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Last change on this file since 1315 was 1312, checked in by toby, 11 years ago
Parametric fit; work on PseudoVars? (more 2 come); minor code cleanups
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1	# -- coding: utf-8 --
2	#GSASIIobj - data objects for GSAS-II
3	########### SVN repository information ###################
4	# $Date: 2014-05-01 02:42:51 +0000 (Thu, 01 May 2014) $
5	# $Author: vondreele $
6	# $Revision: 1312 $
7	# $URL: trunk/GSASIIobj.py $
8	# $Id: GSASIIobj.py 1312 2014-05-01 02:42:51Z vondreele $
9	########### SVN repository information ###################
10
11	'''
12	GSASIIobj: Data objects
13	=========================
14
15	This module defines and/or documents the data structures used in GSAS-II, as well
16	as provides misc. support routines.
17
18	Constraints Tree Item
19	----------------------
20
21	.. _Constraints_table:
22
23	.. index::
24	single: Constraints object description
25	single: Data object descriptions; Constraints
26
27	Constraints are stored in a dict, separated into groups.
28	Note that parameter are named in the following pattern,
29	p: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.
31	If a parameter does not depend on a histogram or phase or is unnumbered, that
32	number is omitted.
33	Note that the contents of each dict item is a List where each element in the
34	list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
35	The constraints in this form are converted in
36	:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
37
38	The keys in the Constraints dict are:
39
40	.. tabularcolumns:: \|l\|p{4.5in}\|
41
42	========== ====================================================
43	key explanation
44	========== ====================================================
45	Hist This specifies a list of constraints on
46	histogram-related parameters,
47	which will be of form :h:<var>:n.
48	HAP 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.
51	Phase This specifies a list of constraints on phase
52	parameters,
53	which will be of form p::<var>:n.
54	Global 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
65	Each constraint is defined as an item in a list. Each constraint is of form::
66
67	[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
68
69	Where 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
75	Note 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
100	Covariance Tree Item
101	--------------------
102
103	.. _Covariance_table:
104
105	.. index::
106	single: Covariance description
107	single: Data object descriptions; Covariance
108
109	The Covariance tree item has results from the last least-squares run. They
110	are stored in a dict with these keys:
111
112	.. tabularcolumns:: \|l\|l\|p{4in}\|
113
114	============= =============== ====================================================
115	key sub-key explanation
116	============= =============== ====================================================
117	newCellDict \ dict with lattice parameters computed by
118	:func:`GSASIIstrMath.GetNewCellParms` (dict)
119	title \ Name of gpx file(?) (str)
120	variables \ Values for all N refined variables
121	(list of float values, length N,
122	ordered to match varyList)
123	sig \ Uncertainty values for all N refined variables
124	(list of float values, length N,
125	ordered to match varyList)
126	varyList \ List of directly refined variables
127	(list of str values, length N)
128	newAtomDict \ dict with atom position values computed in
129	:func:`GSASIIstrMath.ApplyXYZshifts` (dict)
130	Rvals \ 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)
140	covMatrix \ The (NxN) covVariance matrix (np.array)
141	============= =============== ====================================================
142
143	Phase Tree Items
144	----------------
145
146	.. _Phase_table:
147
148	.. index::
149	single: Phase object description
150	single: Data object descriptions; Phase
151
152	Phase information is stored in the GSAS-II data tree as children of the
153	Phases item in a dict with keys:
154
155	.. tabularcolumns:: \|l\|l\|p{4in}\|
156
157	========== =============== ====================================================
158	key sub-key explanation
159	========== =============== ====================================================
160	General \ 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)].
208	ranId \ unique random number Id for phase (int)
209	pId \ Phase Id number for current project (int).
210	Atoms \ 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)
215	Drawing \ 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)
251	RBModels \ Rigid body assignments (note Rigid body definitions
252	are stored in their own main top-level tree entry.)
253	Pawley ref \ Pawley reflections
254	Histograms \ 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)
259	MCSA \ Monte-Carlo simulated annealing parameters (dict)
260	\
261	========== =============== ====================================================
262
263	Rigid 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
272	Rigid body descriptions are available for two types of rigid bodies: 'Vector'
273	and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
274	with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
275	with defined refinable torsion angles.
276
277	.. tabularcolumns:: \|l\|l\|p{4in}\|
278
279	========== =============== ====================================================
280	key sub-key explanation
281	========== =============== ====================================================
282	Vector 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)
293	Residue 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)
306	RBIds \ 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
311	Space 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
320	Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
321	and the information is placed in a SGdata object
322	which is a dict with these keys:
323
324	.. tabularcolumns:: \|l\|p{4.5in}\|
325
326	========== ====================================================
327	key explanation
328	========== ====================================================
329	SpGrp space group symbol (str)
330	Laue 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)
333	SGInv True if centrosymmetric, False if not (bool)
334	SGLatt Lattice centering type. Will be one of
335	P, A, B, C, I, F, R (str)
336	SGUniq unique axis if monoclinic. Will be
337	a, b, or c for monoclinic space groups.
338	Will be blank for non-monoclinic. (str)
339	SGCen 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]])``
342	SGOps 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`
350	SGSys symmetry unit cell: type one of
351	'triclinic', 'monoclinic', 'orthorhombic',
352	'tetragonal', 'rhombohedral', 'trigonal',
353	'hexagonal', 'cubic' (str)
354	SGPolax 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
360	Atom Records
361	------------
362
363	.. _Atoms_table:
364
365	.. index::
366	single: Atoms record description
367	single: Data object descriptions; Atoms record
368
369
370	If ``phasedict`` points to the phase information in the data tree, then
371	atoms are contained in a list of atom records (list) in
372	``phasedict['Atoms']``. Also needed to read atom information
373	are four pointers, ``cx,ct,cs,cia = phasedict['General']['atomPtrs']``,
374	which define locations in the atom record, as shown below. Items shown are
375	always present; additional ones for macromolecular phases are marked 'mm'
376
377	.. tabularcolumns:: \|l\|p{4.5in}\|
378
379	============== ====================================================
380	location explanation
381	============== ====================================================
382	ct-4 mm - residue number (str)
383	ct-3 mm - residue name (e.g. ALA) (str)
384	ct-2 mm - chain label (str)
385	ct-1 atom label (str)
386	ct atom type (str)
387	ct+1 refinement flags; combination of 'F', 'X', 'U' (str)
388	cx,cx+1,cx+2 the x,y and z coordinates (3 floats)
389	cs site symmetry (str)
390	cs+1 site multiplicity (int)
391	cia ADP flag: Isotropic ('I') or Anisotropic ('A')
392	cia+1 Uiso (float)
393	cia+2...cia+6 U11, U22, U33, U12, U13, U23 (6 floats)
394	atom[-1] unique atom identifier (int)
395	============== ====================================================
396
397	Drawing Atom Records
398	--------------------
399
400	.. _Drawing_atoms_table:
401
402	.. index::
403	single: Drawing atoms record description
404	single: Data object descriptions; Drawing atoms record
405
406
407	If ``phasedict`` points to the phase information in the data tree, then
408	drawing atoms are contained in a list of drawing atom records (list) in
409	``phasedict['Drawing']['Atoms']``. Also needed to read atom information
410	are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
411	which define locations in the atom record, as shown below. Items shown are
412	always present; additional ones for macromolecular phases are marked 'mm'
413
414	.. tabularcolumns:: \|l\|p{4.5in}\|
415
416	============== ====================================================
417	location explanation
418	============== ====================================================
419	ct-4 mm - residue number (str)
420	ct-3 mm - residue name (e.g. ALA) (str)
421	ct-2 mm - chain label (str)
422	ct-1 atom label (str)
423	ct atom type (str)
424	cx,cx+1,cx+2 the x,y and z coordinates (3 floats)
425	cs-1 Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
426	cs atom drawing style; e.g. 'balls & sticks' (str)
427	cs+1 atom label style (e.g. 'name') (str)
428	cs+2 atom color (RBG triplet) (int)
429	cs+3 ADP flag: Isotropic ('I') or Anisotropic ('A')
430	cs+4 Uiso (float)
431	cs+5...cs+11 U11, U22, U33, U12, U13, U23 (6 floats)
432	ci unique atom identifier; matches source atom Id in Atom Records (int)
433	============== ====================================================
434
435	Powder Diffraction Tree Items
436	-----------------------------
437
438	.. _Powder_table:
439
440	.. index::
441	single: Powder data object description
442	single: Data object descriptions; Powder Data
443
444	Every powder diffraction histogram is stored in the GSAS-II data tree
445	with a top-level entry named beginning with the string "PWDR ". The
446	diffraction data for that information are directly associated with
447	that tree item and there are a series of children to that item. The
448	routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
449	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
450	load this information into a dictionary where the child tree name is
451	used as a key, and the information in the main entry is assigned
452	a key of ``Data``, as outlined below.
453
454	.. tabularcolumns:: \|l\|l\|p{4in}\|
455
456	====================== =============== ====================================================
457	key sub-key explanation
458	====================== =============== ====================================================
459	Comments \ Text strings extracted from the original powder
460	data header. These cannot be changed by the user;
461	it may be empty.
462	Limits \ A list of two two element lists, as [[Ld,Hd],[L,H]]
463	where L and Ld are the current and default lowest
464	two-theta value to be used and
465	where H and Hd are the current and default highest
466	two-theta value to be used.
467	Reflection Lists \ A dict with an entry for each phase in the
468	histogram. The contents of each dict item
469	is a dict containing reflections, as described in
470	the :ref:`Powder Reflections <PowderRefl_table>`
471	description.
472	Instrument Parameters \ A list containing two dicts where the possible
473	keys in each dict are listed below. The value
474	for each item is a list containing three values:
475	the initial value, the current value and a
476	refinement flag which can have a value of
477	True, False or 0 where 0 indicates a value that
478	cannot be refined. The first and second
479	values are floats unless otherwise noted.
480	Items in the first dict are noted as [1]
481	\ Lam Specifies a wavelength in Angstroms [1]
482	\ Lam1 Specifies the primary wavelength in
483	Angstrom, when an alpha1, alpha2
484	source is used [1]
485	\ Lam2 Specifies the secondary wavelength in
486	Angstrom, when an alpha1, alpha2
487	source is used [1]
488	I(L2)/I(L1) Ratio of Lam2 to Lam1 [1]
489	\ Type Histogram type (str) [1]:
490	* 'PXC' for constant wavelength x-ray
491	* 'PNC' for constant wavelength neutron
492	* 'PNT' for time of flight neutron
493	\ Zero Two-theta zero correction in degrees [1]
494	\ Azimuth Azimuthal setting angle for data recorded
495	with differing setting angles [1]
496	\ U, V, W Cagliotti profile coefficients
497	for Gaussian instrumental broadening, where the
498	FWHM goes as
499	:math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
500	\ X, Y Cauchy (Lorentzian) instrumental broadening
501	coefficients [1]
502	\ SH/L Variant of the Finger-Cox-Jephcoat asymmetric
503	peak broadening ratio. Note that this is the
504	average between S/L and H/L where S is
505	sample height, H is the slit height and
506	L is the goniometer diameter. [1]
507	\ Polariz. Polarization coefficient. [1]
508	wtFactor \ A weighting factor to increase or decrease
509	the leverage of data in the histogram (float).
510	A value of 1.0 weights the data with their
511	standard uncertainties and a larger value
512	increases the weighting of the data (equivalent
513	to decreasing the uncertainties).
514	Sample Parameters \ Specifies a dict with parameters that describe how
515	the data were collected, as listed
516	below. Refinable parameters are a list containing
517	a float and a bool, where the second value
518	specifies if the value is refined, otherwise
519	the value is a float unless otherwise noted.
520	\ Scale The histogram scale factor (refinable)
521	\ Absorption The sample absorption coefficient as
522	:math:`\\mu r` where r is the radius
523	(refinable). Only valid for Debye-Scherrer geometry.
524	\ SurfaceRoughA Surface roughness parameter A as defined by
525	Surotti,J. Appl. Cryst, 5,325-331, 1972.(refinable -
526	only valid for Bragg-Brentano geometry)
527	\ SurfaceRoughB Surface roughness parameter B (refinable -
528	only valid for Bragg-Brentano geometry)
529	\ DisplaceX, Sample displacement from goniometer center
530	DisplaceY where Y is along the beam direction and
531	X is perpendicular. Units are :math:`\\mu m`
532	(refinable).
533	\ Phi, Chi, Goniometer sample setting angles, in degrees.
534	Omega
535	\ Gonio. radius Radius of the diffractometer in mm
536	\ InstrName A name for the instrument, used in preparing
537	a CIF (str).
538	\ Force, Variables that describe how the measurement
539	Temperature, was performed. Not used directly in
540	Humidity, any computations.
541	Pressure,
542	Voltage
543	\ ranId The random-number Id for the histogram
544	(same value as where top-level key is ranId)
545	\ Type Type of diffraction data, may be 'Debye-Scherrer'
546	or 'Bragg-Brentano' (str).
547	\ Diffuse not in use?
548	hId \ The number assigned to the histogram when
549	the project is loaded or edited (can change)
550	ranId \ A random number id for the histogram
551	that does not change
552	Background \ The background is stored as a list with where
553	the first item in the list is list and the second
554	item is a dict. The list contains the background
555	function and its coefficients; the dict contains
556	Debye diffuse terms and background peaks.
557	(TODO: this needs to be expanded.)
558	Data \ The data consist of a list of 6 np.arrays
559	containing in order:
560
561	0. the x-postions (two-theta in degrees),
562	1. the intensity values (Yobs),
563	2. the weights for each Yobs value
564	3. the computed intensity values (Ycalc)
565	4. the background values
566	5. Yobs-Ycalc
567	====================== =============== ====================================================
568
569	Powder Reflection Data Structure
570	--------------------------------
571
572	.. _PowderRefl_table:
573
574	.. index::
575	single: Powder reflection object description
576	single: Data object descriptions; Powder Reflections
577
578	For every phase in a histogram, the ``Reflection Lists`` value is a dict
579	one element of which is `'RefList'`, which is a np.array containing
580	reflections. The columns in that array are documented below.
581
582	========== ====================================================
583	index explanation
584	========== ====================================================
585	0,1,2 h,k,l (float)
586	3 multiplicity
587	4 d-space, Angstrom
588	5 pos, two-theta
589	6 sig, Gaussian width
590	7 gam, Lorenzian width
591	8 :math:`F_{obs}^2`
592	9 :math:`F_{calc}^2`
593	10 reflection phase, in degrees
594	11 intensity correction for reflection, this times
595	:math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
596	========== ====================================================
597
598	Single Crystal Tree Items
599	-------------------------
600
601	.. _Xtal_table:
602
603	.. index::
604	single: Single Crystal data object description
605	single: Data object descriptions; Single crystal data
606
607	Every single crystal diffraction histogram is stored in the GSAS-II data tree
608	with a top-level entry named beginning with the string "HKLF ". The
609	diffraction data for that information are directly associated with
610	that tree item and there are a series of children to that item. The
611	routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
612	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
613	load this information into a dictionary where the child tree name is
614	used as a key, and the information in the main entry is assigned
615	a key of ``Data``, as outlined below.
616
617	.. tabularcolumns:: \|l\|l\|p{4in}\|
618
619	====================== =============== ====================================================
620	key sub-key explanation
621	====================== =============== ====================================================
622	Data \ A dict that contains the
623	reflection table,
624	as described in the
625	:ref:`Single Crystal Reflections
626	<XtalRefl_table>`
627	description.
628
629	Instrument Parameters \ A list containing two dicts where the possible
630	keys in each dict are listed below. The value
631	for most items is a list containing two values:
632	the initial value, the current value.
633	The first and second
634	values are floats unless otherwise noted.
635	\ Lam Specifies a wavelength in Angstroms (two floats)
636	\ Type Histogram type (two str values):
637	* 'SXC' for constant wavelength x-ray
638	* 'SNC' for constant wavelength neutron
639	* 'SNT' for time of flight neutron
640	\ InstrName A name for the instrument, used in preparing
641	a CIF (str).
642
643	wtFactor \ A weighting factor to increase or decrease
644	the leverage of data in the histogram (float).
645	A value of 1.0 weights the data with their
646	standard uncertainties and a larger value
647	increases the weighting of the data (equivalent
648	to decreasing the uncertainties).
649
650	hId \ The number assigned to the histogram when
651	the project is loaded or edited (can change)
652	ranId \ A random number id for the histogram
653	that does not change
654	====================== =============== ====================================================
655
656	Single Crystal Reflection Data Structure
657	----------------------------------------
658
659	.. _XtalRefl_table:
660
661	.. index::
662	single: Single Crystal reflection object description
663	single: Data object descriptions; Single Crystal Reflections
664
665	For every single crystal a histogram, the ``'Data'`` item contains
666	the structure factors as an np.array in item `'RefList'`.
667	The columns in that array are documented below.
668
669	========== ====================================================
670	index explanation
671	========== ====================================================
672	0,1,2 h,k,l (float)
673	3 multiplicity
674	4 d-space, Angstrom
675	5 :math:`F_{obs}^2`
676	6 :math:`\sigma(F_{obs}^2)`
677	7 :math:`F_{calc}^2`
678	8 :math:`F_{obs}^2T`
679	9 :math:`F_{calc}^2T`
680	10 reflection phase, in degrees
681	11 intensity correction for reflection, this times
682	:math:`F_{obs}^2` or :math:`F_{calc}^2`
683	gives Iobs or Icalc
684	========== ====================================================
685
686	Image Data Structure
687	--------------------
688
689	.. _Image_table:
690
691	.. index::
692	image: Image data object description
693	image: Image object descriptions
694
695	Every 2-dimensional image is stored in the GSAS-II data tree
696	with a top-level entry named beginning with the string "IMG ". The
697	image data are directly associated with that tree item and there
698	are a series of children to that item. The routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
699	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
700	load this information into a dictionary where the child tree name is
701	used as a key, and the information in the main entry is assigned
702	a key of ``Data``, as outlined below.
703
704	.. tabularcolumns:: \|l\|l\|p{4in}\|
705
706	====================== ====================== ====================================================
707	key sub-key explanation
708	====================== ====================== ====================================================
709	Comments \ Text strings extracted from the original image data
710	header or a metafile. These cannot be changed by
711	the user; it may be empty.
712	Image Controls azmthOff (float) The offset to be applied to an azimuthal
713	value. Accomodates
714	detector orientations other than with the detector
715	X-axis
716	horizontal.
717	\ background image (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
718	during image integration multiplied by value. It must have the same size/shape as
719	the integrated image. NB: value < 0 for subtraction.
720	\ calibrant (str) The material used for determining the position/orientation
721	of the image. The data is obtained from :func:`ImageCalibrants`
722	and UserCalibrants.py (supplied by user).
723	\ calibdmin (float) The minimum d-spacing used during the last calibration run.
724	\ calibskip (int) The number of expected diffraction lines skipped during the last
725	calibration run.
726	\ center (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
727	strikes the detector plane as determined by calibration. This point
728	does not have to be within the limits of the detector boundaries.
729	\ centerAzm (bool) If True then the azimuth reported for the integrated slice
730	of the image is at the center line otherwise it is at the leading edge.
731	\ color (str) The name of the colormap used to display the image. Default = 'Paired'.
732	\ cutoff (float) The minimum value of I/Ib for a point selected in a diffraction ring for
733	calibration calculations. See pixLimit for details as how point is found.
734	\ DetDepth (float) Coefficient for penetration correction to distance; accounts for diffraction
735	ring offset at higher angles. Optionally determined by calibration.
736	\ DetDepthRef (bool) If True then refine DetDepth during calibration/recalibration calculation.
737	\ distance (float) The distance (mm) from sample to detector plane.
738	\ ellipses (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
739	center (list) is location (mm) of the ellipse center on the detector plane, phi is the
740	rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
741	radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
742	is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
743	\ edgemin (float) Not used; parameter in EdgeFinder code.
744	\ fullIntegrate (bool) If True then integrate over full 360 deg azimuthal range.
745	\ GonioAngles (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
746	Required for texture calculations.
747	\ invert_x (bool) If True display the image with the x-axis inverted.
748	\ invert_y (bool) If True display the image with the y-axis inverted.
749	\ IOtth (list:floats) The minimum and maximum 2-theta values to be used for integration.
750	\ LRazimuth (list:floats) The minimum and maximum azimuth values to be used for integration.
751	\ Oblique (list:float,bool) If True apply a detector absorption correction using the value to the
752	intensities obtained during integration.
753	\ outAzimuths (int) The number of azimuth pie slices.
754	\ outChannels (int) The number of 2-theta steps.
755	\ pixelSize (list:ints) The X,Y dimensions (microns) of each pixel.
756	\ pixLimit (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
757	This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
758	and subject to cutoff in :func:`GSASIIimage.makeRing`.
759	Locations are used to construct rings of points for calibration calcualtions.
760	\ PolaVal (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
761	integration using value.
762	\ rings (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
763	diffraction ring with the same d-spacing (dsp)
764	\ ring (list) The x,y coordinates of the >5 points on an inner ring
765	selected by the user,
766	\ Range (list) The minimum & maximum values of the image
767	\ rotation (float) The angle between the x-axis and the vector about which the
768	detector is tilted. Constrained to -180 to 180 deg.
769	\ SampleShape (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
770	calculations.
771	\ SampleAbs (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
772	to cause correction to be applied.
773	\ setDefault (bool) If True the use the image controls values for all new images to be read. (might be removed)
774	\ setRings (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.
775	\ showLines (bool) If True then isplay the integration limits to be used.
776	\ size (list:int) The number of pixels on the image x & y axes
777	\ type (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
778	\ tilt (float) The angle the detector normal makes with the incident beam; range -90 to 90.
779	\ wavelength (float) Tha radiation wavelength (Angstroms) as entered by the user (or someday obtained from the image header).
780
781	Masks Arcs (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
782	to be excluded from integration
783	\ Frames (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
784	of which is excluded from recalibration and integration. Only one frame is allowed.
785	\ Points (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
786	from integration.
787	\ Polygons (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
788	to be excluded from integration.
789	\ Rings (list: lists) Each entry [2-theta,thickness] describes a ring mask
790	to be excluded from integration.
791	\ Thresholds (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
792	in integrsation. The tuple is the image intensity limits and the list are those set by the user.
793
794	Stress/Strain Sample phi (float) Sample rotation about vertical axis.
795	\ Sample z (float) Sample translation from the calibration sample position (for Sample phi = 0)
796	These will be restricted by space group symmetry; result of strain fit refinement.
797	\ Type (str) 'True' or 'Conventional': The strain model used for the calculation.
798	\ d-zero (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
799	and are used to determine the strain tensor.
800	The dictionary items are:
801	'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
802	'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
803	'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
804	'Esig': (list: float) Esds for Emat from fitting.
805	'pixLimit': (int) Search range to find highest point on ring for each data point
806	'cutoff': (float) I/Ib cutoff for searching.
807	'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
808	'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
809	'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
810
811	====================== ====================== ====================================================
812
813	Parameter Dictionary
814	-------------------------
815
816	.. _parmDict_table:
817
818	.. index::
819	single: Parameter dictionary
820
821	The parameter dictionary contains all of the variable parameters for the refinement.
822	The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
823	It is prepared in two ways. When loaded from the tree
824	(in :meth:`GSASII.GSASII.MakeLSParmDict` and
825	:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
826	the values are lists with two elements: ``[value, refine flag]``
827
828	When loaded from the GPX file (in
829	:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
830	dict is the actual parameter value (usually a float, but sometimes a
831	letter or string flag value (such as I or A for iso/anisotropic).
832
833
834	Classes and routines
835	----------------------
836
837	'''
838	import re
839	import imp
840	import random as ran
841	import sys
842	import GSASIIpath
843	import GSASIImath as G2mth
844	import numpy as np
845
846	GSASIIpath.SetVersionNumber("$Revision: 1312 $")
847
848	DefaultControls = {
849	'deriv type':'analytic Hessian', #default controls
850	'min dM/M':0.0001,'shift factor':1.,'max cyc':3,'F**2':True,
851	'minF/sig':0,
852	'Author':'no name',
853	'FreeVar1':'Sample humidity (%)',
854	'FreeVar2':'Sample voltage (V)',
855	'FreeVar3':'Applied load (MN)',
856	}
857	'''Values to be used as defaults for the initial contents of the ``Controls``
858	data tree item.
859	'''
860
861	def MakeUniqueLabel(lbl,labellist):
862	'''Make sure that every a label is unique against a list by adding
863	digits at the end until it is not found in list.
864
865	:param str lbl: the input label
866	:param list labellist: the labels that have already been encountered
867	:returns: lbl if not found in labellist or lbl with ``_1-9`` (or
868	``_10-99``, etc.) appended at the end
869	'''
870	lbl = lbl.strip()
871	if not lbl: # deal with a blank label
872	lbl = '_1'
873	if lbl not in labellist:
874	labellist.append(lbl)
875	return lbl
876	i = 1
877	prefix = lbl
878	if '_' in lbl:
879	prefix = lbl[:lbl.rfind('_')]
880	suffix = lbl[lbl.rfind('_')+1:]
881	try:
882	i = int(suffix)+1
883	except: # suffix could not be parsed
884	i = 1
885	prefix = lbl
886	while prefix+'_'+str(i) in labellist:
887	i += 1
888	else:
889	lbl = prefix+'_'+str(i)
890	labellist.append(lbl)
891	return lbl
892
893	PhaseIdLookup = {}
894	'''dict listing phase name and random Id keyed by sequential phase index as a str;
895	best to access this using :func:`LookupPhaseName`
896	'''
897	PhaseRanIdLookup = {}
898	'''dict listing phase sequential index keyed by phase random Id;
899	best to access this using :func:`LookupPhaseId`
900	'''
901	HistIdLookup = {}
902	'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
903	best to access this using :func:`LookupHistName`
904	'''
905	HistRanIdLookup = {}
906	'''dict listing histogram sequential index keyed by histogram random Id;
907	best to access this using :func:`LookupHistId`
908	'''
909	AtomIdLookup = {}
910	'''dict listing for each phase index as a str, the atom label and atom random Id,
911	keyed by atom sequential index as a str;
912	best to access this using :func:`LookupAtomLabel`
913	'''
914	AtomRanIdLookup = {}
915	'''dict listing for each phase the atom sequential index keyed by atom random Id;
916	best to access this using :func:`LookupAtomId`
917	'''
918	ShortPhaseNames = {}
919	'''a dict containing a possibly shortened and when non-unique numbered
920	version of the phase name. Keyed by the phase sequential index.
921	'''
922	ShortHistNames = {}
923	'''a dict containing a possibly shortened and when non-unique numbered
924	version of the histogram name. Keyed by the histogram sequential index.
925	'''
926
927	VarDesc = {}
928	''' This dictionary lists descriptions for GSAS-II variables,
929	as set in :func:`CompileVarDesc`. See that function for a description
930	for how keys and values are written.
931	'''
932
933	reVarDesc = {}
934	''' This dictionary lists descriptions for GSAS-II variables with
935	the same values as :attr:`VarDesc` except that keys have been compiled as
936	regular expressions. Initialized in :func:`CompileVarDesc`.
937	'''
938
939	def IndexAllIds(Histograms,Phases):
940	'''Scan through the used phases & histograms and create an index
941	to the random numbers of phases, histograms and atoms. While doing this,
942	confirm that assigned random numbers are unique -- just in case lightning
943	strikes twice in the same place.
944
945	Note: this code assumes that the atom random Id (ranId) is the last
946	element each atom record.
947
948	This is called in two places (only) :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
949	(which loads the histograms and phases from a GPX file) and
950	:meth:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
951	(which loads the histograms and phases from the data tree.)
952
953	TODO: do we need a lookup for rigid body variables?
954	'''
955	# process phases and atoms
956	PhaseIdLookup.clear()
957	PhaseRanIdLookup.clear()
958	AtomIdLookup.clear()
959	AtomRanIdLookup.clear()
960	ShortPhaseNames.clear()
961	for ph in Phases:
962	cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
963	ranId = Phases[ph]['ranId']
964	while ranId in PhaseRanIdLookup:
965	# Found duplicate random Id! note and reassign
966	print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
967	Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxint)
968	pId = str(Phases[ph]['pId'])
969	PhaseIdLookup[pId] = (ph,ranId)
970	PhaseRanIdLookup[ranId] = pId
971	shortname = ph[:10]
972	while shortname in ShortPhaseNames.values():
973	shortname = ph[:8] + ' ('+ pId + ')'
974	ShortPhaseNames[pId] = shortname
975	AtomIdLookup[pId] = {}
976	AtomRanIdLookup[pId] = {}
977	for iatm,at in enumerate(Phases[ph]['Atoms']):
978	ranId = at[-1]
979	while ranId in AtomRanIdLookup[pId]: # check for dups
980	print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
981	at[-1] = ranId = ran.randint(0,sys.maxint)
982	AtomRanIdLookup[pId][ranId] = str(iatm)
983	if Phases[ph]['General']['Type'] == 'macromolecular':
984	label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
985	else:
986	label = at[ct-1]
987	AtomIdLookup[pId][str(iatm)] = (label,ranId)
988	# process histograms
989	HistIdLookup.clear()
990	HistRanIdLookup.clear()
991	ShortHistNames.clear()
992	for hist in Histograms:
993	ranId = Histograms[hist]['ranId']
994	while ranId in HistRanIdLookup:
995	# Found duplicate random Id! note and reassign
996	print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
997	Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxint)
998	hId = str(Histograms[hist]['hId'])
999	HistIdLookup[hId] = (hist,ranId)
1000	HistRanIdLookup[ranId] = hId
1001	shortname = hist[:15]
1002	while shortname in ShortHistNames.values():
1003	shortname = hist[:11] + ' ('+ hId + ')'
1004	ShortHistNames[hId] = shortname
1005
1006	def LookupAtomId(pId,ranId):
1007	'''Get the atom number from a phase and atom random Id
1008
1009	:param int/str pId: the sequential number of the phase
1010	:param int ranId: the random Id assigned to an atom
1011
1012	:returns: the index number of the atom (str)
1013	'''
1014	if not AtomRanIdLookup:
1015	raise Exception,'Error: LookupAtomId called before IndexAllIds was run'
1016	if pId is None or pId == '':
1017	raise KeyError,'Error: phase is invalid (None or blank)'
1018	pId = str(pId)
1019	if pId not in AtomRanIdLookup:
1020	raise KeyError,'Error: LookupAtomId does not have phase '+pId
1021	if ranId not in AtomRanIdLookup[pId]:
1022	raise KeyError,'Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']'
1023	return AtomRanIdLookup[pId][ranId]
1024
1025	def LookupAtomLabel(pId,index):
1026	'''Get the atom label from a phase and atom index number
1027
1028	:param int/str pId: the sequential number of the phase
1029	:param int index: the index of the atom in the list of atoms
1030
1031	:returns: the label for the atom (str) and the random Id of the atom (int)
1032	'''
1033	if not AtomIdLookup:
1034	raise Exception,'Error: LookupAtomLabel called before IndexAllIds was run'
1035	if pId is None or pId == '':
1036	raise KeyError,'Error: phase is invalid (None or blank)'
1037	pId = str(pId)
1038	if pId not in AtomIdLookup:
1039	raise KeyError,'Error: LookupAtomLabel does not have phase '+pId
1040	if index not in AtomIdLookup[pId]:
1041	raise KeyError,'Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']'
1042	return AtomIdLookup[pId][index]
1043
1044	def LookupPhaseId(ranId):
1045	'''Get the phase number and name from a phase random Id
1046
1047	:param int ranId: the random Id assigned to a phase
1048	:returns: the sequential Id (pId) number for the phase (str)
1049	'''
1050	if not PhaseRanIdLookup:
1051	raise Exception,'Error: LookupPhaseId called before IndexAllIds was run'
1052	if ranId not in PhaseRanIdLookup:
1053	raise KeyError,'Error: LookupPhaseId does not have ranId '+str(ranId)
1054	return PhaseRanIdLookup[ranId]
1055
1056	def LookupPhaseName(pId):
1057	'''Get the phase number and name from a phase Id
1058
1059	:param int/str pId: the sequential assigned to a phase
1060	:returns: (phase,ranId) where phase is the name of the phase (str)
1061	and ranId is the random # id for the phase (int)
1062	'''
1063	if not PhaseIdLookup:
1064	raise Exception,'Error: LookupPhaseName called before IndexAllIds was run'
1065	if pId is None or pId == '':
1066	raise KeyError,'Error: phase is invalid (None or blank)'
1067	pId = str(pId)
1068	if pId not in PhaseIdLookup:
1069	raise KeyError,'Error: LookupPhaseName does not have index '+pId
1070	return PhaseIdLookup[pId]
1071
1072	def LookupHistId(ranId):
1073	'''Get the histogram number and name from a histogram random Id
1074
1075	:param int ranId: the random Id assigned to a histogram
1076	:returns: the sequential Id (hId) number for the histogram (str)
1077	'''
1078	if not HistRanIdLookup:
1079	raise Exception,'Error: LookupHistId called before IndexAllIds was run'
1080	if ranId not in HistRanIdLookup:
1081	raise KeyError,'Error: LookupHistId does not have ranId '+str(ranId)
1082	return HistRanIdLookup[ranId]
1083
1084	def LookupHistName(hId):
1085	'''Get the histogram number and name from a histogram Id
1086
1087	:param int/str hId: the sequential assigned to a histogram
1088	:returns: (hist,ranId) where hist is the name of the histogram (str)
1089	and ranId is the random # id for the histogram (int)
1090	'''
1091	if not HistIdLookup:
1092	raise Exception,'Error: LookupHistName called before IndexAllIds was run'
1093	if hId is None or hId == '':
1094	raise KeyError,'Error: histogram is invalid (None or blank)'
1095	hId = str(hId)
1096	if hId not in HistIdLookup:
1097	raise KeyError,'Error: LookupHistName does not have index '+hId
1098	return HistIdLookup[hId]
1099
1100	def fmtVarDescr(varname):
1101	'''Return a string with a more complete description for a GSAS-II variable
1102
1103	:param str varname: A full G2 variable name with 2 or 3 or 4
1104	colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1105
1106	:returns: a string with the description
1107	'''
1108	s,l = VarDescr(varname)
1109	return s+": "+l
1110
1111	def VarDescr(varname):
1112	'''Return two strings with a more complete description for a GSAS-II variable
1113
1114	:param str name: A full G2 variable name with 2 or 3 or 4
1115	colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1116
1117	:returns: (loc,meaning) where loc describes what item the variable is mapped
1118	(phase, histogram, etc.) and meaning describes what the variable does.
1119	'''
1120
1121	# special handling for parameter names without a colons
1122	# for now, assume self-defining
1123	if varname.find(':') == -1:
1124	return "Global",varname
1125
1126	l = getVarDescr(varname)
1127	if not l:
1128	#return ("invalid variable name ("+str(varname)+")!"),""
1129	return "invalid variable name!",""
1130
1131	if not l[-1]:
1132	l[-1] = "(variable needs a definition!)"
1133
1134	s = ""
1135	if l[0] is not None and l[1] is not None: # HAP: keep short
1136	if l[0] == '*':
1137	lbl = 'all'
1138	else:
1139	lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1140	if l[1] == '*':
1141	hlbl = 'all'
1142	else:
1143	hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1144	if hlbl[:4] == 'HKLF':
1145	hlbl = 'Xtl='+hlbl[5:]
1146	elif hlbl[:4] == 'PWDR':
1147	hlbl = 'Pwd='+hlbl[5:]
1148	else:
1149	hlbl = 'Hist='+hlbl
1150	s = "Ph="+str(lbl)+" * "+str(hlbl)
1151	elif l[2] == 'Back': # background parameters are "special", alas
1152	s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1153	l[-1] += ' #'+str(l[3])
1154	elif l[4] is not None: # rigid body parameter
1155	lbl = ShortPhaseNames.get(l[0],'phase?')
1156	s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1157	elif l[3] is not None: # atom parameter,
1158	lbl = ShortPhaseNames.get(l[0],'phase?')
1159	try:
1160	albl = LookupAtomLabel(l[0],l[3])[0]
1161	except KeyError:
1162	albl = 'Atom?'
1163	s = "Atom "+str(albl)+" in "+str(lbl)
1164	elif l[0] == '*':
1165	s = "All phases "
1166	elif l[0] is not None:
1167	lbl = ShortPhaseNames.get(l[0],'phase?')
1168	s = "Phase "+str(lbl)
1169	elif l[1] == '*':
1170	s = 'All hists'
1171	elif l[1] is not None:
1172	hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1173	if hlbl[:4] == 'HKLF':
1174	hlbl = 'Xtl='+hlbl[5:]
1175	elif hlbl[:4] == 'PWDR':
1176	hlbl = 'Pwd='+hlbl[5:]
1177	else:
1178	hlbl = 'Hist='+hlbl
1179	s = str(hlbl)
1180	if not s:
1181	s = 'Global'
1182	return s,l[-1]
1183
1184	def getVarDescr(varname):
1185	'''Return a short description for a GSAS-II variable
1186
1187	:param str name: A full G2 variable name with 2 or 3 or 4
1188	colons (<p>:<h>:name[:<a1>][:<a2>])
1189
1190	:returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1191	where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1192	the histogram number and the atom number; `name` will always be
1193	an str; and `description` is str or `None`.
1194	If the variable name is incorrectly formed (for example, wrong
1195	number of colons), `None` is returned instead of a list.
1196	'''
1197	l = varname.split(':')
1198	if len(l) == 3:
1199	l += [None,None]
1200	elif len(l) == 4:
1201	l += [None]
1202	elif len(l) != 5:
1203	return None
1204	for i in (0,1,3,4):
1205	if l[i] == "":
1206	l[i] = None
1207	l += [getDescr(l[2])]
1208	return l
1209
1210	def CompileVarDesc():
1211	'''Set the values in the variable description lookup table (:attr:`VarDesc`)
1212	into :attr:`reVarDesc`. This is called in :func:`getDescr` so the initialization
1213	is always done before use.
1214
1215	Note that keys may contain regular expressions, where '[xyz]'
1216	matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range of values).
1217	'.*' matches any string. For example::
1218
1219	'AUiso':'Atomic isotropic displacement parameter',
1220
1221	will match variable ``'p::AUiso:a'``.
1222	If parentheses are used in the key, the contents of those parentheses can be
1223	used in the value, such as::
1224
1225	'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1226
1227	will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1228	in the value when used.
1229
1230	'''
1231	if reVarDesc: return # already done
1232	for key,value in {
1233	# derived or other sequential vars
1234	'([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1235	u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1236	u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1237	u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1238	# ambiguous, alas:
1239	'Scale' : 'Phase or Histogram scale factor',
1240	# Phase vars (p::<var>)
1241	'A([0-5])' : 'Reciprocal metric tensor component \\1',
1242	'Vol' : 'Unit cell volume',
1243	# Atom vars (p::<var>:a)
1244	'dA([xyz])' : 'change to atomic coordinate, \\1',
1245	'A([xyz])$' : '\\1 fractional atomic coordinate',
1246	'AUiso':'Atomic isotropic displacement parameter',
1247	'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1248	'Afrac': 'Atomic occupancy parameter',
1249	# Hist & Phase (HAP) vars (p:h:<var>)
1250	'Back': 'Background term',
1251	'BkPkint;(.*)':'Background peak #\\1 intensity',
1252	'BkPkpos;(.*)':'Background peak #\\1 position',
1253	'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1254	'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1255	'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1256	'D([123][123])' : 'Anisotropic strain coef. \\1',
1257	'Extinction' : 'Extinction coef.',
1258	'MD' : 'March-Dollase coef.',
1259	'Mustrain;.*' : 'Microstrain coef.',
1260	'Size;.*' : 'Crystallite size value',
1261	'eA' : '?',
1262	#Histogram vars (:h:<var>)
1263	'Absorption' : 'Absorption coef.',
1264	'Displace([XY])' : 'Debye-Scherrer sample displacement \\1',
1265	'Lam' : 'Wavelength',
1266	'Polariz\.' : 'Polarization correction',
1267	'SH/L' : 'FCJ peak asymmetry correction',
1268	'([UVW])' : 'Gaussian instrument broadening \\1',
1269	'([XY])' : 'Cauchy instrument broadening \\1',
1270	'Zero' : 'Debye-Scherrer zero correction',
1271	'nDebye' : 'Debye model background corr. terms',
1272	'nPeaks' : 'Fixed peak background corr. terms',
1273	'RBV.*' : 'Vector rigid body parameter',
1274	'RBR.*' : 'Residue rigid body parameter',
1275	'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1276	'RBRP([xyz])' : 'Residue rigid body position parameter',
1277	'RBRTr;.*' : 'Residue rigid body torsion parameter',
1278	'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1279	# Global vars (::<var>)
1280	'constr([0-9]*)' : 'Parameter from constraint',
1281	}.items():
1282	VarDesc[key] = value
1283	reVarDesc[re.compile(key)] = value
1284
1285	def getDescr(name):
1286	'''Return a short description for a GSAS-II variable
1287
1288	:param str name: The descriptive part of the variable name without colons (:)
1289
1290	:returns: a short description or None if not found
1291	'''
1292
1293	CompileVarDesc() # compile the regular expressions, if needed
1294	for key in reVarDesc:
1295	m = key.match(name)
1296	if m:
1297	return m.expand(reVarDesc[key])
1298	return None
1299
1300	def GenWildCard(varlist):
1301	'''Generate wildcard versions of G2 variables. These introduce '*'
1302	for a phase, histogram or atom number (but only for one of these
1303	fields) but only when there is more than one matching variable in the
1304	input variable list. So if the input is this::
1305
1306	varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1307
1308	then the output will be this::
1309
1310	wildList = ['::AUiso:0', '0::AUiso:']
1311
1312	:param list varlist: an input list of GSAS-II variable names
1313	(such as 0::AUiso:0)
1314
1315	:returns: wildList, the generated list of wild card variable names.
1316	'''
1317	wild = []
1318	for i in (0,1,3):
1319	currentL = varlist[:]
1320	while currentL:
1321	item1 = currentL.pop(0)
1322	i1splt = item1.split(':')
1323	if i >= len(i1splt): continue
1324	if i1splt[i]:
1325	nextL = []
1326	i1splt[i] = '[0-9]+'
1327	rexp = re.compile(':'.join(i1splt))
1328	matchlist = [item1]
1329	for nxtitem in currentL:
1330	if rexp.match(nxtitem):
1331	matchlist += [nxtitem]
1332	else:
1333	nextL.append(nxtitem)
1334	if len(matchlist) > 1:
1335	i1splt[i] = '*'
1336	wild.append(':'.join(i1splt))
1337	currentL = nextL
1338	return wild
1339
1340	def LookupWildCard(varname,varlist):
1341	'''returns a list of variable names from list varname
1342	that match wildcard name in varname
1343
1344	:param str varname: a G2 variable name containing a wildcard
1345	(such as \*::var)
1346	:param list varlist: the list of all variable names used in
1347	the current project
1348	:returns: a list of matching GSAS-II variables (may be empty)
1349	'''
1350	rexp = re.compile(varname.replace('*','[0-9]+'))
1351	return sorted([var for var in varlist if rexp.match(var)])
1352
1353
1354	def _lookup(dic,key):
1355	'''Lookup a key in a dictionary, where None returns an empty string
1356	but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1357	'''
1358	if key is None:
1359	return ""
1360	elif key == "*":
1361	return "*"
1362	else:
1363	return dic.get(key,'?')
1364
1365	class G2VarObj(object):
1366	'''Defines a GSAS-II variable either using the phase/atom/histogram
1367	unique Id numbers or using a character string that specifies
1368	variables by phase/atom/histogram number (which can change).
1369	Note that :func:`LoadID` should be used to (re)load the current Ids
1370	before creating or later using the G2VarObj object.
1371
1372	This can store rigid body variables, but does not translate the residue # and
1373	body # to/from random Ids
1374
1375	A :class:`G2VarObj` object can be created with a single parameter:
1376
1377	:param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1378	object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1379
1380	* p is the phase number (which may be left blank or may be '*' to indicate all phases);
1381	* h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1382	* a is the atom number (which may be left blank in which case the third colon is omitted).
1383	The atom number can be specified as '' if a phase number is specified (not as '').
1384	For rigid body variables, specify a will be a string of form "residue:body#"
1385
1386	Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1387	Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1388	and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1389	For a rigid body variables, AtomID is a string of form "residue:body#".
1390
1391	If four positional arguments are supplied, they are:
1392
1393	:param str/int phasenum: The number for the phase (or None or '*')
1394	:param str/int histnum: The number for the histogram (or None or '*')
1395	:param str varname: a single value can be used to create a :class:`G2VarObj`
1396	:param str/int atomnum: The number for the atom (or None or '*')
1397
1398	'''
1399	IDdict = {}
1400	IDdict['phases'] = {}
1401	IDdict['hists'] = {}
1402	IDdict['atoms'] = {}
1403	def __init__(self,*args):
1404	self.phase = None
1405	self.histogram = None
1406	self.name = ''
1407	self.atom = None
1408	if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1409	# single arg with 4 values
1410	self.phase,self.histogram,self.name,self.atom = args[0]
1411	elif len(args) == 1 and ':' in args[0]:
1412	#parse a string
1413	lst = args[0].split(':')
1414	if lst[0] == '*':
1415	self.phase = '*'
1416	if len(lst) > 3:
1417	self.atom = lst[3]
1418	self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1419	elif lst[1] == '*':
1420	self.histogram = '*'
1421	self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1422	else:
1423	self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1424	self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1425	if len(lst) == 4:
1426	if lst[3] == '*':
1427	self.atom = '*'
1428	else:
1429	self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1430	elif len(lst) == 5:
1431	self.atom = lst[3]+":"+lst[4]
1432	elif len(lst) == 3:
1433	pass
1434	else:
1435	raise Exception,"Too many colons in var name "+str(args[0])
1436	self.name = lst[2]
1437	elif len(args) == 4:
1438	if args[0] == '*':
1439	self.phase = '*'
1440	self.atom = args[3]
1441	else:
1442	self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1443	if args[3] == '*':
1444	self.atom = '*'
1445	elif args[0] is not None:
1446	self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1447	if args[1] == '*':
1448	self.histogram = '*'
1449	else:
1450	self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1451	self.name = args[2]
1452	else:
1453	raise Exception,"Incorrectly called GSAS-II parameter name"
1454
1455	#print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1456
1457	def __str__(self):
1458	return self.varname()
1459
1460	def varname(self):
1461	'''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1462	string (p:h:<var>:a) or (p:h:<var>)
1463
1464	:returns: the variable name as a str
1465	'''
1466	a = ""
1467	if self.phase == "*":
1468	ph = "*"
1469	if self.atom:
1470	a = ":" + str(self.atom)
1471	else:
1472	ph = _lookup(PhaseRanIdLookup,self.phase)
1473	if self.atom == '*':
1474	a = ':*'
1475	elif self.atom:
1476	if ":" in str(self.atom):
1477	a = ":" + str(self.atom)
1478	elif ph in AtomRanIdLookup:
1479	a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1480	else:
1481	a = ":?"
1482	if self.histogram == "*":
1483	hist = "*"
1484	else:
1485	hist = _lookup(HistRanIdLookup,self.histogram)
1486	s = (ph + ":" + hist + ":" + str(self.name)) + a
1487	return s
1488
1489	def __repr__(self):
1490	'''Return the detailed contents of the object
1491	'''
1492	s = "<"
1493	if self.phase == '*':
1494	s += "Phases: all; "
1495	if self.atom is not None:
1496	if ":" in str(self.atom):
1497	s += "Rigid body" + str(self.atom) + "; "
1498	else:
1499	s += "Atom #" + str(self.atom) + "; "
1500	elif self.phase is not None:
1501	ph = _lookup(PhaseRanIdLookup,self.phase)
1502	s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1503	if self.atom == '*':
1504	s += "Atoms: all; "
1505	elif ":" in self(self.atom):
1506	s += "Rigid body" + str(self.atom) + "; "
1507	elif self.atom is not None:
1508	s += "Atom rId=" + str(self.atom)
1509	if ph in AtomRanIdLookup:
1510	s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1511	else:
1512	s += " (#? -- not found!); "
1513	if self.histogram == '*':
1514	s += "Histograms: all; "
1515	elif self.histogram is not None:
1516	hist = _lookup(HistRanIdLookup,self.histogram)
1517	s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1518	s += 'Variable name="' + str(self.name) + '">'
1519	return s+" ("+self.varname()+")"
1520
1521	def __eq__(self, other):
1522	if type(other) is type(self):
1523	return (self.phase == other.phase and
1524	self.histogram == other.histogram and
1525	self.name == other.name and
1526	self.atom == other.atom)
1527	return False
1528
1529	def _show(self):
1530	'For testing, shows the current lookup table'
1531	print 'phases', self.IDdict['phases']
1532	print 'hists', self.IDdict['hists']
1533	print 'atomDict', self.IDdict['atoms']
1534
1535	#==========================================================================
1536	# shortcut routines
1537	exp = np.exp
1538	sind = lambda x: np.sin(x*np.pi/180.)
1539	tand = lambda x: np.tan(x*np.pi/180.)
1540	cosd = lambda x: np.cos(x*np.pi/180.)
1541	sind = sin = s = lambda x: np.sin(x*np.pi/180.)
1542	cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
1543	tand = tan = t = lambda x: np.tan(x*np.pi/180.)
1544	sqrt = sq = lambda x: np.sqrt(x)
1545	pi = lambda: np.pi
1546	class ExpressionObj(object):
1547	'''Defines an object with a user-defined expression, to be used for
1548	secondary fits or restraints. Object is created null, but is changed
1549	using :meth:`LoadExpression`. This contains only the minimum
1550	information that needs to be stored to save and load the expression
1551	and how it is mapped to GSAS-II variables.
1552	'''
1553	def __init__(self):
1554	self.expression = ''
1555	'The expression as a text string'
1556	self.assgnVars = {}
1557	'''A dict where keys are label names in the expression mapping to a GSAS-II
1558	variable. The value is a list with a G2 variable name and derivative step size.
1559	Note that the G2 variable name may contain a wild-card and correspond to
1560	multiple values.
1561	'''
1562	self.freeVars = {}
1563	'''A dict where keys are label names in the expression mapping to a free
1564	parameter. The value is a list with:
1565
1566	* a name assigned to the parameter
1567	* a value for to the parameter
1568	* a derivative step size and
1569	* a flag to determine if the variable is refined.
1570	'''
1571	self.depVar = None
1572
1573	self.lastError = ('','')
1574	'''Shows last encountered error in processing expression
1575	(list of 1-3 str values)'''
1576
1577	def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varStep,varRefflag):
1578	'''Load the expression and associated settings into the object. Raises
1579	an exception if the expression is not parsed, if not all functions
1580	are defined or if not all needed parameter labels in the expression
1581	are defined.
1582
1583	This will not test if the variable referenced in these definitions
1584	are actually in the parameter dictionary. This is checked when the
1585	computation for the expression is done in :meth:`SetupCalc`.
1586
1587	:param str expr: the expression
1588	:param list exprVarLst: parameter labels found in the expression
1589	:param dict varSelect: this will be 0 for Free parameters
1590	and non-zero for expression labels linked to G2 variables.
1591	:param dict varName: Defines a name (str) associated with each free parameter
1592	:param dict varValue: Defines a value (float) associated with each free parameter
1593	:param dict varStep: Defines a derivative step size (float) for each
1594	parameter labels found in the expression
1595	:param dict varRefflag: Defines a refinement flag (bool)
1596	associated with each free parameter
1597	'''
1598	self.expression = expr
1599	self.compiledExpr = None
1600	self.freeVars = {}
1601	self.assgnVars = {}
1602	for v in exprVarLst:
1603	if varSelect[v] == 0:
1604	self.freeVars[v] = [
1605	varName.get(v),
1606	varValue.get(v),
1607	varStep.get(v),
1608	varRefflag.get(v),
1609	]
1610	else:
1611	self.assgnVars[v] = [
1612	varName[v],
1613	varStep.get(v),
1614	]
1615	self.CheckVars()
1616
1617	def EditExpression(self,exprVarLst,varSelect,varName,varValue,varStep,varRefflag):
1618	'''Load the expression and associated settings from the object into
1619	arrays used for editing.
1620
1621	:param list exprVarLst: parameter labels found in the expression
1622	:param dict varSelect: this will be 0 for Free parameters
1623	and non-zero for expression labels linked to G2 variables.
1624	:param dict varName: Defines a name (str) associated with each free parameter
1625	:param dict varValue: Defines a value (float) associated with each free parameter
1626	:param dict varStep: Defines a derivative step size (float) for each
1627	parameter labels found in the expression
1628	:param dict varRefflag: Defines a refinement flag (bool)
1629	associated with each free parameter
1630
1631	:returns: the expression as a str
1632	'''
1633	for v in self.freeVars:
1634	varSelect[v] = 0
1635	varName[v] = self.freeVars[v][0]
1636	varValue[v] = self.freeVars[v][1]
1637	varStep[v] = self.freeVars[v][2]
1638	varRefflag[v] = self.freeVars[v][3]
1639	for v in self.assgnVars:
1640	varSelect[v] = 1
1641	varName[v] = self.assgnVars[v][0]
1642	varStep[v] = self.assgnVars[v][1]
1643	return self.expression
1644
1645	def GetVaried(self):
1646	'Returns the names of the free parameters that will be refined'
1647	return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][3]]
1648
1649	def GetVariedVarVal(self):
1650	'Returns the names and values of the free parameters that will be refined'
1651	return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][3]]
1652
1653	def UpdateVariedVars(self,varyList,values):
1654	'Updates values for the free parameters (after a refinement); only updates refined vars'
1655	for v in self.freeVars:
1656	if not self.freeVars[v][3]: continue
1657	if "::"+self.freeVars[v][0] not in varyList: continue
1658	indx = varyList.index("::"+self.freeVars[v][0])
1659	self.freeVars[v][1] = values[indx]
1660
1661	def GetIndependentVars(self):
1662	'Returns the names of the required independent parameters used in expression'
1663	return [self.assgnVars[v][0] for v in self.assgnVars]
1664
1665	def CheckVars(self):
1666	'''Check that the expression can be parsed, all functions are
1667	defined and that input loaded into the object is internally
1668	consistent. If not an Exception is raised.
1669
1670	:returns: a dict with references to packages needed to
1671	find functions referenced in the expression.
1672	'''
1673	ret = self.ParseExpression(self.expression)
1674	if not ret:
1675	raise Exception("Expression parse error")
1676	exprLblList,fxnpkgdict = ret
1677	# check each var used in expression is defined
1678	defined = self.assgnVars.keys() + self.freeVars.keys()
1679	notfound = []
1680	for var in exprLblList:
1681	if var not in defined:
1682	notfound.append(var)
1683	if notfound:
1684	msg = 'Not all variables defined'
1685	msg1 = 'The following variables were not defined: '
1686	msg2 = ''
1687	for var in notfound:
1688	if msg: msg += ', '
1689	msg += var
1690	self.lastError = (msg1,' '+msg2)
1691	raise Exception(msg)
1692	return fxnpkgdict
1693
1694	def ParseExpression(self,expr):
1695	'''Parse an expression and return a dict of called functions and
1696	the variables used in the expression. Returns None in case an error
1697	is encountered. If packages are referenced in functions, they are loaded
1698	and the functions are looked up into the modules global
1699	workspace.
1700
1701	Note that no changes are made to the object other than
1702	saving an error message, so that this can be used for testing prior
1703	to the save.
1704
1705	:returns: a list of used variables
1706	'''
1707	self.lastError = ('','')
1708	import ast
1709	def FindFunction(f):
1710	'''Find the object corresponding to function f
1711	:param str f: a function name such as 'numpy.exp'
1712	:returns: (pkgdict,pkgobj) where pkgdict contains a dict
1713	that defines the package location(s) and where pkgobj
1714	defines the object associated with the function.
1715	If the function is not found, pkgobj is None.
1716	'''
1717	df = f.split('.')
1718	pkgdict = {}
1719	# no listed package, try in current namespace
1720	if len(df) == 1:
1721	try:
1722	fxnobj = eval(f)
1723	return pkgdict,fxnobj
1724	except (AttributeError, NameError):
1725	return None,None
1726	else:
1727	try:
1728	fxnobj = eval(f)
1729	pkgdict[df[0]] = eval(df[0])
1730	return pkgdict,fxnobj
1731	except (AttributeError, NameError):
1732	pass
1733	# includes a package, lets try to load the packages
1734	pkgname = ''
1735	path = sys.path
1736	for pkg in f.split('.')[:-1]: # if needed, descend down the tree
1737	if pkgname:
1738	pkgname += '.' + pkg
1739	else:
1740	pkgname = pkg
1741	fp = None
1742	try:
1743	fp, fppath,desc = imp.find_module(pkg,path)
1744	pkgobj = imp.load_module(pkg,fp,fppath,desc)
1745	pkgdict[pkgname] = pkgobj
1746	path = [fppath]
1747	except Exception as msg:
1748	print('load of '+pkgname+' failed with error='+str(msg))
1749	return {},None
1750	finally:
1751	if fp: fp.close()
1752	try:
1753	#print 'before',pkgdict.keys()
1754	fxnobj = eval(f,globals(),pkgdict)
1755	#print 'after 1',pkgdict.keys()
1756	#fxnobj = eval(f,pkgdict)
1757	#print 'after 2',pkgdict.keys()
1758	return pkgdict,fxnobj
1759	except:
1760	continue
1761	return None # not found
1762	def ASTtransverse(node,fxn=False):
1763	'''Transverse a AST-parsed expresson, compiling a list of variables
1764	referenced in the expression. This routine is used recursively.
1765
1766	:returns: varlist,fxnlist where
1767	varlist is a list of referenced variable names and
1768	fxnlist is a list of used functions
1769	'''
1770	varlist = []
1771	fxnlist = []
1772	if isinstance(node, list):
1773	for b in node:
1774	v,f = ASTtransverse(b,fxn)
1775	varlist += v
1776	fxnlist += f
1777	elif isinstance(node, ast.AST):
1778	for a, b in ast.iter_fields(node):
1779	if isinstance(b, ast.AST):
1780	if a == 'func':
1781	fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
1782	continue
1783	v,f = ASTtransverse(b,fxn)
1784	varlist += v
1785	fxnlist += f
1786	elif isinstance(b, list):
1787	v,f = ASTtransverse(b,fxn)
1788	varlist += v
1789	fxnlist += f
1790	elif node.__class__.__name__ == "Name":
1791	varlist += [b]
1792	elif fxn and node.__class__.__name__ == "Attribute":
1793	varlist += [b]
1794	return varlist,fxnlist
1795	try:
1796	exprast = ast.parse(expr)
1797	except SyntaxError as err:
1798	s = ''
1799	import traceback
1800	for i in traceback.format_exc().splitlines()[-3:-1]:
1801	if s: s += "\n"
1802	s += str(i)
1803	self.lastError = ("Error parsing expression:",s)
1804	return
1805	# find the variables & functions
1806	v,f = ASTtransverse(exprast)
1807	varlist = sorted(list(set(v)))
1808	fxnlist = list(set(f))
1809	pkgdict = {}
1810	# check the functions are defined
1811	for fxn in fxnlist:
1812	fxndict,fxnobj = FindFunction(fxn)
1813	if not fxnobj:
1814	self.lastError = ("Error: Invalid function",fxn,
1815	"is not defined")
1816	return
1817	if not hasattr(fxnobj,'__call__'):
1818	self.lastError = ("Error: Not a function.",fxn,
1819	"cannot be called as a function")
1820	return
1821	pkgdict.update(fxndict)
1822	return varlist,pkgdict
1823
1824	def GetDepVar(self):
1825	'return the dependent variable, or None'
1826	return self.depVar
1827
1828	def SetDepVar(self,var):
1829	'Set the dependent variable, if used'
1830	self.depVar = var
1831	#==========================================================================
1832	class ExpressionCalcObj(object):
1833	'''An object used to evaluate an expression from a :class:`ExpressionObj`
1834	object.
1835
1836	:param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
1837	an expression string and mappings for the parameter labels in that object.
1838	'''
1839	def __init__(self,exprObj):
1840	self.eObj = exprObj
1841	'The expression and mappings; a :class:`ExpressionObj` object'
1842	self.compiledExpr = None
1843	'The expression as compiled byte-code'
1844	self.exprDict = {}
1845	'''dict that defines values for labels used in expression and packages
1846	referenced by functions
1847	'''
1848	self.derivStep = {}
1849	'''Contains step sizes for derivatives for variables used in the expression;
1850	if a variable is not included in this the derivatives will be computed as zero
1851	'''
1852	self.lblLookup = {}
1853	'''Lookup table that specifies the expression label name that is
1854	tied to a particular GSAS-II parameters in the parmDict.
1855	'''
1856	self.fxnpkgdict = {}
1857	'''a dict with references to packages needed to
1858	find functions referenced in the expression.
1859	'''
1860	self.varLookup = {}
1861	'''Lookup table that specifies the GSAS-II variable(s)
1862	indexed by the expression label name. (Used for only for diagnostics
1863	not evaluation of expression.)
1864	'''
1865
1866	def SetupCalc(self,parmDict):
1867	'''Do all preparations to use the expression for computation.
1868	Adds the free parameter values to the parameter dict (parmDict).
1869	'''
1870	self.fxnpkgdict = self.eObj.CheckVars()
1871	# all is OK, compile the expression
1872	self.compiledExpr = compile(self.eObj.expression,'','eval')
1873
1874	# look at first value in parmDict to determine its type
1875	parmsInList = True
1876	for key in parmDict:
1877	val = parmDict[key]
1878	if isinstance(val, basestring):
1879	parmsInList = False
1880	break
1881	try: # check if values are in lists
1882	val = parmDict[key][0]
1883	except (TypeError,IndexError):
1884	parmsInList = False
1885	break
1886
1887	# set up the dicts needed to speed computations
1888	self.exprDict = {}
1889	self.derivStep = {}
1890	self.lblLookup = {}
1891	self.varLookup = {}
1892	for v in self.eObj.freeVars:
1893	varname = self.eObj.freeVars[v][0]
1894	varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
1895	self.lblLookup[varname] = v
1896	self.varLookup[v] = varname
1897	if parmsInList:
1898	parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][3]]
1899	else:
1900	parmDict[varname] = self.eObj.freeVars[v][1]
1901	self.exprDict[v] = self.eObj.freeVars[v][1]
1902	if self.eObj.freeVars[v][3]:
1903	self.derivStep[varname] = self.eObj.freeVars[v][2]
1904	for v in self.eObj.assgnVars:
1905	step = self.eObj.assgnVars[v][1]
1906	varname = self.eObj.assgnVars[v][0]
1907	if '*' in varname:
1908	varlist = LookupWildCard(varname,parmDict.keys())
1909	if len(varlist) == 0:
1910	raise Exception,"No variables match "+str(v)
1911	for var in varlist:
1912	self.lblLookup[var] = v
1913	self.derivStep[var] = np.array(
1914	[step if var1 == var else 0 for var1 in varlist]
1915	)
1916	if parmsInList:
1917	self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
1918	else:
1919	self.exprDict[v] = np.array([parmDict[var] for var in varlist])
1920	self.varLookup[v] = [var for var in varlist]
1921	elif varname in parmDict:
1922	self.lblLookup[varname] = v
1923	self.varLookup[v] = varname
1924	if parmsInList:
1925	self.exprDict[v] = parmDict[varname][0]
1926	else:
1927	self.exprDict[v] = parmDict[varname]
1928	self.derivStep[varname] = step
1929	else:
1930	raise Exception,"No value for variable "+str(v)
1931	self.exprDict.update(self.fxnpkgdict)
1932
1933	def UpdateVars(self,varList,valList):
1934	'''Update the dict for the expression with a set of values
1935	:param list varList: a list of variable names
1936	:param list valList: a list of corresponding values
1937	'''
1938	for var,val in zip(varList,valList):
1939	self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
1940
1941	def EvalExpression(self):
1942	'''Evaluate an expression. Note that the expression
1943	and mapping are taken from the :class:`ExpressionObj` expression object
1944	and the parameter values were specified in :meth:`SetupCalc`.
1945	:returns: a single value for the expression. If parameter
1946	values are arrays (for example, from wild-carded variable names),
1947	the sum of the resulting expression is returned.
1948
1949	For example, if the expression is ``'A*B'``,
1950	where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
1951
1952	[0.5, 1, 0.5]
1953
1954	then the result will be ``4.0``.
1955	'''
1956	if self.compiledExpr is None:
1957	raise Exception,"EvalExpression called before SetupCalc"
1958	val = eval(self.compiledExpr,globals(),self.exprDict)
1959	if not np.isscalar(val):
1960	val = np.sum(val)
1961	return val
1962
1963	def EvalDeriv(self,varname,step=None):
1964	'''Evaluate the expression derivative with respect to a
1965	GSAS-II variable name.
1966
1967	:param str varname: a G2 variable name (will not have a wild-card)
1968	:returns: the derivative
1969	'''
1970	if step is None:
1971	if varname not in self.derivStep: return 0.0
1972	step = self.derivStep[varname]
1973	if varname not in self.lblLookup: return 0.0
1974	lbl = self.lblLookup[varname] # what label does this map to in expression?
1975	origval = self.exprDict[lbl]
1976
1977	self.exprDict[lbl] = origval + step
1978	val1 = eval(self.compiledExpr,globals(),self.exprDict)
1979
1980	self.exprDict[lbl] = origval - step
1981	val2 = eval(self.compiledExpr,globals(),self.exprDict)
1982
1983	self.exprDict[lbl] = origval # reset back to central value
1984
1985	val = (val1 - val2) / (2.*np.max(step))
1986	if not np.isscalar(val):
1987	val = np.sum(val)
1988	return val
1989
1990	if __name__ == "__main__":
1991	# test equation evaluation
1992	def showEQ(calcobj):
1993	print 50*'='
1994	print calcobj.eObj.expression,'=',calcobj.EvalExpression()
1995	for v in sorted(calcobj.varLookup):
1996	print " ",v,'=',calcobj.exprDict[v],'=',calcobj.varLookup[v]
1997	print ' Derivatives'
1998	for v in calcobj.derivStep.keys():
1999	print ' d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2000
2001	obj = ExpressionObj()
2002
2003	obj.expression = "A*np.exp(B)"
2004	obj.assgnVars = {'B': ['0::Afrac:1', 0.0001]}
2005	obj.freeVars = {'A': [u'A', 0.5, 0.0001, True]}
2006	#obj.CheckVars()
2007	parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2008	calcobj = ExpressionCalcObj(obj)
2009	calcobj.SetupCalc(parmDict2)
2010	showEQ(calcobj)
2011
2012	obj.expression = "A*np.exp(B)"
2013	obj.assgnVars = {'B': ['0::Afrac:*', 0.0001]}
2014	obj.freeVars = {'A': [u'Free Prm A', 0.5, 0.0001, True]}
2015	#obj.CheckVars()
2016	parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2017	calcobj = ExpressionCalcObj(obj)
2018	calcobj.SetupCalc(parmDict1)
2019	showEQ(calcobj)
2020
2021	calcobj.SetupCalc(parmDict2)
2022	showEQ(calcobj)

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