text: # -*- coding: utf-8 -*-
  #GSASIIobj - data objects for GSAS-II
  ########### SVN repository information ###################
  # $Date: 2019-09-04 17:06:31 -0500 (Wed, 04 Sep 2019) $
  # $Author: toby $
  # $Revision: 4136 $
  # $URL: https://subversion.xray.aps.anl.gov/pyGSAS/trunk/GSASIIobj.py $
  # $Id: GSASIIobj.py 4136 2019-09-04 22:06:31Z 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.
  
  Constraints Tree Item
  ----------------------
  
  .. _Constraints_table:
  
  .. index::
     single: Constraints object description
     single: Data object descriptions; Constraints
  
  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 Tree Item
  --------------------
  
  .. _Covariance_table:
  
  .. index::
     single: Covariance description
     single: Data object descriptions; Covariance
  
  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 with lattice parameters computed by
                                  :func:`GSASIIstrMath.GetNewCellParms` (dict)
  title          \                Name of gpx file(?) (str)
  variables      \                Values for all N refined variables
                                  (list of float values, length N,
                                  ordered to match varyList)
  sig            \                Uncertainty values for all N refined variables
                                  (list of float values, length N,
                                  ordered to match varyList)
  varyList       \                List of directly refined variables
                                  (list of str values, length N)
  newAtomDict    \                dict with atom position values computed in
                                  :func:`GSASIIstrMath.ApplyXYZshifts` (dict)
  Rvals          \                R-factors, GOF, Marquardt value for last
                                  refinement cycle (dict)
  \              Nobs             Number of observed data points (int)
  \              Rwp              overall weighted profile R-factor (%, float)
  \              chisq            sum[w*(Iobs-Icalc)**2] for all data
                                  note this is not the reduced chi squared (float)
  \              lamMax           Marquardt value applied to Hessian diagonal
                                  (float)
  \              GOF              The goodness-of-fit, aka square root of
                                  the reduced chi squared. (float)
  covMatrix      \                The (NxN) covVariance matrix (np.array)
  =============  ===============  ====================================================
  
  Phase Tree Items
  ----------------
  
  .. _Phase_table:
  
  .. index::
     single: Phase object description
     single: Data object descriptions; Phase
  
  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         \            Overall information for the phase (dict)
    \         AtomPtrs         list of four locations to use to pull info
                               from the atom records (list)
    \         F000X            x-ray F(000) intensity (float)
    \         F000N            neutron F(000) intensity (float)
    \         Mydir            directory of current .gpx file (str)
    \         MCSA controls    Monte Carlo-Simulated Annealing controls (dict)
    \         Cell             List with 8 items: cell refinement flag (bool)
                               a, b, c, (Angstrom, float)
                               alpha, beta & gamma (degrees, float)
                               volume (A^3, float)
    \         Type             'nuclear' or 'macromolecular' for now (str)
    \         Map              dict of map parameters
    \         SH Texture       dict of spherical harmonic preferred orientation
                               parameters
    \         Isotope          dict of isotopes for each atom type
    \         Isotopes         dict of scattering lengths for each isotope
                               combination for each element in phase
    \         Name             phase name (str)
    \         SGData           Space group details as a :ref:`space group (SGData) object <SGData_table>`
                               as defined in :func:`GSASIIspc.SpcGroup`.
    \         Pawley neg wt    Restraint value for negative Pawley intensities
                               (float)
    \         Flip             dict of Charge flip controls
    \         Data plot type   data plot type ('Mustrain', 'Size' or
                               'Preferred orientation') for powder data (str)
    \         Mass             Mass of unit cell contents in g/mol
    \         POhkl            March-Dollase preferred orientation direction
    \         Z                dict of atomic numbers for each atom type
    \         vdWRadii         dict of van der Waals radii for each atom type
    \         Color            Colors for atoms (list of (r,b,g) triplets)
    \         AtomTypes        List of atom types
    \         AtomMass         List of masses for atoms
    \         doPawley         Flag for Pawley intensity extraction (bool)
    \         NoAtoms          Number of atoms per unit cell of each type (dict)
    \         Pawley dmin      maximum Q (as d-space) to use for Pawley
                               extraction (float)
    \         BondRadii        Default radius for each atom used to compute
                               interatomic distances (list of floats)
    \         AngleRadii       Default radius for each atom used to compute
                               interatomic angles (list of floats)
    \         DisAglCtls       Dict 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)].
  ranId           \            unique random number Id for phase (int)
  pId             \            Phase Id number for current project (int).
  Atoms           \            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.
                               (list of lists)
  Drawing         \            Display parameters (dict)
  \           ballScale        Size of spheres in ball-and-stick display (float)
  \           bondList         dict with bonds
  \           contourLevel     map contour level in e/A^3 (float)
  \           showABC          Flag to show view point triplet (bool). True=show.
  \           viewDir          cartesian viewing direction (np.array with three
                               elements)
  \           Zclip            clipping distance in A (float)
  \           backColor        background for plot as and R,G,B triplet
                               (default = [0, 0, 0], black).
                               (list with three atoms)
  \           selectedAtoms    List of selected atoms (list of int values)
  \           showRigidBodies  Flag to highlight rigid body placement
  \           sizeH            Size ratio for H atoms (float)
  \           bondRadius       Size of binds in A (float)
  \           atomPtrs         positions of x, type, site sym, ADP flag in Draw Atoms (list)
  \           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])
  \           showHydrogen     Flag to control plotting of H atoms.
  \           unitCellBox      Flag to control display of the unit cell.
  \           ellipseProb      Probability limit for display of thermal
                               ellipsoids in % (float).
  \           vdwScale         Multiplier of van der Waals radius for
                               display of vdW spheres.
  \           Atoms            A list of lists with an entry for each atom
                               that is plotted.
  \           Zstep            Step to de/increase Z-clip (float)
  \           Quaternion       Viewing quaternion (4 element np.array)
  \           radiusFactor     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.
  \           oldxy            previous view point (list with two floats)
  \           cameraPos        Viewing position in A for plot (float)
  \           depthFog         True if use depthFog on plot - set currently as False (bool)
  RBModels        \            Rigid body assignments (note Rigid body definitions
                               are stored in their own main top-level tree entry.)
  Pawley ref      \            Pawley reflections
  Histograms      \            A 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          For protein crystallography. Dictionary with two
                               entries, 'BabA', 'BabU'
  \           Extinction       Extinction parameter (list of float, bool)
  \           HStrain          Hydrostatic strain. List of two lists. 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        The name of the associated histogram (str)
  \           LeBail           Flag for LeBail extraction (bool)
  \           Mustrain         List of microstrain parameters, in order:
  
                                 0. Type, one of u'generalized', u'isotropic',
                                    u'uniaxial'
                                 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.        Preferred Orientation. List of eight parameters.
                               Items marked SH are only used for Spherical Harmonics.
  
                                 0. Type, 'MD' for March-Dollase or 'SH' for
                                    Spherical Harmonics
                                 1. Value, float
                                 2. Refinement flag, bool
                                 3. Preferred direction, list of ints, [h, k, l]
                                 4. SH - number of terms, int
                                 5. SH - dict
                                 6. SH - list
                                 7. SH - float
  \           Scale            Phase fraction, list of [float, bool].
  \           Show             bool
  \           Use              bool
  \           newLeBail        Whether to perform a new LeBail extraction
  MCSA            \            Monte-Carlo simulated annealing parameters (dict)
  \
  ==========  ===============  ====================================================
  
  Rigid Body Objects
  ------------------
  
  .. _RBData_table:
  
  .. index::
     single: Rigid Body Data description
     single: Data object descriptions; Rigid Body Data
  
  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             vector rigid bodies (dict of dict)
  \           AtInfo           Drad, Color: atom drawing radius & color for each atom type (dict)
  \           RBname           Name assigned by user to rigid body (str)
  \           VectMag          vector magnitudes in A (list)
  \           rbXYZ            Cartesian coordinates for Vector rigid body (list of 3 float)
  \           rbRef            3 assigned reference atom nos. in rigid body for origin
                               definition, use center of atoms flag (list of 3 int & 1 bool)
  \           VectRef          refinement flags for VectMag values (list of bool)
  \           rbTypes          Atom types for each atom in rigid body (list of str)
  \           rbVect           Cartesian vectors for each translation used to build rigid body (list of lists)
  \           useCount         Number of times rigid body is used in any structure (int)
  Residue     RBId             residue rigid bodies (dict of dict)
  \           AtInfo           Drad, Color: atom drawing radius & color for each atom type(dict)
  \           RBname           Name assigned by user to rigid body (str)
  \           rbXYZ            Cartesian coordinates for Residue rigid body (list of 3 float)
  \           rbTypes          Atom types for each atom in rigid body (list of str)
  \           atNames          Names of each atom in rigid body (e.g. C1,N2...) (list of str)
  \           rbRef            3 assigned reference atom nos. in rigid body for origin
                               definition, use center of atoms flag (list of 3 int & 1 bool)
  \           rbSeq            Orig,Piv,angle,Riding (list): 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         Number of times rigid body is used in any structure (int)
  RBIds           \            unique Ids generated upon creation of each rigid body (dict)
  \           Vector           Ids for each Vector rigid body (list)
  \           Residue          Ids for each Residue rigid body (list)
  ==========  ===============  ====================================================
  
  Space Group Objects
  -------------------
  
  .. _SGData_table:
  
  .. index::
     single: Space Group Data description
     single: Data object descriptions; Space Group Data
  
  Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
  and the information is placed in a SGdata object
  which is a dict with these keys:
  
  .. tabularcolumns:: |l|p{4.5in}|
  
  ==========  ====================================================
    key         explanation
  ==========  ====================================================
  SpGrp       space group symbol (str)
  Laue        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 (str)
  SGInv       True if centrosymmetric, False if not (bool)
  SGLatt      Lattice centering type. Will be one of
              P, A, B, C, I, F, R (str)
  SGUniq      unique axis if monoclinic. Will be
              a, b, or c for monoclinic space groups.
              Will be blank for non-monoclinic. (str)
  SGCen       Symmetry cell centering vectors. A (n,3) np.array
              of centers. Will always have at least one row:
              ``np.array([[0, 0, 0]])``
  SGOps       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`
  SGSys       symmetry unit cell: type one of
              'triclinic', 'monoclinic', 'orthorhombic',
              'tetragonal', 'rhombohedral', 'trigonal',
              'hexagonal', 'cubic' (str)
  SGPolax     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 ?).
  ==========  ====================================================
  
  .. _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
  ==========  ====================================================
  SSpGrp      superspace group symbol extension to space group
              symbol, accidental spaces removed
  SSGCen      4D cell centering vectors [0,0,0,0] at least
  SSGOps      4D symmetry operations as [M,T] so that M*x+T = x'
  ==========  ====================================================
  
  
  Atom Records
  ------------
  
  .. _Atoms_table:
  
  .. index::
     single: Atoms record description
     single: Data object descriptions; Atoms record
  
  
  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'
  
  .. tabularcolumns:: |l|p{4.5in}|
  
  ==============   ====================================================
  location         explanation
  ==============   ====================================================
  ct-4              mm - residue number (str)
  ct-3              mm - residue name (e.g. ALA) (str)
  ct-2              mm - chain label (str)
  ct-1              atom label (str)
  ct                atom type (str)
  ct+1              refinement flags; combination of 'F', 'X', 'U' (str)
  cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
  cx+3              site occupancy (float)
  cs                site symmetry (str)
  cs+1              site multiplicity (int)
  cia               ADP flag: Isotropic ('I') or Anisotropic ('A')
  cia+1             Uiso (float)
  cia+2...cia+7     U11, U22, U33, U12, U13, U23 (6 floats)
  atom[cia+8]       unique atom identifier (int)
  
  ==============   ====================================================
  
  Drawing Atom Records
  --------------------
  
  .. _Drawing_atoms_table:
  
  .. index::
     single: Drawing atoms record description
     single: Data object descriptions; Drawing atoms record
  
  
  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'
  
  .. tabularcolumns:: |l|p{4.5in}|
  
  ==============   ====================================================
  location         explanation
  ==============   ====================================================
  ct-4              mm - residue number (str)
  ct-3              mm - residue name (e.g. ALA) (str)
  ct-2              mm - chain label (str)
  ct-1              atom label (str)
  ct                atom type (str)
  cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
  cs-1              Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
  cs                atom drawing style; e.g. 'balls & sticks' (str)
  cs+1              atom label style (e.g. 'name') (str)
  cs+2              atom color (RBG triplet) (int)
  cs+3              ADP flag: Isotropic ('I') or Anisotropic ('A')
  cs+4              Uiso (float)
  cs+5...cs+11      U11, U22, U33, U12, U13, U23 (6 floats)
  ci                unique atom identifier; matches source atom Id in Atom Records (int)
  ==============   ====================================================
  
  Powder Diffraction Tree Items
  -----------------------------
  
  .. _Powder_table:
  
  .. index::
     single: Powder data object description
     single: Data object descriptions; Powder Data
  
  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                      \           Text strings extracted from the original powder
                                            data header. These cannot be changed by the user;
                                            it may be empty.
  Limits                       \            A list of 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              \           A dict 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         \           A list containing two dicts where the possible
                                            keys in each dict are listed below. 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 in the first dict are noted as [1]
  \                         Lam             Specifies a wavelength in Angstroms [1]
  \                         Lam1            Specifies the primary wavelength in
                                            Angstrom, when an alpha1, alpha2
                                            source is used [1]
  \                         Lam2            Specifies the secondary wavelength in
                                            Angstrom, when an alpha1, alpha2
                                            source is used [1]
                            I(L2)/I(L1)     Ratio of Lam2 to Lam1 [1]
  \                         Type            Histogram type (str) [1]:
                                             * 'PXC' for constant wavelength x-ray
                                             * 'PNC' for constant wavelength neutron
                                             * 'PNT' for time of flight neutron
  \                         Zero            Two-theta zero correction in *degrees* [1]
  \                         Azimuth         Azimuthal setting angle for data recorded
                                            with differing setting angles [1]
  \                         U, V, W         Cagliotti profile coefficients
                                            for Gaussian instrumental broadening, where the
                                            FWHM goes as
                                            :math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
  \                         X, Y            Cauchy (Lorentzian) instrumental broadening
                                            coefficients [1]
  \                         SH/L            Variant of the Finger-Cox-Jephcoat asymmetric
                                            peak broadening ratio. Note that this is the
                                            average between S/L and H/L where S is
                                            sample height, H is the slit height and
                                            L is the goniometer diameter. [1]
  \                         Polariz.        Polarization coefficient. [1]
  wtFactor                      \           A weighting factor to increase or decrease
                                            the leverage of data in the histogram (float).
                                            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             \           Specifies a dict with 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       A name for the instrument, used in preparing
                                            a CIF (str).
  \                         Force,          Variables that describe how the measurement
                            Temperature,    was performed. Not used directly in
                            Humidity,       any computations.
                            Pressure,
                            Voltage
  \                         ranId           The random-number Id for the histogram
                                            (same value as where top-level key is ranId)
  \                         Type            Type of diffraction data, may be 'Debye-Scherrer'
                                            or 'Bragg-Brentano' (str).
  \                         Diffuse         not in use?
  hId                           \           The number assigned to the histogram when
                                            the project is loaded or edited (can change)
  ranId                         \           A random number id for the histogram
                                            that does not change
  Background                    \           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                          \           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
  ======================  ===============  ====================================================
  
  Powder Reflection Data Structure
  --------------------------------
  
  .. _PowderRefl_table:
  
  .. index::
     single: Powder reflection object description
     single: Data object descriptions; Powder Reflections
  
  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           multiplicity
   4           d-space, Angstrom
   5           pos, two-theta
   6           sig, Gaussian width
   7           gam, Lorenzian width
   8           :math:`F_{obs}^2`
   9           :math:`F_{calc}^2`
   10          reflection phase, in degrees
   11          intensity correction for reflection, this times
               :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
  ==========  ====================================================
  
  Single Crystal Tree Items
  -------------------------
  
  .. _Xtal_table:
  
  .. index::
     single: Single Crystal data object description
     single: Data object descriptions; Single crystal data
  
  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                          \           A dict that contains the
                                            reflection table,
                                            as described in the
                                            :ref:`Single Crystal Reflections
                                            <XtalRefl_table>`
                                            description.
  
  Instrument Parameters         \           A 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             Specifies a wavelength in Angstroms (two floats)
  \                         Type            Histogram type (two str values):
                                             * 'SXC' for constant wavelength x-ray
                                             * 'SNC' for constant wavelength neutron
                                             * 'SNT' for time of flight neutron
  \                         InstrName       A name for the instrument, used in preparing
                                            a CIF (str).
  
  wtFactor                      \           A weighting factor to increase or decrease
                                            the leverage of data in the histogram (float).
                                            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                           \           The number assigned to the histogram when
                                            the project is loaded or edited (can change)
  ranId                         \           A random number id for the histogram
                                            that does not change
  ======================  ===============  ====================================================
  
  Single Crystal Reflection Data Structure
  ----------------------------------------
  
  .. _XtalRefl_table:
  
  .. index::
     single: Single Crystal reflection object description
     single: Data object descriptions; Single Crystal Reflections
  
  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.
  
  ==========  ====================================================
    index         explanation
  ==========  ====================================================
   0,1,2       h,k,l (float)
   3           multiplicity
   4           d-space, Angstrom
   5           :math:`F_{obs}^2`
   6           :math:`\sigma(F_{obs}^2)`
   7           :math:`F_{calc}^2`
   8           :math:`F_{obs}^2T`
   9           :math:`F_{calc}^2T`
   10          reflection phase, in degrees
   11          intensity correction for reflection, this times
               :math:`F_{obs}^2` or :math:`F_{calc}^2`
               gives Iobs or Icalc
  ==========  ====================================================
  
  Image Data Structure
  --------------------
  
  .. _Image_table:
  
  .. index::
     image: Image data object description
     image: Image object descriptions
  
  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                       \                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) Tha radiation wavelength (Angstroms) 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.
  
  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.
  
  ======================  ======================  ====================================================
  
  Parameter Dictionary
  -------------------------
  
  .. _parmDict_table:
  
  .. index::
     single: 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).
  
  
  *Classes and routines*
  ----------------------
  
  '''
  from __future__ import division, print_function
  import platform
  import re
  import imp
  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: 4136 $")
  
  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 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',
          #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',
          'RBR.*' : 'Residue 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.',
          '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',
          'beta-[01q]':'TOF profile term',
          'sig-[012q]':'TOF profile term',
          'dif[ABC]':'TOF to d-space calibration',
          'C\([0-9]*,[0-9]*\)' : 'spherical harmonics preferred orientation coef.',
          }.items():
          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 _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:`LoadID` 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 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):
          if type(other) is type(self):
              return (self.phase == other.phase and
                      self.histogram == other.histogram and
                      self.name == other.name and
                      self.atom == other.atom)
          return False
  
      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],'Diffuse':[],
          '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.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 Angstoms.
           * '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
  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 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 package, try in current namespace
              if len(df) == 1:
                  try:
                      fxnobj = eval(f)
                      return pkgdict,fxnobj
                  except (AttributeError, NameError):
                      return None,None
              else:
                  try:
                      fxnobj = eval(f)
                      pkgdict[df[0]] = eval(df[0])
                      return pkgdict,fxnobj
                  except (AttributeError, NameError):
                      pass
              # includes a package, lets try to load the packages
              pkgname = ''
              path = sys.path+['./',]
              for pkg in f.split('.')[:-1]: # if needed, descend down the tree
                  if pkgname:
                      pkgname += '.' + pkg
                  else:
                      pkgname = pkg
                  fp = None
                  try:
                      fp, fppath,desc = imp.find_module(pkg,path)
                      pkgobj = imp.load_module(pkg,fp,fppath,desc)
                      pkgdict[pkgname] = pkgobj
                      path = [fppath]
                  except Exception as msg:
                      print('load of '+pkgname+' failed with error='+str(msg))
                      return {},None
                  finally:
                      if fp: fp.close()
                  try:
                      #print 'before',pkgdict.keys()
                      fxnobj = eval(f,globals(),pkgdict)
                      #print 'after 1',pkgdict.keys()
                      #fxnobj = eval(f,pkgdict)
                      #print 'after 2',pkgdict.keys()
                      return pkgdict,fxnobj
                  except:
                      continue
              return None # not found
          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))
  #%%
  
  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)
  