source: trunk/GSASIIobj.py @ 1331

Last change on this file since 1331 was 1331, checked in by vondreele, 8 years ago

fix cake integration problem - in G2IO return in wrong indent
fix seq refinement display problem in G2obj self.eObj.assgnVars[v] returned a list not a name

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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2014-05-06 21:41:45 +0000 (Tue, 06 May 2014) $
5# $Author: vondreele $
6# $Revision: 1331 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 1331 2014-05-06 21:41:45Z vondreele $
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. (dict)
259MCSA            \            Monte-Carlo simulated annealing parameters (dict)
260\           
261==========  ===============  ====================================================
262
263Rigid Body Objects
264------------------
265
266.. _RBData_table:
267
268.. index::
269   single: Rigid Body Data description
270   single: Data object descriptions; Rigid Body Data
271   
272Rigid body descriptions are available for two types of rigid bodies: 'Vector'
273and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
274with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
275with defined refinable torsion angles.
276
277.. tabularcolumns:: |l|l|p{4in}|
278
279==========  ===============  ====================================================
280  key         sub-key        explanation
281==========  ===============  ====================================================
282Vector      RBId             vector rigid bodies (dict of dict)
283\           AtInfo           Drad, Color: atom drawing radius & color for each atom type (dict)
284\           RBname           Name assigned by user to rigid body (str)
285\           VectMag          vector magnitudes in A (list)
286\           rbXYZ            Cartesian coordinates for Vector rigid body (list of 3 float)
287\           rbRef            3 assigned reference atom nos. in rigid body for origin
288                             definition, use center of atoms flag (list of 3 int & 1 bool)
289\           VectRef          refinement flags for VectMag values (list of bool)
290\           rbTypes          Atom types for each atom in rigid body (list of str)
291\           rbVect           Cartesian vectors for each translation used to build rigid body (list of lists)
292\           useCount         Number of times rigid body is used in any structure (int)
293Residue     RBId             residue rigid bodies (dict of dict)
294\           AtInfo           Drad, Color: atom drawing radius & color for each atom type(dict)
295\           RBname           Name assigned by user to rigid body (str)
296\           rbXYZ            Cartesian coordinates for Residue rigid body (list of 3 float)
297\           rbTypes          Atom types for each atom in rigid body (list of str)
298\           atNames          Names of each atom in rigid body (e.g. C1,N2...) (list of str)
299\           rbRef            3 assigned reference atom nos. in rigid body for origin
300                             definition, use center of atoms flag (list of 3 int & 1 bool)
301\           rbSeq            Orig,Piv,angle,Riding (list): definition of internal rigid body
302                             torsion; origin atom (int), pivot atom (int), torsion angle (float),
303                             riding atoms (list of int)
304\           SelSeq           [int,int] used by SeqSizer to identify objects
305\           useCount         Number of times rigid body is used in any structure (int)
306RBIds           \            unique Ids generated upon creation of each rigid body (dict)
307\           Vector           Ids for each Vector rigid body (list)
308\           Residue          Ids for each Residue rigid body (list)
309==========  ===============  ====================================================
310
311Space Group Objects
312-------------------
313
314.. _SGData_table:
315
316.. index::
317   single: Space Group Data description
318   single: Data object descriptions; Space Group Data
319
320Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
321and the information is placed in a SGdata object
322which is a dict with these keys:
323
324.. tabularcolumns:: |l|p{4.5in}|
325
326==========  ====================================================
327  key         explanation
328==========  ====================================================
329SpGrp       space group symbol (str)
330Laue        one of the following 14 Laue classes:
331            -1, 2/m, mmm, 4/m, 4/mmm, 3R,
332            3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m (str)
333SGInv       True if centrosymmetric, False if not (bool)
334SGLatt      Lattice centering type. Will be one of
335            P, A, B, C, I, F, R (str)
336SGUniq      unique axis if monoclinic. Will be
337            a, b, or c for monoclinic space groups.
338            Will be blank for non-monoclinic. (str)
339SGCen       Symmetry cell centering vectors. A (n,3) np.array
340            of centers. Will always have at least one row:
341            ``np.array([[0, 0, 0]])``
342SGOps       symmetry operations as a list of form
343            ``[[M1,T1], [M2,T2],...]``
344            where :math:`M_n` is a 3x3 np.array
345            and :math:`T_n` is a length 3 np.array.
346            Atom coordinates are transformed where the
347            Asymmetric unit coordinates [X is (x,y,z)]
348            are transformed using
349            :math:`X^\prime = M_n*X+T_n`
350SGSys       symmetry unit cell: type one of
351            'triclinic', 'monoclinic', 'orthorhombic',
352            'tetragonal', 'rhombohedral', 'trigonal',
353            'hexagonal', 'cubic' (str)
354SGPolax     Axes for space group polarity. Will be one of
355            '', 'x', 'y', 'x y', 'z', 'x z', 'y z',
356            'xyz'. In the case where axes are arbitrary
357            '111' is used (P 1, and ?).
358==========  ====================================================
359
360Atom Records
361------------
362
363.. _Atoms_table:
364
365.. index::
366   single: Atoms record description
367   single: Data object descriptions; Atoms record
368
369
370If ``phasedict`` points to the phase information in the data tree, then
371atoms are contained in a list of atom records (list) in
372``phasedict['Atoms']``. Also needed to read atom information
373are four pointers, ``cx,ct,cs,cia = phasedict['General']['atomPtrs']``,
374which define locations in the atom record, as shown below. Items shown are
375always present; additional ones for macromolecular phases are marked 'mm'
376
377.. tabularcolumns:: |l|p{4.5in}|
378
379==============   ====================================================
380location         explanation
381==============   ====================================================
382ct-4              mm - residue number (str)
383ct-3              mm - residue name (e.g. ALA) (str)
384ct-2              mm - chain label (str)
385ct-1              atom label (str)
386ct                atom type (str)
387ct+1              refinement flags; combination of 'F', 'X', 'U' (str)
388cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
389cs                site symmetry (str)
390cs+1              site multiplicity (int)
391cia               ADP flag: Isotropic ('I') or Anisotropic ('A')
392cia+1             Uiso (float)
393cia+2...cia+6     U11, U22, U33, U12, U13, U23 (6 floats)
394atom[-1]                unique atom identifier (int)
395==============   ====================================================
396
397Drawing Atom Records
398--------------------
399
400.. _Drawing_atoms_table:
401
402.. index::
403   single: Drawing atoms record description
404   single: Data object descriptions; Drawing atoms record
405
406
407If ``phasedict`` points to the phase information in the data tree, then
408drawing atoms are contained in a list of drawing atom records (list) in
409``phasedict['Drawing']['Atoms']``. Also needed to read atom information
410are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
411which define locations in the atom record, as shown below. Items shown are
412always present; additional ones for macromolecular phases are marked 'mm'
413
414.. tabularcolumns:: |l|p{4.5in}|
415
416==============   ====================================================
417location         explanation
418==============   ====================================================
419ct-4              mm - residue number (str)
420ct-3              mm - residue name (e.g. ALA) (str)
421ct-2              mm - chain label (str)
422ct-1              atom label (str)
423ct                atom type (str)
424cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
425cs-1              Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
426cs                atom drawing style; e.g. 'balls & sticks' (str)
427cs+1              atom label style (e.g. 'name') (str)
428cs+2              atom color (RBG triplet) (int)
429cs+3              ADP flag: Isotropic ('I') or Anisotropic ('A')
430cs+4              Uiso (float)
431cs+5...cs+11      U11, U22, U33, U12, U13, U23 (6 floats)
432ci                unique atom identifier; matches source atom Id in Atom Records (int)
433==============   ====================================================
434
435Powder Diffraction Tree Items
436-----------------------------
437
438.. _Powder_table:
439
440.. index::
441   single: Powder data object description
442   single: Data object descriptions; Powder Data
443
444Every powder diffraction histogram is stored in the GSAS-II data tree
445with a top-level entry named beginning with the string "PWDR ". The
446diffraction data for that information are directly associated with
447that tree item and there are a series of children to that item. The
448routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
449and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
450load this information into a dictionary where the child tree name is
451used as a key, and the information in the main entry is assigned
452a key of ``Data``, as outlined below.
453
454.. tabularcolumns:: |l|l|p{4in}|
455
456======================  ===============  ====================================================
457  key                      sub-key        explanation
458======================  ===============  ====================================================
459Comments                      \           Text strings extracted from the original powder
460                                          data header. These cannot be changed by the user;
461                                          it may be empty.
462Limits                       \            A list of two two element lists, as [[Ld,Hd],[L,H]]
463                                          where L and Ld are the current and default lowest
464                                          two-theta value to be used and
465                                          where H and Hd are the current and default highest
466                                          two-theta value to be used.
467Reflection Lists              \           A dict with an entry for each phase in the
468                                          histogram. The contents of each dict item
469                                          is a dict containing reflections, as described in
470                                          the :ref:`Powder Reflections <PowderRefl_table>`
471                                          description.
472Instrument Parameters         \           A list containing two dicts where the possible
473                                          keys in each dict are listed below. The value
474                                          for each item is a list containing three values:
475                                          the initial value, the current value and a
476                                          refinement flag which can have a value of
477                                          True, False or 0 where 0 indicates a value that
478                                          cannot be refined. The first and second
479                                          values are floats unless otherwise noted.
480                                          Items in the first dict are noted as [1]
481\                         Lam             Specifies a wavelength in Angstroms [1]
482\                         Lam1            Specifies the primary wavelength in
483                                          Angstrom, when an alpha1, alpha2
484                                          source is used [1]
485\                         Lam2            Specifies the secondary wavelength in
486                                          Angstrom, when an alpha1, alpha2
487                                          source is used [1]
488                          I(L2)/I(L1)     Ratio of Lam2 to Lam1 [1]           
489\                         Type            Histogram type (str) [1]:
490                                           * 'PXC' for constant wavelength x-ray
491                                           * 'PNC' for constant wavelength neutron
492                                           * 'PNT' for time of flight neutron
493\                         Zero            Two-theta zero correction in *degrees* [1]
494\                         Azimuth         Azimuthal setting angle for data recorded
495                                          with differing setting angles [1]
496\                         U, V, W         Cagliotti profile coefficients
497                                          for Gaussian instrumental broadening, where the
498                                          FWHM goes as
499                                          :math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
500\                         X, Y            Cauchy (Lorentzian) instrumental broadening
501                                          coefficients [1]
502\                         SH/L            Variant of the Finger-Cox-Jephcoat asymmetric
503                                          peak broadening ratio. Note that this is the
504                                          average between S/L and H/L where S is
505                                          sample height, H is the slit height and
506                                          L is the goniometer diameter. [1]
507\                         Polariz.        Polarization coefficient. [1]
508wtFactor                      \           A weighting factor to increase or decrease
509                                          the leverage of data in the histogram (float).
510                                          A value of 1.0 weights the data with their
511                                          standard uncertainties and a larger value
512                                          increases the weighting of the data (equivalent
513                                          to decreasing the uncertainties).
514Sample Parameters             \           Specifies a dict with parameters that describe how
515                                          the data were collected, as listed
516                                          below. Refinable parameters are a list containing
517                                          a float and a bool, where the second value
518                                          specifies if the value is refined, otherwise
519                                          the value is a float unless otherwise noted.
520\                         Scale           The histogram scale factor (refinable)
521\                         Absorption      The sample absorption coefficient as
522                                          :math:`\\mu r` where r is the radius
523                                          (refinable). Only valid for Debye-Scherrer geometry.
524\                         SurfaceRoughA   Surface roughness parameter A as defined by
525                                          Surotti,J. Appl. Cryst, 5,325-331, 1972.(refinable -
526                                          only valid for Bragg-Brentano geometry)                                         
527\                         SurfaceRoughB   Surface roughness parameter B (refinable -
528                                          only valid for Bragg-Brentano geometry)                                         
529\                         DisplaceX,      Sample displacement from goniometer center
530                          DisplaceY       where Y is along the beam direction and
531                                          X is perpendicular. Units are :math:`\\mu m`
532                                          (refinable).
533\                         Phi, Chi,       Goniometer sample setting angles, in degrees.
534                          Omega
535\                         Gonio. radius   Radius of the diffractometer in mm
536\                         InstrName       A name for the instrument, used in preparing
537                                          a CIF (str).
538\                         Force,          Variables that describe how the measurement
539                          Temperature,    was performed. Not used directly in
540                          Humidity,       any computations.
541                          Pressure,
542                          Voltage
543\                         ranId           The random-number Id for the histogram
544                                          (same value as where top-level key is ranId)
545\                         Type            Type of diffraction data, may be 'Debye-Scherrer'
546                                          or 'Bragg-Brentano' (str).
547\                         Diffuse         not in use?
548hId                           \           The number assigned to the histogram when
549                                          the project is loaded or edited (can change)
550ranId                         \           A random number id for the histogram
551                                          that does not change
552Background                    \           The background is stored as a list with where
553                                          the first item in the list is list and the second
554                                          item is a dict. The list contains the background
555                                          function and its coefficients; the dict contains
556                                          Debye diffuse terms and background peaks.
557                                          (TODO: this needs to be expanded.)
558Data                          \           The data consist of a list of 6 np.arrays
559                                          containing in order:
560
561                                           0. the x-postions (two-theta in degrees),
562                                           1. the intensity values (Yobs),
563                                           2. the weights for each Yobs value
564                                           3. the computed intensity values (Ycalc)
565                                           4. the background values
566                                           5. Yobs-Ycalc
567======================  ===============  ====================================================
568
569Powder Reflection Data Structure
570--------------------------------
571
572.. _PowderRefl_table:
573
574.. index::
575   single: Powder reflection object description
576   single: Data object descriptions; Powder Reflections
577   
578For every phase in a histogram, the ``Reflection Lists`` value is a dict
579one element of which is `'RefList'`, which is a np.array containing
580reflections. The columns in that array are documented below.
581
582==========  ====================================================
583  index         explanation
584==========  ====================================================
585 0,1,2       h,k,l (float)
586 3           multiplicity
587 4           d-space, Angstrom
588 5           pos, two-theta
589 6           sig, Gaussian width
590 7           gam, Lorenzian width
591 8           :math:`F_{obs}^2`
592 9           :math:`F_{calc}^2`
593 10          reflection phase, in degrees
594 11          intensity correction for reflection, this times
595             :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
596==========  ====================================================
597
598Single Crystal Tree Items
599-------------------------
600
601.. _Xtal_table:
602
603.. index::
604   single: Single Crystal data object description
605   single: Data object descriptions; Single crystal data
606
607Every single crystal diffraction histogram is stored in the GSAS-II data tree
608with a top-level entry named beginning with the string "HKLF ". The
609diffraction data for that information are directly associated with
610that tree item and there are a series of children to that item. The
611routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
612and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
613load this information into a dictionary where the child tree name is
614used as a key, and the information in the main entry is assigned
615a key of ``Data``, as outlined below.
616
617.. tabularcolumns:: |l|l|p{4in}|
618
619======================  ===============  ====================================================
620  key                      sub-key        explanation
621======================  ===============  ====================================================
622Data                          \           A dict that contains the
623                                          reflection table,
624                                          as described in the
625                                          :ref:`Single Crystal Reflections
626                                          <XtalRefl_table>`
627                                          description.
628
629Instrument Parameters         \           A list containing two dicts where the possible
630                                          keys in each dict are listed below. The value
631                                          for most items is a list containing two values:
632                                          the initial value, the current value.
633                                          The first and second
634                                          values are floats unless otherwise noted.
635\                         Lam             Specifies a wavelength in Angstroms (two floats)
636\                         Type            Histogram type (two str values):
637                                           * 'SXC' for constant wavelength x-ray
638                                           * 'SNC' for constant wavelength neutron
639                                           * 'SNT' for time of flight neutron
640\                         InstrName       A name for the instrument, used in preparing
641                                          a CIF (str).
642
643wtFactor                      \           A weighting factor to increase or decrease
644                                          the leverage of data in the histogram (float).
645                                          A value of 1.0 weights the data with their
646                                          standard uncertainties and a larger value
647                                          increases the weighting of the data (equivalent
648                                          to decreasing the uncertainties).
649
650hId                           \           The number assigned to the histogram when
651                                          the project is loaded or edited (can change)
652ranId                         \           A random number id for the histogram
653                                          that does not change
654======================  ===============  ====================================================
655
656Single Crystal Reflection Data Structure
657----------------------------------------
658
659.. _XtalRefl_table:
660
661.. index::
662   single: Single Crystal reflection object description
663   single: Data object descriptions; Single Crystal Reflections
664   
665For every single crystal a histogram, the ``'Data'`` item contains
666the structure factors as an np.array in item `'RefList'`.
667The columns in that array are documented below.
668
669==========  ====================================================
670  index         explanation
671==========  ====================================================
672 0,1,2       h,k,l (float)
673 3           multiplicity
674 4           d-space, Angstrom
675 5           :math:`F_{obs}^2`
676 6           :math:`\sigma(F_{obs}^2)`
677 7           :math:`F_{calc}^2`
678 8           :math:`F_{obs}^2T`
679 9           :math:`F_{calc}^2T`
680 10          reflection phase, in degrees
681 11          intensity correction for reflection, this times
682             :math:`F_{obs}^2` or :math:`F_{calc}^2`
683             gives Iobs or Icalc
684==========  ====================================================
685
686Image Data Structure
687--------------------
688
689.. _Image_table:
690
691.. index::
692   image: Image data object description
693   image: Image object descriptions
694   
695Every 2-dimensional image is stored in the GSAS-II data tree
696with a top-level entry named beginning with the string "IMG ". The
697image data are directly associated with that tree item and there
698are a series of children to that item. The routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
699and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
700load this information into a dictionary where the child tree name is
701used as a key, and the information in the main entry is assigned
702a key of ``Data``, as outlined below.
703
704.. tabularcolumns:: |l|l|p{4in}|
705
706======================  ======================  ====================================================
707  key                      sub-key              explanation
708======================  ======================  ====================================================
709Comments                       \                Text strings extracted from the original image data
710                                                header or a metafile. These cannot be changed by 
711                                                the user; it may be empty.                                               
712Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
713                                                value. Accomodates
714                                                detector orientations other than with the detector
715                                                X-axis
716                                                horizontal.
717\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
718                                                during image integration multiplied by value. It must have the same size/shape as
719                                                the integrated image. NB: value < 0 for subtraction.
720\                           calibrant           (str) The material used for determining the position/orientation
721                                                of the image. The data is obtained from :func:`ImageCalibrants`
722                                                and UserCalibrants.py (supplied by user).
723\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
724\                           calibskip           (int) The number of expected diffraction lines skipped during the last
725                                                calibration run.
726\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
727                                                strikes the detector plane as determined by calibration. This point
728                                                does not have to be within the limits of the detector boundaries.
729\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
730                                                of the image is at the center line otherwise it is at the leading edge.
731\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
732\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
733                                                calibration calculations. See pixLimit for details as how point is found.           
734\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
735                                                ring offset at higher angles. Optionally determined by calibration.
736\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
737\                           distance            (float) The distance (mm) from sample to detector plane.
738\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
739                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
740                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
741                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
742                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
743\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
744\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
745\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
746                                                Required for texture calculations.
747\                           invert_x            (bool) If True display the image with the x-axis inverted.
748\                           invert_y            (bool) If True display the image with the y-axis inverted.
749\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
750\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
751\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
752                                                intensities obtained during integration.
753\                           outAzimuths         (int) The number of azimuth pie slices.
754\                           outChannels         (int) The number of 2-theta steps.
755\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
756\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
757                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
758                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
759                                                Locations are used to construct rings of points for calibration calcualtions.
760\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
761                                                integration using value.
762\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
763                                                diffraction ring with the same d-spacing (dsp)
764\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
765                                                selected by the user,
766\                           Range               (list) The minimum & maximum values of the image
767\                           rotation            (float) The angle between the x-axis and the vector about which the
768                                                detector is tilted. Constrained to -180 to 180 deg.     
769\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
770                                                calculations.
771\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
772                                                to cause correction to be applied.
773\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
774\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.           
775\                           showLines           (bool) If True then isplay the integration limits to be used.
776\                           size                (list:int) The number of pixels on the image x & y axes
777\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
778\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
779\                           wavelength          (float) Tha radiation wavelength (Angstroms) as entered by the user (or someday obtained from the image header).
780                                               
781Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
782                                                to be excluded from integration
783\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
784                                                of which is excluded from recalibration and integration. Only one frame is allowed.
785\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
786                                                from integration.
787\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
788                                                to be excluded from integration.
789\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
790                                                to be excluded from integration.
791\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
792                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.   
793                                               
794Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
795\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
796                                                These will be restricted by space group symmetry; result of strain fit refinement.
797\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
798\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
799                                                and are used to determine the strain tensor.
800                                                The dictionary items are:
801                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
802                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
803                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
804                                                'Esig': (list: float) Esds for Emat from fitting.
805                                                'pixLimit': (int) Search range to find highest point on ring for each data point
806                                                'cutoff': (float) I/Ib cutoff for searching.
807                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
808                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
809                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
810                                               
811======================  ======================  ====================================================
812
813Parameter Dictionary
814-------------------------
815
816.. _parmDict_table:
817
818.. index::
819   single: Parameter dictionary
820
821The parameter dictionary contains all of the variable parameters for the refinement.
822The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
823It is prepared in two ways. When loaded from the tree
824(in :meth:`GSASII.GSASII.MakeLSParmDict` and
825:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
826the values are lists with two elements: ``[value, refine flag]``
827
828When loaded from the GPX file (in
829:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
830dict is the actual parameter value (usually a float, but sometimes a
831letter or string flag value (such as I or A for iso/anisotropic).
832
833
834*Classes and routines*
835----------------------
836
837'''
838import re
839import imp
840import random as ran
841import sys
842import GSASIIpath
843import GSASIImath as G2mth
844import numpy as np
845
846GSASIIpath.SetVersionNumber("$Revision: 1331 $")
847
848DefaultControls = {
849    'deriv type':'analytic Hessian',    #default controls
850    'min dM/M':0.0001,'shift factor':1.,'max cyc':3,'F**2':True,
851    'minF/sig':0,
852    'Author':'no name',
853    'FreeVar1':'Sample humidity (%)',
854    'FreeVar2':'Sample voltage (V)',
855    'FreeVar3':'Applied load (MN)',
856    }
857'''Values to be used as defaults for the initial contents of the ``Controls``
858data tree item.
859'''
860
861def MakeUniqueLabel(lbl,labellist):
862    '''Make sure that every a label is unique against a list by adding
863    digits at the end until it is not found in list.
864
865    :param str lbl: the input label
866    :param list labellist: the labels that have already been encountered
867    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
868      ``_10-99``, etc.) appended at the end
869    '''
870    lbl = lbl.strip()
871    if not lbl: # deal with a blank label
872        lbl = '_1'
873    if lbl not in labellist:
874        labellist.append(lbl)
875        return lbl
876    i = 1
877    prefix = lbl
878    if '_' in lbl:
879        prefix = lbl[:lbl.rfind('_')]
880        suffix = lbl[lbl.rfind('_')+1:]
881        try:
882            i = int(suffix)+1
883        except: # suffix could not be parsed
884            i = 1
885            prefix = lbl
886    while prefix+'_'+str(i) in labellist:
887        i += 1
888    else:
889        lbl = prefix+'_'+str(i)
890        labellist.append(lbl)
891    return lbl
892
893PhaseIdLookup = {}
894'''dict listing phase name and random Id keyed by sequential phase index as a str;
895best to access this using :func:`LookupPhaseName`
896'''
897PhaseRanIdLookup = {}
898'''dict listing phase sequential index keyed by phase random Id;
899best to access this using :func:`LookupPhaseId`
900'''
901HistIdLookup = {}
902'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
903best to access this using :func:`LookupHistName`
904'''
905HistRanIdLookup = {}
906'''dict listing histogram sequential index keyed by histogram random Id;
907best to access this using :func:`LookupHistId`
908'''
909AtomIdLookup = {}
910'''dict listing for each phase index as a str, the atom label and atom random Id,
911keyed by atom sequential index as a str;
912best to access this using :func:`LookupAtomLabel`
913'''
914AtomRanIdLookup = {}
915'''dict listing for each phase the atom sequential index keyed by atom random Id;
916best to access this using :func:`LookupAtomId`
917'''
918ShortPhaseNames = {}
919'''a dict containing a possibly shortened and when non-unique numbered
920version of the phase name. Keyed by the phase sequential index.
921'''
922ShortHistNames = {}
923'''a dict containing a possibly shortened and when non-unique numbered
924version of the histogram name. Keyed by the histogram sequential index.
925'''
926
927VarDesc = {}
928''' This dictionary lists descriptions for GSAS-II variables,
929as set in :func:`CompileVarDesc`. See that function for a description
930for how keys and values are written.
931'''
932
933reVarDesc = {}
934''' This dictionary lists descriptions for GSAS-II variables with
935the same values as :attr:`VarDesc` except that keys have been compiled as
936regular expressions. Initialized in :func:`CompileVarDesc`.
937'''
938
939def IndexAllIds(Histograms,Phases):
940    '''Scan through the used phases & histograms and create an index
941    to the random numbers of phases, histograms and atoms. While doing this,
942    confirm that assigned random numbers are unique -- just in case lightning
943    strikes twice in the same place.
944
945    Note: this code assumes that the atom random Id (ranId) is the last
946    element each atom record.
947
948    This is called in two places (only) :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
949    (which loads the histograms and phases from a GPX file) and
950    :meth:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
951    (which loads the histograms and phases from the data tree.)
952
953    TODO: do we need a lookup for rigid body variables?
954    '''
955    # process phases and atoms
956    PhaseIdLookup.clear()
957    PhaseRanIdLookup.clear()   
958    AtomIdLookup.clear()
959    AtomRanIdLookup.clear()
960    ShortPhaseNames.clear()
961    for ph in Phases:
962        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
963        ranId = Phases[ph]['ranId'] 
964        while ranId in PhaseRanIdLookup:
965            # Found duplicate random Id! note and reassign
966            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
967            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxint)
968        pId = str(Phases[ph]['pId'])
969        PhaseIdLookup[pId] = (ph,ranId)
970        PhaseRanIdLookup[ranId] = pId
971        shortname = ph[:10]
972        while shortname in ShortPhaseNames.values():
973            shortname = ph[:8] + ' ('+ pId + ')'
974        ShortPhaseNames[pId] = shortname
975        AtomIdLookup[pId] = {}
976        AtomRanIdLookup[pId] = {}
977        for iatm,at in enumerate(Phases[ph]['Atoms']):
978            ranId = at[-1]
979            while ranId in AtomRanIdLookup[pId]: # check for dups
980                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
981                at[-1] = ranId = ran.randint(0,sys.maxint)
982            AtomRanIdLookup[pId][ranId] = str(iatm)
983            if Phases[ph]['General']['Type'] == 'macromolecular':
984                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
985            else:
986                label = at[ct-1]
987            AtomIdLookup[pId][str(iatm)] = (label,ranId)
988    # process histograms
989    HistIdLookup.clear()
990    HistRanIdLookup.clear()
991    ShortHistNames.clear()
992    for hist in Histograms:
993        ranId = Histograms[hist]['ranId']
994        while ranId in HistRanIdLookup:
995            # Found duplicate random Id! note and reassign
996            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
997            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxint)
998        hId = str(Histograms[hist]['hId'])
999        HistIdLookup[hId] = (hist,ranId)
1000        HistRanIdLookup[ranId] = hId
1001        shortname = hist[:15]
1002        while shortname in ShortHistNames.values():
1003            shortname = hist[:11] + ' ('+ hId + ')'
1004        ShortHistNames[hId] = shortname
1005
1006def LookupAtomId(pId,ranId):
1007    '''Get the atom number from a phase and atom random Id
1008
1009    :param int/str pId: the sequential number of the phase
1010    :param int ranId: the random Id assigned to an atom
1011
1012    :returns: the index number of the atom (str)
1013    '''
1014    if not AtomRanIdLookup:
1015        raise Exception,'Error: LookupAtomId called before IndexAllIds was run'
1016    if pId is None or pId == '':
1017        raise KeyError,'Error: phase is invalid (None or blank)'
1018    pId = str(pId)
1019    if pId not in AtomRanIdLookup:
1020        raise KeyError,'Error: LookupAtomId does not have phase '+pId
1021    if ranId not in AtomRanIdLookup[pId]:
1022        raise KeyError,'Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']'
1023    return AtomRanIdLookup[pId][ranId]
1024
1025def LookupAtomLabel(pId,index):
1026    '''Get the atom label from a phase and atom index number
1027
1028    :param int/str pId: the sequential number of the phase
1029    :param int index: the index of the atom in the list of atoms
1030
1031    :returns: the label for the atom (str) and the random Id of the atom (int)
1032    '''
1033    if not AtomIdLookup:
1034        raise Exception,'Error: LookupAtomLabel called before IndexAllIds was run'
1035    if pId is None or pId == '':
1036        raise KeyError,'Error: phase is invalid (None or blank)'
1037    pId = str(pId)
1038    if pId not in AtomIdLookup:
1039        raise KeyError,'Error: LookupAtomLabel does not have phase '+pId
1040    if index not in AtomIdLookup[pId]:
1041        raise KeyError,'Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']'
1042    return AtomIdLookup[pId][index]
1043
1044def LookupPhaseId(ranId):
1045    '''Get the phase number and name from a phase random Id
1046
1047    :param int ranId: the random Id assigned to a phase
1048    :returns: the sequential Id (pId) number for the phase (str)
1049    '''
1050    if not PhaseRanIdLookup:
1051        raise Exception,'Error: LookupPhaseId called before IndexAllIds was run'
1052    if ranId not in PhaseRanIdLookup:
1053        raise KeyError,'Error: LookupPhaseId does not have ranId '+str(ranId)
1054    return PhaseRanIdLookup[ranId]
1055
1056def LookupPhaseName(pId):
1057    '''Get the phase number and name from a phase Id
1058
1059    :param int/str pId: the sequential assigned to a phase
1060    :returns:  (phase,ranId) where phase is the name of the phase (str)
1061      and ranId is the random # id for the phase (int)
1062    '''
1063    if not PhaseIdLookup:
1064        raise Exception,'Error: LookupPhaseName called before IndexAllIds was run'
1065    if pId is None or pId == '':
1066        raise KeyError,'Error: phase is invalid (None or blank)'
1067    pId = str(pId)
1068    if pId not in PhaseIdLookup:
1069        raise KeyError,'Error: LookupPhaseName does not have index '+pId
1070    return PhaseIdLookup[pId]
1071
1072def LookupHistId(ranId):
1073    '''Get the histogram number and name from a histogram random Id
1074
1075    :param int ranId: the random Id assigned to a histogram
1076    :returns: the sequential Id (hId) number for the histogram (str)
1077    '''
1078    if not HistRanIdLookup:
1079        raise Exception,'Error: LookupHistId called before IndexAllIds was run'
1080    if ranId not in HistRanIdLookup:
1081        raise KeyError,'Error: LookupHistId does not have ranId '+str(ranId)
1082    return HistRanIdLookup[ranId]
1083
1084def LookupHistName(hId):
1085    '''Get the histogram number and name from a histogram Id
1086
1087    :param int/str hId: the sequential assigned to a histogram
1088    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1089      and ranId is the random # id for the histogram (int)
1090    '''
1091    if not HistIdLookup:
1092        raise Exception,'Error: LookupHistName called before IndexAllIds was run'
1093    if hId is None or hId == '':
1094        raise KeyError,'Error: histogram is invalid (None or blank)'
1095    hId = str(hId)
1096    if hId not in HistIdLookup:
1097        raise KeyError,'Error: LookupHistName does not have index '+hId
1098    return HistIdLookup[hId]
1099
1100def fmtVarDescr(varname):
1101    '''Return a string with a more complete description for a GSAS-II variable
1102
1103    :param str varname: A full G2 variable name with 2 or 3 or 4
1104       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1105       
1106    :returns: a string with the description
1107    '''
1108    s,l = VarDescr(varname)
1109    return s+": "+l
1110
1111def VarDescr(varname):
1112    '''Return two strings with a more complete description for a GSAS-II variable
1113
1114    :param str name: A full G2 variable name with 2 or 3 or 4
1115       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1116       
1117    :returns: (loc,meaning) where loc describes what item the variable is mapped
1118      (phase, histogram, etc.) and meaning describes what the variable does.
1119    '''
1120   
1121    # special handling for parameter names without a colons
1122    # for now, assume self-defining
1123    if varname.find(':') == -1:
1124        return "Global",varname
1125       
1126    l = getVarDescr(varname)
1127    if not l:
1128        #return ("invalid variable name ("+str(varname)+")!"),""
1129        return "invalid variable name!",""
1130
1131    if not l[-1]:
1132        l[-1] = "(variable needs a definition!)"
1133
1134    s = ""
1135    if l[0] is not None and l[1] is not None: # HAP: keep short
1136        if l[0] == '*':
1137            lbl = 'all'
1138        else:
1139            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1140        if l[1] == '*':
1141            hlbl = 'all'
1142        else:
1143            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1144        if hlbl[:4] == 'HKLF':
1145            hlbl = 'Xtl='+hlbl[5:]
1146        elif hlbl[:4] == 'PWDR':
1147            hlbl = 'Pwd='+hlbl[5:]
1148        else:
1149            hlbl = 'Hist='+hlbl
1150        s = "Ph="+str(lbl)+" * "+str(hlbl)
1151    elif l[2] == 'Back': # background parameters are "special", alas
1152        s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1153        l[-1] += ' #'+str(l[3])
1154    elif l[4] is not None: # rigid body parameter
1155        lbl = ShortPhaseNames.get(l[0],'phase?')
1156        s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1157    elif l[3] is not None: # atom parameter,
1158        lbl = ShortPhaseNames.get(l[0],'phase?')
1159        try:
1160            albl = LookupAtomLabel(l[0],l[3])[0]
1161        except KeyError:
1162            albl = 'Atom?'
1163        s = "Atom "+str(albl)+" in "+str(lbl)
1164    elif l[0] == '*':
1165        s = "All phases "
1166    elif l[0] is not None:
1167        lbl = ShortPhaseNames.get(l[0],'phase?')
1168        s = "Phase "+str(lbl)
1169    elif l[1] == '*':
1170        s = 'All hists'
1171    elif l[1] is not None:
1172        hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1173        if hlbl[:4] == 'HKLF':
1174            hlbl = 'Xtl='+hlbl[5:]
1175        elif hlbl[:4] == 'PWDR':
1176            hlbl = 'Pwd='+hlbl[5:]
1177        else:
1178            hlbl = 'Hist='+hlbl
1179        s = str(hlbl)
1180    if not s:
1181        s = 'Global'
1182    return s,l[-1]
1183
1184def getVarDescr(varname):
1185    '''Return a short description for a GSAS-II variable
1186
1187    :param str name: A full G2 variable name with 2 or 3 or 4
1188       colons (<p>:<h>:name[:<a1>][:<a2>])
1189     
1190    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1191      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1192      the histogram number and the atom number; `name` will always be
1193      an str; and `description` is str or `None`.
1194      If the variable name is incorrectly formed (for example, wrong
1195      number of colons), `None` is returned instead of a list.
1196    '''
1197    l = varname.split(':')
1198    if len(l) == 3:
1199        l += [None,None]
1200    elif len(l) == 4:
1201        l += [None]
1202    elif len(l) != 5:
1203        return None
1204    for i in (0,1,3,4):
1205        if l[i] == "":
1206            l[i] = None
1207    l += [getDescr(l[2])]
1208    return l
1209   
1210def CompileVarDesc():
1211    '''Set the values in the variable description lookup table (:attr:`VarDesc`)
1212    into :attr:`reVarDesc`. This is called in :func:`getDescr` so the initialization
1213    is always done before use.
1214
1215    Note that keys may contain regular expressions, where '[xyz]'
1216    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range of values).
1217    '.*' matches any string. For example::
1218
1219    'AUiso':'Atomic isotropic displacement parameter',
1220
1221    will match variable ``'p::AUiso:a'``.
1222    If parentheses are used in the key, the contents of those parentheses can be
1223    used in the value, such as::
1224
1225    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1226
1227    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1228    in the value when used.
1229   
1230    '''
1231    if reVarDesc: return # already done
1232    for key,value in {
1233        # derived or other sequential vars
1234        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1235        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1236        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1237        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1238        # ambiguous, alas:
1239        'Scale' : 'Phase or Histogram scale factor',
1240        # Phase vars (p::<var>)
1241        'A([0-5])' : 'Reciprocal metric tensor component \\1',
1242        'Vol' : 'Unit cell volume',
1243        # Atom vars (p::<var>:a)
1244        'dA([xyz])' : 'change to atomic coordinate, \\1',
1245        'A([xyz])$' : '\\1 fractional atomic coordinate',
1246        'AUiso':'Atomic isotropic displacement parameter',
1247        'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1248        'Afrac': 'Atomic occupancy parameter',
1249        # Hist & Phase (HAP) vars (p:h:<var>)
1250        'Back': 'Background term',
1251        'BkPkint;(.*)':'Background peak #\\1 intensity',
1252        'BkPkpos;(.*)':'Background peak #\\1 position',
1253        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1254        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1255        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1256        'D([123][123])' : 'Anisotropic strain coef. \\1',
1257        'Extinction' : 'Extinction coef.',
1258        'MD' : 'March-Dollase coef.',
1259        'Mustrain;.*' : 'Microstrain coef.',
1260        'Size;.*' : 'Crystallite size value',
1261        'eA' : '?',
1262        #Histogram vars (:h:<var>)
1263        'Absorption' : 'Absorption coef.',
1264        'Displace([XY])' : 'Debye-Scherrer sample displacement \\1',
1265        'Lam' : 'Wavelength',
1266        'Polariz\.' : 'Polarization correction',
1267        'SH/L' : 'FCJ peak asymmetry correction',
1268        '([UVW])' : 'Gaussian instrument broadening \\1',
1269        '([XY])' : 'Cauchy instrument broadening \\1',
1270        'Zero' : 'Debye-Scherrer zero correction',
1271        'nDebye' : 'Debye model background corr. terms',
1272        'nPeaks' : 'Fixed peak background corr. terms',
1273        'RBV.*' : 'Vector rigid body parameter',
1274        'RBR.*' : 'Residue rigid body parameter',
1275        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1276        'RBRP([xyz])' : 'Residue rigid body position parameter',
1277        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1278        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1279        # Global vars (::<var>)
1280        'constr([0-9]*)' : 'Parameter from constraint',
1281        }.items():
1282        VarDesc[key] = value
1283        reVarDesc[re.compile(key)] = value
1284
1285def getDescr(name):
1286    '''Return a short description for a GSAS-II variable
1287
1288    :param str name: The descriptive part of the variable name without colons (:)
1289     
1290    :returns: a short description or None if not found
1291    '''
1292
1293    CompileVarDesc() # compile the regular expressions, if needed
1294    for key in reVarDesc:
1295        m = key.match(name)
1296        if m:
1297            return m.expand(reVarDesc[key])
1298    return None
1299
1300def GenWildCard(varlist):
1301    '''Generate wildcard versions of G2 variables. These introduce '*'
1302    for a phase, histogram or atom number (but only for one of these
1303    fields) but only when there is more than one matching variable in the
1304    input variable list. So if the input is this::
1305   
1306      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1307
1308    then the output will be this::
1309   
1310       wildList = ['*::AUiso:0', '0::AUiso:*']
1311
1312    :param list varlist: an input list of GSAS-II variable names
1313      (such as 0::AUiso:0)
1314
1315    :returns: wildList, the generated list of wild card variable names.
1316    '''
1317    wild = []
1318    for i in (0,1,3):
1319        currentL = varlist[:]
1320        while currentL:
1321            item1 = currentL.pop(0)
1322            i1splt = item1.split(':')
1323            if i >= len(i1splt): continue
1324            if i1splt[i]:
1325                nextL = []
1326                i1splt[i] = '[0-9]+'
1327                rexp = re.compile(':'.join(i1splt))
1328                matchlist = [item1]
1329                for nxtitem in currentL:
1330                    if rexp.match(nxtitem):
1331                        matchlist += [nxtitem]
1332                    else:
1333                        nextL.append(nxtitem)
1334                if len(matchlist) > 1:
1335                    i1splt[i] = '*'
1336                    wild.append(':'.join(i1splt))
1337                currentL = nextL
1338    return wild
1339
1340def LookupWildCard(varname,varlist):
1341    '''returns a list of variable names from list varname
1342    that match wildcard name in varname
1343   
1344    :param str varname: a G2 variable name containing a wildcard
1345      (such as \*::var)
1346    :param list varlist: the list of all variable names used in
1347      the current project
1348    :returns: a list of matching GSAS-II variables (may be empty) 
1349    '''
1350    rexp = re.compile(varname.replace('*','[0-9]+'))
1351    return sorted([var for var in varlist if rexp.match(var)])
1352
1353
1354def _lookup(dic,key):
1355    '''Lookup a key in a dictionary, where None returns an empty string
1356    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1357    '''
1358    if key is None:
1359        return ""
1360    elif key == "*":
1361        return "*"
1362    else:
1363        return dic.get(key,'?')
1364
1365class G2VarObj(object):
1366    '''Defines a GSAS-II variable either using the phase/atom/histogram
1367    unique Id numbers or using a character string that specifies
1368    variables by phase/atom/histogram number (which can change).
1369    Note that :func:`LoadID` should be used to (re)load the current Ids
1370    before creating or later using the G2VarObj object.
1371
1372    This can store rigid body variables, but does not translate the residue # and
1373    body # to/from random Ids
1374
1375    A :class:`G2VarObj` object can be created with a single parameter:
1376   
1377    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1378      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1379
1380     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
1381     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1382     * a is the atom number (which may be left blank in which case the third colon is omitted).
1383       The atom number can be specified as '*' if a phase number is specified (not as '*').
1384       For rigid body variables, specify a will be a string of form "residue:body#"
1385
1386      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1387      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1388      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1389      For a rigid body variables, AtomID is a string of form "residue:body#".
1390
1391    If four positional arguments are supplied, they are:
1392
1393    :param str/int phasenum: The number for the phase (or None or '*')
1394    :param str/int histnum: The number for the histogram (or None or '*')
1395    :param str varname: a single value can be used to create a :class:`G2VarObj`
1396    :param str/int atomnum: The number for the atom (or None or '*')
1397   
1398    '''
1399    IDdict = {}
1400    IDdict['phases'] = {}
1401    IDdict['hists'] = {}
1402    IDdict['atoms'] = {}
1403    def __init__(self,*args):
1404        self.phase = None
1405        self.histogram = None
1406        self.name = ''
1407        self.atom = None
1408        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1409            # single arg with 4 values
1410            self.phase,self.histogram,self.name,self.atom = args[0]
1411        elif len(args) == 1 and ':' in args[0]:
1412            #parse a string
1413            lst = args[0].split(':')
1414            if lst[0] == '*':
1415                self.phase = '*'
1416                if len(lst) > 3:
1417                    self.atom = lst[3]
1418                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1419            elif lst[1] == '*':           
1420                self.histogram = '*'
1421                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1422            else:
1423                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1424                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1425                if len(lst) == 4:
1426                    if lst[3] == '*':
1427                        self.atom = '*'
1428                    else:
1429                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1430                elif len(lst) == 5:
1431                    self.atom = lst[3]+":"+lst[4]
1432                elif len(lst) == 3:
1433                    pass
1434                else:
1435                    raise Exception,"Too many colons in var name "+str(args[0])
1436            self.name = lst[2]
1437        elif len(args) == 4:
1438            if args[0] == '*':
1439                self.phase = '*'
1440                self.atom = args[3]
1441            else:
1442                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1443                if args[3] == '*':
1444                    self.atom = '*'
1445                elif args[0] is not None:
1446                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1447            if args[1] == '*':
1448                self.histogram = '*'
1449            else:
1450                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1451            self.name = args[2]
1452        else:
1453            raise Exception,"Incorrectly called GSAS-II parameter name"
1454
1455        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1456
1457    def __str__(self):
1458        return self.varname()
1459
1460    def varname(self):
1461        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1462        string (p:h:<var>:a) or (p:h:<var>)
1463
1464        :returns: the variable name as a str
1465        '''
1466        a = ""
1467        if self.phase == "*":
1468            ph = "*"
1469            if self.atom:
1470                a = ":" + str(self.atom)
1471        else:
1472            ph = _lookup(PhaseRanIdLookup,self.phase)
1473            if self.atom == '*':
1474                a = ':*'
1475            elif self.atom:
1476                if ":" in str(self.atom):
1477                    a = ":" + str(self.atom)
1478                elif ph in AtomRanIdLookup:
1479                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1480                else:
1481                    a = ":?"
1482        if self.histogram == "*":
1483            hist = "*"
1484        else:
1485            hist = _lookup(HistRanIdLookup,self.histogram)
1486        s = (ph + ":" + hist + ":" + str(self.name)) + a
1487        return s
1488   
1489    def __repr__(self):
1490        '''Return the detailed contents of the object
1491        '''
1492        s = "<"
1493        if self.phase == '*':
1494            s += "Phases: all; "
1495            if self.atom is not None:
1496                if ":" in str(self.atom):
1497                    s += "Rigid body" + str(self.atom) + "; "
1498                else:
1499                    s += "Atom #" + str(self.atom) + "; "
1500        elif self.phase is not None:
1501            ph =  _lookup(PhaseRanIdLookup,self.phase)
1502            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1503            if self.atom == '*':
1504                s += "Atoms: all; "
1505            elif ":" in self(self.atom):
1506                s += "Rigid body" + str(self.atom) + "; "
1507            elif self.atom is not None:
1508                s += "Atom rId=" + str(self.atom)
1509                if ph in AtomRanIdLookup:
1510                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1511                else:
1512                    s += " (#? -- not found!); "
1513        if self.histogram == '*':
1514            s += "Histograms: all; "
1515        elif self.histogram is not None:
1516            hist = _lookup(HistRanIdLookup,self.histogram)
1517            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1518        s += 'Variable name="' + str(self.name) + '">'
1519        return s+" ("+self.varname()+")"
1520
1521    def __eq__(self, other):
1522        if type(other) is type(self):
1523            return (self.phase == other.phase and
1524                    self.histogram == other.histogram and
1525                    self.name == other.name and
1526                    self.atom == other.atom)
1527        return False
1528
1529    def _show(self):
1530        'For testing, shows the current lookup table'
1531        print 'phases', self.IDdict['phases']
1532        print 'hists', self.IDdict['hists']
1533        print 'atomDict', self.IDdict['atoms']
1534
1535#==========================================================================
1536# shortcut routines
1537exp = np.exp
1538sind = lambda x: np.sin(x*np.pi/180.)
1539tand = lambda x: np.tan(x*np.pi/180.)
1540cosd = lambda x: np.cos(x*np.pi/180.)
1541sind = sin = s = lambda x: np.sin(x*np.pi/180.)
1542cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
1543tand = tan = t = lambda x: np.tan(x*np.pi/180.)
1544sqrt = sq = lambda x: np.sqrt(x)
1545pi = lambda: np.pi
1546class ExpressionObj(object):
1547    '''Defines an object with a user-defined expression, to be used for
1548    secondary fits or restraints. Object is created null, but is changed
1549    using :meth:`LoadExpression`. This contains only the minimum
1550    information that needs to be stored to save and load the expression
1551    and how it is mapped to GSAS-II variables.
1552    '''
1553    def __init__(self):
1554        self.expression = ''
1555        'The expression as a text string'
1556        self.assgnVars = {}
1557        '''A dict where keys are label names in the expression mapping to a GSAS-II
1558        variable. The value is a list with a G2 variable name and derivative step size.
1559        Note that the G2 variable name may contain a wild-card and correspond to
1560        multiple values.
1561        '''
1562        self.freeVars = {}
1563        '''A dict where keys are label names in the expression mapping to a free
1564        parameter. The value is a list with:
1565
1566         * a name assigned to the parameter
1567         * a value for to the parameter and
1568         * a flag to determine if the variable is refined.
1569        ''' 
1570        self.depVar = None
1571
1572        self.lastError = ('','')
1573        '''Shows last encountered error in processing expression
1574        (list of 1-3 str values)'''
1575
1576    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
1577        '''Load the expression and associated settings into the object. Raises
1578        an exception if the expression is not parsed, if not all functions
1579        are defined or if not all needed parameter labels in the expression
1580        are defined.
1581
1582        This will not test if the variable referenced in these definitions
1583        are actually in the parameter dictionary. This is checked when the
1584        computation for the expression is done in :meth:`SetupCalc`.
1585       
1586        :param str expr: the expression
1587        :param list exprVarLst: parameter labels found in the expression
1588        :param dict varSelect: this will be 0 for Free parameters
1589          and non-zero for expression labels linked to G2 variables.
1590        :param dict varName: Defines a name (str) associated with each free parameter
1591        :param dict varValue: Defines a value (float) associated with each free parameter
1592        :param dict varRefflag: Defines a refinement flag (bool)
1593          associated with each free parameter
1594        '''
1595        self.expression = expr
1596        self.compiledExpr = None
1597        self.freeVars = {}
1598        self.assgnVars = {}
1599        for v in exprVarLst:
1600            if varSelect[v] == 0:
1601                self.freeVars[v] = [
1602                    varName.get(v),
1603                    varValue.get(v),
1604                    varRefflag.get(v),
1605                    ]
1606            else:
1607                self.assgnVars[v] = varName[v]
1608        self.CheckVars()
1609
1610    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
1611        '''Load the expression and associated settings from the object into
1612        arrays used for editing.
1613
1614        :param list exprVarLst: parameter labels found in the expression
1615        :param dict varSelect: this will be 0 for Free parameters
1616          and non-zero for expression labels linked to G2 variables.
1617        :param dict varName: Defines a name (str) associated with each free parameter
1618        :param dict varValue: Defines a value (float) associated with each free parameter
1619        :param dict varRefflag: Defines a refinement flag (bool)
1620          associated with each free parameter
1621
1622        :returns: the expression as a str
1623        '''
1624        for v in self.freeVars:
1625            varSelect[v] = 0
1626            varName[v] = self.freeVars[v][0]
1627            varValue[v] = self.freeVars[v][1]
1628            varRefflag[v] = self.freeVars[v][2]
1629        for v in self.assgnVars:
1630            varSelect[v] = 1
1631            varName[v] = self.assgnVars[v]
1632        return self.expression
1633
1634    def GetVaried(self):
1635        'Returns the names of the free parameters that will be refined'
1636        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
1637
1638    def GetVariedVarVal(self):
1639        'Returns the names and values of the free parameters that will be refined'
1640        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
1641
1642    def UpdateVariedVars(self,varyList,values):
1643        'Updates values for the free parameters (after a refinement); only updates refined vars'
1644        for v in self.freeVars:
1645            if not self.freeVars[v][2]: continue
1646            if "::"+self.freeVars[v][0] not in varyList: continue
1647            indx = varyList.index("::"+self.freeVars[v][0])
1648            self.freeVars[v][1] = values[indx]
1649
1650    def GetIndependentVars(self):
1651        'Returns the names of the required independent parameters used in expression'
1652        return [self.assgnVars[v] for v in self.assgnVars]
1653
1654    def CheckVars(self):
1655        '''Check that the expression can be parsed, all functions are
1656        defined and that input loaded into the object is internally
1657        consistent. If not an Exception is raised.
1658
1659        :returns: a dict with references to packages needed to
1660          find functions referenced in the expression.
1661        '''
1662        ret = self.ParseExpression(self.expression)
1663        if not ret:
1664            raise Exception("Expression parse error")
1665        exprLblList,fxnpkgdict = ret
1666        # check each var used in expression is defined
1667        defined = self.assgnVars.keys() + self.freeVars.keys()
1668        notfound = []
1669        for var in exprLblList:
1670            if var not in defined:
1671                notfound.append(var)
1672        if notfound:
1673            msg = 'Not all variables defined'
1674            msg1 = 'The following variables were not defined: '
1675            msg2 = ''
1676            for var in notfound:
1677                if msg: msg += ', '
1678                msg += var
1679            self.lastError = (msg1,'  '+msg2)
1680            raise Exception(msg)
1681        return fxnpkgdict
1682
1683    def ParseExpression(self,expr):
1684        '''Parse an expression and return a dict of called functions and
1685        the variables used in the expression. Returns None in case an error
1686        is encountered. If packages are referenced in functions, they are loaded
1687        and the functions are looked up into the modules global
1688        workspace.
1689       
1690        Note that no changes are made to the object other than
1691        saving an error message, so that this can be used for testing prior
1692        to the save.
1693
1694        :returns: a list of used variables
1695        '''
1696        self.lastError = ('','')
1697        import ast
1698        def FindFunction(f):
1699            '''Find the object corresponding to function f
1700            :param str f: a function name such as 'numpy.exp'
1701            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
1702              that defines the package location(s) and where pkgobj
1703              defines the object associated with the function.
1704              If the function is not found, pkgobj is None.
1705            '''
1706            df = f.split('.')
1707            pkgdict = {}
1708            # no listed package, try in current namespace
1709            if len(df) == 1: 
1710                try:
1711                    fxnobj = eval(f)
1712                    return pkgdict,fxnobj
1713                except (AttributeError, NameError):
1714                    return None,None
1715            else:
1716                try:
1717                    fxnobj = eval(f)
1718                    pkgdict[df[0]] = eval(df[0])
1719                    return pkgdict,fxnobj
1720                except (AttributeError, NameError):
1721                    pass
1722            # includes a package, lets try to load the packages
1723            pkgname = ''
1724            path = sys.path
1725            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
1726                if pkgname:
1727                    pkgname += '.' + pkg
1728                else:
1729                    pkgname = pkg
1730                fp = None
1731                try:
1732                    fp, fppath,desc = imp.find_module(pkg,path)
1733                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
1734                    pkgdict[pkgname] = pkgobj
1735                    path = [fppath]
1736                except Exception as msg:
1737                    print('load of '+pkgname+' failed with error='+str(msg))
1738                    return {},None
1739                finally:
1740                    if fp: fp.close()
1741                try:
1742                    #print 'before',pkgdict.keys()
1743                    fxnobj = eval(f,globals(),pkgdict)
1744                    #print 'after 1',pkgdict.keys()
1745                    #fxnobj = eval(f,pkgdict)
1746                    #print 'after 2',pkgdict.keys()
1747                    return pkgdict,fxnobj
1748                except:
1749                    continue
1750            return None # not found
1751        def ASTtransverse(node,fxn=False):
1752            '''Transverse a AST-parsed expresson, compiling a list of variables
1753            referenced in the expression. This routine is used recursively.
1754
1755            :returns: varlist,fxnlist where
1756              varlist is a list of referenced variable names and
1757              fxnlist is a list of used functions
1758            '''
1759            varlist = []
1760            fxnlist = []
1761            if isinstance(node, list):
1762                for b in node:
1763                    v,f = ASTtransverse(b,fxn)
1764                    varlist += v
1765                    fxnlist += f
1766            elif isinstance(node, ast.AST):
1767                for a, b in ast.iter_fields(node):
1768                    if isinstance(b, ast.AST):
1769                        if a == 'func': 
1770                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
1771                            continue
1772                        v,f = ASTtransverse(b,fxn)
1773                        varlist += v
1774                        fxnlist += f
1775                    elif isinstance(b, list):
1776                        v,f = ASTtransverse(b,fxn)
1777                        varlist += v
1778                        fxnlist += f
1779                    elif node.__class__.__name__ == "Name":
1780                        varlist += [b]
1781                    elif fxn and node.__class__.__name__ == "Attribute":
1782                        varlist += [b]
1783            return varlist,fxnlist
1784        try:
1785            exprast = ast.parse(expr)
1786        except SyntaxError as err:
1787            s = ''
1788            import traceback
1789            for i in traceback.format_exc().splitlines()[-3:-1]:
1790                if s: s += "\n"
1791                s += str(i)
1792            self.lastError = ("Error parsing expression:",s)
1793            return
1794        # find the variables & functions
1795        v,f = ASTtransverse(exprast)
1796        varlist = sorted(list(set(v)))
1797        fxnlist = list(set(f))
1798        pkgdict = {}
1799        # check the functions are defined
1800        for fxn in fxnlist:
1801            fxndict,fxnobj = FindFunction(fxn)
1802            if not fxnobj:
1803                self.lastError = ("Error: Invalid function",fxn,
1804                                  "is not defined")
1805                return
1806            if not hasattr(fxnobj,'__call__'):
1807                self.lastError = ("Error: Not a function.",fxn,
1808                                  "cannot be called as a function")
1809                return
1810            pkgdict.update(fxndict)
1811        return varlist,pkgdict
1812
1813    def GetDepVar(self):
1814        'return the dependent variable, or None'
1815        return self.depVar
1816
1817    def SetDepVar(self,var):
1818        'Set the dependent variable, if used'
1819        self.depVar = var
1820#==========================================================================
1821class ExpressionCalcObj(object):
1822    '''An object used to evaluate an expression from a :class:`ExpressionObj`
1823    object.
1824   
1825    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
1826      an expression string and mappings for the parameter labels in that object.
1827    '''
1828    def __init__(self,exprObj):
1829        self.eObj = exprObj
1830        'The expression and mappings; a :class:`ExpressionObj` object'
1831        self.compiledExpr = None
1832        'The expression as compiled byte-code'
1833        self.exprDict = {}
1834        '''dict that defines values for labels used in expression and packages
1835        referenced by functions
1836        '''
1837        self.lblLookup = {}
1838        '''Lookup table that specifies the expression label name that is
1839        tied to a particular GSAS-II parameters in the parmDict.
1840        '''
1841        self.fxnpkgdict = {}
1842        '''a dict with references to packages needed to
1843        find functions referenced in the expression.
1844        '''
1845        self.varLookup = {}
1846        '''Lookup table that specifies the GSAS-II variable(s)
1847        indexed by the expression label name. (Used for only for diagnostics
1848        not evaluation of expression.)
1849        '''
1850       
1851    def SetupCalc(self,parmDict):
1852        '''Do all preparations to use the expression for computation.
1853        Adds the free parameter values to the parameter dict (parmDict).
1854        '''
1855        self.fxnpkgdict = self.eObj.CheckVars()
1856        # all is OK, compile the expression
1857        self.compiledExpr = compile(self.eObj.expression,'','eval')
1858
1859        # look at first value in parmDict to determine its type
1860        parmsInList = True
1861        for key in parmDict:
1862            val = parmDict[key]
1863            if isinstance(val, basestring):
1864                parmsInList = False
1865                break
1866            try: # check if values are in lists
1867                val = parmDict[key][0]
1868            except (TypeError,IndexError):
1869                parmsInList = False
1870            break
1871           
1872        # set up the dicts needed to speed computations
1873        self.exprDict = {}
1874        self.lblLookup = {}
1875        self.varLookup = {}
1876        for v in self.eObj.freeVars:
1877            varname = self.eObj.freeVars[v][0]
1878            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
1879            self.lblLookup[varname] = v
1880            self.varLookup[v] = varname
1881            if parmsInList:
1882                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
1883            else:
1884                parmDict[varname] = self.eObj.freeVars[v][1]
1885            self.exprDict[v] = self.eObj.freeVars[v][1]
1886        for v in self.eObj.assgnVars:
1887            varname = self.eObj.assgnVars[v][0]         #was [name,value]?
1888            if '*' in varname:
1889                varlist = LookupWildCard(varname,parmDict.keys())
1890                if len(varlist) == 0:
1891                    raise Exception,"No variables match "+str(v)
1892                for var in varlist:
1893                    self.lblLookup[var] = v
1894                if parmsInList:
1895                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
1896                else:
1897                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
1898                self.varLookup[v] = [var for var in varlist]
1899            elif varname in parmDict:
1900                self.lblLookup[varname] = v
1901                self.varLookup[v] = varname
1902                if parmsInList:
1903                    self.exprDict[v] = parmDict[varname][0]
1904                else:
1905                    self.exprDict[v] = parmDict[varname]
1906            else:
1907                raise Exception,"No value for variable "+str(v)
1908        self.exprDict.update(self.fxnpkgdict)
1909
1910    def UpdateVars(self,varList,valList):
1911        '''Update the dict for the expression with a set of values
1912        :param list varList: a list of variable names
1913        :param list valList: a list of corresponding values
1914        '''
1915        for var,val in zip(varList,valList):
1916            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
1917           
1918    def EvalExpression(self):
1919        '''Evaluate an expression. Note that the expression
1920        and mapping are taken from the :class:`ExpressionObj` expression object
1921        and the parameter values were specified in :meth:`SetupCalc`.
1922        :returns: a single value for the expression. If parameter
1923        values are arrays (for example, from wild-carded variable names),
1924        the sum of the resulting expression is returned.
1925
1926        For example, if the expression is ``'A*B'``,
1927        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
1928
1929        [0.5, 1, 0.5]
1930
1931        then the result will be ``4.0``.
1932        '''
1933        if self.compiledExpr is None:
1934            raise Exception,"EvalExpression called before SetupCalc"
1935        val = eval(self.compiledExpr,globals(),self.exprDict)
1936        if not np.isscalar(val):
1937            val = np.sum(val)
1938        return val
1939
1940
1941if __name__ == "__main__":
1942    # test equation evaluation
1943    def showEQ(calcobj):
1944        print 50*'='
1945        print calcobj.eObj.expression,'=',calcobj.EvalExpression()
1946        for v in sorted(calcobj.varLookup):
1947            print "  ",v,'=',calcobj.exprDict[v],'=',calcobj.varLookup[v]
1948        # print '  Derivatives'
1949        # for v in calcobj.derivStep.keys():
1950        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
1951
1952    obj = ExpressionObj()
1953
1954    obj.expression = "A*np.exp(B)"
1955    obj.assgnVars =  {'B': '0::Afrac:1'}
1956    obj.freeVars =  {'A': [u'A', 0.5, True]}
1957    #obj.CheckVars()
1958    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
1959    calcobj = ExpressionCalcObj(obj)
1960    calcobj.SetupCalc(parmDict2)
1961    showEQ(calcobj)
1962
1963    obj.expression = "A*np.exp(B)"
1964    obj.assgnVars =  {'B': '0::Afrac:*'}
1965    obj.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
1966    #obj.CheckVars()
1967    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
1968    calcobj = ExpressionCalcObj(obj)
1969    calcobj.SetupCalc(parmDict1)
1970    showEQ(calcobj)
1971
1972    calcobj.SetupCalc(parmDict2)
1973    showEQ(calcobj)
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