# -*- coding: utf-8 -*-
########### SVN repository information ###################
# $Date: 2023-11-30 08:10:11 -0600 (Thu, 30 Nov 2023) $
# $Author: vondreele $
# $Revision: 5702 $
# $URL: https://subversion.xray.aps.anl.gov/pyGSAS/trunk/GSASIIlattice.py $
# $Id: GSASIIlattice.py 5702 2023-11-30 14:10:11Z vondreele $
########### SVN repository information ###################
'''
:mod:`GSASIIlattice` Classes & routines follow
'''
from __future__ import division, print_function
import math
import time
import copy
import sys
import random as ran
import numpy as np
import numpy.linalg as nl
import scipy.special as spsp
import GSASIIpath
import GSASIImath as G2mth
import GSASIIspc as G2spc
import GSASIIElem as G2elem
GSASIIpath.SetVersionNumber("$Revision: 5702 $")
# trig functions in degrees
sind = lambda x: np.sin(x*np.pi/180.)
asind = lambda x: 180.*np.arcsin(x)/np.pi
tand = lambda x: np.tan(x*np.pi/180.)
atand = lambda x: 180.*np.arctan(x)/np.pi
atan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi
cosd = lambda x: np.cos(x*np.pi/180.)
acosd = lambda x: 180.*np.arccos(x)/np.pi
rdsq2d = lambda x,p: round(1.0/np.sqrt(x),p)
try: # fails on doc build
rpd = np.pi/180.
RSQ2PI = 1./np.sqrt(2.*np.pi)
SQ2 = np.sqrt(2.)
RSQPI = 1./np.sqrt(np.pi)
R2pisq = 1./(2.*np.pi**2)
Forpi = 4.0*np.pi
except TypeError:
pass
nxs = np.newaxis
[docs]
def sec2HMS(sec):
"""Convert time in sec to H:M:S string
:param sec: time in seconds
:return: H:M:S string (to nearest 100th second)
"""
H = int(sec//3600)
M = int(sec//60-H*60)
S = sec-3600*H-60*M
return '%d:%2d:%.2f'%(H,M,S)
[docs]
def rotdMat(angle,axis=0):
"""Prepare rotation matrix for angle in degrees about axis(=0,1,2)
:param angle: angle in degrees
:param axis: axis (0,1,2 = x,y,z) about which for the rotation
:return: rotation matrix - 3x3 numpy array
"""
if axis == 2:
return np.array([[cosd(angle),-sind(angle),0],[sind(angle),cosd(angle),0],[0,0,1]])
elif axis == 1:
return np.array([[cosd(angle),0,-sind(angle)],[0,1,0],[sind(angle),0,cosd(angle)]])
else:
return np.array([[1,0,0],[0,cosd(angle),-sind(angle)],[0,sind(angle),cosd(angle)]])
[docs]
def rotdMat4(angle,axis=0):
"""Prepare rotation matrix for angle in degrees about axis(=0,1,2) with scaling for OpenGL
:param angle: angle in degrees
:param axis: axis (0,1,2 = x,y,z) about which for the rotation
:return: rotation matrix - 4x4 numpy array (last row/column for openGL scaling)
"""
Mat = rotdMat(angle,axis)
return np.concatenate((np.concatenate((Mat,[[0],[0],[0]]),axis=1),[[0,0,0,1],]),axis=0)
[docs]
def fillgmat(cell):
"""Compute lattice metric tensor from unit cell constants
:param cell: tuple with a,b,c,alpha, beta, gamma (degrees)
:return: 3x3 numpy array
"""
a,b,c,alp,bet,gam = cell
g = np.array([
[a*a, a*b*cosd(gam), a*c*cosd(bet)],
[a*b*cosd(gam), b*b, b*c*cosd(alp)],
[a*c*cosd(bet) ,b*c*cosd(alp), c*c]])
return g
[docs]
def cell2Gmat(cell):
"""Compute real and reciprocal lattice metric tensor from unit cell constants
:param cell: tuple with a,b,c,alpha, beta, gamma (degrees)
:return: reciprocal (G) & real (g) metric tensors (list of two numpy 3x3 arrays)
"""
g = fillgmat(cell)
G = nl.inv(g)
return G,g
[docs]
def A2Gmat(A,inverse=True):
"""Fill real & reciprocal metric tensor (G) from A.
:param A: reciprocal metric tensor elements as [G11,G22,G33,2*G12,2*G13,2*G23]
:param bool inverse: if True return both G and g; else just G
:return: reciprocal (G) & real (g) metric tensors (list of two numpy 3x3 arrays)
"""
G = np.array([
[A[0], A[3]/2., A[4]/2.],
[A[3]/2.,A[1], A[5]/2.],
[A[4]/2.,A[5]/2., A[2]]])
if inverse:
g = nl.inv(G)
return G,g
else:
return G
[docs]
def Gmat2A(G):
"""Extract A from reciprocal metric tensor (G)
:param G: reciprocal metric tensor (3x3 numpy array)
:return: A = [G11,G22,G33,2*G12,2*G13,2*G23]
"""
return [G[0][0],G[1][1],G[2][2],2.*G[0][1],2.*G[0][2],2.*G[1][2]]
[docs]
def cell2A(cell):
"""Obtain A = [G11,G22,G33,2*G12,2*G13,2*G23] from lattice parameters
:param cell: [a,b,c,alpha,beta,gamma] (degrees)
:return: G reciprocal metric tensor as 3x3 numpy array
"""
G,g = cell2Gmat(cell)
return Gmat2A(G)
[docs]
def A2cell(A):
"""Compute unit cell constants from A
:param A: [G11,G22,G33,2*G12,2*G13,2*G23] G - reciprocal metric tensor
:return: a,b,c,alpha, beta, gamma (degrees) - lattice parameters
"""
G,g = A2Gmat(A)
return Gmat2cell(g)
[docs]
def Gmat2cell(g):
"""Compute real/reciprocal lattice parameters from real/reciprocal metric tensor (g/G)
The math works the same either way.
:param g (or G): real (or reciprocal) metric tensor 3x3 array
:return: a,b,c,alpha, beta, gamma (degrees) (or a*,b*,c*,alpha*,beta*,gamma* degrees)
"""
oldset = np.seterr('raise')
a = np.sqrt(max(0,g[0][0]))
b = np.sqrt(max(0,g[1][1]))
c = np.sqrt(max(0,g[2][2]))
alp = acosd(g[2][1]/(b*c))
bet = acosd(g[2][0]/(a*c))
gam = acosd(g[0][1]/(a*b))
np.seterr(**oldset)
return a,b,c,alp,bet,gam
[docs]
def invcell2Gmat(invcell):
"""Compute real and reciprocal lattice metric tensor from reciprocal
unit cell constants
:param invcell: [a*,b*,c*,alpha*, beta*, gamma*] (degrees)
:return: reciprocal (G) & real (g) metric tensors (list of two 3x3 arrays)
"""
G = fillgmat(invcell)
g = nl.inv(G)
return G,g
[docs]
def cellDijFill(pfx,phfx,SGData,parmDict):
'''Returns the filled-out reciprocal cell (A) terms
from the parameter dictionaries corrected for Dij.
:param str pfx: parameter prefix ("n::", where n is a phase number)
:param dict SGdata: a symmetry object
:param dict parmDict: a dictionary of parameters
:returns: A,sigA where each is a list of six terms with the A terms
'''
if pfx+'D11' not in parmDict:
return None
if SGData['SGLaue'] in ['-1',]:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A1']+parmDict[phfx+'D22'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],
parmDict[pfx+'A3']+parmDict[phfx+'D12'],parmDict[pfx+'A4']+parmDict[phfx+'D13'],
parmDict[pfx+'A5']+parmDict[phfx+'D23']]
elif SGData['SGLaue'] in ['2/m',]:
if SGData['SGUniq'] == 'a':
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A1']+parmDict[phfx+'D22'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],0,0,parmDict[pfx+'A5']+parmDict[phfx+'D23']]
elif SGData['SGUniq'] == 'b':
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A1']+parmDict[phfx+'D22'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],0,parmDict[pfx+'A4']+parmDict[phfx+'D13'],0]
else:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A1']+parmDict[phfx+'D22'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],parmDict[pfx+'A3']+parmDict[phfx+'D12'],0,0]
elif SGData['SGLaue'] in ['mmm',]:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A1']+parmDict[phfx+'D22'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],0,0,0]
elif SGData['SGLaue'] in ['4/m','4/mmm']:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A0']+parmDict[phfx+'D11'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],0,0,0]
elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A0']+parmDict[phfx+'D11'],
parmDict[pfx+'A2']+parmDict[phfx+'D33'],parmDict[pfx+'A0']+parmDict[phfx+'D11'],0,0]
elif SGData['SGLaue'] in ['3R', '3mR']:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A0']+parmDict[phfx+'D11'],
parmDict[pfx+'A0']+parmDict[phfx+'D11'],
parmDict[pfx+'A3']+parmDict[phfx+'D23'],parmDict[pfx+'A3']+parmDict[phfx+'D23'],
parmDict[pfx+'A3']+parmDict[phfx+'D23']]
elif SGData['SGLaue'] in ['m3m','m3']:
A = [parmDict[pfx+'A0']+parmDict[phfx+'D11'],parmDict[pfx+'A0']+parmDict[phfx+'D11'],
parmDict[pfx+'A0']+parmDict[phfx+'D11'],0,0,0]
return A
[docs]
def CellDijCorr(Cell,SGData,Data,hist):
'''Returns the cell corrected for Dij values.
:param list Cell: lattice parameters
:param dict SGdata: a symmetry object
:param dict Data: phase data structure; contains set of Dij values
:param str hist: histogram name
:returns: cell corrected for Dij values
'''
A = cell2A(Cell)
Dij = Data[hist]['HStrain'][0]
newA = AplusDij(A,Dij,SGData)
return A2cell(newA)
[docs]
def AplusDij(A,Dij,SGData):
''' returns the A corrected by Dij
:param list A: reciprocal metric terms A0-A5
:param array Dij: unique Dij values as stored in Hstrain
:param dict SGdata: a symmetry object
:returns list newA: A corrected by Dij
'''
if SGData['SGLaue'] in ['-1',]:
newA = [A[0]+Dij[0],A[1]+Dij[1],A[2]+Dij[2],A[3]+Dij[3],A[4]+Dij[4],A[5]+Dij[5]]
elif SGData['SGLaue'] in ['2/m',]:
if SGData['SGUniq'] == 'a':
newA = [A[0]+Dij[0],A[1]+Dij[1],A[2]+Dij[2],0,0,A[5]+Dij[3]]
elif SGData['SGUniq'] == 'b':
newA = [A[0]+Dij[0],A[1]+Dij[1],A[2]+Dij[2],0,A[4]+Dij[3],0]
else:
newA = [A[0]+Dij[0],A[1]+Dij[1],A[2]+Dij[2],A[3]+Dij[3],0,0]
elif SGData['SGLaue'] in ['mmm',]:
newA = [A[0]+Dij[0],A[1]+Dij[1],A[2]+Dij[2],0,0,0]
elif SGData['SGLaue'] in ['4/m','4/mmm']:
newA = [A[0]+Dij[0],A[0]+Dij[0],A[2]+Dij[1],0,0,0]
elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
newA = [A[0]+Dij[0],A[0]+Dij[0],A[2]+Dij[1],A[0]+Dij[0],0,0]
elif SGData['SGLaue'] in ['3R', '3mR']:
newA = [A[0]+Dij[0],A[0]+Dij[0],A[0]+Dij[0],A[3]+Dij[1],A[3]+Dij[1],A[3]+Dij[1]]
elif SGData['SGLaue'] in ['m3m','m3']:
newA = [A[0]+Dij[0],A[0]+Dij[0],A[0]+Dij[0],0,0,0]
return newA
[docs]
def prodMGMT(G,Mat):
'''Transform metric tensor by matrix
:param G: array metric tensor
:param Mat: array transformation matrix
:return: array new metric tensor
'''
return np.inner(np.inner(Mat,G),Mat) #right
# return np.inner(Mat,np.inner(Mat,G)) #right
# return np.inner(np.inner(G,Mat).T,Mat) #right
# return np.inner(Mat,np.inner(G,Mat).T) #right
# code to generate lattice constraint relationships between two phases
# (chemical & magnetic) related by a transformation matrix.
[docs]
def symInner(M1,M2):
'''Compute inner product of two square matrices with symbolic processing
Use dot product because sympy does not define an inner product primitive
This requires that M1 & M2 be two sympy objects, as created in
GenerateCellConstraints().
Note that this is only used to do the symbolic math needed to generate
cell relationships. It is not used normally in GSAS-II.
'''
import sympy as sym
prodOuter = []
for i in range(3):
prod = []
for j in range(3):
prod.append(M1[i,:].dot(M2[j,:]))
prodOuter.append(prod)
return sym.Matrix(prodOuter)
[docs]
def GenerateCellConstraints():
'''Generate unit cell constraints for transforming one set of A tensor
values to another using symbolic math (requires the sympy package)
Note that this is only used to do the symbolic math needed to generate
cell relationships. It is not used normally in GSAS-II.
'''
import sympy as sym
# define A tensor for starting cell
A0, A1, A2, A3, A4, A5 = sym.symbols('A0, A1, A2, A3, A4, A5')
G = sym.Matrix([ [A0, A3/2., A4/2.],
[A3/2., A1, A5/2.],
[A4/2., A5/2., A2 ]] )
# define transformation matrix
T00, T10, T20, T01, T11, T21, T02, T12, T22 = sym.symbols(
'T00, T10, T20, T01, T11, T21, T02, T12, T22')
Tr = sym.Matrix([ [T00, T10, T20], [T01, T11, T21], [T02, T12, T22],])
# apply transform
newG = symInner(symInner(Tr,G),Tr).expand()
# define A tensor for converted cell
return [newG[0,0],newG[1,1],newG[2,2],2.*newG[0,1],2.*newG[0,2],2.*newG[1,2]]
[docs]
def subVals(expr,A,T):
'''Evaluate the symbolic expressions by substituting for A0-A5 & Tij
This can be used on the cell relationships created in
:func:`GenerateCellConstraints` like this::
Trans = np.array([ [2/3, 4/3, 1/3], [-1, 0, 0], [-1/3, -2/3, 1/3] ])
T = np.linalg.inv(Trans).T
print([subVals(i,Aold,T) for i in GenerateCellConstraints()])
:param list expr: a list of sympy expressions.
:param list A: This is the A* tensor as defined above.
:param np.array T: a 3x3 transformation matrix where,
Trans = np.array([ [2/3, 4/3, 1/3], [-1, 0, 0], [-1/3, -2/3, 1/3] ])
(for a' = 2/3a + 4/3b + 1/3c; b' = -a; c' = -1/3, -2/3, 1/3)
then T = np.linalg.inv(Trans).T
Note that this is only used to do the symbolic math needed to generate
cell relationships. It is not used normally in GSAS-II.
'''
import sympy as sym
A0, A1, A2, A3, A4, A5 = sym.symbols('A0, A1, A2, A3, A4, A5')
# transformation matrix
T00, T10, T20, T01, T11, T21, T02, T12, T22 = sym.symbols(
'T00, T10, T20, T01, T11, T21, T02, T12, T22')
vals = dict(zip([T00, T10, T20, T01, T11, T21, T02, T12, T22],T.ravel()))
vals.update(dict(zip([A0, A1, A2, A3, A4, A5],A)))
return float(expr.subs(vals))
# some sample test code using the routines above follows::
# Trans = np.array([ [2/3, 4/3, 1/3], [-1, 0, 0], [-1/3, -2/3, 1/3] ])
# Mat = np.linalg.inv(Trans).T
# Aold = [0.05259986634758891, 0.05259986634758891, 0.005290771904550856, 0.052599866347588925, 0, 0]
# Anew = [0.018440738491448085, 0.03944989976069168, 0.034313054205100654, 0, -0.00513684555559103, 0]
# cellConstr = G2lat.GenerateCellConstraints()
# calcA = [G2lat.subVals(i,Aold,Mat) for i in cellConstr]
# print('original xform A',Anew)
# print('calculated xfrom A',calcA)
# print('input')
# print(' old cell',G2lat.A2cell(Aold))
# print(' new cell',G2lat.A2cell(Anew))
# print('derived results')
# print(' from eq.',G2lat.A2cell(calcA))
# print(' diffs ',np.array(G2lat.A2cell(calcA)) - G2lat.A2cell(Anew))
[docs]
def fmtCellConstraints(cellConstr):
'''Format the cell relationships created in :func:`GenerateCellConstraints`
in a format that can be used to generate constraints.
Use::
cXforms = G2lat.fmtCellConstraints(G2lat.GenerateCellConstraints())
Note that this is only used to do the symbolic math needed to generate
cell relationships. It is not used normally in GSAS-II.
'''
import re
import sympy as sym
A3, A4, A5 = sym.symbols('A3, A4, A5')
consDict = {}
for num,cons in enumerate(cellConstr):
cons = str(cons.factor(A3,A4,A5,deep=True).simplify())
cons = re.sub('T([0-2]?)([0-2]?)',r'T[\2,\1]',cons) # Tij to T[j,i]
l = []
for i in str(cons).split('+'):
if ')' in i:
l[-1] += ' + ' + i.strip()
else:
l.append(i.strip())
print("\nA'{} = ".format(num),str(cons))
consDict[num] = l
return consDict
cellXformRelations = {0: ['1.0*A0*T[0,0]**2',
'1.0*A1*T[0,1]**2',
'1.0*A2*T[0,2]**2',
'1.0*A3*T[0,0]*T[0,1]',
'1.0*A4*T[0,0]*T[0,2]',
'1.0*A5*T[0,1]*T[0,2]'],
1: ['1.0*A0*T[1,0]**2',
'1.0*A1*T[1,1]**2',
'1.0*A2*T[1,2]**2',
'1.0*A3*T[1,0]*T[1,1]',
'1.0*A4*T[1,0]*T[1,2]',
'1.0*A5*T[1,1]*T[1,2]'],
2: ['1.0*A0*T[2,0]**2',
'1.0*A1*T[2,1]**2',
'1.0*A2*T[2,2]**2',
'1.0*A3*T[2,0]*T[2,1]',
'1.0*A4*T[2,0]*T[2,2]',
'1.0*A5*T[2,1]*T[2,2]'],
3: ['2.0*A0*T[0,0]*T[1,0]',
'2.0*A1*T[0,1]*T[1,1]',
'2.0*A2*T[0,2]*T[1,2]',
'1.0*A3*(T[0,0]*T[1,1] + T[1,0]*T[0,1])',
'1.0*A4*(T[0,0]*T[1,2] + T[1,0]*T[0,2])',
'1.0*A5*(T[0,1]*T[1,2] + T[1,1]*T[0,2])'],
4: ['2.0*A0*T[0,0]*T[2,0]',
'2.0*A1*T[0,1]*T[2,1]',
'2.0*A2*T[0,2]*T[2,2]',
'1.0*A3*(T[0,0]*T[2,1] + T[2,0]*T[0,1])',
'1.0*A4*(T[0,0]*T[2,2] + T[2,0]*T[0,2])',
'1.0*A5*(T[0,1]*T[2,2] + T[2,1]*T[0,2])'],
5: ['2.0*A0*T[1,0]*T[2,0]',
'2.0*A1*T[1,1]*T[2,1]',
'2.0*A2*T[1,2]*T[2,2]',
'1.0*A3*(T[1,0]*T[2,1] + T[2,0]*T[1,1])',
'1.0*A4*(T[1,0]*T[2,2] + T[2,0]*T[1,2])',
'1.0*A5*(T[1,1]*T[2,2] + T[2,1]*T[1,2])']}
'''cellXformRelations provide the constraints on newA[i] values for a new
cell generated from oldA[i] values.
'''
# cellXformRelations values were generated using::
# from GSASIIlattice import fmtCellConstraints,GenerateCellConstraints
# cellXformRelations = fmtCellConstraints(GenerateCellConstraints())
[docs]
def GenCellConstraints(Trans,origPhase,newPhase,origA,oSGLaue,nSGLaue,debug=False):
'''Generate the constraints between two unit cells constants for a phase transformed
by matrix Trans.
:param np.array Trans: a 3x3 direct cell transformation matrix where,
Trans = np.array([ [2/3, 4/3, 1/3], [-1, 0, 0], [-1/3, -2/3, 1/3] ])
(for a' = 2/3a + 4/3b + 1/3c; b' = -a; c' = -1/3, -2/3, 1/3)
:param int origPhase: phase id (pId) for original phase
:param int newPhase: phase id for the transformed phase to be constrained from
original phase
:param list origA: reciprocal cell ("A*") tensor (used for debug only)
:param dict oSGLaue: space group info for original phase
:param dict nSGLaue: space group info for transformed phase
:param bool debug: If true, the constraint input is used to compute and print A*
and from that the direct cell for the transformed phase.
'''
import GSASIIobj as G2obj
T = Mat = np.linalg.inv(Trans).T
Anew = []
constrList = []
uniqueAnew = cellUnique(nSGLaue)
zeroAorig = cellZeros(oSGLaue)
for i in range(6):
constr = [[-1.0,G2obj.G2VarObj('{}::A{}'.format(newPhase,i))]]
mult = []
for j,item in enumerate(cellXformRelations[i]):
const, aTerm, tTerm = item.split('*',2)
const = float(const) * eval(tTerm)
mult.append(const)
# skip over A terms that are required to be zero
if zeroAorig[int(aTerm[1])]: continue # only add non-zero terms
# ignore terms where either the Transform contribution is zero [= abs() < 1e-8]
# If the multiplier term is zero I don't think this accidental
# but since it will not change there is no reason to include that
# term in any case
if abs(const) < 1e-8: continue
constr.append([const,G2obj.G2VarObj('{}::{}'.format(origPhase,aTerm))])
if i in uniqueAnew:
constrList.append(constr + [0.0,None,'c'])
if debug: Anew.append(np.dot(origA,mult))
if debug:
print('xformed A* ',Anew)
print('xformed cell',A2cell(Anew))
return constrList
[docs]
def cellUnique(SGData):
'''Returns the indices for the unique A tensor terms
based on the Laue class.
Any terms that are determined from others or are zero are not included.
:param dict SGdata: a symmetry object
:returns: a list of 0 to 6 terms with indices of the unique A terms
'''
if SGData['SGLaue'] in ['-1',]:
return [0,1,2,3,4,5]
elif SGData['SGLaue'] in ['2/m',]:
if SGData['SGUniq'] == 'a':
return [0,1,2,5]
elif SGData['SGUniq'] == 'b':
return [0,1,2,4]
else:
return [0,1,2,3]
elif SGData['SGLaue'] in ['mmm',]:
return [0,1,2]
elif SGData['SGLaue'] in ['4/m','4/mmm']:
return [0,2]
elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
return [0,2]
elif SGData['SGLaue'] in ['3R', '3mR']:
return [0,3]
elif SGData['SGLaue'] in ['m3m','m3']:
return [0,]
[docs]
def cellZeros(SGData):
'''Returns a list with the A terms required to be zero based on Laue symmetry
:param dict SGdata: a symmetry object
:returns: A list of six terms where the values are True if the
A term must be zero, False otherwise.
'''
if SGData['SGLaue'] in ['-1',]:
return 6*[False]
elif SGData['SGLaue'] in ['2/m',]:
if SGData['SGUniq'] == 'a':
return [False,False,False,True,True,False]
elif SGData['SGUniq'] == 'b':
return [False,False,False,True,False,True]
else:
return [False,False,False,False,True,True]
elif SGData['SGLaue'] in ['mmm',]:
return [False,False,False,True,True,True]
elif SGData['SGLaue'] in ['4/m','4/mmm']:
return [False,False,False,True,True,True]
elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
return [False,False,False,False,True,True]
elif SGData['SGLaue'] in ['3R', '3mR']:
return 6*[False]
elif SGData['SGLaue'] in ['m3m','m3']:
return [False,False,False,True,True,True]
def TransformXYZ(XYZ,Trans,Vec):
return np.inner(XYZ,Trans)+Vec
def TransformU6(U6,Trans):
Uij = np.inner(Trans,np.inner(U6toUij(U6),Trans).T)/nl.det(Trans)
return UijtoU6(Uij)
def ExpandCell(Atoms,atCodes,cx,Trans):
Unit = [int(max(abs(np.array(unit)))-1) for unit in Trans.T]
nUnit = (Unit[0]+1)*(Unit[1]+1)*(Unit[2]+1)
Ugrid = np.mgrid[0:Unit[0]+1,0:Unit[1]+1,0:Unit[2]+1]
Ugrid = np.reshape(Ugrid,(3,nUnit)).T
Codes = copy.deepcopy(atCodes)
newAtoms = copy.deepcopy(Atoms)
for unit in Ugrid[1:]:
moreAtoms = copy.deepcopy(Atoms)
for atom in moreAtoms:
atom[cx:cx+3] += unit
newAtoms += moreAtoms
codes = copy.deepcopy(atCodes)
moreCodes = [code+'+%d,%d,%d'%(unit[0],unit[1],unit[2]) for code in codes]
Codes += moreCodes
return newAtoms,Codes
[docs]
def FindNonstandard(controls,Phase):
'''
Find nonstandard setting of magnetic cell that aligns with parent nuclear cell
:param controls: list unit cell indexing controls
:param Phase: dict new magnetic phase data (NB:not G2 phase construction); modified here
:return: None
'''
abc = np.eye(3)
cba = np.rot90(np.eye(3))
cba[1,1] *= -1 #makes c-ba
Mats = {'abc':abc,'cab':np.roll(abc,2,1),'bca':np.roll(abc,1,1),
'acb':np.roll(cba,1,1),'bac':np.roll(cba,2,1),'cba':cba} #ok
BNS = {'A':{'abc':'A','cab':'C','bca':'B','acb':'A','bac':'B','cba':'C'},
'B':{'abc':'B','cab':'A','bca':'C','acb':'C','bac':'A','cba':'B'},
'C':{'abc':'C','cab':'B','bca':'A','acb':'B','bac':'C','cba':'A'},
'a':{'abc':'a','cab':'c','bca':'b','acb':'a','bac':'b','cba':'c'}, #Ok
'b':{'abc':'b','cab':'a','bca':'c','acb':'c','bac':'a','cba':'b'},
'c':{'abc':'c','cab':'b','bca':'a','acb':'b','bac':'c','cba':'a'},
'S':{'abc':'S','cab':'S','bca':'S','acb':'S','bac':'S','cba':'S'},
'I':{'abc':'I','cab':'I','bca':'I','acb':'I','bac':'I','cba':'I'},
}
Trans = Phase['Trans']
Uvec = Phase['Uvec']
SGData = Phase['SGData']
MSG = SGData.get('MagSpGrp',SGData['SpGrp']).split(' ',1)
MSG[0] += ' '
bns = ''
if '_' in MSG[0]:
bns = MSG[0][2]
spn = SGData.get('SGSpin',[])
if 'ortho' in SGData['SGSys']:
lattSym = G2spc.getlattSym(Trans)
SpGrp = SGData['SpGrp']
NTrans = np.inner(Mats[lattSym].T,Trans.T) #ok
if len(spn): spn[1:4] = np.inner(np.abs(nl.inv(Mats[lattSym])),spn[1:4]) #ok
SGsym = G2spc.getlattSym(nl.inv(Mats[lattSym]))
if lattSym != 'abc':
NSG = G2spc.altSettingOrtho[SpGrp][SGsym].replace("'",'').split(' ')
if ' '.join(NSG) in ['P 2 21 2',]:
Uvec[1] += .25
elif ' '.join(NSG) in ['P 21 2 2',]:
Uvec[0] += .25
elif ' '.join(NSG) in ['P 2 2 21',]:
Uvec[2] += .25
Bns = ''
if bns:
Bns = BNS[bns][lattSym]
NSG[0] += '_'+Bns+' '
elif len(spn):
for ifld in [1,2,3]:
if spn[ifld] < 0:
NSG[ifld] += "'"
Nresult = [''.join(NSG)+' ',Bns]
return Nresult,Uvec,NTrans
else:
return None
elif 'mono' in SGData['SGSys']: # and not 'P_A' in Phase['Name']: #skip the one that doesn't work
newcell = TransformCell(controls[6:12],Trans)
MatsA = np.array([[1.,0.,0.],[0.,1.,0.],[1.,0,1.]])
MatsB = np.array([[1.,0.,0.],[0.,1.,0.],[-1.,0,1.]])
if not 70. < newcell[4] < 110.:
MSG[1] = MSG[1].replace('c','n')
MSG[0] = MSG[0].replace('C_c','C_B').replace('P_A','P ')
if '_' in MSG[0]:
bns = MSG[0][2]
if newcell[4] > 110.:
if newcell[2] > newcell[0]:
Mats = MatsA
else:
MSG[1] = MSG[1].replace('n','c')
MSG[0] = MSG[0].replace('C ','I ')
Mats = MatsA.T
elif newcell[4] < 70.:
if newcell[2] > newcell[0]:
Mats = MatsB
else:
MSG[1] = MSG[1].replace('n','c')
MSG[0] = MSG[0].replace('C ','I ')
Mats = MatsB.T
Nresult = [' '.join(MSG)+' ',bns]
NTrans = np.inner(Mats,Trans.T)
return Nresult,Uvec,NTrans
return None
def makeBilbaoPhase(result,uvec,trans,ifMag=False):
phase = {}
phase['Name'] = result[0].strip()
phase['Uvec'] = uvec
phase['Trans'] = trans
phase['Keep'] = False
phase['Use'] = False
phase['aType'] = ''
SpGp = result[0].replace("'",'')
SpGrp = G2spc.StandardizeSpcName(SpGp)
phase['SGData'] = G2spc.SpcGroup(SpGrp)[1]
if ifMag:
BNSlatt = phase['SGData']['SGLatt']
if not result[1]:
MSpGrp = G2spc.SplitMagSpSG(result[0])
phase['SGData']['SGSpin'] = G2spc.GetSGSpin(phase['SGData'],MSpGrp)
phase['SGData']['GenSym'],phase['SGData']['GenFlg'],BNSsym = G2spc.GetGenSym(phase['SGData'])
if result[1]:
BNSlatt += '_'+result[1]
if 'P_S' in BNSlatt: BNSlatt = 'P_c' #triclinic fix
phase['SGData']['BNSlattsym'] = [BNSlatt,BNSsym[BNSlatt]]
G2spc.ApplyBNSlatt(phase['SGData'],phase['SGData']['BNSlattsym'])
phase['SGData']['SpnFlp'] = G2spc.GenMagOps(phase['SGData'])[1]
phase['SGData']['MagSpGrp'] = G2spc.MagSGSym(phase['SGData'])
return phase
def FillUnitCell(Phase,Force=True):
Atoms = copy.deepcopy(Phase['Atoms'])
atomData = []
atCodes = []
SGData = Phase['General']['SGData']
SpnFlp = SGData.get('SpnFlp',[])
Amat,Bmat = cell2AB(Phase['General']['Cell'][1:7])
cx,ct,cs,cia = Phase['General']['AtomPtrs']
cm = 0
if Phase['General']['Type'] == 'magnetic':
cm = cx+4
for iat,atom in enumerate(Atoms):
XYZ = np.array(atom[cx:cx+3])
xyz = XYZ
cellj = np.zeros(3,dtype=np.int32)
if Force:
xyz,cellj = G2spc.MoveToUnitCell(xyz)
if atom[cia] == 'A':
Uij = atom[cia+2:cia+8]
result = G2spc.GenAtom(xyz,SGData,False,Uij,Force)
for item in result:
item = list(item)
item[2] += cellj
# if item[0][2] >= .95: item[0][2] -= 1.
atom[cx:cx+3] = item[0]
atom[cia+2:cia+8] = item[1]
if cm:
Opr = abs(item[2])%100
M = SGData['SGOps'][Opr-1][0]
opNum = G2spc.GetOpNum(item[2],SGData)
mom = np.inner(np.array(atom[cm:cm+3]),Bmat)
atom[cm:cm+3] = np.inner(np.inner(mom,M),Amat)*nl.det(M)*SpnFlp[opNum-1]
atCodes.append('%d:%s'%(iat,str(item[2])))
atomData.append(atom[:cia+9]) #not SS stuff
else:
result = G2spc.GenAtom(xyz,SGData,False,Move=Force)
for item in result:
item = list(item)
item[2] += cellj
# if item[0][2] >= .95: item[0][2] -= 1.
atom[cx:cx+3] = item[0]
if cm:
Opr = abs(item[1])%100
M = SGData['SGOps'][Opr-1][0]
opNum = G2spc.GetOpNum(item[1],SGData)
mom = np.inner(np.array(atom[cm:cm+3]),Bmat)
atom[cm:cm+3] = np.inner(np.inner(mom,M),Amat)*nl.det(M)*SpnFlp[opNum-1]
atCodes.append('%d:%s'%(iat,str(item[1])))
atomData.append(atom[:cia+9]) #not SS stuff
return atomData,atCodes
def GetUnique(Phase,atCodes):
def noDuplicate(xyzA,XYZ):
if True in [np.allclose(xyzA%1.,xyzB%1.,atol=0.0002) for xyzB in XYZ]:
return False
return True
cx,ct = Phase['General']['AtomPtrs'][:2]
SGData = Phase['General']['SGData']
Atoms = Phase['Atoms']
Ind = len(Atoms)
newAtoms = []
newAtCodes = []
Indx = {}
XYZ = {}
for ind in range(Ind):
XYZ[ind] = np.array(Atoms[ind][cx:cx+3])%1.
Indx[ind] = True
for ind in range(Ind):
if Indx[ind]:
xyz = XYZ[ind]
for jnd in range(Ind):
if Atoms[ind][ct-1] == Atoms[jnd][ct-1]:
if ind != jnd and Indx[jnd]:
Equiv = G2spc.GenAtom(XYZ[jnd],SGData,Move=True)
xyzs = np.array([equiv[0] for equiv in Equiv])
Indx[jnd] = noDuplicate(xyz,xyzs)
Ind = []
for ind in Indx:
if Indx[ind]:
newAtoms.append(Atoms[ind])
newAtCodes.append(atCodes[ind])
return newAtoms,newAtCodes
[docs]
def calc_rVsq(A):
"""Compute the square of the reciprocal lattice volume (1/V**2) from A'
"""
G,g = A2Gmat(A)
rVsq = nl.det(G)
if rVsq < 0:
return 1
return rVsq
[docs]
def calc_rV(A):
"""Compute the reciprocal lattice volume (V*) from A
"""
return np.sqrt(calc_rVsq(A))
[docs]
def calc_V(A):
"""Compute the real lattice volume (V) from A
"""
return 1./calc_rV(A)
[docs]
def A2invcell(A):
"""Compute reciprocal unit cell constants from A
returns tuple with a*,b*,c*,alpha*, beta*, gamma* (degrees)
"""
G,g = A2Gmat(A)
return Gmat2cell(G)
[docs]
def Gmat2AB(G):
"""Computes orthogonalization matrix from reciprocal metric tensor G
:returns: tuple of two 3x3 numpy arrays (A,B)
* A for crystal to Cartesian transformations (A*x = np.inner(A,x) = X)
* B (= inverse of A) for Cartesian to crystal transformation (B*X = np.inner(B,X) = x)
"""
# cellstar = Gmat2cell(G)
g = nl.inv(G)
cell = Gmat2cell(g)
# A = np.zeros(shape=(3,3))
return cell2AB(cell)
# # from Giacovazzo (Fundamentals 2nd Ed.) p.75
# A[0][0] = cell[0] # a
# A[0][1] = cell[1]*cosd(cell[5]) # b cos(gamma)
# A[0][2] = cell[2]*cosd(cell[4]) # c cos(beta)
# A[1][1] = cell[1]*sind(cell[5]) # b sin(gamma)
# A[1][2] = -cell[2]*cosd(cellstar[3])*sind(cell[4]) # - c cos(alpha*) sin(beta)
# A[2][2] = 1./cellstar[2] # 1/c*
# B = nl.inv(A)
# return A,B
[docs]
def cell2AB(cell,alt=False):
"""Computes orthogonalization matrix from unit cell constants
:param tuple cell: a,b,c, alpha, beta, gamma (degrees)
:returns: tuple of two 3x3 numpy arrays (A,B)
A for crystal to Cartesian transformations A*x = np.inner(A,x) = X
B (= inverse of A) for Cartesian to crystal transformation B*X = np.inner(B,X) = x
both rounded to 12 places (typically zero terms = +/-10e-6 otherwise)
"""
G,g = cell2Gmat(cell)
cellstar = Gmat2cell(G)
A = np.zeros(shape=(3,3))
if alt: #as used in RMCProfile!!
A[0][0] = 1./cellstar[0]
A[0][1] = cell[0]*cosd(cell[5])*sind(cell[3])
A[0][2] = cell[0]*cosd(cell[4])
A[1][1] = cell[1]*sind(cell[3])
A[1][2] = cell[1]*cosd(cell[3])
A[2][2] = cell[2]
A = np.around(A,12)
B = nl.inv(A)
return A,B
# from Giacovazzo (Fundamentals 2nd Ed.) p.75
A[0][0] = cell[0] # a
A[0][1] = cell[1]*cosd(cell[5]) # b cos(gamma)
A[0][2] = cell[2]*cosd(cell[4]) # c cos(beta)
A[1][1] = cell[1]*sind(cell[5]) # b sin(gamma)
A[1][2] = -cell[2]*cosd(cellstar[3])*sind(cell[4]) # - c cos(alpha*) sin(beta)
A[2][2] = 1./cellstar[2] # 1/c*
A = np.around(A,12)
B = nl.inv(A)
return A,B
[docs]
def HKL2SpAng(H,cell,SGData):
"""Computes spherical coords for hkls; view along 001
:param array H: arrays of hkl
:param tuple cell: a,b,c, alpha, beta, gamma (degrees)
:param dict SGData: space group dictionary
:returns: arrays of r,phi,psi (radius,inclination,azimuth) about 001
"""
A,B = cell2AB(cell)
xH = np.inner(B.T,H)
r = np.sqrt(np.sum(xH**2,axis=0))
phi = acosd(xH[2]/r)
psi = atan2d(xH[1],xH[0])
phi = np.where(phi>90.,180.-phi,phi)
return r,phi,psi
[docs]
def U6toUij(U6):
"""Fill matrix (Uij) from U6 = [U11,U22,U33,U12,U13,U23]
NB: there is a non numpy version in GSASIIspc: U2Uij
:param list U6: 6 terms of u11,u22,...
:returns:
Uij - numpy [3][3] array of uij
"""
U = np.array([
[U6[0], U6[3], U6[4]],
[U6[3], U6[1], U6[5]],
[U6[4], U6[5], U6[2]]])
return U
[docs]
def UijtoU6(U):
"""Fill vector [U11,U22,U33,U12,U13,U23] from Uij
NB: there is a non numpy version in GSASIIspc: Uij2U
"""
U6 = np.array([U[0][0],U[1][1],U[2][2],U[0][1],U[0][2],U[1][2]])
return U6
[docs]
def betaij2Uij(betaij,G):
"""
Convert beta-ij to Uij tensors
:param beta-ij - numpy array [beta-ij]
:param G: reciprocal metric tensor
:returns: Uij: numpy array [Uij]
"""
ast = np.sqrt(np.diag(G)) #a*, b*, c*
Mast = np.multiply.outer(ast,ast)
return R2pisq*UijtoU6(U6toUij(betaij)/Mast)
[docs]
def Uij2betaij(Uij,G):
"""
Convert Uij to beta-ij tensors -- stub for eventual completion
:param Uij: numpy array [Uij]
:param G: reciprocal metric tensor
:returns: beta-ij - numpy array [beta-ij]
"""
pass
[docs]
def cell2GS(cell):
''' returns Uij to betaij conversion matrix'''
G,g = cell2Gmat(cell)
GS = G
GS[0][1] = GS[1][0] = math.sqrt(GS[0][0]*GS[1][1])
GS[0][2] = GS[2][0] = math.sqrt(GS[0][0]*GS[2][2])
GS[1][2] = GS[2][1] = math.sqrt(GS[1][1]*GS[2][2])
return GS
[docs]
def Uij2Ueqv(Uij,GS,Amat):
''' returns 1/3 trace of diagonalized U matrix
:param Uij: numpy array [Uij]
:param GS: Uij too betaij conversion matrix
:param Amat: crystal to Cartesian transformation matrix
:returns: 1/3 trace of diagonalized U matrix
:returns: True if nonpositive-definite; False otherwise
'''
U = np.multiply(U6toUij(Uij),GS)
U = np.inner(Amat,np.inner(U,Amat).T)
E,R = nl.eigh(U)
return np.sum(E)/3.,E[0] < 0.
[docs]
def CosAngle(U,V,G):
""" calculate cos of angle between U & V in generalized coordinates
defined by metric tensor G
:param U: 3-vectors assume numpy arrays, can be multiple reflections as (N,3) array
:param V: 3-vectors assume numpy arrays, only as (3) vector
:param G: metric tensor for U & V defined space assume numpy array
:returns:
cos(phi)
"""
u = (U.T/np.sqrt(np.sum(np.inner(U,G)*U,axis=1))).T
v = V/np.sqrt(np.inner(V,np.inner(G,V)))
cosP = np.inner(u,np.inner(G,v))
return cosP
[docs]
def CosSinAngle(U,V,G):
""" calculate sin & cos of angle between U & V in generalized coordinates
defined by metric tensor G
:param U: 3-vectors assume numpy arrays
:param V: 3-vectors assume numpy arrays
:param G: metric tensor for U & V defined space assume numpy array
:returns:
cos(phi) & sin(phi)
"""
u = U/np.sqrt(np.inner(U,np.inner(G,U)))
v = V/np.sqrt(np.inner(V,np.inner(G,V)))
cosP = np.inner(u,np.inner(G,v))
sinP = np.sqrt(max(0.0,1.0-cosP**2))
return cosP,sinP
[docs]
def criticalEllipse(prob):
"""
Calculate critical values for probability ellipsoids from probability
"""
if not ( 0.01 <= prob < 1.0):
return 1.54
coeff = np.array([6.44988E-09,4.16479E-07,1.11172E-05,1.58767E-04,0.00130554,
0.00604091,0.0114921,-0.040301,-0.6337203,1.311582])
llpr = math.log(-math.log(prob))
return np.polyval(coeff,llpr)
[docs]
def CellBlock(nCells):
"""
Generate block of unit cells n*n*n on a side; [0,0,0] centered, n = 2*nCells+1
currently only works for nCells = 0 or 1 (not >1)
"""
if nCells:
N = 2*nCells+1
N2 = N*N
N3 = N*N*N
cellArray = []
A = np.array(range(N3))
cellGen = np.array([A//N2-1,A//N%N-1,A%N-1]).T
for cell in cellGen:
cellArray.append(cell)
return cellArray
else:
return [0,0,0]
[docs]
def CellAbsorption(ElList,Volume):
'''Compute unit cell absorption
:param dict ElList: dictionary of element contents including mu and
number of atoms be cell
:param float Volume: unit cell volume
:returns: mu-total/Volume
'''
muT = 0
for El in ElList:
muT += ElList[El]['mu']*ElList[El]['FormulaNo']
return muT/Volume
#Permutations and Combinations
# Four routines: combinations,uniqueCombinations, selections & permutations
#These taken from Python Cookbook, 2nd Edition. 19.15 p724-726
#
def _combinators(_handle, items, n):
""" factored-out common structure of all following combinators """
if n==0:
yield [ ]
return
for i, item in enumerate(items):
this_one = [ item ]
for cc in _combinators(_handle, _handle(items, i), n-1):
yield this_one + cc
[docs]
def combinations(items, n):
""" take n distinct items, order matters """
def skipIthItem(items, i):
return items[:i] + items[i+1:]
return _combinators(skipIthItem, items, n)
[docs]
def uniqueCombinations(items, n):
""" take n distinct items, order is irrelevant """
def afterIthItem(items, i):
return items[i+1:]
return _combinators(afterIthItem, items, n)
[docs]
def selections(items, n):
""" take n (not necessarily distinct) items, order matters """
def keepAllItems(items, i):
return items
return _combinators(keepAllItems, items, n)
[docs]
def permutations(items):
""" take all items, order matters """
return combinations(items, len(items))
#reflection generation routines
#for these: H = [h,k,l]; A is as used in calc_rDsq; G - inv metric tensor, g - metric tensor;
# cell - a,b,c,alp,bet,gam in A & deg
[docs]
def Pos2dsp(Inst,pos):
''' convert powder pattern position (2-theta or TOF, musec) to d-spacing
is currently only approximate for EDX data; accurate for others.
'''
if 'T' in Inst['Type'][0]:
return TOF2dsp(Inst,pos)
elif 'E' in Inst['Type'][0]:
return 12.398/(2.0*pos*sind(Inst['2-theta'][1]/2.0))
else: #'PKS', 'C' or 'B'
wave = G2mth.getWave(Inst)
return wave/(2.0*sind((pos-Inst.get('Zero',[0,0])[1])/2.0))
[docs]
def TOF2dsp(Inst,Pos):
''' convert powder pattern TOF, musec to d-spacing by successive approximation
Pos can be numpy array
'''
def func(d,pos,Inst):
return (pos-Inst['difA'][1]*d**2-Inst['Zero'][1]-Inst['difB'][1]/d)/Inst['difC'][1]
dsp0 = Pos/Inst['difC'][1]
N = 0
while True: #successive approximations
dsp = func(dsp0,Pos,Inst)
if np.allclose(dsp,dsp0,atol=0.000001):
return dsp
dsp0 = dsp
N += 1
if N > 10:
return dsp
[docs]
def Dsp2pos(Inst,dsp):
''' convert d-spacing to powder pattern position (2-theta or TOF, musec)
'''
if 'T' in Inst['Type'][0]:
pos = Inst['difC'][1]*dsp+Inst['Zero'][1]+Inst['difA'][1]*dsp**2+Inst.get('difB',[0,0,False])[1]/dsp
elif 'E' in Inst['Type'][0]:
return 12.398/(2.0*dsp*sind(Inst['2-theta'][1]/2.0))+Inst['ZE'][1]+Inst['YE'][1]*dsp+Inst['XE'][1]*dsp**2
else: #'C' or 'B'
wave = G2mth.getWave(Inst)
val = min(0.995,wave/(2.*dsp)) #set max at 168deg
pos = 2.0*asind(val)+Inst.get('Zero',[0,0])[1]
return pos
[docs]
def getPeakPos(dataType,parmdict,dsp):
''' convert d-spacing to powder pattern position (2-theta, E or TOF, musec)
'''
if 'T' in dataType:
pos = parmdict['difC']*dsp+parmdict['difA']*dsp**2+parmdict['difB']/dsp+parmdict['Zero']
elif 'E'in dataType:
pos = 12.398/(2.0*dsp*sind(parmdict['2-theta']/2.0)+parmdict['ZE']+parmdict['YE']*dsp+parmdict['XE']*dsp**2)
else: #'C' or 'B'
pos = 2.0*asind(parmdict['Lam']/(2.*dsp))+parmdict['Zero']
return pos
[docs]
def calc_rDsq(H,A):
'needs doc string'
rdsq = H[0]*H[0]*A[0]+H[1]*H[1]*A[1]+H[2]*H[2]*A[2]+H[0]*H[1]*A[3]+H[0]*H[2]*A[4]+H[1]*H[2]*A[5]
return rdsq
[docs]
def calc_rDsq2(H,G):
'needs doc string'
return np.inner(H,np.inner(G,H))
[docs]
def calc_rDsqSS(H,A,vec):
'needs doc string'
rdsq = calc_rDsq(H[:3]+(H[3]*vec).T,A)
return rdsq
[docs]
def calc_rDsqZ(H,A,Z,tth,lam):
'needs doc string'
rdsq = calc_rDsq(H,A)+Z*sind(tth)*2.0*rpd/lam**2
return rdsq
[docs]
def calc_rDsqZSS(H,A,vec,Z,tth,lam):
'needs doc string'
rdsq = calc_rDsq(H[:3]+(H[3][:,np.newaxis]*vec).T,A)+Z*sind(tth)*2.0*rpd/lam**2
return rdsq
[docs]
def calc_rDsqT(H,A,Z,tof,difC):
'needs doc string'
rdsq = calc_rDsq(H,A)+Z/difC
return rdsq
[docs]
def calc_rDsqTSS(H,A,vec,Z,tof,difC):
'needs doc string'
rdsq = calc_rDsq(H[:3]+(H[3][:,np.newaxis]*vec).T,A)+Z/difC
return rdsq
[docs]
def PlaneIntercepts(Amat,H,phase,stack):
''' find unit cell intercepts for a stack of hkl planes
'''
Steps = range(-1,2,2)
if stack:
Steps = range(-10,10,1)
Stack = []
Ux = np.array([[0,0],[1,0],[1,1],[0,1]])
for step in Steps:
HX = []
for i in [0,1,2]:
if H[i]:
h,k,l = [(i+1)%3,(i+2)%3,(i+3)%3]
for j in [0,1,2,3]:
hx = [0,0,0]
intcpt = ((phase)/360.+step-H[h]*Ux[j,0]-H[k]*Ux[j,1])/H[l]
if 0. <= intcpt <= 1.:
hx[h] = Ux[j,0]
hx[k] = Ux[j,1]
hx[l] = intcpt
HX.append(hx)
if len(HX)> 2:
HX = np.array(HX)
DX = np.inner(HX-HX[0],Amat)
D = np.sqrt(np.sum(DX**2,axis=1))
Dsort = np.argsort(D)
HX = HX[Dsort]
DX = DX[Dsort]
D = D[Dsort]
DX[1:,:] = DX[1:,:]/D[1:,nxs]
A = 2.*np.ones(HX.shape[0])
A[1:] = [np.dot(DX[1],dx) for dx in DX[1:]]
HX = HX[np.argsort(A)]
Stack.append(HX)
return Stack
[docs]
def MaxIndex(dmin,A):
'needs doc string'
Hmax = [0,0,0]
try:
cell = A2cell(A)
except:
cell = [1.,1.,1.,90.,90.,90.]
for i in range(3):
Hmax[i] = int(np.round(cell[i]/dmin))
return Hmax
[docs]
def transposeHKLF(transMat,Super,refList):
''' Apply transformation matrix to hkl(m)
param: transmat: 3x3 or 4x4 array
param: Super: 0 or 1 for extra index
param: refList list of h,k,l,....
return: newRefs transformed list of h',k',l',,,
return: badRefs list of noninteger h',k',l'...
'''
newRefs = np.copy(refList)
badRefs = []
for H in newRefs:
newH = np.inner(transMat,H[:3+Super])
H[:3+Super] = np.rint(newH)
if not np.allclose(newH,H[:3+Super],atol=0.01):
badRefs.append(newH)
return newRefs,badRefs
[docs]
def sortHKLd(HKLd,ifreverse,ifdup,ifSS=False):
'''sort reflection list on d-spacing; can sort in either order
:param HKLd: a list of [h,k,l,d,...];
:param ifreverse: True for largest d first
:param ifdup: True if duplicate d-spacings allowed
:return: sorted reflection list
'''
T = []
N = 3
if ifSS:
N = 4
for i,H in enumerate(HKLd):
if ifdup:
T.append((H[N],i))
else:
T.append(H[N])
D = dict(zip(T,HKLd))
T.sort()
if ifreverse:
T.reverse()
X = []
okey = ''
for key in T:
if key != okey: X.append(D[key]) #remove duplicate d-spacings
okey = key
return X
[docs]
def SwapIndx(Axis,H):
'needs doc string'
if Axis in [1,-1]:
return H
elif Axis in [2,-3]:
return [H[1],H[2],H[0]]
else:
return [H[2],H[0],H[1]]
[docs]
def SwapItems(Alist,pos1,pos2):
'exchange 2 items in a list'
try:
get = Alist[pos1],Alist[pos2]
Alist[pos2],Alist[pos1] = get
except IndexError:
pass
return Alist
[docs]
def Rh2Hx(Rh):
'needs doc string'
Hx = [0,0,0]
Hx[0] = Rh[0]-Rh[1]
Hx[1] = Rh[1]-Rh[2]
Hx[2] = np.sum(Rh)
return Hx
[docs]
def Hx2Rh(Hx):
'needs doc string'
Rh = [0,0,0]
itk = -Hx[0]+Hx[1]+Hx[2]
if itk%3 != 0:
return 0 #error - not rhombohedral reflection
else:
Rh[1] = itk//3
Rh[0] = Rh[1]+Hx[0]
Rh[2] = Rh[1]-Hx[1]
if Rh[0] < 0:
for i in range(3):
Rh[i] = -Rh[i]
return Rh
[docs]
def CentCheck(Cent,H):
'needs doc string'
h,k,l = H
if Cent == 'A' and (k+l)%2:
return False
elif Cent == 'B' and (h+l)%2:
return False
elif Cent == 'C' and (h+k)%2:
return False
elif Cent == 'I' and (h+k+l)%2:
return False
elif Cent == 'F' and ((h+k)%2 or (h+l)%2 or (k+l)%2):
return False
elif Cent == 'R' and (-h+k+l)%3:
return False
else:
return True
[docs]
def RBsymCheck(Atoms,ct,cx,cs,AtLookUp,Amat,RBObjIds,SGData):
""" Checks members of a rigid body to see if one is a symmetry equivalent of another.
If so the atom site frac is set to zero.
:param Atoms: atom array as defined in GSAS-II; modified here
:param ct: int location of atom type in Atoms item
:param cx: int location of x,y,z,frac in Atoms item
:param dict AtLookUp: atom lookup by Id table
:param np.array Amat: crystal-to-Cartesian transformation matrix
:param list RBObjIds: atom Id belonging to rigid body being tested
:param dict SGData: GSAS-II space group info.
:returns: Atoms with modified atom frac entries
"""
for i,Id in enumerate(RBObjIds):
XYZo = np.array(Atoms[AtLookUp[Id]][cx:cx+3])%1.
typo = Atoms[AtLookUp[Id]][ct]
for Jd in RBObjIds[i+1:]:
if Atoms[AtLookUp[Jd]][ct] == typo:
XYZt = Atoms[AtLookUp[Jd]][cx:cx+3]
Xeqv = list(G2spc.GenAtom(np.array(XYZt)%1.,SGData,True))
close = [np.allclose(np.inner(Amat,XYZo),np.inner(Amat,eqv[0]),atol=0.1) for eqv in Xeqv]
if True in close:
Atoms[AtLookUp[Jd]][cx+3] = 0.0
Sytsym,Mult = G2spc.SytSym(Atoms[AtLookUp[Id]][cx:cx+3],SGData)[:2]
Atoms[AtLookUp[Id]][cs] = Sytsym
Atoms[AtLookUp[Id]][cs+1] = Mult
return Atoms
[docs]
def GetBraviasNum(center,system):
"""Determine the Bravais lattice number, as used in GenHBravais
:param center: one of: 'P', 'C', 'I', 'F', 'R' (see SGLatt from GSASIIspc.SpcGroup)
:param system: one of 'cubic', 'hexagonal', 'tetragonal', 'orthorhombic', 'trigonal' (for R)
'monoclinic', 'triclinic' (see SGSys from GSASIIspc.SpcGroup)
:return: a number between 0 and 13
or throws a ValueError exception if the combination of center, system is not found (i.e. non-standard)
"""
if center.upper() == 'F' and system.lower() == 'cubic':
return 0
elif center.upper() == 'I' and system.lower() == 'cubic':
return 1
elif center.upper() == 'P' and system.lower() == 'cubic':
return 2
elif center.upper() == 'R' and system.lower() == 'trigonal':
return 3
elif center.upper() == 'P' and system.lower() == 'hexagonal':
return 4
elif center.upper() == 'I' and system.lower() == 'tetragonal':
return 5
elif center.upper() == 'P' and system.lower() == 'tetragonal':
return 6
elif center.upper() == 'F' and system.lower() == 'orthorhombic':
return 7
elif center.upper() == 'I' and system.lower() == 'orthorhombic':
return 8
elif center.upper() == 'A' and system.lower() == 'orthorhombic':
return 9
elif center.upper() == 'B' and system.lower() == 'orthorhombic':
return 10
elif center.upper() == 'C' and system.lower() == 'orthorhombic':
return 11
elif center.upper() == 'P' and system.lower() == 'orthorhombic':
return 12
elif center.upper() == 'C' and system.lower() == 'monoclinic':
return 13
elif center.upper() == 'P' and system.lower() == 'monoclinic':
return 14
elif center.upper() == 'P' and system.lower() == 'triclinic':
return 15
raise ValueError('non-standard Bravais lattice center=%s, cell=%s' % (center,system))
def _GenHBravais_cctbx(dmin, Bravais, A, sg_type, uctbx_unit_cell, miller_index_generator):
'''Alternate form of :func:`GenHBravais` that uses CCTBX internals
'''
g_inv = np.array([[A[0], A[3]/2, A[4]/2],
[A[3]/2, A[1], A[5]/2],
[A[4]/2, A[5]/2, A[2]]])
g = np.linalg.inv(g_inv)
g_elems = (g[0][0], g[1][1], g[2][2], g[0][1], g[0][2], g[1][2])
try:
uc = uctbx_unit_cell(metrical_matrix=g_elems)
except ValueError: # this function sometimes receives an A matrix that gives
# numbers <0 in the diagonal elems of g. Not sure why.
return []
#if sg_type is None:
# sg_type = make_sgtype(Bravais)
mig = miller_index_generator(uc, sg_type, 0, dmin)
result = []
for h,k,l in mig:
d = uc.d((h,k,l))
result.append([h, k, l, d, -1])
result.sort(key=lambda l: l[3], reverse=True)
return result
[docs]
def GenHBravais(dmin, Bravais, A, cctbx_args=None):
"""Generate the positionally unique powder diffraction reflections
:param dmin: minimum d-spacing in A
:param Bravais: lattice type (see GetBraviasNum). Bravais is one of:
* 0 F cubic
* 1 I cubic
* 2 P cubic
* 3 R hexagonal (trigonal not rhombohedral)
* 4 P hexagonal
* 5 I tetragonal
* 6 P tetragonal
* 7 F orthorhombic
* 8 I orthorhombic
* 9 A orthorhombic
* 10 B orthorhombic
* 11 C orthorhombic
* 12 P orthorhombic
* 13 I monoclinic
* 14 A monoclinic
* 15 C monoclinic
* 16 P monoclinic
* 17 P triclinic
:param A: reciprocal metric tensor elements as [G11,G22,G33,2*G12,2*G13,2*G23]
:param dict cctbx_args: items defined in CCTBX:
* 'sg_type': value from cctbx.sgtbx.space_group_type(symmorphic_sgs[ibrav])
* 'uctbx_unit_cell': pointer to :meth:`cctbx.uctbx.unit_cell`
* 'miller_index_generator': pointer to :meth:`cctbx.miller.index_generator`
:returns: HKL unique d list of [h,k,l,d,-1] sorted with largest d first
"""
if cctbx_args:
return _GenHBravais_cctbx(dmin, Bravais, A,
cctbx_args['sg_type'], cctbx_args['uctbx_unit_cell'], cctbx_args['miller_index_generator'])
if Bravais in [9,14]:
Cent = 'A'
elif Bravais in [10,]:
Cent = 'B'
elif Bravais in [11,15]:
Cent = 'C'
elif Bravais in [1,5,8,13]:
Cent = 'I'
elif Bravais in [0,7]:
Cent = 'F'
elif Bravais in [3]:
Cent = 'R'
else:
Cent = 'P'
Hmax = MaxIndex(dmin,A)
dminsq = 1./(dmin**2)
HKL = []
if Bravais == 17: #triclinic
for l in range(-Hmax[2],Hmax[2]+1):
for k in range(-Hmax[1],Hmax[1]+1):
hmin = 0
if (k < 0): hmin = 1
if (k ==0 and l < 0): hmin = 1
for h in range(hmin,Hmax[0]+1):
H=[h,k,l]
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,rdsq2d(rdsq,6),-1])
elif Bravais in [13,14,15,16]: #monoclinic - b unique
Hmax = SwapIndx(2,Hmax)
for h in range(Hmax[0]+1):
for k in range(-Hmax[1],Hmax[1]+1):
lmin = 0
if k < 0:lmin = 1
for l in range(lmin,Hmax[2]+1):
[h,k,l] = SwapIndx(-2,[h,k,l])
H = []
if CentCheck(Cent,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,rdsq2d(rdsq,6),-1])
[h,k,l] = SwapIndx(2,[h,k,l])
elif Bravais in [7,8,9,10,11,12]: #orthorhombic
for h in range(Hmax[0]+1):
for k in range(Hmax[1]+1):
for l in range(Hmax[2]+1):
H = []
if CentCheck(Cent,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,rdsq2d(rdsq,6),-1])
elif Bravais in [5,6]: #tetragonal
for l in range(Hmax[2]+1):
for k in range(Hmax[1]+1):
for h in range(k,Hmax[0]+1):
H = []
if CentCheck(Cent,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,rdsq2d(rdsq,6),-1])
elif Bravais in [3,4]:
lmin = 0
if Bravais == 3: lmin = -Hmax[2] #hexagonal/trigonal
for l in range(lmin,Hmax[2]+1):
for k in range(Hmax[1]+1):
hmin = k
if l < 0: hmin += 1
for h in range(hmin,Hmax[0]+1):
H = []
if CentCheck(Cent,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,rdsq2d(rdsq,6),-1])
else: #cubic
for l in range(Hmax[2]+1):
for k in range(l,Hmax[1]+1):
for h in range(k,Hmax[0]+1):
H = []
if CentCheck(Cent,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,rdsq2d(rdsq,6),-1])
return sortHKLd(HKL,True,False)
[docs]
def getHKLmax(dmin,SGData,A):
'finds maximum allowed hkl for given A within dmin'
SGLaue = SGData['SGLaue']
if SGLaue in ['3R','3mR']: #Rhombohedral axes
Hmax = [0,0,0]
cell = A2cell(A)
aHx = cell[0]*math.sqrt(2.0*(1.0-cosd(cell[3])))
cHx = cell[0]*math.sqrt(3.0*(1.0+2.0*cosd(cell[3])))
Hmax[0] = Hmax[1] = int(round(aHx/dmin))
Hmax[2] = int(round(cHx/dmin))
#print Hmax,aHx,cHx
else: # all others
Hmax = MaxIndex(dmin,A)
return Hmax
[docs]
def GenHLaue(dmin,SGData,A):
"""Generate the crystallographically unique powder diffraction reflections
for a lattice and Bravais type
:param dmin: minimum d-spacing
:param SGData: space group dictionary with at least
* 'SGLaue': Laue group symbol: one of '-1','2/m','mmm','4/m','6/m','4/mmm','6/mmm', '3m1', '31m', '3', '3R', '3mR', 'm3', 'm3m'
* 'SGLatt': lattice centering: one of 'P','A','B','C','I','F'
* 'SGUniq': code for unique monoclinic axis one of 'a','b','c' (only if 'SGLaue' is '2/m') otherwise an empty string
:param A: reciprocal metric tensor elements as [G11,G22,G33,2*G12,2*G13,2*G23]
:return: HKL = list of [h,k,l,d] sorted with largest d first and is unique
part of reciprocal space ignoring anomalous dispersion
"""
import math
SGLaue = SGData['SGLaue']
SGLatt = SGData['SGLatt']
SGUniq = SGData['SGUniq']
#finds maximum allowed hkl for given A within dmin
Hmax = getHKLmax(dmin,SGData,A)
dminsq = 1./(dmin**2)
HKL = []
if SGLaue == '-1': #triclinic
for l in range(-Hmax[2],Hmax[2]+1):
for k in range(-Hmax[1],Hmax[1]+1):
hmin = 0
if (k < 0) or (k ==0 and l < 0): hmin = 1
for h in range(hmin,Hmax[0]+1):
H = []
if CentCheck(SGLatt,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,1./math.sqrt(rdsq)])
elif SGLaue == '2/m': #monoclinic
axisnum = 1 + ['a','b','c'].index(SGUniq)
Hmax = SwapIndx(axisnum,Hmax)
for h in range(Hmax[0]+1):
for k in range(-Hmax[1],Hmax[1]+1):
lmin = 0
if k < 0:lmin = 1
for l in range(lmin,Hmax[2]+1):
[h,k,l] = SwapIndx(-axisnum,[h,k,l])
H = []
if CentCheck(SGLatt,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,1./math.sqrt(rdsq)])
[h,k,l] = SwapIndx(axisnum,[h,k,l])
elif SGLaue in ['mmm','4/m','6/m']: #orthorhombic
for l in range(Hmax[2]+1):
for h in range(Hmax[0]+1):
kmin = 1
if SGLaue == 'mmm' or h ==0: kmin = 0
for k in range(kmin,Hmax[1]+1):
H = []
if CentCheck(SGLatt,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,1./math.sqrt(rdsq)])
elif SGLaue in ['4/mmm','6/mmm']: #tetragonal & hexagonal
for l in range(Hmax[2]+1):
for h in range(Hmax[0]+1):
for k in range(h+1):
H = []
if CentCheck(SGLatt,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,1./math.sqrt(rdsq)])
elif SGLaue in ['3m1','31m','3','3R','3mR']: #trigonals
for l in range(-Hmax[2],Hmax[2]+1):
hmin = 0
if l < 0: hmin = 1
for h in range(hmin,Hmax[0]+1):
if SGLaue in ['3R','3']:
kmax = h
kmin = -int((h-1.)/2.)
else:
kmin = 0
kmax = h
if SGLaue in ['3m1','3mR'] and l < 0: kmax = h-1
if SGLaue == '31m' and l < 0: kmin = 1
for k in range(kmin,kmax+1):
H = []
if CentCheck(SGLatt,[h,k,l]): H=[h,k,l]
if SGLaue in ['3R','3mR']:
H = Hx2Rh(H)
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([H[0],H[1],H[2],1./math.sqrt(rdsq)])
else: #cubic
for h in range(Hmax[0]+1):
for k in range(h+1):
lmin = 0
lmax = k
if SGLaue =='m3':
lmax = h-1
if h == k: lmax += 1
for l in range(lmin,lmax+1):
H = []
if CentCheck(SGLatt,[h,k,l]): H=[h,k,l]
if H:
rdsq = calc_rDsq(H,A)
if 0 < rdsq <= dminsq:
HKL.append([h,k,l,1./math.sqrt(rdsq)])
return sortHKLd(HKL,True,True)
[docs]
def GenPfHKLs(nMax,SGData,A):
"""Generate the unique pole figure reflections for a lattice and Bravais type.
Min d-spacing=1.0A & no more than nMax returned
:param nMax: maximum number of hkls returned
:param SGData: space group dictionary with at least
* 'SGLaue': Laue group symbol: one of '-1','2/m','mmm','4/m','6/m','4/mmm','6/mmm', '3m1', '31m', '3', '3R', '3mR', 'm3', 'm3m'
* 'SGLatt': lattice centering: one of 'P','A','B','C','I','F'
* 'SGUniq': code for unique monoclinic axis one of 'a','b','c' (only if 'SGLaue' is '2/m') otherwise an empty string
:param A: reciprocal metric tensor elements as [G11,G22,G33,2*G12,2*G13,2*G23]
:return: HKL = list of 'h k l' strings sorted with largest d first; no duplicate zones
"""
HKL = np.array(GenHLaue(1.0,SGData,A)).T[:3].T #strip d-spacings
N = min(nMax,len(HKL))
return ['%d %d %d'%(h[0],h[1],h[2]) for h in HKL[:N]]
[docs]
def GenSSHLaue(dmin,SGData,SSGData,Vec,maxH,A):
'needs a doc string'
ifMag = False
if 'MagSpGrp' in SGData:
ifMag = True
HKLs = []
vec = np.array(Vec)
vstar = np.sqrt(calc_rDsq(vec,A)) #find extra needed for -n SS reflections
dvec = 1./(maxH*vstar+1./dmin)
HKL = GenHLaue(dvec,SGData,A)
SSdH = [vec*h for h in range(-maxH,maxH+1)]
SSdH = dict(zip(range(-maxH,maxH+1),SSdH))
for h,k,l,d in HKL:
ext = G2spc.GenHKLf([h,k,l],SGData)[0] #h,k,l must be integral values here
if not ext and d >= dmin:
HKLs.append([h,k,l,0,d])
for dH in SSdH:
if dH:
DH = SSdH[dH]
H = [h+DH[0],k+DH[1],l+DH[2]]
d = 1./np.sqrt(calc_rDsq(H,A))
if d >= dmin:
HKLM = np.array([h,k,l,dH])
if (G2spc.checkSSLaue([h,k,l,dH],SGData,SSGData) and G2spc.checkSSextc(HKLM,SSGData)) or ifMag:
HKLs.append([h,k,l,dH,d])
return HKLs
[docs]
def LaueUnique2(SGData,refList):
''' Impose Laue symmetry on hkl
:param SGData: space group data from 'P '+Laue
:param HKLF: np.array([[h,k,l,...]]) reflection set to be converted
:return: HKLF new reflection array with imposed Laue symmetry
'''
for ref in refList:
H = ref[:3]
Uniq = G2spc.GenHKLf(H,SGData)[2]
Uniq = G2mth.sortArray(G2mth.sortArray(G2mth.sortArray(Uniq,2),1),0)
ref[:3] = Uniq[-1]
return refList
[docs]
def LaueUnique(Laue,HKLF):
''' Impose Laue symmetry on hkl
:param str Laue: Laue symbol, as below
centrosymmetric Laue groups::
['-1','2/m','112/m','2/m11','mmm','-42m','-4m2','4/mmm','-3','-3m',
'-31m','-3m1','6/m','6/mmm','m3','m3m']
noncentrosymmetric Laue groups::
['1','2','211','112','m','m11','11m','222','mm2','m2m','2mm',
'4','-4','422','4mm','3','312','321','3m','31m','3m1','6','-6',
'622','6mm','-62m','-6m2','23','432','-43m']
:param HKLF: np.array([[h,k,l,...]]) reflection set to be converted
:returns: HKLF new reflection array with imposed Laue symmetry
'''
HKLFT = HKLF.T
mat41 = np.array([[0,1,0],[-1,0,0],[0,0,1]]) #hkl -> k,-h,l
mat43 = np.array([[0,-1,0],[1,0,0],[0,0,1]]) #hkl -> -k,h,l
mat4bar = np.array([[0,-1,0],[1,0,0],[0,0,-1]]) #hkl -> k,-h,-l
mat31 = np.array([[-1,-1,0],[1,0,0],[0,0,1]]) #hkl -> ihl = -h-k,h,l
mat32 = np.array([[0,1,0],[-1,-1,0],[0,0,1]]) #hkl -> kil = k,-h-k,l
matd3 = np.array([[0,1,0],[0,0,1],[1,0,0]]) #hkl -> k,l,h
matd3q = np.array([[0,0,-1],[-1,0,0],[0,1,0]]) #hkl -> -l,-h,k
matd3t = np.array([[0,0,-1],[1,0,0],[0,-1,0]]) #hkl -> -l,h,-k
mat6 = np.array([[1,1,0],[-1,0,0],[0,0,1]]) #hkl -> h+k,-h,l really 65
matdm = np.array([[0,1,0],[1,0,0],[0,0,1]]) #hkl -> k,h,l
matdmp = np.array([[-1,-1,0],[0,1,0],[0,0,1]]) #hkl -> -h-k,k,l
matkm = np.array([[-1,0,0],[1,1,0],[0,0,1]]) #hkl -> -h,h+k,l
matd2 = np.array([[0,1,0],[1,0,0],[0,0,-1]]) #hkl -> k,h,-l
matdm3 = np.array([[1,0,0],[0,0,1],[0,1,0]]) #hkl -> h,l,k
mat2d43 = np.array([[0,1,0],[1,0,0],[0,0,1]]) #hkl -> k,-h,l
matk2 = np.array([[-1,0,0],[1,1,0],[0,0,-1]]) #hkl -> -h,-i,-l
#triclinic
if Laue == '1': #ok
pass
elif Laue == '-1': #ok
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]<0),HKLFT[:3]*np.array([-1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([-1,-1,-1])[:,nxs],HKLFT[:3])
#monoclinic
#noncentrosymmetric - all ok
elif Laue == '2':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([-1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '1 1 2':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]<0),HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
elif Laue == '2 1 1':
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
elif Laue == 'm':
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
elif Laue == 'm 1 1':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
elif Laue == '1 1 m':
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
#centrosymmetric - all ok
elif Laue == '2/m 1 1':
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]*HKLFT[0]==0)&(HKLFT[1]<0),HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
elif Laue == '2/m':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]*HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '1 1 2/m':
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[1]*HKLFT[2]==0)&(HKLFT[0]<0),HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
#orthorhombic
#noncentrosymmetric - all OK
elif Laue == '2 2 2':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == 'm m 2':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
elif Laue == '2 m m':
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == 'm 2 m':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
#centrosymmetric - all ok
elif Laue == 'm m m':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
#tetragonal
#noncentrosymmetric - all ok
elif Laue == '4':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat43[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]>0),np.squeeze(np.inner(HKLF[:,:3],mat41[nxs,:,:])).T,HKLFT[:3])
elif Laue == '-4':
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<=0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '4 2 2':
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat43[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[1]<HKLFT[0]),np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]==0,np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3]) #in lieu od 2-fold
elif Laue == '4 m m':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat43[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
elif Laue == '-4 2 m':
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<=0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '-4 m 2':
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[1]<=0),np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]<0),HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[1]==0),np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[0]>HKLFT[1]),np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
#centrosymmetric - all ok
elif Laue == '4/m':
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat43[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]>0),np.squeeze(np.inner(HKLF[:,:3],mat41[nxs,:,:])).T,HKLFT[:3])
elif Laue == '4/m m m':
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat43[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],mat41[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
#trigonal - all hex cell
#noncentrosymmetric - all ok
elif Laue == '3':
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
elif Laue == '3 1 2':
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],matk2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],matk2[nxs,:,:])).T,HKLFT[:3])
elif Laue == '3 2 1':
HKLFT[:3] = np.where(HKLFT[0]<=-2*HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<-2*HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>0)&(HKLFT[1]==HKLFT[0]),np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T
HKLFT[:3] = np.where((HKLFT[0]!=0)&(HKLFT[2]>0)&(HKLFT[0]==-2*HKLFT[1]),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '3 1 m':
HKLFT[:3] = np.where(HKLFT[0]>=HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(2*HKLFT[1]<-HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]>-2*HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],matdmp[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T
elif (Laue == '3 m 1' or Laue == '3 m'):
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[1]+HKLFT[0])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],matkm[nxs,:,:])).T,HKLFT[:3])
#centrosymmetric
elif Laue == '-3': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([-1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[0]<0),-np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],-mat31[nxs,:,:])).T,HKLFT[:3])
elif (Laue == '-3 m 1' or Laue == '-3 m'): #ok
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[1]+HKLFT[0])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],matkm[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[1]<HKLFT[0]),np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
elif Laue == '-3 1 m': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([-1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,np.squeeze(np.inner(HKLF[:,:3],-mat31[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
#hexagonal
#noncentrosymmetric
elif Laue == '6': #ok
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]==0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
elif Laue == '-6': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
elif Laue == '6 2 2': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[0]>HKLFT[1]),np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
elif Laue == '6 m m': #ok
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]==0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]>HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
elif Laue == '-6 m 2': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],matk2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat31[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],matk2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '-6 2 m': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=-2*HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<-2*HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>0)&(HKLFT[1]==HKLFT[0]),np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T
HKLFT[:3] = np.where(HKLFT[2]<0,np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]>HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
#centrosymmetric
elif Laue == '6/m': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]==0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
elif Laue == '6/m m m': #ok
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]+HKLFT[1])<0,np.squeeze(np.inner(HKLF[:,:3],mat32[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,np.squeeze(np.inner(HKLF[:,:3],mat6[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]>HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],matdm.T[nxs,:,:])).T,HKLFT[:3])
#cubic - all ok
#noncentrosymmetric -
elif Laue == '2 3':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]<0)&((HKLFT[0]>-HKLFT[2])|(HKLFT[1]>-HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3t[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]<0)&((HKLFT[0]>-HKLFT[2])|(HKLFT[1]>=-HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3t[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([-1,1,-1])[:,nxs],HKLFT[:3])
elif Laue == '4 3 2':
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,-1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,np.squeeze(np.inner(HKLF[:,:3],mat43[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]==0)&(HKLFT[1]<HKLFT[0]),np.squeeze(np.inner(HKLF[:,:3],matd2[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]==0,np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3]) #in lieu od 2-fold
HKLFT[:3] = np.where((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2]),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2]),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]==0,np.squeeze(np.inner(HKLF[:,:3],mat2d43[nxs,:,:])).T,HKLFT[:3])
elif Laue == '-4 3 m':
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]<=0,HKLFT[:3]*np.array([-1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<=0,np.squeeze(np.inner(HKLF[:,:3],mat4bar[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[1]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<HKLFT[0],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]==0)&(HKLFT[2]<0),HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&(HKLFT[1]<HKLFT[0]),np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([-1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]<0)&(HKLFT[2]<-HKLFT[0])&(HKLFT[1]>HKLFT[2]),np.squeeze(np.inner(HKLF[:,:3],matd3q[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[0]<0)&(HKLFT[2]>=-HKLFT[0])&(HKLFT[1]>HKLFT[2]),np.squeeze(np.inner(HKLF[:,:3],matdm3[nxs,:,:])).T,HKLFT[:3])
#centrosymmetric
elif Laue == 'm 3':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
elif Laue == 'm 3 m':
HKLFT[:3] = np.where(HKLFT[0]<0,HKLFT[:3]*np.array([-1,1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[1]<0,HKLFT[:3]*np.array([1,-1,1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[2]<0,HKLFT[:3]*np.array([1,1,-1])[:,nxs],HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where((HKLFT[2]>=0)&((HKLFT[0]>=HKLFT[2])|(HKLFT[1]>HKLFT[2])),np.squeeze(np.inner(HKLF[:,:3],matd3[nxs,:,:])).T,HKLFT[:3])
HKLFT[:3] = np.where(HKLFT[0]>HKLFT[1],np.squeeze(np.inner(HKLF[:,:3],matdm[nxs,:,:])).T,HKLFT[:3])
return HKLFT.T
#Spherical harmonics routines
[docs]
def RBChk(sytsym,L,M):
'''finds symmetry rules for spherical harmonic coefficients for site symmetries
:param str sytsym: atom site symmetry symbol
:param int L: principal harmonic term L>0
:param int M: second harmonic term; can be -L <= M <= L
:returns True if allowed and sign for term
NB: not complete for all possible site symmetries! Many are missing
Based on Tables 2 & 4 of M. Kara & K. Kurki-Suonio, Acta Cryst. A37, 201-210 (1981).
'''
if M <= L:
if sytsym == '53m':
if not L%2 and M > 0:
if L in [6,10,12,16,18]:
if L%12 == 2:
if M <= L//12: return True,1.0
else:
if M <= L//12+1: return True,1.0
elif sytsym == '23': #cubics use different Fourier expansion than those below
if 2 < L < 11 and [L,M] in [[3,1],[4,1],[6,1],[6,2],[7,1],[8,1],[9,1],[9,2],[10,1],[10,2]]:
return True,1.0
elif sytsym == 'm3':
if 2 < L < 11 and [L,M] in [[4,1],[6,1],[6,2],[8,1],[10,1],[10,2]]:
return True,1.0
elif sytsym == '432':
if 2 < L < 11 and [L,M] in [[4,1],[6,1],[8,1],[9,2],[10,1]]:
return True,1.0
elif sytsym == '-43m':
if 2 < L < 11 and [L,M] in [[3,1],[4,1],[6,1],[7,1],[8,1],[9,1],[10,1]]:
return True,1.0
elif sytsym == 'm3m': #correct for L < 21 by generator
if not L%2 and M > 0:
if L%12 == 2:
if M <= L//12: return True,1.0
else:
if M <= L//12+1: return True,1.0
elif sytsym == '6':
if not M%6: return True,1.0 #P?
elif sytsym == '-6': #L=M+2J
if L != 1 and not M%3: #P?
if not L%2 and not M%6: return True,1.0
elif L%2 and (M//3)%2: return True,1.0
elif sytsym == '6/m':
if not L%2 and not M%6: return True,1.0 #P?
elif sytsym == '622':
if not M%6: return True,-1.**M
elif sytsym == '6mm':
if not M%6: return True,1.0
elif sytsym in ['-6m2(100)','-6m2']: #L=M+2J
if L != 1 and not M%3:
if not L%2 and not M%6: return True,1.0
elif L%2 and (M//3)%2: return True,1.0
elif sytsym == '-6m2(120)': #L=M+2J
if L != 1 and not M%3:
if not L%2 and not M%6: return True,1.0
elif L%2 and (M//3)%2: return True,-1.**M
elif sytsym == '6/mmm':
if not L%2 and not M%6: return True,1.0
elif sytsym == '4(z)':
if not M%4: return True,1.0 #P?
elif sytsym == '-4(z)': #m=2l-4j
if L%2 and (M//2)%2: return True,1.0 #P?
if not L%2 and not (M//2)%2: return True,1.0
elif sytsym == '4/m(z)':
if not M%4: return True,1.0 #P?
elif sytsym == '422(z)':
if not M%4: return True,-1.0**L
elif sytsym == '4mm(z)':
if not M%4: return True,1.0
elif sytsym in ['-42m(z)','-42m']: #m=2l-4j
if L%2 and (M//2)%2: return True,1.0
if not L%2 and not (M//2)%2: return True,-1.0**L
elif sytsym == '-4m2(z)': #m=2l-4j
if L%2 and (M//2)%2: return True,1.0
if not L%2 and not (M//2)%2: return True,1.0
elif sytsym == '4/mmm(z)':
if not L%2 and not M%4: return True,1.0
elif sytsym == '3' or sytsym == '3(111)':
if not M%3: return True,1.0 #P?
elif sytsym == '-3' or sytsym == '-3(111)':
if not L%2 and not M%3: return True,1.0 #P?
elif sytsym in ['32','32(100)','32(111)']:
if not M%3: return True,-1.0**L
elif sytsym == '32(120)':
if not M%3: return True,-1.0**(L-M)
elif sytsym in ['3m','3m(100)','3m(111)']:
if not M%3: return True,-1.0**M
elif sytsym == '3m(120)':
if not M%3: return True,1.0
elif sytsym in ['-3m(100)','-3m(111)','-3m']:
if not L%2 and not M%3: return True,-1.0**M
elif sytsym == '-3m(120)':
if not L%2 and not M%3: return True,1.0
elif '222' in sytsym:
if M%2: return True,-1.0**L
elif 'mm2(x)' in sytsym: #m=l-2j
if L%2 and M%2: return True,1.0 #both odd
if not L%2 and not M%2: return True,1.0 #both even
elif 'mm2(y)' in sytsym: #m=l-2j
if L%2 and M%2: return True,-1.0**L #both odd
if not L%2 and not M%2: return True,-1.0**L #both even
elif 'mm2(z)' in sytsym:
if M%2: return True,1.0
elif 'mmm' in sytsym :
if not L%2 and not M%2: return True,1.0
elif sytsym == '2(x)':
return True,-1.0**(L-M)
elif sytsym == '2(y)':
return True,-1.0**L
elif sytsym == '2(z)':
if not M%2: return True,1.0 #P?
elif sytsym == 'm(x)':
if not L%2 : return True,-1.0**M
elif sytsym == 'm(y)':
return True,1.0
elif sytsym == 'm(z)': #m=l-2j
if L%2 and M%2: return True,1.0 #P?
if not L%2 and not M%2: return True,1.0 #P?
elif sytsym == '2/m(x)':
if not L%2 : return True,-1.0**M
elif sytsym in ['2/m(y)','2/m']:
if not L%2: return True,1.0
elif sytsym == '2/m(z)':
if not L%2 and not M%2: return True,1.0
elif sytsym == '1': #P?
return True,1.0
elif sytsym == '-1': #P?
if not L%2: return True,1.0
return False,0.
[docs]
def RBsymChk(RBsym,cubic,coefNames,L=18):
'''imposes rigid body symmetry on spherical harmonics terms
Key problem is noncubic RB symmetries in cubic site symmetries & vice versa.
:param str RBsym: molecular point symmetry symbol
:param bool cubic: True if atom site symmetry is cubic
:param list coefNames: sp. harm coefficient names to be checked/converted
:param int L: maximum spherical harmonic order no. for cubic generation if needed
'''
# cubicsigns = {'C(3,1)c':[-1,],'C(4,1)c':[1,1,],'C(6,1)c':[1,-1],'C(6,2)c':[1,-1],'C(7,1)c':[1,-1],'C(8,1)c':[1,1,1],
# 'C(9,1)c':[1,-1],'C(9,2)c':[1,-1],'C(10,1)c':[1,-1,-1],'C(10,2)c':[1,1,-1]}
# cubicnames = {'C(3,1)c':['C(3,2)',],'C(4,1)c':['C(4,0)','C(4,4)'],'C(6,1)c':['C(6,0)','C(6,4)'],
# 'C(6,2)c':['C(6,2)','C(6,6)'],'C(7,1)c':['C(7,2)','C(7,6)'],'C(8,1)c':['C(8,0)','C(8,4)','C(8,8)'],
# 'C(9,1)c':['C(9,2)','C((9,6)'],'C(9,2)c':['C(9,4)','C(9,8)'],
# 'C(10,1)c':['C(10,0)','C(10,4)','C(10,8)'],'C(10,2)c':['C(10,2)','C(10,6)','C(10,10)']}
newNames = []
newSgns = []
if cubic: #sytsym is a cubic site
if RBsym in ['53m','532']:
for name in coefNames:
LM = eval(name[1:-1])
if LM[0] in [6,10,12,16,18]:
newNames.append(name)
newSgns.append(1.0)
elif RBsym in ['m3m','-43m']: #take all terms?
for name in coefNames:
LM = eval(name[1:-1])
rbChk,sgn = RBChk(RBsym,LM[0],LM[1])
if rbChk:
newNames.append(name)
newSgns.append(1.0)
else: #RBsym not cubic or icosahedral
for name in coefNames: #these are cubic names
LM = eval(name[1:-1])
if (LM[0]+LM[1])%2: #even L odd M or vv
if LM[0]%2:
M = [4*m for m in range(LM[0]//2)[1:] if 4*m <= LM[0]]
else:
M = [4*m for m in range(LM[0]//2) if 4*m <= LM[0]]
else: #both even or both odd
M = [4*m+2 for m in range(LM[0]//2) if 4*m+2 <= LM[0]]
for m in M:
rbChk,sgn = RBChk(RBsym,LM[0],m)
if rbChk:
newNames.append('C(%d,%d)'%(LM[0],m))
newSgns.append(sgn)
else:
if RBsym in ['m3m','-43m','53m']: #force mol. sym. here
for L in range(L+1):
cubNames,cubSgns = GenShCoeff(RBsym,L)
newNames += cubNames
newSgns += cubSgns
else:
for name in coefNames:
LM = eval(name[1:])
rbChk,sgn = RBChk(RBsym,LM[0],LM[1])
if rbChk:
newNames.append(name)
newSgns.append(sgn)
return newNames,newSgns
[docs]
def GenRBCoeff(sytsym,RBsym,L):
'''imposes rigid body symmetry on spherical harmonics terms
Key problem is noncubic RB symmetries in cubic site symmetries & vice versa.
:param str sytsym: atom position site symmetry symbol
:param str RBsym: molecular point symmetry symbol
:param int L: spherical harmonic order no.
:returns list newNames: spherical harmonic term of order L as either C(L,M) or C(L,M)c for cubic terms
:returns list newSgns: matching coefficient signs as +/- 1.0
'''
coefNames = []
coefSgns = []
cubic = False
if sytsym in ['23','m3','432','-43m','m3m']:
cubic = True
for iord in range(L+1):
if not iord: continue
for n in range(iord+1):
rbChk,sgn = RBChk(sytsym,iord,n)
if rbChk:
if cubic:
coefNames.append('C(%d,%d)c'%(iord,n))
else:
coefNames.append('C(%d,%d)'%(iord,n))
coefSgns.append(sgn)
if RBsym == '1':
return coefNames,coefSgns
newNames,newSgns = RBsymChk(RBsym,cubic,coefNames,L)
return newNames,newSgns
[docs]
def GenShCoeff(sytsym,L):
'''Generate spherical harmonic coefficient names for atom site symmetry
:param str sytsym: site symmetry or perhaps molecular symmetry
:param int L:spherical harmonic order no.
:returns list newNames: spherical harmonic term of order L as either C(L,M) or C(L,M)c for cubic terms
:returns list newSgns: matching coefficient signs as +/- 1.0
'''
coefNames = []
coefSgns = []
cubic = False
if sytsym in ['23','m3','432','-43m','m3m','53m']:
cubic = True
for n in range(L+1):
rbChk,sgn = RBChk(sytsym,L,n)
if rbChk:
if cubic:
coefNames.append('C(%d,%d)c'%(L,n))
else:
coefNames.append('C(%d,%d)'%(L,n))
coefSgns.append(sgn)
newNames,newSgns = RBsymChk(sytsym,cubic,coefNames,L)
return newNames,newSgns
[docs]
def OdfChk(SGLaue,L,M):
'''finds symmetry rules for spherical harmonic coefficients for Laue groups
:param str SGLaue: Laue symbol
:param int L: principal harmonic term; only evens are used
:param int M: second harmonic term; can be -L <= M <= L
:returns True if allowed
'''
if not L%2 and abs(M) <= L:
if SGLaue == '0': #cylindrical symmetry
if M == 0: return True
elif SGLaue == '-1':
return True
elif SGLaue == '2/m':
if not abs(M)%2: return True
elif SGLaue == 'mmm':
if not abs(M)%2 and M >= 0: return True
elif SGLaue == '4/m':
if not abs(M)%4: return True
elif SGLaue == '4/mmm':
if not abs(M)%4 and M >= 0: return True
elif SGLaue in ['3R','3']:
if not abs(M)%3: return True
elif SGLaue in ['3mR','3m1','31m']:
if not abs(M)%3 and M >= 0: return True
elif SGLaue == '6/m':
if not abs(M)%6: return True
elif SGLaue == '6/mmm':
if not abs(M)%6 and M >= 0: return True
elif SGLaue in ['m3']: #cubics use different Fourier expansion than those above
if M > 0:
if L%12 == 2:
if M <= L//12: return True
else:
if M <= L//12+1: return True
elif SGLaue in ['m3m']:
if M > 0:
if L%12 == 2:
if M <= L//12: return True
else:
if M <= L//12+1: return True
return False
[docs]
def GenSHCoeff(SGLaue,SamSym,L,IfLMN=True):
'''Generate spherical harmonics coefficient names for texture
:param str SGLaue: Laue symbol
:param str SamSym: sample symmetry symbol
:param int L: spherical harmonic order no.
:param bool IfLMN: if TRUE return sp.harm. name as C(L,M,N); else return C(L,N)
:returns coefficient name as C(L,M,N) or C(L,N)
'''
coeffNames = []
for iord in [2*i+2 for i in range(L//2)]:
for m in [i-iord for i in range(2*iord+1)]:
if OdfChk(SamSym,iord,m):
for n in [i-iord for i in range(2*iord+1)]:
if OdfChk(SGLaue,iord,n):
if IfLMN:
coeffNames.append('C(%d,%d,%d)'%(iord,m,n))
else:
coeffNames.append('C(%d,%d)'%(iord,n))
return coeffNames
[docs]
def CrsAng(H,cell,SGData):
'''Convert HKL to polar coordinates with proper orientation WRT space group point group
:param array H: hkls
:param list cell: lattice parameters
:param dict SGData: space group data
:returns arrays phi,beta: polar, azimuthal angles for HKL
'''
a,b,c,al,be,ga = cell
SQ3 = 1.732050807569
H1 = np.array([1,0,0])
H2 = np.array([0,1,0])
H3 = np.array([0,0,1])
H4 = np.array([1,1,1])
G,g = cell2Gmat(cell)
Laue = SGData['SGLaue']
Naxis = SGData['SGUniq']
if len(H.shape) == 1:
DH = np.inner(H,np.inner(G,H))
else:
DH = np.array([np.inner(h,np.inner(G,h)) for h in H])
if Laue == '2/m':
if Naxis == 'a':
DR = np.inner(H1,np.inner(G,H1))
DHR = np.inner(H,np.inner(G,H1))
elif Naxis == 'b':
DR = np.inner(H2,np.inner(G,H2))
DHR = np.inner(H,np.inner(G,H2))
else:
DR = np.inner(H3,np.inner(G,H3))
DHR = np.inner(H,np.inner(G,H3))
elif Laue in ['R3','R3m']:
DR = np.inner(H4,np.inner(G,H4))
DHR = np.inner(H,np.inner(G,H4))
else:
DR = np.inner(H3,np.inner(G,H3))
DHR = np.inner(H,np.inner(G,H3))
DHR /= np.sqrt(DR*DH)
phi = np.where(DHR <= 1.0,acosd(DHR),0.0)
if Laue == '-1':
BA = H.T[1]*a/(b-H.T[0]*cosd(ga))
BB = H.T[0]*sind(ga)**2
elif Laue == '2/m':
if Naxis == 'a':
BA = H.T[2]*b/(c-H.T[1]*cosd(al))
BB = H.T[1]*sind(al)**2
elif Naxis == 'b':
BA = H.T[0]*c/(a-H.T[2]*cosd(be))
BB = H.T[2]*sind(be)**2
else:
BA = H.T[1]*a/(b-H.T[0]*cosd(ga))
BB = H.T[0]*sind(ga)**2
elif Laue in ['mmm','4/m','4/mmm']:
BA = H.T[1]*a
BB = H.T[0]*b
elif Laue in ['3R','3mR']:
BA = H.T[0]+H.T[1]-2.0*H.T[2]
BB = SQ3*(H.T[0]-H.T[1])
elif Laue in ['m3','m3m']:
BA = H.T[1]
BB = H.T[0]
else:
BA = H.T[0]+2.0*H.T[1]
BB = SQ3*H.T[0]
beta = atan2d(BA,BB)
return phi,beta
[docs]
def SamAng(Tth,Gangls,Sangl,IFCoup):
"""Compute sample orientation angles vs laboratory coord. system
:param Tth: Signed theta
:param Gangls: Sample goniometer angles phi,chi,omega,azmuth
:param Sangl: Sample angle zeros om-0, chi-0, phi-0
:param IFCoup: True if omega & 2-theta coupled in CW scan
:returns:
psi,gam: Sample odf angles
dPSdA,dGMdA: Angle zero derivatives
"""
if IFCoup:
GSomeg = sind(Gangls[2]+Tth)
GComeg = cosd(Gangls[2]+Tth)
else:
GSomeg = sind(Gangls[2])
GComeg = cosd(Gangls[2])
GSTth = sind(Tth)
GCTth = cosd(Tth)
GSazm = sind(Gangls[3])
GCazm = cosd(Gangls[3])
GSchi = sind(Gangls[1])
GCchi = cosd(Gangls[1])
GSphi = sind(Gangls[0]+Sangl[2])
GCphi = cosd(Gangls[0]+Sangl[2])
SSomeg = sind(Sangl[0])
SComeg = cosd(Sangl[0])
SSchi = sind(Sangl[1])
SCchi = cosd(Sangl[1])
AT = -GSTth*GComeg+GCTth*GCazm*GSomeg
BT = GSTth*GSomeg+GCTth*GCazm*GComeg
CT = -GCTth*GSazm*GSchi
DT = -GCTth*GSazm*GCchi
BC1 = -AT*GSphi+(CT+BT*GCchi)*GCphi
BC2 = DT-BT*GSchi
BC3 = AT*GCphi+(CT+BT*GCchi)*GSphi
BC = BC1*SComeg*SCchi+BC2*SComeg*SSchi-BC3*SSomeg
psi = acosd(BC)
BD = 1.0-BC**2
C = np.where(BD>1.e-6,rpd/np.sqrt(BD),0.)
dPSdA = [-C*(-BC1*SSomeg*SCchi-BC2*SSomeg*SSchi-BC3*SComeg),
-C*(-BC1*SComeg*SSchi+BC2*SComeg*SCchi),
-C*(-BC1*SSomeg-BC3*SComeg*SCchi)]
BA = -BC1*SSchi+BC2*SCchi
BB = BC1*SSomeg*SCchi+BC2*SSomeg*SSchi+BC3*SComeg
gam = atan2d(BB,BA)
BD = (BA**2+BB**2)/rpd
dBAdO = 0
dBAdC = -BC1*SCchi-BC2*SSchi
dBAdF = BC3*SSchi
dBBdO = BC1*SComeg*SCchi+BC2*SComeg*SSchi-BC3*SSomeg
dBBdC = -BC1*SSomeg*SSchi+BC2*SSomeg*SCchi
dBBdF = BC1*SComeg-BC3*SSomeg*SCchi
dGMdA = np.where(BD > 1.e-6,[(BA*dBBdO-BB*dBAdO)/BD,(BA*dBBdC-BB*dBAdC)/BD, \
(BA*dBBdF-BB*dBAdF)/BD],[np.zeros_like(BD),np.zeros_like(BD),np.zeros_like(BD)])
return psi,gam,dPSdA,dGMdA
BOH = {
'L=2':[[],[],[]],
'L=4':[[0.30469720,0.36418281],[],[]],
'L=6':[[-0.14104740,0.52775103],[],[]],
'L=8':[[0.28646862,0.21545346,0.32826995],[],[]],
'L=10':[[-0.16413497,0.33078546,0.39371345],[],[]],
'L=12':[[0.26141975,0.27266871,0.03277460,0.32589402],
[0.09298802,-0.23773812,0.49446631,0.0],[]],
'L=14':[[-0.17557309,0.25821932,0.27709173,0.33645360],[],[]],
'L=16':[[0.24370673,0.29873515,0.06447688,0.00377,0.32574495],
[0.12039646,-0.25330128,0.23950998,0.40962508,0.0],[]],
'L=18':[[-0.16914245,0.17017340,0.34598142,0.07433932,0.32696037],
[-0.06901768,0.16006562,-0.24743528,0.47110273,0.0],[]],
'L=20':[[0.23067026,0.31151832,0.09287682,0.01089683,0.00037564,0.32573563],
[0.13615420,-0.25048007,0.12882081,0.28642879,0.34620433,0.0],[]],
'L=22':[[-0.16109560,0.10244188,0.36285175,0.13377513,0.01314399,0.32585583],
[-0.09620055,0.20244115,-0.22389483,0.17928946,0.42017231,0.0],[]],
'L=24':[[0.22050742,0.31770654,0.11661736,0.02049853,0.00150861,0.00003426,0.32573505],
[0.13651722,-0.21386648,0.00522051,0.33939435,0.10837396,0.32914497,0.0],
[0.05378596,-0.11945819,0.16272298,-0.26449730,0.44923956,0.0,0.0]],
'L=26':[[-0.15435003,0.05261630,0.35524646,0.18578869,0.03259103,0.00186197,0.32574594],
[-0.11306511,0.22072681,-0.18706142,0.05439948,0.28122966,0.35634355,0.0],[]],
'L=28':[[0.21225019,0.32031716,0.13604702,0.03132468,0.00362703,0.00018294,0.00000294,0.32573501],
[0.13219496,-0.17206256,-0.08742608,0.32671661,0.17973107,0.02567515,0.32619598,0.0],
[0.07989184,-0.16735346,0.18839770,-0.20705337,0.12926808,0.42715602,0.0,0.0]],
'L=30':[[-0.14878368,0.01524973,0.33628434,0.22632587,0.05790047,0.00609812,0.00022898,0.32573594],
[-0.11721726,0.20915005,-0.11723436,-0.07815329,0.31318947,0.13655742,0.33241385,0.0],
[-0.04297703,0.09317876,-0.11831248,0.17355132,-0.28164031,0.42719361,0.0,0.0]],
'L=32':[[0.20533892,0.32087437,0.15187897,0.04249238,0.00670516,0.00054977,0.00002018,0.00000024,0.32573501],
[0.12775091,-0.13523423,-0.14935701,0.28227378,0.23670434,0.05661270,0.00469819,0.32578978,0.0],
[0.09703829,-0.19373733,0.18610682,-0.14407046,0.00220535,0.26897090,0.36633402,0.0,0.0]],
'L=34':[[-0.14409234,-0.01343681,0.31248977,0.25557722,0.08571889,0.01351208,0.00095792,0.00002550,0.32573508],
[-0.11527834,0.18472133,-0.04403280,-0.16908618,0.27227021,0.21086614,0.04041752,0.32688152,0.0],
[-0.06773139,0.14120811,-0.15835721,0.18357456,-0.19364673,0.08377174,0.43116318,0.0,0.0]]
}
Lnorm = lambda L: 4.*np.pi/(2.0*L+1.)
[docs]
def GetKcl(L,N,SGLaue,phi,beta):
'needs doc string'
import pytexture as ptx
if SGLaue in ['m3','m3m']:
if 'array' in str(type(phi)) and np.any(phi.shape):
Kcl = np.zeros_like(phi)
else:
Kcl = 0.
for j in range(0,L+1,4):
im = j//4
if 'array' in str(type(phi)) and np.any(phi.shape):
pcrs = ptx.pyplmpsi(L,j,len(phi),phi)[0]
else:
pcrs = ptx.pyplmpsi(L,j,1,phi)[0]
Kcl += BOH['L=%d'%(L)][N-1][im]*pcrs*cosd(j*beta)
else:
if 'array' in str(type(phi)) and np.any(phi.shape):
pcrs = ptx.pyplmpsi(L,N,len(phi),phi)[0]
else:
pcrs = ptx.pyplmpsi(L,N,1,phi)[0]
pcrs *= RSQ2PI
if N:
pcrs *= SQ2
if SGLaue in ['mmm','4/mmm','6/mmm','R3mR','3m1','31m']:
if SGLaue in ['3mR','3m1','31m']:
if N%6 == 3:
Kcl = pcrs*sind(N*beta)
else:
Kcl = pcrs*cosd(N*beta)
else:
Kcl = pcrs*cosd(N*beta)
else:
Kcl = pcrs*(cosd(N*beta)+sind(N*beta))
return Kcl
[docs]
def GetKsl(L,M,SamSym,psi,gam):
'needs doc string'
import pytexture as ptx
if 'array' in str(type(psi)) and np.any(psi.shape):
psrs,dpdps = ptx.pyplmpsi(L,M,len(psi),psi)
else:
psrs,dpdps = ptx.pyplmpsi(L,M,1,psi)
psrs *= RSQ2PI
dpdps *= RSQ2PI
if M:
psrs *= SQ2
dpdps *= SQ2
if SamSym in ['mmm',]:
dum = cosd(M*gam)
Ksl = psrs*dum
dKsdp = dpdps*dum
dKsdg = -psrs*M*sind(M*gam)
else:
dum = cosd(M*gam)+sind(M*gam)
Ksl = psrs*dum
dKsdp = dpdps*dum
dKsdg = psrs*M*(-sind(M*gam)+cosd(M*gam))
return Ksl,dKsdp,dKsdg
[docs]
def GetKclKsl(L,N,SGLaue,psi,phi,beta):
"""
This is used for spherical harmonics description of preferred orientation;
cylindrical symmetry only (M=0) and no sample angle derivatives returned
"""
import pytexture as ptx
Ksl,x = ptx.pyplmpsi(L,0,1,psi)
Ksl *= RSQ2PI
if SGLaue in ['m3','m3m']:
Kcl = 0.0
for j in range(0,L+1,4):
im = j//4
pcrs,dum = ptx.pyplmpsi(L,j,1,phi)
Kcl += BOH['L=%d'%(L)][N-1][im]*pcrs*cosd(j*beta)
else:
pcrs,dum = ptx.pyplmpsi(L,N,1,phi)
pcrs *= RSQ2PI
if N:
pcrs *= SQ2
if SGLaue in ['mmm','4/mmm','6/mmm','R3mR','3m1','31m']:
if SGLaue in ['3mR','3m1','31m']:
if N%6 == 3:
Kcl = pcrs*sind(N*beta)
else:
Kcl = pcrs*cosd(N*beta)
else:
Kcl = pcrs*cosd(N*beta)
else:
Kcl = pcrs*(cosd(N*beta)+sind(N*beta))
return Kcl*Ksl,Lnorm(L)
[docs]
def H2ThPh(H,Bmat,Q):
'''Convert HKL to spherical polar & azimuth angles
:param array H: array of hkl as [n,3]
:param [3,3] array Bmat: inv crystal to Cartesian transformation
:param array Q: quaternion for rotation of HKL to new polar axis
:returns array Th: HKL azimuth angles
:returns array Ph: HKL polar angles
'''
# A,V = G2mth.Q2AVdeg(Q)
# QR,R = G2mth.make2Quat(V,np.array([0.,0.,1.0]))
# QA = G2mth.AVdeg2Q(A,np.array([0.,0.,1.0]))
# Q2 = G2mth.prodQQ(QR,QA)
Qmat = G2mth.Q2Mat(Q)
CH1 = np.inner(H,Bmat.T)
CH = np.inner(CH1,Qmat.T)
N = nl.norm(CH,axis=1)
CH /= N[:,nxs]
H3 = np.array([0,0,1.])
DHR = np.inner(CH,H3)
Ph = np.where(DHR <= 1.0,acosd(DHR),0.0) #polar angle 0<=Ph<=180.; correct
TH = CH*np.array([1.,1.,0.])[nxs,:] #projection of CH onto xy plane
N = nl.norm(TH,axis=1)
N = np.where(N > 1.e-5,N,1.)
TH /= N[:,nxs]
Th = atan2d(TH[:,1],TH[:,0]) #azimuth angle 0<=Th<360<
Th = np.where(Th<0.,Th+360.,Th)
return Th,Ph #azimuth,polar angles
[docs]
def SHarmcal(SytSym,SHFln,psi,gam):
'''Perform a surface spherical harmonics computation.
Presently only used for plotting
Note that the the number of gam values must either be 1 or must match psi
:param str SytSym: sit symmetry - only looking for cubics - remove this
:param dict SHFln: spherical harmonics coefficients; key has L & M
:param float/array psi: Azimuthal coordinate 0 <= Th <= 360
:param float/array gam: Polar coordinate 0<= Ph <= 180
:returns array SHVal: spherical harmonics array for psi,gam values
'''
SHVal = np.ones_like(psi)/(4.*np.pi)
for term in SHFln:
trm = term.strip('+').strip('-') #patch
if 'C(' in term[:3]:
l,m = eval(trm.strip('C').strip('c'))
if SytSym in ['m3m','m3','43m','432','23'] or 'c' in trm:
Ksl = CubicSHarm(l,m,psi,gam)
else:
p = SHFln[term][2]
Ksl = SphHarmAng(l,m,p,psi,gam)
SHVal += SHFln[term][0]*Ksl
return SHVal
[docs]
def KslCalc(trm,psi,gam):
'''Compute one angular part term in spherical harmonics
:param str trm:sp. harm term name in the form of 'C(l,m)' or 'C(l,m)c' for cubic
:param float/array psi: Azimuthal coordinate 0 <= Th <= 360
:param float/array gam: Polar coordinate 0<= Ph <= 180
:returns array Ksl: spherical harmonics angular part for psi,gam pairs
'''
l,m = eval(trm.strip('C').strip('c'))
if 'c' in trm:
return CubicSHarm(l,m,psi,gam)
else:
return SphHarmAng(l,m,1.0,psi,gam)
[docs]
def SphHarmAng(L,M,P,Th,Ph):
''' Compute spherical harmonics values using scipy.special.sph_harm
:param int L: degree of the harmonic (L >= 0)
:param int M: order number (\\|M\\| <= L)
:param int P: sign flag = -1 or 1
:param float/array Th: Azimuthal coordinate 0 <= Th <= 360
:param float/array Ph: Polar coordinate 0<= Ph <= 180
:returns ylmp value/array: as reals
'''
ylmp = spsp.sph_harm(M,L,rpd*Th,rpd*Ph) #wants radians; order then degree
if M > 0:
return (-1)**M*P*np.real(ylmp)*SQ2
elif M == 0:
return P*np.real(ylmp)
else:
return (-1)**M*P*np.imag(ylmp)*SQ2
[docs]
def CubicSHarm(L,M,Th,Ph):
'''Calculation of the cubic harmonics given in Table 3 in M.Kara & K. Kurki-Suonio,
Acta Cryt. A37, 201 (1981). For L = 14,20 only for m3m from F.M. Mueller and M.G. Priestley,
Phys Rev 148, 638 (1966)
:param int L: degree of the harmonic (L >= 0)
:param int M: order number [\\|M\\| <= L]
:param float/array Th: Azimuthal coordinate 0 <= Th <= 360
:param float/array Ph: Polar coordinate 0<= Ph <= 180
:returns klm value/array: cubic harmonics
'''
if L == 0:
return SphHarmAng(L,M,1,Th,Ph)
elif L == 3:
return SphHarmAng(3,2,-1,Th,Ph)
elif L == 4:
klm = 0.5*np.sqrt(7.0/3.0)*SphHarmAng(4,0,1,Th,Ph)
klm += 0.5*np.sqrt(5.0/3.0)*SphHarmAng(4,4,1,Th,Ph)
elif L == 6:
if M == 1:
klm = 0.5*np.sqrt(0.5)*SphHarmAng(6,0,1,Th,Ph)
klm -= 0.5*np.sqrt(7.0/2.0)*SphHarmAng(6,4,1,Th,Ph)
else:
klm = 0.25*np.sqrt(11.0)*SphHarmAng(6,2,1,Th,Ph)
klm -= 0.25*np.sqrt(5.0)*SphHarmAng(6,6,1,Th,Ph)
elif L == 7:
klm = 0.5*np.sqrt(13./6.)*SphHarmAng(7,2,-1,Th,Ph)
klm += 0.5*np.sqrt(11./6.)*SphHarmAng(7,6,-1,Th,Ph)
elif L == 8:
klm = 0.125*np.sqrt(33.)*SphHarmAng(8,0,1,Th,Ph)
klm += 0.25*np.sqrt(7./3.)*SphHarmAng(8,4,1,Th,Ph)
klm += 0.125*np.sqrt(65./3.)*SphHarmAng(8,8,1,Th,Ph)
elif L == 9:
if M == 1:
klm = 0.25*np.sqrt(3.)*SphHarmAng(9,2,-1,Th,Ph)
klm -= 0.25*np.sqrt(13.)*SphHarmAng(9,6,-1,Th,Ph)
else:
klm = 0.5*np.sqrt(17./6.)*SphHarmAng(9,4,-1,Th,Ph)
klm -= 0.5*np.sqrt(7./6.)*SphHarmAng(9,8,-1,Th,Ph)
elif L == 10:
if M == 1:
klm = 0.125*np.sqrt(65./6.)*SphHarmAng(10,0,1,Th,Ph)
klm -= 0.25*np.sqrt(11.0/2.0)*SphHarmAng(10,4,1,Th,Ph)
klm -= 0.125*np.sqrt(187.0/6.0)*SphHarmAng(10,8,1,Th,Ph)
else:
klm = 0.125*np.sqrt(247./6.)*SphHarmAng(10,2,1,Th,Ph)
klm += (1./16.)*np.sqrt(19./3.)*SphHarmAng(10,6,1,Th,Ph)
klm -= (1./16.)*np.sqrt(85.)*SphHarmAng(10,10,1,Th,Ph)
#only m3m cubics from here down; from F.M. Mueller and M.G. Priestley, Phys Rev 148, 638 (1966)
elif L == 12:
if M == 1:
klm = 0.69550265*SphHarmAng(12,0,1,Th,Ph)
klm += 0.31412555*SphHarmAng(12,4,1,Th,Ph)
klm += 0.34844954*SphHarmAng(12,8,1,Th,Ph)
klm += 0.54422797*SphHarmAng(12,12,1,Th,Ph)
else:
klm = 0.55897937*SphHarmAng(12,4,1,Th,Ph)
klm -= 0.80626751*SphHarmAng(12,8,1,Th,Ph)
klm += 0.19358400*SphHarmAng(12,12,1,Th,Ph)
elif L == 14:
klm = 0.44009645*SphHarmAng(14,0,1,Th,Ph)
klm -= 0.45768183*SphHarmAng(14,4,1,Th,Ph)
klm -= 0.49113230*SphHarmAng(14,8,1,Th,Ph)
klm -= 0.59634848*SphHarmAng(14,12,1,Th,Ph)
elif L == 16:
if M == 1:
klm = 0.68136168*SphHarmAng(16,0,1,Th,Ph)
klm += 0.27586801*SphHarmAng(16,4,1,Th,Ph)
klm += 0.29048987*SphHarmAng(16,8,1,Th,Ph)
klm += 0.32756975*SphHarmAng(16,12,1,Th,Ph)
klm += 0.51764542*SphHarmAng(16,16,1,Th,Ph)
else:
klm = 0.63704821*SphHarmAng(16,4,1,Th,Ph)
klm -= 0.32999033*SphHarmAng(16,8,1,Th,Ph)
klm -= 0.64798073*SphHarmAng(16,12,1,Th,Ph)
klm += 0.25572816*SphHarmAng(16,16,1,Th,Ph)
elif L == 18:
if M == 1:
klm = 0.45791513*SphHarmAng(18,0,1,Th,Ph)
klm -= 0.38645598*SphHarmAng(18,4,1,Th,Ph)
klm -= 0.40209462*SphHarmAng(18,8,1,Th,Ph)
klm -= 0.43746593*SphHarmAng(18,12,1,Th,Ph)
klm -= 0.53657149*SphHarmAng(18,16,1,Th,Ph)
else:
klm = 0.14872751*SphHarmAng(18,4,1,Th,Ph)
klm -= 0.63774601*SphHarmAng(18,8,1,Th,Ph)
klm += 0.72334167*SphHarmAng(18,12,1,Th,Ph)
klm -= 0.21894515*SphHarmAng(18,16,1,Th,Ph)
elif L == 20:
if M == 1:
klm = 0.67141495*SphHarmAng(20,0,1,Th,Ph)
klm += 0.24982619*SphHarmAng(20,4,1,Th,Ph)
klm += 0.25782846*SphHarmAng(20,8,1,Th,Ph)
klm += 0.27469333*SphHarmAng(20,12,1,Th,Ph)
klm += 0.31248919*SphHarmAng(20,16,1,Th,Ph)
klm += 0.49719956*SphHarmAng(20,20,1,Th,Ph)
else:
klm = 0.66299538*SphHarmAng(20,4,1,Th,Ph)
klm -= 0.11295259*SphHarmAng(20,8,1,Th,Ph)
klm -= 0.42738441*SphHarmAng(20,12,1,Th,Ph)
klm -= 0.52810433*SphHarmAng(20,16,1,Th,Ph)
klm += 0.29347435*SphHarmAng(20,20,1,Th,Ph)
else: #shouldn't happen
return 0.0
return klm
[docs]
def Glnh(SHCoef,psi,gam,SamSym):
'needs doc string'
import pytexture as ptx
Fln = np.zeros(len(SHCoef))
for i,term in enumerate(SHCoef):
l,m,n = eval(term.strip('C'))
pcrs,dum = ptx.pyplmpsi(l,m,1,psi)
pcrs *= RSQPI
if m == 0:
pcrs /= SQ2
if SamSym in ['mmm',]:
Ksl = pcrs*cosd(m*gam)
else:
Ksl = pcrs*(cosd(m*gam)+sind(m*gam))
Fln[i] = SHCoef[term]*Ksl*Lnorm(l)
ODFln = dict(zip(SHCoef.keys(),list(zip(SHCoef.values(),Fln))))
return ODFln
[docs]
def Flnh(SHCoef,phi,beta,SGData):
'needs doc string'
import pytexture as ptx
Fln = np.zeros(len(SHCoef))
for i,term in enumerate(SHCoef):
l,m,n = eval(term.strip('C'))
if SGData['SGLaue'] in ['m3','m3m']:
Kcl = 0.0
for j in range(0,l+1,4):
im = j//4
pcrs,dum = ptx.pyplmpsi(l,j,1,phi)
Kcl += BOH['L='+str(l)][n-1][im]*pcrs*cosd(j*beta)
else: #all but cubic
pcrs,dum = ptx.pyplmpsi(l,n,1,phi)
pcrs *= RSQPI
if n == 0:
pcrs /= SQ2
if SGData['SGLaue'] in ['mmm','4/mmm','6/mmm','R3mR','3m1','31m']:
if SGData['SGLaue'] in ['3mR','3m1','31m']:
if n%6 == 3:
Kcl = pcrs*sind(n*beta)
else:
Kcl = pcrs*cosd(n*beta)
else:
Kcl = pcrs*cosd(n*beta)
else:
Kcl = pcrs*(cosd(n*beta)+sind(n*beta))
Fln[i] = SHCoef[term]*Kcl*Lnorm(l)
ODFln = dict(zip(SHCoef.keys(),list(zip(SHCoef.values(),Fln))))
return ODFln
[docs]
def polfcal(ODFln,SamSym,psi,gam):
'''Perform a pole figure computation.
Note that the the number of gam values must either be 1 or must
match psi. Updated for numpy 1.8.0
'''
import pytexture as ptx
PolVal = np.ones_like(psi)
for term in ODFln:
if abs(ODFln[term][1]) > 1.e-3:
l,m,n = eval(term.strip('C'))
psrs,dum = ptx.pyplmpsi(l,m,len(psi),psi)
if SamSym in ['-1','2/m']:
if m:
Ksl = RSQPI*psrs*(cosd(m*gam)+sind(m*gam))
else:
Ksl = RSQPI*psrs/SQ2
else:
if m:
Ksl = RSQPI*psrs*cosd(m*gam)
else:
Ksl = RSQPI*psrs/SQ2
PolVal += ODFln[term][1]*Ksl
return PolVal
[docs]
def invpolfcal(ODFln,SGData,phi,beta):
'needs doc string'
import pytexture as ptx
invPolVal = np.ones_like(beta)
for term in ODFln:
if abs(ODFln[term][1]) > 1.e-3:
l,m,n = eval(term.strip('C'))
if SGData['SGLaue'] in ['m3','m3m']:
Kcl = 0.0
for j in range(0,l+1,4):
im = j//4
pcrs,dum = ptx.pyplmpsi(l,j,len(beta),phi)
Kcl += BOH['L=%d'%(l)][n-1][im]*pcrs*cosd(j*beta)
else: #all but cubic
pcrs,dum = ptx.pyplmpsi(l,n,len(beta),phi)
pcrs *= RSQPI
if n == 0:
pcrs /= SQ2
if SGData['SGLaue'] in ['mmm','4/mmm','6/mmm','R3mR','3m1','31m']:
if SGData['SGLaue'] in ['3mR','3m1','31m']:
if n%6 == 3:
Kcl = pcrs*sind(n*beta)
else:
Kcl = pcrs*cosd(n*beta)
else:
Kcl = pcrs*cosd(n*beta)
else:
Kcl = pcrs*(cosd(n*beta)+sind(n*beta))
invPolVal += ODFln[term][1]*Kcl
return invPolVal
[docs]
def textureIndex(SHCoef):
'needs doc string'
Tindx = 1.0
for term in SHCoef:
l = eval(term.strip('C'))[0]
Tindx += SHCoef[term]**2/(2.0*l+1.)
return Tindx
UniqueCellByLaue = [
[['m3','m3m'],(0,)],
[['3R','3mR'],(0,3)],
[['3','3m1','31m','6/m','6/mmm','4/m','4/mmm'],(0,2)],
[['mmm'],(0,1,2)],
[['2/m'+'a'],(0,1,2,3)],
[['2/m'+'b'],(0,1,2,4)],
[['2/m'+'c'],(0,1,2,5)],
[['-1'],(0,1,2,3,4,5)],
]
'''List the unique cell terms by index for each Laue class'''
cellAlbl = ('a','b','c', 'alpha', 'beta', 'gamma')
'ASCII labels for a, b, c, alpha, beta, gamma'
cellUlbl = ('a','b','c',u'\u03B1',u'\u03B2',u'\u03B3')
'unicode labels for a, b, c, alpha, beta, gamma'
# self-test materials follow.
selftestlist = []
'''Defines a list of self-tests'''
selftestquiet = True
def _ReportTest():
'Report name and doc string of current routine when ``selftestquiet`` is False'
if not selftestquiet:
import inspect
caller = inspect.stack()[1][3]
doc = eval(caller).__doc__
if doc is not None:
print('testing '+__file__+' with '+caller+' ('+doc+')')
else:
print('testing '+__file__()+" with "+caller)
NeedTestData = True
def TestData():
array = np.array
global NeedTestData
NeedTestData = False
global CellTestData
# output from uctbx computed on platform darwin on 2010-05-28
CellTestData = [
# cell, g, G, cell*, V, V*
[(4, 4, 4, 90, 90, 90),
array([[ 1.60000000e+01, 9.79717439e-16, 9.79717439e-16],
[ 9.79717439e-16, 1.60000000e+01, 9.79717439e-16],
[ 9.79717439e-16, 9.79717439e-16, 1.60000000e+01]]), array([[ 6.25000000e-02, 3.82702125e-18, 3.82702125e-18],
[ 3.82702125e-18, 6.25000000e-02, 3.82702125e-18],
[ 3.82702125e-18, 3.82702125e-18, 6.25000000e-02]]), (0.25, 0.25, 0.25, 90.0, 90.0, 90.0), 64.0, 0.015625],
# cell, g, G, cell*, V, V*
[(4.0999999999999996, 5.2000000000000002, 6.2999999999999998, 100, 80, 130),
array([[ 16.81 , -13.70423184, 4.48533243],
[-13.70423184, 27.04 , -5.6887143 ],
[ 4.48533243, -5.6887143 , 39.69 ]]), array([[ 0.10206349, 0.05083339, -0.00424823],
[ 0.05083339, 0.06344997, 0.00334956],
[-0.00424823, 0.00334956, 0.02615544]]), (0.31947376387537696, 0.25189277536327803, 0.16172643497798223, 85.283666420376008, 94.716333579624006, 50.825714168082683), 100.98576357983838, 0.0099023858863968445],
# cell, g, G, cell*, V, V*
[(3.5, 3.5, 6, 90, 90, 120),
array([[ 1.22500000e+01, -6.12500000e+00, 1.28587914e-15],
[ -6.12500000e+00, 1.22500000e+01, 1.28587914e-15],
[ 1.28587914e-15, 1.28587914e-15, 3.60000000e+01]]), array([[ 1.08843537e-01, 5.44217687e-02, 3.36690552e-18],
[ 5.44217687e-02, 1.08843537e-01, 3.36690552e-18],
[ 3.36690552e-18, 3.36690552e-18, 2.77777778e-02]]), (0.32991443953692895, 0.32991443953692895, 0.16666666666666669, 90.0, 90.0, 60.000000000000021), 63.652867178156257, 0.015710211406520427],
]
global CoordTestData
CoordTestData = [
# cell, ((frac, ortho),...)
((4,4,4,90,90,90,), [
((0.10000000000000001, 0.0, 0.0),(0.40000000000000002, 0.0, 0.0)),
((0.0, 0.10000000000000001, 0.0),(2.4492935982947065e-17, 0.40000000000000002, 0.0)),
((0.0, 0.0, 0.10000000000000001),(2.4492935982947065e-17, -2.4492935982947065e-17, 0.40000000000000002)),
((0.10000000000000001, 0.20000000000000001, 0.29999999999999999),(0.40000000000000013, 0.79999999999999993, 1.2)),
((0.20000000000000001, 0.29999999999999999, 0.10000000000000001),(0.80000000000000016, 1.2, 0.40000000000000002)),
((0.29999999999999999, 0.20000000000000001, 0.10000000000000001),(1.2, 0.80000000000000004, 0.40000000000000002)),
((0.5, 0.5, 0.5),(2.0, 1.9999999999999998, 2.0)),
]),
# cell, ((frac, ortho),...)
((4.1,5.2,6.3,100,80,130,), [
((0.10000000000000001, 0.0, 0.0),(0.40999999999999998, 0.0, 0.0)),
((0.0, 0.10000000000000001, 0.0),(-0.33424955703700043, 0.39834311042186865, 0.0)),
((0.0, 0.0, 0.10000000000000001),(0.10939835193016617, -0.051013289294572106, 0.6183281045774256)),
((0.10000000000000001, 0.20000000000000001, 0.29999999999999999),(0.069695941716497567, 0.64364635296002093, 1.8549843137322766)),
((0.20000000000000001, 0.29999999999999999, 0.10000000000000001),(-0.073350319180835066, 1.1440160419710339, 0.6183281045774256)),
((0.29999999999999999, 0.20000000000000001, 0.10000000000000001),(0.67089923785616512, 0.74567293154916525, 0.6183281045774256)),
((0.5, 0.5, 0.5),(0.92574397446582857, 1.7366491056364828, 3.0916405228871278)),
]),
# cell, ((frac, ortho),...)
((3.5,3.5,6,90,90,120,), [
((0.10000000000000001, 0.0, 0.0),(0.35000000000000003, 0.0, 0.0)),
((0.0, 0.10000000000000001, 0.0),(-0.17499999999999993, 0.3031088913245536, 0.0)),
((0.0, 0.0, 0.10000000000000001),(3.6739403974420595e-17, -3.6739403974420595e-17, 0.60000000000000009)),
((0.10000000000000001, 0.20000000000000001, 0.29999999999999999),(2.7675166561703527e-16, 0.60621778264910708, 1.7999999999999998)),
((0.20000000000000001, 0.29999999999999999, 0.10000000000000001),(0.17500000000000041, 0.90932667397366063, 0.60000000000000009)),
((0.29999999999999999, 0.20000000000000001, 0.10000000000000001),(0.70000000000000018, 0.6062177826491072, 0.60000000000000009)),
((0.5, 0.5, 0.5),(0.87500000000000067, 1.5155444566227676, 3.0)),
]),
]
global LaueTestData #generated by GSAS
LaueTestData = {
'R 3 m':[(4.,4.,6.,90.,90.,120.),((1,0,1,6),(1,0,-2,6),(0,0,3,2),(1,1,0,6),(2,0,-1,6),(2,0,2,6),
(1,1,3,12),(1,0,4,6),(2,1,1,12),(2,1,-2,12),(3,0,0,6),(1,0,-5,6),(2,0,-4,6),(3,0,-3,6),(3,0,3,6),
(0,0,6,2),(2,2,0,6),(2,1,4,12),(2,0,5,6),(3,1,-1,12),(3,1,2,12),(1,1,6,12),(2,2,3,12),(2,1,-5,12))],
'R 3':[(4.,4.,6.,90.,90.,120.),((1,0,1,6),(1,0,-2,6),(0,0,3,2),(1,1,0,6),(2,0,-1,6),(2,0,2,6),(1,1,3,6),
(1,1,-3,6),(1,0,4,6),(3,-1,1,6),(2,1,1,6),(3,-1,-2,6),(2,1,-2,6),(3,0,0,6),(1,0,-5,6),(2,0,-4,6),
(2,2,0,6),(3,0,3,6),(3,0,-3,6),(0,0,6,2),(3,-1,4,6),(2,0,5,6),(2,1,4,6),(4,-1,-1,6),(3,1,-1,6),
(3,1,2,6),(4,-1,2,6),(2,2,-3,6),(1,1,-6,6),(1,1,6,6),(2,2,3,6),(2,1,-5,6),(3,-1,-5,6))],
'P 3':[(4.,4.,6.,90.,90.,120.),((0,0,1,2),(1,0,0,6),(1,0,1,6),(0,0,2,2),(1,0,-1,6),(1,0,2,6),(1,0,-2,6),
(1,1,0,6),(0,0,3,2),(1,1,1,6),(1,1,-1,6),(1,0,3,6),(1,0,-3,6),(2,0,0,6),(2,0,-1,6),(1,1,-2,6),
(1,1,2,6),(2,0,1,6),(2,0,-2,6),(2,0,2,6),(0,0,4,2),(1,1,-3,6),(1,1,3,6),(1,0,-4,6),(1,0,4,6),
(2,0,-3,6),(2,1,0,6),(2,0,3,6),(3,-1,0,6),(2,1,1,6),(3,-1,-1,6),(2,1,-1,6),(3,-1,1,6),(1,1,4,6),
(3,-1,2,6),(3,-1,-2,6),(1,1,-4,6),(0,0,5,2),(2,1,2,6),(2,1,-2,6),(3,0,0,6),(3,0,1,6),(2,0,4,6),
(2,0,-4,6),(3,0,-1,6),(1,0,-5,6),(1,0,5,6),(3,-1,-3,6),(2,1,-3,6),(2,1,3,6),(3,-1,3,6),(3,0,-2,6),
(3,0,2,6),(1,1,5,6),(1,1,-5,6),(2,2,0,6),(3,0,3,6),(3,0,-3,6),(0,0,6,2),(2,0,-5,6),(2,1,-4,6),
(2,2,-1,6),(3,-1,-4,6),(2,2,1,6),(3,-1,4,6),(2,1,4,6),(2,0,5,6),(1,0,-6,6),(1,0,6,6),(4,-1,0,6),
(3,1,0,6),(3,1,-1,6),(3,1,1,6),(4,-1,-1,6),(2,2,2,6),(4,-1,1,6),(2,2,-2,6),(3,1,2,6),(3,1,-2,6),
(3,0,4,6),(3,0,-4,6),(4,-1,-2,6),(4,-1,2,6),(2,2,-3,6),(1,1,6,6),(1,1,-6,6),(2,2,3,6),(3,-1,5,6),
(2,1,5,6),(2,1,-5,6),(3,-1,-5,6))],
'P 3 m 1':[(4.,4.,6.,90.,90.,120.),((0,0,1,2),(1,0,0,6),(1,0,-1,6),(1,0,1,6),(0,0,2,2),(1,0,-2,6),
(1,0,2,6),(1,1,0,6),(0,0,3,2),(1,1,1,12),(1,0,-3,6),(1,0,3,6),(2,0,0,6),(1,1,2,12),(2,0,1,6),
(2,0,-1,6),(0,0,4,2),(2,0,-2,6),(2,0,2,6),(1,1,3,12),(1,0,-4,6),(1,0,4,6),(2,0,3,6),(2,1,0,12),
(2,0,-3,6),(2,1,1,12),(2,1,-1,12),(1,1,4,12),(2,1,2,12),(0,0,5,2),(2,1,-2,12),(3,0,0,6),(1,0,-5,6),
(3,0,1,6),(3,0,-1,6),(1,0,5,6),(2,0,4,6),(2,0,-4,6),(2,1,3,12),(2,1,-3,12),(3,0,-2,6),(3,0,2,6),
(1,1,5,12),(3,0,-3,6),(0,0,6,2),(2,2,0,6),(3,0,3,6),(2,1,4,12),(2,2,1,12),(2,0,5,6),(2,1,-4,12),
(2,0,-5,6),(1,0,-6,6),(1,0,6,6),(3,1,0,12),(3,1,-1,12),(3,1,1,12),(2,2,2,12),(3,1,2,12),
(3,0,4,6),(3,1,-2,12),(3,0,-4,6),(1,1,6,12),(2,2,3,12))],
'P 3 1 m':[(4.,4.,6.,90.,90.,120.),((0,0,1,2),(1,0,0,6),(0,0,2,2),(1,0,1,12),(1,0,2,12),(1,1,0,6),
(0,0,3,2),(1,1,-1,6),(1,1,1,6),(1,0,3,12),(2,0,0,6),(2,0,1,12),(1,1,2,6),(1,1,-2,6),(2,0,2,12),
(0,0,4,2),(1,1,-3,6),(1,1,3,6),(1,0,4,12),(2,1,0,12),(2,0,3,12),(2,1,1,12),(2,1,-1,12),(1,1,-4,6),
(1,1,4,6),(0,0,5,2),(2,1,-2,12),(2,1,2,12),(3,0,0,6),(1,0,5,12),(2,0,4,12),(3,0,1,12),(2,1,-3,12),
(2,1,3,12),(3,0,2,12),(1,1,5,6),(1,1,-5,6),(3,0,3,12),(0,0,6,2),(2,2,0,6),(2,1,-4,12),(2,0,5,12),
(2,2,-1,6),(2,2,1,6),(2,1,4,12),(3,1,0,12),(1,0,6,12),(2,2,2,6),(3,1,-1,12),(2,2,-2,6),(3,1,1,12),
(3,1,-2,12),(3,0,4,12),(3,1,2,12),(1,1,-6,6),(2,2,3,6),(2,2,-3,6),(1,1,6,6))],
}
global FLnhTestData
FLnhTestData = [{
'C(4,0,0)': (0.965, 0.42760447),
'C(2,0,0)': (1.0122, -0.80233610),
'C(2,0,2)': (0.0061, 8.37491546E-03),
'C(6,0,4)': (-0.0898, 4.37985696E-02),
'C(6,0,6)': (-0.1369, -9.04081762E-02),
'C(6,0,0)': (0.5935, -0.18234928),
'C(4,0,4)': (0.1872, 0.16358127),
'C(6,0,2)': (0.6193, 0.27573633),
'C(4,0,2)': (-0.1897, 0.12530720)},[1,0,0]]
def test0():
if NeedTestData: TestData()
msg = 'test cell2Gmat, fillgmat, Gmat2cell'
for (cell, tg, tG, trcell, tV, trV) in CellTestData:
G, g = cell2Gmat(cell)
assert np.allclose(G,tG),msg
assert np.allclose(g,tg),msg
tcell = Gmat2cell(g)
assert np.allclose(cell,tcell),msg
tcell = Gmat2cell(G)
assert np.allclose(tcell,trcell),msg
if __name__ == '__main__': selftestlist.append(test0)
[docs]
def test1():
'test cell2A and A2Gmat'
_ReportTest()
if NeedTestData: TestData()
msg = 'test cell2A and A2Gmat'
for (cell, tg, tG, trcell, tV, trV) in CellTestData:
G, g = A2Gmat(cell2A(cell))
assert np.allclose(G,tG),msg
assert np.allclose(g,tg),msg
if __name__ == '__main__': selftestlist.append(test1)
[docs]
def test2():
'test Gmat2A, A2cell, A2Gmat, Gmat2cell'
_ReportTest()
if NeedTestData: TestData()
msg = 'test Gmat2A, A2cell, A2Gmat, Gmat2cell'
for (cell, tg, tG, trcell, tV, trV) in CellTestData:
G, g = cell2Gmat(cell)
tcell = A2cell(Gmat2A(G))
assert np.allclose(cell,tcell),msg
if __name__ == '__main__': selftestlist.append(test2)
[docs]
def test3():
'test invcell2Gmat'
_ReportTest()
if NeedTestData: TestData()
msg = 'test invcell2Gmat'
for (cell, tg, tG, trcell, tV, trV) in CellTestData:
G, g = invcell2Gmat(trcell)
assert np.allclose(G,tG),msg
assert np.allclose(g,tg),msg
if __name__ == '__main__': selftestlist.append(test3)
[docs]
def test4():
'test calc_rVsq, calc_rV, calc_V'
_ReportTest()
if NeedTestData: TestData()
msg = 'test calc_rVsq, calc_rV, calc_V'
for (cell, tg, tG, trcell, tV, trV) in CellTestData:
assert np.allclose(calc_rV(cell2A(cell)),trV), msg
assert np.allclose(calc_V(cell2A(cell)),tV), msg
if __name__ == '__main__': selftestlist.append(test4)
[docs]
def test5():
'test A2invcell'
_ReportTest()
if NeedTestData: TestData()
msg = 'test A2invcell'
for (cell, tg, tG, trcell, tV, trV) in CellTestData:
rcell = A2invcell(cell2A(cell))
assert np.allclose(rcell,trcell),msg
if __name__ == '__main__': selftestlist.append(test5)
[docs]
def test6():
'test cell2AB'
_ReportTest()
if NeedTestData: TestData()
msg = 'test cell2AB'
for (cell,coordlist) in CoordTestData:
A,B = cell2AB(cell)
for (frac,ortho) in coordlist:
to = np.inner(A,frac)
tf = np.inner(B,to)
assert np.allclose(ortho,to), msg
assert np.allclose(frac,tf), msg
to = np.sum(A*frac,axis=1)
tf = np.sum(B*to,axis=1)
assert np.allclose(ortho,to), msg
assert np.allclose(frac,tf), msg
if __name__ == '__main__': selftestlist.append(test6)
[docs]
def test7():
'test GetBraviasNum(...) and GenHBravais(...)'
_ReportTest()
import os.path
import sys
import GSASIIspc as spc
testdir = os.path.join(os.path.split(os.path.abspath( __file__ ))[0],'testinp')
if os.path.exists(testdir):
if testdir not in sys.path: sys.path.insert(0,testdir)
import sgtbxlattinp
derror = 1e-4
def indexmatch(hklin, hkllist, system):
for hklref in hkllist:
hklref = list(hklref)
# these permutations are far from complete, but are sufficient to
# allow the test to complete
if system == 'cubic':
permlist = [(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1),]
elif system == 'monoclinic':
permlist = [(1,2,3),(-1,2,-3)]
else:
permlist = [(1,2,3)]
for perm in permlist:
hkl = [abs(i) * hklin[abs(i)-1] / i for i in perm]
if hkl == hklref: return True
if [-i for i in hkl] == hklref: return True
else:
return False
for key in sgtbxlattinp.sgtbx7:
spdict = spc.SpcGroup(key)
cell = sgtbxlattinp.sgtbx7[key][0]
system = spdict[1]['SGSys']
center = spdict[1]['SGLatt']
bravcode = GetBraviasNum(center, system)
g2list = GenHBravais(sgtbxlattinp.dmin, bravcode, cell2A(cell))
assert len(sgtbxlattinp.sgtbx7[key][1]) == len(g2list), 'Reflection lists differ for %s' % key
for h,k,l,d,num in g2list:
for hkllist,dref in sgtbxlattinp.sgtbx7[key][1]:
if abs(d-dref) < derror:
if indexmatch((h,k,l,), hkllist, system):
break
else:
assert 0,'No match for %s at %s (%s)' % ((h,k,l),d,key)
if __name__ == '__main__': selftestlist.append(test7)
[docs]
def test8():
'test GenHLaue'
_ReportTest()
import GSASIIspc as spc
import sgtbxlattinp
derror = 1e-4
dmin = sgtbxlattinp.dmin
def indexmatch(hklin, hklref, system, axis):
# these permutations are far from complete, but are sufficient to
# allow the test to complete
if system == 'cubic':
permlist = [(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1),]
elif system == 'monoclinic' and axis=='b':
permlist = [(1,2,3),(-1,2,-3)]
elif system == 'monoclinic' and axis=='a':
permlist = [(1,2,3),(1,-2,-3)]
elif system == 'monoclinic' and axis=='c':
permlist = [(1,2,3),(-1,-2,3)]
elif system == 'trigonal':
permlist = [(1,2,3),(2,1,3),(-1,-2,3),(-2,-1,3)]
elif system == 'rhombohedral':
permlist = [(1,2,3),(2,3,1),(3,1,2)]
else:
permlist = [(1,2,3)]
hklref = list(hklref)
for perm in permlist:
hkl = [abs(i) * hklin[abs(i)-1] / i for i in perm]
if hkl == hklref: return True
if [-i for i in hkl] == hklref: return True
return False
for key in sgtbxlattinp.sgtbx8:
spdict = spc.SpcGroup(key)[1]
cell = sgtbxlattinp.sgtbx8[key][0]
Axis = spdict['SGUniq']
system = spdict['SGSys']
g2list = GenHLaue(dmin,spdict,cell2A(cell))
#if len(g2list) != len(sgtbxlattinp.sgtbx8[key][1]):
# print 'failed',key,':' ,len(g2list),'vs',len(sgtbxlattinp.sgtbx8[key][1])
# print 'GSAS-II:'
# for h,k,l,d in g2list: print ' ',(h,k,l),d
# print 'SGTBX:'
# for hkllist,dref in sgtbxlattinp.sgtbx8[key][1]: print ' ',hkllist,dref
assert len(g2list) == len(sgtbxlattinp.sgtbx8[key][1]), (
'Reflection lists differ for %s' % key
)
#match = True
for h,k,l,d in g2list:
for hkllist,dref in sgtbxlattinp.sgtbx8[key][1]:
if abs(d-dref) < derror:
if indexmatch((h,k,l,), hkllist, system, Axis): break
else:
assert 0,'No match for %s at %s (%s)' % ((h,k,l),d,key)
#match = False
#if not match:
#for hkllist,dref in sgtbxlattinp.sgtbx8[key][1]: print ' ',hkllist,dref
#print center, Laue, Axis, system
if __name__ == '__main__': selftestlist.append(test8)
[docs]
def test9():
'test GenHLaue'
_ReportTest()
import GSASIIspc as G2spc
if NeedTestData: TestData()
for spc in LaueTestData:
data = LaueTestData[spc]
cell = data[0]
hklm = np.array(data[1])
H = hklm[-1][:3]
hklO = hklm.T[:3].T
A = cell2A(cell)
dmin = 1./np.sqrt(calc_rDsq(H,A))
SGData = G2spc.SpcGroup(spc)[1]
hkls = np.array(GenHLaue(dmin,SGData,A))
hklN = hkls.T[:3].T
#print spc,hklO.shape,hklN.shape
err = True
for H in hklO:
if H not in hklN:
print ('%d %s'%(H,' missing from hkl from GSASII'))
err = False
assert(err)
if __name__ == '__main__': selftestlist.append(test9)
if __name__ == '__main__':
# run self-tests
selftestquiet = False
for test in selftestlist:
test()
print ("OK")