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source: trunk/GSASIIobj.py @ 1620

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1	# -- coding: utf-8 --
2	#GSASIIobj - data objects for GSAS-II
3	########### SVN repository information ###################
4	# $Date: 2014-12-19 18:51:48 +0000 (Fri, 19 Dec 2014) $
5	# $Author: vondreele $
6	# $Revision: 1614 $
7	# $URL: trunk/GSASIIobj.py $
8	# $Id: GSASIIobj.py 1614 2014-12-19 18:51:48Z 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+7 U11, U22, U33, U12, U13, U23 (6 floats)
394	atom[cia+8] unique atom identifier (int)
395
396	============== ====================================================
397
398	Drawing 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
408	If ``phasedict`` points to the phase information in the data tree, then
409	drawing atoms are contained in a list of drawing atom records (list) in
410	``phasedict['Drawing']['Atoms']``. Also needed to read atom information
411	are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
412	which define locations in the atom record, as shown below. Items shown are
413	always present; additional ones for macromolecular phases are marked 'mm'
414
415	.. tabularcolumns:: \|l\|p{4.5in}\|
416
417	============== ====================================================
418	location explanation
419	============== ====================================================
420	ct-4 mm - residue number (str)
421	ct-3 mm - residue name (e.g. ALA) (str)
422	ct-2 mm - chain label (str)
423	ct-1 atom label (str)
424	ct atom type (str)
425	cx,cx+1,cx+2 the x,y and z coordinates (3 floats)
426	cs-1 Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
427	cs atom drawing style; e.g. 'balls & sticks' (str)
428	cs+1 atom label style (e.g. 'name') (str)
429	cs+2 atom color (RBG triplet) (int)
430	cs+3 ADP flag: Isotropic ('I') or Anisotropic ('A')
431	cs+4 Uiso (float)
432	cs+5...cs+11 U11, U22, U33, U12, U13, U23 (6 floats)
433	ci unique atom identifier; matches source atom Id in Atom Records (int)
434	============== ====================================================
435
436	Powder 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
445	Every powder diffraction histogram is stored in the GSAS-II data tree
446	with a top-level entry named beginning with the string "PWDR ". The
447	diffraction data for that information are directly associated with
448	that tree item and there are a series of children to that item. The
449	routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
450	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
451	load this information into a dictionary where the child tree name is
452	used as a key, and the information in the main entry is assigned
453	a key of ``Data``, as outlined below.
454
455	.. tabularcolumns:: \|l\|l\|p{4in}\|
456
457	====================== =============== ====================================================
458	key sub-key explanation
459	====================== =============== ====================================================
460	Comments \ Text strings extracted from the original powder
461	data header. These cannot be changed by the user;
462	it may be empty.
463	Limits \ 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.
468	Reflection 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.
473	Instrument 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]
509	wtFactor \ 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).
515	Sample 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?
549	hId \ The number assigned to the histogram when
550	the project is loaded or edited (can change)
551	ranId \ A random number id for the histogram
552	that does not change
553	Background \ 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.)
559	Data \ 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
570	Powder 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
579	For every phase in a histogram, the ``Reflection Lists`` value is a dict
580	one element of which is `'RefList'`, which is a np.array containing
581	reflections. 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
599	Single 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
608	Every single crystal diffraction histogram is stored in the GSAS-II data tree
609	with a top-level entry named beginning with the string "HKLF ". The
610	diffraction data for that information are directly associated with
611	that tree item and there are a series of children to that item. The
612	routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
613	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
614	load this information into a dictionary where the child tree name is
615	used as a key, and the information in the main entry is assigned
616	a key of ``Data``, as outlined below.
617
618	.. tabularcolumns:: \|l\|l\|p{4in}\|
619
620	====================== =============== ====================================================
621	key sub-key explanation
622	====================== =============== ====================================================
623	Data \ A dict that contains the
624	reflection table,
625	as described in the
626	:ref:`Single Crystal Reflections
627	<XtalRefl_table>`
628	description.
629
630	Instrument 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
644	wtFactor \ 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
651	hId \ The number assigned to the histogram when
652	the project is loaded or edited (can change)
653	ranId \ A random number id for the histogram
654	that does not change
655	====================== =============== ====================================================
656
657	Single 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
666	For every single crystal a histogram, the ``'Data'`` item contains
667	the structure factors as an np.array in item `'RefList'`.
668	The 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
687	Image Data Structure
688	--------------------
689
690	.. _Image_table:
691
692	.. index::
693	image: Image data object description
694	image: Image object descriptions
695
696	Every 2-dimensional image is stored in the GSAS-II data tree
697	with a top-level entry named beginning with the string "IMG ". The
698	image data are directly associated with that tree item and there
699	are a series of children to that item. The routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
700	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
701	load this information into a dictionary where the child tree name is
702	used as a key, and the information in the main entry is assigned
703	a key of ``Data``, as outlined below.
704
705	.. tabularcolumns:: \|l\|l\|p{4in}\|
706
707	====================== ====================== ====================================================
708	key sub-key explanation
709	====================== ====================== ====================================================
710	Comments \ 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.
713	Image 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
782	Masks 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
795	Stress/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
814	Parameter Dictionary
815	-------------------------
816
817	.. _parmDict_table:
818
819	.. index::
820	single: Parameter dictionary
821
822	The parameter dictionary contains all of the variable parameters for the refinement.
823	The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
824	It is prepared in two ways. When loaded from the tree
825	(in :meth:`GSASII.GSASII.MakeLSParmDict` and
826	:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
827	the values are lists with two elements: ``[value, refine flag]``
828
829	When loaded from the GPX file (in
830	:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
831	dict is the actual parameter value (usually a float, but sometimes a
832	letter or string flag value (such as I or A for iso/anisotropic).
833
834
835	Classes and routines
836	----------------------
837
838	'''
839	import re
840	import imp
841	import random as ran
842	import sys
843	import GSASIIpath
844	import GSASIImath as G2mth
845	import numpy as np
846
847	GSASIIpath.SetVersionNumber("$Revision: 1614 $")
848
849	DefaultControls = {
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	'FreeVar1':'Sample humidity (%)',
855	'FreeVar2':'Sample voltage (V)',
856	'FreeVar3':'Applied load (MN)',
857	}
858	'''Values to be used as defaults for the initial contents of the ``Controls``
859	data tree item.
860	'''
861
862	def 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
894	PhaseIdLookup = {}
895	'''dict listing phase name and random Id keyed by sequential phase index as a str;
896	best to access this using :func:`LookupPhaseName`
897	'''
898	PhaseRanIdLookup = {}
899	'''dict listing phase sequential index keyed by phase random Id;
900	best to access this using :func:`LookupPhaseId`
901	'''
902	HistIdLookup = {}
903	'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
904	best to access this using :func:`LookupHistName`
905	'''
906	HistRanIdLookup = {}
907	'''dict listing histogram sequential index keyed by histogram random Id;
908	best to access this using :func:`LookupHistId`
909	'''
910	AtomIdLookup = {}
911	'''dict listing for each phase index as a str, the atom label and atom random Id,
912	keyed by atom sequential index as a str;
913	best to access this using :func:`LookupAtomLabel`
914	'''
915	AtomRanIdLookup = {}
916	'''dict listing for each phase the atom sequential index keyed by atom random Id;
917	best to access this using :func:`LookupAtomId`
918	'''
919	ShortPhaseNames = {}
920	'''a dict containing a possibly shortened and when non-unique numbered
921	version of the phase name. Keyed by the phase sequential index.
922	'''
923	ShortHistNames = {}
924	'''a dict containing a possibly shortened and when non-unique numbered
925	version of the histogram name. Keyed by the histogram sequential index.
926	'''
927
928	VarDesc = {}
929	''' This dictionary lists descriptions for GSAS-II variables,
930	as set in :func:`CompileVarDesc`. See that function for a description
931	for how keys and values are written.
932	'''
933
934	reVarDesc = {}
935	''' This dictionary lists descriptions for GSAS-II variables with
936	the same values as :attr:`VarDesc` except that keys have been compiled as
937	regular expressions. Initialized in :func:`CompileVarDesc`.
938	'''
939
940	def 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
1009	def 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
1028	def 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
1047	def 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
1059	def 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
1075	def 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
1087	def 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
1103	def 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
1114	def 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
1195	def 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
1223	def 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	'([XYZ])sin' : 'Sin position wave for \\1',
1301	'([XYZ])cos' : 'Cos position wave for \\1',
1302	'U([123][123])sin$' : 'Sin thermal wave for U\\1',
1303	'U([123][123])cos$' : 'Cos thermal wave for U\\1',
1304	'M([XYZ])sin$' : 'Sin mag. moment wave for \\1',
1305	'M([XYZ])cos$' : 'Cos mag. moment wave for \\1',
1306	# SASD vars (l:<var>;l = component)
1307	'Aspect ratio' : 'Particle aspect ratio',
1308	'Length' : 'Cylinder length',
1309	'Diameter' : 'Cylinder/disk diameter',
1310	'Thickness' : 'Disk thickness',
1311	'Dist' : 'Interparticle distance',
1312	'VolFr' : 'Dense scatterer volume fraction',
1313	'epis' : 'Sticky sphere epsilon',
1314	'Sticky' : 'Stickyness',
1315	'Depth' : 'Well depth',
1316	'Width' : 'Well width',
1317	'Volume' : 'Particle volume',
1318	'Radius' : 'Sphere/cylinder/disk radius',
1319	'Mean' : 'Particle mean radius',
1320	'StdDev' : 'Standard deviation in Mean',
1321	'G$': 'Guinier prefactor',
1322	'Rg$': 'Guinier radius of gyration',
1323	'B$': 'Porod prefactor',
1324	'P$': 'Porod power',
1325	'Cutoff': 'Porod cutoff',
1326	'PkInt': 'Bragg peak intensity',
1327	'PkPos': 'Bragg peak position',
1328	'PkSig': 'Bragg peak sigma',
1329	'PkGam': 'Bragg peak gamma',
1330	'e([12][12])' : 'strain tensor e\1', # strain vars e11, e22, e12
1331	'Dcalc': 'Calc. d-spacing',
1332	'Back$': 'background parameter',
1333	'pos$': 'peak position',
1334	'int$': 'peak intensity',
1335	}.items():
1336	VarDesc[key] = value
1337	reVarDesc[re.compile(key)] = value
1338
1339	def getDescr(name):
1340	'''Return a short description for a GSAS-II variable
1341
1342	:param str name: The descriptive part of the variable name without colons (:)
1343
1344	:returns: a short description or None if not found
1345	'''
1346
1347	CompileVarDesc() # compile the regular expressions, if needed
1348	for key in reVarDesc:
1349	m = key.match(name)
1350	if m:
1351	reVarDesc[key]
1352	return m.expand(reVarDesc[key])
1353	return None
1354
1355	def GenWildCard(varlist):
1356	'''Generate wildcard versions of G2 variables. These introduce '*'
1357	for a phase, histogram or atom number (but only for one of these
1358	fields) but only when there is more than one matching variable in the
1359	input variable list. So if the input is this::
1360
1361	varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1362
1363	then the output will be this::
1364
1365	wildList = ['::AUiso:0', '0::AUiso:']
1366
1367	:param list varlist: an input list of GSAS-II variable names
1368	(such as 0::AUiso:0)
1369
1370	:returns: wildList, the generated list of wild card variable names.
1371	'''
1372	wild = []
1373	for i in (0,1,3):
1374	currentL = varlist[:]
1375	while currentL:
1376	item1 = currentL.pop(0)
1377	i1splt = item1.split(':')
1378	if i >= len(i1splt): continue
1379	if i1splt[i]:
1380	nextL = []
1381	i1splt[i] = '[0-9]+'
1382	rexp = re.compile(':'.join(i1splt))
1383	matchlist = [item1]
1384	for nxtitem in currentL:
1385	if rexp.match(nxtitem):
1386	matchlist += [nxtitem]
1387	else:
1388	nextL.append(nxtitem)
1389	if len(matchlist) > 1:
1390	i1splt[i] = '*'
1391	wild.append(':'.join(i1splt))
1392	currentL = nextL
1393	return wild
1394
1395	def LookupWildCard(varname,varlist):
1396	'''returns a list of variable names from list varname
1397	that match wildcard name in varname
1398
1399	:param str varname: a G2 variable name containing a wildcard
1400	(such as \*::var)
1401	:param list varlist: the list of all variable names used in
1402	the current project
1403	:returns: a list of matching GSAS-II variables (may be empty)
1404	'''
1405	rexp = re.compile(varname.replace('*','[0-9]+'))
1406	return sorted([var for var in varlist if rexp.match(var)])
1407
1408
1409	def _lookup(dic,key):
1410	'''Lookup a key in a dictionary, where None returns an empty string
1411	but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1412	'''
1413	if key is None:
1414	return ""
1415	elif key == "*":
1416	return "*"
1417	else:
1418	return dic.get(key,'?')
1419
1420	class G2VarObj(object):
1421	'''Defines a GSAS-II variable either using the phase/atom/histogram
1422	unique Id numbers or using a character string that specifies
1423	variables by phase/atom/histogram number (which can change).
1424	Note that :func:`LoadID` should be used to (re)load the current Ids
1425	before creating or later using the G2VarObj object.
1426
1427	This can store rigid body variables, but does not translate the residue # and
1428	body # to/from random Ids
1429
1430	A :class:`G2VarObj` object can be created with a single parameter:
1431
1432	:param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1433	object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1434
1435	* p is the phase number (which may be left blank or may be '*' to indicate all phases);
1436	* h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1437	* a is the atom number (which may be left blank in which case the third colon is omitted).
1438	The atom number can be specified as '' if a phase number is specified (not as '').
1439	For rigid body variables, specify a will be a string of form "residue:body#"
1440
1441	Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1442	Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1443	and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1444	For a rigid body variables, AtomID is a string of form "residue:body#".
1445
1446	If four positional arguments are supplied, they are:
1447
1448	:param str/int phasenum: The number for the phase (or None or '*')
1449	:param str/int histnum: The number for the histogram (or None or '*')
1450	:param str varname: a single value can be used to create a :class:`G2VarObj`
1451	:param str/int atomnum: The number for the atom (or None or '*')
1452
1453	'''
1454	IDdict = {}
1455	IDdict['phases'] = {}
1456	IDdict['hists'] = {}
1457	IDdict['atoms'] = {}
1458	def __init__(self,*args):
1459	self.phase = None
1460	self.histogram = None
1461	self.name = ''
1462	self.atom = None
1463	if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1464	# single arg with 4 values
1465	self.phase,self.histogram,self.name,self.atom = args[0]
1466	elif len(args) == 1 and ':' in args[0]:
1467	#parse a string
1468	lst = args[0].split(':')
1469	if lst[0] == '*':
1470	self.phase = '*'
1471	if len(lst) > 3:
1472	self.atom = lst[3]
1473	self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1474	elif lst[1] == '*':
1475	self.histogram = '*'
1476	self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1477	else:
1478	self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1479	self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1480	if len(lst) == 4:
1481	if lst[3] == '*':
1482	self.atom = '*'
1483	else:
1484	self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1485	elif len(lst) == 5:
1486	self.atom = lst[3]+":"+lst[4]
1487	elif len(lst) == 3:
1488	pass
1489	else:
1490	raise Exception,"Too many colons in var name "+str(args[0])
1491	self.name = lst[2]
1492	elif len(args) == 4:
1493	if args[0] == '*':
1494	self.phase = '*'
1495	self.atom = args[3]
1496	else:
1497	self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1498	if args[3] == '*':
1499	self.atom = '*'
1500	elif args[0] is not None:
1501	self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1502	if args[1] == '*':
1503	self.histogram = '*'
1504	else:
1505	self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1506	self.name = args[2]
1507	else:
1508	raise Exception,"Incorrectly called GSAS-II parameter name"
1509
1510	#print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1511
1512	def __str__(self):
1513	return self.varname()
1514
1515	def varname(self):
1516	'''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1517	string (p:h:<var>:a) or (p:h:<var>)
1518
1519	:returns: the variable name as a str
1520	'''
1521	a = ""
1522	if self.phase == "*":
1523	ph = "*"
1524	if self.atom:
1525	a = ":" + str(self.atom)
1526	else:
1527	ph = _lookup(PhaseRanIdLookup,self.phase)
1528	if self.atom == '*':
1529	a = ':*'
1530	elif self.atom:
1531	if ":" in str(self.atom):
1532	a = ":" + str(self.atom)
1533	elif ph in AtomRanIdLookup:
1534	a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1535	else:
1536	a = ":?"
1537	if self.histogram == "*":
1538	hist = "*"
1539	else:
1540	hist = _lookup(HistRanIdLookup,self.histogram)
1541	s = (ph + ":" + hist + ":" + str(self.name)) + a
1542	return s
1543
1544	def __repr__(self):
1545	'''Return the detailed contents of the object
1546	'''
1547	s = "<"
1548	if self.phase == '*':
1549	s += "Phases: all; "
1550	if self.atom is not None:
1551	if ":" in str(self.atom):
1552	s += "Rigid body" + str(self.atom) + "; "
1553	else:
1554	s += "Atom #" + str(self.atom) + "; "
1555	elif self.phase is not None:
1556	ph = _lookup(PhaseRanIdLookup,self.phase)
1557	s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1558	if self.atom == '*':
1559	s += "Atoms: all; "
1560	elif ":" in self(self.atom):
1561	s += "Rigid body" + str(self.atom) + "; "
1562	elif self.atom is not None:
1563	s += "Atom rId=" + str(self.atom)
1564	if ph in AtomRanIdLookup:
1565	s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1566	else:
1567	s += " (#? -- not found!); "
1568	if self.histogram == '*':
1569	s += "Histograms: all; "
1570	elif self.histogram is not None:
1571	hist = _lookup(HistRanIdLookup,self.histogram)
1572	s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1573	s += 'Variable name="' + str(self.name) + '">'
1574	return s+" ("+self.varname()+")"
1575
1576	def __eq__(self, other):
1577	if type(other) is type(self):
1578	return (self.phase == other.phase and
1579	self.histogram == other.histogram and
1580	self.name == other.name and
1581	self.atom == other.atom)
1582	return False
1583
1584	def _show(self):
1585	'For testing, shows the current lookup table'
1586	print 'phases', self.IDdict['phases']
1587	print 'hists', self.IDdict['hists']
1588	print 'atomDict', self.IDdict['atoms']
1589
1590	#==========================================================================
1591	# shortcut routines
1592	exp = np.exp
1593	sind = sin = s = lambda x: np.sin(x*np.pi/180.)
1594	cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
1595	tand = tan = t = lambda x: np.tan(x*np.pi/180.)
1596	sqrt = sq = lambda x: np.sqrt(x)
1597	pi = lambda: np.pi
1598	class ExpressionObj(object):
1599	'''Defines an object with a user-defined expression, to be used for
1600	secondary fits or restraints. Object is created null, but is changed
1601	using :meth:`LoadExpression`. This contains only the minimum
1602	information that needs to be stored to save and load the expression
1603	and how it is mapped to GSAS-II variables.
1604	'''
1605	def __init__(self):
1606	self.expression = ''
1607	'The expression as a text string'
1608	self.assgnVars = {}
1609	'''A dict where keys are label names in the expression mapping to a GSAS-II
1610	variable. The value a G2 variable name.
1611	Note that the G2 variable name may contain a wild-card and correspond to
1612	multiple values.
1613	'''
1614	self.freeVars = {}
1615	'''A dict where keys are label names in the expression mapping to a free
1616	parameter. The value is a list with:
1617
1618	* a name assigned to the parameter
1619	* a value for to the parameter and
1620	* a flag to determine if the variable is refined.
1621	'''
1622	self.depVar = None
1623
1624	self.lastError = ('','')
1625	'''Shows last encountered error in processing expression
1626	(list of 1-3 str values)'''
1627
1628	def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
1629	'''Load the expression and associated settings into the object. Raises
1630	an exception if the expression is not parsed, if not all functions
1631	are defined or if not all needed parameter labels in the expression
1632	are defined.
1633
1634	This will not test if the variable referenced in these definitions
1635	are actually in the parameter dictionary. This is checked when the
1636	computation for the expression is done in :meth:`SetupCalc`.
1637
1638	:param str expr: the expression
1639	:param list exprVarLst: parameter labels found in the expression
1640	:param dict varSelect: this will be 0 for Free parameters
1641	and non-zero for expression labels linked to G2 variables.
1642	:param dict varName: Defines a name (str) associated with each free parameter
1643	:param dict varValue: Defines a value (float) associated with each free parameter
1644	:param dict varRefflag: Defines a refinement flag (bool)
1645	associated with each free parameter
1646	'''
1647	self.expression = expr
1648	self.compiledExpr = None
1649	self.freeVars = {}
1650	self.assgnVars = {}
1651	for v in exprVarLst:
1652	if varSelect[v] == 0:
1653	self.freeVars[v] = [
1654	varName.get(v),
1655	varValue.get(v),
1656	varRefflag.get(v),
1657	]
1658	else:
1659	self.assgnVars[v] = varName[v]
1660	self.CheckVars()
1661
1662	def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
1663	'''Load the expression and associated settings from the object into
1664	arrays used for editing.
1665
1666	:param list exprVarLst: parameter labels found in the expression
1667	:param dict varSelect: this will be 0 for Free parameters
1668	and non-zero for expression labels linked to G2 variables.
1669	:param dict varName: Defines a name (str) associated with each free parameter
1670	:param dict varValue: Defines a value (float) associated with each free parameter
1671	:param dict varRefflag: Defines a refinement flag (bool)
1672	associated with each free parameter
1673
1674	:returns: the expression as a str
1675	'''
1676	for v in self.freeVars:
1677	varSelect[v] = 0
1678	varName[v] = self.freeVars[v][0]
1679	varValue[v] = self.freeVars[v][1]
1680	varRefflag[v] = self.freeVars[v][2]
1681	for v in self.assgnVars:
1682	varSelect[v] = 1
1683	varName[v] = self.assgnVars[v]
1684	return self.expression
1685
1686	def GetVaried(self):
1687	'Returns the names of the free parameters that will be refined'
1688	return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
1689
1690	def GetVariedVarVal(self):
1691	'Returns the names and values of the free parameters that will be refined'
1692	return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
1693
1694	def UpdateVariedVars(self,varyList,values):
1695	'Updates values for the free parameters (after a refinement); only updates refined vars'
1696	for v in self.freeVars:
1697	if not self.freeVars[v][2]: continue
1698	if "::"+self.freeVars[v][0] not in varyList: continue
1699	indx = varyList.index("::"+self.freeVars[v][0])
1700	self.freeVars[v][1] = values[indx]
1701
1702	def GetIndependentVars(self):
1703	'Returns the names of the required independent parameters used in expression'
1704	return [self.assgnVars[v] for v in self.assgnVars]
1705
1706	def CheckVars(self):
1707	'''Check that the expression can be parsed, all functions are
1708	defined and that input loaded into the object is internally
1709	consistent. If not an Exception is raised.
1710
1711	:returns: a dict with references to packages needed to
1712	find functions referenced in the expression.
1713	'''
1714	ret = self.ParseExpression(self.expression)
1715	if not ret:
1716	raise Exception("Expression parse error")
1717	exprLblList,fxnpkgdict = ret
1718	# check each var used in expression is defined
1719	defined = self.assgnVars.keys() + self.freeVars.keys()
1720	notfound = []
1721	for var in exprLblList:
1722	if var not in defined:
1723	notfound.append(var)
1724	if notfound:
1725	msg = 'Not all variables defined'
1726	msg1 = 'The following variables were not defined: '
1727	msg2 = ''
1728	for var in notfound:
1729	if msg: msg += ', '
1730	msg += var
1731	self.lastError = (msg1,' '+msg2)
1732	raise Exception(msg)
1733	return fxnpkgdict
1734
1735	def ParseExpression(self,expr):
1736	'''Parse an expression and return a dict of called functions and
1737	the variables used in the expression. Returns None in case an error
1738	is encountered. If packages are referenced in functions, they are loaded
1739	and the functions are looked up into the modules global
1740	workspace.
1741
1742	Note that no changes are made to the object other than
1743	saving an error message, so that this can be used for testing prior
1744	to the save.
1745
1746	:returns: a list of used variables
1747	'''
1748	self.lastError = ('','')
1749	import ast
1750	def FindFunction(f):
1751	'''Find the object corresponding to function f
1752	:param str f: a function name such as 'numpy.exp'
1753	:returns: (pkgdict,pkgobj) where pkgdict contains a dict
1754	that defines the package location(s) and where pkgobj
1755	defines the object associated with the function.
1756	If the function is not found, pkgobj is None.
1757	'''
1758	df = f.split('.')
1759	pkgdict = {}
1760	# no listed package, try in current namespace
1761	if len(df) == 1:
1762	try:
1763	fxnobj = eval(f)
1764	return pkgdict,fxnobj
1765	except (AttributeError, NameError):
1766	return None,None
1767	else:
1768	try:
1769	fxnobj = eval(f)
1770	pkgdict[df[0]] = eval(df[0])
1771	return pkgdict,fxnobj
1772	except (AttributeError, NameError):
1773	pass
1774	# includes a package, lets try to load the packages
1775	pkgname = ''
1776	path = sys.path
1777	for pkg in f.split('.')[:-1]: # if needed, descend down the tree
1778	if pkgname:
1779	pkgname += '.' + pkg
1780	else:
1781	pkgname = pkg
1782	fp = None
1783	try:
1784	fp, fppath,desc = imp.find_module(pkg,path)
1785	pkgobj = imp.load_module(pkg,fp,fppath,desc)
1786	pkgdict[pkgname] = pkgobj
1787	path = [fppath]
1788	except Exception as msg:
1789	print('load of '+pkgname+' failed with error='+str(msg))
1790	return {},None
1791	finally:
1792	if fp: fp.close()
1793	try:
1794	#print 'before',pkgdict.keys()
1795	fxnobj = eval(f,globals(),pkgdict)
1796	#print 'after 1',pkgdict.keys()
1797	#fxnobj = eval(f,pkgdict)
1798	#print 'after 2',pkgdict.keys()
1799	return pkgdict,fxnobj
1800	except:
1801	continue
1802	return None # not found
1803	def ASTtransverse(node,fxn=False):
1804	'''Transverse a AST-parsed expresson, compiling a list of variables
1805	referenced in the expression. This routine is used recursively.
1806
1807	:returns: varlist,fxnlist where
1808	varlist is a list of referenced variable names and
1809	fxnlist is a list of used functions
1810	'''
1811	varlist = []
1812	fxnlist = []
1813	if isinstance(node, list):
1814	for b in node:
1815	v,f = ASTtransverse(b,fxn)
1816	varlist += v
1817	fxnlist += f
1818	elif isinstance(node, ast.AST):
1819	for a, b in ast.iter_fields(node):
1820	if isinstance(b, ast.AST):
1821	if a == 'func':
1822	fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
1823	continue
1824	v,f = ASTtransverse(b,fxn)
1825	varlist += v
1826	fxnlist += f
1827	elif isinstance(b, list):
1828	v,f = ASTtransverse(b,fxn)
1829	varlist += v
1830	fxnlist += f
1831	elif node.__class__.__name__ == "Name":
1832	varlist += [b]
1833	elif fxn and node.__class__.__name__ == "Attribute":
1834	varlist += [b]
1835	return varlist,fxnlist
1836	try:
1837	exprast = ast.parse(expr)
1838	except SyntaxError as err:
1839	s = ''
1840	import traceback
1841	for i in traceback.format_exc().splitlines()[-3:-1]:
1842	if s: s += "\n"
1843	s += str(i)
1844	self.lastError = ("Error parsing expression:",s)
1845	return
1846	# find the variables & functions
1847	v,f = ASTtransverse(exprast)
1848	varlist = sorted(list(set(v)))
1849	fxnlist = list(set(f))
1850	pkgdict = {}
1851	# check the functions are defined
1852	for fxn in fxnlist:
1853	fxndict,fxnobj = FindFunction(fxn)
1854	if not fxnobj:
1855	self.lastError = ("Error: Invalid function",fxn,
1856	"is not defined")
1857	return
1858	if not hasattr(fxnobj,'__call__'):
1859	self.lastError = ("Error: Not a function.",fxn,
1860	"cannot be called as a function")
1861	return
1862	pkgdict.update(fxndict)
1863	return varlist,pkgdict
1864
1865	def GetDepVar(self):
1866	'return the dependent variable, or None'
1867	return self.depVar
1868
1869	def SetDepVar(self,var):
1870	'Set the dependent variable, if used'
1871	self.depVar = var
1872	#==========================================================================
1873	class ExpressionCalcObj(object):
1874	'''An object used to evaluate an expression from a :class:`ExpressionObj`
1875	object.
1876
1877	:param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
1878	an expression string and mappings for the parameter labels in that object.
1879	'''
1880	def __init__(self,exprObj):
1881	self.eObj = exprObj
1882	'The expression and mappings; a :class:`ExpressionObj` object'
1883	self.compiledExpr = None
1884	'The expression as compiled byte-code'
1885	self.exprDict = {}
1886	'''dict that defines values for labels used in expression and packages
1887	referenced by functions
1888	'''
1889	self.lblLookup = {}
1890	'''Lookup table that specifies the expression label name that is
1891	tied to a particular GSAS-II parameters in the parmDict.
1892	'''
1893	self.fxnpkgdict = {}
1894	'''a dict with references to packages needed to
1895	find functions referenced in the expression.
1896	'''
1897	self.varLookup = {}
1898	'''Lookup table that specifies the GSAS-II variable(s)
1899	indexed by the expression label name. (Used for only for diagnostics
1900	not evaluation of expression.)
1901	'''
1902	# Patch: for old-style expressions with a (now removed step size)
1903	for v in self.eObj.assgnVars:
1904	if not isinstance(self.eObj.assgnVars[v], basestring):
1905	self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
1906
1907	def SetupCalc(self,parmDict):
1908	'''Do all preparations to use the expression for computation.
1909	Adds the free parameter values to the parameter dict (parmDict).
1910	'''
1911	self.fxnpkgdict = self.eObj.CheckVars()
1912	# all is OK, compile the expression
1913	self.compiledExpr = compile(self.eObj.expression,'','eval')
1914
1915	# look at first value in parmDict to determine its type
1916	parmsInList = True
1917	for key in parmDict:
1918	val = parmDict[key]
1919	if isinstance(val, basestring):
1920	parmsInList = False
1921	break
1922	try: # check if values are in lists
1923	val = parmDict[key][0]
1924	except (TypeError,IndexError):
1925	parmsInList = False
1926	break
1927
1928	# set up the dicts needed to speed computations
1929	self.exprDict = {}
1930	self.lblLookup = {}
1931	self.varLookup = {}
1932	for v in self.eObj.freeVars:
1933	varname = self.eObj.freeVars[v][0]
1934	varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
1935	self.lblLookup[varname] = v
1936	self.varLookup[v] = varname
1937	if parmsInList:
1938	parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
1939	else:
1940	parmDict[varname] = self.eObj.freeVars[v][1]
1941	self.exprDict[v] = self.eObj.freeVars[v][1]
1942	for v in self.eObj.assgnVars:
1943	varname = self.eObj.assgnVars[v]
1944	if '*' in varname:
1945	varlist = LookupWildCard(varname,parmDict.keys())
1946	if len(varlist) == 0:
1947	raise Exception,"No variables match "+str(v)
1948	for var in varlist:
1949	self.lblLookup[var] = v
1950	if parmsInList:
1951	self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
1952	else:
1953	self.exprDict[v] = np.array([parmDict[var] for var in varlist])
1954	self.varLookup[v] = [var for var in varlist]
1955	elif varname in parmDict:
1956	self.lblLookup[varname] = v
1957	self.varLookup[v] = varname
1958	if parmsInList:
1959	self.exprDict[v] = parmDict[varname][0]
1960	else:
1961	self.exprDict[v] = parmDict[varname]
1962	else:
1963	raise Exception,"No value for variable "+str(v)
1964	self.exprDict.update(self.fxnpkgdict)
1965
1966	def UpdateVars(self,varList,valList):
1967	'''Update the dict for the expression with a set of values
1968	:param list varList: a list of variable names
1969	:param list valList: a list of corresponding values
1970	'''
1971	for var,val in zip(varList,valList):
1972	self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
1973
1974	def UpdateDict(self,parmDict):
1975	'''Update the dict for the expression with values in a dict
1976	:param list parmDict: a dict of values some of which may be in use here
1977	'''
1978	for var in parmDict:
1979	if var in self.lblLookup:
1980	self.exprDict[self.lblLookup[var]] = parmDict[var]
1981
1982	def EvalExpression(self):
1983	'''Evaluate an expression. Note that the expression
1984	and mapping are taken from the :class:`ExpressionObj` expression object
1985	and the parameter values were specified in :meth:`SetupCalc`.
1986	:returns: a single value for the expression. If parameter
1987	values are arrays (for example, from wild-carded variable names),
1988	the sum of the resulting expression is returned.
1989
1990	For example, if the expression is ``'A*B'``,
1991	where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
1992
1993	[0.5, 1, 0.5]
1994
1995	then the result will be ``4.0``.
1996	'''
1997	if self.compiledExpr is None:
1998	raise Exception,"EvalExpression called before SetupCalc"
1999	val = eval(self.compiledExpr,globals(),self.exprDict)
2000	if not np.isscalar(val):
2001	val = np.sum(val)
2002	return val
2003
2004
2005	if __name__ == "__main__":
2006	# test equation evaluation
2007	def showEQ(calcobj):
2008	print 50*'='
2009	print calcobj.eObj.expression,'=',calcobj.EvalExpression()
2010	for v in sorted(calcobj.varLookup):
2011	print " ",v,'=',calcobj.exprDict[v],'=',calcobj.varLookup[v]
2012	# print ' Derivatives'
2013	# for v in calcobj.derivStep.keys():
2014	# print ' d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2015
2016	obj = ExpressionObj()
2017
2018	obj.expression = "A*np.exp(B)"
2019	obj.assgnVars = {'B': '0::Afrac:1'}
2020	obj.freeVars = {'A': [u'A', 0.5, True]}
2021	#obj.CheckVars()
2022	parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2023	calcobj = ExpressionCalcObj(obj)
2024	calcobj.SetupCalc(parmDict2)
2025	showEQ(calcobj)
2026
2027	obj.expression = "A*np.exp(B)"
2028	obj.assgnVars = {'B': '0::Afrac:*'}
2029	obj.freeVars = {'A': [u'Free Prm A', 0.5, True]}
2030	#obj.CheckVars()
2031	parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2032	calcobj = ExpressionCalcObj(obj)
2033	calcobj.SetupCalc(parmDict1)
2034	showEQ(calcobj)
2035
2036	calcobj.SetupCalc(parmDict2)
2037	showEQ(calcobj)

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