source: trunk/GSASIIobj.py @ 4661

# -*- coding: utf-8 -*-
#GSASIIobj - data objects for GSAS-II
########### SVN repository information ###################
# $Date: 2020-11-28 02:48:26 +0000 (Sat, 28 Nov 2020) $
# $Author: toby $
# $Revision: 4661 $
# $URL: trunk/GSASIIobj.py $
# $Id: GSASIIobj.py 4661 2020-11-28 02:48:26Z toby $
########### SVN repository information ###################

'''
*GSASIIobj: Data objects*
=========================

This module defines and/or documents the data structures used in GSAS-II, as well
as provides misc. support routines.

.. Next command allows \\AA to be used in HTML

.. only:: html

   :math:`\\require{mediawiki-texvc}`

.. _Constraints_table:

.. index::
   single: Constraints object description
   single: Data object descriptions; Constraints

Constraints Tree Item
----------------------

Constraints are stored in a dict, separated into groups.
Note that parameter are named in the following pattern,
p:h:<var>:n, where p is the phase number, h is the histogram number
<var> is a variable name and n is the parameter number.
If a parameter does not depend on a histogram or phase or is unnumbered, that
number is omitted.
Note that the contents of each dict item is a List where each element in the
list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
The constraints in this form are converted in
:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`

The keys in the Constraints dict are:

.. tabularcolumns:: |l|p{4.5in}|

==========  ====================================================
  key         explanation
==========  ====================================================
Hist        This specifies a list of constraints on
            histogram-related parameters,
            which will be of form :h:<var>:n.
HAP         This specifies a list of constraints on parameters
            that are defined for every histogram in each phase
            and are of form p:h:<var>:n.
Phase       This specifies a list of constraints on phase
            parameters,
            which will be of form p::<var>:n.
Global      This specifies a list of constraints on parameters
            that are not tied to a histogram or phase and
            are of form ::<var>:n
==========  ====================================================

.. _Constraint_definitions_table:

.. index::
   single: Constraint definition object description
   single: Data object descriptions; Constraint Definition

Each constraint is defined as an item in a list. Each constraint is of form::

[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]

Where the variable pair list item containing two values [<mult>, <var>], where:

  * <mult> is a multiplier for the constraint (float)
  * <var> a :class:`G2VarObj` object (previously a str variable name of form
      'p:h:name[:at]')

Note that the last three items in the list play a special role:

 * <fixedval> is the fixed value for a `constant equation` (``constype=c``)
   constraint or is None. For a `New variable` (``constype=f``) constraint,
   a variable name can be specified as a str (used for externally
   generated constraints)
 * <varyflag> is True or False for `New variable` (``constype=f``) constraints
   or is None. This indicates if this variable should be refined.
 * <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:

    * 'e' defines a set of equivalent variables. Only the first variable is refined (if the
      appropriate refine flag is set) and and all other equivalent variables in the list
      are generated from that variable, using the appropriate multipliers.
    * 'c' defines a constraint equation of form,
      :math:`m_1 \\times var_1 + m_2 \\times var_2 + ... = c`
    * 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
      even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
      constraint and the mult value is ignored.
      This is of particular value when needing to hold one or more variables where a
      single flag controls a set of variables such as, coordinates,
      the reciprocal metric tensor or anisotropic displacement parameter.
    * 'f' defines a new variable (function) according to relationship
      :math:`newvar = m_1 \\times var_1 + m_2 \\times var_2 + ...`

.. _Covariance_table:

.. index::
   single: Covariance description
   single: Data object descriptions; Covariance

Covariance Tree Item
--------------------

The Covariance tree item has results from the last least-squares run. They
are stored in a dict with these keys:

.. tabularcolumns:: |l|l|p{4in}|

=============  ===============  ====================================================
  key            sub-key        explanation
=============  ===============  ====================================================
newCellDict    \\                (dict) ith lattice parameters computed by
                                :func:`GSASIIstrMath.GetNewCellParms`
title          \\                (str) Name of gpx file(?) 
variables      \\                (list) Values for all N refined variables
                                (list of float values, length N,
                                ordered to match varyList)
sig            \\                (list) Uncertainty values for all N refined variables
                                (list of float values, length N,
                                ordered to match varyList)
varyList       \\                (list of str values, length N) List of directly refined variables
                                
newAtomDict    \\                (dict) atom position values computed in
                                :func:`GSASIIstrMath.ApplyXYZshifts` 
Rvals          \\                (dict) R-factors, GOF, Marquardt value for last
                                refinement cycle 
\\              Nobs             (int) Number of observed data points 
\\              Rwp              (float) overall weighted profile R-factor (%)
\\              chisq            (float) :math:`\\sum w*(I_{obs}-I_{calc})^2`                                
                                for all data.
                                Note: this is not the reduced :math:`\\chi^2`. 
\\              lamMax           (float) Marquardt value applied to Hessian diagonal
\\              GOF              (float) The goodness-of-fit, aka square root of
                                the reduced chi squared. 
covMatrix      \\                (np.array) The (NxN) covVariance matrix 
=============  ===============  ====================================================

.. _Phase_table:

.. index::
   single: Phase object description
   single: Data object descriptions; Phase

Phase Tree Items
----------------

Phase information is stored in the GSAS-II data tree as children of the
Phases item in a dict with keys:

.. tabularcolumns:: |l|l|p{4in}|

==========  ===============     =====================================================================================================
  key         sub-key           explanation
==========  ===============     =====================================================================================================
General         \\               (dict) Overall information for the phase 
  \\         3Dproj              (list of str) projections for 3D pole distribution plots
  \\         AngleRadii          (list of floats) Default radius for each atom used to compute
                                interatomic angles 
  \\         AtomMass            (list of floats) Masses for atoms
  \\         AtomPtrs            (list of int) four locations (cx,ct,cs & cu) to use to pull info
                                from the atom records 
  \\         AtomTypes           (llist of str) Atom types
  \\         BondRadii           (list of floats) Default radius for each atom used to compute
                                interatomic distances 
  \\         Cell                Unit cell parameters & ref. flag
                                (list with 8 items. All but first item are float.)

                                 0: cell refinement flag (True/False),
                                 1-3: a, b, c, (:math:`\\AA`)
                                 4-6: alpha, beta & gamma, (degrees)
                                 7: volume (:math:`\\AA^3`)
  \\         Color               (list of (r,b,g) triplets) Colors for atoms 
  \\         Compare             (dict) Polygon comparison parameters
  \\         Data plot type      (str) data plot type ('Mustrain', 'Size' or
                                'Preferred orientation') for powder data 
  \\         DisAglCtls          (dDict) with distance/angle search controls,
                                which has keys 'Name', 'AtomTypes',
                                'BondRadii', 'AngleRadii' which are as above
                                except are possibly edited. Also contains
                                'Factors', which is a 2 element list with
                                a multiplier for bond and angle search range
                                [typically (0.85,0.85)].
  \\         F000X               (float) x-ray F(000) intensity 
  \\         F000N               (float) neutron F(000) intensity 
  \\         Flip                (dict) Charge flip controls
  \\         HydIds              (dict) geometrically generated hydrogen atoms
  \\         Isotope             (dict) Isotopes for each atom type
  \\         Isotopes            (dict) Scattering lengths for each isotope
                                combination for each element in phase
  \\         MCSA controls       (dict) Monte Carlo-Simulated Annealing controls 
  \\         Map                 (dict) Map parameters
  \\         Mass                (float) Mass of unit cell contents in g/mol
  \\         Modulated           (bool) True if phase modulated
  \\         Mydir               (str) Directory of current .gpx file 
  \\         Name                (str) Phase name 
  \\         NoAtoms             (dict) Number of atoms per unit cell of each type 
  \\         POhkl               (list) March-Dollase preferred orientation direction
  \\         Pawley dmin         (float) maximum Q (as d-space) to use for Pawley extraction 
  \\         Pawley dmax         (float) minimum Q (as d-space) to use for Pawley extraction 
  \\         Pawley neg wt       (float) Restraint value for negative Pawley intensities
  \\         SGData              (object) Space group details as a 
                                :ref:`space group (SGData) <SGData_table>` 
                                object, as defined in :func:`GSASIIspc.SpcGroup`.
  \\         SH Texture          (dict) Spherical harmonic preferred orientation parameters
  \\         Super               (int) dimension of super group (0,1 only)
  \\         Type                (str) phase type (e.g. 'nuclear')
  \\         Z                   (dict) Atomic numbers for each atom type
  \\         doDysnomia          (bool) flag for max ent map modification via Dysnomia
  \\         doPawley            (bool) Flag for Pawley intensity extraction
  \\         vdWRadii            (dict) Van der Waals radii for each atom type
ranId           \\               (int) unique random number Id for phase 
pId             \\               (int) Phase Id number for current project.
Atoms           \\               (list of lists) Atoms in phase as a list of lists. The outer list
                                is for each atom, the inner list contains varying
                                items depending on the type of phase, see
                                the :ref:`Atom Records <Atoms_table>` description.
Drawing         \\               (dict) Display parameters 
\\           Atoms               (list of lists) with an entry for each atom that is drawn
\\           Plane               (list) Controls for contour density plane display
\\           Quaternion          (4 element np.array) Viewing quaternion 
\\           Zclip               (float) clipping distance in :math:`\\AA`
\\           Zstep               (float) Step to de/increase Z-clip 
\\           atomPtrs            (list) positions of x, type, site sym, ADP flag in Draw Atoms 
\\           backColor           (list) background for plot as and R,G,B triplet
                                (default = [0, 0, 0], black).
\\           ballScale           (float) Radius of spheres in ball-and-stick display 
\\           bondList            (dict) Bonds
\\           bondRadius          (float) Radius of binds in :math:`\\AA` 
\\           cameraPos           (float) Viewing position in :math:`\\AA` for plot 
\\           contourLevel        (float) map contour level in :math:`e/\\AA^3` 
\\           contourMax          (float) map contour maximum
\\           depthFog            (bool) True if use depthFog on plot - set currently as False 
\\           ellipseProb         (float) Probability limit for display of thermal
                                ellipsoids in % .
\\           magMult             (float) multiplier for magnetic moment arrows
\\           mapSize             (float) x & y dimensions of contourmap (fixed internally)
\\           modelView           (4,4 array) from openGL drawing transofmation matrix
\\           oldxy               (list with two floats) previous view point 
\\           radiusFactor        (float) Distance ratio for searching for bonds. Bonds
                                are located that are within r(Ra+Rb) and (Ra+Rb)/r
                                where Ra and Rb are the atomic radii.
\\           selectedAtoms       (list of int values) List of selected atoms 
\\           showABC             (bool) Flag to show view point triplet. True=show.
\\           showHydrogen        (bool) Flag to control plotting of H atoms.
\\           showRigidBodies     (bool) Flag to highlight rigid body placement
\\           showSlice           (bool) flag to show contour map
\\           sizeH               (float) Size ratio for H atoms 
\\           unitCellBox         (bool) Flag to control display of the unit cell.
\\           vdwScale            (float) Multiplier of van der Waals radius for display of vdW spheres.
\\           viewDir             (np.array with three floats) cartesian viewing direction 
\\           viewPoint           (list of lists) First item in list is [x,y,z]
                                in fractional coordinates for the center of
                                the plot. Second item list of previous & current
                                atom number viewed (may be [0,0])
RBModels        \\               Rigid body assignments (note Rigid body definitions
                                are stored in their own main top-level tree entry.)
RMC             \\               (dict) RMCProfile & rmcfull controls
Pawley ref      \\               (list) Pawley reflections
Histograms      \\               (dict of dicts) The key for the outer dict is
                                the histograms tied to this phase. The inner
                                dict contains the combined phase/histogram
                                parameters for items such as scale factors,
                                size and strain parameters. The following are the
                                keys to the inner dict. (dict)
\\           Babinet             (dict) For protein crystallography. Dictionary with two
                                entries, 'BabA', 'BabU'
\\           Extinction          (list of float, bool) Extinction parameter 
\\           Flack               (list of [float, bool]) Flack parameter & refine flag
\\           HStrain             (list of two lists) Hydrostatic strain. The first is
                                a list of the HStrain parameters (1, 2, 3, 4, or 6
                                depending on unit cell), the second is a list of boolean
                                refinement parameters (same length)
\\           Histogram           (str) The name of the associated histogram 
\\           Layer Disp          (list of [float, bool]) Layer displacement in beam direction & refine flag
\\           LeBail              (bool) Flag for LeBail extraction 
\\           Mustrain            (list) Microstrain parameters, in order:
    
                                0. Type, one of  u'isotropic', u'uniaxial', u'generalized'
                                1. Isotropic/uniaxial parameters - list of 3 floats
                                2. Refinement flags - list of 3 bools
                                3. Microstrain axis - list of 3 ints, [h, k, l]
                                4. Generalized mustrain parameters - list of 2-6 floats, depending on space group
                                5. Generalized refinement flags - list of bools, corresponding to the parameters of (4)
\\           Pref.Ori.           (list) Preferred Orientation. List of eight parameters.
                                Items marked SH are only used for Spherical Harmonics.
                                
                                0. (str) Type, 'MD' for March-Dollase or 'SH' for Spherical Harmonics
                                1. (float) Value 
                                2. (bool) Refinement flag 
                                3. (list) Preferred direction, list of ints, [h, k, l]
                                4. (int) SH - number of terms
                                5. (dict) SH -  
                                6. (list) SH
                                7. (float) SH 
\\           Scale               (list of [float, bool]) Phase fraction & refine flag
\\           Size                List of crystallite size parameters, in order:

                                0. (str) Type, one of  u'isotropic', u'uniaxial', u'ellipsoidal'
                                1. (list) Isotropic/uniaxial parameters - list of 3 floats
                                2. (list) Refinement flags - list of 3 bools
                                3. (list) Size axis - list of 3 ints, [h, k, l]
                                4. (list) Ellipsoidal size parameters - list of 6 floats
                                5. (list) Ellipsoidal refinement flags - list of bools, corresponding to the parameters of (4)
\\           Use                 (bool) True if this histogram is to be used in refinement
\\           newLeBail           (bool) Whether to perform a new LeBail extraction
MCSA            \\               (dict) Monte-Carlo simulated annealing parameters 
==========  ===============     =====================================================================================================

.. _RBData_table:

.. index::
   single: Rigid Body Data description
   single: Data object descriptions; Rigid Body Data

Rigid Body Objects
------------------

Rigid body descriptions are available for two types of rigid bodies: 'Vector'
and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
with defined refinable torsion angles.

.. tabularcolumns:: |l|l|p{4in}|

==========  ===============     ====================================================
  key         sub-key           explanation
==========  ===============     ====================================================
Vector      RBId                (dict of dict) vector rigid bodies 
\\           AtInfo              (dict) Drad, Color: atom drawing radius & color for each atom type 
\\           RBname              (str) Name assigned by user to rigid body 
\\           VectMag             (list) vector magnitudes in :math:`\\AA` 
\\           rbXYZ               (list of 3 float Cartesian coordinates for Vector rigid body )
\\           rbRef               (list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin
                                definition, use center of atoms flag 
\\           VectRef             (list of bool refinement flags for VectMag values )
\\           rbTypes             (list of str) Atom types for each atom in rigid body 
\\           rbVect              (list of lists) Cartesian vectors for each translation used to build rigid body 
\\           useCount            (int) Number of times rigid body is used in any structure 
Residue     RBId                (dict of dict) residue rigid bodies 
\\           AtInfo              (dict) Drad, Color: atom drawing radius & color for each atom type
\\           RBname              (str) Name assigned by user to rigid body 
\\           rbXYZ               (list of 3 float) Cartesian coordinates for Residue rigid body 
\\           rbTypes             (list of str) Atom types for each atom in rigid body 
\\           atNames             (list of str) Names of each atom in rigid body (e.g. C1,N2...) 
\\           rbRef               (list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin
                                definition, use center of atoms flag 
\\           rbSeq               (list) Orig,Piv,angle,Riding : definition of internal rigid body
                                torsion; origin atom (int), pivot atom (int), torsion angle (float),
                                riding atoms (list of int)
\\           SelSeq              (int,int) used by SeqSizer to identify objects
\\           useCount            (int)Number of times rigid body is used in any structure 
RBIds           \\               (dict) unique Ids generated upon creation of each rigid body 
\\           Vector              (list) Ids for each Vector rigid body 
\\           Residue             (list) Ids for each Residue rigid body 
==========  ===============     ====================================================

.. _SGData_table:

.. index::
   single: Space Group Data description
   single: Data object descriptions; Space Group Data

Space Group Objects
-------------------

Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
and the information is placed in a SGdata object
which is a dict with these keys. Magnetic ones are marked "mag"

.. tabularcolumns:: |l|p{4.5in}|

==========  ========================================================================================
  key         explanation
==========  ========================================================================================
BNSlattsym  mag - (str) BNS magnetic space group symbol and centering vector
GenFlg      mag - (list) symmetry generators indices
GenSym      mag - (list) names for each generator
MagMom      mag - (list) "time reversals" for each magnetic operator
MagPtGp     mag - (str) Magnetic point group symbol
MagSpGrp    mag - (str) Magnetic space group symbol
OprNames    mag - (list) names for each space group operation
SGCen       (np.array) Symmetry cell centering vectors. A (n,3) np.array
            of centers. Will always have at least one row: ``np.array([[0, 0, 0]])``
SGFixed     (bool) Only True if phase mported from a magnetic cif file
            then the space group can not be changed by the user because 
            operator set from cif may be nonstandard
SGGen       (list) generators
SGGray      (bool) True if space group is a gray group (incommensurate magnetic structures)
SGInv       (bool) True if centrosymmetric, False if not
SGLatt      (str)Lattice centering type. Will be one of
            P, A, B, C, I, F, R 
SGLaue      (str) one of the following 14 Laue classes:
            -1, 2/m, mmm, 4/m, 4/mmm, 3R,
            3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m
SGOps       (list) symmetry operations as a list of form
            ``[[M1,T1], [M2,T2],...]``
            where :math:`M_n` is a 3x3 np.array
            and :math:`T_n` is a length 3 np.array.
            Atom coordinates are transformed where the
            Asymmetric unit coordinates [X is (x,y,z)]
            are transformed using
            :math:`X^\\prime = M_n*X+T_n`
SGPolax     (str) Axes for space group polarity. Will be one of
            '', 'x', 'y', 'x y', 'z', 'x z', 'y z',
            'xyz'. In the case where axes are arbitrary
            '111' is used (P 1, and ?).
SGPtGrp     (str) Point group of the space group
SGUniq      unique axis if monoclinic. Will be
            a, b, or c for monoclinic space groups.
            Will be blank for non-monoclinic.
SGSpin      mag - (list) of spin flip operatiors (+1 or -1) for the space group operations
SGSys       (str) symmetry unit cell: type one of
            'triclinic', 'monoclinic', 'orthorhombic',
            'tetragonal', 'rhombohedral', 'trigonal',
            'hexagonal', 'cubic' 
SSGK1       (list) Superspace multipliers
SpGrp       (str) space group symbol 
SpnFlp      mag - (list) Magnetic spin flips for every magnetic space group operator
==========  ========================================================================================

.. _SSGData_table:

.. index::
   single: Superspace Group Data description
   single: Data object descriptions; Superspace Group Data

Superspace groups [3+1] are interpreted by :func:`GSASIIspc.SSpcGroup`
and the information is placed in a SSGdata object
which is a dict with these keys:

.. tabularcolumns:: |l|p{4.5in}|

==========  ====================================================
  key         explanation
==========  ====================================================
SSGCen      (list) 4D cell centering vectors [0,0,0,0] at least
SSGK1       (list) Superspace multipliers
SSGOps      (list) 4D symmetry operations as [M,T] so that M*x+T = x'
SSpGrp      (str) superspace group symbol extension to space group
            symbol, accidental spaces removed
modQ        (list) modulation/propagation vector
modSymb     (list of str) Modulation symbols
==========  ====================================================


.. _Atoms_table:

.. index::
   single: Atoms record description
   single: Data object descriptions; Atoms record

Atom Records
------------

If ``phasedict`` points to the phase information in the data tree, then
atoms are contained in a list of atom records (list) in
``phasedict['Atoms']``. Also needed to read atom information
are four pointers, ``cx,ct,cs,cia = phasedict['General']['AtomPtrs']``,
which define locations in the atom record, as shown below. Items shown are
always present; additional ones for macromolecular phases are marked 'mm', 
and those for magnetic structures are marked 'mg'

.. tabularcolumns:: |l|p{4.5in}|

==============      ====================================================
location            explanation
==============      ====================================================
ct-4                mm - (str) residue number
ct-3                mm - (str) residue name (e.g. ALA) 
ct-2                mm - (str) chain label 
ct-1                (str) atom label 
ct                  (str) atom type 
ct+1                (str) refinement flags; combination of 'F', 'X', 'U', 'M' 
cx,cx+1,cx+2        (3 floats) the x,y and z coordinates 
cx+3                (float) site occupancy 
cx+4,cx+5,cx+6      mg - (list) atom magnetic moment along a,b,c in Bohr magnetons 
cs                  (str) site symmetry 
cs+1                (int) site multiplicity 
cia                 (str) ADP flag: Isotropic ('I') or Anisotropic ('A')
cia+1               (float) Uiso 
cia+2...cia+7       (6 floats) U11, U22, U33, U12, U13, U23 
atom[cia+8]         (int) unique atom identifier 

==============      ====================================================

.. _Drawing_atoms_table:

.. index::
   single: Drawing atoms record description
   single: Data object descriptions; Drawing atoms record

Drawing Atom Records
--------------------

If ``phasedict`` points to the phase information in the data tree, then
drawing atoms are contained in a list of drawing atom records (list) in
``phasedict['Drawing']['Atoms']``. Also needed to read atom information
are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
which define locations in the atom record, as shown below. Items shown are
always present; additional ones for macromolecular phases are marked 'mm',
and those for magnetic structures are marked 'mg'

.. tabularcolumns:: |l|p{4.5in}|

==============   ===================================================================================
location            explanation
==============   ===================================================================================
ct-4                mm - (str) residue number 
ct-3                mm - (str) residue name (e.g. ALA) 
ct-2                mm - (str) chain label 
ct-1                (str) atom label
ct                  (str) atom type 
cx,cx+1,cx+2        (3 floats) the x,y and z coordinates 
cx+3,cx+4,cx+5      mg - (3 floats) atom magnetic moment along a,b,c in Bohr magnetons 
cs-1                (str) Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') 
cs                  (str) atom drawing style; e.g. 'balls & sticks' 
cs+1                (str) atom label style (e.g. 'name') 
cs+2                (int) atom color (RBG triplet) 
cs+3                (str) ADP flag: Isotropic ('I') or Anisotropic ('A')
cs+4                (float) Uiso 
cs+5...cs+11        (6 floats) U11, U22, U33, U12, U13, U23 
ci                  (int) unique atom identifier; matches source atom Id in Atom Records 
==============   ===================================================================================

.. _Powder_table:

.. index::
   single: Powder data object description
   single: Data object descriptions; Powder Data

Powder Diffraction Tree Items
-----------------------------

Every powder diffraction histogram is stored in the GSAS-II data tree
with a top-level entry named beginning with the string "PWDR ". The
diffraction data for that information are directly associated with
that tree item and there are a series of children to that item. The
routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
load this information into a dictionary where the child tree name is
used as a key, and the information in the main entry is assigned
a key of ``Data``, as outlined below.

.. tabularcolumns:: |p{1in}|p{1in}|p{4in}|

======================     ===============  ===========================================================
  key                       sub-key          explanation
======================     ===============  ===========================================================
Comments                    \\               (list of str) Text strings extracted from the original powder
                                            data header. These cannot be changed by the user;
                                            it may be empty.
Limits                      \\               (list) two two element lists, as [[Ld,Hd],[L,H]]
                                            where L and Ld are the current and default lowest
                                            two-theta value to be used and
                                            where H and Hd are the current and default highest
                                            two-theta value to be used.
Reflection Lists            \\               (dict of dicts) with an entry for each phase in the
                                            histogram. The contents of each dict item
                                            is a dict containing reflections, as described in
                                            the :ref:`Powder Reflections <PowderRefl_table>`
                                            description.
Instrument Parameters       \\               (dict) The instrument parameters uses different dicts 
                                            for the constant wavelength (CW) and time-of-flight (TOF)
                                            cases. See below for the descriptions of each. 
wtFactor                    \\               (float) A weighting factor to increase or decrease
                                            the leverage of data in the histogram .
                                            A value of 1.0 weights the data with their
                                            standard uncertainties and a larger value
                                            increases the weighting of the data (equivalent
                                            to decreasing the uncertainties).
Sample Parameters           \\               (dict) Parameters that describe how
                                            the data were collected, as listed
                                            below. Refinable parameters are a list containing
                                            a float and a bool, where the second value
                                            specifies if the value is refined, otherwise
                                            the value is a float unless otherwise noted.
\\                           Scale           The histogram scale factor (refinable)
\\                           Absorption      The sample absorption coefficient as
                                            :math:`\\mu r` where r is the radius
                                            (refinable). Only valid for Debye-Scherrer geometry.
\\                           SurfaceRoughA   Surface roughness parameter A as defined by
                                            Surotti, *J. Appl. Cryst*, **5**, 325-331, 1972.
                                            (refinable - only valid for Bragg-Brentano geometry)
\\                           SurfaceRoughB   Surface roughness parameter B (refinable -
                                            only valid for Bragg-Brentano geometry)
\\                           DisplaceX,      Sample displacement from goniometer center
                            DisplaceY       where Y is along the beam direction and
                                            X is perpendicular. Units are :math:`\\mu m`
                                            (refinable).
\\                           Phi, Chi,       Goniometer sample setting angles, in degrees.
                            Omega
\\                           Gonio. radius   Radius of the diffractometer in mm
\\                           InstrName       (str) A name for the instrument, used in preparing
                                            a CIF .
\\                           Force,          Variables that describe how the measurement
                            Temperature,    was performed. Not used directly in
                            Humidity,       any computations.
                            Pressure,
                            Voltage
\\                           ranId           (int) The random-number Id for the histogram
                                            (same value as where top-level key is ranId)
\\                           Type            (str) Type of diffraction data, may be 'Debye-Scherrer'
                                            or 'Bragg-Brentano' .
hId                         \\               (int) The number assigned to the histogram when
                                            the project is loaded or edited (can change)
ranId                       \\               (int) A random number id for the histogram
                                            that does not change
Background                  \\               (list) The background is stored as a list with where
                                            the first item in the list is list and the second
                                            item is a dict. The list contains the background
                                            function and its coefficients; the dict contains
                                            Debye diffuse terms and background peaks.
                                            (TODO: this needs to be expanded.)
Data                        \\               (list) The data consist of a list of 6 np.arrays
                                            containing in order:

                                            0. the x-postions (two-theta in degrees),
                                            1. the intensity values (Yobs),
                                            2. the weights for each Yobs value
                                            3. the computed intensity values (Ycalc)
                                            4. the background values
                                            5. Yobs-Ycalc
======================     ===============  ===========================================================

.. _CWPowder_table:

.. index::
   single: Powder data CW Instrument Parameters

-----------------------------
CW Instrument Parameters
-----------------------------

Instrument Parameters are placed in a list of two dicts, 
where the keys in the first dict are listed below. Note that the dict contents are different for 
constant wavelength (CW) vs. time-of-flight (TOF) histograms. 
The value for each item is a list containing three values: the initial value, the current value
and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that
cannot be refined. The first and second values are floats unless otherwise noted.
Items not refined are noted as [*]

.. tabularcolumns:: |l|p{1in}|p{4in}|

========================    ===============  ===========================================================
  key                       sub-key           explanation
========================    ===============  ===========================================================
Instrument Parameters[0]    Type [*]            (str) Histogram type:
                                                * 'PXC' for constant wavelength x-ray
                                                * 'PNC' for constant wavelength neutron
\\                           Bank [*]            (int) Data set number in a multidata file (usually 1)
\\                           Lam                 (float) Specifies a wavelength in :math:`\\AA`
\\                           Lam1 [*]            (float) Specifies the primary wavelength in
                                                :math:`\\AA`, used in place of Lam 
                                                when an :math:`\\alpha_1, \\alpha_2`
                                                source is used.
\\                           Lam2 [*]            (float) Specifies the secondary wavelength in
                                                :math:`\\AA`, used with Lam1
\\                           I(L2)/I(L1)         (float) Ratio of Lam2 to Lam1, used with Lam1
\\                           Zero                (float) Two-theta zero correction in *degrees*
\\                           Azimuth [*]         (float) Azimuthal setting angle for data recorded with differing setting angles
\\                           U, V, W             (float) Cagliotti profile coefficients
                                                for Gaussian instrumental broadening, where the
                                                FWHM goes as
                                                :math:`U \\tan^2\\theta + V \\tan\\theta + W`
\\                           X, Y, Z             (float) Cauchy (Lorentzian) instrumental broadening coefficients
\\                           SH/L                (float) Variant of the Finger-Cox-Jephcoat asymmetric
                                                peak broadening ratio. Note that this is the
                                                sum of S/L and H/L where S is
                                                sample height, H is the slit height and
                                                L is the goniometer diameter.
\\                           Polariz.            (float) Polarization coefficient. 
Instrument Parameters[1]                        (empty dict)
========================    ===============  ===========================================================

.. _TOFPowder_table:

.. index::
   single: Powder data TOF Instrument Parameters

-----------------------------
TOF Instrument Parameters
-----------------------------

Instrument Parameters are also placed in a list of two dicts, 
where the keys in each dict listed below, but here for 
time-of-flight (TOF) histograms. 
The value for each item is a list containing three values: the initial value, the current value
and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that
cannot be refined. The first and second values are floats unless otherwise noted.
Items not refined are noted as [*]

.. tabularcolumns:: |l|p{1.5in}|p{4in}|

========================    ===============  ===========================================================
  key                        sub-key          explanation
========================    ===============  ===========================================================
Instrument Parameters[0]    Type [*]            (str) Histogram type:
                                                * 'PNT' for time of flight neutron
\\                           Bank                (int) Data set number in a multidata file
\\                           2-theta [*]         (float) Nominal scattering angle for the detector
\\                           fltPath [*]         (float) Total flight path source-sample-detector
\\                           Azimuth [*]         (float) Azimuth angle for detector right hand rotation 
                                                from horizontal away from source
\\                           difC,difA,          (float) Diffractometer constants for conversion of d-spacing to TOF
                            difB                in microseconds
\\                           Zero                (float) Zero point offset (microseconds)
\\                           alpha               (float) Exponential rise profile coefficients
\\                           beta-0              (float) Exponential decay profile coefficients
                            beta-1
                            beta-q
\\                           sig-0               (float) Gaussian profile coefficients
                            sig-1
                            sig-2
                            sig-q    
\\                           X,Y,Z               (float) Lorentzian profile coefficients
Instrument Parameters[1]    Pdabc               (list of 4 float lists) Originally created for use in gsas as optional tables 
                                                of d, alp, bet, d-true; for a reflection alpha & beta are obtained via interpolation
                                                from the d-spacing and these tables. The d-true column is apparently unused.
========================    ===============  ===========================================================


.. _PowderRefl_table:

.. index::
   single: Powder reflection object description
   single: Data object descriptions; Powder Reflections

Powder Reflection Data Structure
--------------------------------

For every phase in a histogram, the ``Reflection Lists`` value is a dict
one element of which is `'RefList'`, which is a np.array containing
reflections. The columns in that array are documented below.

==========  ====================================================
  index         explanation
==========  ====================================================
 0,1,2          h,k,l (float)
 3              (int) multiplicity
 4              (float) d-space, :math:`\\AA`
 5              (float) pos, two-theta
 6              (float) sig, Gaussian width
 7              (float) gam, Lorenzian width
 8              (float) :math:`F_{obs}^2`
 9              (float) :math:`F_{calc}^2`
 10             (float) reflection phase, in degrees
 11             (float) intensity correction for reflection, this times
                :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
 12             (float) Preferred orientation correction
 13             (float) Transmission (absorption correction)
 14             (float) Extinction correction
==========  ====================================================

.. _Xtal_table:

.. index::
   single: Single Crystal data object description
   single: Data object descriptions; Single crystal data

Single Crystal Tree Items
-------------------------

Every single crystal diffraction histogram is stored in the GSAS-II data tree
with a top-level entry named beginning with the string "HKLF ". The
diffraction data for that information are directly associated with
that tree item and there are a series of children to that item. The
routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
load this information into a dictionary where the child tree name is
used as a key, and the information in the main entry is assigned
a key of ``Data``, as outlined below.

.. tabularcolumns:: |l|l|p{4in}|

======================  ===============     ====================================================
  key                      sub-key          explanation
======================  ===============     ====================================================
Data                        \\               (dict) that contains the
                                            reflection table,
                                            as described in the
                                            :ref:`Single Crystal Reflections
                                            <XtalRefl_table>`
                                            description.

Instrument Parameters       \\               (list) containing two dicts where the possible
                                            keys in each dict are listed below. The value
                                            for most items is a list containing two values:
                                            the initial value, the current value.
                                            The first and second
                                            values are floats unless otherwise noted.
\\                           Lam             (two floats) Specifies a wavelength in :math:`\\AA` 
\\                           Type            (two str values) Histogram type :
                                            * 'SXC' for constant wavelength x-ray
                                            * 'SNC' for constant wavelength neutron
                                            * 'SNT' for time of flight neutron
\\                           InstrName       (str) A name for the instrument, used in preparing a CIF
wtFactor                    \\               (float) A weighting factor to increase or decrease
                                            the leverage of data in the histogram.
                                            A value of 1.0 weights the data with their
                                            standard uncertainties and a larger value
                                            increases the weighting of the data (equivalent
                                            to decreasing the uncertainties).

hId                         \\               (int) The number assigned to the histogram when
                                            the project is loaded or edited (can change)
ranId                       \\               (int) A random number id for the histogram
                                            that does not change
======================  ===============     ====================================================

.. _XtalRefl_table:

.. index::
   single: Single Crystal reflection object description
   single: Data object descriptions; Single Crystal Reflections

Single Crystal Reflection Data Structure
----------------------------------------

For every single crystal a histogram, the ``'Data'`` item contains
the structure factors as an np.array in item `'RefList'`.
The columns in that array are documented below.

.. tabularcolumns:: |l|p{4in}|

==========  ====================================================
  index         explanation
==========  ====================================================
 0,1,2          (float) h,k,l 
 3              (int) multiplicity
 4              (float) d-space, :math:`\\AA`
 5              (float) :math:`F_{obs}^2`
 6              (float) :math:`\\sigma(F_{obs}^2)`
 7              (float) :math:`F_{calc}^2`
 8              (float) :math:`F_{obs}^2T`
 9              (float) :math:`F_{calc}^2T`
 10             (float) reflection phase, in degrees
 11             (float) intensity correction for reflection, this times
                :math:`F_{obs}^2` or :math:`F_{calc}^2`
                gives Iobs or Icalc
==========  ====================================================

.. _Image_table:

.. index::
   image: Image data object description
   image: Image object descriptions

Image Data Structure
--------------------

Every 2-dimensional image is stored in the GSAS-II data tree
with a top-level entry named beginning with the string "IMG ". The
image data are directly associated with that tree item and there
are a series of children to that item. The routines :func:`GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
load this information into a dictionary where the child tree name is
used as a key, and the information in the main entry is assigned
a key of ``Data``, as outlined below.

.. tabularcolumns:: |l|l|p{4in}|

======================  ======================  ====================================================
  key                      sub-key              explanation
======================  ======================  ====================================================
Comments                    \\                   (list of str) Text strings extracted from the original image data
                                                header or a metafile. These cannot be changed by
                                                the user; it may be empty.
Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
                                                value. Accomodates
                                                detector orientations other than with the detector
                                                X-axis
                                                horizontal.
\\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
                                                during image integration multiplied by value. It must have the same size/shape as
                                                the integrated image. NB: value < 0 for subtraction.
\\                           calibrant           (str) The material used for determining the position/orientation
                                                of the image. The data is obtained from :func:`ImageCalibrants`
                                                and UserCalibrants.py (supplied by user).
\\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
\\                           calibskip           (int) The number of expected diffraction lines skipped during the last
                                                calibration run.
\\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
                                                strikes the detector plane as determined by calibration. This point
                                                does not have to be within the limits of the detector boundaries.
\\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
                                                of the image is at the center line otherwise it is at the leading edge.
\\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
\\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
                                                calibration calculations. See pixLimit for details as how point is found.
\\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
                                                ring offset at higher angles. Optionally determined by calibration.
\\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
\\                           distance            (float) The distance (mm) from sample to detector plane.
\\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
\\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
\\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
\\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
                                                Required for texture calculations.
\\                           invert_x            (bool) If True display the image with the x-axis inverted.
\\                           invert_y            (bool) If True display the image with the y-axis inverted.
\\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
\\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
\\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
                                                intensities obtained during integration.
\\                           outAzimuths         (int) The number of azimuth pie slices.
\\                           outChannels         (int) The number of 2-theta steps.
\\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
\\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
                                                Locations are used to construct rings of points for calibration calcualtions.
\\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
                                                integration using value.
\\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
                                                diffraction ring with the same d-spacing (dsp)
\\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
                                                selected by the user,
\\                           Range               (list) The minimum & maximum values of the image
\\                           rotation            (float) The angle between the x-axis and the vector about which the
                                                detector is tilted. Constrained to -180 to 180 deg.
\\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
                                                calculations.
\\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
                                                to cause correction to be applied.
\\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
\\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.
\\                           showLines           (bool) If True then isplay the integration limits to be used.
\\                           size                (list:int) The number of pixels on the image x & y axes
\\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
\\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
\\                           wavelength          (float) The radiation wavelength (:math:`\\AA`) as entered by the user 
                                                (or someday obtained from the image header).
Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
                                                to be excluded from integration
\\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
                                                of which is excluded from recalibration and integration. Only one frame is allowed.
\\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
                                                from integration.
\\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
                                                to be excluded from integration.
\\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
                                                to be excluded from integration.
\\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.
\\                           SpotMask            (dict: int & array)
                                                'esdMul'(int) number of standard deviations above mean ring intensity to mask
                                                'spotMask' (bool array) the spot mask for every pixel in image         

Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
\\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
                                                These will be restricted by space group symmetry; result of strain fit refinement.
\\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
\\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
                                                and are used to determine the strain tensor.
                                                The dictionary items are:
                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
                                                'Esig': (list: float) Esds for Emat from fitting.
                                                'pixLimit': (int) Search range to find highest point on ring for each data point
                                                'cutoff': (float) I/Ib cutoff for searching.
                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.

======================  ======================  ====================================================

.. _parmDict_table:

.. index::
   single: Parameter dictionary

Parameter Dictionary
-------------------------

The parameter dictionary contains all of the variable parameters for the refinement.
The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
It is prepared in two ways. When loaded from the tree
(in :meth:`GSASIIdataGUI.GSASII.MakeLSParmDict` and
:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
the values are lists with two elements: ``[value, refine flag]``

When loaded from the GPX file (in
:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
dict is the actual parameter value (usually a float, but sometimes a
letter or string flag value (such as I or A for iso/anisotropic).

Texture implementation
------------------------------

There are two different places where texture can be treated in GSAS-II. 
One is for mitigating the effects of texture in a structural refinement.
The other is for texture characterization. 

For reducing the effect of texture in a structural refinement
there are entries labeled preferred orientation in each phase's
data tab. Two different 
approaches can be used for this, the March-Dollase model and 
spherical harmonics.
For the March-Dollase model, one axis in reciprocal space is designated as 
unique (defaulting to the 001 axis) and reflections are corrected 
according to the angle they make with this axis depending on 
the March-Dollase ratio. (If unity, no correction is made). 
The ratio can be greater than one or less than one depending on if 
crystallites oriented along the designated axis are 
overrepresented or underrepresented. For most crystal systems there is an 
obvious choice for the direction of the unique axis and then only a single
term needs to be refined. If the number is close to 1, then the correction 
is not needed. 

The second method for reducing the effect of texture in a structural 
refinement is to create a probability surface as an expansion in 
terms spherical harmonic functions. Only functions consistent with 
cylindrical diffraction suymmetry and having texture symmetry 
consistent with the Laue class of phase are used and are allowed, 
so the higher the symmetry 
the fewer terms that are available for a given spherical harmonics order. 
For use of this correction, select the lowest order that provides 
refinable terms and perform a refinement. If the texture index remains close to 
one, then the correction is not needed. If a significant improvement is 
noted in the profile Rwp, one may wish to see if a higher order expansion
gives an even larger improvement. 

To characterize texture in a material, one needs data collected with the 
sample at multiple orientations or, for TOF, with detectors at multiple 
locations around the sample. In this case the detector orientation is given in 
each histogram's Sample Parameters and the sample's orientation is described 
with the Euler angles specifed on the phase's Texture tab, which is also 
where the texture type (cylindrical, rolling,...) and the sherical 
harmonic order is selected. This should not be used with a single dataset and 
should not be used if the preferred orientations corrections are used. 

The coordinate system used for texture characterization is defined where 
the sample coordinates (Psi, gamma) are defined with an instrument coordinate
system (I, J, K) such that I is normal to the diffraction plane and J is coincident with the
direction of the incident radiation beam pointing away from the source. We further define
a standard set of right-handed goniometer eulerian angles (Omega, Chi, Phi) so that Omega and Phi are
rotations about I and Chi is a rotation about J when Omega, Chi, Phi = 0. Finally, as the sample
may be mounted so that the sample coordinate system (Is, Js, Ks) does not coincide with
the instrument coordinate system (I, J, K), we define three eulerian sample rotation angles
(Omega-s, Chi-s, Phi-s) that describe the rotation from (I, J, K) to (Is, Js, Ks). The sample rotation
angles are defined so that with the goniometer angles at zero Omega-s and Phi-s are rotations
about I and Chi-s is a rotation about J.

ISODISTORT implementation
------------------------------

CIFs prepared with the ISODISTORT web site 
https://stokes.byu.edu/iso/isodistort_version5.6.1/isodistort.php
[B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, "ISODISPLACE: An Internet Tool for Exploring Structural Distortions." J. Appl. Cryst. 39, 607-614 (2006).]
can be read into GSAS-II using import CIF. This will cause constraints to be established for structural distortion modes read from the CIF.
At present, of the five types of modes  only displacive(``_iso_displacivemode``...) and occupancy (``_iso_occupancymode``...) are processed. Not yet processed: ``_iso_magneticmode``..., ``_iso_rotationalmode``... & ``_iso_strainmode``...

The CIF importer :mod:`G2phase_CIF` implements class :class:`G2phase_CIF.CIFPhaseReader` which offers two methods associated with ISODISTORT (ID) input. Method :meth:`G2phase_CIF.CIFPhaseReader.ISODISTORT_test`
checks to see if a CIF block contains the loops with ``_iso_displacivemode_label`` or  ``_iso_occupancymode_label`` items.
If so, method :meth:`G2phase_CIF.CIFPhaseReader.ISODISTORT_proc` is called to read and interpret them.
The results are placed into the reader object's ``.Phase`` class variable as a dict item with key ``'ISODISTORT'``. 

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 :func:`G2phase_CIF.ISODISTORT_shortLbl` is used to create a short name for this,
such as R5_T1u(a) which is made unique by addition of _n if the short name is duplicated.
As each mode is processed, a constraint corresponding to that mode is 
created and is added to list in the reader object's ``.Constraints`` class variable. Items placed into that list can either be a list, which corresponds to a function (new var) type :ref:`constraint definition <Constraints_table>` entry, or an item can be a dict, which provides help information for each constraint.

------------------------------
Displacive modes
------------------------------

The coordinate variables, as named by ISODISTORT, are placed in 
``.Phase['ISODISTORT']['IsoVarList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2VarList']``. The mode variables,
as named by ISODISTORT, are placed in ``.Phase['ISODISTORT']['IsoModeList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2ModeList']``.
[Use ``str(G2VarObj)`` to get the variable name from the G2VarObj object, but note that the phase number, *n*, for the prefix "*n*::" cannot be determined as the phase number is not yet assigned.]

Displacive modes are a bit complex in that they relate to delta displacements, relative to an offset value for each coordinate, and because the modes are normalized, while GSAS-II also uses displacements, but these are added to the coordinates after each refinement cycle and the delta values are set to zero. ISODISTORT uses fixed offsets (subtracted from the actual position to obtain the delta values) that are taken from ``_iso_coordinate_formula`` and these are placed in ``.Phase['ISODISTORT']['ParentStructure]`` (keyed by atom label). The normalization factors (which the delta values are divided by) are taken from ``_iso_displacivemodenorm_value`` and are placed in ``.Phase['ISODISTORT']['NormList']`` in the same order as as ``...['IsoModeList']`` and
``...['G2ModeList']``.

The CIF contains a sparse matrix, from the ``loop_`` containing 
``_iso_displacivemodematrix_value`` which provides the equations for determining the mode values from the coordinates, that matrix is placed in ``.Phase['ISODISTORT']['Mode2VarMatrix']``. The matrix is inverted to produce
``.Phase['ISODISTORT']['Var2ModeMatrix']``, which determines how to compute the
mode values from the delta coordinate values. These values are used for the 
in :func:`GSASIIconstrGUI.ShowIsoDistortCalc` which shows coordinate and mode
values, the latter with s.u. values. 


------------------------------
Occupancy modes
------------------------------


The delta occupancy variables, as named by ISODISTORT, are placed in 
``.Phase['ISODISTORT']['OccVarList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2OccVarList']``. The mode variables, as named by ISODISTORT, are placed in ``.Phase['ISODISTORT']['OccModeList']`` and the corresponding :class:`GSASIIobj.G2VarObj` objects for each are placed in ``.Phase['ISODISTORT']['G2OccModeList']``.

Occupancy modes, like Displacive modes, are also refined as delta values.  However, GSAS-II directly refines the fractional occupancies. 
Offset values for each atom, are taken from ``_iso_occupancy_formula`` and are placed in 
``.Phase['ISODISTORT']['ParentOcc]``. 
(Offset values are subtracted from the actual position to obtain the delta values.) 
Modes are normalized (where the mode values are divided by the normalization factor) 
are taken from ``_iso_occupancymodenorm_value`` and are placed in ``.Phase['ISODISTORT']['OccNormList']`` in the same order as as ``...['OccModeList']`` and
``...['G2OccModeList']``.

The CIF contains a sparse matrix, from the ``loop_`` containing 
``_iso_occupancymodematrix_value``, which provides the equations for determining the mode values from the coordinates. That matrix is placed in ``.Phase['ISODISTORT']['Occ2VarMatrix']``. The matrix is inverted to produce
``.Phase['ISODISTORT']['Var2OccMatrix']``, which determines how to compute the
mode values from the delta coordinate values.


------------------------------
Mode Computations
------------------------------

Constraints are processed after the CIF has been read in
:meth:`GSASIIdataGUI.GSASII.OnImportPhase` or  
:meth:`GSASIIscriptable.G2Project.add_phase` by moving them from the reader
object's ``.Constraints`` class variable to 
the Constraints tree entry's ['Phase'] list (for list items defining constraints) or
the Constraints tree entry's ['_Explain'] dict (for dict items defining constraint help information)

The information in ``.Phase['ISODISTORT']`` is used 
in :func:`GSASIIconstrGUI.ShowIsoDistortCalc` which shows coordinate and mode
values, the latter with s.u. values. This can be called from the Constraints and Phase/Atoms tree items. 

Before each refinement, constraints are processed as
:ref:`described elsewhere <Constraints_processing>`. After a refinement
is complete, :func:`GSASIImapvars.PrintIndependentVars` shows the
shifts and s.u.'s on the refined modes, using GSAS-II values, but 
:func:`GSASIIstrIO.PrintISOmodes` prints the ISODISTORT modes as computed
in the web site.


.. _ParameterLimits:

.. index::
   single: Parameter limits

Parameter Limits
------------------------------

One of the most often requested "enhancements" for GSAS-II would be the inclusion 
of constraints to force parameters such as occupancies or Uiso values to stay within 
expected ranges. While it is possible for users to supply their own restraints that would
perform this by supplying an appropriate expression with the "General" restraints, the 
GSAS-II authors do not feel that use of restraints or constraints are a good solution for
this common problem where parameters refine to non-physical values. This is because when 
this occurs, most likely one of the following cases is occurring: 

#. there is a significant problem 
   with the model, for example for an x-ray fit if an O atom is placed where a S is actually 
   present, the Uiso will refine artificially small or the occupancy much larger than unity 
   to try to compensate for the missing electrons; or
 
#. the data are simply insensitive 
   to the parameter or combination of parameters, for example unless very high-Q data 
   are included, the effects of a occupancy and Uiso value can have compensating effects,
   so an assumption must be made; likewise, with neutron data natural-abundance V atoms 
   are nearly invisible due to weak coherent scattering. No parameters can be fit for a 
   V atom with neutrons.

#. the parameter is non-physical (such as a negative Uiso value) but within 
   two sigma (sigma = standard uncertainty, aka e.s.d.) of a reasonable value, 
   in which case the
   value is not problematic as it is experimentally indistinguishable from an 
   expected value.  

#. there is a systematic problem with the data (experimental error)

In all these cases, this situation needs to be reviewed by a crystallographer to decide 
how to best determine a structural model for these data. An implementation with a constraint
or restraint is likely to simply hide the problem from the user, making it more probable 
that a poor model choice is obtained. 

What GSAS-II does implement is to allow users to specify ranges for parameters 
that works by disabling 
refinement of parameters that refine beyond either a lower limit or an upper limit, where 
either or both may be optionally specified. Parameters limits are specified in the Controls 
tree entry in dicts named as ``Controls['parmMaxDict']`` and ``Controls['parmMinDict']``, where 
the keys are :class:`G2VarObj` objects corresponding to standard GSAS-II variable 
(see :func:`getVarDescr` and :func:`CompileVarDesc`) names, where a 
wildcard ('*') may optionally be used for histogram number or atom number 
(phase number is intentionally not  allowed as a wildcard as it makes little sense 
to group the same parameter together different phases). Note
that :func:`prmLookup` is used to see if a name matches a wildcard. The upper or lower limit
is placed into these dicts as a float value. These values can be edited using the window 
created by the Calculate/"View LS parms" menu command or in scripting with the 
:meth:`GSASIIscriptable.G2Project.set_Controls` function. 
In the GUI, a checkbox labeled "match all histograms/atoms" is used to insert a wildcard
into the appropriate part of the variable name.

When a refinement is conducted, routine :func:`GSASIIstrMain.dropOOBvars` is used to 
find parameters that have refined to values outside their limits. If this occurs, the parameter
is set to the limiting value and the variable name is added to a list of frozen variables 
(as a :class:`G2VarObj` objects) kept in a list in the
``Controls['parmFrozen']`` dict. In a sequential refinement, this is kept separate for 
each histogram as a list in 
``Controls['parmFrozen'][histogram]`` (where the key is the histogram name) or as a list in 
``Controls['parmFrozen']['FrozenList']`` for a non-sequential fit. 
This allows different variables
to be frozen in each section of a sequential fit. 
Frozen parameters are not included in refinements through removal from the 
list of parameters to be refined (``varyList``) in :func:`GSASIIstrMain.Refine` or 
:func:`GSASIIstrMain.SeqRefine`. 
The data window for the Controls tree item shows the number of Frozen variables and
the individual variables can be viewed with the Calculate/"View LS parms" menu window or 
obtained with :meth:`GSASIIscriptable.G2Project.get_Frozen`.
Once a variable is frozen, it will not be refined in any 
future refinements unless the the variable is removed (manually) from the list. This can also 
be done with the Calculate/"View LS parms" menu window or 
:meth:`GSASIIscriptable.G2Project.set_Frozen`.


.. seealso::
  :class:`G2VarObj`
  :func:`getVarDescr` 
  :func:`CompileVarDesc`
  :func:`prmLookup`
  :class:`GSASIIctrlGUI.ShowLSParms`
  :class:`GSASIIctrlGUI.VirtualVarBox`
  :func:`GSASIIstrIO.SetUsedHistogramsAndPhases`
  :func:`GSASIIstrIO.SaveUpdatedHistogramsAndPhases`
  :func:`GSASIIstrIO.SetSeqResult`
  :func:`GSASIIstrMain.dropOOBvars`
  :meth:`GSASIIscriptable.G2Project.set_Controls`
  :meth:`GSASIIscriptable.G2Project.get_Frozen`
  :meth:`GSASIIscriptable.G2Project.set_Frozen`

*Classes and routines*
----------------------

'''
from __future__ import division, print_function
import platform
import re
import random as ran
import sys
import os.path as ospath
if '2' in platform.python_version_tuple()[0]:
    import cPickle
else:
    import pickle as cPickle
import GSASIIpath
import GSASIImath as G2mth
import GSASIIspc as G2spc
import numpy as np

GSASIIpath.SetVersionNumber("$Revision: 4661 $")

DefaultControls = {
    'deriv type':'analytic Hessian',
    'min dM/M':0.001,'shift factor':1.,'max cyc':3,'F**2':False,'SVDtol':1.e-6,
    'UsrReject':{'minF/sig':0.,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
    'Copy2Next':False,'Reverse Seq':False,'HatomFix':False,
    'Author':'no name',
    'FreePrm1':'Sample humidity (%)',
    'FreePrm2':'Sample voltage (V)',
    'FreePrm3':'Applied load (MN)',
    'ShowCell':False,
    }
'''Values to be used as defaults for the initial contents of the ``Controls``
data tree item.
'''
def StripUnicode(string,subs='.'):
    '''Strip non-ASCII characters from strings

    :param str string: string to strip Unicode characters from
    :param str subs: character(s) to place into string in place of each
      Unicode character. Defaults to '.'

    :returns: a new string with only ASCII characters
    '''
    s = ''
    for c in string:
        if ord(c) < 128:
            s += c
        else:
            s += subs
    return s
#    return s.encode('ascii','replace')

def MakeUniqueLabel(lbl,labellist):
    '''Make sure that every a label is unique against a list by adding
    digits at the end until it is not found in list.

    :param str lbl: the input label
    :param list labellist: the labels that have already been encountered
    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
      ``_10-99``, etc.) appended at the end
    '''
    lbl = StripUnicode(lbl.strip(),'_')
    if not lbl: # deal with a blank label
        lbl = '_1'
    if lbl not in labellist:
        labellist.append(lbl)
        return lbl
    i = 1
    prefix = lbl
    if '_' in lbl:
        prefix = lbl[:lbl.rfind('_')]
        suffix = lbl[lbl.rfind('_')+1:]
        try:
            i = int(suffix)+1
        except: # suffix could not be parsed
            i = 1
            prefix = lbl
    while prefix+'_'+str(i) in labellist:
        i += 1
    else:
        lbl = prefix+'_'+str(i)
        labellist.append(lbl)
    return lbl

PhaseIdLookup = {}
'''dict listing phase name and random Id keyed by sequential phase index as a str;
best to access this using :func:`LookupPhaseName`
'''
PhaseRanIdLookup = {}
'''dict listing phase sequential index keyed by phase random Id;
best to access this using :func:`LookupPhaseId`
'''
HistIdLookup = {}
'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
best to access this using :func:`LookupHistName`
'''
HistRanIdLookup = {}
'''dict listing histogram sequential index keyed by histogram random Id;
best to access this using :func:`LookupHistId`
'''
AtomIdLookup = {}
'''dict listing for each phase index as a str, the atom label and atom random Id,
keyed by atom sequential index as a str;
best to access this using :func:`LookupAtomLabel`
'''
AtomRanIdLookup = {}
'''dict listing for each phase the atom sequential index keyed by atom random Id;
best to access this using :func:`LookupAtomId`
'''
ShortPhaseNames = {}
'''a dict containing a possibly shortened and when non-unique numbered
version of the phase name. Keyed by the phase sequential index.
'''
ShortHistNames = {}
'''a dict containing a possibly shortened and when non-unique numbered
version of the histogram name. Keyed by the histogram sequential index.
'''

#VarDesc = {}  # removed 1/30/19 BHT as no longer needed (I think)
#''' This dictionary lists descriptions for GSAS-II variables,
#as set in :func:`CompileVarDesc`. See that function for a description
#for how keys and values are written.
#'''

reVarDesc = {}
''' This dictionary lists descriptions for GSAS-II variables where
keys are compiled regular expressions that will match the name portion
of a parameter name. Initialized in :func:`CompileVarDesc`.
'''

reVarStep = {}
''' This dictionary lists the preferred step size for numerical 
derivative computation w/r to a GSAS-II variable. Keys are compiled 
regular expressions and values are the step size for that parameter. 
Initialized in :func:`CompileVarDesc`.
'''
# create a default space group object for P1; N.B. fails when building documentation
try:
    P1SGData = G2spc.SpcGroup('P 1')[1] # data structure for default space group
except:
    pass

def GetPhaseNames(fl):
    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
    NB: there is another one of these in GSASIIstrIO.py that uses the gpx filename

    :param file fl: opened .gpx file
    :return: list of phase names
    '''
    PhaseNames = []
    while True:
        try:
            data = cPickle.load(fl)
        except EOFError:
            break
        datum = data[0]
        if 'Phases' == datum[0]:
            for datus in data[1:]:
                PhaseNames.append(datus[0])
    fl.seek(0)          #reposition file
    return PhaseNames

def SetNewPhase(Name='New Phase',SGData=None,cell=None,Super=None):
    '''Create a new phase dict with default values for various parameters

    :param str Name: Name for new Phase

    :param dict SGData: space group data from :func:`GSASIIspc:SpcGroup`;
      defaults to data for P 1

    :param list cell: unit cell parameter list; defaults to
      [1.0,1.0,1.0,90.,90,90.,1.]

    '''
    if SGData is None: SGData = P1SGData
    if cell is None: cell=[1.0,1.0,1.0,90.,90.,90.,1.]
    phaseData = {
        'ranId':ran.randint(0,sys.maxsize),
        'General':{
            'Name':Name,
            'Type':'nuclear',
            'Modulated':False,
            'AtomPtrs':[3,1,7,9],
            'SGData':SGData,
            'Cell':[False,]+cell,
            'Pawley dmin':1.0,
            'Data plot type':'None',
            'SH Texture':{
                'Order':0,
                'Model':'cylindrical',
                'Sample omega':[False,0.0],
                'Sample chi':[False,0.0],
                'Sample phi':[False,0.0],
                'SH Coeff':[False,{}],
                'SHShow':False,
                'PFhkl':[0,0,1],
                'PFxyz':[0,0,1],
                'PlotType':'Pole figure',
                'Penalty':[['',],0.1,False,1.0]}},
        'Atoms':[],
        'Drawing':{},
        'Histograms':{},
        'Pawley ref':[],
        'RBModels':{},
        }
    if Super and Super.get('Use',False):
        phaseData['General'].update({'Modulated':True,'Super':True,'SuperSg':Super['ssSymb']})
        phaseData['General']['SSGData'] = G2spc.SSpcGroup(SGData,Super['ssSymb'])[1]
        phaseData['General']['SuperVec'] = [Super['ModVec'],False,Super['maxH']]

    return phaseData

def ReadCIF(URLorFile):
    '''Open a CIF, which may be specified as a file name or as a URL using PyCifRW
    (from James Hester).
    The open routine gets confused with DOS names that begin with a letter and colon
    "C:\\dir\" so this routine will try to open the passed name as a file and if that
    fails, try it as a URL

    :param str URLorFile: string containing a URL or a file name. Code will try first
      to open it as a file and then as a URL.

    :returns: a PyCifRW CIF object.
    '''
    import CifFile as cif # PyCifRW from James Hester

    # alternate approach:
    #import urllib
    #ciffile = 'file:'+urllib.pathname2url(filename)

    try:
        fp = open(URLorFile,'r')
        cf = cif.ReadCif(fp)
        fp.close()
        return cf
    except IOError:
        return cif.ReadCif(URLorFile)

def TestIndexAll():
    '''Test if :func:`IndexAllIds` has been called to index all phases and 
    histograms (this is needed before :func:`G2VarObj` can be used. 

    :returns: Returns True if indexing is needed.
    '''
    if PhaseIdLookup or AtomIdLookup or HistIdLookup:
        return False
    return True
        
def IndexAllIds(Histograms,Phases):
    '''Scan through the used phases & histograms and create an index
    to the random numbers of phases, histograms and atoms. While doing this,
    confirm that assigned random numbers are unique -- just in case lightning
    strikes twice in the same place.

    Note: this code assumes that the atom random Id (ranId) is the last
    element each atom record.

    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
    (which loads the histograms and phases from a GPX file),
    :meth:`~GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree`
    (which loads the histograms and phases from the data tree.) and
    :meth:`GSASIIconstrGUI.UpdateConstraints`
    (which displays & edits the constraints in a GUI)

    TODO: do we need a lookup for rigid body variables?
    '''
    # process phases and atoms
    PhaseIdLookup.clear()
    PhaseRanIdLookup.clear()
    AtomIdLookup.clear()
    AtomRanIdLookup.clear()
    ShortPhaseNames.clear()
    for ph in Phases:
        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
        ranId = Phases[ph]['ranId']
        while ranId in PhaseRanIdLookup:
            # Found duplicate random Id! note and reassign
            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxsize)
        pId = str(Phases[ph]['pId'])
        PhaseIdLookup[pId] = (ph,ranId)
        PhaseRanIdLookup[ranId] = pId
        shortname = ph  #[:10]
        while shortname in ShortPhaseNames.values():
            shortname = ph[:8] + ' ('+ pId + ')'
        ShortPhaseNames[pId] = shortname
        AtomIdLookup[pId] = {}
        AtomRanIdLookup[pId] = {}
        for iatm,at in enumerate(Phases[ph]['Atoms']):
            ranId = at[cia+8]
            while ranId in AtomRanIdLookup[pId]: # check for dups
                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
                at[cia+8] = ranId = ran.randint(0,sys.maxsize)
            AtomRanIdLookup[pId][ranId] = str(iatm)
            if Phases[ph]['General']['Type'] == 'macromolecular':
                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
            else:
                label = at[ct-1]
            AtomIdLookup[pId][str(iatm)] = (label,ranId)
    # process histograms
    HistIdLookup.clear()
    HistRanIdLookup.clear()
    ShortHistNames.clear()
    for hist in Histograms:
        ranId = Histograms[hist]['ranId']
        while ranId in HistRanIdLookup:
            # Found duplicate random Id! note and reassign
            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxsize)
        hId = str(Histograms[hist]['hId'])
        HistIdLookup[hId] = (hist,ranId)
        HistRanIdLookup[ranId] = hId
        shortname = hist[:15]
        while shortname in ShortHistNames.values():
            shortname = hist[:11] + ' ('+ hId + ')'
        ShortHistNames[hId] = shortname

def LookupAtomId(pId,ranId):
    '''Get the atom number from a phase and atom random Id

    :param int/str pId: the sequential number of the phase
    :param int ranId: the random Id assigned to an atom

    :returns: the index number of the atom (str)
    '''
    if not AtomRanIdLookup:
        raise Exception('Error: LookupAtomId called before IndexAllIds was run')
    if pId is None or pId == '':
        raise KeyError('Error: phase is invalid (None or blank)')
    pId = str(pId)
    if pId not in AtomRanIdLookup:
        raise KeyError('Error: LookupAtomId does not have phase '+pId)
    if ranId not in AtomRanIdLookup[pId]:
        raise KeyError('Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']')
    return AtomRanIdLookup[pId][ranId]

def LookupAtomLabel(pId,index):
    '''Get the atom label from a phase and atom index number

    :param int/str pId: the sequential number of the phase
    :param int index: the index of the atom in the list of atoms

    :returns: the label for the atom (str) and the random Id of the atom (int)
    '''
    if not AtomIdLookup:
        raise Exception('Error: LookupAtomLabel called before IndexAllIds was run')
    if pId is None or pId == '':
        raise KeyError('Error: phase is invalid (None or blank)')
    pId = str(pId)
    if pId not in AtomIdLookup:
        raise KeyError('Error: LookupAtomLabel does not have phase '+pId)
    if index not in AtomIdLookup[pId]:
        raise KeyError('Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']')
    return AtomIdLookup[pId][index]

def LookupPhaseId(ranId):
    '''Get the phase number and name from a phase random Id

    :param int ranId: the random Id assigned to a phase
    :returns: the sequential Id (pId) number for the phase (str)
    '''
    if not PhaseRanIdLookup:
        raise Exception('Error: LookupPhaseId called before IndexAllIds was run')
    if ranId not in PhaseRanIdLookup:
        raise KeyError('Error: LookupPhaseId does not have ranId '+str(ranId))
    return PhaseRanIdLookup[ranId]

def LookupPhaseName(pId):
    '''Get the phase number and name from a phase Id

    :param int/str pId: the sequential assigned to a phase
    :returns:  (phase,ranId) where phase is the name of the phase (str)
      and ranId is the random # id for the phase (int)
    '''
    if not PhaseIdLookup:
        raise Exception('Error: LookupPhaseName called before IndexAllIds was run')
    if pId is None or pId == '':
        raise KeyError('Error: phase is invalid (None or blank)')
    pId = str(pId)
    if pId not in PhaseIdLookup:
        raise KeyError('Error: LookupPhaseName does not have index '+pId)
    return PhaseIdLookup[pId]

def LookupHistId(ranId):
    '''Get the histogram number and name from a histogram random Id

    :param int ranId: the random Id assigned to a histogram
    :returns: the sequential Id (hId) number for the histogram (str)
    '''
    if not HistRanIdLookup:
        raise Exception('Error: LookupHistId called before IndexAllIds was run')
    if ranId not in HistRanIdLookup:
        raise KeyError('Error: LookupHistId does not have ranId '+str(ranId))
    return HistRanIdLookup[ranId]

def LookupHistName(hId):
    '''Get the histogram number and name from a histogram Id

    :param int/str hId: the sequential assigned to a histogram
    :returns:  (hist,ranId) where hist is the name of the histogram (str)
      and ranId is the random # id for the histogram (int)
    '''
    if not HistIdLookup:
        raise Exception('Error: LookupHistName called before IndexAllIds was run')
    if hId is None or hId == '':
        raise KeyError('Error: histogram is invalid (None or blank)')
    hId = str(hId)
    if hId not in HistIdLookup:
        raise KeyError('Error: LookupHistName does not have index '+hId)
    return HistIdLookup[hId]

def fmtVarDescr(varname):
    '''Return a string with a more complete description for a GSAS-II variable

    :param str varname: A full G2 variable name with 2 or 3 or 4
       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])

    :returns: a string with the description
    '''
    s,l = VarDescr(varname)
    return s+": "+l

def VarDescr(varname):
    '''Return two strings with a more complete description for a GSAS-II variable

    :param str name: A full G2 variable name with 2 or 3 or 4
       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])

    :returns: (loc,meaning) where loc describes what item the variable is mapped
      (phase, histogram, etc.) and meaning describes what the variable does.
    '''

    # special handling for parameter names without a colon
    # for now, assume self-defining
    if varname.find(':') == -1:
        return "Global",varname

    l = getVarDescr(varname)
    if not l:
        return ("invalid variable name ("+str(varname)+")!"),""
#        return "invalid variable name!",""

    if not l[-1]:
        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"

    if len(l) == 3:         #SASD variable name!
        s = 'component:'+l[1]
        return s,l[-1]
    s = ""
    if l[0] is not None and l[1] is not None: # HAP: keep short
        if l[2] == "Scale": # fix up ambigous name
            l[5] = "Phase fraction"
        if l[0] == '*':
            lbl = 'Seq. ref.'
        else:
            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
        if l[1] == '*':
            hlbl = 'Seq. ref.'
        else:
            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
        if hlbl[:4] == 'HKLF':
            hlbl = 'Xtl='+hlbl[5:]
        elif hlbl[:4] == 'PWDR':
            hlbl = 'Pwd='+hlbl[5:]
        else:
            hlbl = 'Hist='+hlbl
        s = "Ph="+str(lbl)+" * "+str(hlbl)
    else:
        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
            l[5] = "Scale factor"
        if l[2] == 'Back': # background parameters are "special", alas
            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
            l[-1] += ' #'+str(l[3])
        elif l[4] is not None: # rigid body parameter or modulation parm
            lbl = ShortPhaseNames.get(l[0],'phase?')
            if 'RB' in l[2]:    #rigid body parm
                s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
            else: #modulation parm
                s = 'Atom %s wave %s in %s'%(LookupAtomLabel(l[0],l[3])[0],l[4],lbl)
        elif l[3] is not None: # atom parameter,
            lbl = ShortPhaseNames.get(l[0],'phase?')
            try:
                albl = LookupAtomLabel(l[0],l[3])[0]
            except KeyError:
                albl = 'Atom?'
            s = "Atom "+str(albl)+" in "+str(lbl)
        elif l[0] == '*':
            s = "All phases "
        elif l[0] is not None:
            lbl = ShortPhaseNames.get(l[0],'phase?')
            s = "Phase "+str(lbl)
        elif l[1] == '*':
            s = 'All hists'
        elif l[1] is not None:
            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
            if hlbl[:4] == 'HKLF':
                hlbl = 'Xtl='+hlbl[5:]
            elif hlbl[:4] == 'PWDR':
                hlbl = 'Pwd='+hlbl[5:]
            else:
                hlbl = 'Hist='+hlbl
            s = str(hlbl)
    if not s:
        s = 'Global'
    return s,l[-1]

def getVarDescr(varname):
    '''Return a short description for a GSAS-II variable

    :param str name: A full G2 variable name with 2 or 3 or 4
       colons (<p>:<h>:name[:<a1>][:<a2>])

    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
      the histogram number and the atom number; `name` will always be
      a str; and `description` is str or `None`.
      If the variable name is incorrectly formed (for example, wrong
      number of colons), `None` is returned instead of a list.
    '''
    l = varname.split(':')
    if len(l) == 2:     #SASD parameter name
        return varname,l[0],getDescr(l[1])
    if len(l) == 3:
        l += [None,None]
    elif len(l) == 4:
        l += [None]
    elif len(l) != 5:
        return None
    for i in (0,1,3,4):
        if l[i] == "":
            l[i] = None
    l += [getDescr(l[2])]
    return l

def CompileVarDesc():
    '''Set the values in the variable lookup tables 
    (:attr:`reVarDesc` and :attr:`reVarStep`).
    This is called in :func:`getDescr` and :func:`getVarStep` so this
    initialization is always done before use.

    Note that keys may contain regular expressions, where '[xyz]'
    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range 
    of values). '.*' matches any string. For example::

    'AUiso':'Atomic isotropic displacement parameter',

    will match variable ``'p::AUiso:a'``.
    If parentheses are used in the key, the contents of those parentheses can be
    used in the value, such as::

    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',

    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
    in the value when used.

    '''
    if reVarDesc: return # already done
    for key,value in {
        # derived or other sequential vars
        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
        # ambiguous, alas:
        'Scale' : 'Phase or Histogram scale factor',
        # Phase vars (p::<var>)
        'A([0-5])' : ('Reciprocal metric tensor component \\1',1e-5),
        '[vV]ol' : 'Unit cell volume', # probably an error that both upper and lower case are used
        # Atom vars (p::<var>:a)
        'dA([xyz])$' : ('change to atomic coordinate, \\1',1e-6),
        'A([xyz])$' : '\\1 fractional atomic coordinate',
        'AUiso':('Atomic isotropic displacement parameter',1e-4),
        'AU([123][123])':('Atomic anisotropic displacement parameter U\\1',1e-4),
        'Afrac': ('Atomic site fraction parameter',1e-5),
        'Amul': 'Atomic site multiplicity value',
        'AM([xyz])$' : 'Atomic magnetic moment parameter, \\1',
        # Hist & Phase (HAP) vars (p:h:<var>)
        'Back': 'Background term',
        'BkPkint;(.*)':'Background peak #\\1 intensity',
        'BkPkpos;(.*)':'Background peak #\\1 position',
        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
        'D([123][123])' : 'Anisotropic strain coef. \\1',
        'Extinction' : 'Extinction coef.',
        'MD' : 'March-Dollase coef.',
        'Mustrain;.*' : 'Microstrain coef.',
        'Size;.*' : 'Crystallite size value',
        'eA$' : 'Cubic mustrain value',
        'Ep$' : 'Primary extinction',
        'Es$' : 'Secondary type II extinction',
        'Eg$' : 'Secondary type I extinction',
        'Flack' : 'Flack parameter',
        'TwinFr' : 'Twin fraction',
        'Layer Disp'  : 'Layer displacement along beam',
        #Histogram vars (:h:<var>)
        'Absorption' : 'Absorption coef.',
        'Displace([XY])' : ('Debye-Scherrer sample displacement \\1',0.1),
        'Lam' : ('Wavelength',1e-6),
        'I\\(L2\\)\\/I\\(L1\\)' : ('Ka2/Ka1 intensity ratio',0.001),
        'Polariz\\.' : ('Polarization correction',1e-3),
        'SH/L' : ('FCJ peak asymmetry correction',1e-4),
        '([UVW])$' : ('Gaussian instrument broadening \\1',1e-5),
        '([XYZ])$' : ('Cauchy instrument broadening \\1',1e-5),
        'Zero' : 'Debye-Scherrer zero correction',
        'Shift' : 'Bragg-Brentano sample displ.',
        'SurfRoughA' : 'Bragg-Brenano surface roughness A',
        'SurfRoughB' : 'Bragg-Brenano surface roughness B',
        'Transparency' : 'Bragg-Brentano sample tranparency',
        'DebyeA' : 'Debye model amplitude',
        'DebyeR' : 'Debye model radius',
        'DebyeU' : 'Debye model Uiso',
        'RBV.*' : 'Vector rigid body parameter',
        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
        'RBRP([xyz])' : 'Residue rigid body position parameter',
        'RBRTr;.*' : 'Residue rigid body torsion parameter',
        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
        'RBRU' : 'Residue rigid body group Uiso param.',
        'constr([0-9]*)' : 'Parameter from constraint',
        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
        'mV([0-2])$' : 'Modulation vector component \\1',
        'Fsin'  :   'Sin site fraction modulation',
        'Fcos'  :   'Cos site fraction modulation',
        'Fzero'  :   'Crenel function offset',      #may go away
        'Fwid'   :   'Crenel function width',
        'Tmin'   :   'ZigZag/Block min location',
        'Tmax'   :   'ZigZag/Block max location',
        '([XYZ])max': 'ZigZag/Block max value for \\1',
        '([XYZ])sin'  : 'Sin position wave for \\1',
        '([XYZ])cos'  : 'Cos position wave for \\1',
        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
        # PDF peak parms (l:<var>;l = peak no.)
        'PDFpos'  : 'PDF peak position',
        'PDFmag'  : 'PDF peak magnitude',
        'PDFsig'  : 'PDF peak std. dev.',
        # SASD vars (l:<var>;l = component)
        'Aspect ratio' : 'Particle aspect ratio',
        'Length' : 'Cylinder length',
        'Diameter' : 'Cylinder/disk diameter',
        'Thickness' : 'Disk thickness',
        'Shell thickness' : 'Multiplier to get inner(<1) or outer(>1) sphere radius',
        'Dist' : 'Interparticle distance',
        'VolFr' : 'Dense scatterer volume fraction',
        'epis' : 'Sticky sphere epsilon',
        'Sticky' : 'Stickyness',
        'Depth' : 'Well depth',
        'Width' : 'Well width',
        'Volume' : 'Particle volume',
        'Radius' : 'Sphere/cylinder/disk radius',
        'Mean' : 'Particle mean radius',
        'StdDev' : 'Standard deviation in Mean',
        'G$': 'Guinier prefactor',
        'Rg$': 'Guinier radius of gyration',
        'B$': 'Porod prefactor',
        'P$': 'Porod power',
        'Cutoff': 'Porod cutoff',
        'PkInt': 'Bragg peak intensity',
        'PkPos': 'Bragg peak position',
        'PkSig': 'Bragg peak sigma',
        'PkGam': 'Bragg peak gamma',
        'e([12][12])' : 'strain tensor e\\1',   # strain vars e11, e22, e12
        'Dcalc': 'Calc. d-spacing',
        'Back$': 'background parameter',
        'pos$': 'peak position',
        'int$': 'peak intensity',
        'WgtFrac':'phase weight fraction',
        'alpha':'TOF profile term',
        'alpha-[01]':'Pink profile term',
        'beta-[01q]':'TOF/Pink profile term',
        'sig-[012q]':'TOF profile term',
        'dif[ABC]':'TOF to d-space calibration',
        'C\\([0-9]*,[0-9]*\\)' : 'spherical harmonics preferred orientation coef.',
        'Pressure': 'Pressure level for measurement in MPa',
        'Temperature': 'T value for measurement, K',
        'FreePrm([123])': 'User defined measurement parameter \\1',
        'Gonio. radius': 'Distance from sample to detector, mm',
        }.items():
        # Needs documentation: HAP: LayerDisp, LeBail, newLeBail
        # hist: Azimuth, Chi, Omega, Phi, Bank, nDebye, nPeaks
        
        if len(value) == 2:
            #VarDesc[key] = value[0]
            reVarDesc[re.compile(key)] = value[0]
            reVarStep[re.compile(key)] = value[1]
        else:
            #VarDesc[key] = value
            reVarDesc[re.compile(key)] = value

def removeNonRefined(parmList):
    '''Remove items from variable list that are not refined and should not 
    appear as options for constraints

    :param list parmList: a list of strings of form "p:h:VAR:a" where
      VAR is the variable name

    :returns: a list after removing variables where VAR matches a 
      entry in local variable NonRefinedList
    '''
    NonRefinedList = ['Omega','Type','Chi','Phi', 'Azimuth','Gonio. radius',
                          'Lam1','Lam2','Back','Temperature','Pressure',
                          'FreePrm1','FreePrm2','FreePrm3',
                          'Source','nPeaks','LeBail','newLeBail','Bank',
                          'nDebye', #'',
                    ]
    return [prm for prm in parmList if prm.split(':')[2] not in NonRefinedList]
        
def getDescr(name):
    '''Return a short description for a GSAS-II variable

    :param str name: The descriptive part of the variable name without colons (:)

    :returns: a short description or None if not found
    '''

    CompileVarDesc() # compile the regular expressions, if needed
    for key in reVarDesc:
        m = key.match(name)
        if m:
            reVarDesc[key]
            return m.expand(reVarDesc[key])
    return None

def getVarStep(name,parmDict=None):
    '''Return a step size for computing the derivative of a GSAS-II variable

    :param str name: A complete variable name (with colons, :)
    :param dict parmDict: A dict with parameter values or None (default)

    :returns: a float that should be an appropriate step size, either from 
      the value supplied in :func:`CompileVarDesc` or based on the value for 
      name in parmDict, if supplied. If not found or the value is zero, 
      a default value of 1e-5 is used. If parmDict is None (default) and 
      no value is provided in :func:`CompileVarDesc`, then None is returned.
    '''
    CompileVarDesc() # compile the regular expressions, if needed
    for key in reVarStep:
        m = key.match(name)
        if m:
            return reVarStep[key]
    if parmDict is None: return None
    val = parmDict.get(key,0.0)
    if abs(val) > 0.05:
        return abs(val)/1000.
    else:
        return 1e-5

def GenWildCard(varlist):
    '''Generate wildcard versions of G2 variables. These introduce '*'
    for a phase, histogram or atom number (but only for one of these
    fields) but only when there is more than one matching variable in the
    input variable list. So if the input is this::

      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']

    then the output will be this::

       wildList = ['*::AUiso:0', '0::AUiso:*']

    :param list varlist: an input list of GSAS-II variable names
      (such as 0::AUiso:0)

    :returns: wildList, the generated list of wild card variable names.
    '''
    wild = []
    for i in (0,1,3):
        currentL = varlist[:]
        while currentL:
            item1 = currentL.pop(0)
            i1splt = item1.split(':')
            if i >= len(i1splt): continue
            if i1splt[i]:
                nextL = []
                i1splt[i] = '[0-9]+'
                rexp = re.compile(':'.join(i1splt))
                matchlist = [item1]
                for nxtitem in currentL:
                    if rexp.match(nxtitem):
                        matchlist += [nxtitem]
                    else:
                        nextL.append(nxtitem)
                if len(matchlist) > 1:
                    i1splt[i] = '*'
                    wild.append(':'.join(i1splt))
                currentL = nextL
    return wild

def LookupWildCard(varname,varlist):
    '''returns a list of variable names from list varname
    that match wildcard name in varname

    :param str varname: a G2 variable name containing a wildcard
      (such as \\*::var)
    :param list varlist: the list of all variable names used in
      the current project
    :returns: a list of matching GSAS-II variables (may be empty)
    '''
    rexp = re.compile(varname.replace('*','[0-9]+'))
    return sorted([var for var in varlist if rexp.match(var)])

def prmLookup(name,prmDict):
    '''Looks for a parameter in a min/max dictionary, optionally
    considering a wild card for histogram or atom number (use of
    both will never occur at the same time).

    :param name: a GSAS-II parameter name (str, see :func:`getVarDescr` 
      and :func:`CompileVarDesc`) or a :class:`G2VarObj` object. 
    :param dict prmDict: a min/max dictionary, (parmMinDict 
      or parmMaxDict in Controls) where keys are :class:`G2VarObj`
      objects. 
    :returns: Two values, (**matchname**, **value**), are returned where:

       * **matchname** *(str)* is the :class:`G2VarObj` object 
         corresponding to the actual matched name, 
         which could contain a wildcard even if **name** does not; and 
       * **value** *(float)* which contains the parameter limit.
    '''
    for key,value in prmDict.items():
        if str(key) == str(name): return key,value
        if key == name: return key,value
    return None,None
        

def _lookup(dic,key):
    '''Lookup a key in a dictionary, where None returns an empty string
    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
    '''
    if key is None:
        return ""
    elif key == "*":
        return "*"
    else:
        return dic.get(key,'?')

def SortVariables(varlist):
    '''Sorts variable names in a sensible manner
    '''
    def cvnnums(var):
        v = []
        for i in var.split(':'):
            if i == '':
                v.append(-1)
                continue
            try:
                v.append(int(i))
            except:
                v.append(i)
        return v
    return sorted(varlist,key=cvnnums)

class G2VarObj(object):
    '''Defines a GSAS-II variable either using the phase/atom/histogram
    unique Id numbers or using a character string that specifies
    variables by phase/atom/histogram number (which can change).
    Note that :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`, 
    which calls :func:`IndexAllIds` (or 
    :func:`GSASIIscriptable.G2Project.index_ids`) should be used to 
    (re)load the current Ids
    before creating or later using the G2VarObj object.

    This can store rigid body variables, but does not translate the residue # and
    body # to/from random Ids

    A :class:`G2VarObj` object can be created with a single parameter:

    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where

     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
     * a is the atom number (which may be left blank in which case the third colon is omitted).
       The atom number can be specified as '*' if a phase number is specified (not as '*').
       For rigid body variables, specify a will be a string of form "residue:body#"

      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
      For a rigid body variables, AtomID is a string of form "residue:body#".

    If four positional arguments are supplied, they are:

    :param str/int phasenum: The number for the phase (or None or '*')
    :param str/int histnum: The number for the histogram (or None or '*')
    :param str varname: a single value can be used to create a :class:`G2VarObj`
    :param str/int atomnum: The number for the atom (or None or '*')

    '''
    IDdict = {}
    IDdict['phases'] = {}
    IDdict['hists'] = {}
    IDdict['atoms'] = {}
    def __init__(self,*args):
        self.phase = None
        self.histogram = None
        self.name = ''
        self.atom = None
        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
            # single arg with 4 values
            self.phase,self.histogram,self.name,self.atom = args[0]
        elif len(args) == 1 and ':' in args[0]:
            #parse a string
            lst = args[0].split(':')
            if lst[0] == '*':
                self.phase = '*'
                if len(lst) > 3:
                    self.atom = lst[3]
                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
            elif lst[1] == '*':
                self.histogram = '*'
                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
            else:
                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
                if len(lst) == 4:
                    if lst[3] == '*':
                        self.atom = '*'
                    else:
                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
                elif len(lst) == 5:
                    self.atom = lst[3]+":"+lst[4]
                elif len(lst) == 3:
                    pass
                else:
                    raise Exception("Too many colons in var name "+str(args[0]))
            self.name = lst[2]
        elif len(args) == 4:
            if args[0] == '*':
                self.phase = '*'
                self.atom = args[3]
            else:
                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
                if args[3] == '*':
                    self.atom = '*'
                elif args[0] is not None:
                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
            if args[1] == '*':
                self.histogram = '*'
            else:
                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
            self.name = args[2]
        else:
            raise Exception("Incorrectly called GSAS-II parameter name")

        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom

    def __str__(self):
        return self.varname()

    def __hash__(self):
        'Allow G2VarObj to be a dict key by implementing hashing'
        return hash(self.varname())

    def varname(self):
        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
        string (p:h:<var>:a) or (p:h:<var>)

        :returns: the variable name as a str
        '''
        a = ""
        if self.phase == "*":
            ph = "*"
            if self.atom:
                a = ":" + str(self.atom)
        else:
            ph = _lookup(PhaseRanIdLookup,self.phase)
            if self.atom == '*':
                a = ':*'
            elif self.atom:
                if ":" in str(self.atom):
                    a = ":" + str(self.atom)
                elif ph in AtomRanIdLookup:
                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
                else:
                    a = ":?"
        if self.histogram == "*":
            hist = "*"
        else:
            hist = _lookup(HistRanIdLookup,self.histogram)
        s = (ph + ":" + hist + ":" + str(self.name)) + a
        return s

    def __repr__(self):
        '''Return the detailed contents of the object
        '''
        s = "<"
        if self.phase == '*':
            s += "Phases: all; "
            if self.atom is not None:
                if ":" in str(self.atom):
                    s += "Rigid body" + str(self.atom) + "; "
                else:
                    s += "Atom #" + str(self.atom) + "; "
        elif self.phase is not None:
            ph =  _lookup(PhaseRanIdLookup,self.phase)
            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
            if self.atom == '*':
                s += "Atoms: all; "
            elif ":" in str(self.atom):
                s += "Rigid body" + str(self.atom) + "; "
            elif self.atom is not None:
                s += "Atom rId=" + str(self.atom)
                if ph in AtomRanIdLookup:
                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
                else:
                    s += " (#? -- not found!); "
        if self.histogram == '*':
            s += "Histograms: all; "
        elif self.histogram is not None:
            hist = _lookup(HistRanIdLookup,self.histogram)
            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
        s += 'Variable name="' + str(self.name) + '">'
        return s+" ("+self.varname()+")"

    def __eq__(self, other):
        '''Allow comparison of G2VarObj to other G2VarObj objects or strings.
        If any field is a wildcard ('*') that field matches.
        '''
        if type(other) is str:
            other = G2VarObj(other)
        elif type(other) is not G2VarObj:
            raise Exception("Invalid type ({}) for G2VarObj comparison with {}"
                            .format(type(other),other))
        if self.phase != other.phase and self.phase != '*' and other.phase != '*':
            return False
        if self.histogram != other.histogram and self.histogram != '*' and other.histogram != '*':
            return False
        if self.atom != other.atom and self.atom != '*' and other.atom != '*':
            return False
        if self.name != other.name:
            return False
        return True

    def _show(self):
        'For testing, shows the current lookup table'
        print ('phases'+ self.IDdict['phases'])
        print ('hists'+ self.IDdict['hists'])
        print ('atomDict'+ self.IDdict['atoms'])

#==========================================================================
def SetDefaultSample():
    'Fills in default items for the Sample dictionary for Debye-Scherrer & SASD'
    return {
        'InstrName':'',
        'ranId':ran.randint(0,sys.maxsize),
        'Scale':[1.0,True],'Type':'Debye-Scherrer','Absorption':[0.0,False],
        'DisplaceX':[0.0,False],'DisplaceY':[0.0,False],
        'Temperature':300.,'Pressure':0.1,'Time':0.0,
        'FreePrm1':0.,'FreePrm2':0.,'FreePrm3':0.,
        'Gonio. radius':200.0,
        'Omega':0.0,'Chi':0.0,'Phi':0.0,'Azimuth':0.0,
#SASD items
        'Materials':[{'Name':'vacuum','VolFrac':1.0,},{'Name':'vacuum','VolFrac':0.0,}],
        'Thick':1.0,'Contrast':[0.0,0.0],       #contrast & anomalous contrast
        'Trans':1.0,                            #measured transmission
        'SlitLen':0.0,                          #Slit length - in Q(A-1)
        }
######################################################################
class ImportBaseclass(object):
    '''Defines a base class for the reading of input files (diffraction
    data, coordinates,...). See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use a subclass of this class.
    '''
    class ImportException(Exception):
        '''Defines an Exception that is used when an import routine hits an expected error,
        usually in .Reader.

        Good practice is that the Reader should define a value in self.errors that
        tells the user some information about what is wrong with their file.
        '''
        pass

    UseReader = True  # in __init__ set value of self.UseReader to False to skip use of current importer
    def __init__(self,formatName,longFormatName=None,
                 extensionlist=[],strictExtension=False,):
        self.formatName = formatName # short string naming file type
        if longFormatName: # longer string naming file type
            self.longFormatName = longFormatName
        else:
            self.longFormatName = formatName
        # define extensions that are allowed for the file type
        # for windows, remove any extensions that are duplicate, as case is ignored
        if sys.platform == 'windows' and extensionlist:
            extensionlist = list(set([s.lower() for s in extensionlist]))
        self.extensionlist = extensionlist
        # If strictExtension is True, the file will not be read, unless
        # the extension matches one in the extensionlist
        self.strictExtension = strictExtension
        self.errors = ''
        self.warnings = ''
        self.SciPy = False          #image reader needed scipy
        # used for readers that will use multiple passes to read
        # more than one data block
        self.repeat = False
        self.selections = []
        self.repeatcount = 0
        self.readfilename = '?'
        self.scriptable = False
        #print 'created',self.__class__

    def ReInitialize(self):
        'Reinitialize the Reader to initial settings'
        self.errors = ''
        self.warnings = ''
        self.SciPy = False          #image reader needed scipy
        self.repeat = False
        self.repeatcount = 0
        self.readfilename = '?'


#    def Reader(self, filename, filepointer, ParentFrame=None, **unused):
#        '''This method must be supplied in the child class to read the file.
#        if the read fails either return False or raise an Exception
#        preferably of type ImportException.
#        '''
#        #start reading
#        raise ImportException("Error occurred while...")
#        self.errors += "Hint for user on why the error occur
#        return False # if an error occurs
#        return True # if read OK

    def ExtensionValidator(self, filename):
        '''This methods checks if the file has the correct extension
        
        :returns:
        
          * False if this filename will not be supported by this reader (only
            when strictExtension is True)
          * True if the extension matches the list supplied by the reader
          * None if the reader allows un-registered extensions
          
        '''
        if filename:
            ext = ospath.splitext(filename)[1]
            if not ext and self.strictExtension: return False
            for ext in self.extensionlist:                
                if sys.platform == 'windows':
                    if filename.lower().endswith(ext): return True
                else:
                    if filename.endswith(ext): return True
        if self.strictExtension:
            return False
        else:
            return None

    def ContentsValidator(self, filename):
        '''This routine will attempt to determine if the file can be read
        with the current format.
        This will typically be overridden with a method that
        takes a quick scan of [some of]
        the file contents to do a "sanity" check if the file
        appears to match the selected format.
        the file must be opened here with the correct format (binary/text)
        '''
        #filepointer.seek(0) # rewind the file pointer
        return True

    def CIFValidator(self, filepointer):
        '''A :meth:`ContentsValidator` for use to validate CIF files.
        '''
        filepointer.seek(0)
        for i,l in enumerate(filepointer):
            if i >= 1000: return True
            '''Encountered only blank lines or comments in first 1000
            lines. This is unlikely, but assume it is CIF anyway, since we are
            even less likely to find a file with nothing but hashes and
            blank lines'''
            line = l.strip()
            if len(line) == 0: # ignore blank lines
                continue
            elif line.startswith('#'): # ignore comments
                continue
            elif line.startswith('data_'): # on the right track, accept this file
                return True
            else: # found something invalid
                self.errors = 'line '+str(i+1)+' contains unexpected data:\n'
                if all([ord(c) < 128 and ord(c) != 0 for c in str(l)]): # show only if ASCII
                    self.errors += '  '+str(l)
                else:
                    self.errors += '  (binary)'
                self.errors += '\n  Note: a CIF should only have blank lines or comments before'
                self.errors += '\n        a data_ statement begins a block.'
                return False

######################################################################
class ImportPhase(ImportBaseclass):
    '''Defines a base class for the reading of files with coordinates

    Objects constructed that subclass this (in import/G2phase_*.py etc.) will be used
    in :meth:`GSASIIdataGUI.GSASII.OnImportPhase` and in 
    :func:`GSASIIscriptable.import_generic`.
    See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use this class.

    '''
    def __init__(self,formatName,longFormatName=None,extensionlist=[],
        strictExtension=False,):
        # call parent __init__
        ImportBaseclass.__init__(self,formatName,longFormatName,
            extensionlist,strictExtension)
        self.Phase = None # a phase must be created with G2IO.SetNewPhase in the Reader
        self.SymOps = {} # specified when symmetry ops are in file (e.g. CIF)
        self.Constraints = None

######################################################################
class ImportStructFactor(ImportBaseclass):
    '''Defines a base class for the reading of files with tables
    of structure factors.

    Structure factors are read with a call to :meth:`GSASIIdataGUI.GSASII.OnImportSfact`
    which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`, which calls
    methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
    :meth:`Reader`.

    See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use import classes in general. The specifics
    for reading a structure factor histogram require that
    the ``Reader()`` routine in the import
    class need to do only a few things: It
    should load :attr:`RefDict` item ``'RefList'`` with the reflection list,
    and set :attr:`Parameters` with the instrument parameters
    (initialized with :meth:`InitParameters` and set with :meth:`UpdateParameters`).
    '''
    def __init__(self,formatName,longFormatName=None,extensionlist=[],
        strictExtension=False,):
        ImportBaseclass.__init__(self,formatName,longFormatName,
            extensionlist,strictExtension)

        # define contents of Structure Factor entry
        self.Parameters = []
        'self.Parameters is a list with two dicts for data parameter settings'
        self.InitParameters()
        self.RefDict = {'RefList':[],'FF':{},'Super':0}
        self.Banks = []             #for multi bank data (usually TOF)
        '''self.RefDict is a dict containing the reflection information, as read from the file.
        Item 'RefList' contains the reflection information. See the
        :ref:`Single Crystal Reflection Data Structure<XtalRefl_table>`
        for the contents of each row. Dict element 'FF'
        contains the form factor values for each element type; if this entry
        is left as initialized (an empty list) it will be initialized as needed later.
        '''
    def ReInitialize(self):
        'Reinitialize the Reader to initial settings'
        ImportBaseclass.ReInitialize(self)
        self.InitParameters()
        self.Banks = []             #for multi bank data (usually TOF)
        self.RefDict = {'RefList':[],'FF':{},'Super':0}

    def InitParameters(self):
        'initialize the instrument parameters structure'
        Lambda = 0.70926
        HistType = 'SXC'
        self.Parameters = [{'Type':[HistType,HistType], # create the structure
                            'Lam':[Lambda,Lambda]
                            }, {}]
        'Parameters is a list with two dicts for data parameter settings'

    def UpdateParameters(self,Type=None,Wave=None):
        'Revise the instrument parameters'
        if Type is not None:
            self.Parameters[0]['Type'] = [Type,Type]
        if Wave is not None:
            self.Parameters[0]['Lam'] = [Wave,Wave]

######################################################################
class ImportPowderData(ImportBaseclass):
    '''Defines a base class for the reading of files with powder data.

    Objects constructed that subclass this (in import/G2pwd_*.py etc.) will be used
    in :meth:`GSASIIdataGUI.GSASII.OnImportPowder` and in 
    :func:`GSASIIscriptable.import_generic`.
    See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use this class.
    '''
    def __init__(self,formatName,longFormatName=None,
        extensionlist=[],strictExtension=False,):
        ImportBaseclass.__init__(self,formatName,longFormatName,
            extensionlist,strictExtension)
        self.clockWd = None  # used in TOF
        self.ReInitialize()

    def ReInitialize(self):
        'Reinitialize the Reader to initial settings'
        ImportBaseclass.ReInitialize(self)
        self.powderentry = ['',None,None] #  (filename,Pos,Bank)
        self.powderdata = [] # Powder dataset
        '''A powder data set is a list with items [x,y,w,yc,yb,yd]:
                np.array(x), # x-axis values
                np.array(y), # powder pattern intensities
                np.array(w), # 1/sig(intensity)^2 values (weights)
                np.array(yc), # calc. intensities (zero)
                np.array(yb), # calc. background (zero)
                np.array(yd), # obs-calc profiles
        '''
        self.comments = []
        self.idstring = ''
        self.Sample = SetDefaultSample() # default sample parameters
        self.Controls = {}  # items to be placed in top-level Controls
        self.GSAS = None     # used in TOF
        self.repeat_instparm = True # Should a parm file be
        #                             used for multiple histograms?
        self.instparm = None # name hint from file of instparm to use
        self.instfile = '' # full path name to instrument parameter file
        self.instbank = '' # inst parm bank number
        self.instmsg = ''  # a label that gets printed to show
                           # where instrument parameters are from
        self.numbanks = 1
        self.instdict = {} # place items here that will be transferred to the instrument parameters
        self.pwdparms = {} # place parameters that are transferred directly to the tree
                           # here (typically from an existing GPX file)
######################################################################
class ImportSmallAngleData(ImportBaseclass):
    '''Defines a base class for the reading of files with small angle data.
    See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use this class.
    '''
    def __init__(self,formatName,longFormatName=None,extensionlist=[],
        strictExtension=False,):

        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
            strictExtension)
        self.ReInitialize()

    def ReInitialize(self):
        'Reinitialize the Reader to initial settings'
        ImportBaseclass.ReInitialize(self)
        self.smallangleentry = ['',None,None] #  (filename,Pos,Bank)
        self.smallangledata = [] # SASD dataset
        '''A small angle data set is a list with items [x,y,w,yc,yd]:
                np.array(x), # x-axis values
                np.array(y), # powder pattern intensities
                np.array(w), # 1/sig(intensity)^2 values (weights)
                np.array(yc), # calc. intensities (zero)
                np.array(yd), # obs-calc profiles
                np.array(yb), # preset bkg
        '''
        self.comments = []
        self.idstring = ''
        self.Sample = SetDefaultSample()
        self.GSAS = None     # used in TOF
        self.clockWd = None  # used in TOF
        self.numbanks = 1
        self.instdict = {} # place items here that will be transferred to the instrument parameters

######################################################################
class ImportReflectometryData(ImportBaseclass):
    '''Defines a base class for the reading of files with reflectometry data.
    See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use this class.
    '''
    def __init__(self,formatName,longFormatName=None,extensionlist=[],
        strictExtension=False,):

        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
            strictExtension)
        self.ReInitialize()

    def ReInitialize(self):
        'Reinitialize the Reader to initial settings'
        ImportBaseclass.ReInitialize(self)
        self.reflectometryentry = ['',None,None] #  (filename,Pos,Bank)
        self.reflectometrydata = [] # SASD dataset
        '''A small angle data set is a list with items [x,y,w,yc,yd]:
                np.array(x), # x-axis values
                np.array(y), # powder pattern intensities
                np.array(w), # 1/sig(intensity)^2 values (weights)
                np.array(yc), # calc. intensities (zero)
                np.array(yd), # obs-calc profiles
                np.array(yb), # preset bkg
        '''
        self.comments = []
        self.idstring = ''
        self.Sample = SetDefaultSample()
        self.GSAS = None     # used in TOF
        self.clockWd = None  # used in TOF
        self.numbanks = 1
        self.instdict = {} # place items here that will be transferred to the instrument parameters

######################################################################
class ImportPDFData(ImportBaseclass):
    '''Defines a base class for the reading of files with PDF G(R) data.
    See :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use this class.
    '''
    def __init__(self,formatName,longFormatName=None,extensionlist=[],
        strictExtension=False,):

        ImportBaseclass.__init__(self,formatName,longFormatName,extensionlist,
            strictExtension)
        self.ReInitialize()

    def ReInitialize(self):
        'Reinitialize the Reader to initial settings'
        ImportBaseclass.ReInitialize(self)
        self.pdfentry = ['',None,None] #  (filename,Pos,Bank)
        self.pdfdata = [] # PDF G(R) dataset
        '''A pdf g(r) data set is a list with items [x,y]:
                np.array(x), # r-axis values
                np.array(y), # pdf g(r)
        '''
        self.comments = []
        self.idstring = ''
        self.numbanks = 1

######################################################################
class ImportImage(ImportBaseclass):
    '''Defines a base class for the reading of images

    Images are read in only these places:

      * Initial reading is typically done from a menu item
        with a call to :meth:`GSASIIdataGUI.GSASII.OnImportImage`
        which in turn calls :meth:`GSASIIdataGUI.GSASII.OnImportGeneric`. That calls
        methods :meth:`ExtensionValidator`, :meth:`ContentsValidator` and
        :meth:`Reader`. This returns a list of reader objects for each read image.
        Also used in :func:`GSASIIscriptable.import_generic`.

      * Images are read alternatively in :func:`GSASIIIO.ReadImages`, which puts image info
        directly into the data tree.

      * Images are reloaded with :func:`GSASIIIO.GetImageData`.

    When reading an image, the ``Reader()`` routine in the ImportImage class
    should set:

      * :attr:`Comments`: a list of strings (str),
      * :attr:`Npix`: the number of pixels in the image (int),
      * :attr:`Image`: the actual image as a numpy array (np.array)
      * :attr:`Data`: a dict defining image parameters (dict). Within this dict the following
        data items are needed:

         * 'pixelSize': size of each pixel in microns (such as ``[200.,200.]``.
         * 'wavelength': wavelength in :math:`\\AA`.
         * 'distance': distance of detector from sample in cm.
         * 'center': uncalibrated center of beam on detector (such as ``[204.8,204.8]``.
         * 'size': size of image (such as ``[2048,2048]``).
         * 'ImageTag': image number or other keyword used to retrieve image from
           a multi-image data file (defaults to ``1`` if not specified).
         * 'sumfile': holds sum image file name if a sum was produced from a multi image file

    optional data items:

      * :attr:`repeat`: set to True if there are additional images to
        read in the file, False otherwise
      * :attr:`repeatcount`: set to the number of the image.

    Note that the above is initialized with :meth:`InitParameters`.
    (Also see :ref:`Writing a Import Routine<import_routines>`
    for an explanation on how to use import classes in general.)
    '''
    def __init__(self,formatName,longFormatName=None,extensionlist=[],
        strictExtension=False,):
        ImportBaseclass.__init__(self,formatName,longFormatName,
            extensionlist,strictExtension)
        self.InitParameters()

    def ReInitialize(self):
        'Reinitialize the Reader to initial settings -- not used at present'
        ImportBaseclass.ReInitialize(self)
        self.InitParameters()

    def InitParameters(self):
        'initialize the instrument parameters structure'
        self.Comments = ['No comments']
        self.Data = {}
        self.Npix = 0
        self.Image = None
        self.repeat = False
        self.repeatcount = 1
        self.sumfile = ''

    def LoadImage(self,ParentFrame,imagefile,imagetag=None):
        '''Optionally, call this after reading in an image to load it into the tree.
        This saves time by preventing a reread of the same information.
        '''
        if ParentFrame:
            ParentFrame.ImageZ = self.Image   # store the image for plotting
            ParentFrame.oldImagefile = imagefile # save the name of the last image file read
            ParentFrame.oldImageTag = imagetag   # save the tag of the last image file read

#################################################################################################
# shortcut routines
exp = np.exp
sind = sin = s = lambda x: np.sin(x*np.pi/180.)
cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
tand = tan = t = lambda x: np.tan(x*np.pi/180.)
sqrt = sq = lambda x: np.sqrt(x)
pi = lambda: np.pi

def FindFunction(f):
    '''Find the object corresponding to function f

    :param str f: a function name such as 'numpy.exp'
    :returns: (pkgdict,pkgobj) where pkgdict contains a dict
      that defines the package location(s) and where pkgobj
      defines the object associated with the function.
      If the function is not found, pkgobj is None.
    '''
    df = f.split('.')
    pkgdict = {}
    # no listed module name, try in current namespace
    if len(df) == 1:
        try:
            fxnobj = eval(f)
            return pkgdict,fxnobj
        except (AttributeError, NameError):
            return None,None

    # includes a package, see if package is already imported
    pkgnam = '.'.join(df[:-1])
    try:
        fxnobj = eval(f)
        pkgdict[pkgnam] = eval(pkgnam)
        return pkgdict,fxnobj
    except (AttributeError, NameError):
        pass
    # package not yet imported, so let's try
    if '.' not in sys.path: sys.path.append('.')
    pkgnam = '.'.join(df[:-1])
    #for pkg in f.split('.')[:-1]: # if needed, descend down the tree
    #    if pkgname:
    #        pkgname += '.' + pkg
    #    else:
    #        pkgname = pkg
    try:
        exec('import '+pkgnam)
        pkgdict[pkgnam] = eval(pkgnam)
        fxnobj = eval(f)
    except Exception as msg:
        print('load of '+pkgnam+' failed with error='+str(msg))
        return {},None
    # can we access the function? I am not exactly sure what
    #    I intended this to test originally (BHT)
    try:
        fxnobj = eval(f,globals(),pkgdict)
        return pkgdict,fxnobj
    except Exception as msg:
        print('call to',f,' failed with error=',str(msg))
        return None,None # not found
                
class ExpressionObj(object):
    '''Defines an object with a user-defined expression, to be used for
    secondary fits or restraints. Object is created null, but is changed
    using :meth:`LoadExpression`. This contains only the minimum
    information that needs to be stored to save and load the expression
    and how it is mapped to GSAS-II variables.
    '''
    def __init__(self):
        self.expression = ''
        'The expression as a text string'
        self.assgnVars = {}
        '''A dict where keys are label names in the expression mapping to a GSAS-II
        variable. The value a G2 variable name.
        Note that the G2 variable name may contain a wild-card and correspond to
        multiple values.
        '''
        self.freeVars = {}
        '''A dict where keys are label names in the expression mapping to a free
        parameter. The value is a list with:

         * a name assigned to the parameter
         * a value for to the parameter and
         * a flag to determine if the variable is refined.
        '''
        self.depVar = None

        self.lastError = ('','')
        '''Shows last encountered error in processing expression
        (list of 1-3 str values)'''

        self.distance_dict  = None  # to be used for defining atom phase/symmetry info
        self.distance_atoms = None  # to be used for defining atom distances

    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
        '''Load the expression and associated settings into the object. Raises
        an exception if the expression is not parsed, if not all functions
        are defined or if not all needed parameter labels in the expression
        are defined.

        This will not test if the variable referenced in these definitions
        are actually in the parameter dictionary. This is checked when the
        computation for the expression is done in :meth:`SetupCalc`.

        :param str expr: the expression
        :param list exprVarLst: parameter labels found in the expression
        :param dict varSelect: this will be 0 for Free parameters
          and non-zero for expression labels linked to G2 variables.
        :param dict varName: Defines a name (str) associated with each free parameter
        :param dict varValue: Defines a value (float) associated with each free parameter
        :param dict varRefflag: Defines a refinement flag (bool)
          associated with each free parameter
        '''
        self.expression = expr
        self.compiledExpr = None
        self.freeVars = {}
        self.assgnVars = {}
        for v in exprVarLst:
            if varSelect[v] == 0:
                self.freeVars[v] = [
                    varName.get(v),
                    varValue.get(v),
                    varRefflag.get(v),
                    ]
            else:
                self.assgnVars[v] = varName[v]
        self.CheckVars()

    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
        '''Load the expression and associated settings from the object into
        arrays used for editing.

        :param list exprVarLst: parameter labels found in the expression
        :param dict varSelect: this will be 0 for Free parameters
          and non-zero for expression labels linked to G2 variables.
        :param dict varName: Defines a name (str) associated with each free parameter
        :param dict varValue: Defines a value (float) associated with each free parameter
        :param dict varRefflag: Defines a refinement flag (bool)
          associated with each free parameter

        :returns: the expression as a str
        '''
        for v in self.freeVars:
            varSelect[v] = 0
            varName[v] = self.freeVars[v][0]
            varValue[v] = self.freeVars[v][1]
            varRefflag[v] = self.freeVars[v][2]
        for v in self.assgnVars:
            varSelect[v] = 1
            varName[v] = self.assgnVars[v]
        return self.expression

    def GetVaried(self):
        'Returns the names of the free parameters that will be refined'
        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]

    def GetVariedVarVal(self):
        'Returns the names and values of the free parameters that will be refined'
        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]

    def UpdateVariedVars(self,varyList,values):
        'Updates values for the free parameters (after a refinement); only updates refined vars'
        for v in self.freeVars:
            if not self.freeVars[v][2]: continue
            if "::"+self.freeVars[v][0] not in varyList: continue
            indx = list(varyList).index("::"+self.freeVars[v][0])
            self.freeVars[v][1] = values[indx]

    def GetIndependentVars(self):
        'Returns the names of the required independent parameters used in expression'
        return [self.assgnVars[v] for v in self.assgnVars]

    def CheckVars(self):
        '''Check that the expression can be parsed, all functions are
        defined and that input loaded into the object is internally
        consistent. If not an Exception is raised.

        :returns: a dict with references to packages needed to
          find functions referenced in the expression.
        '''
        ret = self.ParseExpression(self.expression)
        if not ret:
            raise Exception("Expression parse error")
        exprLblList,fxnpkgdict = ret
        # check each var used in expression is defined
        defined = list(self.assgnVars.keys()) + list(self.freeVars.keys())
        notfound = []
        for var in exprLblList:
            if var not in defined:
                notfound.append(var)
        if notfound:
            msg = 'Not all variables defined'
            msg1 = 'The following variables were not defined: '
            msg2 = ''
            for var in notfound:
                if msg: msg += ', '
                msg += var
            self.lastError = (msg1,'  '+msg2)
            raise Exception(msg)
        return fxnpkgdict

    def ParseExpression(self,expr):
        '''Parse an expression and return a dict of called functions and
        the variables used in the expression. Returns None in case an error
        is encountered. If packages are referenced in functions, they are loaded
        and the functions are looked up into the modules global
        workspace.

        Note that no changes are made to the object other than
        saving an error message, so that this can be used for testing prior
        to the save.

        :returns: a list of used variables
        '''
        self.lastError = ('','')
        import ast
        def ASTtransverse(node,fxn=False):
            '''Transverse a AST-parsed expresson, compiling a list of variables
            referenced in the expression. This routine is used recursively.

            :returns: varlist,fxnlist where
              varlist is a list of referenced variable names and
              fxnlist is a list of used functions
            '''
            varlist = []
            fxnlist = []
            if isinstance(node, list):
                for b in node:
                    v,f = ASTtransverse(b,fxn)
                    varlist += v
                    fxnlist += f
            elif isinstance(node, ast.AST):
                for a, b in ast.iter_fields(node):
                    if isinstance(b, ast.AST):
                        if a == 'func':
                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
                            continue
                        v,f = ASTtransverse(b,fxn)
                        varlist += v
                        fxnlist += f
                    elif isinstance(b, list):
                        v,f = ASTtransverse(b,fxn)
                        varlist += v
                        fxnlist += f
                    elif node.__class__.__name__ == "Name":
                        varlist += [b]
                    elif fxn and node.__class__.__name__ == "Attribute":
                        varlist += [b]
            return varlist,fxnlist
        try:
            exprast = ast.parse(expr)
        except SyntaxError:
            s = ''
            import traceback
            for i in traceback.format_exc().splitlines()[-3:-1]:
                if s: s += "\n"
                s += str(i)
            self.lastError = ("Error parsing expression:",s)
            return
        # find the variables & functions
        v,f = ASTtransverse(exprast)
        varlist = sorted(list(set(v)))
        fxnlist = list(set(f))
        pkgdict = {}
        # check the functions are defined
        for fxn in fxnlist:
            fxndict,fxnobj = FindFunction(fxn)
            if not fxnobj:
                self.lastError = ("Error: Invalid function",fxn,
                                  "is not defined")
                return
            if not hasattr(fxnobj,'__call__'):
                self.lastError = ("Error: Not a function.",fxn,
                                  "cannot be called as a function")
                return
            pkgdict.update(fxndict)
        return varlist,pkgdict

    def GetDepVar(self):
        'return the dependent variable, or None'
        return self.depVar

    def SetDepVar(self,var):
        'Set the dependent variable, if used'
        self.depVar = var
#==========================================================================
class ExpressionCalcObj(object):
    '''An object used to evaluate an expression from a :class:`ExpressionObj`
    object.

    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
      an expression string and mappings for the parameter labels in that object.
    '''
    def __init__(self,exprObj):
        self.eObj = exprObj
        'The expression and mappings; a :class:`ExpressionObj` object'
        self.compiledExpr = None
        'The expression as compiled byte-code'
        self.exprDict = {}
        '''dict that defines values for labels used in expression and packages
        referenced by functions
        '''
        self.lblLookup = {}
        '''Lookup table that specifies the expression label name that is
        tied to a particular GSAS-II parameters in the parmDict.
        '''
        self.fxnpkgdict = {}
        '''a dict with references to packages needed to
        find functions referenced in the expression.
        '''
        self.varLookup = {}
        '''Lookup table that specifies the GSAS-II variable(s)
        indexed by the expression label name. (Used for only for diagnostics
        not evaluation of expression.)
        '''
        self.su = None
        '''Standard error evaluation where supplied by the evaluator
        '''
        # Patch: for old-style expressions with a (now removed step size)
        if '2' in platform.python_version_tuple()[0]: 
            basestr = basestring
        else:
            basestr = str
        for v in self.eObj.assgnVars:
            if not isinstance(self.eObj.assgnVars[v], basestr):
                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
        self.parmDict = {}
        '''A copy of the parameter dictionary, for distance and angle computation
        '''

    def SetupCalc(self,parmDict):
        '''Do all preparations to use the expression for computation.
        Adds the free parameter values to the parameter dict (parmDict).
        '''
        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
            return
        self.fxnpkgdict = self.eObj.CheckVars()
        # all is OK, compile the expression
        self.compiledExpr = compile(self.eObj.expression,'','eval')

        # look at first value in parmDict to determine its type
        parmsInList = True
        if '2' in platform.python_version_tuple()[0]: 
            basestr = basestring
        else:
            basestr = str
        for key in parmDict:
            val = parmDict[key]
            if isinstance(val, basestr):
                parmsInList = False
                break
            try: # check if values are in lists
                val = parmDict[key][0]
            except (TypeError,IndexError):
                parmsInList = False
            break

        # set up the dicts needed to speed computations
        self.exprDict = {}
        self.lblLookup = {}
        self.varLookup = {}
        for v in self.eObj.freeVars:
            varname = self.eObj.freeVars[v][0]
            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
            self.lblLookup[varname] = v
            self.varLookup[v] = varname
            if parmsInList:
                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
            else:
                parmDict[varname] = self.eObj.freeVars[v][1]
            self.exprDict[v] = self.eObj.freeVars[v][1]
        for v in self.eObj.assgnVars:
            varname = self.eObj.assgnVars[v]
            if varname in parmDict:
                self.lblLookup[varname] = v
                self.varLookup[v] = varname
                if parmsInList:
                    self.exprDict[v] = parmDict[varname][0]
                else:
                    self.exprDict[v] = parmDict[varname]
            elif '*' in varname:
                varlist = LookupWildCard(varname,list(parmDict.keys()))
                if len(varlist) == 0:
                    raise Exception("No variables match "+str(v))
                for var in varlist:
                    self.lblLookup[var] = v
                if parmsInList:
                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
                else:
                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
                self.varLookup[v] = [var for var in varlist]
            else:
                self.exprDict[v] = None
#                raise Exception,"No value for variable "+str(v)
        self.exprDict.update(self.fxnpkgdict)

    def UpdateVars(self,varList,valList):
        '''Update the dict for the expression with a set of values
        :param list varList: a list of variable names
        :param list valList: a list of corresponding values
        '''
        for var,val in zip(varList,valList):
            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val

    def UpdateDict(self,parmDict):
        '''Update the dict for the expression with values in a dict
        :param dict parmDict: a dict of values, items not in use are ignored
        '''
        if self.eObj.expression.startswith('Dist') or self.eObj.expression.startswith('Angle'):
            self.parmDict = parmDict
            return
        for var in parmDict:
            if var in self.lblLookup:
                self.exprDict[self.lblLookup[var]] = parmDict[var]

    def EvalExpression(self):
        '''Evaluate an expression. Note that the expression
        and mapping are taken from the :class:`ExpressionObj` expression object
        and the parameter values were specified in :meth:`SetupCalc`.
        :returns: a single value for the expression. If parameter
        values are arrays (for example, from wild-carded variable names),
        the sum of the resulting expression is returned.

        For example, if the expression is ``'A*B'``,
        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::

        [0.5, 1, 0.5]

        then the result will be ``4.0``.
        '''
        self.su = None
        if self.eObj.expression.startswith('Dist'):
#            GSASIIpath.IPyBreak()
            dist = G2mth.CalcDist(self.eObj.distance_dict, self.eObj.distance_atoms, self.parmDict)
            return dist
        elif self.eObj.expression.startswith('Angle'):
            angle = G2mth.CalcAngle(self.eObj.angle_dict, self.eObj.angle_atoms, self.parmDict)
            return angle
        if self.compiledExpr is None:
            raise Exception("EvalExpression called before SetupCalc")
        try:
            val = eval(self.compiledExpr,globals(),self.exprDict)
        except TypeError:
            val = None
        if not np.isscalar(val):
            val = np.sum(val)
        return val

class G2Exception(Exception):
    'A generic GSAS-II exception class'
    def __init__(self,msg):
        self.msg = msg
    def __str__(self):
        return repr(self.msg)

class G2RefineCancel(Exception):
    'Raised when Cancel is pressed in a refinement dialog'
    def __init__(self,msg):
        self.msg = msg
    def __str__(self):
        return repr(self.msg)
    
def HowDidIgetHere(wherecalledonly=False):
    '''Show a traceback with calls that brought us to the current location.
    Used for debugging.
    '''
    import traceback
    if wherecalledonly:
        i = traceback.format_list(traceback.extract_stack()[:-1])[-2]
        print(i.strip().rstrip())
    else:
        print (70*'*')
        for i in traceback.format_list(traceback.extract_stack()[:-1]): print(i.strip().rstrip())
        print (70*'*')

# Note that this is GUI code and should be moved at somepoint
def CreatePDFitems(G2frame,PWDRtree,ElList,Qlimits,numAtm=1,FltBkg=0,PDFnames=[]):
    '''Create and initialize a new set of PDF tree entries

    :param Frame G2frame: main GSAS-II tree frame object
    :param str PWDRtree: name of PWDR to be used to create PDF item
    :param dict ElList: data structure with composition
    :param list Qlimits: Q limits to be used for computing the PDF
    :param float numAtm: no. atom in chemical formula
    :param float FltBkg: flat background value
    :param list PDFnames: previously used PDF names

    :returns: the Id of the newly created PDF entry
    '''
    PDFname = 'PDF '+PWDRtree[4:] # this places two spaces after PDF, which is needed is some places
    if PDFname in PDFnames:
        print('Skipping, entry already exists: '+PDFname)
        return None
    #PDFname = MakeUniqueLabel(PDFname,PDFnames)
    Id = G2frame.GPXtree.AppendItem(parent=G2frame.root,text=PDFname)
    Data = {
        'Sample':{'Name':PWDRtree,'Mult':1.0},
        'Sample Bkg.':{'Name':'','Mult':-1.0,'Refine':False},
        'Container':{'Name':'','Mult':-1.0,'Refine':False},
        'Container Bkg.':{'Name':'','Mult':-1.0},'ElList':ElList,
        'Geometry':'Cylinder','Diam':1.0,'Pack':0.50,'Form Vol':10.0*numAtm,'Flat Bkg':FltBkg,
        'DetType':'Area detector','ObliqCoeff':0.2,'Ruland':0.025,'QScaleLim':Qlimits,
        'Lorch':False,'BackRatio':0.0,'Rmax':100.,'noRing':False,'IofQmin':1.0,'Rmin':1.0,
        'I(Q)':[],'S(Q)':[],'F(Q)':[],'G(R)':[]}
    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Controls'),Data)
    G2frame.GPXtree.SetItemPyData(G2frame.GPXtree.AppendItem(Id,text='PDF Peaks'),
        {'Limits':[1.,5.],'Background':[2,[0.,-0.2*np.pi],False],'Peaks':[]})
    return Id
#%%
class ShowTiming(object):
    '''An object to use for timing repeated sections of code.

    Create the object with::
       tim0 = ShowTiming()

    Tag sections of code to be timed with::
       tim0.start('start')
       tim0.start('in section 1')
       tim0.start('in section 2')
       
    etc. (Note that each section should have a unique label.)

    After the last section, end timing with::
       tim0.end()

    Show timing results with::
       tim0.show()
       
    '''
    def __init__(self):
        self.timeSum =  []
        self.timeStart = []
        self.label = []
        self.prev = None
    def start(self,label):
        import time
        if label in self.label:
            i = self.label.index(label)
            self.timeStart[i] = time.time()
        else:
            i = len(self.label)
            self.timeSum.append(0.0)
            self.timeStart.append(time.time())
            self.label.append(label)
        if self.prev is not None:
            self.timeSum[self.prev] += self.timeStart[i] - self.timeStart[self.prev]
        self.prev = i
    def end(self):
        import time
        if self.prev is not None:
            self.timeSum[self.prev] += time.time() - self.timeStart[self.prev]
        self.prev = None
    def show(self):
        sumT = sum(self.timeSum)
        print('Timing results (total={:.2f} sec)'.format(sumT))
        for i,(lbl,val) in enumerate(zip(self.label,self.timeSum)):
            print('{} {:20} {:8.2f} ms {:5.2f}%'.format(i,lbl,1000.*val,100*val/sumT))
#%%

def validateAtomDrawType(typ,generalData={}):
    '''Confirm that the selected Atom drawing type is valid for the current 
    phase. If not, use 'vdW balls'. This is currently used only for setting a 
    default when atoms are added to the atoms draw list.
    '''
    if typ in ('lines','vdW balls','sticks','balls & sticks','ellipsoids'):
        return typ
    # elif generalData.get('Type','') == 'macromolecular':
    #     if typ in ('backbone',):
    #         return typ
    return 'vdW balls'

if __name__ == "__main__":
    # test variable descriptions
    for var in '0::Afrac:*',':1:Scale','1::dAx:0','::undefined':
        v = var.split(':')[2]
        print(var+':\t', getDescr(v),getVarStep(v))
    import sys; sys.exit()
    # test equation evaluation
    def showEQ(calcobj):
        print (50*'=')
        print (calcobj.eObj.expression+'='+calcobj.EvalExpression())
        for v in sorted(calcobj.varLookup):
            print ("  "+v+'='+calcobj.exprDict[v]+'='+calcobj.varLookup[v])
        # print '  Derivatives'
        # for v in calcobj.derivStep.keys():
        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)

    obj = ExpressionObj()

    obj.expression = "A*np.exp(B)"
    obj.assgnVars =  {'B': '0::Afrac:1'}
    obj.freeVars =  {'A': [u'A', 0.5, True]}
    #obj.CheckVars()
    calcobj = ExpressionCalcObj(obj)

    obj1 = ExpressionObj()
    obj1.expression = "A*np.exp(B)"
    obj1.assgnVars =  {'B': '0::Afrac:*'}
    obj1.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
    #obj.CheckVars()
    calcobj1 = ExpressionCalcObj(obj1)

    obj2 = ExpressionObj()
    obj2.distance_stuff = np.array([[0,1],[1,-1]])
    obj2.expression = "Dist(1,2)"
    GSASIIpath.InvokeDebugOpts()
    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
    calcobj2 = ExpressionCalcObj(obj2)
    calcobj2.SetupCalc(parmDict2)
    showEQ(calcobj2)

    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
    print ('\nDict = '+parmDict1)
    calcobj.SetupCalc(parmDict1)
    showEQ(calcobj)
    calcobj1.SetupCalc(parmDict1)
    showEQ(calcobj1)

    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
    print ('Dict = '+parmDict2)
    calcobj.SetupCalc(parmDict2)
    showEQ(calcobj)
    calcobj1.SetupCalc(parmDict2)
    showEQ(calcobj1)
    calcobj2.SetupCalc(parmDict2)
    showEQ(calcobj2)