.array(w), # 1/sig(intensity)^2 values (weights)
2130                np.array(yc), # calc. intensities (zero)
2131                np.array(yd), # obs-calc profiles
2132                np.array(yb), # preset bkg
2133        '''
2134        self.comments = []
2135        self.idstring = ''
2136        self.Sample = SetDefaultSample()
2137        self.GSAS = None     # used in TOF
2138        self.clockWd = None  # used in TOF
2139        self.numbanks = 1
2140        self.instdict = {} # place items here that will be transferred to the instrument parameters
2141
2142######################################################################
2143class ImportPDFData(ImportBaseclass):
2144    '''Defines a base class for the reading of files with PDF G(R) data.
2145    See :ref:`Writing a Import Routine<Import_Routines>`
2146    for an explanation on how to use this class.
2147    '''
2148    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2149        strictExtension=False,):
2150
2151        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
2152            strictExtension)
2153        self.ReInitialize()
2154
2155    def ReInitialize(self):
2156        'Reinitialize the Reader to initial settings'
2157        ImportBaseclass.ReInitialize(self)
2158        self.pdfentry = ['',None,None] #  (filename,Pos,Bank)
2159        self.pdfdata = [] # PDF G(R) dataset
2160        '''A pdf g(r) data set is a list with items [x,y]:
2161                np.array(x), # r-axis values
2162                np.array(y), # pdf g(r)
2163        '''
2164        self.comments = []
2165        self.idstring = ''
2166        self.numbanks = 1
2167
2168######################################################################
2169class ImportImage(ImportBaseclass):
2170    '''Defines a base class for the reading of images
2171
2172    Images are read in only these places:
2173
2174      * Initial reading is typically done from a menu item
2175        with a call to :meth:`GSASIIdataGUI.GSASII.OnImportImage`
2176        which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`. That calls
2177        methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
2178        :meth:`Reader`. This returns a list of reader objects for each read image.
2179
2180      * Images are read alternatively in :func:`GSASIIIO.ReadImages`, which puts image info
2181        directly into the data tree.
2182
2183      * Images are reloaded with :func:`GSASIIIO.GetImageData`.
2184
2185    .. _Image_import_routines:
2186
2187    When reading an image, the ``Reader()`` routine in the ImportImage class
2188    should set:
2189
2190      * :attr:`Comments`: a list of strings (str),
2191      * :attr:`Npix`: the number of pixels in the image (int),
2192      * :attr:`Image`: the actual image as a numpy array (np.array)
2193      * :attr:`Data`: a dict defining image parameters (dict). Within this dict the following
2194        data items are needed:
2195
2196         * 'pixelSize': size of each pixel in microns (such as ``[200.,200.]``.
2197         * 'wavelength': wavelength in Angstoms.
2198         * 'distance': distance of detector from sample in cm.
2199         * 'center': uncalibrated center of beam on detector (such as ``[204.8,204.8]``.
2200         * 'size': size of image (such as ``[2048,2048]``).
2201         * 'ImageTag': image number or other keyword used to retrieve image from
2202           a multi-image data file (defaults to ``1`` if not specified).
2203         * 'sumfile': holds sum image file name if a sum was produced from a multi image file
2204
2205    optional data items:
2206
2207      * :attr:`repeat`: set to True if there are additional images to
2208        read in the file, False otherwise
2209      * :attr:`repeatcount`: set to the number of the image.
2210
2211    Note that the above is initialized with :meth:`InitParameters`.
2212    (Also see :ref:`Writing a Import Routine<Import_Routines>`
2213    for an explanation on how to use import classes in general.)
2214    '''
2215    def __init__(self,formatName,longFormatName=None,extensionlist=[],
2216        strictExtension=False,):
2217        ImportBaseclass.__init__(self,formatName,longFormatName,
2218            extensionlist,strictExtension)
2219        self.InitParameters()
2220
2221    def ReInitialize(self):
2222        'Reinitialize the Reader to initial settings -- not used at present'
2223        ImportBaseclass.ReInitialize(self)
2224        self.InitParameters()
2225
2226    def InitParameters(self):
2227        'initialize the instrument parameters structure'
2228        self.Comments = ['No comments']
2229        self.Data = {}
2230        self.Npix = 0
2231        self.Image = None
2232        self.repeat = False
2233        self.repeatcount = 1
2234        self.sumfile = ''
2235
2236    def LoadImage(self,ParentFrame,imagefile,imagetag=None):
2237        '''Optionally, call this after reading in an image to load it into the tree.
2238        This saves time by preventing a reread of the same information.
2239        '''
2240        if ParentFrame:
2241            ParentFrame.ImageZ = self.Image   # store the image for plotting
2242            ParentFrame.oldImagefile = imagefile # save the name of the last image file read
2243            ParentFrame.oldImageTag = imagetag   # save the tag of the last image file read
2244
2245#################################################################################################
2246# shortcut routines
2247exp = np.exp
2248sind = sin = s = lambda x: np.sin(x*np.pi/180.)
2249cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
2250tand = tan = t = lambda x: np.tan(x*np.pi/180.)
2251sqrt = sq = lambda x: np.sqrt(x)
2252pi = lambda: np.pi
2253class ExpressionObj(object):
2254    '''Defines an object with a user-defined expression, to be used for
2255    secondary fits or restraints. Object is created null, but is changed
2256    using :meth:`LoadExpression`. This contains only the minimum
2257    information that needs to be stored to save and load the expression
2258    and how it is mapped to GSAS-II variables.
2259    '''
2260    def __init__(self):
2261        self.expression = ''
2262        'The expression as a text string'
2263        self.assgnVars = {}
2264        '''A dict where keys are label names in the expression mapping to a GSAS-II
2265        variable. The value a G2 variable name.
2266        Note that the G2 variable name may contain a wild-card and correspond to
2267        multiple values.
2268        '''
2269        self.freeVars = {}
2270        '''A dict where keys are label names in the expression mapping to a free
2271        parameter. The value is a list with:
2272
2273         * a name assigned to the parameter
2274         * a value for to the parameter and
2275         * a flag to determine if the variable is refined.
2276        '''
2277        self.depVar = None
2278
2279        self.lastError = ('','')
2280        '''Shows last encountered error in processing expression
2281        (list of 1-3 str values)'''
2282
2283        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
2284        self.distance_atoms = None  # to be used for defining atom distances
2285
2286    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
2287        '''Load the expression and associated settings into the object. Raises
2288        an exception if the expression is not parsed, if not all functions
2289        are defined or if not all needed parameter labels in the expression
2290        are defined.
2291
2292        This will not test if the variable referenced in these definitions
2293        are actually in the parameter dictionary. This is checked when the
2294        computation for the expression is done in :meth:`SetupCalc`.
2295
2296        :param str expr: the expression
2297        :param list exprVarLst: parameter labels found in the expression
2298        :param dict varSelect: this will be 0 for Free parameters
2299          and non-zero for expression labels linked to G2 variables.
2300        :param dict varName: Defines a name (str) associated with each free parameter
2301        :param dict varValue: Defines a value (float) associated with each free parameter
2302        :param dict varRefflag: Defines a refinement flag (bool)
2303          associated with each free parameter
2304        '''
2305        self.expression = expr
2306        self.compiledExpr = None
2307        self.freeVars = {}
2308        self.assgnVars = {}
2309        for v in exprVarLst:
2310            if varSelect[v] == 0:
2311                self.freeVars[v] = [
2312                    varName.get(v),
2313                    varValue.get(v),
2314                    varRefflag.get(v),
2315                    ]
2316            else:
2317                self.assgnVars[v] = varName[v]
2318        self.CheckVars()
2319
2320    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
2321        '''Load the expression and associated settings from the object into
2322        arrays used for editing.
2323
2324        :param list exprVarLst: parameter labels found in the expression
2325        :param dict varSelect: this will be 0 for Free parameters
2326          and non-zero for expression labels linked to G2 variables.
2327        :param dict varName: Defines a name (str) associated with each free parameter
2328        :param dict varValue: Defines a value (float) associated with each free parameter
2329        :param dict varRefflag: Defines a refinement flag (bool)
2330          associated with each free parameter
2331
2332        :returns: the expression as a str
2333        '''
2334        for v in self.freeVars:
2335            varSelect[v] = 0
2336            varName[v] = self.freeVars[v][0]
2337            varValue[v] = self.freeVars[v][1]
2338            varRefflag[v] = self.freeVars[v][2]
2339        for v in self.assgnVars:
2340            varSelect[v] = 1
2341            varName[v] = self.assgnVars[v]
2342        return self.expression
2343
2344    def GetVaried(self):
2345        'Returns the names of the free parameters that will be refined'
2346        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
2347
2348    def GetVariedVarVal(self):
2349        'Returns the names and values of the free parameters that will be refined'
2350        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
2351
2352    def UpdateVariedVars(self,varyList,values):
2353        'Updates values for the free parameters (after a refinement); only updates refined vars'
2354        for v in self.freeVars:
2355            if not self.freeVars[v][2]: continue
2356            if "::"+self.freeVars[v][0] not in varyList: continue
2357            indx = varyList.index("::"+self.freeVars[v][0])
2358            self.freeVars[v][1] = values[indx]
2359
2360    def GetIndependentVars(self):
2361        'Returns the names of the required independent parameters used in expression'
2362        return [self.assgnVars[v] for v in self.assgnVars]
2363
2364    def CheckVars(self):
2365        '''Check that the expression can be parsed, all functions are
2366        defined and that input loaded into the object is internally
2367        consistent. If not an Exception is raised.
2368
2369        :returns: a dict with references to packages needed to
2370          find functions referenced in the expression.
2371        '''
2372        ret = self.ParseExpression(self.expression)
2373        if not ret:
2374            raise Exception("Expression parse error")
2375        exprLblList,fxnpkgdict = ret
2376        # check each var used in expression is defined
2377        defined = self.assgnVars.keys() + self.freeVars.keys()
2378        notfound = []
2379        for var in exprLblList:
2380            if var not in defined:
2381                notfound.append(var)
2382        if notfound:
2383            msg = 'Not all variables defined'
2384            msg1 = 'The following variables were not defined: '
2385            msg2 = ''
2386            for var in notfound:
2387                if msg: msg += ', '
2388                msg += var
2389            self.lastError = (msg1,'  '+msg2)
2390            raise Exception(msg)
2391        return fxnpkgdict
2392
2393    def ParseExpression(self,expr):
2394        '''Parse an expression and return a dict of called functions and
2395        the variables used in the expression. Returns None in case an error
2396        is encountered. If packages are referenced in functions, they are loaded
2397        and the functions are looked up into the modules global
2398        workspace.
2399
2400        Note that no changes are made to the object other than
2401        saving an error message, so that this can be used for testing prior
2402        to the save.
2403
2404        :returns: a list of used variables
2405        '''
2406        self.lastError = ('','')
2407        import ast
2408        def FindFunction(f):
2409            '''Find the object corresponding to function f
2410            :param str f: a function name such as 'numpy.exp'
2411            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
2412              that defines the package location(s) and where pkgobj
2413              defines the object associated with the function.
2414              If the function is not found, pkgobj is None.
2415            '''
2416            df = f.split('.')
2417            pkgdict = {}
2418            # no listed package, try in current namespace
2419            if len(df) == 1:
2420                try:
2421                    fxnobj = eval(f)
2422                    return pkgdict,fxnobj
2423                except (AttributeError, NameError):
2424                    return None,None
2425            else:
2426                try:
2427                    fxnobj = eval(f)
2428                    pkgdict[df[0]] = eval(df[0])
2429                    return pkgdict,fxnobj
2430                except (AttributeError, NameError):
2431                    pass
2432            # includes a package, lets try to load the packages
2433            pkgname = ''
2434            path = sys.path+['./',]
2435            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
2436                if pkgname:
2437                    pkgname += '.' + pkg
2438                else:
2439                    pkgname = pkg
2440                fp = None
2441                try:
2442                    fp, fppath,desc = imp.find_module(pkg,path)
2443                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
2444                    pkgdict[pkgname] = pkgobj
2445                    path = [fppath]
2446                except Exception as msg:
2447                    print('load of '+pkgname+' failed with error='+str(msg))
2448                    return {},None
2449                finally:
2450                    if fp: fp.close()
2451                try:
2452                    #print 'before',pkgdict.keys()
2453                    fxnobj = eval(f,globals(),pkgdict)
2454                    #print 'after 1',pkgdict.keys()
2455                    #fxnobj = eval(f,pkgdict)
2456                    #print 'after 2',pkgdict.keys()
2457                    return pkgdict,fxnobj
2458                except:
2459                    continue
2460            return None # not found
2461        def ASTtransverse(node,fxn=False):
2462            '''Transverse a AST-parsed expresson, compiling a list of variables
2463            referenced in the expression. This routine is used recursively.
2464
2465            :returns: varlist,fxnlist where
2466              varlist is a list of referenced variable names and
2467              fxnlist is a list of used functions
2468            '''
2469            varlist = []
2470            fxnlist = []
2471            if isinstance(node, list):
2472                for b in node:
2473                    v,f = ASTtransverse(b,fxn)
2474                    varlist += v
2475                    fxnlist += f
2476            elif isinstance(node, ast.AST):
2477                for a, b in ast.iter_fields(node):
2478                    if isinstance(b, ast.AST):
2479                        if a == 'func':
2480                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
2481                            continue
2482                        v,f = ASTtransverse(b,fxn)
2483                        varlist += v
2484                        fxnlist += f
2485                    elif isinstance(b, list):
2486                        v,f = ASTtransverse(b,fxn)
2487                        varlist += v
2488                        fxnlist += f
2489                    elif node.__class__.__name__ == "Name":
2490                        varlist += [b]
2491                    elif fxn and node.__class__.__name__ == "Attribute":
2492                        varlist += [b]
2493            return varlist,fxnlist
2494        try:
2495            exprast = ast.parse(expr)
2496        except SyntaxError:
2497            s = ''
2498            import traceback
2499            for i in traceback.format_exc().splitlines()[-3:-1]:
2500                if s: s += "\n"
2501                s += str(i)
2502            self.lastError = ("Error parsing expression:",s)
2503            return
2504        # find the variables & functions
2505        v,f = ASTtransverse(exprast)
2506        varlist = sorted(list(set(v)))
2507        fxnlist = list(set(f))
2508        pkgdict = {}
2509        # check the functions are defined
2510        for fxn in fxnlist:
2511            fxndict,fxnobj = FindFunction(fxn)
2512            if not fxnobj:
2513                self.lastError = ("Error: Invalid function",fxn,
2514                                  "is not defined")
2515                return
2516            if not hasattr(fxnobj,'__call__'):
2517                self.lastError = ("Error: Not a function.",fxn,
2518                                  "cannot be called as a function")
2519                return
2520            pkgdict.update(fxndict)
2521        return varlist,pkgdict
2522
2523    def GetDepVar(self):
2524        'return the dependent variable, or None'
2525        return self.depVar
2526
2527    def SetDepVar(self,var):
2528        'Set the dependent variable, if used'
2529        self.depVar = var
2530#==========================================================================
2531class ExpressionCalcObj(object):
2532    '''An object used to evaluate an expression from a :class:`ExpressionObj`
2533    object.
2534
2535    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
2536      an expression string and mappings for the parameter labels in that object.
2537    '''
2538    def __init__(self,exprObj):
2539        self.eObj = exprObj
2540        'The expression and mappings; a :class:`ExpressionObj` object'
2541        self.compiledExpr = None
2542        'The expression as compiled byte-code'
2543        self.exprDict = {}
2544        '''dict that defines values for labels used in expression and packages
2545        referenced by functions
2546        '''
2547        self.lblLookup = {}
2548        '''Lookup table that specifies the expression label name that is
2549        tied to a particular GSAS-II parameters in the parmDict.
2550        '''
2551        self.fxnpkgdict = {}
2552        '''a dict with references to packages needed to
2553        find functions referenced in the expression.
2554        '''
2555        self.varLookup = {}
2556        '''Lookup table that specifies the GSAS-II variable(s)
2557        indexed by the expression label name. (Used for only for diagnostics
2558        not evaluation of expression.)
2559        '''
2560        self.su = None
2561        '''Standard error evaluation where supplied by the evaluator
2562        '''
2563        # Patch: for old-style expressions with a (now removed step size)
2564        if '2' in platform.python_version_tuple()[0]: 
2565            basestr = basestring
2566        else:
2567            basestr = str
2568        for v in self.eObj.assgnVars:
2569            if not isinstance(self.eObj.assgnVars[v], basestr):
2570                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
2571        self.parmDict = {}
2572        '''A copy of the parameter dictionary, for distance and angle computation
2573        '''
2574
2575    def SetupCalc(self,parmDict):
2576        '''Do all preparations to use the expression for computation.
2577        Adds the free parameter values to the parameter dict (parmDict).
2578        '''
2579        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2580            return
2581        self.fxnpkgdict = self.eObj.CheckVars()
2582        # all is OK, compile the expression
2583        self.compiledExpr = compile(self.eObj.expression,'','eval')
2584
2585        # look at first value in parmDict to determine its type
2586        parmsInList = True
2587        if '2' in platform.python_version_tuple()[0]: 
2588            basestr = basestring
2589        else:
2590            basestr = str
2591        for key in parmDict:
2592            val = parmDict[key]
2593            if isinstance(val, basestr):
2594                parmsInList = False
2595                break
2596            try: # check if values are in lists
2597                val = parmDict[key][0]
2598            except (TypeError,IndexError):
2599                parmsInList = False
2600            break
2601
2602        # set up the dicts needed to speed computations
2603        self.exprDict = {}
2604        self.lblLookup = {}
2605        self.varLookup = {}
2606        for v in self.eObj.freeVars:
2607            varname = self.eObj.freeVars[v][0]
2608            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
2609            self.lblLookup[varname] = v
2610            self.varLookup[v] = varname
2611            if parmsInList:
2612                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
2613            else:
2614                parmDict[varname] = self.eObj.freeVars[v][1]
2615            self.exprDict[v] = self.eObj.freeVars[v][1]
2616        for v in self.eObj.assgnVars:
2617            varname = self.eObj.assgnVars[v]
2618            if varname in parmDict:
2619                self.lblLookup[varname] = v
2620                self.varLookup[v] = varname
2621                if parmsInList:
2622                    self.exprDict[v] = parmDict[varname][0]
2623                else:
2624                    self.exprDict[v] = parmDict[varname]
2625            elif '*' in varname:
2626                varlist = LookupWildCard(varname,list(parmDict.keys()))
2627                if len(varlist) == 0:
2628                    raise Exception("No variables match "+str(v))
2629                for var in varlist:
2630                    self.lblLookup[var] = v
2631                if parmsInList:
2632                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
2633                else:
2634                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
2635                self.varLookup[v] = [var for var in varlist]
2636            else:
2637                self.exprDict[v] = None
2638#                raise Exception,"No value for variable "+str(v)
2639        self.exprDict.update(self.fxnpkgdict)
2640
2641    def UpdateVars(self,varList,valList):
2642        '''Update the dict for the expression with a set of values
2643        :param list varList: a list of variable names
2644        :param list valList: a list of corresponding values
2645        '''
2646        for var,val in zip(varList,valList):
2647            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
2648
2649    def UpdateDict(self,parmDict):
2650        '''Update the dict for the expression with values in a dict
2651        :param list parmDict: a dict of values some of which may be in use here
2652        '''
2653        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
2654            self.parmDict = parmDict
2655            return
2656        for var in parmDict:
2657            if var in self.lblLookup:
2658                self.exprDict[self.lblLookup[var]] = parmDict[var]
2659
2660    def EvalExpression(self):
2661        '''Evaluate an expression. Note that the expression
2662        and mapping are taken from the :class:`ExpressionObj` expression object
2663        and the parameter values were specified in :meth:`SetupCalc`.
2664        :returns: a single value for the expression. If parameter
2665        values are arrays (for example, from wild-carded variable names),
2666        the sum of the resulting expression is returned.
2667
2668        For example, if the expression is ``'A*B'``,
2669        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
2670
2671        [0.5, 1, 0.5]
2672
2673        then the result will be ``4.0``.
2674        '''
2675        self.su = None
2676        if self.eObj.expression.startswith('Dist'):
2677#            GSASIIpath.IPyBreak()
2678            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
2679            return dist
2680        elif self.eObj.expression.startswith('Angle'):
2681            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
2682            return angle
2683        if self.compiledExpr is None:
2684            raise Exception("EvalExpression called before SetupCalc")
2685        try:
2686            val = eval(self.compiledExpr,globals(),self.exprDict)
2687        except TypeError:
2688            val = None
2689        if not np.isscalar(val):
2690            val = np.sum(val)
2691        return val
2692
2693class G2Exception(Exception):
2694    def __init__(self,msg):
2695        self.msg = msg
2696    def __str__(self):
2697        return repr(self.msg)
2698
2699def HowDidIgetHere(wherecalledonly=False):
2700    '''Show a traceback with calls that brought us to the current location.
2701    Used for debugging.
2702    '''
2703    import traceback
2704    if wherecalledonly:
2705        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
2706        print(i.strip().rstrip())
2707    else:
2708        print (70*'*')
2709        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
2710        print (70*'*')
2711
2712def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
2713    '''Create and initialize a new set of PDF tree entries
2714
2715    :param Frame G2frame: main GSAS-II tree frame object
2716    :param str PWDRtree: name of PWDR to be used to create PDF item
2717    :param dict ElList: data structure with composition
2718    :param list Qlimits: Q limits to be used for computing the PDF
2719    :param float numAtm: no. atom in chemical formula
2720    :param float FltBkg: flat background value
2721    :param list PDFnames: previously used PDF names
2722
2723    :returns: the Id of the newly created PDF entry
2724    '''
2725    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
2726    if PDFname in PDFnames:
2727        print('Skipping, entry already exists: '+PDFname)
2728        return None
2729    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
2730    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
2731    Data = {
2732        'Sample':{'Name':PWDRtree,'Mult':1.0},
2733        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
2734        'Container':{'Name':'','Mult':-1.0,'Refine':False},
2735        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
2736        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
2737        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
2738        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
2739        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
2740    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
2741    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
2742        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
2743    return Id
2744
2745class ShowTiming(object):
2746    '''An object to use for timing repeated sections of code.
2747
2748    Create the object with::
2749       tim0 = ShowTiming()
2750
2751    Tag sections of code to be timed with::
2752       tim0.start('start')
2753       tim0.start('in section 1')
2754       tim0.start('in section 2')
2755       
2756    etc. (Note that each section should have a unique label.)
2757
2758    After the last section, end timing with::
2759       tim0.end()
2760
2761    Show timing results with::
2762       tim0.show()
2763       
2764    '''
2765    import time
2766    def __init__(self):
2767        self.timeSum =  []
2768        self.timeStart = []
2769        self.label = []
2770        self.prev = None
2771    def start(self,label):
2772        if label in self.label:
2773            i = self.label.index(label)
2774            self.timeStart[i] = time.time()
2775        else:
2776            i = len(self.label)
2777            self.timeSum.append(0.0)
2778            self.timeStart.append(time.time())
2779            self.label.append(label)
2780        if self.prev is not None:
2781            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
2782        self.prev = i
2783    def end(self):
2784        if self.prev is not None:
2785            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
2786        self.prev = None
2787    def show(self):
2788        sumT = sum(self.timeSum)
2789        print('Timing results (total={:.2f} sec)'.format(sumT))
2790        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
2791            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
2792
2793
2794if __name__ == "__main__":
2795    # test equation evaluation
2796    def showEQ(calcobj):
2797        print (50*'=')
2798        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
2799        for v in sorted(calcobj.varLookup):
2800            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
2801        # print '  Derivatives'
2802        # for v in calcobj.derivStep.keys():
2803        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2804
2805    obj = ExpressionObj()
2806
2807    obj.expression = "A*np.exp(B)"
2808    obj.assgnVars =  {'B': '0::Afrac:1'}
2809    obj.freeVars =  {'A': [u'A', 0.5, True]}
2810    #obj.CheckVars()
2811    calcobj = ExpressionCalcObj(obj)
2812
2813    obj1 = ExpressionObj()
2814    obj1.expression = "A*np.exp(B)"
2815    obj1.assgnVars =  {'B': '0::Afrac:*'}
2816    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
2817    #obj.CheckVars()
2818    calcobj1 = ExpressionCalcObj(obj1)
2819
2820    obj2 = ExpressionObj()
2821    obj2.distance_stuff = np.array([[0,1],[1,-1]])
2822    obj2.expression = "Dist(1,2)"
2823    GSASIIpath.InvokeDebugOpts()
2824    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2825    calcobj2 = ExpressionCalcObj(obj2)
2826    calcobj2.SetupCalc(parmDict2)
2827    showEQ(calcobj2)
2828
2829    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2830    print ('\nDict = '+parmDict1)
2831    calcobj.SetupCalc(parmDict1)
2832    showEQ(calcobj)
2833    calcobj1.SetupCalc(parmDict1)
2834    showEQ(calcobj1)
2835
2836    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2837    print ('Dict = '+parmDict2)
2838    calcobj.SetupCalc(parmDict2)
2839    showEQ(calcobj)
2840    calcobj1.SetupCalc(parmDict2)
2841    showEQ(calcobj1)
2842    calcobj2.SetupCalc(parmDict2)
2843    showEQ(calcobj2)
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