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GSASIIobj.rst

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1	GSASIIobj: Data objects & Docs
2	=================================================
3
4	Summary/Contents
5	----------------------------
6
7	This module defines and/or documents the data structures used in GSAS-II, as well
8	as provides misc. support routines.
9
10	.. contents:: Section Contents
11
12	.. index::
13	single: Parameter names
14	single: GSAS-II variable naming
15
16	.. _VarNames_table:
17
18	Variable names in GSAS-II
19	----------------------------
20
21	Parameter are named using the following pattern,
22	``p:h:<var>:n``, where ``<var>`` is a variable name, as shown in the following table. Also,
23	``p`` is the phase number, ``h`` is the histogram number,
24	and ``n`` is the atom parameter number
25	If a parameter does not depend on a histogram, phase or atom, ``h``, ``p`` and/or ``n`` will be omitted,
26	so ``p::<var>:n``, ``:h:<var>`` and ``p:h:<var>`` are all valid names.
27
28	.. include:: vars.rst
29
30	.. _Constraints_table:
31
32	.. index::
33	single: Constraints object description
34	single: Data object descriptions; Constraints
35
36	Constraints Tree Item
37	----------------------
38
39	Constraints are stored in a dict, separated into groups.
40	Note that parameter are named in the following pattern,
41	p:h:<var>:n, where p is the phase number, h is the histogram number
42	<var> is a variable name and n is the parameter number.
43	If a parameter does not depend on a histogram or phase or is unnumbered, that
44	number is omitted.
45	Note that the contents of each dict item is a List where each element in the
46	list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
47	The constraints in this form are converted in
48	:func:`GSASIImapvars.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
49
50	The keys in the Constraints dict are:
51
52	.. tabularcolumns:: \|l\|p{4.5in}\|
53
54	========== ====================================================
55	key explanation
56	========== ====================================================
57	Hist This specifies a list of constraints on
58	histogram-related parameters,
59	which will be of form :h:<var>:n.
60	HAP This specifies a list of constraints on parameters
61	that are defined for every histogram in each phase
62	and are of form p:h:<var>:n.
63	Phase This specifies a list of constraints on phase
64	parameters,
65	which will be of form p::<var>:n.
66	Global This specifies a list of constraints on parameters
67	that are not tied to a histogram or phase and
68	are of form ::<var>:n
69	========== ====================================================
70
71	.. _Constraint_definitions_table:
72
73	.. index::
74	single: Constraint definition object description
75	single: Data object descriptions; Constraint Definition
76
77	Each constraint is defined as an item in a list. Each constraint is of form::
78
79	[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
80
81	Where the variable pair list item containing two values [<mult>, <var>], where:
82
83	* <mult> is a multiplier for the constraint (float)
84	* <var> a :class:`G2VarObj` object. (Note that in very old .gpx files this might be a str with a variable name of form 'p:h:name[:at]')
85
86	Note that the last three items in the list play a special role:
87
88	* <fixedval> is the fixed value for a `constant equation` (``constype=c``)
89	constraint or is None. For a `New variable` (``constype=f``) constraint,
90	a variable name can be specified as a str (used for externally
91	generated constraints)
92	* <varyflag> is True or False for `New variable` (``constype=f``) constraints
93	or is None. This indicates if this variable should be refined.
94	* <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:
95
96	* 'e' defines a set of equivalent variables. Only the first variable is refined (if the
97	appropriate refine flag is set) and and all other equivalent variables in the list
98	are generated from that variable, using the appropriate multipliers.
99	* 'c' defines a constraint equation of form,
100	:math:`m_1 \times var_1 + m_2 \times var_2 + ... = c`
101	* 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
102	even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
103	constraint and the mult value is ignored.
104	This is of particular value when needing to hold one or more variables where a
105	single flag controls a set of variables such as, coordinates,
106	the reciprocal metric tensor or anisotropic displacement parameter.
107	* 'f' defines a new variable (function) according to relationship
108	:math:`newvar = m_1 \times var_1 + m_2 \times var_2 + ...`
109
110	.. _Covariance_table:
111
112	.. index::
113	single: Covariance description
114	single: Data object descriptions; Covariance
115
116	Covariance Tree Item
117	--------------------
118
119	The Covariance tree item has results from the last least-squares run. They
120	are stored in a dict with these keys:
121
122	.. tabularcolumns:: \|l\|l\|p{4in}\|
123
124	============= =============== ====================================================
125	key sub-key explanation
126	============= =============== ====================================================
127	newCellDict \ (dict) ith lattice parameters computed by
128	:func:`GSASIIstrMath.GetNewCellParms`
129	title \ (str) Name of gpx file(?)
130	variables \ (list) Values for all N refined variables
131	(list of float values, length N,
132	ordered to match varyList)
133	sig \ (list) Uncertainty values for all N refined variables
134	(list of float values, length N,
135	ordered to match varyList)
136	varyList \ (list of str values, length N) List of directly refined variables
137
138	newAtomDict \ (dict) atom position values computed in
139	:func:`GSASIIstrMath.ApplyXYZshifts`
140	Rvals \ (dict) R-factors, GOF, Marquardt value for last
141	refinement cycle
142	\ Nobs (int) Number of observed data points
143	\ Rwp (float) overall weighted profile R-factor (%)
144	\ chisq (float) :math:`\sum w*(I_{obs}-I_{calc})^2`
145	for all data.
146	Note: this is not the reduced :math:`\chi^2`.
147	\ lamMax (float) Marquardt value applied to Hessian diagonal
148	\ GOF (float) The goodness-of-fit, aka square root of
149	the reduced chi squared.
150	covMatrix \ (np.array) The (NxN) covVariance matrix
151	============= =============== ====================================================
152
153	.. _Phase_table:
154
155	.. index::
156	single: Phase object description
157	single: Data object descriptions; Phase
158
159	Phase Tree Items
160	----------------
161
162	Phase information is stored in the GSAS-II data tree as children of the
163	Phases item in a dict with keys:
164
165	.. tabularcolumns:: \|l\|l\|p{4in}\|
166
167	========== =============== =====================================================================================================
168	key sub-key explanation
169	========== =============== =====================================================================================================
170	General \ (dict) Overall information for the phase
171	\ 3Dproj (list of str) projections for 3D pole distribution plots
172	\ AngleRadii (list of floats) Default radius for each atom used to compute
173	interatomic angles
174	\ AtomMass (list of floats) Masses for atoms
175	\ AtomPtrs (list of int) four locations (cx,ct,cs & cu) to use to pull info
176	from the atom records
177	\ AtomTypes (llist of str) Atom types
178	\ BondRadii (list of floats) Default radius for each atom used to compute
179	interatomic distances
180	\ Cell Unit cell parameters & ref. flag
181	(list with 8 items. All but first item are float.)
182
183	0: cell refinement flag (True/False),
184
185	1-3: a, b, c, (:math:`\AA`)
186
187	4-6: alpha, beta & gamma, (degrees)
188
189	7: volume (:math:`\AA^3`)
190
191	\ Color (list of (r,b,g) triplets) Colors for atoms
192	\ Compare (dict) Polygon comparison parameters
193	\ Data plot type (str) data plot type ('Mustrain', 'Size' or
194	'Preferred orientation') for powder data
195	\ DisAglCtls (dDict) with distance/angle search controls,
196	which has keys 'Name', 'AtomTypes',
197	'BondRadii', 'AngleRadii' which are as above
198	except are possibly edited. Also contains
199	'Factors', which is a 2 element list with
200	a multiplier for bond and angle search range
201	[typically (0.85,0.85)].
202	\ F000X (float) x-ray F(000) intensity
203	\ F000N (float) neutron F(000) intensity
204	\ Flip (dict) Charge flip controls
205	\ HydIds (dict) geometrically generated hydrogen atoms
206	\ Isotope (dict) Isotopes for each atom type
207	\ Isotopes (dict) Scattering lengths for each isotope
208	combination for each element in phase
209	\ MCSA controls (dict) Monte Carlo-Simulated Annealing controls
210	\ Map (dict) Map parameters
211	\ Mass (float) Mass of unit cell contents in g/mol
212	\ Modulated (bool) True if phase modulated
213	\ Mydir (str) Directory of current .gpx file
214	\ Name (str) Phase name
215	\ NoAtoms (dict) Number of atoms per unit cell of each type
216	\ POhkl (list) March-Dollase preferred orientation direction
217	\ Pawley dmin (float) maximum Q (as d-space) to use for Pawley extraction
218	\ Pawley dmax (float) minimum Q (as d-space) to use for Pawley extraction
219	\ Pawley neg wt (float) Restraint value for negative Pawley intensities
220	\ SGData (object) Space group details as a
221	:ref:`space group (SGData) <SGData_table>`
222	object, as defined in :func:`GSASIIspc.SpcGroup`.
223	\ SH Texture (dict) Spherical harmonic preferred orientation parameters
224	\ Super (int) dimension of super group (0,1 only)
225	\ Type (str) phase type (e.g. 'nuclear')
226	\ Z (dict) Atomic numbers for each atom type
227	\ doDysnomia (bool) flag for max ent map modification via Dysnomia
228	\ doPawley (bool) Flag for Pawley intensity extraction
229	\ vdWRadii (dict) Van der Waals radii for each atom type
230	ranId \ (int) unique random number Id for phase
231	pId \ (int) Phase Id number for current project.
232	Atoms \ (list of lists) Atoms in phase as a list of lists. The outer list
233	is for each atom, the inner list contains varying
234	items depending on the type of phase, see
235	the :ref:`Atom Records <Atoms_table>` description.
236	Drawing \ (dict) Display parameters
237	\ Atoms (list of lists) with an entry for each atom that is drawn
238	\ Plane (list) Controls for contour density plane display
239	\ Quaternion (4 element np.array) Viewing quaternion
240	\ Zclip (float) clipping distance in :math:`\AA`
241	\ Zstep (float) Step to de/increase Z-clip
242	\ atomPtrs (list) positions of x, type, site sym, ADP flag in Draw Atoms
243	\ backColor (list) background for plot as and R,G,B triplet
244	(default = [0, 0, 0], black).
245	\ ballScale (float) Radius of spheres in ball-and-stick display
246	\ bondList (dict) Bonds
247	\ bondRadius (float) Radius of binds in :math:`\AA`
248	\ cameraPos (float) Viewing position in :math:`\AA` for plot
249	\ contourLevel (float) map contour level in :math:`e/\AA^3`
250	\ contourMax (float) map contour maximum
251	\ depthFog (bool) True if use depthFog on plot - set currently as False
252	\ ellipseProb (float) Probability limit for display of thermal
253	ellipsoids in % .
254	\ magMult (float) multiplier for magnetic moment arrows
255	\ mapSize (float) x & y dimensions of contourmap (fixed internally)
256	\ modelView (4,4 array) from openGL drawing transofmation matrix
257	\ oldxy (list with two floats) previous view point
258	\ radiusFactor (float) Distance ratio for searching for bonds. Bonds
259	are located that are within r(Ra+Rb) and (Ra+Rb)/r
260	where Ra and Rb are the atomic radii.
261	\ selectedAtoms (list of int values) List of selected atoms
262	\ showABC (bool) Flag to show view point triplet. True=show.
263	\ showHydrogen (bool) Flag to control plotting of H atoms.
264	\ showRigidBodies (bool) Flag to highlight rigid body placement
265	\ showSlice (bool) flag to show contour map
266	\ sizeH (float) Size ratio for H atoms
267	\ unitCellBox (bool) Flag to control display of the unit cell.
268	\ vdwScale (float) Multiplier of van der Waals radius for display of vdW spheres.
269	\ viewDir (np.array with three floats) cartesian viewing direction
270	\ viewPoint (list of lists) First item in list is [x,y,z]
271	in fractional coordinates for the center of
272	the plot. Second item list of previous & current
273	atom number viewed (may be [0,0])
274	ISODISTORT \ (dict) contains controls for running ISODISTORT and results from it
275	\ ISOmethod (int) ISODISTORT method (currently 1 or 4; 2 & 3 not implemented in GSAS-II)
276	\ ParentCIF (str) parent cif file name for ISODISTORT method 4
277	\ ChildCIF (str) child cif file name for ISODISTORT method 4
278	\ SGselect (dict) selection list for lattice types in radio result from ISODISTORT method 1
279	\ selection (int) chosen selection from radio
280	\ radio (list) results from ISODISTORT method 1
281	\ ChildMatrix (3x3 array) transformation matrix for method 3 (not currently used)
282	\ ChildSprGp (str) child space group for method 3 (not currently used)
283	\ ChildCell (str) cell ordering for nonstandard orthorhombic ChildSprGrp in method 3 (not currently used)
284	\ G2ModeList (list) ISODISTORT mode names
285	\ modeDispl (list) distortion mode values; refinable parameters
286	\ ISOmodeDispl (list) distortion mode values as determined in method 4 by ISODISTORT
287	\ NormList (list) ISODISTORT normalization values; to convert mode value to fractional coordinate dsplacement
288	\ G2parentCoords (list) full set of parent structure coordinates transformed to child structure; starting basis for mode displacements
289	\ G2VarList (list)
290	\ IsoVarList (list)
291	\ G2coordOffset (list) only adjustible set of parent structure coordinates
292	\ G2OccVarList (list)
293	\ Var2ModeMatrix (array) atom variable to distortion mode transformation
294	\ Mode2VarMatrix (array) distortion mode to atom variable transformation
295	\ rundata (dict) saved input information for use by ISODISTORT method 1
296
297	RBModels \ Rigid body assignments (note Rigid body definitions
298	are stored in their own main top-level tree entry.)
299	RMC \ (dict) RMCProfile, PDFfit & fullrmc controls
300	Pawley ref \ (list) Pawley reflections
301	Histograms \ (dict of dicts) The key for the outer dict is
302	the histograms tied to this phase. The inner
303	dict contains the combined phase/histogram
304	parameters for items such as scale factors,
305	size and strain parameters. The following are the
306	keys to the inner dict. (dict)
307	\ Babinet (dict) For protein crystallography. Dictionary with two
308	entries, 'BabA', 'BabU'
309	\ Extinction (list of float, bool) Extinction parameter
310	\ Flack (list of [float, bool]) Flack parameter & refine flag
311	\ HStrain (list of two lists) Hydrostatic strain. The first is
312	a list of the HStrain parameters (1, 2, 3, 4, or 6
313	depending on unit cell), the second is a list of boolean
314	refinement parameters (same length)
315	\ Histogram (str) The name of the associated histogram
316	\ Layer Disp (list of [float, bool]) Layer displacement in beam direction & refine flag
317	\ LeBail (bool) Flag for LeBail extraction
318	\ Mustrain (list) Microstrain parameters, in order:
319
320	0. Type, one of u'isotropic', u'uniaxial', u'generalized'
321	1. Isotropic/uniaxial parameters - list of 3 floats
322	2. Refinement flags - list of 3 bools
323	3. Microstrain axis - list of 3 ints, [h, k, l]
324	4. Generalized mustrain parameters - list of 2-6 floats, depending on space group
325	5. Generalized refinement flags - list of bools, corresponding to the parameters of (4)
326	\ Pref.Ori. (list) Preferred Orientation. List of eight parameters.
327	Items marked SH are only used for Spherical Harmonics.
328
329	0. (str) Type, 'MD' for March-Dollase or 'SH' for Spherical Harmonics
330	1. (float) Value
331	2. (bool) Refinement flag
332	3. (list) Preferred direction, list of ints, [h, k, l]
333	4. (int) SH - number of terms
334	5. (dict) SH -
335	6. (list) SH
336	7. (float) SH
337	\ Scale (list of [float, bool]) Phase fraction & refine flag
338	\ Size List of crystallite size parameters, in order:
339
340	0. (str) Type, one of u'isotropic', u'uniaxial', u'ellipsoidal'
341	1. (list) Isotropic/uniaxial parameters - list of 3 floats
342	2. (list) Refinement flags - list of 3 bools
343	3. (list) Size axis - list of 3 ints, [h, k, l]
344	4. (list) Ellipsoidal size parameters - list of 6 floats
345	5. (list) Ellipsoidal refinement flags - list of bools, corresponding to the parameters of (4)
346	\ Use (bool) True if this histogram is to be used in refinement
347	MCSA \ (dict) Monte-Carlo simulated annealing parameters
348	========== =============== =====================================================================================================
349
350	.. _RBData_table:
351
352	.. index::
353	single: Rigid Body Data description
354	single: Data object descriptions; Rigid Body Data
355
356	Rigid Body Objects
357	------------------
358
359	Rigid body descriptions are available for two types of rigid bodies: 'Vector'
360	and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
361	with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
362	with defined refinable torsion angles.
363
364	.. tabularcolumns:: \|l\|l\|p{4in}\|
365
366	========== =============== ====================================================
367	key sub-key explanation
368	========== =============== ====================================================
369	Vector RBId (dict of dict) vector rigid bodies
370	\ AtInfo (dict) Drad, Color: atom drawing radius & color for each atom type
371	\ RBname (str) Name assigned by user to rigid body
372	\ VectMag (list) vector magnitudes in :math:`\AA`
373	\ rbXYZ (list of 3 float Cartesian coordinates for Vector rigid body )
374	\ rbRef (list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin
375	definition, use center of atoms flag
376	\ VectRef (list of bool refinement flags for VectMag values )
377	\ rbTypes (list of str) Atom types for each atom in rigid body
378	\ rbVect (list of lists) Cartesian vectors for each translation used to build rigid body
379	\ useCount (int) Number of times rigid body is used in any structure
380	Residue RBId (dict of dict) residue rigid bodies
381	\ AtInfo (dict) Drad, Color: atom drawing radius & color for each atom type
382	\ RBname (str) Name assigned by user to rigid body
383	\ rbXYZ (list of 3 float) Cartesian coordinates for Residue rigid body
384	\ rbTypes (list of str) Atom types for each atom in rigid body
385	\ atNames (list of str) Names of each atom in rigid body (e.g. C1,N2...)
386	\ rbRef (list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin
387	definition, use center of atoms flag
388	\ rbSeq (list) Orig,Piv,angle,Riding : definition of internal rigid body
389	torsion; origin atom (int), pivot atom (int), torsion angle (float),
390	riding atoms (list of int)
391	\ SelSeq (int,int) used by SeqSizer to identify objects
392	\ useCount (int)Number of times rigid body is used in any structure
393	RBIds \ (dict) unique Ids generated upon creation of each rigid body
394	\ Vector (list) Ids for each Vector rigid body
395	\ Residue (list) Ids for each Residue rigid body
396	========== =============== ====================================================
397
398	.. _SGData_table:
399
400	.. index::
401	single: Space Group Data description
402	single: Data object descriptions; Space Group Data
403
404	Space Group Objects
405	-------------------
406
407	Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
408	and the information is placed in a SGdata object
409	which is a dict with these keys. Magnetic ones are marked "mag"
410
411	.. tabularcolumns:: \|l\|p{4.5in}\|
412
413	========== ========================================================================================
414	key explanation
415	========== ========================================================================================
416	BNSlattsym mag - (str) BNS magnetic space group symbol and centering vector
417	GenFlg mag - (list) symmetry generators indices
418	GenSym mag - (list) names for each generator
419	MagMom mag - (list) "time reversals" for each magnetic operator
420	MagPtGp mag - (str) Magnetic point group symbol
421	MagSpGrp mag - (str) Magnetic space group symbol
422	OprNames mag - (list) names for each space group operation
423	SGCen (np.array) Symmetry cell centering vectors. A (n,3) np.array
424	of centers. Will always have at least one row: ``np.array([[0, 0, 0]])``
425	SGFixed (bool) Only True if phase mported from a magnetic cif file
426	then the space group can not be changed by the user because
427	operator set from cif may be nonstandard
428	SGGen (list) generators
429	SGGray (bool) True if space group is a gray group (incommensurate magnetic structures)
430	SGInv (bool) True if centrosymmetric, False if not
431	SGLatt (str)Lattice centering type. Will be one of
432	P, A, B, C, I, F, R
433	SGLaue (str) one of the following 14 Laue classes:
434	-1, 2/m, mmm, 4/m, 4/mmm, 3R,
435	3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m
436	SGOps (list) symmetry operations as a list of form
437	``[[M1,T1], [M2,T2],...]``
438	where :math:`M_n` is a 3x3 np.array
439	and :math:`T_n` is a length 3 np.array.
440	Atom coordinates are transformed where the
441	Asymmetric unit coordinates [X is (x,y,z)]
442	are transformed using
443	:math:`X^\prime = M_n*X+T_n`
444	SGPolax (str) Axes for space group polarity. Will be one of
445	'', 'x', 'y', 'x y', 'z', 'x z', 'y z',
446	'xyz'. In the case where axes are arbitrary
447	'111' is used (P 1, and ?).
448	SGPtGrp (str) Point group of the space group
449	SGUniq unique axis if monoclinic. Will be
450	a, b, or c for monoclinic space groups.
451	Will be blank for non-monoclinic.
452	SGSpin mag - (list) of spin flip operatiors (+1 or -1) for the space group operations
453	SGSys (str) symmetry unit cell: type one of
454	'triclinic', 'monoclinic', 'orthorhombic',
455	'tetragonal', 'rhombohedral', 'trigonal',
456	'hexagonal', 'cubic'
457	SSGK1 (list) Superspace multipliers
458	SpGrp (str) space group symbol
459	SpnFlp mag - (list) Magnetic spin flips for every magnetic space group operator
460	========== ========================================================================================
461
462	.. _SSGData_table:
463
464	.. index::
465	single: Superspace Group Data description
466	single: Data object descriptions; Superspace Group Data
467
468	Superspace groups [3+1] are interpreted by :func:`GSASIIspc.SSpcGroup`
469	and the information is placed in a SSGdata object
470	which is a dict with these keys:
471
472	.. tabularcolumns:: \|l\|p{4.5in}\|
473
474	========== ====================================================
475	key explanation
476	========== ====================================================
477	SSGCen (list) 4D cell centering vectors [0,0,0,0] at least
478	SSGK1 (list) Superspace multipliers
479	SSGOps (list) 4D symmetry operations as [M,T] so that M*x+T = x'
480	SSpGrp (str) superspace group symbol extension to space group
481	symbol, accidental spaces removed
482	modQ (list) modulation/propagation vector
483	modSymb (list of str) Modulation symbols
484	========== ====================================================
485
486
487	Phase Information
488	--------------------
489
490	.. index::
491	single: Phase information record description
492
493	Phase information is placed in one of the following keys:
494
495	.. tabularcolumns:: \|l\|p{4.5in}\|
496
497	========== ==============================================================
498	key explanation
499	========== ==============================================================
500	General Overall information about a phase
501	Histograms Information about each histogram linked to the
502	current phase as well as parameters that
503	are defined for each histogram and phase
504	(such as sample peak widths and preferred
505	orientation parameters.
506	Atoms Contains a list of atoms, as described in the
507	:ref:`Atom Records <Atoms_table>` description.
508	Drawing Parameters that determine how the phase is
509	displayed, including a list of atoms to be
510	included, as described in the
511	:ref:`Drawing Atom Records <Drawing_atoms_table>`
512	description
513	MCSA Monte-Carlo simulated annealing parameters
514	pId The index of each phase in the project, numbered
515	starting at 0
516	ranId An int value with a unique value for each phase
517	RBModels A list of dicts with parameters for each
518	rigid body inserted into the current phase,
519	as defined in the
520	:ref:`Rigid Body Insertions <Rigid_Body_Insertions>`.
521	Note that the rigid bodies are defined as
522	:ref:`Rigid Body Objects <RBData_table>`
523	RMC PDF modeling parameters
524	Pawley ref Pawley refinement parameters
525
526	========== ==============================================================
527
528	.. _Atoms_table:
529
530	.. index::
531	single: Atoms record description
532	single: Data object descriptions; Atoms record
533
534	--------------------
535	Atom Records
536	--------------------
537
538	If ``phasedict`` points to the phase information in the data tree, then
539	atoms are contained in a list of atom records (list) in
540	``phasedict['Atoms']``. Also needed to read atom information
541	are four pointers, ``cx,ct,cs,cia = phasedict['General']['AtomPtrs']``,
542	which define locations in the atom record, as shown below. Items shown are
543	always present; additional ones for macromolecular phases are marked 'mm',
544	and those for magnetic structures are marked 'mg'
545
546	.. tabularcolumns:: \|l\|p{4.5in}\|
547
548	============== ====================================================
549	location explanation
550	============== ====================================================
551	ct-4 mm - (str) residue number
552	ct-3 mm - (str) residue name (e.g. ALA)
553	ct-2 mm - (str) chain label
554	ct-1 (str) atom label
555	ct (str) atom type
556	ct+1 (str) refinement flags; combination of 'F', 'X', 'U', 'M'
557	cx,cx+1,cx+2 (3 floats) the x,y and z coordinates
558	cx+3 (float) site occupancy
559	cx+4,cx+5,cx+6 mg - (list) atom magnetic moment along a,b,c in Bohr magnetons
560	cs (str) site symmetry
561	cs+1 (int) site multiplicity
562	cia (str) ADP flag: Isotropic ('I') or Anisotropic ('A')
563	cia+1 (float) Uiso
564	cia+2...cia+7 (6 floats) U11, U22, U33, U12, U13, U23
565	atom[cia+8] (int) unique atom identifier
566
567	============== ====================================================
568
569	.. _Drawing_atoms_table:
570
571	.. index::
572	single: Drawing atoms record description
573	single: Data object descriptions; Drawing atoms record
574
575	----------------------------
576	Drawing Atom Records
577	----------------------------
578
579	If ``phasedict`` points to the phase information in the data tree, then
580	drawing atoms are contained in a list of drawing atom records (list) in
581	``phasedict['Drawing']['Atoms']``. Also needed to read atom information
582	are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
583	which define locations in the atom record, as shown below. Items shown are
584	always present; additional ones for macromolecular phases are marked 'mm',
585	and those for magnetic structures are marked 'mg'
586
587	.. tabularcolumns:: \|l\|p{4.5in}\|
588
589	============== ===================================================================================
590	location explanation
591	============== ===================================================================================
592	ct-4 mm - (str) residue number
593	ct-3 mm - (str) residue name (e.g. ALA)
594	ct-2 mm - (str) chain label
595	ct-1 (str) atom label
596	ct (str) atom type
597	cx,cx+1,cx+2 (3 floats) the x,y and z coordinates
598	cx+3,cx+4,cx+5 mg - (3 floats) atom magnetic moment along a,b,c in Bohr magnetons
599	cs-1 (str) Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1')
600	cs (str) atom drawing style; e.g. 'balls & sticks'
601	cs+1 (str) atom label style (e.g. 'name')
602	cs+2 (int) atom color (RBG triplet)
603	cs+3 (str) ADP flag: Isotropic ('I') or Anisotropic ('A')
604	cs+4 (float) Uiso
605	cs+5...cs+11 (6 floats) U11, U22, U33, U12, U13, U23
606	ci (int) unique atom identifier; matches source atom Id in Atom Records
607	============== ===================================================================================
608
609	.. _Rigid_Body_Insertions:
610
611	----------------------------
612	Rigid Body Insertions
613	----------------------------
614
615	If ``phasedict`` points to the phase information in the data tree, then
616	rigid body information is contained in list(s) in
617	``phasedict['RBModels']['Residue']`` and/or ``phasedict['RBModels']['Vector']``
618	for each rigid body inserted into the current phase.
619
620	.. tabularcolumns:: \|l\|p{4.5in}\|
621
622	============== ===================================================================================
623	key explanation
624	============== ===================================================================================
625	fixOrig Should the origin be fixed (when editing, not the refinement flag)
626	Ids Ids for assignment of atoms in the rigid body
627	numChain Chain number for macromolecular fits
628	Orient Orientation of the RB as a quaternion and a refinement flag (' ', 'A' or 'AV')
629	OrientVec Orientation of the RB expressed as a vector and azimuthal rotation angle
630	Orig Origin of the RB in fractional coordinates and refinement flag (bool)
631	RBId References the unique ID of a rigid body in the
632	:ref:`Rigid Body Objects <RBData_table>`
633	RBname The name for the rigid body (str)
634	AtomFrac The atom fractions for the rigid body
635	ThermalMotion The thermal motion description for the rigid body, which includes a choice for
636	the model and can include TLS parameters or an overall Uiso value.
637	Torsions Defines the torsion angle and refinement flag for each torsion defined in
638	the :ref:`Rigid Body Object <RBData_table>`
639	============== ===================================================================================
640
641	.. _Powder_table:
642
643	.. index::
644	single: Powder data object description
645	single: Data object descriptions; Powder Data
646
647	Powder Diffraction Tree Items
648	-----------------------------
649
650	Every powder diffraction histogram is stored in the GSAS-II data tree
651	with a top-level entry named beginning with the string "PWDR ". The
652	diffraction data for that information are directly associated with
653	that tree item and there are a series of children to that item. The
654	routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
655	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
656	load this information into a dictionary where the child tree name is
657	used as a key, and the information in the main entry is assigned
658	a key of ``Data``, as outlined below.
659
660	.. tabularcolumns:: \|p{1in}\|p{1in}\|p{4in}\|
661
662	====================== =============== ===========================================================
663	key sub-key explanation
664	====================== =============== ===========================================================
665	Comments \ (list of str) Text strings extracted from the original powder
666	data header. These cannot be changed by the user;
667	it may be empty.
668	Limits \ (list) two two element lists, as [[Ld,Hd],[L,H]]
669	where L and Ld are the current and default lowest
670	two-theta value to be used and
671	where H and Hd are the current and default highest
672	two-theta value to be used.
673	Reflection Lists \ (dict of dicts) with an entry for each phase in the
674	histogram. The contents of each dict item
675	is a dict containing reflections, as described in
676	the :ref:`Powder Reflections <PowderRefl_table>`
677	description.
678	Instrument Parameters \ (dict) The instrument parameters uses different dicts
679	for the constant wavelength (CW) and time-of-flight (TOF)
680	cases. See below for the descriptions of each.
681	wtFactor \ (float) A weighting factor to increase or decrease
682	the leverage of data in the histogram .
683	A value of 1.0 weights the data with their
684	standard uncertainties and a larger value
685	increases the weighting of the data (equivalent
686	to decreasing the uncertainties).
687	Sample Parameters \ (dict) Parameters that describe how
688	the data were collected, as listed
689	below. Refinable parameters are a list containing
690	a float and a bool, where the second value
691	specifies if the value is refined, otherwise
692	the value is a float unless otherwise noted.
693	\ Scale The histogram scale factor (refinable)
694	\ Absorption The sample absorption coefficient as
695	:math:`\mu r` where r is the radius
696	(refinable). Only valid for Debye-Scherrer geometry.
697	\ SurfaceRoughA Surface roughness parameter A as defined by
698	Surotti, J. Appl. Cryst, 5, 325-331, 1972.
699	(refinable - only valid for Bragg-Brentano geometry)
700	\ SurfaceRoughB Surface roughness parameter B (refinable -
701	only valid for Bragg-Brentano geometry)
702	\ DisplaceX, Sample displacement from goniometer center
703	DisplaceY where Y is along the beam direction and
704	X is perpendicular. Units are :math:`\mu m`
705	(refinable).
706	\ Phi, Chi, Goniometer sample setting angles, in degrees.
707	Omega
708	\ Gonio. radius Radius of the diffractometer in mm
709	\ InstrName (str) A name for the instrument, used in preparing
710	a CIF .
711	\ Force, Variables that describe how the measurement
712	Temperature, was performed. Not used directly in
713	Humidity, any computations.
714	Pressure,
715	Voltage
716	\ ranId (int) The random-number Id for the histogram
717	(same value as where top-level key is ranId)
718	\ Type (str) Type of diffraction data, may be 'Debye-Scherrer'
719	or 'Bragg-Brentano' .
720	hId \ (int) The number assigned to the histogram when
721	the project is loaded or edited (can change)
722	ranId \ (int) A random number id for the histogram
723	that does not change
724	Background \ (list) The background is stored as a list with where
725	the first item in the list is list and the second
726	item is a dict. The list contains the background
727	function and its coefficients; the dict contains
728	Debye diffuse terms and background peaks.
729	(TODO: this needs to be expanded.)
730	Data \ (list) The data consist of a list of 6 np.arrays
731	containing in order:
732
733	0. the x-postions (two-theta in degrees),
734	1. the intensity values (Yobs),
735	2. the weights for each Yobs value
736	3. the computed intensity values (Ycalc)
737	4. the background values
738	5. Yobs-Ycalc
739	====================== =============== ===========================================================
740
741	.. _CWPowder_table:
742
743	.. index::
744	single: Powder data CW Instrument Parameters
745
746	-----------------------------
747	CW Instrument Parameters
748	-----------------------------
749
750	Instrument Parameters are placed in a list of two dicts,
751	where the keys in the first dict are listed below. Note that the dict contents are different for
752	constant wavelength (CW) vs. time-of-flight (TOF) histograms.
753	The value for each item is a list containing three values: the initial value, the current value
754	and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that
755	cannot be refined. The first and second values are floats unless otherwise noted.
756	Items not refined are noted as [*]
757
758	.. tabularcolumns:: \|l\|p{1in}\|p{4in}\|
759
760	======================== =============== ===========================================================
761	key sub-key explanation
762	======================== =============== ===========================================================
763	Instrument Parameters[0] Type [*] (str) Histogram type:
764	* 'PXC' for constant wavelength x-ray
765	* 'PNC' for constant wavelength neutron
766	\ Bank [*] (int) Data set number in a multidata file (usually 1)
767	\ Lam (float) Specifies a wavelength in :math:`\AA`
768	\ Lam1 [*] (float) Specifies the primary wavelength in
769	:math:`\AA`, used in place of Lam
770	when an :math:`\alpha_1, \alpha_2`
771	source is used.
772	\ Lam2 [*] (float) Specifies the secondary wavelength in
773	:math:`\AA`, used with Lam1
774	\ I(L2)/I(L1) (float) Ratio of Lam2 to Lam1, used with Lam1
775	\ Zero (float) Two-theta zero correction in degrees
776	\ Azimuth [*] (float) Azimuthal setting angle for data recorded with differing setting angles
777	\ U, V, W (float) Cagliotti profile coefficients
778	for Gaussian instrumental broadening, where the
779	FWHM goes as
780	:math:`U \tan^2\theta + V \tan\theta + W`
781	\ X, Y, Z (float) Cauchy (Lorentzian) instrumental broadening coefficients
782	\ SH/L (float) Variant of the Finger-Cox-Jephcoat asymmetric
783	peak broadening ratio. Note that this is the
784	sum of S/L and H/L where S is
785	sample height, H is the slit height and
786	L is the goniometer diameter.
787	\ Polariz. (float) Polarization coefficient.
788	Instrument Parameters[1] (empty dict)
789	======================== =============== ===========================================================
790
791	.. _TOFPowder_table:
792
793	.. index::
794	single: Powder data TOF Instrument Parameters
795
796	-----------------------------
797	TOF Instrument Parameters
798	-----------------------------
799
800	Instrument Parameters are also placed in a list of two dicts,
801	where the keys in each dict listed below, but here for
802	time-of-flight (TOF) histograms.
803	The value for each item is a list containing three values: the initial value, the current value
804	and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that
805	cannot be refined. The first and second values are floats unless otherwise noted.
806	Items not refined are noted as [*]
807
808	.. tabularcolumns:: \|l\|p{1.5in}\|p{4in}\|
809
810	======================== =============== ===========================================================
811	key sub-key explanation
812	======================== =============== ===========================================================
813	Instrument Parameters[0] Type [*] (str) Histogram type:
814	* 'PNT' for time of flight neutron
815	\ Bank (int) Data set number in a multidata file
816	\ 2-theta [*] (float) Nominal scattering angle for the detector
817	\ fltPath [*] (float) Total flight path source-sample-detector
818	\ Azimuth [*] (float) Azimuth angle for detector right hand rotation
819	from horizontal away from source
820	\ difC,difA, (float) Diffractometer constants for conversion of d-spacing to TOF
821	difB in microseconds
822	\ Zero (float) Zero point offset (microseconds)
823	\ alpha (float) Exponential rise profile coefficients
824	\ beta-0 (float) Exponential decay profile coefficients
825	beta-1
826	beta-q
827	\ sig-0 (float) Gaussian profile coefficients
828	sig-1
829	sig-2
830	sig-q
831	\ X,Y,Z (float) Lorentzian profile coefficients
832	Instrument Parameters[1] Pdabc (list of 4 float lists) Originally created for use in gsas as optional tables
833	of d, alp, bet, d-true; for a reflection alpha & beta are obtained via interpolation
834	from the d-spacing and these tables. The d-true column is apparently unused.
835	======================== =============== ===========================================================
836
837
838	.. _PowderRefl_table:
839
840	.. index::
841	single: Powder reflection object description
842	single: Data object descriptions; Powder Reflections
843
844	Powder Reflection Data Structure
845	--------------------------------
846
847	For every phase in a histogram, the ``Reflection Lists`` value is a dict
848	one element of which is `'RefList'`, which is a np.array containing
849	reflections. The columns in that array are documented below.
850
851	========== ====================================================
852	index explanation
853	========== ====================================================
854	0,1,2 h,k,l (float)
855	3 (int) multiplicity
856	4 (float) d-space, :math:`\AA`
857	5 (float) pos, two-theta
858	6 (float) sig, Gaussian width
859	7 (float) gam, Lorenzian width
860	8 (float) :math:`F_{obs}^2`
861	9 (float) :math:`F_{calc}^2`
862	10 (float) reflection phase, in degrees
863	11 (float) intensity correction for reflection, this times
864	:math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
865	12 (float) Preferred orientation correction
866	13 (float) Transmission (absorption correction)
867	14 (float) Extinction correction
868	========== ====================================================
869
870	.. _Xtal_table:
871
872	.. index::
873	single: Single Crystal data object description
874	single: Data object descriptions; Single crystal data
875
876	Single Crystal Tree Items
877	-------------------------
878
879	Every single crystal diffraction histogram is stored in the GSAS-II data tree
880	with a top-level entry named beginning with the string "HKLF ". The
881	diffraction data for that information are directly associated with
882	that tree item and there are a series of children to that item. The
883	routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
884	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
885	load this information into a dictionary where the child tree name is
886	used as a key, and the information in the main entry is assigned
887	a key of ``Data``, as outlined below.
888
889	.. tabularcolumns:: \|l\|l\|p{4in}\|
890
891	====================== =============== ====================================================
892	key sub-key explanation
893	====================== =============== ====================================================
894	Data \ (dict) that contains the
895	reflection table,
896	as described in the
897	:ref:`Single Crystal Reflections
898	<XtalRefl_table>`
899	description.
900
901	Instrument Parameters \ (list) containing two dicts where the possible
902	keys in each dict are listed below. The value
903	for most items is a list containing two values:
904	the initial value, the current value.
905	The first and second
906	values are floats unless otherwise noted.
907	\ Lam (two floats) Specifies a wavelength in :math:`\AA`
908	\ Type (two str values) Histogram type :
909	* 'SXC' for constant wavelength x-ray
910	* 'SNC' for constant wavelength neutron
911	* 'SNT' for time of flight neutron
912	* 'SEC' for constant wavelength electrons (e.g. micro-ED)
913	\ InstrName (str) A name for the instrument, used in preparing a CIF
914	wtFactor \ (float) A weighting factor to increase or decrease
915	the leverage of data in the histogram.
916	A value of 1.0 weights the data with their
917	standard uncertainties and a larger value
918	increases the weighting of the data (equivalent
919	to decreasing the uncertainties).
920
921	hId \ (int) The number assigned to the histogram when
922	the project is loaded or edited (can change)
923	ranId \ (int) A random number id for the histogram
924	that does not change
925	====================== =============== ====================================================
926
927	.. _XtalRefl_table:
928
929	.. index::
930	single: Single Crystal reflection object description
931	single: Data object descriptions; Single Crystal Reflections
932
933	Single Crystal Reflection Data Structure
934	----------------------------------------
935
936	For every single crystal a histogram, the ``'Data'`` item contains
937	the structure factors as an np.array in item `'RefList'`.
938	The columns in that array are documented below.
939
940	.. tabularcolumns:: \|l\|p{4in}\|
941
942	========== ====================================================
943	index explanation
944	========== ====================================================
945	0,1,2 (float) h,k,l
946	3 (int) multiplicity
947	4 (float) d-space, :math:`\AA`
948	5 (float) :math:`F_{obs}^2`
949	6 (float) :math:`\sigma(F_{obs}^2)`
950	7 (float) :math:`F_{calc}^2`
951	8 (float) :math:`F_{obs}^2T`
952	9 (float) :math:`F_{calc}^2T`
953	10 (float) reflection phase, in degrees
954	11 (float) intensity correction for reflection, this times
955	:math:`F_{obs}^2` or :math:`F_{calc}^2`
956	gives Iobs or Icalc
957	========== ====================================================
958
959	.. _Image_table:
960
961	.. index::
962	image: Image data object description
963	image: Image object descriptions
964
965	Image Data Structure
966	--------------------
967
968	Every 2-dimensional image is stored in the GSAS-II data tree
969	with a top-level entry named beginning with the string "IMG ". The
970	image data are directly associated with that tree item and there
971	are a series of children to that item. The routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
972	and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
973	load this information into a dictionary where the child tree name is
974	used as a key, and the information in the main entry is assigned
975	a key of ``Data``, as outlined below.
976
977	.. tabularcolumns:: \|l\|l\|p{4in}\|
978
979	====================== ====================== ====================================================
980	key sub-key explanation
981	====================== ====================== ====================================================
982	Comments \ (list of str) Text strings extracted from the original image data
983	header or a metafile. These cannot be changed by
984	the user; it may be empty.
985	Image Controls azmthOff (float) The offset to be applied to an azimuthal
986	value. Accomodates
987	detector orientations other than with the detector
988	X-axis
989	horizontal.
990	\ background image (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
991	during image integration multiplied by value. It must have the same size/shape as
992	the integrated image. NB: value < 0 for subtraction.
993	\ calibrant (str) The material used for determining the position/orientation
994	of the image. The data is obtained from :func:`ImageCalibrants`
995	and UserCalibrants.py (supplied by user).
996	\ calibdmin (float) The minimum d-spacing used during the last calibration run.
997	\ calibskip (int) The number of expected diffraction lines skipped during the last
998	calibration run.
999	\ center (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
1000	strikes the detector plane as determined by calibration. This point
1001	does not have to be within the limits of the detector boundaries.
1002	\ centerAzm (bool) If True then the azimuth reported for the integrated slice
1003	of the image is at the center line otherwise it is at the leading edge.
1004	\ color (str) The name of the colormap used to display the image. Default = 'Paired'.
1005	\ cutoff (float) The minimum value of I/Ib for a point selected in a diffraction ring for
1006	calibration calculations. See pixLimit for details as how point is found.
1007	\ DetDepth (float) Coefficient for penetration correction to distance; accounts for diffraction
1008	ring offset at higher angles. Optionally determined by calibration.
1009	\ DetDepthRef (bool) If True then refine DetDepth during calibration/recalibration calculation.
1010	\ distance (float) The distance (mm) from sample to detector plane.
1011	\ ellipses (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
1012	center (list) is location (mm) of the ellipse center on the detector plane, phi is the
1013	rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
1014	radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
1015	is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
1016	\ edgemin (float) Not used; parameter in EdgeFinder code.
1017	\ fullIntegrate (bool) If True then integrate over full 360 deg azimuthal range.
1018	\ GonioAngles (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
1019	Required for texture calculations.
1020	\ invert_x (bool) If True display the image with the x-axis inverted.
1021	\ invert_y (bool) If True display the image with the y-axis inverted.
1022	\ IOtth (list:floats) The minimum and maximum 2-theta values to be used for integration.
1023	\ LRazimuth (list:floats) The minimum and maximum azimuth values to be used for integration.
1024	\ Oblique (list:float,bool) If True apply a detector absorption correction using the value to the
1025	intensities obtained during integration.
1026	\ outAzimuths (int) The number of azimuth pie slices.
1027	\ outChannels (int) The number of 2-theta steps.
1028	\ pixelSize (list:ints) The X,Y dimensions (microns) of each pixel.
1029	\ pixLimit (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
1030	This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
1031	and subject to cutoff in :func:`GSASIIimage.makeRing`.
1032	Locations are used to construct rings of points for calibration calcualtions.
1033	\ PolaVal (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
1034	integration using value.
1035	\ rings (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
1036	diffraction ring with the same d-spacing (dsp)
1037	\ ring (list) The x,y coordinates of the >5 points on an inner ring
1038	selected by the user,
1039	\ Range (list) The minimum & maximum values of the image
1040	\ rotation (float) The angle between the x-axis and the vector about which the
1041	detector is tilted. Constrained to -180 to 180 deg.
1042	\ SampleShape (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
1043	calculations.
1044	\ SampleAbs (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
1045	to cause correction to be applied.
1046	\ setDefault (bool) If True the use the image controls values for all new images to be read. (might be removed)
1047	\ setRings (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.
1048	\ showLines (bool) If True then isplay the integration limits to be used.
1049	\ size (list:int) The number of pixels on the image x & y axes
1050	\ type (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
1051	\ tilt (float) The angle the detector normal makes with the incident beam; range -90 to 90.
1052	\ wavelength (float) The radiation wavelength (:math:`\AA`) as entered by the user
1053	(or someday obtained from the image header).
1054	Masks Arcs (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
1055	to be excluded from integration
1056	\ Frames (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
1057	of which is excluded from recalibration and integration. Only one frame is allowed.
1058	\ Points (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
1059	from integration.
1060	\ Polygons (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
1061	to be excluded from integration.
1062	\ Rings (list: lists) Each entry [2-theta,thickness] describes a ring mask
1063	to be excluded from integration.
1064	\ Thresholds (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
1065	in integrsation. The tuple is the image intensity limits and the list are those set by the user.
1066	\ SpotMask (dict: int & array)
1067	'esdMul'(int) number of standard deviations above mean ring intensity to mask
1068	'spotMask' (bool array) the spot mask for every pixel in image
1069
1070	Stress/Strain Sample phi (float) Sample rotation about vertical axis.
1071	\ Sample z (float) Sample translation from the calibration sample position (for Sample phi = 0)
1072	These will be restricted by space group symmetry; result of strain fit refinement.
1073	\ Type (str) 'True' or 'Conventional': The strain model used for the calculation.
1074	\ d-zero (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
1075	and are used to determine the strain tensor.
1076	The dictionary items are:
1077	'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
1078	'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
1079	'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
1080	'Esig': (list: float) Esds for Emat from fitting.
1081	'pixLimit': (int) Search range to find highest point on ring for each data point
1082	'cutoff': (float) I/Ib cutoff for searching.
1083	'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
1084	'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
1085	'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
1086
1087	====================== ====================== ====================================================
1088
1089	.. _parmDict_table:
1090
1091	.. index::
1092	single: Parameter dictionary
1093
1094	Parameter Dictionary
1095	-------------------------
1096
1097	The parameter dictionary contains all of the variable parameters for the refinement.
1098	The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
1099	It is prepared in two ways. When loaded from the tree
1100	(in :meth:`GSASIIdataGUI.GSASII.MakeLSParmDict` and
1101	:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
1102	the values are lists with two elements: ``[value, refine flag]``
1103
1104	When loaded from the GPX file (in
1105	:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
1106	dict is the actual parameter value (usually a float, but sometimes a
1107	letter or string flag value (such as I or A for iso/anisotropic).
1108
1109	Texture implementation
1110	------------------------------
1111
1112	There are two different places where texture can be treated in GSAS-II.
1113	One is for mitigating the effects of texture in a structural refinement.
1114	The other is for texture characterization.
1115
1116	For reducing the effect of texture in a structural refinement
1117	there are entries labeled preferred orientation in each phase's
1118	data tab. Two different approaches can be used for this, the March-Dollase
1119	model and spherical harmonics.
1120
1121	For the March-Dollase model, one axis in reciprocal space is designated as
1122	unique (defaulting to the 001 axis) and reflections are corrected
1123	according to the angle they make with this axis depending on
1124	the March-Dollase ratio. (If unity, no correction is made).
1125	The ratio can be greater than one or less than one depending on if
1126	crystallites oriented along the designated axis are
1127	overrepresented or underrepresented. For most crystal systems there is an
1128	obvious choice for the direction of the unique axis and then only a single
1129	term needs to be refined. If the number is close to 1, then the correction
1130	is not needed.
1131
1132	The second method for reducing the effect of texture in a structural
1133	refinement is to create a crystallite orientation probability surface as an
1134	expansion in terms spherical harmonic functions. Only functions consistent with
1135	cylindrical diffraction suymmetry and having texture symmetry
1136	consistent with the Laue class of phase are used and are allowed,
1137	so the higher the symmetry the fewer terms that are available for a given spherical harmonics order.
1138	To use this correction, select the lowest order that provides
1139	refinable terms and perform a refinement. If the texture index remains close to
1140	one, then the correction is not needed. If a significant improvement is
1141	noted in the profile Rwp, one may wish to see if a higher order expansion
1142	gives an even larger improvement.
1143
1144	To characterize texture in a material, generally one needs data collected with the
1145	sample at multiple orientations or, for TOF, with detectors at multiple
1146	locations around the sample. In this case the detector orientation is given in
1147	each histogram's Sample Parameters and the sample's orientation is described
1148	with the Euler angles specifed on the phase's Texture tab, which is also
1149	where the texture type (cylindrical, rolling,...) and the spherical
1150	harmonic order is selected. This should not be used with a single dataset and
1151	should not be used if the preferred orientations corrections are used.
1152
1153	The coordinate system used for texture characterization is defined where
1154	the sample coordinates (Psi, gamma) are defined with an instrument coordinate
1155	system (I, J, K) such that K is normal to the diffraction plane and J is coincident with the
1156	direction of the incident radiation beam toward the source. We further define
1157	a standard set of right-handed goniometer eulerian angles (Omega, Chi, Phi) so that Omega and Phi are
1158	rotations about K and Chi is a rotation about J when Omega = 0. Finally, as the sample
1159	may be mounted so that the sample coordinate system (Is, Js, Ks) does not coincide with
1160	the instrument coordinate system (I, J, K), we define three eulerian sample rotation angles
1161	(Omega-s, Chi-s, Phi-s) that describe the rotation from (Is, Js, Ks) to (I, J, K). The sample rotation
1162	angles are defined so that with the goniometer angles at zero Omega-s and Phi-s are rotations
1163	about K and Chi-s is a rotation about J.
1164
1165	Three typical examples:
1166
1167	1) Bragg-Brentano laboratory diffractometer: Chi=0
1168	2) Debye-Scherrer counter detector; sample capillary axis perpendicular to diffraction plane: Chi=90
1169	3) Debye-Scherrer 2D area detector positioned directly behind sample; sample capillary axis horizontal; Chi=0
1170
1171	NB: The area detector azimuthal angle will equal 0 in horizontal plane to right as viewed from x-ray source and will equal
1172	90 at vertical "up" direction.
1173
1174	ISODISTORT implementation
1175	------------------------------
1176
1177	CIFs prepared with the ISODISTORT web site
1178	https://stokes.byu.edu/iso/isodistort_version5.6.1/isodistort.php
1179	[B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, "ISODISPLACE: An Internet Tool for Exploring Structural Distortions."
1180	J. Appl. Cryst. 39, 607-614 (2006).] can be read into GSAS-II using import CIF. This will cause constraints to be established for
1181	structural distortion modes read from the CIF. At present, of the five types of modes only displacive(``_iso_displacivemode``...)
1182	and occupancy (``_iso_occupancymode``...) are processed. Not yet processed: ``_iso_magneticmode``...,
1183	``_iso_rotationalmode``... & ``_iso_strainmode``...
1184
1185	The CIF importer :mod:`G2phase_CIF` implements class :class:`G2phase_CIF.CIFPhaseReader` which offers two methods associated
1186	with ISODISTORT (ID) input. Method :meth:`G2phase_CIF.CIFPhaseReader.ISODISTORT_test` checks to see if a CIF block contains
1187	the loops with ``_iso_displacivemode_label`` or ``_iso_occupancymode_label`` items. If so, method
1188	:meth:`G2phase_CIF.CIFPhaseReader.ISODISTORT_proc` is called to read and interpret them. The results are placed into the
1189	reader object's ``.Phase`` class variable as a dict item with key ``'ISODISTORT'``.
1190
1191	Note that each mode ID has a long label with a name such as Pm-3m[1/2,1/2,1/2]R5+(a,a,0)[La:b:dsp]T1u(a). Function
1192	:func:`G2phase_CIF.ISODISTORT_shortLbl` is used to create a short name for this, such as R5_T1u(a) which is made unique
1193	by addition of _n if the short name is duplicated. As each mode is processed, a constraint corresponding to that mode is
1194	created and is added to list in the reader object's ``.Constraints`` class variable. Items placed into that list can either
1195	be a list, which corresponds to a function (new var) type :ref:`constraint definition <Constraints_table>` entry, or an item
1196	can be a dict, which provides help information for each constraint.
1197
1198	------------------------------
1199	Displacive modes
1200	------------------------------
1201
1202	The coordinate variables, as named by ISODISTORT, are placed in ``.Phase['ISODISTORT']['IsoVarList']`` and the
1203	corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2VarList']``.
1204	The mode variables, as named by ISODISTORT, are placed in ``.Phase['ISODISTORT']['IsoModeList']`` and the
1205	corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2ModeList']``.
1206	[Use ``str(G2VarObj)`` to get the variable name from the G2VarObj object, but note that the phase number, n, for the prefix
1207	"n::" cannot be determined as the phase number is not yet assigned.]
1208
1209	Displacive modes are a bit complex in that they relate to delta displacements, relative to an offset value for each coordinate,
1210	and because the modes are normalized. While GSAS-II also uses displacements, these are added to the coordinates after
1211	each refinement cycle and then the delta values are set to zero.
1212	ISODISTORT uses fixed offsets (subtracted from the actual position
1213	to obtain the delta values) that are taken from the parent structure coordinate and the initial offset value
1214	(in ``_iso_deltacoordinate_value``) and these are placed in
1215	``.Phase['ISODISTORT']['G2coordOffset']`` in the same order as ``.Phase['ISODISTORT']['G2ModeList']``,
1216	``.Phase['ISODISTORT']['IsoVarList']`` and ''.Phase[ISODISTORT']['G2parentCoords']''.'
1217
1218	The normalization factors (which the delta values are divided by)
1219	are taken from ``_iso_displacivemodenorm_value`` and are placed in ``.Phase['ISODISTORT']['NormList']`` in the same
1220	order as as ``...['IsoModeList']`` and ``...['G2ModeList']``.
1221
1222	The CIF contains a sparse matrix, from the ``loop_`` containing ``_iso_displacivemodematrix_value`` which provides the equations
1223	for determining the mode values from the coordinates, that matrix is placed in ``.Phase['ISODISTORT']['Mode2VarMatrix']``.
1224	The matrix is inverted to produce ``.Phase['ISODISTORT']['Var2ModeMatrix']``, which determines how to compute the
1225	mode values from the delta coordinate values. These values are used for the in :func:`GSASIIconstrGUI.ShowIsoDistortCalc`,
1226	which shows coordinate and mode values, the latter with s.u. values.
1227
1228	------------------------------
1229	Occupancy modes
1230	------------------------------
1231
1232
1233	The delta occupancy variables, as named by ISODISTORT, are placed in
1234	``.Phase['ISODISTORT']['OccVarList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed
1235	in ``.Phase['ISODISTORT']['G2OccVarList']``. The mode variables, as named by ISODISTORT, are placed in
1236	``.Phase['ISODISTORT']['OccModeList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed
1237	in ``.Phase['ISODISTORT']['G2OccModeList']``.
1238
1239	Occupancy modes, like Displacive modes, are also refined as delta values. However, GSAS-II directly refines the fractional
1240	occupancies. Offset values for each atom, are taken from ``_iso_occupancy_formula`` and are placed in
1241	``.Phase['ISODISTORT']['ParentOcc]``. (Offset values are subtracted from the actual position to obtain the delta values.)
1242	Modes are normalized (where the mode values are divided by the normalization factor) are taken from ``_iso_occupancymodenorm_value``
1243	and are placed in ``.Phase['ISODISTORT']['OccNormList']`` in the same order as as ``...['OccModeList']`` and
1244	``...['G2OccModeList']``.
1245
1246	The CIF contains a sparse matrix, from the ``loop_`` containing ``_iso_occupancymodematrix_value``, which provides the
1247	equations for determining the mode values from the coordinates. That matrix is placed in ``.Phase['ISODISTORT']['Occ2VarMatrix']``.
1248	The matrix is inverted to produce ``.Phase['ISODISTORT']['Var2OccMatrix']``, which determines how to compute the
1249	mode values from the delta coordinate values.
1250
1251
1252	------------------------------
1253	Mode Computations
1254	------------------------------
1255
1256	Constraints are processed after the CIF has been read in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` or
1257	:meth:`GSASIIscriptable.G2Project.add_phase` by moving them from the reader object's ``.Constraints``
1258	class variable to the Constraints tree entry's ['Phase'] list (for list items defining constraints) or
1259	the Constraints tree entry's ['_Explain'] dict (for dict items defining constraint help information)
1260
1261	The information in ``.Phase['ISODISTORT']`` is used in :func:`GSASIIconstrGUI.ShowIsoDistortCalc` which shows coordinate and mode
1262	values, the latter with s.u. values. This can be called from the Constraints and Phase/Atoms tree items.
1263
1264	Before each refinement, constraints are processed as :ref:`described elsewhere <Constraints_processing>`. After a refinement
1265	is complete, :func:`GSASIIstrIO.PrintIndependentVars` shows the shifts and s.u.'s on the refined modes,
1266	using GSAS-II values, but :func:`GSASIIstrIO.PrintISOmodes` prints the ISODISTORT modes as computed in the web site.
1267
1268
1269	.. _ParameterLimits:
1270
1271	.. index::
1272	single: Parameter limits
1273
1274	Parameter Limits
1275	------------------------------
1276
1277	One of the most often requested "enhancements" for GSAS-II would be the inclusion
1278	of constraints to force parameters such as occupancies or Uiso values to stay within
1279	expected ranges. While it is possible for users to supply their own restraints that would
1280	perform this by supplying an appropriate expression with the "General" restraints, the
1281	GSAS-II authors do not feel that use of restraints or constraints are a good solution for
1282	this common problem where parameters refine to non-physical values. This is because when
1283	this occurs, most likely one of the following cases is occurring:
1284
1285	#. there is a significant problem
1286	with the model, for example for an x-ray fit if an O atom is placed where a S is actually
1287	present, the Uiso will refine artificially small or the occupancy much larger than unity
1288	to try to compensate for the missing electrons; or
1289
1290	#. the data are simply insensitive
1291	to the parameter or combination of parameters, for example unless very high-Q data
1292	are included, the effects of a occupancy and Uiso value can have compensating effects,
1293	so an assumption must be made; likewise, with neutron data natural-abundance V atoms
1294	are nearly invisible due to weak coherent scattering. No parameters can be fit for a
1295	V atom with neutrons.
1296
1297	#. the parameter is non-physical (such as a negative Uiso value) but within
1298	two sigma (sigma = standard uncertainty, aka e.s.d.) of a reasonable value,
1299	in which case the
1300	value is not problematic as it is experimentally indistinguishable from an
1301	expected value.
1302
1303	#. there is a systematic problem with the data (experimental error)
1304
1305	In all these cases, this situation needs to be reviewed by a crystallographer to decide
1306	how to best determine a structural model for these data. An implementation with a constraint
1307	or restraint is likely to simply hide the problem from the user, making it more probable
1308	that a poor model choice is obtained.
1309
1310	What GSAS-II does implement is to allow users to specify ranges for parameters
1311	that works by disabling
1312	refinement of parameters that refine beyond either a lower limit or an upper limit, where
1313	either or both may be optionally specified. Parameters limits are specified in the Controls
1314	tree entry in dicts named as ``Controls['parmMaxDict']`` and ``Controls['parmMinDict']``, where
1315	the keys are :class:`G2VarObj` objects corresponding to standard GSAS-II variable
1316	(see :func:`getVarDescr` and :func:`CompileVarDesc`) names, where a
1317	wildcard ('*') may optionally be used for histogram number or atom number
1318	(phase number is intentionally not allowed as a wildcard as it makes little sense
1319	to group the same parameter together different phases). Note
1320	that :func:`prmLookup` is used to see if a name matches a wildcard. The upper or lower limit
1321	is placed into these dicts as a float value. These values can be edited using the window
1322	created by the Calculate/"View LS parms" menu command or in scripting with the
1323	:meth:`GSASIIscriptable.G2Project.set_Controls` function.
1324	In the GUI, a checkbox labeled "match all histograms/atoms" is used to insert a wildcard
1325	into the appropriate part of the variable name.
1326
1327	When a refinement is conducted, routine :func:`GSASIIstrMain.dropOOBvars` is used to
1328	find parameters that have refined to values outside their limits. If this occurs, the parameter
1329	is set to the limiting value and the variable name is added to a list of frozen variables
1330	(as a :class:`G2VarObj` objects) kept in a list in the
1331	``Controls['parmFrozen']`` dict. In a sequential refinement, this is kept separate for
1332	each histogram as a list in
1333	``Controls['parmFrozen'][histogram]`` (where the key is the histogram name) or as a list in
1334	``Controls['parmFrozen']['FrozenList']`` for a non-sequential fit.
1335	This allows different variables
1336	to be frozen in each section of a sequential fit.
1337	Frozen parameters are not included in refinements through removal from the
1338	list of parameters to be refined (``varyList``) in :func:`GSASIIstrMain.Refine` or
1339	:func:`GSASIIstrMain.SeqRefine`.
1340	The data window for the Controls tree item shows the number of Frozen variables and
1341	the individual variables can be viewed with the Calculate/"View LS parms" menu window or
1342	obtained with :meth:`GSASIIscriptable.G2Project.get_Frozen`.
1343	Once a variable is frozen, it will not be refined in any
1344	future refinements unless the the variable is removed (manually) from the list. This can also
1345	be done with the Calculate/"View LS parms" menu window or
1346	:meth:`GSASIIscriptable.G2Project.set_Frozen`.
1347
1348
1349	.. seealso::
1350	:class:`G2VarObj`
1351	:func:`getVarDescr`
1352	:func:`CompileVarDesc`
1353	:func:`prmLookup`
1354	:class:`GSASIIctrlGUI.ShowLSParms`
1355	:class:`GSASIIctrlGUI.VirtualVarBox`
1356	:func:`GSASIIstrIO.SetUsedHistogramsAndPhases`
1357	:func:`GSASIIstrIO.SaveUpdatedHistogramsAndPhases`
1358	:func:`GSASIIstrIO.SetSeqResult`
1359	:func:`GSASIIstrMain.dropOOBvars`
1360	:meth:`GSASIIscriptable.G2Project.set_Controls`
1361	:meth:`GSASIIscriptable.G2Project.get_Frozen`
1362	:meth:`GSASIIscriptable.G2Project.set_Frozen`
1363
1364	GSASIIobj Classes and routines
1365	------------------------------------
1366
1367
1368	.. automodule:: GSASIIobj
1369	:members:
1370	:private-members:
1371	:special-members:

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