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source: trunk/GSASIIobj.py @ 1751

Last change on this file since 1751 was 1698, checked in by toby, 10 years ago
Allow powder data importers to set Controls values (such as FreePrm? labels); fix FreePrm? initialization
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1	# -- coding: utf-8 --
2	#GSASIIobj - data objects for GSAS-II
3	########### SVN repository information ###################
4	# $Date: 2015-03-12 22:09:00 +0000 (Thu, 12 Mar 2015) $
5	# $Author: vondreele $
6	# $Revision: 1698 $
7	# $URL: trunk/GSASIIobj.py $
8	# $Id: GSASIIobj.py 1698 2015-03-12 22:09:00Z 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: 1698 $")
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	'FreePrm1':'Sample humidity (%)',
855	'FreePrm2':'Sample voltage (V)',
856	'FreePrm3':'Applied load (MN)',
857	}
858	'''Values to be used as defaults for the initial contents of the ``Controls``
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	'Fzero' : 'Crenel function offset',
1301	'Fwid' : 'Crenel function width',
1302	'Tzero' : 'Sawtooth/ZigZag location',
1303	'([XYZ])slope': 'Sawtooth/ZigZag slope for \\1',
1304	'([XYZ])sin' : 'Sin position wave for \\1',
1305	'([XYZ])cos' : 'Cos position wave for \\1',
1306	'U([123][123])sin$' : 'Sin thermal wave for U\\1',
1307	'U([123][123])cos$' : 'Cos thermal wave for U\\1',
1308	'M([XYZ])sin$' : 'Sin mag. moment wave for \\1',
1309	'M([XYZ])cos$' : 'Cos mag. moment wave for \\1',
1310	# SASD vars (l:<var>;l = component)
1311	'Aspect ratio' : 'Particle aspect ratio',
1312	'Length' : 'Cylinder length',
1313	'Diameter' : 'Cylinder/disk diameter',
1314	'Thickness' : 'Disk thickness',
1315	'Dist' : 'Interparticle distance',
1316	'VolFr' : 'Dense scatterer volume fraction',
1317	'epis' : 'Sticky sphere epsilon',
1318	'Sticky' : 'Stickyness',
1319	'Depth' : 'Well depth',
1320	'Width' : 'Well width',
1321	'Volume' : 'Particle volume',
1322	'Radius' : 'Sphere/cylinder/disk radius',
1323	'Mean' : 'Particle mean radius',
1324	'StdDev' : 'Standard deviation in Mean',
1325	'G$': 'Guinier prefactor',
1326	'Rg$': 'Guinier radius of gyration',
1327	'B$': 'Porod prefactor',
1328	'P$': 'Porod power',
1329	'Cutoff': 'Porod cutoff',
1330	'PkInt': 'Bragg peak intensity',
1331	'PkPos': 'Bragg peak position',
1332	'PkSig': 'Bragg peak sigma',
1333	'PkGam': 'Bragg peak gamma',
1334	'e([12][12])' : 'strain tensor e\1', # strain vars e11, e22, e12
1335	'Dcalc': 'Calc. d-spacing',
1336	'Back$': 'background parameter',
1337	'pos$': 'peak position',
1338	'int$': 'peak intensity',
1339	}.items():
1340	VarDesc[key] = value
1341	reVarDesc[re.compile(key)] = value
1342
1343	def getDescr(name):
1344	'''Return a short description for a GSAS-II variable
1345
1346	:param str name: The descriptive part of the variable name without colons (:)
1347
1348	:returns: a short description or None if not found
1349	'''
1350
1351	CompileVarDesc() # compile the regular expressions, if needed
1352	for key in reVarDesc:
1353	m = key.match(name)
1354	if m:
1355	reVarDesc[key]
1356	return m.expand(reVarDesc[key])
1357	return None
1358
1359	def GenWildCard(varlist):
1360	'''Generate wildcard versions of G2 variables. These introduce '*'
1361	for a phase, histogram or atom number (but only for one of these
1362	fields) but only when there is more than one matching variable in the
1363	input variable list. So if the input is this::
1364
1365	varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1366
1367	then the output will be this::
1368
1369	wildList = ['::AUiso:0', '0::AUiso:']
1370
1371	:param list varlist: an input list of GSAS-II variable names
1372	(such as 0::AUiso:0)
1373
1374	:returns: wildList, the generated list of wild card variable names.
1375	'''
1376	wild = []
1377	for i in (0,1,3):
1378	currentL = varlist[:]
1379	while currentL:
1380	item1 = currentL.pop(0)
1381	i1splt = item1.split(':')
1382	if i >= len(i1splt): continue
1383	if i1splt[i]:
1384	nextL = []
1385	i1splt[i] = '[0-9]+'
1386	rexp = re.compile(':'.join(i1splt))
1387	matchlist = [item1]
1388	for nxtitem in currentL:
1389	if rexp.match(nxtitem):
1390	matchlist += [nxtitem]
1391	else:
1392	nextL.append(nxtitem)
1393	if len(matchlist) > 1:
1394	i1splt[i] = '*'
1395	wild.append(':'.join(i1splt))
1396	currentL = nextL
1397	return wild
1398
1399	def LookupWildCard(varname,varlist):
1400	'''returns a list of variable names from list varname
1401	that match wildcard name in varname
1402
1403	:param str varname: a G2 variable name containing a wildcard
1404	(such as \*::var)
1405	:param list varlist: the list of all variable names used in
1406	the current project
1407	:returns: a list of matching GSAS-II variables (may be empty)
1408	'''
1409	rexp = re.compile(varname.replace('*','[0-9]+'))
1410	return sorted([var for var in varlist if rexp.match(var)])
1411
1412
1413	def _lookup(dic,key):
1414	'''Lookup a key in a dictionary, where None returns an empty string
1415	but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1416	'''
1417	if key is None:
1418	return ""
1419	elif key == "*":
1420	return "*"
1421	else:
1422	return dic.get(key,'?')
1423
1424	class G2VarObj(object):
1425	'''Defines a GSAS-II variable either using the phase/atom/histogram
1426	unique Id numbers or using a character string that specifies
1427	variables by phase/atom/histogram number (which can change).
1428	Note that :func:`LoadID` should be used to (re)load the current Ids
1429	before creating or later using the G2VarObj object.
1430
1431	This can store rigid body variables, but does not translate the residue # and
1432	body # to/from random Ids
1433
1434	A :class:`G2VarObj` object can be created with a single parameter:
1435
1436	:param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1437	object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1438
1439	* p is the phase number (which may be left blank or may be '*' to indicate all phases);
1440	* h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1441	* a is the atom number (which may be left blank in which case the third colon is omitted).
1442	The atom number can be specified as '' if a phase number is specified (not as '').
1443	For rigid body variables, specify a will be a string of form "residue:body#"
1444
1445	Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1446	Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1447	and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1448	For a rigid body variables, AtomID is a string of form "residue:body#".
1449
1450	If four positional arguments are supplied, they are:
1451
1452	:param str/int phasenum: The number for the phase (or None or '*')
1453	:param str/int histnum: The number for the histogram (or None or '*')
1454	:param str varname: a single value can be used to create a :class:`G2VarObj`
1455	:param str/int atomnum: The number for the atom (or None or '*')
1456
1457	'''
1458	IDdict = {}
1459	IDdict['phases'] = {}
1460	IDdict['hists'] = {}
1461	IDdict['atoms'] = {}
1462	def __init__(self,*args):
1463	self.phase = None
1464	self.histogram = None
1465	self.name = ''
1466	self.atom = None
1467	if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1468	# single arg with 4 values
1469	self.phase,self.histogram,self.name,self.atom = args[0]
1470	elif len(args) == 1 and ':' in args[0]:
1471	#parse a string
1472	lst = args[0].split(':')
1473	if lst[0] == '*':
1474	self.phase = '*'
1475	if len(lst) > 3:
1476	self.atom = lst[3]
1477	self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1478	elif lst[1] == '*':
1479	self.histogram = '*'
1480	self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1481	else:
1482	self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1483	self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1484	if len(lst) == 4:
1485	if lst[3] == '*':
1486	self.atom = '*'
1487	else:
1488	self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1489	elif len(lst) == 5:
1490	self.atom = lst[3]+":"+lst[4]
1491	elif len(lst) == 3:
1492	pass
1493	else:
1494	raise Exception,"Too many colons in var name "+str(args[0])
1495	self.name = lst[2]
1496	elif len(args) == 4:
1497	if args[0] == '*':
1498	self.phase = '*'
1499	self.atom = args[3]
1500	else:
1501	self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1502	if args[3] == '*':
1503	self.atom = '*'
1504	elif args[0] is not None:
1505	self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1506	if args[1] == '*':
1507	self.histogram = '*'
1508	else:
1509	self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1510	self.name = args[2]
1511	else:
1512	raise Exception,"Incorrectly called GSAS-II parameter name"
1513
1514	#print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1515
1516	def __str__(self):
1517	return self.varname()
1518
1519	def varname(self):
1520	'''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1521	string (p:h:<var>:a) or (p:h:<var>)
1522
1523	:returns: the variable name as a str
1524	'''
1525	a = ""
1526	if self.phase == "*":
1527	ph = "*"
1528	if self.atom:
1529	a = ":" + str(self.atom)
1530	else:
1531	ph = _lookup(PhaseRanIdLookup,self.phase)
1532	if self.atom == '*':
1533	a = ':*'
1534	elif self.atom:
1535	if ":" in str(self.atom):
1536	a = ":" + str(self.atom)
1537	elif ph in AtomRanIdLookup:
1538	a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1539	else:
1540	a = ":?"
1541	if self.histogram == "*":
1542	hist = "*"
1543	else:
1544	hist = _lookup(HistRanIdLookup,self.histogram)
1545	s = (ph + ":" + hist + ":" + str(self.name)) + a
1546	return s
1547
1548	def __repr__(self):
1549	'''Return the detailed contents of the object
1550	'''
1551	s = "<"
1552	if self.phase == '*':
1553	s += "Phases: all; "
1554	if self.atom is not None:
1555	if ":" in str(self.atom):
1556	s += "Rigid body" + str(self.atom) + "; "
1557	else:
1558	s += "Atom #" + str(self.atom) + "; "
1559	elif self.phase is not None:
1560	ph = _lookup(PhaseRanIdLookup,self.phase)
1561	s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1562	if self.atom == '*':
1563	s += "Atoms: all; "
1564	elif ":" in self(self.atom):
1565	s += "Rigid body" + str(self.atom) + "; "
1566	elif self.atom is not None:
1567	s += "Atom rId=" + str(self.atom)
1568	if ph in AtomRanIdLookup:
1569	s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1570	else:
1571	s += " (#? -- not found!); "
1572	if self.histogram == '*':
1573	s += "Histograms: all; "
1574	elif self.histogram is not None:
1575	hist = _lookup(HistRanIdLookup,self.histogram)
1576	s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1577	s += 'Variable name="' + str(self.name) + '">'
1578	return s+" ("+self.varname()+")"
1579
1580	def __eq__(self, other):
1581	if type(other) is type(self):
1582	return (self.phase == other.phase and
1583	self.histogram == other.histogram and
1584	self.name == other.name and
1585	self.atom == other.atom)
1586	return False
1587
1588	def _show(self):
1589	'For testing, shows the current lookup table'
1590	print 'phases', self.IDdict['phases']
1591	print 'hists', self.IDdict['hists']
1592	print 'atomDict', self.IDdict['atoms']
1593
1594	#==========================================================================
1595	# shortcut routines
1596	exp = np.exp
1597	sind = sin = s = lambda x: np.sin(x*np.pi/180.)
1598	cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
1599	tand = tan = t = lambda x: np.tan(x*np.pi/180.)
1600	sqrt = sq = lambda x: np.sqrt(x)
1601	pi = lambda: np.pi
1602	class ExpressionObj(object):
1603	'''Defines an object with a user-defined expression, to be used for
1604	secondary fits or restraints. Object is created null, but is changed
1605	using :meth:`LoadExpression`. This contains only the minimum
1606	information that needs to be stored to save and load the expression
1607	and how it is mapped to GSAS-II variables.
1608	'''
1609	def __init__(self):
1610	self.expression = ''
1611	'The expression as a text string'
1612	self.assgnVars = {}
1613	'''A dict where keys are label names in the expression mapping to a GSAS-II
1614	variable. The value a G2 variable name.
1615	Note that the G2 variable name may contain a wild-card and correspond to
1616	multiple values.
1617	'''
1618	self.freeVars = {}
1619	'''A dict where keys are label names in the expression mapping to a free
1620	parameter. The value is a list with:
1621
1622	* a name assigned to the parameter
1623	* a value for to the parameter and
1624	* a flag to determine if the variable is refined.
1625	'''
1626	self.depVar = None
1627
1628	self.lastError = ('','')
1629	'''Shows last encountered error in processing expression
1630	(list of 1-3 str values)'''
1631
1632	def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
1633	'''Load the expression and associated settings into the object. Raises
1634	an exception if the expression is not parsed, if not all functions
1635	are defined or if not all needed parameter labels in the expression
1636	are defined.
1637
1638	This will not test if the variable referenced in these definitions
1639	are actually in the parameter dictionary. This is checked when the
1640	computation for the expression is done in :meth:`SetupCalc`.
1641
1642	:param str expr: the expression
1643	:param list exprVarLst: parameter labels found in the expression
1644	:param dict varSelect: this will be 0 for Free parameters
1645	and non-zero for expression labels linked to G2 variables.
1646	:param dict varName: Defines a name (str) associated with each free parameter
1647	:param dict varValue: Defines a value (float) associated with each free parameter
1648	:param dict varRefflag: Defines a refinement flag (bool)
1649	associated with each free parameter
1650	'''
1651	self.expression = expr
1652	self.compiledExpr = None
1653	self.freeVars = {}
1654	self.assgnVars = {}
1655	for v in exprVarLst:
1656	if varSelect[v] == 0:
1657	self.freeVars[v] = [
1658	varName.get(v),
1659	varValue.get(v),
1660	varRefflag.get(v),
1661	]
1662	else:
1663	self.assgnVars[v] = varName[v]
1664	self.CheckVars()
1665
1666	def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
1667	'''Load the expression and associated settings from the object into
1668	arrays used for editing.
1669
1670	:param list exprVarLst: parameter labels found in the expression
1671	:param dict varSelect: this will be 0 for Free parameters
1672	and non-zero for expression labels linked to G2 variables.
1673	:param dict varName: Defines a name (str) associated with each free parameter
1674	:param dict varValue: Defines a value (float) associated with each free parameter
1675	:param dict varRefflag: Defines a refinement flag (bool)
1676	associated with each free parameter
1677
1678	:returns: the expression as a str
1679	'''
1680	for v in self.freeVars:
1681	varSelect[v] = 0
1682	varName[v] = self.freeVars[v][0]
1683	varValue[v] = self.freeVars[v][1]
1684	varRefflag[v] = self.freeVars[v][2]
1685	for v in self.assgnVars:
1686	varSelect[v] = 1
1687	varName[v] = self.assgnVars[v]
1688	return self.expression
1689
1690	def GetVaried(self):
1691	'Returns the names of the free parameters that will be refined'
1692	return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
1693
1694	def GetVariedVarVal(self):
1695	'Returns the names and values of the free parameters that will be refined'
1696	return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
1697
1698	def UpdateVariedVars(self,varyList,values):
1699	'Updates values for the free parameters (after a refinement); only updates refined vars'
1700	for v in self.freeVars:
1701	if not self.freeVars[v][2]: continue
1702	if "::"+self.freeVars[v][0] not in varyList: continue
1703	indx = varyList.index("::"+self.freeVars[v][0])
1704	self.freeVars[v][1] = values[indx]
1705
1706	def GetIndependentVars(self):
1707	'Returns the names of the required independent parameters used in expression'
1708	return [self.assgnVars[v] for v in self.assgnVars]
1709
1710	def CheckVars(self):
1711	'''Check that the expression can be parsed, all functions are
1712	defined and that input loaded into the object is internally
1713	consistent. If not an Exception is raised.
1714
1715	:returns: a dict with references to packages needed to
1716	find functions referenced in the expression.
1717	'''
1718	ret = self.ParseExpression(self.expression)
1719	if not ret:
1720	raise Exception("Expression parse error")
1721	exprLblList,fxnpkgdict = ret
1722	# check each var used in expression is defined
1723	defined = self.assgnVars.keys() + self.freeVars.keys()
1724	notfound = []
1725	for var in exprLblList:
1726	if var not in defined:
1727	notfound.append(var)
1728	if notfound:
1729	msg = 'Not all variables defined'
1730	msg1 = 'The following variables were not defined: '
1731	msg2 = ''
1732	for var in notfound:
1733	if msg: msg += ', '
1734	msg += var
1735	self.lastError = (msg1,' '+msg2)
1736	raise Exception(msg)
1737	return fxnpkgdict
1738
1739	def ParseExpression(self,expr):
1740	'''Parse an expression and return a dict of called functions and
1741	the variables used in the expression. Returns None in case an error
1742	is encountered. If packages are referenced in functions, they are loaded
1743	and the functions are looked up into the modules global
1744	workspace.
1745
1746	Note that no changes are made to the object other than
1747	saving an error message, so that this can be used for testing prior
1748	to the save.
1749
1750	:returns: a list of used variables
1751	'''
1752	self.lastError = ('','')
1753	import ast
1754	def FindFunction(f):
1755	'''Find the object corresponding to function f
1756	:param str f: a function name such as 'numpy.exp'
1757	:returns: (pkgdict,pkgobj) where pkgdict contains a dict
1758	that defines the package location(s) and where pkgobj
1759	defines the object associated with the function.
1760	If the function is not found, pkgobj is None.
1761	'''
1762	df = f.split('.')
1763	pkgdict = {}
1764	# no listed package, try in current namespace
1765	if len(df) == 1:
1766	try:
1767	fxnobj = eval(f)
1768	return pkgdict,fxnobj
1769	except (AttributeError, NameError):
1770	return None,None
1771	else:
1772	try:
1773	fxnobj = eval(f)
1774	pkgdict[df[0]] = eval(df[0])
1775	return pkgdict,fxnobj
1776	except (AttributeError, NameError):
1777	pass
1778	# includes a package, lets try to load the packages
1779	pkgname = ''
1780	path = sys.path
1781	for pkg in f.split('.')[:-1]: # if needed, descend down the tree
1782	if pkgname:
1783	pkgname += '.' + pkg
1784	else:
1785	pkgname = pkg
1786	fp = None
1787	try:
1788	fp, fppath,desc = imp.find_module(pkg,path)
1789	pkgobj = imp.load_module(pkg,fp,fppath,desc)
1790	pkgdict[pkgname] = pkgobj
1791	path = [fppath]
1792	except Exception as msg:
1793	print('load of '+pkgname+' failed with error='+str(msg))
1794	return {},None
1795	finally:
1796	if fp: fp.close()
1797	try:
1798	#print 'before',pkgdict.keys()
1799	fxnobj = eval(f,globals(),pkgdict)
1800	#print 'after 1',pkgdict.keys()
1801	#fxnobj = eval(f,pkgdict)
1802	#print 'after 2',pkgdict.keys()
1803	return pkgdict,fxnobj
1804	except:
1805	continue
1806	return None # not found
1807	def ASTtransverse(node,fxn=False):
1808	'''Transverse a AST-parsed expresson, compiling a list of variables
1809	referenced in the expression. This routine is used recursively.
1810
1811	:returns: varlist,fxnlist where
1812	varlist is a list of referenced variable names and
1813	fxnlist is a list of used functions
1814	'''
1815	varlist = []
1816	fxnlist = []
1817	if isinstance(node, list):
1818	for b in node:
1819	v,f = ASTtransverse(b,fxn)
1820	varlist += v
1821	fxnlist += f
1822	elif isinstance(node, ast.AST):
1823	for a, b in ast.iter_fields(node):
1824	if isinstance(b, ast.AST):
1825	if a == 'func':
1826	fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
1827	continue
1828	v,f = ASTtransverse(b,fxn)
1829	varlist += v
1830	fxnlist += f
1831	elif isinstance(b, list):
1832	v,f = ASTtransverse(b,fxn)
1833	varlist += v
1834	fxnlist += f
1835	elif node.__class__.__name__ == "Name":
1836	varlist += [b]
1837	elif fxn and node.__class__.__name__ == "Attribute":
1838	varlist += [b]
1839	return varlist,fxnlist
1840	try:
1841	exprast = ast.parse(expr)
1842	except SyntaxError as err:
1843	s = ''
1844	import traceback
1845	for i in traceback.format_exc().splitlines()[-3:-1]:
1846	if s: s += "\n"
1847	s += str(i)
1848	self.lastError = ("Error parsing expression:",s)
1849	return
1850	# find the variables & functions
1851	v,f = ASTtransverse(exprast)
1852	varlist = sorted(list(set(v)))
1853	fxnlist = list(set(f))
1854	pkgdict = {}
1855	# check the functions are defined
1856	for fxn in fxnlist:
1857	fxndict,fxnobj = FindFunction(fxn)
1858	if not fxnobj:
1859	self.lastError = ("Error: Invalid function",fxn,
1860	"is not defined")
1861	return
1862	if not hasattr(fxnobj,'__call__'):
1863	self.lastError = ("Error: Not a function.",fxn,
1864	"cannot be called as a function")
1865	return
1866	pkgdict.update(fxndict)
1867	return varlist,pkgdict
1868
1869	def GetDepVar(self):
1870	'return the dependent variable, or None'
1871	return self.depVar
1872
1873	def SetDepVar(self,var):
1874	'Set the dependent variable, if used'
1875	self.depVar = var
1876	#==========================================================================
1877	class ExpressionCalcObj(object):
1878	'''An object used to evaluate an expression from a :class:`ExpressionObj`
1879	object.
1880
1881	:param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
1882	an expression string and mappings for the parameter labels in that object.
1883	'''
1884	def __init__(self,exprObj):
1885	self.eObj = exprObj
1886	'The expression and mappings; a :class:`ExpressionObj` object'
1887	self.compiledExpr = None
1888	'The expression as compiled byte-code'
1889	self.exprDict = {}
1890	'''dict that defines values for labels used in expression and packages
1891	referenced by functions
1892	'''
1893	self.lblLookup = {}
1894	'''Lookup table that specifies the expression label name that is
1895	tied to a particular GSAS-II parameters in the parmDict.
1896	'''
1897	self.fxnpkgdict = {}
1898	'''a dict with references to packages needed to
1899	find functions referenced in the expression.
1900	'''
1901	self.varLookup = {}
1902	'''Lookup table that specifies the GSAS-II variable(s)
1903	indexed by the expression label name. (Used for only for diagnostics
1904	not evaluation of expression.)
1905	'''
1906	# Patch: for old-style expressions with a (now removed step size)
1907	for v in self.eObj.assgnVars:
1908	if not isinstance(self.eObj.assgnVars[v], basestring):
1909	self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
1910
1911	def SetupCalc(self,parmDict):
1912	'''Do all preparations to use the expression for computation.
1913	Adds the free parameter values to the parameter dict (parmDict).
1914	'''
1915	self.fxnpkgdict = self.eObj.CheckVars()
1916	# all is OK, compile the expression
1917	self.compiledExpr = compile(self.eObj.expression,'','eval')
1918
1919	# look at first value in parmDict to determine its type
1920	parmsInList = True
1921	for key in parmDict:
1922	val = parmDict[key]
1923	if isinstance(val, basestring):
1924	parmsInList = False
1925	break
1926	try: # check if values are in lists
1927	val = parmDict[key][0]
1928	except (TypeError,IndexError):
1929	parmsInList = False
1930	break
1931
1932	# set up the dicts needed to speed computations
1933	self.exprDict = {}
1934	self.lblLookup = {}
1935	self.varLookup = {}
1936	for v in self.eObj.freeVars:
1937	varname = self.eObj.freeVars[v][0]
1938	varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
1939	self.lblLookup[varname] = v
1940	self.varLookup[v] = varname
1941	if parmsInList:
1942	parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
1943	else:
1944	parmDict[varname] = self.eObj.freeVars[v][1]
1945	self.exprDict[v] = self.eObj.freeVars[v][1]
1946	for v in self.eObj.assgnVars:
1947	varname = self.eObj.assgnVars[v]
1948	if '*' in varname:
1949	varlist = LookupWildCard(varname,parmDict.keys())
1950	if len(varlist) == 0:
1951	raise Exception,"No variables match "+str(v)
1952	for var in varlist:
1953	self.lblLookup[var] = v
1954	if parmsInList:
1955	self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
1956	else:
1957	self.exprDict[v] = np.array([parmDict[var] for var in varlist])
1958	self.varLookup[v] = [var for var in varlist]
1959	elif varname in parmDict:
1960	self.lblLookup[varname] = v
1961	self.varLookup[v] = varname
1962	if parmsInList:
1963	self.exprDict[v] = parmDict[varname][0]
1964	else:
1965	self.exprDict[v] = parmDict[varname]
1966	else:
1967	raise Exception,"No value for variable "+str(v)
1968	self.exprDict.update(self.fxnpkgdict)
1969
1970	def UpdateVars(self,varList,valList):
1971	'''Update the dict for the expression with a set of values
1972	:param list varList: a list of variable names
1973	:param list valList: a list of corresponding values
1974	'''
1975	for var,val in zip(varList,valList):
1976	self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
1977
1978	def UpdateDict(self,parmDict):
1979	'''Update the dict for the expression with values in a dict
1980	:param list parmDict: a dict of values some of which may be in use here
1981	'''
1982	for var in parmDict:
1983	if var in self.lblLookup:
1984	self.exprDict[self.lblLookup[var]] = parmDict[var]
1985
1986	def EvalExpression(self):
1987	'''Evaluate an expression. Note that the expression
1988	and mapping are taken from the :class:`ExpressionObj` expression object
1989	and the parameter values were specified in :meth:`SetupCalc`.
1990	:returns: a single value for the expression. If parameter
1991	values are arrays (for example, from wild-carded variable names),
1992	the sum of the resulting expression is returned.
1993
1994	For example, if the expression is ``'A*B'``,
1995	where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
1996
1997	[0.5, 1, 0.5]
1998
1999	then the result will be ``4.0``.
2000	'''
2001	if self.compiledExpr is None:
2002	raise Exception,"EvalExpression called before SetupCalc"
2003	val = eval(self.compiledExpr,globals(),self.exprDict)
2004	if not np.isscalar(val):
2005	val = np.sum(val)
2006	return val
2007
2008
2009	if __name__ == "__main__":
2010	# test equation evaluation
2011	def showEQ(calcobj):
2012	print 50*'='
2013	print calcobj.eObj.expression,'=',calcobj.EvalExpression()
2014	for v in sorted(calcobj.varLookup):
2015	print " ",v,'=',calcobj.exprDict[v],'=',calcobj.varLookup[v]
2016	# print ' Derivatives'
2017	# for v in calcobj.derivStep.keys():
2018	# print ' d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2019
2020	obj = ExpressionObj()
2021
2022	obj.expression = "A*np.exp(B)"
2023	obj.assgnVars = {'B': '0::Afrac:1'}
2024	obj.freeVars = {'A': [u'A', 0.5, True]}
2025	#obj.CheckVars()
2026	parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2027	calcobj = ExpressionCalcObj(obj)
2028	calcobj.SetupCalc(parmDict2)
2029	showEQ(calcobj)
2030
2031	obj.expression = "A*np.exp(B)"
2032	obj.assgnVars = {'B': '0::Afrac:*'}
2033	obj.freeVars = {'A': [u'Free Prm A', 0.5, True]}
2034	#obj.CheckVars()
2035	parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2036	calcobj = ExpressionCalcObj(obj)
2037	calcobj.SetupCalc(parmDict1)
2038	showEQ(calcobj)
2039
2040	calcobj.SetupCalc(parmDict2)
2041	showEQ(calcobj)

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