source: trunk/GSASIIobj.py @ 1698

Last change on this file since 1698 was 1698, checked in by toby, 7 years ago

Allow powder data importers to set Controls values (such as FreePrm? labels); fix FreePrm? initialization

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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2015-03-12 22:09:00 +0000 (Thu, 12 Mar 2015) $
5# $Author: toby $
6# $Revision: 1698 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 1698 2015-03-12 22:09:00Z toby $
9########### SVN repository information ###################
10
11'''
12*GSASIIobj: Data objects*
13=========================
14
15This module defines and/or documents the data structures used in GSAS-II, as well
16as provides misc. support routines.
17
18Constraints Tree Item
19----------------------
20
21.. _Constraints_table:
22
23.. index::
24   single: Constraints object description
25   single: Data object descriptions; Constraints
26
27Constraints are stored in a dict, separated into groups.
28Note that parameter are named in the following pattern,
29p:h:<var>:n, where p is the phase number, h is the histogram number
30<var> is a variable name and n is the parameter number.
31If a parameter does not depend on a histogram or phase or is unnumbered, that
32number is omitted.
33Note that the contents of each dict item is a List where each element in the
34list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
35The constraints in this form are converted in
36:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
37
38The keys in the Constraints dict are:
39
40.. tabularcolumns:: |l|p{4.5in}|
41
42==========  ====================================================
43  key         explanation
44==========  ====================================================
45Hist        This specifies a list of constraints on
46            histogram-related parameters,
47            which will be of form :h:<var>:n.
48HAP         This specifies a list of constraints on parameters
49            that are defined for every histogram in each phase
50            and are of form p:h:<var>:n.           
51Phase       This specifies a list of constraints on phase
52            parameters,
53            which will be of form p::<var>:n.
54Global      This specifies a list of constraints on parameters
55            that are not tied to a histogram or phase and
56            are of form ::<var>:n
57==========  ====================================================
58
59.. _Constraint_definitions_table:
60
61.. index::
62   single: Constraint definition object description
63   single: Data object descriptions; Constraint Definition
64
65Each constraint is defined as an item in a list. Each constraint is of form::
66
67[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
68
69Where the variable pair list item containing two values [<mult>, <var>], where:
70
71  * <mult> is a multiplier for the constraint (float)
72  * <var> a :class:`G2VarObj` object (previously a str variable name of form
73      'p:h:name[:at]')
74
75Note that the last three items in the list play a special role:
76
77 * <fixedval> is the fixed value for a `constant equation` (``constype=c``)
78   constraint or is None. For a `New variable` (``constype=f``) constraint,
79   a variable name can be specified as a str (used for externally
80   generated constraints)
81 * <varyflag> is True or False for `New variable` (``constype=f``) constraints
82   or is None. This will be implemented in the future to indicate if these variables
83   should be refined.
84 * <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:
85
86    * 'e' defines a set of equivalent variables. Only the first variable is refined (if the
87      appropriate refine flag is set) and and all other equivalent variables in the list
88      are generated from that variable, using the appropriate multipliers.
89    * 'c' defines a constraint equation of form,
90      :math:`m_1 \\times var_1 + m_2 \\times var_2 + ... = c`
91    * 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
92      even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
93      constraint and the mult value is ignored.
94      This is of particular value when needing to hold one or more variables where a
95      single flag controls a set of variables such as, coordinates,
96      the reciprocal metric tensor or anisotropic displacement parameter.
97    * 'f' defines a new variable (function) according to relationship
98      :math:`newvar = m_1 \\times var_1 + m_2 \\times var_2 + ...`
99
100Covariance Tree Item
101--------------------
102
103.. _Covariance_table:
104
105.. index::
106   single: Covariance description
107   single: Data object descriptions; Covariance
108
109The Covariance tree item has results from the last least-squares run. They
110are stored in a dict with these keys:
111
112.. tabularcolumns:: |l|l|p{4in}|
113
114=============  ===============  ====================================================
115  key            sub-key        explanation
116=============  ===============  ====================================================
117newCellDict    \                dict with lattice parameters computed by
118                                :func:`GSASIIstrMath.GetNewCellParms` (dict)
119title          \                Name of gpx file(?) (str)
120variables      \                Values for all N refined variables
121                                (list of float values, length N,
122                                ordered to match varyList)
123sig            \                Uncertainty values for all N refined variables
124                                (list of float values, length N,
125                                ordered to match varyList)
126varyList       \                List of directly refined variables
127                                (list of str values, length N)
128newAtomDict    \                dict with atom position values computed in
129                                :func:`GSASIIstrMath.ApplyXYZshifts` (dict)
130Rvals          \                R-factors, GOF, Marquardt value for last
131                                refinement cycle (dict)
132\              Nobs             Number of observed data points (int)
133\              Rwp              overall weighted profile R-factor (%, float)
134\              chisq            sum[w*(Iobs-Icalc)**2] for all data
135                                note this is not the reduced chi squared (float)
136\              lamMax           Marquardt value applied to Hessian diagonal
137                                (float)
138\              GOF              The goodness-of-fit, aka square root of
139                                the reduced chi squared. (float)
140covMatrix      \                The (NxN) covVariance matrix (np.array)
141=============  ===============  ====================================================
142
143Phase Tree Items
144----------------
145
146.. _Phase_table:
147
148.. index::
149   single: Phase object description
150   single: Data object descriptions; Phase
151
152Phase information is stored in the GSAS-II data tree as children of the
153Phases item in a dict with keys:
154
155.. tabularcolumns:: |l|l|p{4in}|
156
157==========  ===============  ====================================================
158  key         sub-key        explanation
159==========  ===============  ====================================================
160General         \            Overall information for the phase (dict)
161  \         AtomPtrs         list of four locations to use to pull info
162                             from the atom records (list)
163  \         F000X            x-ray F(000) intensity (float)
164  \         F000N            neutron F(000) intensity (float)
165  \         Mydir            directory of current .gpx file (str)
166  \         MCSA controls    Monte Carlo-Simulated Annealing controls (dict)
167  \         Cell             List with 8 items: cell refinement flag (bool)
168                             a, b, c, (Angstrom, float)
169                             alpha, beta & gamma (degrees, float)
170                             volume (A^3, float)
171  \         Type             'nuclear' or 'macromolecular' for now (str)
172  \         Map              dict of map parameters
173  \         SH Texture       dict of spherical harmonic preferred orientation
174                             parameters
175  \         Isotope          dict of isotopes for each atom type
176  \         Isotopes         dict of scattering lengths for each isotope
177                             combination for each element in phase 
178  \         Name             phase name (str)
179  \         SGData           Space group details as a :ref:`space group (SGData) object <SGData_table>`
180                             as defined in :func:`GSASIIspc.SpcGroup`.
181  \         Pawley neg wt    Restraint value for negative Pawley intensities
182                             (float)
183  \         Flip             dict of Charge flip controls
184  \         Data plot type   data plot type ('Mustrain', 'Size' or
185                             'Preferred orientation') for powder data (str)
186  \         Mass             Mass of unit cell contents in g/mol
187  \         POhkl            March-Dollase preferred orientation direction
188  \         Z                dict of atomic numbers for each atom type
189  \         vdWRadii         dict of van der Waals radii for each atom type
190  \         Color            Colors for atoms (list of (r,b,g) triplets)
191  \         AtomTypes        List of atom types
192  \         AtomMass         List of masses for atoms
193  \         doPawley         Flag for Pawley intensity extraction (bool)
194  \         NoAtoms          Number of atoms per unit cell of each type (dict)
195  \         Pawley dmin      maximum Q (as d-space) to use for Pawley
196                             extraction (float)
197  \         BondRadii        Default radius for each atom used to compute
198                             interatomic distances (list of floats)
199  \         AngleRadii       Default radius for each atom used to compute
200                             interatomic angles (list of floats)
201  \         DisAglCtls       Dict with distance/angle search controls,
202                             which has keys 'Name', 'AtomTypes',
203                             'BondRadii', 'AngleRadii' which are as above
204                             except are possibly edited. Also contains
205                             'Factors', which is a 2 element list with
206                             a multiplier for bond and angle search range
207                             [typically (0.85,0.85)].
208ranId           \            unique random number Id for phase (int)
209pId             \            Phase Id number for current project (int).
210Atoms           \            Atoms in phase as a list of lists. The outer list
211                             is for each atom, the inner list contains varying
212                             items depending on the type of phase, see
213                             the :ref:`Atom Records <Atoms_table>` description.
214                             (list of lists)
215Drawing         \            Display parameters (dict)
216\           ballScale        Size of spheres in ball-and-stick display (float)
217\           bondList         dict with bonds
218\           contourLevel     map contour level in e/A^3 (float)
219\           showABC          Flag to show view point triplet (bool). True=show.
220\           viewDir          cartesian viewing direction (np.array with three
221                             elements)
222\           Zclip            clipping distance in A (float)
223\           backColor        background for plot as and R,G,B triplet
224                             (default = [0, 0, 0], black).
225                             (list with three atoms)
226\           selectedAtoms    List of selected atoms (list of int values)
227\           showRigidBodies  Flag to highlight rigid body placement
228\           sizeH            Size ratio for H atoms (float)
229\           bondRadius       Size of binds in A (float)
230\           atomPtrs         positions of x, type, site sym, ADP flag in Draw Atoms (list)
231\           viewPoint        list of lists. First item in list is [x,y,z]
232                             in fractional coordinates for the center of
233                             the plot. Second item list of previous & current
234                             atom number viewed (may be [0,0])
235\           showHydrogen     Flag to control plotting of H atoms.
236\           unitCellBox      Flag to control display of the unit cell.
237\           ellipseProb      Probability limit for display of thermal
238                             ellipsoids in % (float).
239\           vdwScale         Multiplier of van der Waals radius for
240                             display of vdW spheres.
241\           Atoms            A list of lists with an entry for each atom
242                             that is plotted.
243\           Zstep            Step to de/increase Z-clip (float)
244\           Quaternion       Viewing quaternion (4 element np.array)
245\           radiusFactor     Distance ratio for searching for bonds. ? Bonds
246                             are located that are within r(Ra+Rb) and (Ra+Rb)/r
247                             where Ra and Rb are the atomic radii.
248\           oldxy            previous view point (list with two floats)
249\           cameraPos        Viewing position in A for plot (float)
250\           depthFog         True if use depthFog on plot - set currently as False (bool)
251RBModels        \            Rigid body assignments (note Rigid body definitions
252                             are stored in their own main top-level tree entry.)
253Pawley ref      \            Pawley reflections
254Histograms      \            A dict of dicts. The key for the outer dict is
255                             the histograms tied to this phase. The inner
256                             dict contains the combined phase/histogram
257                             parameters for items such as scale factors,
258                             size and strain parameters. (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+7     U11, U22, U33, U12, U13, U23 (6 floats)
394atom[cia+8]       unique atom identifier (int)
395
396==============   ====================================================
397
398Drawing Atom Records
399--------------------
400
401.. _Drawing_atoms_table:
402
403.. index::
404   single: Drawing atoms record description
405   single: Data object descriptions; Drawing atoms record
406
407
408If ``phasedict`` points to the phase information in the data tree, then
409drawing atoms are contained in a list of drawing atom records (list) in
410``phasedict['Drawing']['Atoms']``. Also needed to read atom information
411are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
412which define locations in the atom record, as shown below. Items shown are
413always present; additional ones for macromolecular phases are marked 'mm'
414
415.. tabularcolumns:: |l|p{4.5in}|
416
417==============   ====================================================
418location         explanation
419==============   ====================================================
420ct-4              mm - residue number (str)
421ct-3              mm - residue name (e.g. ALA) (str)
422ct-2              mm - chain label (str)
423ct-1              atom label (str)
424ct                atom type (str)
425cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
426cs-1              Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
427cs                atom drawing style; e.g. 'balls & sticks' (str)
428cs+1              atom label style (e.g. 'name') (str)
429cs+2              atom color (RBG triplet) (int)
430cs+3              ADP flag: Isotropic ('I') or Anisotropic ('A')
431cs+4              Uiso (float)
432cs+5...cs+11      U11, U22, U33, U12, U13, U23 (6 floats)
433ci                unique atom identifier; matches source atom Id in Atom Records (int)
434==============   ====================================================
435
436Powder Diffraction Tree Items
437-----------------------------
438
439.. _Powder_table:
440
441.. index::
442   single: Powder data object description
443   single: Data object descriptions; Powder Data
444
445Every powder diffraction histogram is stored in the GSAS-II data tree
446with a top-level entry named beginning with the string "PWDR ". The
447diffraction data for that information are directly associated with
448that tree item and there are a series of children to that item. The
449routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
450and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
451load this information into a dictionary where the child tree name is
452used as a key, and the information in the main entry is assigned
453a key of ``Data``, as outlined below.
454
455.. tabularcolumns:: |l|l|p{4in}|
456
457======================  ===============  ====================================================
458  key                      sub-key        explanation
459======================  ===============  ====================================================
460Comments                      \           Text strings extracted from the original powder
461                                          data header. These cannot be changed by the user;
462                                          it may be empty.
463Limits                       \            A list of two two element lists, as [[Ld,Hd],[L,H]]
464                                          where L and Ld are the current and default lowest
465                                          two-theta value to be used and
466                                          where H and Hd are the current and default highest
467                                          two-theta value to be used.
468Reflection Lists              \           A dict with an entry for each phase in the
469                                          histogram. The contents of each dict item
470                                          is a dict containing reflections, as described in
471                                          the :ref:`Powder Reflections <PowderRefl_table>`
472                                          description.
473Instrument Parameters         \           A list containing two dicts where the possible
474                                          keys in each dict are listed below. The value
475                                          for each item is a list containing three values:
476                                          the initial value, the current value and a
477                                          refinement flag which can have a value of
478                                          True, False or 0 where 0 indicates a value that
479                                          cannot be refined. The first and second
480                                          values are floats unless otherwise noted.
481                                          Items in the first dict are noted as [1]
482\                         Lam             Specifies a wavelength in Angstroms [1]
483\                         Lam1            Specifies the primary wavelength in
484                                          Angstrom, when an alpha1, alpha2
485                                          source is used [1]
486\                         Lam2            Specifies the secondary wavelength in
487                                          Angstrom, when an alpha1, alpha2
488                                          source is used [1]
489                          I(L2)/I(L1)     Ratio of Lam2 to Lam1 [1]           
490\                         Type            Histogram type (str) [1]:
491                                           * 'PXC' for constant wavelength x-ray
492                                           * 'PNC' for constant wavelength neutron
493                                           * 'PNT' for time of flight neutron
494\                         Zero            Two-theta zero correction in *degrees* [1]
495\                         Azimuth         Azimuthal setting angle for data recorded
496                                          with differing setting angles [1]
497\                         U, V, W         Cagliotti profile coefficients
498                                          for Gaussian instrumental broadening, where the
499                                          FWHM goes as
500                                          :math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
501\                         X, Y            Cauchy (Lorentzian) instrumental broadening
502                                          coefficients [1]
503\                         SH/L            Variant of the Finger-Cox-Jephcoat asymmetric
504                                          peak broadening ratio. Note that this is the
505                                          average between S/L and H/L where S is
506                                          sample height, H is the slit height and
507                                          L is the goniometer diameter. [1]
508\                         Polariz.        Polarization coefficient. [1]
509wtFactor                      \           A weighting factor to increase or decrease
510                                          the leverage of data in the histogram (float).
511                                          A value of 1.0 weights the data with their
512                                          standard uncertainties and a larger value
513                                          increases the weighting of the data (equivalent
514                                          to decreasing the uncertainties).
515Sample Parameters             \           Specifies a dict with parameters that describe how
516                                          the data were collected, as listed
517                                          below. Refinable parameters are a list containing
518                                          a float and a bool, where the second value
519                                          specifies if the value is refined, otherwise
520                                          the value is a float unless otherwise noted.
521\                         Scale           The histogram scale factor (refinable)
522\                         Absorption      The sample absorption coefficient as
523                                          :math:`\\mu r` where r is the radius
524                                          (refinable). Only valid for Debye-Scherrer geometry.
525\                         SurfaceRoughA   Surface roughness parameter A as defined by
526                                          Surotti,J. Appl. Cryst, 5,325-331, 1972.(refinable -
527                                          only valid for Bragg-Brentano geometry)                                         
528\                         SurfaceRoughB   Surface roughness parameter B (refinable -
529                                          only valid for Bragg-Brentano geometry)                                         
530\                         DisplaceX,      Sample displacement from goniometer center
531                          DisplaceY       where Y is along the beam direction and
532                                          X is perpendicular. Units are :math:`\\mu m`
533                                          (refinable).
534\                         Phi, Chi,       Goniometer sample setting angles, in degrees.
535                          Omega
536\                         Gonio. radius   Radius of the diffractometer in mm
537\                         InstrName       A name for the instrument, used in preparing
538                                          a CIF (str).
539\                         Force,          Variables that describe how the measurement
540                          Temperature,    was performed. Not used directly in
541                          Humidity,       any computations.
542                          Pressure,
543                          Voltage
544\                         ranId           The random-number Id for the histogram
545                                          (same value as where top-level key is ranId)
546\                         Type            Type of diffraction data, may be 'Debye-Scherrer'
547                                          or 'Bragg-Brentano' (str).
548\                         Diffuse         not in use?
549hId                           \           The number assigned to the histogram when
550                                          the project is loaded or edited (can change)
551ranId                         \           A random number id for the histogram
552                                          that does not change
553Background                    \           The background is stored as a list with where
554                                          the first item in the list is list and the second
555                                          item is a dict. The list contains the background
556                                          function and its coefficients; the dict contains
557                                          Debye diffuse terms and background peaks.
558                                          (TODO: this needs to be expanded.)
559Data                          \           The data consist of a list of 6 np.arrays
560                                          containing in order:
561
562                                           0. the x-postions (two-theta in degrees),
563                                           1. the intensity values (Yobs),
564                                           2. the weights for each Yobs value
565                                           3. the computed intensity values (Ycalc)
566                                           4. the background values
567                                           5. Yobs-Ycalc
568======================  ===============  ====================================================
569
570Powder Reflection Data Structure
571--------------------------------
572
573.. _PowderRefl_table:
574
575.. index::
576   single: Powder reflection object description
577   single: Data object descriptions; Powder Reflections
578   
579For every phase in a histogram, the ``Reflection Lists`` value is a dict
580one element of which is `'RefList'`, which is a np.array containing
581reflections. The columns in that array are documented below.
582
583==========  ====================================================
584  index         explanation
585==========  ====================================================
586 0,1,2       h,k,l (float)
587 3           multiplicity
588 4           d-space, Angstrom
589 5           pos, two-theta
590 6           sig, Gaussian width
591 7           gam, Lorenzian width
592 8           :math:`F_{obs}^2`
593 9           :math:`F_{calc}^2`
594 10          reflection phase, in degrees
595 11          intensity correction for reflection, this times
596             :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
597==========  ====================================================
598
599Single Crystal Tree Items
600-------------------------
601
602.. _Xtal_table:
603
604.. index::
605   single: Single Crystal data object description
606   single: Data object descriptions; Single crystal data
607
608Every single crystal diffraction histogram is stored in the GSAS-II data tree
609with a top-level entry named beginning with the string "HKLF ". The
610diffraction data for that information are directly associated with
611that tree item and there are a series of children to that item. The
612routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
613and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
614load this information into a dictionary where the child tree name is
615used as a key, and the information in the main entry is assigned
616a key of ``Data``, as outlined below.
617
618.. tabularcolumns:: |l|l|p{4in}|
619
620======================  ===============  ====================================================
621  key                      sub-key        explanation
622======================  ===============  ====================================================
623Data                          \           A dict that contains the
624                                          reflection table,
625                                          as described in the
626                                          :ref:`Single Crystal Reflections
627                                          <XtalRefl_table>`
628                                          description.
629
630Instrument Parameters         \           A list containing two dicts where the possible
631                                          keys in each dict are listed below. The value
632                                          for most items is a list containing two values:
633                                          the initial value, the current value.
634                                          The first and second
635                                          values are floats unless otherwise noted.
636\                         Lam             Specifies a wavelength in Angstroms (two floats)
637\                         Type            Histogram type (two str values):
638                                           * 'SXC' for constant wavelength x-ray
639                                           * 'SNC' for constant wavelength neutron
640                                           * 'SNT' for time of flight neutron
641\                         InstrName       A name for the instrument, used in preparing
642                                          a CIF (str).
643
644wtFactor                      \           A weighting factor to increase or decrease
645                                          the leverage of data in the histogram (float).
646                                          A value of 1.0 weights the data with their
647                                          standard uncertainties and a larger value
648                                          increases the weighting of the data (equivalent
649                                          to decreasing the uncertainties).
650
651hId                           \           The number assigned to the histogram when
652                                          the project is loaded or edited (can change)
653ranId                         \           A random number id for the histogram
654                                          that does not change
655======================  ===============  ====================================================
656
657Single Crystal Reflection Data Structure
658----------------------------------------
659
660.. _XtalRefl_table:
661
662.. index::
663   single: Single Crystal reflection object description
664   single: Data object descriptions; Single Crystal Reflections
665   
666For every single crystal a histogram, the ``'Data'`` item contains
667the structure factors as an np.array in item `'RefList'`.
668The columns in that array are documented below.
669
670==========  ====================================================
671  index         explanation
672==========  ====================================================
673 0,1,2       h,k,l (float)
674 3           multiplicity
675 4           d-space, Angstrom
676 5           :math:`F_{obs}^2`
677 6           :math:`\sigma(F_{obs}^2)`
678 7           :math:`F_{calc}^2`
679 8           :math:`F_{obs}^2T`
680 9           :math:`F_{calc}^2T`
681 10          reflection phase, in degrees
682 11          intensity correction for reflection, this times
683             :math:`F_{obs}^2` or :math:`F_{calc}^2`
684             gives Iobs or Icalc
685==========  ====================================================
686
687Image Data Structure
688--------------------
689
690.. _Image_table:
691
692.. index::
693   image: Image data object description
694   image: Image object descriptions
695   
696Every 2-dimensional image is stored in the GSAS-II data tree
697with a top-level entry named beginning with the string "IMG ". The
698image data are directly associated with that tree item and there
699are a series of children to that item. The routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
700and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
701load this information into a dictionary where the child tree name is
702used as a key, and the information in the main entry is assigned
703a key of ``Data``, as outlined below.
704
705.. tabularcolumns:: |l|l|p{4in}|
706
707======================  ======================  ====================================================
708  key                      sub-key              explanation
709======================  ======================  ====================================================
710Comments                       \                Text strings extracted from the original image data
711                                                header or a metafile. These cannot be changed by 
712                                                the user; it may be empty.                                               
713Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
714                                                value. Accomodates
715                                                detector orientations other than with the detector
716                                                X-axis
717                                                horizontal.
718\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
719                                                during image integration multiplied by value. It must have the same size/shape as
720                                                the integrated image. NB: value < 0 for subtraction.
721\                           calibrant           (str) The material used for determining the position/orientation
722                                                of the image. The data is obtained from :func:`ImageCalibrants`
723                                                and UserCalibrants.py (supplied by user).
724\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
725\                           calibskip           (int) The number of expected diffraction lines skipped during the last
726                                                calibration run.
727\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
728                                                strikes the detector plane as determined by calibration. This point
729                                                does not have to be within the limits of the detector boundaries.
730\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
731                                                of the image is at the center line otherwise it is at the leading edge.
732\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
733\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
734                                                calibration calculations. See pixLimit for details as how point is found.           
735\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
736                                                ring offset at higher angles. Optionally determined by calibration.
737\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
738\                           distance            (float) The distance (mm) from sample to detector plane.
739\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
740                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
741                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
742                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
743                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
744\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
745\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
746\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
747                                                Required for texture calculations.
748\                           invert_x            (bool) If True display the image with the x-axis inverted.
749\                           invert_y            (bool) If True display the image with the y-axis inverted.
750\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
751\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
752\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
753                                                intensities obtained during integration.
754\                           outAzimuths         (int) The number of azimuth pie slices.
755\                           outChannels         (int) The number of 2-theta steps.
756\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
757\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
758                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
759                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
760                                                Locations are used to construct rings of points for calibration calcualtions.
761\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
762                                                integration using value.
763\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
764                                                diffraction ring with the same d-spacing (dsp)
765\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
766                                                selected by the user,
767\                           Range               (list) The minimum & maximum values of the image
768\                           rotation            (float) The angle between the x-axis and the vector about which the
769                                                detector is tilted. Constrained to -180 to 180 deg.     
770\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
771                                                calculations.
772\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
773                                                to cause correction to be applied.
774\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
775\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.           
776\                           showLines           (bool) If True then isplay the integration limits to be used.
777\                           size                (list:int) The number of pixels on the image x & y axes
778\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
779\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
780\                           wavelength          (float) Tha radiation wavelength (Angstroms) as entered by the user (or someday obtained from the image header).
781                                               
782Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
783                                                to be excluded from integration
784\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
785                                                of which is excluded from recalibration and integration. Only one frame is allowed.
786\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
787                                                from integration.
788\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
789                                                to be excluded from integration.
790\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
791                                                to be excluded from integration.
792\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
793                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.   
794                                               
795Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
796\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
797                                                These will be restricted by space group symmetry; result of strain fit refinement.
798\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
799\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
800                                                and are used to determine the strain tensor.
801                                                The dictionary items are:
802                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
803                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
804                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
805                                                'Esig': (list: float) Esds for Emat from fitting.
806                                                'pixLimit': (int) Search range to find highest point on ring for each data point
807                                                'cutoff': (float) I/Ib cutoff for searching.
808                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
809                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
810                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
811                                               
812======================  ======================  ====================================================
813
814Parameter Dictionary
815-------------------------
816
817.. _parmDict_table:
818
819.. index::
820   single: Parameter dictionary
821
822The parameter dictionary contains all of the variable parameters for the refinement.
823The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
824It is prepared in two ways. When loaded from the tree
825(in :meth:`GSASII.GSASII.MakeLSParmDict` and
826:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
827the values are lists with two elements: ``[value, refine flag]``
828
829When loaded from the GPX file (in
830:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
831dict is the actual parameter value (usually a float, but sometimes a
832letter or string flag value (such as I or A for iso/anisotropic).
833
834
835*Classes and routines*
836----------------------
837
838'''
839import re
840import imp
841import random as ran
842import sys
843import GSASIIpath
844import GSASIImath as G2mth
845import numpy as np
846
847GSASIIpath.SetVersionNumber("$Revision: 1698 $")
848
849DefaultControls = {
850    'deriv type':'analytic Hessian',    #default controls
851    'min dM/M':0.0001,'shift factor':1.,'max cyc':3,'F**2':True,
852    'minF/sig':0,
853    'Author':'no name',
854    'FreePrm1':'Sample humidity (%)',
855    'FreePrm2':'Sample voltage (V)',
856    'FreePrm3':'Applied load (MN)',
857    }
858'''Values to be used as defaults for the initial contents of the ``Controls``
859data tree item.
860'''
861
862def MakeUniqueLabel(lbl,labellist):
863    '''Make sure that every a label is unique against a list by adding
864    digits at the end until it is not found in list.
865
866    :param str lbl: the input label
867    :param list labellist: the labels that have already been encountered
868    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
869      ``_10-99``, etc.) appended at the end
870    '''
871    lbl = lbl.strip()
872    if not lbl: # deal with a blank label
873        lbl = '_1'
874    if lbl not in labellist:
875        labellist.append(lbl)
876        return lbl
877    i = 1
878    prefix = lbl
879    if '_' in lbl:
880        prefix = lbl[:lbl.rfind('_')]
881        suffix = lbl[lbl.rfind('_')+1:]
882        try:
883            i = int(suffix)+1
884        except: # suffix could not be parsed
885            i = 1
886            prefix = lbl
887    while prefix+'_'+str(i) in labellist:
888        i += 1
889    else:
890        lbl = prefix+'_'+str(i)
891        labellist.append(lbl)
892    return lbl
893
894PhaseIdLookup = {}
895'''dict listing phase name and random Id keyed by sequential phase index as a str;
896best to access this using :func:`LookupPhaseName`
897'''
898PhaseRanIdLookup = {}
899'''dict listing phase sequential index keyed by phase random Id;
900best to access this using :func:`LookupPhaseId`
901'''
902HistIdLookup = {}
903'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
904best to access this using :func:`LookupHistName`
905'''
906HistRanIdLookup = {}
907'''dict listing histogram sequential index keyed by histogram random Id;
908best to access this using :func:`LookupHistId`
909'''
910AtomIdLookup = {}
911'''dict listing for each phase index as a str, the atom label and atom random Id,
912keyed by atom sequential index as a str;
913best to access this using :func:`LookupAtomLabel`
914'''
915AtomRanIdLookup = {}
916'''dict listing for each phase the atom sequential index keyed by atom random Id;
917best to access this using :func:`LookupAtomId`
918'''
919ShortPhaseNames = {}
920'''a dict containing a possibly shortened and when non-unique numbered
921version of the phase name. Keyed by the phase sequential index.
922'''
923ShortHistNames = {}
924'''a dict containing a possibly shortened and when non-unique numbered
925version of the histogram name. Keyed by the histogram sequential index.
926'''
927
928VarDesc = {}
929''' This dictionary lists descriptions for GSAS-II variables,
930as set in :func:`CompileVarDesc`. See that function for a description
931for how keys and values are written.
932'''
933
934reVarDesc = {}
935''' This dictionary lists descriptions for GSAS-II variables with
936the same values as :attr:`VarDesc` except that keys have been compiled as
937regular expressions. Initialized in :func:`CompileVarDesc`.
938'''
939
940def IndexAllIds(Histograms,Phases):
941    '''Scan through the used phases & histograms and create an index
942    to the random numbers of phases, histograms and atoms. While doing this,
943    confirm that assigned random numbers are unique -- just in case lightning
944    strikes twice in the same place.
945
946    Note: this code assumes that the atom random Id (ranId) is the last
947    element each atom record.
948
949    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
950    (which loads the histograms and phases from a GPX file),
951    :meth:`~GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
952    (which loads the histograms and phases from the data tree.) and
953    :meth:`GSASIIconstrGUI.UpdateConstraints`
954    (which displays & edits the constraints in a GUI)
955
956    TODO: do we need a lookup for rigid body variables?
957    '''
958    # process phases and atoms
959    PhaseIdLookup.clear()
960    PhaseRanIdLookup.clear()   
961    AtomIdLookup.clear()
962    AtomRanIdLookup.clear()
963    ShortPhaseNames.clear()
964    for ph in Phases:
965        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
966        ranId = Phases[ph]['ranId'] 
967        while ranId in PhaseRanIdLookup:
968            # Found duplicate random Id! note and reassign
969            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
970            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxint)
971        pId = str(Phases[ph]['pId'])
972        PhaseIdLookup[pId] = (ph,ranId)
973        PhaseRanIdLookup[ranId] = pId
974        shortname = ph[:10]
975        while shortname in ShortPhaseNames.values():
976            shortname = ph[:8] + ' ('+ pId + ')'
977        ShortPhaseNames[pId] = shortname
978        AtomIdLookup[pId] = {}
979        AtomRanIdLookup[pId] = {}
980        for iatm,at in enumerate(Phases[ph]['Atoms']):
981            ranId = at[cia+8]
982            while ranId in AtomRanIdLookup[pId]: # check for dups
983                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
984                at[cia+8] = ranId = ran.randint(0,sys.maxint)
985            AtomRanIdLookup[pId][ranId] = str(iatm)
986            if Phases[ph]['General']['Type'] == 'macromolecular':
987                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
988            else:
989                label = at[ct-1]
990            AtomIdLookup[pId][str(iatm)] = (label,ranId)
991    # process histograms
992    HistIdLookup.clear()
993    HistRanIdLookup.clear()
994    ShortHistNames.clear()
995    for hist in Histograms:
996        ranId = Histograms[hist]['ranId']
997        while ranId in HistRanIdLookup:
998            # Found duplicate random Id! note and reassign
999            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1000            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxint)
1001        hId = str(Histograms[hist]['hId'])
1002        HistIdLookup[hId] = (hist,ranId)
1003        HistRanIdLookup[ranId] = hId
1004        shortname = hist[:15]
1005        while shortname in ShortHistNames.values():
1006            shortname = hist[:11] + ' ('+ hId + ')'
1007        ShortHistNames[hId] = shortname
1008
1009def LookupAtomId(pId,ranId):
1010    '''Get the atom number from a phase and atom random Id
1011
1012    :param int/str pId: the sequential number of the phase
1013    :param int ranId: the random Id assigned to an atom
1014
1015    :returns: the index number of the atom (str)
1016    '''
1017    if not AtomRanIdLookup:
1018        raise Exception,'Error: LookupAtomId called before IndexAllIds was run'
1019    if pId is None or pId == '':
1020        raise KeyError,'Error: phase is invalid (None or blank)'
1021    pId = str(pId)
1022    if pId not in AtomRanIdLookup:
1023        raise KeyError,'Error: LookupAtomId does not have phase '+pId
1024    if ranId not in AtomRanIdLookup[pId]:
1025        raise KeyError,'Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']'
1026    return AtomRanIdLookup[pId][ranId]
1027
1028def LookupAtomLabel(pId,index):
1029    '''Get the atom label from a phase and atom index number
1030
1031    :param int/str pId: the sequential number of the phase
1032    :param int index: the index of the atom in the list of atoms
1033
1034    :returns: the label for the atom (str) and the random Id of the atom (int)
1035    '''
1036    if not AtomIdLookup:
1037        raise Exception,'Error: LookupAtomLabel called before IndexAllIds was run'
1038    if pId is None or pId == '':
1039        raise KeyError,'Error: phase is invalid (None or blank)'
1040    pId = str(pId)
1041    if pId not in AtomIdLookup:
1042        raise KeyError,'Error: LookupAtomLabel does not have phase '+pId
1043    if index not in AtomIdLookup[pId]:
1044        raise KeyError,'Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']'
1045    return AtomIdLookup[pId][index]
1046
1047def LookupPhaseId(ranId):
1048    '''Get the phase number and name from a phase random Id
1049
1050    :param int ranId: the random Id assigned to a phase
1051    :returns: the sequential Id (pId) number for the phase (str)
1052    '''
1053    if not PhaseRanIdLookup:
1054        raise Exception,'Error: LookupPhaseId called before IndexAllIds was run'
1055    if ranId not in PhaseRanIdLookup:
1056        raise KeyError,'Error: LookupPhaseId does not have ranId '+str(ranId)
1057    return PhaseRanIdLookup[ranId]
1058
1059def LookupPhaseName(pId):
1060    '''Get the phase number and name from a phase Id
1061
1062    :param int/str pId: the sequential assigned to a phase
1063    :returns:  (phase,ranId) where phase is the name of the phase (str)
1064      and ranId is the random # id for the phase (int)
1065    '''
1066    if not PhaseIdLookup:
1067        raise Exception,'Error: LookupPhaseName called before IndexAllIds was run'
1068    if pId is None or pId == '':
1069        raise KeyError,'Error: phase is invalid (None or blank)'
1070    pId = str(pId)
1071    if pId not in PhaseIdLookup:
1072        raise KeyError,'Error: LookupPhaseName does not have index '+pId
1073    return PhaseIdLookup[pId]
1074
1075def LookupHistId(ranId):
1076    '''Get the histogram number and name from a histogram random Id
1077
1078    :param int ranId: the random Id assigned to a histogram
1079    :returns: the sequential Id (hId) number for the histogram (str)
1080    '''
1081    if not HistRanIdLookup:
1082        raise Exception,'Error: LookupHistId called before IndexAllIds was run'
1083    if ranId not in HistRanIdLookup:
1084        raise KeyError,'Error: LookupHistId does not have ranId '+str(ranId)
1085    return HistRanIdLookup[ranId]
1086
1087def LookupHistName(hId):
1088    '''Get the histogram number and name from a histogram Id
1089
1090    :param int/str hId: the sequential assigned to a histogram
1091    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1092      and ranId is the random # id for the histogram (int)
1093    '''
1094    if not HistIdLookup:
1095        raise Exception,'Error: LookupHistName called before IndexAllIds was run'
1096    if hId is None or hId == '':
1097        raise KeyError,'Error: histogram is invalid (None or blank)'
1098    hId = str(hId)
1099    if hId not in HistIdLookup:
1100        raise KeyError,'Error: LookupHistName does not have index '+hId
1101    return HistIdLookup[hId]
1102
1103def fmtVarDescr(varname):
1104    '''Return a string with a more complete description for a GSAS-II variable
1105
1106    :param str varname: A full G2 variable name with 2 or 3 or 4
1107       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1108       
1109    :returns: a string with the description
1110    '''
1111    s,l = VarDescr(varname)
1112    return s+": "+l
1113
1114def VarDescr(varname):
1115    '''Return two strings with a more complete description for a GSAS-II variable
1116
1117    :param str name: A full G2 variable name with 2 or 3 or 4
1118       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1119       
1120    :returns: (loc,meaning) where loc describes what item the variable is mapped
1121      (phase, histogram, etc.) and meaning describes what the variable does.
1122    '''
1123   
1124    # special handling for parameter names without a colons
1125    # for now, assume self-defining
1126    if varname.find(':') == -1:
1127        return "Global",varname
1128       
1129    l = getVarDescr(varname)
1130    if not l:
1131        return ("invalid variable name ("+str(varname)+")!"),""
1132#        return "invalid variable name!",""
1133
1134    if not l[-1]:
1135        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1136
1137    if len(l) == 3:         #SASD variable name!
1138        s = 'component:'+l[1]
1139        return s,l[-1]
1140    s = ""
1141    if l[0] is not None and l[1] is not None: # HAP: keep short
1142        if l[2] == "Scale": # fix up ambigous name
1143            l[5] = "Phase fraction"
1144        if l[0] == '*':
1145            lbl = 'all'
1146        else:
1147            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1148        if l[1] == '*':
1149            hlbl = 'all'
1150        else:
1151            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1152        if hlbl[:4] == 'HKLF':
1153            hlbl = 'Xtl='+hlbl[5:]
1154        elif hlbl[:4] == 'PWDR':
1155            hlbl = 'Pwd='+hlbl[5:]
1156        else:
1157            hlbl = 'Hist='+hlbl
1158        s = "Ph="+str(lbl)+" * "+str(hlbl)
1159    else:
1160        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1161            l[5] = "Scale factor"
1162        if l[2] == 'Back': # background parameters are "special", alas
1163            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1164            l[-1] += ' #'+str(l[3])
1165        elif l[4] is not None: # rigid body parameter
1166            lbl = ShortPhaseNames.get(l[0],'phase?')
1167            s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1168        elif l[3] is not None: # atom parameter,
1169            lbl = ShortPhaseNames.get(l[0],'phase?')
1170            try:
1171                albl = LookupAtomLabel(l[0],l[3])[0]
1172            except KeyError:
1173                albl = 'Atom?'
1174            s = "Atom "+str(albl)+" in "+str(lbl)
1175        elif l[0] == '*':
1176            s = "All phases "
1177        elif l[0] is not None:
1178            lbl = ShortPhaseNames.get(l[0],'phase?')
1179            s = "Phase "+str(lbl)
1180        elif l[1] == '*':
1181            s = 'All hists'
1182        elif l[1] is not None:
1183            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1184            if hlbl[:4] == 'HKLF':
1185                hlbl = 'Xtl='+hlbl[5:]
1186            elif hlbl[:4] == 'PWDR':
1187                hlbl = 'Pwd='+hlbl[5:]
1188            else:
1189                hlbl = 'Hist='+hlbl
1190            s = str(hlbl)
1191    if not s:
1192        s = 'Global'
1193    return s,l[-1]
1194
1195def getVarDescr(varname):
1196    '''Return a short description for a GSAS-II variable
1197
1198    :param str name: A full G2 variable name with 2 or 3 or 4
1199       colons (<p>:<h>:name[:<a1>][:<a2>])
1200     
1201    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1202      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1203      the histogram number and the atom number; `name` will always be
1204      a str; and `description` is str or `None`.
1205      If the variable name is incorrectly formed (for example, wrong
1206      number of colons), `None` is returned instead of a list.
1207    '''
1208    l = varname.split(':')
1209    if len(l) == 2:     #SASD parameter name
1210        return varname,l[0],getDescr(l[1])
1211    if len(l) == 3:
1212        l += [None,None]
1213    elif len(l) == 4:
1214        l += [None]
1215    elif len(l) != 5:
1216        return None
1217    for i in (0,1,3,4):
1218        if l[i] == "":
1219            l[i] = None
1220    l += [getDescr(l[2])]
1221    return l
1222   
1223def CompileVarDesc():
1224    '''Set the values in the variable description lookup table (:attr:`VarDesc`)
1225    into :attr:`reVarDesc`. This is called in :func:`getDescr` so the initialization
1226    is always done before use.
1227
1228    Note that keys may contain regular expressions, where '[xyz]'
1229    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range of values).
1230    '.*' matches any string. For example::
1231
1232    'AUiso':'Atomic isotropic displacement parameter',
1233
1234    will match variable ``'p::AUiso:a'``.
1235    If parentheses are used in the key, the contents of those parentheses can be
1236    used in the value, such as::
1237
1238    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1239
1240    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1241    in the value when used.
1242   
1243    '''
1244    if reVarDesc: return # already done
1245    for key,value in {
1246        # derived or other sequential vars
1247        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1248        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1249        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1250        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1251        # ambiguous, alas:
1252        'Scale' : 'Phase or Histogram scale factor',
1253        # Phase vars (p::<var>)
1254        'A([0-5])' : 'Reciprocal metric tensor component \\1',
1255        'Vol' : 'Unit cell volume',
1256        # Atom vars (p::<var>:a)
1257        'dA([xyz])$' : 'change to atomic coordinate, \\1',
1258        'A([xyz])$' : '\\1 fractional atomic coordinate',
1259        'AUiso':'Atomic isotropic displacement parameter',
1260        'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1261        'Afrac': 'Atomic occupancy parameter',
1262        # Hist & Phase (HAP) vars (p:h:<var>)
1263        'Back': 'Background term',
1264        'BkPkint;(.*)':'Background peak #\\1 intensity',
1265        'BkPkpos;(.*)':'Background peak #\\1 position',
1266        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1267        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1268        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1269        'D([123][123])' : 'Anisotropic strain coef. \\1',
1270        'Extinction' : 'Extinction coef.',
1271        'MD' : 'March-Dollase coef.',
1272        'Mustrain;.*' : 'Microstrain coef.',
1273        'Size;.*' : 'Crystallite size value',
1274        'eA$' : 'Cubic mustrain value',
1275        'Ep$' : 'Primary extinction',
1276        'Es$' : 'Secondary type II extinction',
1277        'Eg$' : 'Secondary type I extinction',
1278        #Histogram vars (:h:<var>)
1279        'Absorption' : 'Absorption coef.',
1280        'Displace([XY])' : 'Debye-Scherrer sample displacement \\1',
1281        'Lam' : 'Wavelength',
1282        'Polariz\.' : 'Polarization correction',
1283        'SH/L' : 'FCJ peak asymmetry correction',
1284        '([UVW])$' : 'Gaussian instrument broadening \\1',
1285        '([XY])$' : 'Cauchy instrument broadening \\1',
1286        'Zero' : 'Debye-Scherrer zero correction',
1287        'nDebye' : 'Debye model background corr. terms',
1288        'nPeaks' : 'Fixed peak background corr. terms',
1289        'RBV.*' : 'Vector rigid body parameter',
1290        'RBR.*' : 'Residue rigid body parameter',
1291        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1292        'RBRP([xyz])' : 'Residue rigid body position parameter',
1293        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1294        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1295        'constr([0-9]*)' : 'Parameter from constraint',
1296        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1297        'mV([0-2])$' : 'Modulation vector component \\1',
1298        'Fsin'  :   'Sin site fraction modulation',
1299        'Fcos'  :   'Cos site fraction modulation',
1300        'Fzero'  :   'Crenel function offset',
1301        'Fwid'   :   'Crenel function width',
1302        'Tzero'  :   'Sawtooth/ZigZag location',
1303        '([XYZ])slope': 'Sawtooth/ZigZag slope for \\1',
1304        '([XYZ])sin'  : 'Sin position wave for \\1',
1305        '([XYZ])cos'  : 'Cos position wave for \\1',
1306        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1307        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1308        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1309        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1310        # SASD vars (l:<var>;l = component)
1311        'Aspect ratio' : 'Particle aspect ratio',
1312        'Length' : 'Cylinder length',
1313        'Diameter' : 'Cylinder/disk diameter',
1314        'Thickness' : 'Disk thickness',
1315        'Dist' : 'Interparticle distance',
1316        'VolFr' : 'Dense scatterer volume fraction',
1317        'epis' : 'Sticky sphere epsilon',
1318        'Sticky' : 'Stickyness',
1319        'Depth' : 'Well depth',
1320        'Width' : 'Well width',
1321        'Volume' : 'Particle volume',
1322        'Radius' : 'Sphere/cylinder/disk radius',
1323        'Mean' : 'Particle mean radius',
1324        'StdDev' : 'Standard deviation in Mean',
1325        'G$': 'Guinier prefactor',
1326        'Rg$': 'Guinier radius of gyration',
1327        'B$': 'Porod prefactor',
1328        'P$': 'Porod power',
1329        'Cutoff': 'Porod cutoff',
1330        'PkInt': 'Bragg peak intensity',
1331        'PkPos': 'Bragg peak position',
1332        'PkSig': 'Bragg peak sigma',
1333        'PkGam': 'Bragg peak gamma',
1334        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1335        'Dcalc': 'Calc. d-spacing',
1336        'Back$': 'background parameter',
1337        'pos$': 'peak position',
1338        'int$': 'peak intensity',
1339        }.items():
1340        VarDesc[key] = value
1341        reVarDesc[re.compile(key)] = value
1342
1343def getDescr(name):
1344    '''Return a short description for a GSAS-II variable
1345
1346    :param str name: The descriptive part of the variable name without colons (:)
1347     
1348    :returns: a short description or None if not found
1349    '''
1350
1351    CompileVarDesc() # compile the regular expressions, if needed
1352    for key in reVarDesc:
1353        m = key.match(name)
1354        if m:
1355            reVarDesc[key]
1356            return m.expand(reVarDesc[key])
1357    return None
1358
1359def GenWildCard(varlist):
1360    '''Generate wildcard versions of G2 variables. These introduce '*'
1361    for a phase, histogram or atom number (but only for one of these
1362    fields) but only when there is more than one matching variable in the
1363    input variable list. So if the input is this::
1364   
1365      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1366
1367    then the output will be this::
1368   
1369       wildList = ['*::AUiso:0', '0::AUiso:*']
1370
1371    :param list varlist: an input list of GSAS-II variable names
1372      (such as 0::AUiso:0)
1373
1374    :returns: wildList, the generated list of wild card variable names.
1375    '''
1376    wild = []
1377    for i in (0,1,3):
1378        currentL = varlist[:]
1379        while currentL:
1380            item1 = currentL.pop(0)
1381            i1splt = item1.split(':')
1382            if i >= len(i1splt): continue
1383            if i1splt[i]:
1384                nextL = []
1385                i1splt[i] = '[0-9]+'
1386                rexp = re.compile(':'.join(i1splt))
1387                matchlist = [item1]
1388                for nxtitem in currentL:
1389                    if rexp.match(nxtitem):
1390                        matchlist += [nxtitem]
1391                    else:
1392                        nextL.append(nxtitem)
1393                if len(matchlist) > 1:
1394                    i1splt[i] = '*'
1395                    wild.append(':'.join(i1splt))
1396                currentL = nextL
1397    return wild
1398
1399def LookupWildCard(varname,varlist):
1400    '''returns a list of variable names from list varname
1401    that match wildcard name in varname
1402   
1403    :param str varname: a G2 variable name containing a wildcard
1404      (such as \*::var)
1405    :param list varlist: the list of all variable names used in
1406      the current project
1407    :returns: a list of matching GSAS-II variables (may be empty) 
1408    '''
1409    rexp = re.compile(varname.replace('*','[0-9]+'))
1410    return sorted([var for var in varlist if rexp.match(var)])
1411
1412
1413def _lookup(dic,key):
1414    '''Lookup a key in a dictionary, where None returns an empty string
1415    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1416    '''
1417    if key is None:
1418        return ""
1419    elif key == "*":
1420        return "*"
1421    else:
1422        return dic.get(key,'?')
1423
1424class G2VarObj(object):
1425    '''Defines a GSAS-II variable either using the phase/atom/histogram
1426    unique Id numbers or using a character string that specifies
1427    variables by phase/atom/histogram number (which can change).
1428    Note that :func:`LoadID` should be used to (re)load the current Ids
1429    before creating or later using the G2VarObj object.
1430
1431    This can store rigid body variables, but does not translate the residue # and
1432    body # to/from random Ids
1433
1434    A :class:`G2VarObj` object can be created with a single parameter:
1435   
1436    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1437      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1438
1439     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
1440     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1441     * a is the atom number (which may be left blank in which case the third colon is omitted).
1442       The atom number can be specified as '*' if a phase number is specified (not as '*').
1443       For rigid body variables, specify a will be a string of form "residue:body#"
1444
1445      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1446      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1447      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1448      For a rigid body variables, AtomID is a string of form "residue:body#".
1449
1450    If four positional arguments are supplied, they are:
1451
1452    :param str/int phasenum: The number for the phase (or None or '*')
1453    :param str/int histnum: The number for the histogram (or None or '*')
1454    :param str varname: a single value can be used to create a :class:`G2VarObj`
1455    :param str/int atomnum: The number for the atom (or None or '*')
1456   
1457    '''
1458    IDdict = {}
1459    IDdict['phases'] = {}
1460    IDdict['hists'] = {}
1461    IDdict['atoms'] = {}
1462    def __init__(self,*args):
1463        self.phase = None
1464        self.histogram = None
1465        self.name = ''
1466        self.atom = None
1467        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1468            # single arg with 4 values
1469            self.phase,self.histogram,self.name,self.atom = args[0]
1470        elif len(args) == 1 and ':' in args[0]:
1471            #parse a string
1472            lst = args[0].split(':')
1473            if lst[0] == '*':
1474                self.phase = '*'
1475                if len(lst) > 3:
1476                    self.atom = lst[3]
1477                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1478            elif lst[1] == '*':           
1479                self.histogram = '*'
1480                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1481            else:
1482                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1483                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1484                if len(lst) == 4:
1485                    if lst[3] == '*':
1486                        self.atom = '*'
1487                    else:
1488                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1489                elif len(lst) == 5:
1490                    self.atom = lst[3]+":"+lst[4]
1491                elif len(lst) == 3:
1492                    pass
1493                else:
1494                    raise Exception,"Too many colons in var name "+str(args[0])
1495            self.name = lst[2]
1496        elif len(args) == 4:
1497            if args[0] == '*':
1498                self.phase = '*'
1499                self.atom = args[3]
1500            else:
1501                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1502                if args[3] == '*':
1503                    self.atom = '*'
1504                elif args[0] is not None:
1505                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1506            if args[1] == '*':
1507                self.histogram = '*'
1508            else:
1509                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1510            self.name = args[2]
1511        else:
1512            raise Exception,"Incorrectly called GSAS-II parameter name"
1513
1514        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1515
1516    def __str__(self):
1517        return self.varname()
1518
1519    def varname(self):
1520        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1521        string (p:h:<var>:a) or (p:h:<var>)
1522
1523        :returns: the variable name as a str
1524        '''
1525        a = ""
1526        if self.phase == "*":
1527            ph = "*"
1528            if self.atom:
1529                a = ":" + str(self.atom)
1530        else:
1531            ph = _lookup(PhaseRanIdLookup,self.phase)
1532            if self.atom == '*':
1533                a = ':*'
1534            elif self.atom:
1535                if ":" in str(self.atom):
1536                    a = ":" + str(self.atom)
1537                elif ph in AtomRanIdLookup:
1538                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1539                else:
1540                    a = ":?"
1541        if self.histogram == "*":
1542            hist = "*"
1543        else:
1544            hist = _lookup(HistRanIdLookup,self.histogram)
1545        s = (ph + ":" + hist + ":" + str(self.name)) + a
1546        return s
1547   
1548    def __repr__(self):
1549        '''Return the detailed contents of the object
1550        '''
1551        s = "<"
1552        if self.phase == '*':
1553            s += "Phases: all; "
1554            if self.atom is not None:
1555                if ":" in str(self.atom):
1556                    s += "Rigid body" + str(self.atom) + "; "
1557                else:
1558                    s += "Atom #" + str(self.atom) + "; "
1559        elif self.phase is not None:
1560            ph =  _lookup(PhaseRanIdLookup,self.phase)
1561            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1562            if self.atom == '*':
1563                s += "Atoms: all; "
1564            elif ":" in self(self.atom):
1565                s += "Rigid body" + str(self.atom) + "; "
1566            elif self.atom is not None:
1567                s += "Atom rId=" + str(self.atom)
1568                if ph in AtomRanIdLookup:
1569                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1570                else:
1571                    s += " (#? -- not found!); "
1572        if self.histogram == '*':
1573            s += "Histograms: all; "
1574        elif self.histogram is not None:
1575            hist = _lookup(HistRanIdLookup,self.histogram)
1576            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1577        s += 'Variable name="' + str(self.name) + '">'
1578        return s+" ("+self.varname()+")"
1579
1580    def __eq__(self, other):
1581        if type(other) is type(self):
1582            return (self.phase == other.phase and
1583                    self.histogram == other.histogram and
1584                    self.name == other.name and
1585                    self.atom == other.atom)
1586        return False
1587
1588    def _show(self):
1589        'For testing, shows the current lookup table'
1590        print 'phases', self.IDdict['phases']
1591        print 'hists', self.IDdict['hists']
1592        print 'atomDict', self.IDdict['atoms']
1593
1594#==========================================================================
1595# shortcut routines
1596exp = np.exp
1597sind = sin = s = lambda x: np.sin(x*np.pi/180.)
1598cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
1599tand = tan = t = lambda x: np.tan(x*np.pi/180.)
1600sqrt = sq = lambda x: np.sqrt(x)
1601pi = lambda: np.pi
1602class ExpressionObj(object):
1603    '''Defines an object with a user-defined expression, to be used for
1604    secondary fits or restraints. Object is created null, but is changed
1605    using :meth:`LoadExpression`. This contains only the minimum
1606    information that needs to be stored to save and load the expression
1607    and how it is mapped to GSAS-II variables.
1608    '''
1609    def __init__(self):
1610        self.expression = ''
1611        'The expression as a text string'
1612        self.assgnVars = {}
1613        '''A dict where keys are label names in the expression mapping to a GSAS-II
1614        variable. The value a G2 variable name.
1615        Note that the G2 variable name may contain a wild-card and correspond to
1616        multiple values.
1617        '''
1618        self.freeVars = {}
1619        '''A dict where keys are label names in the expression mapping to a free
1620        parameter. The value is a list with:
1621
1622         * a name assigned to the parameter
1623         * a value for to the parameter and
1624         * a flag to determine if the variable is refined.
1625        ''' 
1626        self.depVar = None
1627
1628        self.lastError = ('','')
1629        '''Shows last encountered error in processing expression
1630        (list of 1-3 str values)'''
1631
1632    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
1633        '''Load the expression and associated settings into the object. Raises
1634        an exception if the expression is not parsed, if not all functions
1635        are defined or if not all needed parameter labels in the expression
1636        are defined.
1637
1638        This will not test if the variable referenced in these definitions
1639        are actually in the parameter dictionary. This is checked when the
1640        computation for the expression is done in :meth:`SetupCalc`.
1641       
1642        :param str expr: the expression
1643        :param list exprVarLst: parameter labels found in the expression
1644        :param dict varSelect: this will be 0 for Free parameters
1645          and non-zero for expression labels linked to G2 variables.
1646        :param dict varName: Defines a name (str) associated with each free parameter
1647        :param dict varValue: Defines a value (float) associated with each free parameter
1648        :param dict varRefflag: Defines a refinement flag (bool)
1649          associated with each free parameter
1650        '''
1651        self.expression = expr
1652        self.compiledExpr = None
1653        self.freeVars = {}
1654        self.assgnVars = {}
1655        for v in exprVarLst:
1656            if varSelect[v] == 0:
1657                self.freeVars[v] = [
1658                    varName.get(v),
1659                    varValue.get(v),
1660                    varRefflag.get(v),
1661                    ]
1662            else:
1663                self.assgnVars[v] = varName[v]
1664        self.CheckVars()
1665
1666    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
1667        '''Load the expression and associated settings from the object into
1668        arrays used for editing.
1669
1670        :param list exprVarLst: parameter labels found in the expression
1671        :param dict varSelect: this will be 0 for Free parameters
1672          and non-zero for expression labels linked to G2 variables.
1673        :param dict varName: Defines a name (str) associated with each free parameter
1674        :param dict varValue: Defines a value (float) associated with each free parameter
1675        :param dict varRefflag: Defines a refinement flag (bool)
1676          associated with each free parameter
1677
1678        :returns: the expression as a str
1679        '''
1680        for v in self.freeVars:
1681            varSelect[v] = 0
1682            varName[v] = self.freeVars[v][0]
1683            varValue[v] = self.freeVars[v][1]
1684            varRefflag[v] = self.freeVars[v][2]
1685        for v in self.assgnVars:
1686            varSelect[v] = 1
1687            varName[v] = self.assgnVars[v]
1688        return self.expression
1689
1690    def GetVaried(self):
1691        'Returns the names of the free parameters that will be refined'
1692        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
1693
1694    def GetVariedVarVal(self):
1695        'Returns the names and values of the free parameters that will be refined'
1696        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
1697
1698    def UpdateVariedVars(self,varyList,values):
1699        'Updates values for the free parameters (after a refinement); only updates refined vars'
1700        for v in self.freeVars:
1701            if not self.freeVars[v][2]: continue
1702            if "::"+self.freeVars[v][0] not in varyList: continue
1703            indx = varyList.index("::"+self.freeVars[v][0])
1704            self.freeVars[v][1] = values[indx]
1705
1706    def GetIndependentVars(self):
1707        'Returns the names of the required independent parameters used in expression'
1708        return [self.assgnVars[v] for v in self.assgnVars]
1709
1710    def CheckVars(self):
1711        '''Check that the expression can be parsed, all functions are
1712        defined and that input loaded into the object is internally
1713        consistent. If not an Exception is raised.
1714
1715        :returns: a dict with references to packages needed to
1716          find functions referenced in the expression.
1717        '''
1718        ret = self.ParseExpression(self.expression)
1719        if not ret:
1720            raise Exception("Expression parse error")
1721        exprLblList,fxnpkgdict = ret
1722        # check each var used in expression is defined
1723        defined = self.assgnVars.keys() + self.freeVars.keys()
1724        notfound = []
1725        for var in exprLblList:
1726            if var not in defined:
1727                notfound.append(var)
1728        if notfound:
1729            msg = 'Not all variables defined'
1730            msg1 = 'The following variables were not defined: '
1731            msg2 = ''
1732            for var in notfound:
1733                if msg: msg += ', '
1734                msg += var
1735            self.lastError = (msg1,'  '+msg2)
1736            raise Exception(msg)
1737        return fxnpkgdict
1738
1739    def ParseExpression(self,expr):
1740        '''Parse an expression and return a dict of called functions and
1741        the variables used in the expression. Returns None in case an error
1742        is encountered. If packages are referenced in functions, they are loaded
1743        and the functions are looked up into the modules global
1744        workspace.
1745       
1746        Note that no changes are made to the object other than
1747        saving an error message, so that this can be used for testing prior
1748        to the save.
1749
1750        :returns: a list of used variables
1751        '''
1752        self.lastError = ('','')
1753        import ast
1754        def FindFunction(f):
1755            '''Find the object corresponding to function f
1756            :param str f: a function name such as 'numpy.exp'
1757            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
1758              that defines the package location(s) and where pkgobj
1759              defines the object associated with the function.
1760              If the function is not found, pkgobj is None.
1761            '''
1762            df = f.split('.')
1763            pkgdict = {}
1764            # no listed package, try in current namespace
1765            if len(df) == 1: 
1766                try:
1767                    fxnobj = eval(f)
1768                    return pkgdict,fxnobj
1769                except (AttributeError, NameError):
1770                    return None,None
1771            else:
1772                try:
1773                    fxnobj = eval(f)
1774                    pkgdict[df[0]] = eval(df[0])
1775                    return pkgdict,fxnobj
1776                except (AttributeError, NameError):
1777                    pass
1778            # includes a package, lets try to load the packages
1779            pkgname = ''
1780            path = sys.path
1781            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
1782                if pkgname:
1783                    pkgname += '.' + pkg
1784                else:
1785                    pkgname = pkg
1786                fp = None
1787                try:
1788                    fp, fppath,desc = imp.find_module(pkg,path)
1789                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
1790                    pkgdict[pkgname] = pkgobj
1791                    path = [fppath]
1792                except Exception as msg:
1793                    print('load of '+pkgname+' failed with error='+str(msg))
1794                    return {},None
1795                finally:
1796                    if fp: fp.close()
1797                try:
1798                    #print 'before',pkgdict.keys()
1799                    fxnobj = eval(f,globals(),pkgdict)
1800                    #print 'after 1',pkgdict.keys()
1801                    #fxnobj = eval(f,pkgdict)
1802                    #print 'after 2',pkgdict.keys()
1803                    return pkgdict,fxnobj
1804                except:
1805                    continue
1806            return None # not found
1807        def ASTtransverse(node,fxn=False):
1808            '''Transverse a AST-parsed expresson, compiling a list of variables
1809            referenced in the expression. This routine is used recursively.
1810
1811            :returns: varlist,fxnlist where
1812              varlist is a list of referenced variable names and
1813              fxnlist is a list of used functions
1814            '''
1815            varlist = []
1816            fxnlist = []
1817            if isinstance(node, list):
1818                for b in node:
1819                    v,f = ASTtransverse(b,fxn)
1820                    varlist += v
1821                    fxnlist += f
1822            elif isinstance(node, ast.AST):
1823                for a, b in ast.iter_fields(node):
1824                    if isinstance(b, ast.AST):
1825                        if a == 'func': 
1826                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
1827                            continue
1828                        v,f = ASTtransverse(b,fxn)
1829                        varlist += v
1830                        fxnlist += f
1831                    elif isinstance(b, list):
1832                        v,f = ASTtransverse(b,fxn)
1833                        varlist += v
1834                        fxnlist += f
1835                    elif node.__class__.__name__ == "Name":
1836                        varlist += [b]
1837                    elif fxn and node.__class__.__name__ == "Attribute":
1838                        varlist += [b]
1839            return varlist,fxnlist
1840        try:
1841            exprast = ast.parse(expr)
1842        except SyntaxError as err:
1843            s = ''
1844            import traceback
1845            for i in traceback.format_exc().splitlines()[-3:-1]:
1846                if s: s += "\n"
1847                s += str(i)
1848            self.lastError = ("Error parsing expression:",s)
1849            return
1850        # find the variables & functions
1851        v,f = ASTtransverse(exprast)
1852        varlist = sorted(list(set(v)))
1853        fxnlist = list(set(f))
1854        pkgdict = {}
1855        # check the functions are defined
1856        for fxn in fxnlist:
1857            fxndict,fxnobj = FindFunction(fxn)
1858            if not fxnobj:
1859                self.lastError = ("Error: Invalid function",fxn,
1860                                  "is not defined")
1861                return
1862            if not hasattr(fxnobj,'__call__'):
1863                self.lastError = ("Error: Not a function.",fxn,
1864                                  "cannot be called as a function")
1865                return
1866            pkgdict.update(fxndict)
1867        return varlist,pkgdict
1868
1869    def GetDepVar(self):
1870        'return the dependent variable, or None'
1871        return self.depVar
1872
1873    def SetDepVar(self,var):
1874        'Set the dependent variable, if used'
1875        self.depVar = var
1876#==========================================================================
1877class ExpressionCalcObj(object):
1878    '''An object used to evaluate an expression from a :class:`ExpressionObj`
1879    object.
1880   
1881    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
1882      an expression string and mappings for the parameter labels in that object.
1883    '''
1884    def __init__(self,exprObj):
1885        self.eObj = exprObj
1886        'The expression and mappings; a :class:`ExpressionObj` object'
1887        self.compiledExpr = None
1888        'The expression as compiled byte-code'
1889        self.exprDict = {}
1890        '''dict that defines values for labels used in expression and packages
1891        referenced by functions
1892        '''
1893        self.lblLookup = {}
1894        '''Lookup table that specifies the expression label name that is
1895        tied to a particular GSAS-II parameters in the parmDict.
1896        '''
1897        self.fxnpkgdict = {}
1898        '''a dict with references to packages needed to
1899        find functions referenced in the expression.
1900        '''
1901        self.varLookup = {}
1902        '''Lookup table that specifies the GSAS-II variable(s)
1903        indexed by the expression label name. (Used for only for diagnostics
1904        not evaluation of expression.)
1905        '''
1906        # Patch: for old-style expressions with a (now removed step size)
1907        for v in self.eObj.assgnVars:
1908            if not isinstance(self.eObj.assgnVars[v], basestring):
1909                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
1910
1911    def SetupCalc(self,parmDict):
1912        '''Do all preparations to use the expression for computation.
1913        Adds the free parameter values to the parameter dict (parmDict).
1914        '''
1915        self.fxnpkgdict = self.eObj.CheckVars()
1916        # all is OK, compile the expression
1917        self.compiledExpr = compile(self.eObj.expression,'','eval')
1918
1919        # look at first value in parmDict to determine its type
1920        parmsInList = True
1921        for key in parmDict:
1922            val = parmDict[key]
1923            if isinstance(val, basestring):
1924                parmsInList = False
1925                break
1926            try: # check if values are in lists
1927                val = parmDict[key][0]
1928            except (TypeError,IndexError):
1929                parmsInList = False
1930            break
1931           
1932        # set up the dicts needed to speed computations
1933        self.exprDict = {}
1934        self.lblLookup = {}
1935        self.varLookup = {}
1936        for v in self.eObj.freeVars:
1937            varname = self.eObj.freeVars[v][0]
1938            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
1939            self.lblLookup[varname] = v
1940            self.varLookup[v] = varname
1941            if parmsInList:
1942                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
1943            else:
1944                parmDict[varname] = self.eObj.freeVars[v][1]
1945            self.exprDict[v] = self.eObj.freeVars[v][1]
1946        for v in self.eObj.assgnVars:
1947            varname = self.eObj.assgnVars[v]
1948            if '*' in varname:
1949                varlist = LookupWildCard(varname,parmDict.keys())
1950                if len(varlist) == 0:
1951                    raise Exception,"No variables match "+str(v)
1952                for var in varlist:
1953                    self.lblLookup[var] = v
1954                if parmsInList:
1955                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
1956                else:
1957                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
1958                self.varLookup[v] = [var for var in varlist]
1959            elif varname in parmDict:
1960                self.lblLookup[varname] = v
1961                self.varLookup[v] = varname
1962                if parmsInList:
1963                    self.exprDict[v] = parmDict[varname][0]
1964                else:
1965                    self.exprDict[v] = parmDict[varname]
1966            else:
1967                raise Exception,"No value for variable "+str(v)
1968        self.exprDict.update(self.fxnpkgdict)
1969
1970    def UpdateVars(self,varList,valList):
1971        '''Update the dict for the expression with a set of values
1972        :param list varList: a list of variable names
1973        :param list valList: a list of corresponding values
1974        '''
1975        for var,val in zip(varList,valList):
1976            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
1977
1978    def UpdateDict(self,parmDict):
1979        '''Update the dict for the expression with values in a dict
1980        :param list parmDict: a dict of values some of which may be in use here
1981        '''
1982        for var in parmDict:
1983            if var in self.lblLookup:
1984                self.exprDict[self.lblLookup[var]] = parmDict[var]
1985           
1986    def EvalExpression(self):
1987        '''Evaluate an expression. Note that the expression
1988        and mapping are taken from the :class:`ExpressionObj` expression object
1989        and the parameter values were specified in :meth:`SetupCalc`.
1990        :returns: a single value for the expression. If parameter
1991        values are arrays (for example, from wild-carded variable names),
1992        the sum of the resulting expression is returned.
1993
1994        For example, if the expression is ``'A*B'``,
1995        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
1996
1997        [0.5, 1, 0.5]
1998
1999        then the result will be ``4.0``.
2000        '''
2001        if self.compiledExpr is None:
2002            raise Exception,"EvalExpression called before SetupCalc"
2003        val = eval(self.compiledExpr,globals(),self.exprDict)
2004        if not np.isscalar(val):
2005            val = np.sum(val)
2006        return val
2007
2008
2009if __name__ == "__main__":
2010    # test equation evaluation
2011    def showEQ(calcobj):
2012        print 50*'='
2013        print calcobj.eObj.expression,'=',calcobj.EvalExpression()
2014        for v in sorted(calcobj.varLookup):
2015            print "  ",v,'=',calcobj.exprDict[v],'=',calcobj.varLookup[v]
2016        # print '  Derivatives'
2017        # for v in calcobj.derivStep.keys():
2018        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2019
2020    obj = ExpressionObj()
2021
2022    obj.expression = "A*np.exp(B)"
2023    obj.assgnVars =  {'B': '0::Afrac:1'}
2024    obj.freeVars =  {'A': [u'A', 0.5, True]}
2025    #obj.CheckVars()
2026    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2027    calcobj = ExpressionCalcObj(obj)
2028    calcobj.SetupCalc(parmDict2)
2029    showEQ(calcobj)
2030
2031    obj.expression = "A*np.exp(B)"
2032    obj.assgnVars =  {'B': '0::Afrac:*'}
2033    obj.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
2034    #obj.CheckVars()
2035    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2036    calcobj = ExpressionCalcObj(obj)
2037    calcobj.SetupCalc(parmDict1)
2038    showEQ(calcobj)
2039
2040    calcobj.SetupCalc(parmDict2)
2041    showEQ(calcobj)
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