source: trunk/GSASIIobj.py @ 1168

# -*- coding: utf-8 -*-
#GSASIIobj - data objects for GSAS-II
########### SVN repository information ###################
# $Date: 2013-12-16 16:43:01 +0000 (Mon, 16 Dec 2013) $
# $Author: toby $
# $Revision: 1168 $
# $URL: trunk/GSASIIobj.py $
# $Id: GSASIIobj.py 1168 2013-12-16 16:43:01Z 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 will be implemented in the future to indicate if these variables
   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. (dict)
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 ?).
==========  ====================================================

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)
cs                site symmetry (str)
cs+1              site multiplicity (int)
cia               ADP flag: Isotropic ('I') or Anisotropic ('A')
cia+1             Uiso (float)
cia+2...cia+6     U11, U22, U33, U12, U13, U23 (6 floats)
atom[-1]                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:`GSASII.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
======================  ===============  ====================================================
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).
\                         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:

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


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

'''
import random as ran
import sys
import GSASIIpath
import GSASIImath as G2mth

GSASIIpath.SetVersionNumber("$Revision: 1168 $")

DefaultControls = {
    'deriv type':'analytic Hessian',    #default controls
    'min dM/M':0.0001,'shift factor':1.,'max cyc':3,'F**2':True,
    'minF/sig':0,
    'Author':'no name',
    'FreeVar1':'Sample humidity (%)',
    'FreeVar2':'Sample voltage (V)',
    'FreeVar3':'Applied load (MN)',
    }
'''Values to be used as defaults for the initial contents of the ``Controls``
data tree item.
'''

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 = 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 = {}
''' 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 with
the same values as :attr:`VarDesc` except that keys have been compiled as
regular expressions. Initialized in :func:`CompileVarDesc`.
'''

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 two places (only) :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
    (which loads the histograms and phases from a GPX file) and
    :meth:`GSASII.GSASII.GetUsedHistogramsAndPhases`
    (which loads the histograms and phases from the data tree.)

    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.maxint)
        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[-1]
            while ranId in AtomRanIdLookup[pId]: # check for dups
                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
                at[-1] = ranId = ran.randint(0,sys.maxint)
            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.maxint)
        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 

    TODO: This will not handle rigid body parameters yet

    :param str name: A full G2 variable name with 2 or 3
       colons (<p>:<h>:name[:<a>])
       
    :returns: a string with the description
    '''
    
    l = getVarDescr(varname)
    if not l:
        return "invalid variable name ("+str(varname)+")!"

    if not l[4]:
        l[4] = "(variable needs a definition!)"

    s = ""
    if l[0] is not None and l[1] is not None: # HAP: keep short
        lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
        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)+": "
    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] is not None:
        lbl = ShortPhaseNames.get(l[0],'phase?')
        s = "Phase "+str(lbl)+": "
    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: '
    s += l[4]
    return s

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

    :param str name: A full G2 variable name with 2 or 3
       colons (<p>:<h>:name[:<a>])
      
    :returns: a five element list as [`p`,`h`,`name`,`a`,`description`],
      where `p`, `h`, `a` are str values or `None`, for the phase number,
      the histogram number and the atom number; `name` will always be
      an 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) == 3:
        l += [None]
    if len(l) != 4:
        return None
    for i in (0,1,3):
        if l[i] == "":
            l[i] = None
    l += [getDescr(l[2])]
    return l
    
def CompileVarDesc():
    '''Set the values in the variable description lookup table (:attr:`VarDesc`)
    into :attr:`reVarDesc`. This is called in :func:`getDescr` so the 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.
    
    '''
    import re
    if reVarDesc: return # already done
    for key,value in {
        # Phase vars (p::<var>)
        'A([0-5])' : 'Reciprocal metric tensor component \\1',
        'Vol' : 'Unit cell volume????',
        # Atom vars (p::<var>:a)
        'dA([xyz])' : 'change to atomic position \\1',
        'AUiso':'Atomic isotropic displacement parameter',
        'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
        'Afrac': 'Atomic occupancy parameter',
        # Hist & Phase (HAP) vars (p:h:<var>)
        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
        'D([123][123])' : 'Anisotropic strain coef. \\1',
        'Extinction' : 'Extinction coef.',
        'MD' : 'March-Dollase coef.',
        'Mustrain;.*' : 'Microstrain coef.',
        'Scale' : 'Phase scale factor',
        'Size;.*' : 'Crystallite size value',
        'eA' : '?',
        #Histogram vars (:h:<var>)
        'Absorption' : 'Absorption coef.',
        'Displace([XY])' : 'Debye-Scherrer sample displacement \\1',
        'Lam' : 'Wavelength',
        'Polariz\.' : 'Polarization correction',
        'SH/L' : 'FCJ peak asymmetry correction',
        'Scale' : 'Histogram scale factor',
        '([UVW])' : 'Gaussian instrument broadening \\1',
        '([XY])' : 'Cauchy instrument broadening \\1',
        'Zero' : 'Debye-Scherrer zero correction',
        'nDebye' : 'Debye model background corr. terms',
        'nPeaks' : 'Fixed peak background corr. terms',
        # Global vars (::<var>)
        }.items():
        VarDesc[key] = value
        reVarDesc[re.compile(key)] = value

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:
            return m.expand(reVarDesc[key])
    return None

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

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.

    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); 
     * h is the histogram number (which may be left blank); 
     * a is the atom number (which may be left blank in which case the third colon is omitted).

      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
      Phase, Histogram, and AtomID are None or are ranId values and VarName is a string.     

    If four positional arguments are supplied, they are:

    :param str/int phasenum: The number for the phase
    :param str/int histnum: The number for the histogram
    :param str varname: a single value can be used to create a :class:`G2VarObj`
    :param str/int atomnum: The number for the atom
    
    '''
    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:
            self.phase,self.histogram,self.name,self.atom = args[0]
        elif len(args) == 1 and ':' in args[0]:            
            lst = args[0].split(':')
            self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
            self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
            self.name = lst[2]
            if len(lst) > 3:
                self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
        elif len(args) == 4:
            self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
            self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
            self.name = args[2]
            self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
        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
        '''
        ph = _lookup(PhaseRanIdLookup,self.phase)
        hist = _lookup(HistRanIdLookup,self.histogram)
        s = (ph + ":" + hist + ":" + 
             str(self.name))
        if self.atom:
            if ph in AtomRanIdLookup:
                s += ":" + AtomRanIdLookup[ph].get(self.atom,'?')
            else:
                s += ":?"
        return s
    
    def __repr__(self):
        '''Return the detailed contents of the object
        '''
        s = "<"
        if self.phase is not None:
            ph =  _lookup(PhaseRanIdLookup,self.phase)
            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
        if self.histogram is not None:
            hist = _lookup(HistRanIdLookup,self.histogram)
            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
        if 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!); "
        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']