# -*- coding: utf-8 -*-
#GSASIImath - major mathematics routines
########### SVN repository information ###################
# $Date: 2022-11-01 16:14:03 +0000 (Tue, 01 Nov 2022) $
# $Author: vondreele $
# $Revision: 5361 $
# $URL: https://subversion.xray.aps.anl.gov/pyGSAS/trunk/GSASIImath.py $
# $Id: GSASIImath.py 5361 2022-11-01 16:14:03Z vondreele $
########### SVN repository information ###################
'''
*GSASIImath: computation module*
================================
Routines for least-squares minimization and other stuff
'''
from __future__ import division, print_function
import random as rn
import numpy as np
import numpy.linalg as nl
import numpy.ma as ma
import time
import math
import copy
import GSASIIpath
GSASIIpath.SetVersionNumber("$Revision: 5361 $")
import GSASIIElem as G2el
import GSASIIlattice as G2lat
import GSASIIspc as G2spc
import GSASIIpwd as G2pwd
import GSASIIobj as G2obj
import GSASIIfiles as G2fil
import numpy.fft as fft
import scipy.optimize as so
try:
import pypowder as pwd
except ImportError:
print ('pypowder is not available - profile calcs. not allowed')
sind = lambda x: np.sin(x*np.pi/180.)
cosd = lambda x: np.cos(x*np.pi/180.)
tand = lambda x: np.tan(x*np.pi/180.)
asind = lambda x: 180.*np.arcsin(x)/np.pi
acosd = lambda x: 180.*np.arccos(x)/np.pi
atand = lambda x: 180.*np.arctan(x)/np.pi
atan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi
try: # fails on doc build
twopi = 2.0*np.pi
twopisq = 2.0*np.pi**2
_double_min = np.finfo(float).min
_double_max = np.finfo(float).max
except TypeError:
pass
nxs = np.newaxis
################################################################################
#### Hessian least-squares Levenberg-Marquardt routine
################################################################################
[docs]class G2NormException(Exception): pass
[docs]def pinv(a, rcond=1e-15 ):
'''
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Modified from numpy.linalg.pinv; assumes a is Hessian & returns no. zeros found
Calculate the generalized inverse of a matrix using its
singular-value decomposition (SVD) and including all
*large* singular values.
:param array a: (M, M) array_like - here assumed to be LS Hessian
Matrix to be pseudo-inverted.
:param float rcond: Cutoff for small singular values.
Singular values smaller (in modulus) than
`rcond` * largest_singular_value (again, in modulus)
are set to zero.
:returns: B : (M, M) ndarray
The pseudo-inverse of `a`
Raises: LinAlgError
If the SVD computation does not converge.
Notes:
The pseudo-inverse of a matrix A, denoted :math:`A^+`, is
defined as: "the matrix that 'solves' [the least-squares problem]
:math:`Ax = b`," i.e., if :math:`\\bar{x}` is said solution, then
:math:`A^+` is that matrix such that :math:`\\bar{x} = A^+b`.
It can be shown that if :math:`Q_1 \\Sigma Q_2^T = A` is the singular
value decomposition of A, then
:math:`A^+ = Q_2 \\Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are
orthogonal matrices, :math:`\\Sigma` is a diagonal matrix consisting
of A's so-called singular values, (followed, typically, by
zeros), and then :math:`\\Sigma^+` is simply the diagonal matrix
consisting of the reciprocals of A's singular values
(again, followed by zeros). [1]
References:
.. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pp. 139-142.
'''
u, s, vt = nl.svd(a)
cutoff = rcond*np.maximum.reduce(s)
s = np.where(s>cutoff,1./s,0.)
nzero = s.shape[0]-np.count_nonzero(s)
res = np.dot(vt.T,s[:,nxs]*u.T)
return res,nzero
[docs]def dropTerms(bad, hessian, indices, *vectors):
'''Remove the 'bad' terms from the Hessian and vector
:param tuple bad: a list of variable (row/column) numbers that should be
removed from the hessian and vector. Example: (0,3) removes the 1st and
4th column/row
:param np.array hessian: a square matrix of length n x n
:param np.array indices: the indices of the least-squares vector of length n
referenced to the initial variable list; as this routine is called
multiple times, more terms may be removed from this list
:param additional-args: various least-squares model values, length n
:returns: hessian, indices, vector0, vector1,... where the lengths are
now n' x n' and n', with n' = n - len(bad)
'''
out = [np.delete(np.delete(hessian,bad,1),bad,0),np.delete(indices,bad)]
for v in vectors:
out.append(np.delete(v,bad))
return out
[docs]def setHcorr(info,Amat,xtol,problem=False):
'''Find & report high correlation terms in covariance matrix
'''
Adiag = np.sqrt(np.diag(Amat))
if np.any(np.abs(Adiag) < 1.e-14): raise G2NormException # test for any hard singularities
Anorm = np.outer(Adiag,Adiag)
Amat = Amat/Anorm
Bmat,Nzeros = pinv(Amat,xtol) #Moore-Penrose inversion (via SVD) & count of zeros
Bmat = Bmat/Anorm
sig = np.sqrt(np.diag(Bmat))
xvar = np.outer(sig,np.ones_like(sig))
AcovUp = abs(np.triu(np.divide(np.divide(Bmat,xvar),xvar.T),1)) # elements above diagonal
if Nzeros or problem: # something is wrong, so report what is found
m = min(0.99,0.99*np.amax(AcovUp))
else:
m = max(0.95,0.99*np.amax(AcovUp))
info['Hcorr'] = [(i,j,AcovUp[i,j]) for i,j in zip(*np.where(AcovUp > m))]
return Bmat,Nzeros
[docs]def setSVDwarn(info,Amat,Nzeros,indices):
'''Find & report terms causing SVN zeros
'''
if Nzeros == 0: return
d = np.abs(np.diag(nl.qr(Amat)[1]))
svdsing = list(np.where(d < 1.e-14)[0])
if len(svdsing) < Nzeros: # try to get the Nzeros worst terms
svdsing = list(np.where(d <= sorted(d)[Nzeros-1])[0])
if not len(svdsing): # make sure at least the worst term is shown
svdsing = [np.argmin(d)]
info['SVDsing'] = [indices[i] for i in svdsing]
[docs]def HessianLSQ(func,x0,Hess,args=(),ftol=1.49012e-8,xtol=1.e-6, maxcyc=0,lamda=-3,Print=False,refPlotUpdate=None):
'''
Minimize the sum of squares of a function (:math:`f`) evaluated on a series of
values (y): :math:`\\sum_{y=0}^{N_{obs}} f(y,{args})`
where :math:`x = arg min(\\sum_{y=0}^{N_{obs}} (func(y)^2,axis=0))`
:param function func: callable method or function
should take at least one (possibly length N vector) argument and
returns M floating point numbers.
:param np.ndarray x0: The starting estimate for the minimization of length N
:param function Hess: callable method or function
A required function or method to compute the weighted vector and Hessian for func.
It must be a symmetric NxN array
:param tuple args: Any extra arguments to func are placed in this tuple.
:param float ftol: Relative error desired in the sum of squares.
:param float xtol: Relative tolerance of zeros in the SVD solution in nl.pinv.
:param int maxcyc: The maximum number of cycles of refinement to execute, if -1 refine
until other limits are met (ftol, xtol)
:param int lamda: initial Marquardt lambda=10**lamda
:param bool Print: True for printing results (residuals & times) by cycle
:returns: (x,cov_x,infodict) where
* x : ndarray
The solution (or the result of the last iteration for an unsuccessful
call).
* cov_x : ndarray
Uses the fjac and ipvt optional outputs to construct an
estimate of the jacobian around the solution. ``None`` if a
singular matrix encountered (indicates very flat curvature in
some direction). This matrix must be multiplied by the
residual standard deviation to get the covariance of the
parameter estimates -- see curve_fit.
* infodict : dict, a dictionary of optional outputs with the keys:
* 'fvec' : the function evaluated at the output
* 'num cyc':
* 'nfev': number of objective function evaluation calls
* 'lamMax':
* 'psing': list of variable variables that have been removed from the refinement
* 'SVD0': -1 for singlar matrix, -2 for objective function exception, Nzeroes = # of SVD 0's
* 'Hcorr': list entries (i,j,c) where i & j are of highly correlated variables & c is correlation coeff.
'''
ifConverged = False
deltaChi2 = -10.
x0 = np.array(x0, ndmin=1, dtype=np.float64) # make sure that x0 float 1-D
# array (in case any parameters were set to int)
n = len(x0)
if type(args) != type(()):
args = (args,)
dlg = None
if hasattr(args[-1],'Update'): dlg = args[-1]
if hasattr(dlg,'AdvanceCycle'): dlg.AdvanceCycle(-1)
icycle = 0
AmatAll = None # changed only if cycles > 0
lamMax = lam = 0 # start w/o Marquardt and add it in if needed
nfev = 0
if Print:
G2fil.G2Print(' Hessian Levenberg-Marquardt SVD refinement on %d variables:'%(n))
XvecAll = np.zeros(n)
try:
M2 = func(x0,*args)
except Exception as Msg:
if not hasattr(Msg,'msg'): Msg.msg = str(Msg)
G2fil.G2Print('\nouch #0 unable to evaluate initial objective function\nCheck for an invalid parameter value',mode='error')
G2fil.G2Print('Use Calculate/"View LS parms" to list all parameter values\n',mode='warn')
G2fil.G2Print('Error message: '+Msg.msg,mode='warn')
if GSASIIpath.GetConfigValue('debug'):
import traceback
print(traceback.format_exc())
raise G2obj.G2Exception('HessianLSQ -- ouch #0: look for invalid parameter (see console)')
chisq00 = np.sum(M2**2) # starting Chi**2
Nobs = len(M2)
if Print:
G2fil.G2Print('initial chi^2 %.5g with %d obs.'%(chisq00,Nobs))
if n == 0:
info = {'num cyc':0,'fvec':M2,'nfev':1,'lamMax':0,'psing':[],'SVD0':0}
info['msg'] = 'no variables: skipping refinement\n'
info.update({'Converged':True, 'DelChi2':0, 'Xvec':None, 'chisq0':chisq00})
return [x0,np.array([]),info]
indices = range(n)
while icycle < maxcyc:
M = M2
time0 = time.time()
nfev += 1
chisq0 = np.sum(M**2)
YvecAll,AmatAll = Hess(x0,*args) # compute hessian & vectors with all variables
Yvec = copy.copy(YvecAll)
Amat = copy.copy(AmatAll)
Xvec = copy.copy(XvecAll)
# we could remove vars that were dropped in previous cycles here (use indices), but for
# now let's reset them each cycle in case the singularities go away
indices = range(n)
Adiag = np.sqrt(np.diag(Amat))
psing = np.where(np.abs(Adiag) < 1.e-14)[0] # find any hard singularities
if len(psing):
G2fil.G2Print('ouch #1 dropping singularities for variable(s) #{}'.format(
psing), mode='warn')
Amat, indices, Xvec, Yvec, Adiag = dropTerms(psing,Amat, indices, Xvec, Yvec, Adiag)
Anorm = np.outer(Adiag,Adiag) # normalize matrix & vector
Yvec /= Adiag
Amat /= Anorm
chitol = ftol
maxdrop = 3 # max number of drop var attempts
loops = 0
while True: #--------- loop as we increase lamda and possibly drop terms
lamMax = max(lamMax,lam)
Amatlam = Amat*(1.+np.eye(Amat.shape[0])*lam)
try:
Nzeros = 1
Ainv,Nzeros = pinv(Amatlam,xtol) # Moore-Penrose SVD inversion
except nl.LinAlgError:
loops += 1
d = np.abs(np.diag(nl.qr(Amatlam)[1]))
psing = list(np.where(d < 1.e-14)[0])
if not len(psing): # make sure at least the worst term is removed
psing = [np.argmin(d)]
G2fil.G2Print('ouch #2 bad SVD inversion; dropping terms for for variable(s) #{}'.
format(psing), mode='warn')
Amat, indices, Xvec, Yvec, Adiag = dropTerms(psing,Amat, indices, Xvec, Yvec, Adiag)
if loops < maxdrop: continue # try again, same lam but fewer vars
G2fil.G2Print('giving up with ouch #2', mode='error')
info = {'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':lamMax,'SVD0':Nzeros}
info['psing'] = [i for i in range(n) if i not in indices]
info['msg'] = 'SVD inversion failure\n'
return [x0,None,info]
Xvec = np.inner(Ainv,Yvec)/Adiag #solve for LS terms
XvecAll[indices] = Xvec # expand
try:
M2 = func(x0+XvecAll,*args)
except Exception as Msg:
if not hasattr(Msg,'msg'): Msg.msg = str(Msg)
G2fil.G2Print(Msg.msg,mode='warn')
loops += 1
d = np.abs(np.diag(nl.qr(Amatlam)[1]))
G2fil.G2Print('ouch #3 unable to evaluate objective function;',mode='error')
info = {'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':lamMax,'SVD0':Nzeros}
info['psing'] = [i for i in range(n) if i not in indices]
try: # try to report highly correlated parameters from full Hessian
setHcorr(info,AmatAll,xtol,problem=True)
except nl.LinAlgError:
G2fil.G2Print('Warning: Hessian too ill-conditioned to get full covariance matrix')
except G2NormException:
G2fil.G2Print('Warning: Hessian normalization problem')
except Exception as Msg:
if not hasattr(Msg,'msg'): Msg.msg = str(Msg)
G2fil.G2Print('Error determining highly correlated vars',mode='warn')
G2fil.G2Print(Msg.msg,mode='warn')
info['msg'] = Msg.msg + '\n\n'
setSVDwarn(info,Amatlam,Nzeros,indices)
return [x0,None,info]
nfev += 1
chisq1 = np.sum(M2**2)
if chisq1 > chisq0*(1.+chitol): #TODO put Alan Coehlo's criteria for lambda here?
if lam == 0:
lam = 10.**lamda # set to initial Marquardt term
else:
lam *= 10.
if Print:
G2fil.G2Print(('divergence: chi^2 %.5g on %d obs. (%d SVD zeros)\n'+
'\tincreasing Marquardt lambda to %.1e')%(chisq1,Nobs,Nzeros,lam))
if lam > 10.:
G2fil.G2Print('ouch #4 stuck: chisq-new %.4g > chisq0 %.4g with lambda %.1g'%
(chisq1,chisq0,lam), mode='warn')
if GSASIIpath.GetConfigValue('debug'):
print('Cycle %d: %.2fs' % (icycle,time.time()-time0))
try: # report highly correlated parameters from full Hessian, if we can
info = {'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':lamMax,
'Converged':False, 'DelChi2':deltaChi2, 'Xvec':XvecAll,
'chisq0':chisq00, 'Ouch#4':True}
info['psing'] = [i for i in range(n) if i not in indices]
Bmat,Nzeros = setHcorr(info,AmatAll,xtol,problem=True)
info['SVD0'] = Nzeros
setSVDwarn(info,Amatlam,Nzeros,indices)
return [x0,Bmat,info]
except Exception as Msg:
if not hasattr(Msg,'msg'): Msg.msg = str(Msg)
G2fil.G2Print('Error determining highly correlated vars',mode='warn')
G2fil.G2Print(Msg.msg,mode='warn')
maxcyc = -1 # no more cycles
break
chitol *= 2
else: # refinement succeeded
x0 += XvecAll
lam /= 10. # drop lam on next cycle
break
# complete current cycle
if hasattr(dlg,'AdvanceCycle'): dlg.AdvanceCycle(icycle)
deltaChi2 = (chisq0-chisq1)/chisq0
if Print:
if n-len(indices):
G2fil.G2Print(
'Cycle %d: %.2fs Chi2: %.5g; Obs: %d; Lam: %.3g Del: %.3g; drop=%d, SVD=%d'%
(icycle,time.time()-time0,chisq1,Nobs,lamMax,deltaChi2,n-len(indices),Nzeros))
else:
G2fil.G2Print(
'Cycle %d: %.2fs, Chi**2: %.5g for %d obs., Lambda: %.3g, Delta: %.3g, SVD=%d'%
(icycle,time.time()-time0,chisq1,Nobs,lamMax,deltaChi2,Nzeros))
Histograms = args[0][0]
if refPlotUpdate is not None: refPlotUpdate(Histograms,icycle) # update plot
if deltaChi2 < ftol:
ifConverged = True
if Print:
G2fil.G2Print("converged")
break
icycle += 1
#----------------------- refinement complete, compute Covariance matrix w/o Levenberg-Marquardt
nfev += 1
try:
if icycle == 0: # no parameter changes, skip recalc
M = M2
else:
M = func(x0,*args)
except Exception as Msg:
if not hasattr(Msg,'msg'): Msg.msg = str(Msg)
G2fil.G2Print(Msg.msg,mode='warn')
G2fil.G2Print('ouch #5 final objective function re-eval failed',mode='error')
psing = [i for i in range(n) if i not in indices]
info = {'num cyc':icycle,'fvec':M2,'nfev':nfev,'lamMax':lamMax,'psing':psing,'SVD0':-2}
info['msg'] = Msg.msg + '\n'
setSVDwarn(info,Amatlam,Nzeros,indices)
return [x0,None,info]
chisqf = np.sum(M**2) # ending chi**2
if not maxcyc: #zero cycle calc exit here
info = {'num cyc':0,'fvec':M,'nfev':0,'lamMax':0,'SVD0':0,
'Converged':True, 'DelChi2':0., 'Xvec':XvecAll, 'chisq0':chisqf}
return [x0,None,info]
psing_prev = [i for i in range(n) if i not in indices] # save dropped vars
if AmatAll is None: # Save some time and use Hessian from the last refinement cycle
Yvec,Amat = Hess(x0,*args)
else:
Yvec = copy.copy(YvecAll)
Amat = copy.copy(AmatAll)
indices = range(n)
info = {}
try: # report highly correlated parameters from full Hessian, if we can
Bmat,Nzeros = setHcorr(info,Amat,xtol,problem=False)
info.update({'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':lamMax,'SVD0':Nzeros,'psing':psing_prev,
'Converged':ifConverged, 'DelChi2':deltaChi2, 'chisq0':chisq00})
if icycle > 0: info.update({'Xvec':XvecAll})
setSVDwarn(info,Amat,Nzeros,indices)
# expand Bmat by filling with zeros if columns have been dropped
if len(psing_prev):
ins = [j-i for i,j in enumerate(psing_prev)]
Bmat = np.insert(np.insert(Bmat,ins,0,1),ins,0,0)
return [x0,Bmat,info]
except nl.LinAlgError:
G2fil.G2Print('Warning: Hessian too ill-conditioned to get full covariance matrix')
except G2NormException:
G2fil.G2Print('Warning: Hessian normalization problem')
except Exception as Msg:
if not hasattr(Msg,'msg'): Msg.msg = str(Msg)
G2fil.G2Print('Error determining highly correlated vars',mode='warn')
G2fil.G2Print(Msg.msg,mode='warn')
# matrix above inversion failed, drop previously removed variables & try again
Amat, indices, Yvec = dropTerms(psing_prev, Amat, indices, Yvec)
Adiag = np.sqrt(np.diag(Amat))
Anorm = np.outer(Adiag,Adiag)
Amat = Amat/Anorm
try:
Bmat,Nzeros = pinv(Amat,xtol) #Moore-Penrose inversion (via SVD) & count of zeros
Bmat = Bmat/Anorm
except nl.LinAlgError: # this is unexpected. How did we get this far with a singular matrix?
G2fil.G2Print('ouch #6 linear algebra error in making final v-cov matrix', mode='error')
psing = list(np.where(np.abs(np.diag(nl.qr(Amat)[1])) < 1.e-14)[0])
if not len(psing): # make sure at least the worst term is flagged
d = np.abs(np.diag(nl.qr(Amat)[1]))
psing = [np.argmin(d)]
Amat, indices, Yvec = dropTerms(psing, Amat, indices, Yvec)
info = {'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':lamMax,'SVD0':-1,'Xvec':None, 'chisq0':chisqf}
info['psing'] = [i for i in range(n) if i not in indices]
return [x0,None,info]
# expand Bmat by filling with zeros if columns have been dropped
psing = [i for i in range(n) if i not in indices]
if len(psing):
ins = [j-i for i,j in enumerate(psing)]
Bmat = np.insert(np.insert(Bmat,ins,0,1),ins,0,0)
info.update({'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':lamMax,'SVD0':Nzeros,
'Converged':ifConverged, 'DelChi2':deltaChi2, 'Xvec':XvecAll, 'chisq0':chisq00})
info['psing'] = [i for i in range(n) if i not in indices]
setSVDwarn(info,Amat,Nzeros,indices)
return [x0,Bmat,info]
[docs]def HessianSVD(func,x0,Hess,args=(),ftol=1.49012e-8,xtol=1.e-6, maxcyc=0,lamda=-3,Print=False,refPlotUpdate=None):
'''
Minimize the sum of squares of a function (:math:`f`) evaluated on a series of
values (y): :math:`\\sum_{y=0}^{N_{obs}} f(y,{args})`
where :math:`x = arg min(\\sum_{y=0}^{N_{obs}} (func(y)^2,axis=0))`
:param function func: callable method or function
should take at least one (possibly length N vector) argument and
returns M floating point numbers.
:param np.ndarray x0: The starting estimate for the minimization of length N
:param function Hess: callable method or function
A required function or method to compute the weighted vector and Hessian for func.
It must be a symmetric NxN array
:param tuple args: Any extra arguments to func are placed in this tuple.
:param float ftol: Relative error desired in the sum of squares.
:param float xtol: Relative tolerance of zeros in the SVD solution in nl.pinv.
:param int maxcyc: The maximum number of cycles of refinement to execute, if -1 refine
until other limits are met (ftol, xtol)
:param bool Print: True for printing results (residuals & times) by cycle
:returns: (x,cov_x,infodict) where
* x : ndarray
The solution (or the result of the last iteration for an unsuccessful
call).
* cov_x : ndarray
Uses the fjac and ipvt optional outputs to construct an
estimate of the jacobian around the solution. ``None`` if a
singular matrix encountered (indicates very flat curvature in
some direction). This matrix must be multiplied by the
residual standard deviation to get the covariance of the
parameter estimates -- see curve_fit.
* infodict : dict
a dictionary of optional outputs with the keys:
* 'fvec' : the function evaluated at the output
* 'num cyc':
* 'nfev':
* 'lamMax':0.
* 'psing':
* 'SVD0':
'''
ifConverged = False
deltaChi2 = -10.
x0 = np.array(x0, ndmin=1) #might be redundant?
n = len(x0)
if type(args) != type(()):
args = (args,)
icycle = 0
nfev = 0
if Print:
G2fil.G2Print(' Hessian SVD refinement on %d variables:'%(n))
chisq00 = None
while icycle < maxcyc:
time0 = time.time()
M = func(x0,*args)
nfev += 1
chisq0 = np.sum(M**2)
if chisq00 is None: chisq00 = chisq0
Yvec,Amat = Hess(x0,*args)
Adiag = np.sqrt(np.diag(Amat))
psing = np.where(np.abs(Adiag) < 1.e-14,True,False)
if np.any(psing): #hard singularity in matrix
return [x0,None,{'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':0.,'psing':psing,'SVD0':-1}]
Anorm = np.outer(Adiag,Adiag)
Yvec /= Adiag
Amat /= Anorm
if Print:
G2fil.G2Print('initial chi^2 %.5g'%(chisq0))
try:
Ainv,Nzeros = pinv(Amat,xtol) #do Moore-Penrose inversion (via SVD)
except nl.LinAlgError:
G2fil.G2Print('ouch #1 bad SVD inversion; change parameterization', mode='warn')
psing = list(np.where(np.abs(np.diag(nl.qr(Amat)[1])) < 1.e-14)[0])
return [x0,None,{'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':0.,'psing':psing,'SVD0':-1}]
Xvec = np.inner(Ainv,Yvec) #solve
Xvec /= Adiag
M2 = func(x0+Xvec,*args)
nfev += 1
chisq1 = np.sum(M2**2)
deltaChi2 = (chisq0-chisq1)/chisq0
if Print:
G2fil.G2Print(' Cycle: %d, Time: %.2fs, Chi**2: %.5g, Delta: %.3g'%(
icycle,time.time()-time0,chisq1,deltaChi2))
Histograms = args[0][0]
if refPlotUpdate is not None: refPlotUpdate(Histograms,icycle) # update plot
if deltaChi2 < ftol:
ifConverged = True
if Print: G2fil.G2Print("converged")
break
icycle += 1
M = func(x0,*args)
nfev += 1
Yvec,Amat = Hess(x0,*args)
Adiag = np.sqrt(np.diag(Amat))
Anorm = np.outer(Adiag,Adiag)
Amat = Amat/Anorm
try:
Bmat,Nzero = pinv(Amat,xtol) #Moore-Penrose inversion (via SVD) & count of zeros
G2fil.G2Print('Found %d SVD zeros'%(Nzero), mode='warn')
# Bmat = nl.inv(Amatlam); Nzeros = 0
Bmat = Bmat/Anorm
return [x0,Bmat,{'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':0.,'psing':[],
'SVD0':Nzero,'Converged': ifConverged, 'DelChi2':deltaChi2,
'chisq0':chisq00}]
except nl.LinAlgError:
G2fil.G2Print('ouch #2 linear algebra error in making v-cov matrix', mode='error')
psing = []
if maxcyc:
psing = list(np.where(np.diag(nl.qr(Amat)[1]) < 1.e-14)[0])
return [x0,None,{'num cyc':icycle,'fvec':M,'nfev':nfev,'lamMax':0.,'psing':psing,'SVD0':-1,
'chisq0':chisq00}]
[docs]def getVCov(varyNames,varyList,covMatrix):
'''obtain variance-covariance terms for a set of variables. NB: the varyList
and covMatrix were saved by the last least squares refinement so they must match.
:param list varyNames: variable names to find v-cov matric for
:param list varyList: full list of all variables in v-cov matrix
:param nparray covMatrix: full variance-covariance matrix from the last
least squares refinement
:returns: nparray vcov: variance-covariance matrix for the variables given
in varyNames
'''
vcov = np.zeros((len(varyNames),len(varyNames)))
for i1,name1 in enumerate(varyNames):
for i2,name2 in enumerate(varyNames):
try:
vcov[i1][i2] = covMatrix[varyList.index(name1)][varyList.index(name2)]
except ValueError:
vcov[i1][i2] = 0.0
# if i1 == i2:
# vcov[i1][i2] = 1e-20
# else:
# vcov[i1][i2] = 0.0
return vcov
################################################################################
#### Atom manipulations
################################################################################
[docs]def getAtomPtrs(data,draw=False):
''' get atom data pointers cx,ct,cs,cia in Atoms or Draw Atoms lists
NB:may not match column numbers in displayed table
param: dict: data phase data structure
draw: boolean True if Draw Atoms list pointers are required
return: cx,ct,cs,cia pointers to atom xyz, type, site sym, uiso/aniso flag
'''
if draw:
return data['Drawing']['atomPtrs']
else:
return data['General']['AtomPtrs']
def FindMolecule(ind,generalData,atomData): #uses numpy & masks - very fast even for proteins!
def getNeighbors(atom,radius):
Dx = UAtoms-np.array(atom[cx:cx+3])
dist = ma.masked_less(np.sqrt(np.sum(np.inner(Amat,Dx)**2,axis=0)),0.5) #gets rid of disorder "bonds" < 0.5A
sumR = Radii+radius
return set(ma.nonzero(ma.masked_greater(dist-factor*sumR,0.))[0]) #get indices of bonded atoms
import numpy.ma as ma
indices = (-1,0,1)
Units = np.array([[h,k,l] for h in indices for k in indices for l in indices],dtype='f')
cx,ct,cs,ci = generalData['AtomPtrs']
DisAglCtls = generalData['DisAglCtls']
SGData = generalData['SGData']
Amat,Bmat = G2lat.cell2AB(generalData['Cell'][1:7])
radii = DisAglCtls['BondRadii']
atomTypes = DisAglCtls['AtomTypes']
factor = DisAglCtls['Factors'][0]
unit = np.zeros(3)
try:
indH = atomTypes.index('H')
radii[indH] = 0.5
except:
pass
nAtom = len(atomData)
Indx = list(range(nAtom))
UAtoms = []
Radii = []
for atom in atomData:
UAtoms.append(np.array(atom[cx:cx+3]))
Radii.append(radii[atomTypes.index(atom[ct])])
UAtoms = np.array(UAtoms)
Radii = np.array(Radii)
for nOp,Op in enumerate(SGData['SGOps'][1:]):
UAtoms = np.concatenate((UAtoms,(np.inner(Op[0],UAtoms[:nAtom]).T+Op[1])))
Radii = np.concatenate((Radii,Radii[:nAtom]))
Indx += Indx[:nAtom]
for icen,cen in enumerate(SGData['SGCen'][1:]):
UAtoms = np.concatenate((UAtoms,(UAtoms+cen)))
Radii = np.concatenate((Radii,Radii))
Indx += Indx[:nAtom]
if SGData['SGInv']:
UAtoms = np.concatenate((UAtoms,-UAtoms))
Radii = np.concatenate((Radii,Radii))
Indx += Indx
UAtoms %= 1.
mAtoms = len(UAtoms)
for unit in Units:
if np.any(unit): #skip origin cell
UAtoms = np.concatenate((UAtoms,UAtoms[:mAtoms]+unit))
Radii = np.concatenate((Radii,Radii[:mAtoms]))
Indx += Indx[:mAtoms]
UAtoms = np.array(UAtoms)
Radii = np.array(Radii)
newAtoms = [atomData[ind],]
atomData[ind] = None
radius = Radii[ind]
IndB = getNeighbors(newAtoms[-1],radius)
while True:
if not len(IndB):
break
indb = IndB.pop()
if atomData[Indx[indb]] == None:
continue
while True:
try:
jndb = IndB.index(indb)
IndB.remove(jndb)
except:
break
newAtom = copy.copy(atomData[Indx[indb]])
newAtom[cx:cx+3] = UAtoms[indb] #NB: thermal Uij, etc. not transformed!
newAtoms.append(newAtom)
atomData[Indx[indb]] = None
IndB = set(list(IndB)+list(getNeighbors(newAtoms[-1],radius)))
if len(IndB) > nAtom:
return 'Assemble molecule cannot be used on extended structures'
for atom in atomData:
if atom != None:
newAtoms.append(atom)
return newAtoms
[docs]def FindAtomIndexByIDs(atomData,loc,IDs,Draw=True):
'''finds the set of atom array indices for a list of atom IDs. Will search
either the Atom table or the drawAtom table.
:param list atomData: Atom or drawAtom table containting coordinates, etc.
:param int loc: location of atom id in atomData record
:param list IDs: atom IDs to be found
:param bool Draw: True if drawAtom table to be searched; False if Atom table
is searched
:returns: list indx: atom (or drawAtom) indices
'''
indx = []
for i,atom in enumerate(atomData):
if Draw and atom[loc] in IDs:
indx.append(i)
elif atom[loc] in IDs:
indx.append(i)
return indx
[docs]def FillAtomLookUp(atomData,indx):
'''create a dictionary of atom indexes with atom IDs as keys
:param list atomData: Atom table to be used
:param int indx: pointer to position of atom id in atom record (typically cia+8)
:returns: dict atomLookUp: dictionary of atom indexes with atom IDs as keys
'''
return {atom[indx]:iatm for iatm,atom in enumerate(atomData)}
[docs]def DrawAtomsReplaceByID(data,loc,atom,ID):
'''Replace all atoms in drawing array with an ID matching the specified value'''
atomData = data['Drawing']['Atoms']
indx = FindAtomIndexByIDs(atomData,loc,[ID,])
for ind in indx:
atomData[ind] = MakeDrawAtom(data,atom,atomData[ind])
[docs]def MakeDrawAtom(data,atom,oldatom=None):
'needs a description'
AA3letter = ['ALA','ARG','ASN','ASP','CYS','GLN','GLU','GLY','HIS','ILE',
'LEU','LYS','MET','PHE','PRO','SER','THR','TRP','TYR','VAL','MSE','HOH','WAT','UNK']
AA1letter = ['A','R','N','D','C','Q','E','G','H','I',
'L','K','M','F','P','S','T','W','Y','V','M',' ',' ',' ']
generalData = data['General']
Amat,Bmat = G2lat.cell2AB(generalData['Cell'][1:7])
SGData = generalData['SGData']
deftype = G2obj.validateAtomDrawType(GSASIIpath.GetConfigValue('DrawAtoms_default'),generalData)
if generalData['Type'] in ['nuclear','faulted',]:
if oldatom:
opr = oldatom[5]
if atom[9] == 'A':
X,U = G2spc.ApplyStringOps(opr,SGData,atom[3:6],atom[11:17])
atomInfo = [atom[:2]+list(X)+oldatom[5:9]+atom[9:11]+list(U)+oldatom[17:]][0]
else:
X = G2spc.ApplyStringOps(opr,SGData,atom[3:6])
atomInfo = [atom[:2]+list(X)+oldatom[5:9]+atom[9:]+oldatom[17:]][0]
else:
atomInfo = [atom[:2]+atom[3:6]+['1',]+[deftype]+
['',]+[[255,255,255],]+atom[9:]+[[],[]]][0]
ct,cs = [1,8] #type & color
elif generalData['Type'] == 'magnetic':
if oldatom:
opr = oldatom[8]
mom = np.array(atom[7:10])
if generalData['Super']:
SSGData = generalData['SSGData']
Mom = G2spc.ApplyStringOpsMom(opr,SGData,SSGData,mom)
else:
Mom = G2spc.ApplyStringOpsMom(opr,SGData,None,mom)
if atom[12] == 'A':
X,U = G2spc.ApplyStringOps(opr,SGData,atom[3:6],atom[14:20])
atomInfo = [atom[:2]+list(X)+list(Mom)+oldatom[8:12]+atom[12:14]+list(U)+oldatom[20:]][0]
else:
X = G2spc.ApplyStringOps(opr,SGData,atom[3:6])
atomInfo = [atom[:2]+list(X)+list(Mom)+oldatom[8:12]+atom[12:]+oldatom[20:]][0]
else:
atomInfo = [atom[:2]+atom[3:6]+atom[7:10]+['1',]+[deftype]+
['',]+[[255,255,255],]+atom[12:]+[[],[]]][0]
ct,cs = [1,11] #type & color
elif generalData['Type'] == 'macromolecular':
try:
oneLetter = AA3letter.index(atom[1])
except ValueError:
oneLetter = -1
atomInfo = [[atom[1].strip()+atom[0],]+
[AA1letter[oneLetter]+atom[0],]+atom[2:5]+
atom[6:9]+['1',]+[deftype]+['',]+[[255,255,255],]+atom[12:]+[[],[]]][0]
ct,cs = [4,11] #type & color
atNum = generalData['AtomTypes'].index(atom[ct])
atomInfo[cs] = list(generalData['Color'][atNum])
return atomInfo
[docs]def GetAtomsById(atomData,atomLookUp,IdList):
'''gets a list of atoms from Atom table that match a set of atom IDs
:param list atomData: Atom table to be used
:param dict atomLookUp: dictionary of atom indexes with atom IDs as keys
:param list IdList: atom IDs to be found
:returns: list atoms: list of atoms found
'''
atoms = []
for Id in IdList:
atoms.append(atomData[atomLookUp[Id]])
return atoms
[docs]def GetAtomItemsById(atomData,atomLookUp,IdList,itemLoc,numItems=1):
'''gets atom parameters for atoms using atom IDs
:param list atomData: Atom table to be used
:param dict atomLookUp: dictionary of atom indexes with atom IDs as keys
:param list IdList: atom IDs to be found
:param int itemLoc: pointer to desired 1st item in an atom table entry
:param int numItems: number of items to be retrieved
:returns: type name: description
'''
Items = []
if not isinstance(IdList,list):
IdList = [IdList,]
for Id in IdList:
if numItems == 1:
Items.append(atomData[atomLookUp[Id]][itemLoc])
else:
Items.append(atomData[atomLookUp[Id]][itemLoc:itemLoc+numItems])
return Items
[docs]def GetAtomCoordsByID(pId,parmDict,AtLookup,indx):
'''default doc string
:param type name: description
:returns: type name: description
'''
pfx = [str(pId)+'::A'+i+':' for i in ['x','y','z']]
dpfx = [str(pId)+'::dA'+i+':' for i in ['x','y','z']]
XYZ = []
for ind in indx:
names = [pfx[i]+str(AtLookup[ind]) for i in range(3)]
dnames = [dpfx[i]+str(AtLookup[ind]) for i in range(3)]
XYZ.append([parmDict[name]+parmDict[dname] for name,dname in zip(names,dnames)])
return XYZ
[docs]def GetAtomFracByID(pId,parmDict,AtLookup,indx):
'''default doc string
:param type name: description
:returns: type name: description
'''
pfx = str(pId)+'::Afrac:'
Frac = []
for ind in indx:
name = pfx+str(AtLookup[ind])
Frac.append(parmDict[name])
return Frac
# for Atom in Atoms:
# XYZ = Atom[cx:cx+3]
# if 'A' in Atom[cia]:
# U6 = Atom[cia+2:cia+8]
[docs]def ApplySeqData(data,seqData,PF2=False):
'''Applies result from seq. refinement to drawing atom positions & Uijs
:param dict data: GSAS-II phase data structure
:param dict seqData: GSAS-II sequential refinement results structure
:param bool PF2: if True then seqData is from a sequential run of PDFfit2
:returns: list drawAtoms: revised Draw Atoms list
'''
cx,ct,cs,cia = getAtomPtrs(data)
drawingData = data['Drawing']
dcx,dct,dcs,dci = getAtomPtrs(data,True)
atoms = data['Atoms']
drawAtoms = drawingData['Atoms']
parmDict = copy.deepcopy(seqData['parmDict'])
if PF2:
PDFData = data['RMC']['PDFfit']
SGData = data['General']['SGData']
AtmConstr = PDFData['AtomConstr']
for ia,atom in enumerate(atoms):
atxyz = atom[cx:cx+3]
for ix in [0,1,2]:
item = AtmConstr[ia][ix+2]
if '@' in item:
Ids = [itm[:2] for itm in item.split('@')[1:]]
for Id in Ids:
item = item.replace('@'+Id,str(parmDict[Id][0]))
atxyz[ix] = eval(item)
if '@' in AtmConstr[ia][6]:
itm = AtmConstr[ia][6].split('@')[:2][1]
atuij = np.array([parmDict[itm][0],parmDict[itm][0],parmDict[itm][0],0.0,0.0,0.0])
indx = FindAtomIndexByIDs(drawAtoms,dci,[atom[cia+8],],True)
for ind in indx:
drawatom = drawAtoms[ind]
opr = drawatom[dcs-1]
#how do I handle Sfrac? - fade the atoms?
X,U = G2spc.ApplyStringOps(opr,SGData,atxyz,atuij)
drawatom[dcx:dcx+3] = X
drawatom[dci-6:dci] = U
else:
SGData = data['General']['SGData']
pId = data['pId']
pfx = '%d::'%(pId)
for ia,atom in enumerate(atoms):
dxyz = np.array([parmDict[pfx+'dAx:'+str(ia)],parmDict[pfx+'dAy:'+str(ia)],parmDict[pfx+'dAz:'+str(ia)]])
if atom[cia] == 'A':
atuij = np.array([parmDict[pfx+'AU11:'+str(ia)],parmDict[pfx+'AU22:'+str(ia)],parmDict[pfx+'AU33:'+str(ia)],
parmDict[pfx+'AU12:'+str(ia)],parmDict[pfx+'AU13:'+str(ia)],parmDict[pfx+'AU23:'+str(ia)]])
else:
atuiso = parmDict[pfx+'AUiso:'+str(ia)]
atxyz = G2spc.MoveToUnitCell(np.array(atom[cx:cx+3])+dxyz)[0]
indx = FindAtomIndexByIDs(drawAtoms,dci,[atom[cia+8],],True)
for ind in indx:
drawatom = drawAtoms[ind]
opr = drawatom[dcs-1]
#how do I handle Sfrac? - fade the atoms?
if atom[cia] == 'A':
X,U = G2spc.ApplyStringOps(opr,SGData,atxyz,atuij)
drawatom[dcx:dcx+3] = X
drawatom[dci-6:dci] = U
else:
X = G2spc.ApplyStringOps(opr,SGData,atxyz)
drawatom[dcx:dcx+3] = X
drawatom[dci-7] = atuiso
return drawAtoms
def FindNeighbors(phase,FrstName,AtNames,notName=''):
General = phase['General']
cx,ct,cs,cia = getAtomPtrs(phase)
Atoms = phase['Atoms']
atNames = [atom[ct-1] for atom in Atoms]
Cell = General['Cell'][1:7]
Amat,Bmat = G2lat.cell2AB(Cell)
atTypes = General['AtomTypes']
Radii = np.array(General['BondRadii'])
try:
DisAglCtls = General['DisAglCtls']
radiusFactor = DisAglCtls['Factors'][0]
except:
radiusFactor = 0.85
AtInfo = dict(zip(atTypes,Radii)) #or General['BondRadii']
Orig = atNames.index(FrstName)
OId = Atoms[Orig][cia+8]
OType = Atoms[Orig][ct]
XYZ = getAtomXYZ(Atoms,cx)
Neigh = []
Ids = []
Dx = np.inner(Amat,XYZ-XYZ[Orig]).T
dist = np.sqrt(np.sum(Dx**2,axis=1))
sumR = np.array([AtInfo[OType]+AtInfo[atom[ct]] for atom in Atoms])
IndB = ma.nonzero(ma.masked_greater(dist-radiusFactor*sumR,0.))
for j in IndB[0]:
if j != Orig:
if AtNames[j] not in notName:
Neigh.append([AtNames[j],dist[j],True])
Ids.append(Atoms[j][cia+8])
return Neigh,[OId,Ids]
def FindOctahedron(results):
Octahedron = np.array([[1.,0,0],[0,1.,0],[0,0,1.],[-1.,0,0],[0,-1.,0],[0,0,-1.]])
Polygon = np.array([result[3] for result in results])
Dists = np.array([np.sqrt(np.sum(axis**2)) for axis in Polygon])
bond = np.mean(Dists)
std = np.std(Dists)
Norms = Polygon/Dists[:,nxs]
Tilts = acosd(np.dot(Norms,Octahedron[0]))
iAng = np.argmin(Tilts)
Qavec = np.cross(Norms[iAng],Octahedron[0])
QA = AVdeg2Q(Tilts[iAng],Qavec)
newNorms = prodQVQ(QA,Norms)
Rots = acosd(np.dot(newNorms,Octahedron[1]))
jAng = np.argmin(Rots)
Qbvec = np.cross(Norms[jAng],Octahedron[1])
QB = AVdeg2Q(Rots[jAng],Qbvec)
QQ = prodQQ(QA,QB)
newNorms = prodQVQ(QQ,Norms)
dispVecs = np.array([norm[:,nxs]-Octahedron.T for norm in newNorms])
disp = np.sqrt(np.sum(dispVecs**2,axis=1))
dispids = np.argmin(disp,axis=1)
vecDisp = np.array([dispVecs[i,:,dispid] for i,dispid in enumerate(dispids)])
Disps = np.array([disp[i,dispid] for i,dispid in enumerate(dispids)])
meanDisp = np.mean(Disps)
stdDisp = np.std(Disps)
A,V = Q2AVdeg(QQ)
return bond,std,meanDisp,stdDisp,A,V,vecDisp
def FindTetrahedron(results):
Tetrahedron = np.array([[1.,1,1],[1,-1,-1],[-1,1,-1],[-1,-1,1]])/np.sqrt(3.)
Polygon = np.array([result[3] for result in results])
Dists = np.array([np.sqrt(np.sum(axis**2)) for axis in Polygon])
bond = np.mean(Dists)
std = np.std(Dists)
Norms = Polygon/Dists[:,nxs]
Tilts = acosd(np.dot(Norms,Tetrahedron[0]))
iAng = np.argmin(Tilts)
Qavec = np.cross(Norms[iAng],Tetrahedron[0])
QA = AVdeg2Q(Tilts[iAng],Qavec)
newNorms = prodQVQ(QA,Norms)
Rots = acosd(np.dot(newNorms,Tetrahedron[1]))
jAng = np.argmin(Rots)
Qbvec = np.cross(Norms[jAng],Tetrahedron[1])
QB = AVdeg2Q(Rots[jAng],Qbvec)
QQ = prodQQ(QA,QB)
newNorms = prodQVQ(QQ,Norms)
dispVecs = np.array([norm[:,nxs]-Tetrahedron.T for norm in newNorms])
disp = np.sqrt(np.sum(dispVecs**2,axis=1))
dispids = np.argmin(disp,axis=1)
vecDisp = np.array([dispVecs[i,:,dispid] for i,dispid in enumerate(dispids)])
Disps = np.array([disp[i,dispid] for i,dispid in enumerate(dispids)])
meanDisp = np.mean(Disps)
stdDisp = np.std(Disps)
A,V = Q2AVdeg(QQ)
return bond,std,meanDisp,stdDisp,A,V,vecDisp
[docs]def FindAllNeighbors(phase,FrstName,AtNames,notName='',Orig=None,Short=False,
searchType='Bond'):
'''Find neighboring atoms
Uses Bond search criteria unless searchType is set to non-default
'''
if searchType == 'Bond':
skey = 'BondRadii'
sindex = 0
else:
skey = 'AngleRadii'
sindex = 1
General = phase['General']
cx,ct,cs,cia = getAtomPtrs(phase)
Atoms = phase['Atoms']
atNames = [atom[ct-1] for atom in Atoms]
atTypes = [atom[ct] for atom in Atoms]
Cell = General['Cell'][1:7]
Amat,Bmat = G2lat.cell2AB(Cell)
SGData = General['SGData']
indices = (-1,0,1)
Units = np.array([[h,k,l] for h in indices for k in indices for l in indices])
AtTypes = General['AtomTypes']
Radii = copy.copy(np.array(General[skey]))
try:
DisAglCtls = General['DisAglCtls']
radiusFactor = DisAglCtls['Factors'][sindex]
Radii = DisAglCtls[skey]
except:
radiusFactor = 0.85
AtInfo = dict(zip(AtTypes,Radii)) #or General['BondRadii']
if Orig is None:
Orig = atNames.index(FrstName)
OId = Atoms[Orig][cia+8]
OType = Atoms[Orig][ct]
XYZ = getAtomXYZ(Atoms,cx)
Oxyz = XYZ[Orig]
Neigh = []
Ids = []
sumR = np.array([AtInfo[OType]+AtInfo[atom[ct]] for atom in Atoms])
sumR = np.reshape(np.tile(sumR,27),(27,-1))
results = []
for xyz in XYZ:
results.append(G2spc.GenAtom(xyz,SGData,False,Move=False))
for iA,result in enumerate(results):
for [Txyz,Top,Tunit,Spn] in result:
Dx = np.array([Txyz-Oxyz+unit for unit in Units])
dx = np.inner(Dx,Amat)
dist = np.sqrt(np.sum(dx**2,axis=1))
IndB = ma.nonzero(ma.masked_greater(dist-radiusFactor*sumR[:,iA],0.))
for iU in IndB[0]:
if dist[iU] < 0.001: continue
if AtNames[iA%len(AtNames)] != notName:
unit = Units[iU]
if np.any(unit):
Topstr = ' +(%4d)[%2d,%2d,%2d]'%(Top,unit[0],unit[1],unit[2])
else:
Topstr = ' +(%4d)'%(Top)
if Short:
Neigh.append([AtNames[iA%len(AtNames)],dist[iU],True])
else:
Neigh.append([AtNames[iA]+Topstr,atTypes[iA],dist[iU],dx[iU]])
Ids.append(Atoms[iA][cia+8])
return Neigh,[OId,Ids]
def calcBond(A,Ax,Bx,MTCU):
cell = G2lat.A2cell(A)
Amat,Bmat = G2lat.cell2AB(cell)
M,T,C,U = MTCU
Btx = np.inner(M,Bx)+T+C+U
Dx = Btx-Ax
dist = np.sqrt(np.inner(Amat,Dx))
return dist
def AddHydrogens(AtLookUp,General,Atoms,AddHydId):
def getTransMat(RXYZ,OXYZ,TXYZ,Amat):
Vec = np.inner(Amat,np.array([OXYZ-TXYZ[0],RXYZ-TXYZ[0]])).T
Vec /= np.sqrt(np.sum(Vec**2,axis=1))[:,nxs]
Mat2 = np.cross(Vec[0],Vec[1]) #UxV
Mat2 /= np.sqrt(np.sum(Mat2**2))
Mat3 = np.cross(Mat2,Vec[0]) #(UxV)xU
return nl.inv(np.array([Vec[0],Mat2,Mat3]))
cx,ct,cs,cia = General['AtomPtrs']
Cell = General['Cell'][1:7]
Amat,Bmat = G2lat.cell2AB(Cell)
nBonds = AddHydId[-1]+len(AddHydId[1])
Oatom = GetAtomsById(Atoms,AtLookUp,[AddHydId[0],])[0]
OXYZ = np.array(Oatom[cx:cx+3])
if 'I' in Oatom[cia]:
Uiso = Oatom[cia+1]
else:
Uiso = (Oatom[cia+2]+Oatom[cia+3]+Oatom[cia+4])/3.0 #simple average
Uiso = max(Uiso,0.005) #set floor!
Tatoms = GetAtomsById(Atoms,AtLookUp,AddHydId[1])
TXYZ = np.array([tatom[cx:cx+3] for tatom in Tatoms]) #3 x xyz
if nBonds == 4:
if AddHydId[-1] == 1:
Vec = TXYZ-OXYZ
Len = np.sqrt(np.sum(np.inner(Amat,Vec).T**2,axis=0))
Vec = np.sum(Vec/Len,axis=0)
Len = np.sqrt(np.sum(Vec**2))
Hpos = OXYZ-0.98*np.inner(Bmat,Vec).T/Len
HU = 1.1*Uiso
return [Hpos,],[HU,]
elif AddHydId[-1] == 2:
Vec = np.inner(Amat,TXYZ-OXYZ).T
Vec[0] += Vec[1] #U - along bisector
Vec /= np.sqrt(np.sum(Vec**2,axis=1))[:,nxs]
Mat2 = np.cross(Vec[0],Vec[1]) #UxV
Mat2 /= np.sqrt(np.sum(Mat2**2))
Mat3 = np.cross(Mat2,Vec[0]) #(UxV)xU
iMat = nl.inv(np.array([Vec[0],Mat2,Mat3]))
Hpos = np.array([[-0.97*cosd(54.75),0.97*sind(54.75),0.],
[-0.97*cosd(54.75),-0.97*sind(54.75),0.]])
HU = 1.2*Uiso*np.ones(2)
Hpos = np.inner(Bmat,np.inner(iMat,Hpos).T).T+OXYZ
return Hpos,HU
else:
Ratom = GetAtomsById(Atoms,AtLookUp,[AddHydId[2],])[0]
RXYZ = np.array(Ratom[cx:cx+3])
iMat = getTransMat(RXYZ,OXYZ,TXYZ,Amat)
a = 0.96*cosd(70.5)
b = 0.96*sind(70.5)
Hpos = np.array([[a,0.,-b],[a,-b*cosd(30.),0.5*b],[a,b*cosd(30.),0.5*b]])
Hpos = np.inner(Bmat,np.inner(iMat,Hpos).T).T+OXYZ
HU = 1.5*Uiso*np.ones(3)
return Hpos,HU
elif nBonds == 3:
if AddHydId[-1] == 1:
Vec = np.sum(TXYZ-OXYZ,axis=0)
Len = np.sqrt(np.sum(np.inner(Amat,Vec).T**2))
Vec = -0.93*Vec/Len
Hpos = OXYZ+Vec
HU = 1.1*Uiso
return [Hpos,],[HU,]
elif AddHydId[-1] == 2:
Ratom = GetAtomsById(Atoms,AtLookUp,[AddHydId[2],])[0]
RXYZ = np.array(Ratom[cx:cx+3])
iMat = getTransMat(RXYZ,OXYZ,TXYZ,Amat)
a = 0.93*cosd(60.)
b = 0.93*sind(60.)
Hpos = [[a,b,0],[a,-b,0]]
Hpos = np.inner(Bmat,np.inner(iMat,Hpos).T).T+OXYZ
HU = 1.2*Uiso*np.ones(2)
return Hpos,HU
else: #2 bonds
if 'C' in Oatom[ct]:
Vec = TXYZ[0]-OXYZ
Len = np.sqrt(np.sum(np.inner(Amat,Vec).T**2))
Vec = -0.93*Vec/Len
Hpos = OXYZ+Vec
HU = 1.1*Uiso
return [Hpos,],[HU,]
elif 'O' in Oatom[ct]:
mapData = General['Map']
Ratom = GetAtomsById(Atoms,AtLookUp,[AddHydId[2],])[0]
RXYZ = np.array(Ratom[cx:cx+3])
iMat = getTransMat(RXYZ,OXYZ,TXYZ,Amat)
a = 0.82*cosd(70.5)
b = 0.82*sind(70.5)
azm = np.arange(0.,360.,5.)
Hpos = np.array([[a,b*cosd(x),b*sind(x)] for x in azm])
Hpos = np.inner(Bmat,np.inner(iMat,Hpos).T).T+OXYZ
Rhos = np.array([getRho(pos,mapData) for pos in Hpos])
imax = np.argmax(Rhos)
HU = 1.5*Uiso
return [Hpos[imax],],[HU,]
return [],[]
#def AtomUij2TLS(atomData,atPtrs,Amat,Bmat,rbObj): #unfinished & not used
# '''default doc string
#
# :param type name: description
#
# :returns: type name: description
#
# '''
# for atom in atomData:
# XYZ = np.inner(Amat,atom[cx:cx+3])
# if atom[cia] == 'A':
# UIJ = atom[cia+2:cia+8]
[docs]def TLS2Uij(xyz,g,Amat,rbObj): #not used anywhere, but could be?
'''default doc string
:param type name: description
:returns: type name: description
'''
TLStype,TLS = rbObj['ThermalMotion'][:2]
Tmat = np.zeros((3,3))
Lmat = np.zeros((3,3))
Smat = np.zeros((3,3))
gvec = np.sqrt(np.array([g[0][0]**2,g[1][1]**2,g[2][2]**2,
g[0][0]*g[1][1],g[0][0]*g[2][2],g[1][1]*g[2][2]]))
if 'T' in TLStype:
Tmat = G2lat.U6toUij(TLS[:6])
if 'L' in TLStype:
Lmat = G2lat.U6toUij(TLS[6:12])
if 'S' in TLStype:
Smat = np.array([[TLS[18],TLS[12],TLS[13]],[TLS[14],TLS[19],TLS[15]],[TLS[16],TLS[17],0] ])
XYZ = np.inner(Amat,xyz)
Axyz = np.array([[ 0,XYZ[2],-XYZ[1]], [-XYZ[2],0,XYZ[0]], [XYZ[1],-XYZ[0],0]] )
Umat = Tmat+np.inner(Axyz,Smat)+np.inner(Smat.T,Axyz.T)+np.inner(np.inner(Axyz,Lmat),Axyz.T)
beta = np.inner(np.inner(g,Umat),g)
return G2lat.UijtoU6(beta)*gvec
[docs]def AtomTLS2UIJ(atomData,atPtrs,Amat,rbObj): #not used anywhere, but could be?
'''default doc string
:param type name: description
:returns: type name: description
'''
cx,ct,cs,cia = atPtrs
TLStype,TLS = rbObj['ThermalMotion'][:2]
Tmat = np.zeros((3,3))
Lmat = np.zeros((3,3))
Smat = np.zeros((3,3))
G,g = G2lat.A2Gmat(Amat)
gvec = 1./np.sqrt(np.array([g[0][0],g[1][1],g[2][2],g[0][1],g[0][2],g[1][2]]))
if 'T' in TLStype:
Tmat = G2lat.U6toUij(TLS[:6])
if 'L' in TLStype:
Lmat = G2lat.U6toUij(TLS[6:12])
if 'S' in TLStype:
Smat = np.array([ [TLS[18],TLS[12],TLS[13]], [TLS[14],TLS[19],TLS[15]], [TLS[16],TLS[17],0] ])
for atom in atomData:
XYZ = np.inner(Amat,atom[cx:cx+3])
Axyz = np.array([ 0,XYZ[2],-XYZ[1], -XYZ[2],0,XYZ[0], XYZ[1],-XYZ[0],0],ndmin=2 )
if 'U' in TLStype:
atom[cia+1] = TLS[0]
atom[cia] = 'I'
else:
atom[cia] = 'A'
Umat = Tmat+np.inner(Axyz,Smat)+np.inner(Smat.T,Axyz.T)+np.inner(np.inner(Axyz,Lmat),Axyz.T)
beta = np.inner(np.inner(g,Umat),g)
atom[cia+2:cia+8] = G2spc.U2Uij(beta/gvec)
[docs]def GetXYZDist(xyz,XYZ,Amat):
'''gets distance from position xyz to all XYZ, xyz & XYZ are np.array
and are in crystal coordinates; Amat is crystal to Cart matrix
:param type name: description
:returns: type name: description
'''
return np.sqrt(np.sum(np.inner(Amat,XYZ-xyz)**2,axis=0))
[docs]def getAtomXYZ(atoms,cx):
'''Create an array of fractional coordinates from the atoms list
:param list atoms: atoms object as found in tree
:param int cx: offset to where coordinates are found
:returns: np.array with shape (n,3)
'''
XYZ = []
for atom in atoms:
XYZ.append(atom[cx:cx+3])
return np.array(XYZ)
[docs]def getRBTransMat(X,Y):
'''Get transformation for Cartesian axes given 2 vectors
X will be parallel to new X-axis; X cross Y will be new Z-axis &
(X cross Y) cross Y will be new Y-axis
Useful for rigid body axes definintion
:param array X: normalized vector
:param array Y: normalized vector
:returns: array M: transformation matrix
use as XYZ' = np.inner(M,XYZ) where XYZ are Cartesian
'''
Mat2 = np.cross(X,Y) #UxV-->Z
Mat2 /= np.sqrt(np.sum(Mat2**2))
Mat3 = np.cross(Mat2,X) #(UxV)xU-->Y
Mat3 /= np.sqrt(np.sum(Mat3**2))
return np.array([X,Mat3,Mat2])
[docs]def RotateRBXYZ(Bmat,Cart,oriQ,symAxis=None):
'''rotate & transform cartesian coordinates to crystallographic ones
no translation applied. To be used for numerical derivatives
:param array Bmat: Orthogonalization matrix, see :func:`GSASIIlattice.cell2AB`
:param array Cart: 2D array of coordinates
:param array Q: quaternion as an np.array
:param tuple symAxis: if not None (default), specifies the symmetry
axis of the rigid body, which will be aligned to the quaternion vector.
:returns: 2D array of fractional coordinates, without translation to origin
'''
if symAxis is None:
Q = oriQ
else:
a,v = Q2AV(oriQ)
symaxis = np.array(symAxis)
vdotsym = min(1.0,max(-1.0,np.vdot(v,symaxis)))
xformAng = np.arccos(vdotsym)
xformVec = np.cross(symaxis,v)
Q = prodQQ(oriQ,AV2Q(xformAng,xformVec))
XYZ = np.zeros_like(Cart)
for i,xyz in enumerate(Cart):
XYZ[i] = np.inner(Bmat,prodQVQ(Q,xyz))
return XYZ
[docs]def UpdateRBXYZ(Bmat,RBObj,RBData,RBType):
'''returns crystal coordinates for atoms described by RBObj.
Note that RBObj['symAxis'], if present, determines the symmetry
axis of the rigid body, which will be aligned to the
quaternion direction.
:param np.array Bmat: see :func:`GSASIIlattice.cell2AB`
:param dict rbObj: rigid body selection/orientation information
:param dict RBData: rigid body tree data structure
:param str RBType: rigid body type, 'Vector' or 'Residue'
:returns: coordinates for rigid body as XYZ,Cart where XYZ is
the location in crystal coordinates and Cart is in cartesian
'''
RBRes = RBData[RBType][RBObj['RBId']]
if RBType == 'Vector':
vecs = RBRes['rbVect']
mags = RBRes['VectMag']
Cart = np.zeros_like(vecs[0])
for vec,mag in zip(vecs,mags):
Cart += vec*mag
elif RBType == 'Residue':
Cart = np.array(RBRes['rbXYZ'])
for tor,seq in zip(RBObj['Torsions'],RBRes['rbSeq']):
QuatA = AVdeg2Q(tor[0],Cart[seq[0]]-Cart[seq[1]])
Cart[seq[3]] = prodQVQ(QuatA,(Cart[seq[3]]-Cart[seq[1]]))+Cart[seq[1]]
elif RBType == 'Spin':
Cart = [np.zeros(3),]
# if symmetry axis is defined, place symmetry axis along quaternion
if RBObj.get('symAxis') is None:
Q = RBObj['Orient'][0]
else:
a,v = Q2AV(RBObj['Orient'][0])
symaxis = np.array(RBObj.get('symAxis'))
vdotsym = min(1.0,max(-1.0,np.vdot(v,symaxis)))
xformAng = np.arccos(vdotsym)
xformVec = np.cross(symaxis,v)
Q = prodQQ(RBObj['Orient'][0],AV2Q(xformAng,xformVec))
XYZ = np.zeros_like(Cart)
for i,xyz in enumerate(Cart):
XYZ[i] = np.inner(Bmat,prodQVQ(Q,xyz))+RBObj['Orig'][0]
return XYZ,Cart
[docs]def UpdateMCSAxyz(Bmat,MCSA):
'''default doc string
:param type name: description
:returns: type name: description
'''
xyz = []
atTypes = []
iatm = 0
for model in MCSA['Models'][1:]: #skip the MD model
if model['Type'] == 'Atom':
xyz.append(model['Pos'][0])
atTypes.append(model['atType'])
iatm += 1
else:
RBRes = MCSA['rbData'][model['Type']][model['RBId']]
Pos = np.array(model['Pos'][0])
Ori = np.array(model['Ori'][0])
Qori = AVdeg2Q(Ori[0],Ori[1:])
if model['Type'] == 'Vector':
vecs = RBRes['rbVect']
mags = RBRes['VectMag']
Cart = np.zeros_like(vecs[0])
for vec,mag in zip(vecs,mags):
Cart += vec*mag
elif model['Type'] == 'Residue':
Cart = np.array(RBRes['rbXYZ'])
for itor,seq in enumerate(RBRes['rbSeq']):
QuatA = AVdeg2Q(model['Tor'][0][itor],Cart[seq[0]]-Cart[seq[1]])
Cart[seq[3]] = prodQVQ(QuatA,(Cart[seq[3]]-Cart[seq[1]]))+Cart[seq[1]]
if model['MolCent'][1]:
Cart -= model['MolCent'][0]
for i,x in enumerate(Cart):
xyz.append(np.inner(Bmat,prodQVQ(Qori,x))+Pos)
atType = RBRes['rbTypes'][i]
atTypes.append(atType)
iatm += 1
return np.array(xyz),atTypes
[docs]def SetMolCent(model,RBData):
'''default doc string
:param type name: description
:returns: type name: description
'''
rideList = []
RBRes = RBData[model['Type']][model['RBId']]
if model['Type'] == 'Vector':
vecs = RBRes['rbVect']
mags = RBRes['VectMag']
Cart = np.zeros_like(vecs[0])
for vec,mag in zip(vecs,mags):
Cart += vec*mag
elif model['Type'] == 'Residue':
Cart = np.array(RBRes['rbXYZ'])
for seq in RBRes['rbSeq']:
rideList += seq[3]
centList = set(range(len(Cart)))-set(rideList)
cent = np.zeros(3)
for i in centList:
cent += Cart[i]
model['MolCent'][0] = cent/len(centList)
###############################################################################
#### Various utilities
###############################################################################
[docs]def UpdateRBUIJ(Bmat,Cart,RBObj):
'''default doc string
:param type name: description
:returns: type name: description
'''
''' returns atom I/A, Uiso or UIJ for atoms at XYZ as described by RBObj
'''
TLStype,TLS = RBObj['ThermalMotion'][:2]
T = np.zeros(6)
L = np.zeros(6)
S = np.zeros(8)
if 'T' in TLStype:
T = TLS[:6]
if 'L' in TLStype:
L = np.array(TLS[6:12])*(np.pi/180.)**2
if 'S' in TLStype:
S = np.array(TLS[12:])*(np.pi/180.)
g = nl.inv(np.inner(Bmat,Bmat))
gvec = np.sqrt(np.array([g[0][0]**2,g[1][1]**2,g[2][2]**2,
g[0][0]*g[1][1],g[0][0]*g[2][2],g[1][1]*g[2][2]]))
Uout = []
Q = RBObj['Orient'][0]
for X in Cart:
X = prodQVQ(Q,X)
if 'U' in TLStype:
Uout.append(['I',TLS[0],0,0,0,0,0,0])
elif not 'N' in TLStype:
U = [0,0,0,0,0,0]
U[0] = T[0]+L[1]*X[2]**2+L[2]*X[1]**2-2.0*L[5]*X[1]*X[2]+2.0*(S[2]*X[2]-S[4]*X[1])
U[1] = T[1]+L[0]*X[2]**2+L[2]*X[0]**2-2.0*L[4]*X[0]*X[2]+2.0*(S[5]*X[0]-S[0]*X[2])
U[2] = T[2]+L[1]*X[0]**2+L[0]*X[1]**2-2.0*L[3]*X[1]*X[0]+2.0*(S[1]*X[1]-S[3]*X[0])
U[3] = T[3]+L[4]*X[1]*X[2]+L[5]*X[0]*X[2]-L[3]*X[2]**2-L[2]*X[0]*X[1]+ \
S[4]*X[0]-S[5]*X[1]-(S[6]+S[7])*X[2]
U[4] = T[4]+L[3]*X[1]*X[2]+L[5]*X[0]*X[1]-L[4]*X[1]**2-L[1]*X[0]*X[2]+ \
S[3]*X[2]-S[2]*X[0]+S[6]*X[1]
U[5] = T[5]+L[3]*X[0]*X[2]+L[4]*X[0]*X[1]-L[5]*X[0]**2-L[0]*X[2]*X[1]+ \
S[0]*X[1]-S[1]*X[2]+S[7]*X[0]
Umat = G2lat.U6toUij(U)
beta = np.inner(np.inner(Bmat.T,Umat),Bmat)
Uout.append(['A',0.0,]+list(G2lat.UijtoU6(beta)*gvec))
else:
Uout.append(['N',])
return Uout
[docs]def GetSHCoeff(pId,parmDict,SHkeys):
'''default doc string
:param type name: description
:returns: type name: description
'''
SHCoeff = {}
for shkey in SHkeys:
shname = str(pId)+'::'+shkey
SHCoeff[shkey] = parmDict[shname]
return SHCoeff
[docs]def getMass(generalData):
'''Computes mass of unit cell contents
:param dict generalData: The General dictionary in Phase
:returns: float mass: Crystal unit cell mass in AMU.
'''
mass = 0.
for i,elem in enumerate(generalData['AtomTypes']):
mass += generalData['NoAtoms'][elem]*generalData['AtomMass'][i]
return max(mass,1.0)
[docs]def getDensity(generalData):
'''calculate crystal structure density
:param dict generalData: The General dictionary in Phase
:returns: float density: crystal density in gm/cm^3
'''
mass = getMass(generalData)
Volume = generalData['Cell'][7]
density = mass/(0.6022137*Volume)
return density,Volume/mass
[docs]def getWave(Parms):
'''returns wavelength from Instrument parameters dictionary
:param dict Parms: Instrument parameters;
must contain:
Lam: single wavelength
or
Lam1: Ka1 radiation wavelength
:returns: float wave: wavelength
'''
try:
return Parms['Lam'][1]
except KeyError:
return Parms['Lam1'][1]
[docs]def getMeanWave(Parms):
'''returns mean wavelength from Instrument parameters dictionary
:param dict Parms: Instrument parameters;
must contain:
Lam: single wavelength
or
Lam1,Lam2: Ka1,Ka2 radiation wavelength
I(L2)/I(L1): Ka2/Ka1 ratio
:returns: float wave: mean wavelength
'''
try:
return Parms['Lam'][1]
except KeyError:
meanLam = (Parms['Lam1'][1]+Parms['I(L2)/I(L1)'][1]*Parms['Lam2'][1])/ \
(1.+Parms['I(L2)/I(L1)'][1])
return meanLam
[docs]def El2Mass(Elements):
'''compute molecular weight from Elements
:param dict Elements: elements in molecular formula;
each must contain
Num: number of atoms in formula
Mass: at. wt.
:returns: float mass: molecular weight.
'''
mass = 0
for El in Elements:
mass += Elements[El]['Num']*Elements[El]['Mass']
return mass
[docs]def Den2Vol(Elements,density):
'''converts density to molecular volume
:param dict Elements: elements in molecular formula;
each must contain
Num: number of atoms in formula
Mass: at. wt.
:param float density: material density in gm/cm^3
:returns: float volume: molecular volume in A^3
'''
return El2Mass(Elements)/(density*0.6022137)
[docs]def Vol2Den(Elements,volume):
'''converts volume to density
:param dict Elements: elements in molecular formula;
each must contain
Num: number of atoms in formula
Mass: at. wt.
:param float volume: molecular volume in A^3
:returns: float density: material density in gm/cm^3
'''
return El2Mass(Elements)/(volume*0.6022137)
[docs]def El2EstVol(Elements):
'''Estimate volume from molecular formula; assumes atom volume = 10A^3
:param dict Elements: elements in molecular formula;
each must contain
Num: number of atoms in formula
:returns: float volume: estimate of molecular volume in A^3
'''
vol = 0
for El in Elements:
vol += 10.*Elements[El]['Num']
return vol
[docs]def XScattDen(Elements,vol,wave=0.):
'''Estimate X-ray scattering density from molecular formula & volume;
ignores valence, but includes anomalous effects
:param dict Elements: elements in molecular formula;
each element must contain
Num: number of atoms in formula
Z: atomic number
:param float vol: molecular volume in A^3
:param float wave: optional wavelength in A
:returns: float rho: scattering density in 10^10cm^-2;
if wave > 0 the includes f' contribution
:returns: float mu: if wave>0 absorption coeff in cm^-1 ; otherwise 0
:returns: float fpp: if wave>0 f" in 10^10cm^-2; otherwise 0
'''
rho = 0
mu = 0
fpp = 0
if wave:
Xanom = XAnomAbs(Elements,wave)
for El in Elements:
f0 = Elements[El]['Z']
if wave:
f0 += Xanom[El][0]
fpp += Xanom[El][1]*Elements[El]['Num']
mu += Xanom[El][2]*Elements[El]['Num']
rho += Elements[El]['Num']*f0
return 28.179*rho/vol,mu/vol,28.179*fpp/vol
[docs]def NCScattDen(Elements,vol,wave=0.):
'''Estimate neutron scattering density from molecular formula & volume;
ignores valence, but includes anomalous effects
:param dict Elements: elements in molecular formula;
each element must contain
Num: number of atoms in formula
Z: atomic number
:param float vol: molecular volume in A^3
:param float wave: optional wavelength in A
:returns: float rho: scattering density in 10^10cm^-2;
if wave > 0 the includes f' contribution
:returns: float mu: if wave>0 absorption coeff in cm^-1 ; otherwise 0
:returns: float fpp: if wave>0 f" in 10^10cm^-2; otherwise 0
'''
rho = 0
mu = 0
bpp = 0
for El in Elements:
isotope = Elements[El]['Isotope']
b0 = Elements[El]['Isotopes'][isotope]['SL'][0]
mu += Elements[El]['Isotopes'][isotope].get('SA',0.)*Elements[El]['Num']
if wave and 'BW-LS' in Elements[El]['Isotopes'][isotope]:
Re,Im,E0,gam,A,E1,B,E2 = Elements[El]['Isotopes'][isotope]['BW-LS'][1:]
Emev = 81.80703/wave**2
T0 = Emev-E0
T1 = Emev-E1
T2 = Emev-E2
D0 = T0**2+gam**2
D1 = T1**2+gam**2
D2 = T2**2+gam**2
b0 += Re*(T0/D0+A*T1/D1+B*T2/D2)
bpp += Im*(1/D0+A/D1+B/D2)
else:
bpp += Elements[El]['Isotopes'][isotope]['SL'][1]
rho += Elements[El]['Num']*b0
if wave: mu *= wave
return 100.*rho/vol,mu/vol,100.*bpp/vol
[docs]def wavekE(wavekE):
'''Convert wavelength to energy & vise versa
:param float waveKe:wavelength in A or energy in kE
:returns float waveKe:the other one
'''
return 12.397639/wavekE
def XAnomAbs(Elements,wave):
kE = wavekE(wave)
Xanom = {}
for El in Elements:
Orbs = G2el.GetXsectionCoeff(El)
Xanom[El] = G2el.FPcalc(Orbs, kE)
return Xanom #f',f", mu
################################################################################
#### Modulation math
################################################################################
[docs]def makeWaves(waveTypes,FSSdata,XSSdata,USSdata,MSSdata,Mast):
'''
waveTypes: array nAtoms: 'Fourier','ZigZag' or 'Block'
FSSdata: array 2 x atoms x waves (sin,cos terms)
XSSdata: array 2x3 x atoms X waves (sin,cos terms)
USSdata: array 2x6 x atoms X waves (sin,cos terms)
MSSdata: array 2x3 x atoms X waves (sin,cos terms)
Mast: array orthogonalization matrix for Uij
'''
ngl = 36 #selected for integer steps for 1/6,1/4,1/3...
glTau,glWt = pwd.pygauleg(0.,1.,ngl) #get Gauss-Legendre intervals & weights
Ax = np.array(XSSdata[:3]).T #atoms x waves x sin pos mods
Bx = np.array(XSSdata[3:]).T #...cos pos mods
Af = np.array(FSSdata[0]).T #sin frac mods x waves x atoms
Bf = np.array(FSSdata[1]).T #cos frac mods...
Au = Mast*np.array(G2lat.U6toUij(USSdata[:6])).T #atoms x waves x sin Uij mods as betaij
Bu = Mast*np.array(G2lat.U6toUij(USSdata[6:])).T #...cos Uij mods as betaij
Am = np.array(MSSdata[:3]).T #atoms x waves x sin pos mods
Bm = np.array(MSSdata[3:]).T #...cos pos mods
nWaves = [Af.shape[1],Ax.shape[1],Au.shape[1],Am.shape[1]]
if nWaves[0]:
tauF = np.arange(1.,nWaves[0]+1)[:,nxs]*glTau #Fwaves x ngl
FmodA = Af[:,:,nxs]*np.sin(twopi*tauF[nxs,:,:]) #atoms X Fwaves X ngl
FmodB = Bf[:,:,nxs]*np.cos(twopi*tauF[nxs,:,:])
Fmod = np.sum(1.0+FmodA+FmodB,axis=1) #atoms X ngl; sum waves
else:
Fmod = 1.0
XmodZ = np.zeros((Ax.shape[0],Ax.shape[1],3,ngl))
XmodA = np.zeros((Ax.shape[0],Ax.shape[1],3,ngl))
XmodB = np.zeros((Ax.shape[0],Ax.shape[1],3,ngl))
for iatm in range(Ax.shape[0]):
nx = 0
if 'ZigZag' in waveTypes[iatm]:
nx = 1
Tmm = Ax[iatm][0][:2]
XYZmax = np.array([Ax[iatm][0][2],Bx[iatm][0][0],Bx[iatm][0][1]])
XmodZ[iatm][0] += posZigZag(glTau,Tmm,XYZmax).T
elif 'Block' in waveTypes[iatm]:
nx = 1
Tmm = Ax[iatm][0][:2]
XYZmax = np.array([Ax[iatm][0][2],Bx[iatm][0][0],Bx[iatm][0][1]])
XmodZ[iatm][0] += posBlock(glTau,Tmm,XYZmax).T
tauX = np.arange(1.,nWaves[1]+1-nx)[:,nxs]*glTau #Xwaves x ngl
if nx:
XmodA[iatm][:-nx] = Ax[iatm,nx:,:,nxs]*np.sin(twopi*tauX[nxs,:,nxs,:]) #atoms X waves X 3 X ngl
XmodB[iatm][:-nx] = Bx[iatm,nx:,:,nxs]*np.cos(twopi*tauX[nxs,:,nxs,:]) #ditto
else:
XmodA[iatm] = Ax[iatm,:,:,nxs]*np.sin(twopi*tauX[nxs,:,nxs,:]) #atoms X waves X 3 X ngl
XmodB[iatm] = Bx[iatm,:,:,nxs]*np.cos(twopi*tauX[nxs,:,nxs,:]) #ditto
Xmod = np.sum(XmodA+XmodB+XmodZ,axis=1) #atoms X 3 X ngl; sum waves
Xmod = np.swapaxes(Xmod,1,2)
if nWaves[2]:
tauU = np.arange(1.,nWaves[2]+1)[:,nxs]*glTau #Uwaves x ngl
UmodA = Au[:,:,:,:,nxs]*np.sin(twopi*tauU[nxs,:,nxs,nxs,:]) #atoms x waves x 3x3 x ngl
UmodB = Bu[:,:,:,:,nxs]*np.cos(twopi*tauU[nxs,:,nxs,nxs,:]) #ditto
Umod = np.swapaxes(np.sum(UmodA+UmodB,axis=1),1,3) #atoms x 3x3 x ngl; sum waves
else:
Umod = 1.0
if nWaves[3]:
tauM = np.arange(1.,nWaves[3]+1-nx)[:,nxs]*glTau #Mwaves x ngl
MmodA = Am[:,:,:,nxs]*np.sin(twopi*tauM[nxs,:,nxs,:]) #atoms X waves X 3 X tau
MmodB = Bm[:,:,:,nxs]*np.cos(twopi*tauM[nxs,:,nxs,:]) #ditto
Mmod = np.sum(MmodA+MmodB,axis=1)
Mmod = np.swapaxes(Mmod,1,2) #Mxyz,Ntau,Natm
else:
Mmod = 1.0
return ngl,nWaves,Fmod,Xmod,Umod,Mmod,glTau,glWt
[docs]def MagMod(glTau,XYZ,modQ,MSSdata,SGData,SSGData):
'''
this needs to make magnetic moment modulations & magnitudes as
fxn of gTau points; NB: this allows only 1 mag. wave fxn.
'''
Am = np.array(MSSdata[3:]).T[:,0,:] #atoms x cos mag mods; only 1 wave used
Bm = np.array(MSSdata[:3]).T[:,0,:] #...sin mag mods
SGMT = np.array([ops[0] for ops in SGData['SGOps']]) #not .T!! (no diff for MnWO4 & best for DyMnGe)
Sinv = np.array([nl.inv(ops[0]) for ops in SSGData['SSGOps']])
SGT = np.array([ops[1] for ops in SSGData['SSGOps']])
if SGData['SGInv']:
SGMT = np.vstack((SGMT,-SGMT))
Sinv = np.vstack((Sinv,-Sinv))
SGT = np.vstack((SGT,-SGT))
SGMT = np.vstack([SGMT for cen in SGData['SGCen']])
Sinv = np.vstack([Sinv for cen in SGData['SGCen']])
SGT = np.vstack([SGT+cen for cen in SSGData['SSGCen']])%1.
if SGData['SGGray']:
SGMT = np.vstack((SGMT,SGMT))
Sinv = np.vstack((Sinv,Sinv))
SGT = np.vstack((SGT,SGT+np.array([0.,0.,0.,.5])))%1.
AMR = np.swapaxes(np.inner(Am,SGMT),0,1) #Nops,Natm,Mxyz
BMR = np.swapaxes(np.inner(Bm,SGMT),0,1)
epsinv = Sinv[:,3,3]
mst = np.inner(Sinv[:,:3,:3],modQ)-epsinv[:,nxs]*modQ #van Smaalen Eq. 3.3
phi = np.inner(XYZ,modQ).T+np.inner(SGT[:,:3],modQ)[:,nxs]+SGT[:,3,nxs] # +,+ best for MnWO4 & DyMnGe
TA = np.sum(mst[nxs,:,:]*(XYZ-SGT[:,:3][nxs,:,:]),axis=-1).T
phase = TA[nxs,:,:] + epsinv[nxs,:,nxs]*glTau[:,nxs,nxs]+phi[nxs,:,:] #+ best for MnWO4
psin = np.sin(twopi*phase) #tau,ops,atms
pcos = np.cos(twopi*phase)
MmodAR = AMR[nxs,:,:,:]*pcos[:,:,:,nxs] #Re cos term; tau,ops,atms, Mxyz
MmodBR = BMR[nxs,:,:,:]*psin[:,:,:,nxs] #Re sin term
MmodAI = AMR[nxs,:,:,:]*psin[:,:,:,nxs] #Im cos term
MmodBI = BMR[nxs,:,:,:]*pcos[:,:,:,nxs] #Im sin term
return MmodAR,MmodBR,MmodAI,MmodBI #Ntau,Nops,Natm,Mxyz; Re, Im cos & sin parts
[docs]def MagMod2(glTau,xyz,modQ,MSSdata,SGData,SSGData):
'''
this needs to make magnetic moment modulations & magnitudes as
fxn of gTau points; NB: this allows only 1 mag. wave fxn.
'''
Am = np.array(MSSdata[3:]).T[:,0,:] #atoms x cos mag mods; only 1 wave used
Bm = np.array(MSSdata[:3]).T[:,0,:] #...sin mag mods
SGMT = np.array([ops[0] for ops in SGData['SGOps']]) #not .T!! (no diff for MnWO4 & best for DyMnGe)
Sinv = np.array([nl.inv(ops[0]) for ops in SSGData['SSGOps']])
SGT = np.array([ops[1] for ops in SSGData['SSGOps']])
if SGData['SGInv']:
SGMT = np.vstack((SGMT,-SGMT))
Sinv = np.vstack((Sinv,-Sinv))
SGT = np.vstack((SGT,-SGT))
SGMT = np.vstack([SGMT for cen in SGData['SGCen']])
Sinv = np.vstack([Sinv for cen in SGData['SGCen']])
SGT = np.vstack([SGT+cen for cen in SSGData['SSGCen']])%1.
if SGData['SGGray']:
SGMT = np.vstack((SGMT,SGMT))
Sinv = np.vstack((Sinv,Sinv))
SGT = np.vstack((SGT,SGT+np.array([0.,0.,0.,.5])))%1.
XYZ = np.array([(np.inner(xyzi,SGMT)+SGT[:,:3])%1. for xyzi in xyz.T]) #Natn,Nop,xyz
AMR = np.swapaxes(np.inner(Am,SGMT),0,1) #Nops,Natm,Mxyz
BMR = np.swapaxes(np.inner(Bm,SGMT),0,1)
epsinv = Sinv[:,3,3]
mst = np.inner(Sinv[:,:3,:3],modQ)-epsinv[:,nxs]*modQ #van Smaalen Eq. 3.3
phi = np.inner(XYZ,modQ).T+np.inner(SGT[:,:3],modQ)[:,nxs]+SGT[:,3,nxs] # +,+ best for MnWO4 & DyMnGe
TA = np.sum(mst[nxs,:,:]*(XYZ-SGT[:,:3][nxs,:,:]),axis=-1).T
phase = TA[nxs,:,:] + epsinv[nxs,:,nxs]*glTau[:,nxs,nxs]+phi[nxs,:,:] #+ best for MnWO4
psin = np.sin(twopi*phase) #tau,ops,atms
pcos = np.cos(twopi*phase)
MmodAR = AMR[nxs,:,:,:]*pcos[:,:,:,nxs] #Re cos term; tau,ops,atms, Mxyz
MmodBR = BMR[nxs,:,:,:]*psin[:,:,:,nxs] #Re sin term
MmodAI = AMR[nxs,:,:,:]*psin[:,:,:,nxs] #Im cos term
MmodBI = BMR[nxs,:,:,:]*pcos[:,:,:,nxs] #Im sin term
return XYZ,MmodAR,MmodBR,MmodAI,MmodBI #Ntau,Nops,Natm,Mxyz; Re, Im cos & sin parts
[docs]def Modulation(H,HP,nWaves,Fmod,Xmod,Umod,glTau,glWt):
'''
H: array nRefBlk x ops X hklt
HP: array nRefBlk x ops X hklt proj to hkl
nWaves: list number of waves for frac, pos, uij & mag
Fmod: array 2 x atoms x waves (sin,cos terms)
Xmod: array atoms X 3 X ngl
Umod: array atoms x 3x3 x ngl
glTau,glWt: arrays Gauss-Lorentzian pos & wts
'''
if nWaves[2]: #uij (adp) waves
if len(HP.shape) > 2:
HbH = np.exp(-np.sum(HP[:,:,nxs,nxs,:]*np.inner(HP,Umod),axis=-1)) # refBlk x ops x atoms x ngl add Overhauser corr.?
else:
HbH = np.exp(-np.sum(HP[:,nxs,nxs,:]*np.inner(HP,Umod),axis=-1)) # refBlk x ops x atoms x ngl add Overhauser corr.?
else:
HbH = 1.0
HdotX = np.inner(HP,Xmod) #refBlk x ops x atoms X ngl
if len(H.shape) > 2:
D = H[:,:,3:]*glTau[nxs,nxs,:] #m*e*tau; refBlk x ops X ngl
HdotXD = twopi*(HdotX+D[:,:,nxs,:])
else:
D = H[:,3:]*glTau[nxs,:] #m*e*tau; refBlk x ops X ngl
HdotXD = twopi*(HdotX+D[:,nxs,:])
cosHA = np.sum(Fmod*HbH*np.cos(HdotXD)*glWt,axis=-1) #real part; refBlk X ops x atoms; sum for G-L integration
sinHA = np.sum(Fmod*HbH*np.sin(HdotXD)*glWt,axis=-1) #imag part; ditto
return np.array([cosHA,sinHA]) # 2 x refBlk x SGops x atoms
[docs]def ModulationTw(H,HP,nWaves,Fmod,Xmod,Umod,glTau,glWt):
'''
H: array nRefBlk x tw x ops X hklt
HP: array nRefBlk x tw x ops X hklt proj to hkl
Fmod: array 2 x atoms x waves (sin,cos terms)
Xmod: array atoms X ngl X 3
Umod: array atoms x ngl x 3x3
glTau,glWt: arrays Gauss-Lorentzian pos & wts
'''
if nWaves[2]:
if len(HP.shape) > 3: #Blocks of reflections
HbH = np.exp(-np.sum(HP[:,:,nxs,nxs,:]*np.inner(HP,Umod),axis=-1)) # refBlk x ops x atoms x ngl add Overhauser corr.?
else: #single reflections
HbH = np.exp(-np.sum(HP[:,nxs,nxs,:]*np.inner(HP,Umod),axis=-1)) # refBlk x ops x atoms x ngl add Overhauser corr.?
else:
HbH = 1.0
HdotX = np.inner(HP,Xmod) #refBlk x tw x ops x atoms X ngl
if len(H.shape) > 3:
D = glTau*H[:,:,:,3:,nxs] #m*e*tau; refBlk x tw x ops X ngl
HdotXD = twopi*(HdotX+D[:,:,:,nxs,:])
else:
D = H*glTau[nxs,:] #m*e*tau; refBlk x ops X ngl
HdotXD = twopi*(HdotX+D[:,nxs,:])
cosHA = np.sum(Fmod*HbH*np.cos(HdotXD)*glWt,axis=-1) #real part; refBlk X ops x atoms; sum for G-L integration
sinHA = np.sum(Fmod*HbH*np.sin(HdotXD)*glWt,axis=-1) #imag part; ditto
return np.array([cosHA,sinHA]) # 2 x refBlk x SGops x atoms
[docs]def makeWavesDerv(ngl,waveTypes,FSSdata,XSSdata,USSdata,Mast):
'''
Only for Fourier waves for fraction, position & adp (probably not used for magnetism)
FSSdata: array 2 x atoms x waves (sin,cos terms)
XSSdata: array 2x3 x atoms X waves (sin,cos terms)
USSdata: array 2x6 x atoms X waves (sin,cos terms)
Mast: array orthogonalization matrix for Uij
'''
glTau,glWt = pwd.pygauleg(0.,1.,ngl) #get Gauss-Legendre intervals & weights
waveShapes = [FSSdata.T.shape,XSSdata.T.shape,USSdata.T.shape]
Af = np.array(FSSdata[0]).T #sin frac mods x waves x atoms
Bf = np.array(FSSdata[1]).T #cos frac mods...
Ax = np.array(XSSdata[:3]).T #...cos pos mods x waves x atoms
Bx = np.array(XSSdata[3:]).T #...cos pos mods
Au = Mast*np.array(G2lat.U6toUij(USSdata[:6])).T #atoms x waves x sin Uij mods
Bu = Mast*np.array(G2lat.U6toUij(USSdata[6:])).T #...cos Uij mods
nWaves = [Af.shape[1],Ax.shape[1],Au.shape[1]]
StauX = np.zeros((Ax.shape[0],Ax.shape[1],3,ngl)) #atoms x waves x 3 x ngl
CtauX = np.zeros((Ax.shape[0],Ax.shape[1],3,ngl))
ZtauXt = np.zeros((Ax.shape[0],2,3,ngl)) #atoms x Tminmax x 3 x ngl
ZtauXx = np.zeros((Ax.shape[0],3,ngl)) #atoms x XYZmax x ngl
for iatm in range(Ax.shape[0]):
nx = 0
if 'ZigZag' in waveTypes[iatm]:
nx = 1
elif 'Block' in waveTypes[iatm]:
nx = 1
tauX = np.arange(1.,nWaves[1]+1-nx)[:,nxs]*glTau #Xwaves x ngl
if nx:
StauX[iatm][nx:] = np.ones_like(Ax)[iatm,nx:,:,nxs]*np.sin(twopi*tauX)[nxs,:,nxs,:] #atoms X waves X 3(xyz) X ngl
CtauX[iatm][nx:] = np.ones_like(Bx)[iatm,nx:,:,nxs]*np.cos(twopi*tauX)[nxs,:,nxs,:] #ditto
else:
StauX[iatm] = np.ones_like(Ax)[iatm,:,:,nxs]*np.sin(twopi*tauX)[nxs,:,nxs,:] #atoms X waves X 3(xyz) X ngl
CtauX[iatm] = np.ones_like(Bx)[iatm,:,:,nxs]*np.cos(twopi*tauX)[nxs,:,nxs,:] #ditto
if nWaves[0]:
tauF = np.arange(1.,nWaves[0]+1)[:,nxs]*glTau #Fwaves x ngl
StauF = np.ones_like(Af)[:,:,nxs]*np.sin(twopi*tauF)[nxs,:,:] #also dFmod/dAf
CtauF = np.ones_like(Bf)[:,:,nxs]*np.cos(twopi*tauF)[nxs,:,:] #also dFmod/dBf
else:
StauF = 1.0
CtauF = 1.0
if nWaves[2]:
tauU = np.arange(1.,nWaves[2]+1)[:,nxs]*glTau #Uwaves x ngl
StauU = np.ones_like(Au)[:,:,:,:,nxs]*np.sin(twopi*tauU)[nxs,:,nxs,nxs,:] #also dUmodA/dAu
CtauU = np.ones_like(Bu)[:,:,:,:,nxs]*np.cos(twopi*tauU)[nxs,:,nxs,nxs,:] #also dUmodB/dBu
UmodA = Au[:,:,:,:,nxs]*StauU #atoms x waves x 3x3 x ngl
UmodB = Bu[:,:,:,:,nxs]*CtauU #ditto
#derivs need to be ops x atoms x waves x 6uij; ops x atoms x waves x ngl x 6uij before sum
StauU = np.rollaxis(np.rollaxis(np.swapaxes(StauU,2,4),-1),-1)
CtauU = np.rollaxis(np.rollaxis(np.swapaxes(CtauU,2,4),-1),-1)
else:
StauU = 1.0
CtauU = 1.0
UmodA = 0.
UmodB = 0.
return waveShapes,[StauF,CtauF],[StauX,CtauX,ZtauXt,ZtauXx],[StauU,CtauU],UmodA+UmodB
[docs]def ModulationDerv(H,HP,Hij,nWaves,waveShapes,Fmod,Xmod,UmodAB,SCtauF,SCtauX,SCtauU,glTau,glWt):
'''
Compute Fourier modulation derivatives
H: array ops X hklt proj to hkl
HP: array ops X hklt proj to hkl
Hij: array 2pi^2[a*^2h^2 b*^2k^2 c*^2l^2 a*b*hk a*c*hl b*c*kl] of projected hklm to hkl space
'''
Mf = [H.shape[0],]+list(waveShapes[0]) #=[ops,atoms,waves,2] (sin+cos frac mods)
dGdMfC = np.zeros(Mf)
dGdMfS = np.zeros(Mf)
Mx = [H.shape[0],]+list(waveShapes[1]) #=[ops,atoms,waves,6] (sin+cos pos mods)
dGdMxC = np.zeros(Mx)
dGdMxS = np.zeros(Mx)
Mu = [H.shape[0],]+list(waveShapes[2]) #=[ops,atoms,waves,12] (sin+cos Uij mods)
dGdMuC = np.zeros(Mu)
dGdMuS = np.zeros(Mu)
D = twopi*H[:,3][:,nxs]*glTau[nxs,:] #m*e*tau; ops X ngl
HdotX = twopi*np.inner(HP,Xmod) #ops x atoms X ngl
HdotXD = HdotX+D[:,nxs,:]
if nWaves[2]:
Umod = np.swapaxes((UmodAB),2,4) #atoms x waves x ngl x 3x3 (symmetric so I can do this!)
HuH = np.sum(HP[:,nxs,nxs,nxs]*np.inner(HP,Umod),axis=-1) #ops x atoms x waves x ngl
HuH = np.sum(HP[:,nxs,nxs,nxs]*np.inner(HP,Umod),axis=-1) #ops x atoms x waves x ngl
HbH = np.exp(-np.sum(HuH,axis=-2)) # ops x atoms x ngl; sum waves - OK vs Modulation version
# part1 = -np.exp(-HuH)*Fmod[nxs,:,nxs,:] #ops x atoms x waves x ngl
part1 = -np.exp(-HuH)*Fmod #ops x atoms x waves x ngl
dUdAu = Hij[:,nxs,nxs,nxs,:]*np.rollaxis(G2lat.UijtoU6(SCtauU[0]),0,4)[nxs,:,:,:,:] #ops x atoms x waves x ngl x 6sinUij
dUdBu = Hij[:,nxs,nxs,nxs,:]*np.rollaxis(G2lat.UijtoU6(SCtauU[1]),0,4)[nxs,:,:,:,:] #ops x atoms x waves x ngl x 6cosUij
dGdMuCa = np.sum(part1[:,:,:,:,nxs]*dUdAu*np.cos(HdotXD)[:,:,nxs,:,nxs]*glWt[nxs,nxs,nxs,:,nxs],axis=-2) #ops x atoms x waves x 6uij; G-L sum
dGdMuCb = np.sum(part1[:,:,:,:,nxs]*dUdBu*np.cos(HdotXD)[:,:,nxs,:,nxs]*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMuC = np.concatenate((dGdMuCa,dGdMuCb),axis=-1) #ops x atoms x waves x 12uij
dGdMuSa = np.sum(part1[:,:,:,:,nxs]*dUdAu*np.sin(HdotXD)[:,:,nxs,:,nxs]*glWt[nxs,nxs,nxs,:,nxs],axis=-2) #ops x atoms x waves x 6uij; G-L sum
dGdMuSb = np.sum(part1[:,:,:,:,nxs]*dUdBu*np.sin(HdotXD)[:,:,nxs,:,nxs]*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMuS = np.concatenate((dGdMuSa,dGdMuSb),axis=-1) #ops x atoms x waves x 12uij
else:
HbH = np.ones_like(HdotX)
dHdXA = twopi*HP[:,nxs,nxs,nxs,:]*np.swapaxes(SCtauX[0],-1,-2)[nxs,:,:,:,:] #ops x atoms x sine waves x ngl x xyz
dHdXB = twopi*HP[:,nxs,nxs,nxs,:]*np.swapaxes(SCtauX[1],-1,-2)[nxs,:,:,:,:] #ditto - cos waves
# ops x atoms x waves x 2xyz - real part - good
# dGdMxCa = -np.sum((Fmod[nxs,:,:]*HbH)[:,:,nxs,:,nxs]*(dHdXA*np.sin(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
# dGdMxCb = -np.sum((Fmod[nxs,:,:]*HbH)[:,:,nxs,:,nxs]*(dHdXB*np.sin(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMxCa = -np.sum((Fmod*HbH)[:,:,nxs,:,nxs]*(dHdXA*np.sin(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMxCb = -np.sum((Fmod*HbH)[:,:,nxs,:,nxs]*(dHdXB*np.sin(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMxC = np.concatenate((dGdMxCa,dGdMxCb),axis=-1)
# ops x atoms x waves x 2xyz - imag part - good
# dGdMxSa = np.sum((Fmod[nxs,:,:]*HbH)[:,:,nxs,:,nxs]*(dHdXA*np.cos(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
# dGdMxSb = np.sum((Fmod[nxs,:,:]*HbH)[:,:,nxs,:,nxs]*(dHdXB*np.cos(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMxSa = np.sum((Fmod*HbH)[:,:,nxs,:,nxs]*(dHdXA*np.cos(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMxSb = np.sum((Fmod*HbH)[:,:,nxs,:,nxs]*(dHdXB*np.cos(HdotXD)[:,:,nxs,:,nxs])*glWt[nxs,nxs,nxs,:,nxs],axis=-2)
dGdMxS = np.concatenate((dGdMxSa,dGdMxSb),axis=-1)
return [dGdMfC,dGdMfS],[dGdMxC,dGdMxS],[dGdMuC,dGdMuS]
def posFourier(tau,psin,pcos):
A = np.array([ps[:,nxs]*np.sin(2*np.pi*(i+1)*tau) for i,ps in enumerate(psin)])
B = np.array([pc[:,nxs]*np.cos(2*np.pi*(i+1)*tau) for i,pc in enumerate(pcos)])
return np.sum(A,axis=0)+np.sum(B,axis=0)
def posZigZag(T,Tmm,Xmax):
DT = Tmm[1]-Tmm[0]
Su = 2.*Xmax/DT
Sd = 2.*Xmax/(1.-DT)
A = np.array([np.where( 0.< (t-Tmm[0])%1. <= DT, -Xmax+Su*((t-Tmm[0])%1.), Xmax-Sd*((t-Tmm[1])%1.)) for t in T])
return A
#def posZigZagDerv(T,Tmm,Xmax):
# DT = Tmm[1]-Tmm[0]
# Su = 2.*Xmax/DT
# Sd = 2.*Xmax/(1.-DT)
# dAdT = np.zeros((2,3,len(T)))
# dAdT[0] = np.array([np.where(Tmm[0] < t <= Tmm[1],Su*(t-Tmm[0]-1)/DT,-Sd*(t-Tmm[1])/(1.-DT)) for t in T]).T
# dAdT[1] = np.array([np.where(Tmm[0] < t <= Tmm[1],-Su*(t-Tmm[0])/DT,Sd*(t-Tmm[1])/(1.-DT)) for t in T]).T
# dAdX = np.ones(3)[:,nxs]*np.array([np.where(Tmm[0] < t%1. <= Tmm[1],-1.+2.*(t-Tmm[0])/DT,1.-2.*(t-Tmm[1])%1./DT) for t in T])
# return dAdT,dAdX
def posBlock(T,Tmm,Xmax):
A = np.array([np.where(Tmm[0] < t%1. <= Tmm[1],-Xmax,Xmax) for t in T])
return A
#def posBlockDerv(T,Tmm,Xmax):
# dAdT = np.zeros((2,3,len(T)))
# ind = np.searchsorted(T,Tmm)
# dAdT[0,:,ind[0]] = -Xmax/len(T)
# dAdT[1,:,ind[1]] = Xmax/len(T)
# dAdX = np.ones(3)[:,nxs]*np.array([np.where(Tmm[0] < t <= Tmm[1],-1.,1.) for t in T]) #OK
# return dAdT,dAdX
def fracCrenel(tau,Toff,Twid):
Tau = (tau-Toff)%1.
A = np.where(Tau<Twid,1.,0.)
return A
def fracFourier(tau,fsin,fcos):
if len(fsin) == 1:
A = np.array([fsin[0]*np.sin(2.*np.pi*tau)])
B = np.array([fcos[0]*np.cos(2.*np.pi*tau)])
else:
A = np.array([fs[:,nxs]*np.sin(2.*np.pi*(i+1)*tau) for i,fs in enumerate(fsin)])
B = np.array([fc[:,nxs]*np.cos(2.*np.pi*(i+1)*tau) for i,fc in enumerate(fcos)])
return np.sum(A,axis=0)+np.sum(B,axis=0)
[docs]def ApplyModulation(data,tau):
'''Applies modulation to drawing atom positions & Uijs for given tau
'''
generalData = data['General']
cell = generalData['Cell'][1:7]
G,g = G2lat.cell2Gmat(cell)
SGData = generalData['SGData']
SSGData = generalData['SSGData']
cx,ct,cs,cia = getAtomPtrs(data)
drawingData = data['Drawing']
modul = generalData['SuperVec'][0]
dcx,dct,dcs,dci = getAtomPtrs(data,True)
atoms = data['Atoms']
drawAtoms = drawingData['Atoms']
Fade = np.ones(len(drawAtoms))
for atom in atoms:
atxyz = np.array(atom[cx:cx+3])
atuij = np.array(atom[cia+2:cia+8])
Sfrac = atom[-1]['SS1']['Sfrac']
Spos = atom[-1]['SS1']['Spos']
Sadp = atom[-1]['SS1']['Sadp']
if generalData['Type'] == 'magnetic':
Smag = atom[-1]['SS1']['Smag']
atmom = np.array(atom[cx+4:cx+7])
indx = FindAtomIndexByIDs(drawAtoms,dci,[atom[cia+8],],True)
for ind in indx:
drawatom = drawAtoms[ind]
opr = drawatom[dcs-1]
sop,ssop,icent,cent,unit = G2spc.OpsfromStringOps(opr,SGData,SSGData)
drxyz = (np.inner(sop[0],atxyz)+sop[1]+cent)*icent+np.array(unit)
tauT = G2spc.getTauT(tau,sop,ssop,drxyz,modul)[-1]
tauT *= icent #invert wave on -1
# print(tau,tauT,opr,G2spc.MT2text(sop).replace(' ',''),G2spc.SSMT2text(ssop).replace(' ',''))
wave = np.zeros(3)
uwave = np.zeros(6)
mom = np.zeros(3)
if len(Sfrac):
scof = []
ccof = []
waveType = Sfrac[0]
for i,sfrac in enumerate(Sfrac[1:]):
if not i and 'Crenel' in waveType:
Fade[ind] += fracCrenel(tauT,sfrac[0][0],sfrac[0][1])
else:
scof.append(sfrac[0][0])
ccof.append(sfrac[0][1])
if len(scof):
Fade[ind] += np.sum(fracFourier(tauT,scof,ccof))
if len(Spos):
scof = []
ccof = []
waveType = Spos[0]
for i,spos in enumerate(Spos[1:]):
if waveType in ['ZigZag','Block'] and not i:
Tminmax = spos[0][:2]
XYZmax = np.array(spos[0][2:5])
if waveType == 'Block':
wave = np.array(posBlock([tauT,],Tminmax,XYZmax))[0]
elif waveType == 'ZigZag':
wave = np.array(posZigZag([tauT,],Tminmax,XYZmax))[0]
else:
scof.append(spos[0][:3])
ccof.append(spos[0][3:])
if len(scof):
wave += np.sum(posFourier(tauT,np.array(scof),np.array(ccof)),axis=1)
if generalData['Type'] == 'magnetic' and len(Smag):
scof = []
ccof = []
waveType = Smag[0]
for i,spos in enumerate(Smag[1:]):
scof.append(spos[0][:3])
ccof.append(spos[0][3:])
if len(scof):
mom += np.sum(posFourier(tauT,np.array(scof),np.array(ccof)),axis=1)
if len(Sadp):
scof = []
ccof = []
waveType = Sadp[0]
for i,sadp in enumerate(Sadp[1:]):
scof.append(sadp[0][:6])
ccof.append(sadp[0][6:])
ures = posFourier(tauT,np.array(scof),np.array(ccof))
if np.any(ures):
uwave += np.sum(ures,axis=1)
if atom[cia] == 'A':
X,U = G2spc.ApplyStringOps(opr,SGData,atxyz+wave,atuij+uwave)
drawatom[dcx:dcx+3] = X
drawatom[dci-6:dci] = U
else:
X = G2spc.ApplyStringOps(opr,SGData,atxyz+wave)
drawatom[dcx:dcx+3] = X
if generalData['Type'] == 'magnetic':
M = G2spc.ApplyStringOpsMom(opr,SGData,SSGData,atmom+mom)
drawatom[dcx+3:dcx+6] = M
return drawAtoms,Fade
[docs]def patchIsoDisp(ISO):
'''patch: look for older ISODISTORT imports (<Nov 2021)'''
print('''
======================================================================
Warning: The ISODISTORT modes were read before the importer
was corrected to save displacement offsets. Will attempt to correct
from ParentStructure (correct only if displacivemode values are all
zero in initial CIF.) Reimporting is suggested.
======================================================================
''')
ISO['G2coordOffset'] = []
for Ilbl in ISO['IsoVarList']:
albl = Ilbl[:Ilbl.rfind('_')]
v = Ilbl[Ilbl.rfind('_')+1:]
ISO['G2coordOffset'].append(
ISO['ParentStructure'][albl][['dx','dy','dz'].index(v)]
) # this will be wrong if the _iso_deltacoordinate_value are not zero
[docs]def CalcIsoDisp(Phase,parmDict={},covdata={}):
'''Compute the ISODISTORT displacement variable values from the
atomic coordinates, applying the p::dA?:n displacements if parmDict
is supplied. Uncertainties are computed if covdata is supplied.
'''
ISO = Phase['ISODISTORT']
if 'G2coordOffset' not in ISO: patchIsoDisp(ISO) # patch Nov 2021
atmIndex = {a[-1]:i for i,a in enumerate(Phase['Atoms'])}
cx,ct,cs,ci = getAtomPtrs(Phase,False)
coordOffset = {xyz:cx+i for i,xyz in enumerate(('x','y','z'))}
# get uncertainties on modes and compute them for displacements
if 'varyList' in covdata:
modes = [i.name for i in ISO['G2ModeList']]
covDict = dict(zip(covdata.get('varyList',[]),covdata.get('sig',[])))
modeEsds = [covDict.get(str(g2),-1) for g2 in modes]
vcov = getVCov(modes,covdata['varyList'],covdata['covMatrix'])
normMode2Var = ISO['Mode2VarMatrix']*ISO['NormList']
# to get displacements from modes use np.dot(normMode2Var,vector-of-mode-values)
sigMat = np.inner(normMode2Var,np.inner(normMode2Var,vcov))
var = np.diag(sigMat)
dispEsds = list(np.where(var>0.,np.sqrt(var),-0.0001))
else:
dispEsds = len(ISO['G2VarList'])*[-0.0001]
modeEsds = len(ISO['G2ModeList'])*[-0.0001]
dispValues = []
for iso,g2,off in zip(ISO['IsoVarList'],ISO['G2VarList'],ISO['G2coordOffset']):
if g2.atom not in atmIndex:
print('Atom not found in atom list',g2)
return [],[],[],[]
atm = Phase['Atoms'][atmIndex[g2.atom]]
pos = atm[coordOffset[g2.name[-1]]] + parmDict.get(str(g2),0.0) - off
dispValues.append(pos)
modeValues = np.dot(ISO['Var2ModeMatrix'],dispValues) / ISO['NormList']
return dispValues,dispEsds,modeValues,modeEsds
[docs]def CalcIsoCoords(Phase,parmDict,covdata={}):
'''Compute the coordinate positions from ISODISTORT displacement mode values
Uncertainties are computed if covdata is supplied.
:param dict Phase: contents of tree entry for selected phase
:param dict parmDict: a dict with values for the modes; note that in the
parmDict from refinements the mode values are not normalized,
but this assumes they are.
:param dict Phase: full covariance information from tree
:returns: modeDict,posDict where modeDict contains pairs of mode values
and mode s.u. values; posDict contains pairs of displacement values
and their s.u. values.
'''
ISO = Phase['ISODISTORT']
if 'G2coordOffset' not in ISO: patchIsoDisp(ISO) # patch Nov 2021
modes = [i.name for i in ISO['G2ModeList']] # modes from the parmDict
normMode2Var = ISO['Mode2VarMatrix']*ISO['NormList']
modeVals = []
for i in modes:
if i not in parmDict:
print('Mode ',i,'not defined in the parameter dictionary')
return {},{}
try:
modeVals.append(float(parmDict[i][0]))
except:
modeVals.append(float(parmDict[i]))
if 'varyList' in covdata:
covDict = dict(zip(covdata.get('varyList',[]),covdata.get('sig',[])))
modeEsds = [covDict.get(str(g2),-1) for g2 in modes]
vcov = getVCov(modes,covdata['varyList'],covdata['covMatrix'])
sigMat = np.inner(normMode2Var,np.inner(normMode2Var,vcov))
var = np.diag(sigMat)
dispEsds = list(np.where(var>0.,np.sqrt(var),-0.0001))
else:
modeEsds = len(ISO['G2ModeList'])*[-0.0001]
dispEsds = len(ISO['G2VarList'])*[-0.0001]
dispValues = np.dot(normMode2Var,modeVals)
modeDict = {str(g2):([val,esd]) for val,g2,esd in
zip(modeVals,ISO['G2ModeList'],modeEsds)}
posDict = {str(g2).replace('::dA','::A'):([dsp,esd]) for dsp,g2,off,esd in
zip(dispValues,ISO['G2VarList'],ISO['G2coordOffset'],dispEsds)}
return modeDict,posDict
[docs]def ApplyModeDisp(data):
''' Applies ISODISTORT mode displacements to atom lists.
This changes the contents of the Draw Atoms positions and
the Atoms positions.
:param dict data: the contents of the Phase data tree item for a
particular phase
'''
generalData = data['General']
Atoms= data['Atoms']
ISOdata = data['ISODISTORT']
coords = ISOdata['G2parentCoords']
modeDisp = np.array(ISOdata['modeDispl'])*np.array(ISOdata['NormList'])
mode2var = np.array(ISOdata['Mode2VarMatrix'])
varDisp = np.sum(mode2var*modeDisp,axis=1)
vardict = dict(zip(ISOdata['IsoVarList'],varDisp))
cell = generalData['Cell'][1:7]
G,g = G2lat.cell2Gmat(cell)
SGData = generalData['SGData']
cx,ct,cs,cia = getAtomPtrs(data)
atNames = [atm[ct-1] for atm in Atoms]
parNames = [[atName+'_dx',atName+'_dy',atName+'_dz',] for atName in atNames]
if data['Drawing']:
drawingData = data['Drawing']
dcx,dct,dcs,dci = getAtomPtrs(data,True)
atoms = data['Atoms']
drawAtoms = drawingData['Atoms']
for iat,atom in enumerate(atoms):
atxyz = coords[iat]
SytSym = G2spc.SytSym(atxyz,SGData)[0]
CSIX = G2spc.GetCSxinel(SytSym)
displ = np.zeros(3)
for ip,parm in enumerate(parNames[iat]):
if parm in vardict:
displ[ip] = vardict[parm]
displ = G2spc.AtomDxSymFix(displ,SytSym,CSIX)
atom[cx:cx+3] = atxyz+displ
indx = FindAtomIndexByIDs(drawAtoms,dci,[atom[cia+8],],True)
for ind in indx:
drawatom = drawAtoms[ind]
opr = drawatom[dcs-1]
X = G2spc.ApplyStringOps(opr,SGData,atxyz+displ)
drawatom[dcx:dcx+3] = X
return None
else:
return 'Draw structure first'
# gauleg.py Gauss Legendre numerical quadrature, x and w computation
# integrate from a to b using n evaluations of the function f(x)
# usage: from gauleg import gaulegf
# x,w = gaulegf( a, b, n)
# area = 0.0
# for i in range(1,n+1): # yes, 1..n
# area += w[i]*f(x[i])
def gaulegf(a, b, n):
x = range(n+1) # x[0] unused
w = range(n+1) # w[0] unused
eps = 3.0E-14
m = (n+1)/2
xm = 0.5*(b+a)
xl = 0.5*(b-a)
for i in range(1,m+1):
z = math.cos(3.141592654*(i-0.25)/(n+0.5))
while True:
p1 = 1.0
p2 = 0.0
for j in range(1,n+1):
p3 = p2
p2 = p1
p1 = ((2.0*j-1.0)*z*p2-(j-1.0)*p3)/j
pp = n*(z*p1-p2)/(z*z-1.0)
z1 = z
z = z1 - p1/pp
if abs(z-z1) <= eps:
break
x[i] = xm - xl*z
x[n+1-i] = xm + xl*z
w[i] = 2.0*xl/((1.0-z*z)*pp*pp)
w[n+1-i] = w[i]
return np.array(x), np.array(w)
# end gaulegf
[docs]def BessJn(nmax,x):
''' compute Bessel function J(n,x) from scipy routine & recurrance relation
returns sequence of J(n,x) for n in range [-nmax...0...nmax]
:param integer nmax: maximul order for Jn(x)
:param float x: argument for Jn(x)
:returns numpy array: [J(-nmax,x)...J(0,x)...J(nmax,x)]
'''
import scipy.special as sp
bessJn = np.zeros(2*nmax+1)
bessJn[nmax] = sp.j0(x)
bessJn[nmax+1] = sp.j1(x)
bessJn[nmax-1] = -bessJn[nmax+1]
for i in range(2,nmax+1):
bessJn[i+nmax] = 2*(i-1)*bessJn[nmax+i-1]/x-bessJn[nmax+i-2]
bessJn[nmax-i] = bessJn[i+nmax]*(-1)**i
return bessJn
[docs]def BessIn(nmax,x):
''' compute modified Bessel function I(n,x) from scipy routines & recurrance relation
returns sequence of I(n,x) for n in range [-nmax...0...nmax]
:param integer nmax: maximul order for In(x)
:param float x: argument for In(x)
:returns numpy array: [I(-nmax,x)...I(0,x)...I(nmax,x)]
'''
import scipy.special as sp
bessIn = np.zeros(2*nmax+1)
bessIn[nmax] = sp.i0(x)
bessIn[nmax+1] = sp.i1(x)
bessIn[nmax-1] = bessIn[nmax+1]
for i in range(2,nmax+1):
bessIn[i+nmax] = bessIn[nmax+i-2]-2*(i-1)*bessIn[nmax+i-1]/x
bessIn[nmax-i] = bessIn[i+nmax]
return bessIn
################################################################################
#### distance, angle, planes, torsion stuff
################################################################################
def CalcDist(distance_dict, distance_atoms, parmDict):
if not len(parmDict):
return 0.
pId = distance_dict['pId']
A = [parmDict['%s::A%d'%(pId,i)] for i in range(6)]
Amat = G2lat.cell2AB(G2lat.A2cell(A))[0]
Oxyz = [parmDict['%s::A%s:%d'%(pId,x,distance_atoms[0])] for x in ['x','y','z']]
Txyz = [parmDict['%s::A%s:%d'%(pId,x,distance_atoms[1])] for x in ['x','y','z']]
inv = 1
symNo = distance_dict['symNo']
if symNo < 0:
inv = -1
symNo *= -1
cen = symNo//100
op = symNo%100-1
M,T = distance_dict['SGData']['SGOps'][op]
D = T*inv+distance_dict['SGData']['SGCen'][cen]
D += distance_dict['cellNo']
Txyz = np.inner(M*inv,Txyz)+D
dist = np.sqrt(np.sum(np.inner(Amat,(Txyz-Oxyz))**2))
# GSASIIpath.IPyBreak()
return dist
def CalcDistDeriv(distance_dict, distance_atoms, parmDict):
if not len(parmDict):
return None
pId = distance_dict['pId']
A = [parmDict['%s::A%d'%(pId,i)] for i in range(6)]
Amat = G2lat.cell2AB(G2lat.A2cell(A))[0]
Oxyz = [parmDict['%s::A%s:%d'%(pId,x,distance_atoms[0])] for x in ['x','y','z']]
Txyz = [parmDict['%s::A%s:%d'%(pId,x,distance_atoms[1])] for x in ['x','y','z']]
symNo = distance_dict['symNo']
Tunit = distance_dict['cellNo']
SGData = distance_dict['SGData']
deriv = getDistDerv(Oxyz,Txyz,Amat,Tunit,symNo,SGData)
return deriv
def CalcAngle(angle_dict, angle_atoms, parmDict):
if not len(parmDict):
return 0.
pId = angle_dict['pId']
A = [parmDict['%s::A%d'%(pId,i)] for i in range(6)]
Amat = G2lat.cell2AB(G2lat.A2cell(A))[0]
Oxyz = [parmDict['%s::A%s:%d'%(pId,x,angle_atoms[0])] for x in ['x','y','z']]
Axyz = [parmDict['%s::A%s:%d'%(pId,x,angle_atoms[1][0])] for x in ['x','y','z']]
Bxyz = [parmDict['%s::A%s:%d'%(pId,x,angle_atoms[1][1])] for x in ['x','y','z']]
ABxyz = [Axyz,Bxyz]
symNo = angle_dict['symNo']
vec = np.zeros((2,3))
for i in range(2):
inv = 1
if symNo[i] < 0:
inv = -1
cen = inv*symNo[i]//100
op = inv*symNo[i]%100-1
M,T = angle_dict['SGData']['SGOps'][op]
D = T*inv+angle_dict['SGData']['SGCen'][cen]
D += angle_dict['cellNo'][i]
ABxyz[i] = np.inner(M*inv,ABxyz[i])+D
vec[i] = np.inner(Amat,(ABxyz[i]-Oxyz))
dist = np.sqrt(np.sum(vec[i]**2))
if not dist:
return 0.
vec[i] /= dist
angle = acosd(np.sum(vec[0]*vec[1]))
return angle
def CalcAngleDeriv(angle_dict, angle_atoms, parmDict):
if not len(parmDict):
return None
pId = angle_dict['pId']
A = [parmDict['%s::A%d'%(pId,i)] for i in range(6)]
Amat = G2lat.cell2AB(G2lat.A2cell(A))[0]
Oxyz = [parmDict['%s::A%s:%d'%(pId,x,angle_atoms[0])] for x in ['x','y','z']]
Axyz = [parmDict['%s::A%s:%d'%(pId,x,angle_atoms[1][0])] for x in ['x','y','z']]
Bxyz = [parmDict['%s::A%s:%d'%(pId,x,angle_atoms[1][1])] for x in ['x','y','z']]
symNo = angle_dict['symNo']
Tunit = angle_dict['cellNo']
SGData = angle_dict['SGData']
deriv = getAngleDerv(Oxyz,Axyz,Bxyz,Amat,Tunit,symNo,SGData)
return deriv
[docs]def getSyXYZ(XYZ,ops,SGData):
'''default doc
:param type name: description
:returns: type name: description
'''
XYZout = np.zeros_like(XYZ)
for i,[xyz,op] in enumerate(zip(XYZ,ops)):
if op == '1':
XYZout[i] = xyz
else:
oprs = op.split('+')
unit = [0,0,0]
if len(oprs)>1:
unit = np.array(list(eval(oprs[1])))
syop =int(oprs[0])
inv = syop//abs(syop)
syop *= inv
cent = syop//100
syop %= 100
syop -= 1
M,T = SGData['SGOps'][syop]
XYZout[i] = (np.inner(M,xyz)+T)*inv+SGData['SGCen'][cent]+unit
return XYZout
[docs]def getRestDist(XYZ,Amat):
'''default doc string
:param type name: description
:returns: type name: description
'''
return np.sqrt(np.sum(np.inner(Amat,(XYZ[1]-XYZ[0]))**2))
[docs]def getRestDeriv(Func,XYZ,Amat,ops,SGData):
'''default doc string
:param type name: description
:returns: type name: description
'''
deriv = np.zeros((len(XYZ),3))
dx = 0.00001
for j,xyz in enumerate(XYZ):
for i,x in enumerate(np.array([[dx,0,0],[0,dx,0],[0,0,dx]])):
XYZ[j] -= x
d1 = Func(getSyXYZ(XYZ,ops,SGData),Amat)
XYZ[j] += 2*x
d2 = Func(getSyXYZ(XYZ,ops,SGData),Amat)
XYZ[j] -= x
deriv[j][i] = (d1-d2)/(2*dx)
return deriv.flatten()
[docs]def getRestAngle(XYZ,Amat):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcVec(Ox,Tx,Amat):
return np.inner(Amat,(Tx-Ox))
VecA = calcVec(XYZ[1],XYZ[0],Amat)
VecA /= np.sqrt(np.sum(VecA**2))
VecB = calcVec(XYZ[1],XYZ[2],Amat)
VecB /= np.sqrt(np.sum(VecB**2))
edge = VecB-VecA
edge = np.sum(edge**2)
angle = (2.-edge)/2.
angle = max(angle,-1.)
return acosd(angle)
[docs]def getRestPlane(XYZ,Amat):
'''default doc string
:param type name: description
:returns: type name: description
'''
sumXYZ = np.zeros(3)
for xyz in XYZ:
sumXYZ += xyz
sumXYZ /= len(XYZ)
XYZ = np.array(XYZ)-sumXYZ
XYZ = np.inner(Amat,XYZ).T
Zmat = np.zeros((3,3))
for i,xyz in enumerate(XYZ):
Zmat += np.outer(xyz.T,xyz)
Evec,Emat = nl.eig(Zmat)
Evec = np.sqrt(Evec)/(len(XYZ)-3)
Order = np.argsort(Evec)
return Evec[Order[0]]
[docs]def getRestChiral(XYZ,Amat):
'''default doc string
:param type name: description
:returns: type name: description
'''
VecA = np.empty((3,3))
VecA[0] = np.inner(XYZ[1]-XYZ[0],Amat)
VecA[1] = np.inner(XYZ[2]-XYZ[0],Amat)
VecA[2] = np.inner(XYZ[3]-XYZ[0],Amat)
return nl.det(VecA)
[docs]def getRestTorsion(XYZ,Amat):
'''default doc string
:param type name: description
:returns: type name: description
'''
VecA = np.empty((3,3))
VecA[0] = np.inner(XYZ[1]-XYZ[0],Amat)
VecA[1] = np.inner(XYZ[2]-XYZ[1],Amat)
VecA[2] = np.inner(XYZ[3]-XYZ[2],Amat)
D = nl.det(VecA)
Mag = np.sqrt(np.sum(VecA*VecA,axis=1))
P12 = np.sum(VecA[0]*VecA[1])/(Mag[0]*Mag[1])
P13 = np.sum(VecA[0]*VecA[2])/(Mag[0]*Mag[2])
P23 = np.sum(VecA[1]*VecA[2])/(Mag[1]*Mag[2])
Ang = 1.0
if abs(P12) < 1.0 and abs(P23) < 1.0:
Ang = (P12*P23-P13)/(np.sqrt(1.-P12**2)*np.sqrt(1.-P23**2))
TOR = (acosd(Ang)*D/abs(D)+720.)%360.
return TOR
[docs]def calcTorsionEnergy(TOR,Coeff=[]):
'''default doc string
:param type name: description
:returns: type name: description
'''
sum = 0.
if len(Coeff):
cof = np.reshape(Coeff,(3,3)).T
delt = TOR-cof[1]
delt = np.where(delt<-180.,delt+360.,delt)
delt = np.where(delt>180.,delt-360.,delt)
term = -cof[2]*delt**2
val = cof[0]*np.exp(term/1000.0)
pMax = cof[0][np.argmin(val)]
Eval = np.sum(val)
sum = Eval-pMax
return sum,Eval
[docs]def getTorsionDeriv(XYZ,Amat,Coeff):
'''default doc string
:param type name: description
:returns: type name: description
'''
deriv = np.zeros((len(XYZ),3))
dx = 0.00001
for j,xyz in enumerate(XYZ):
for i,x in enumerate(np.array([[dx,0,0],[0,dx,0],[0,0,dx]])):
XYZ[j] -= x
tor = getRestTorsion(XYZ,Amat)
p1,d1 = calcTorsionEnergy(tor,Coeff)
XYZ[j] += 2*x
tor = getRestTorsion(XYZ,Amat)
p2,d2 = calcTorsionEnergy(tor,Coeff)
XYZ[j] -= x
deriv[j][i] = (p2-p1)/(2*dx)
return deriv.flatten()
[docs]def getRestRama(XYZ,Amat):
'''Computes a pair of torsion angles in a 5 atom string
:param nparray XYZ: crystallographic coordinates of 5 atoms
:param nparray Amat: crystal to cartesian transformation matrix
:returns: list (phi,psi) two torsion angles in degrees
'''
phi = getRestTorsion(XYZ[:5],Amat)
psi = getRestTorsion(XYZ[1:],Amat)
return phi,psi
[docs]def calcRamaEnergy(phi,psi,Coeff=[]):
'''Computes pseudo potential energy from a pair of torsion angles and a
numerical description of the potential energy surface. Used to create
penalty function in LS refinement:
:math:`Eval(\\phi,\\psi) = C[0]*exp(-V/1000)`
where :math:`V = -C[3] * (\\phi-C[1])^2 - C[4]*(\\psi-C[2])^2 - 2*(\\phi-C[1])*(\\psi-C[2])`
:param float phi: first torsion angle (:math:`\\phi`)
:param float psi: second torsion angle (:math:`\\psi`)
:param list Coeff: pseudo potential coefficients
:returns: list (sum,Eval): pseudo-potential difference from minimum & value;
sum is used for penalty function.
'''
sum = 0.
Eval = 0.
if len(Coeff):
cof = Coeff.T
dPhi = phi-cof[1]
dPhi = np.where(dPhi<-180.,dPhi+360.,dPhi)
dPhi = np.where(dPhi>180.,dPhi-360.,dPhi)
dPsi = psi-cof[2]
dPsi = np.where(dPsi<-180.,dPsi+360.,dPsi)
dPsi = np.where(dPsi>180.,dPsi-360.,dPsi)
val = -cof[3]*dPhi**2-cof[4]*dPsi**2-2.0*cof[5]*dPhi*dPsi
val = cof[0]*np.exp(val/1000.)
pMax = cof[0][np.argmin(val)]
Eval = np.sum(val)
sum = Eval-pMax
return sum,Eval
[docs]def getRamaDeriv(XYZ,Amat,Coeff):
'''Computes numerical derivatives of torsion angle pair pseudo potential
with respect of crystallographic atom coordinates of the 5 atom sequence
:param nparray XYZ: crystallographic coordinates of 5 atoms
:param nparray Amat: crystal to cartesian transformation matrix
:param list Coeff: pseudo potential coefficients
:returns: list (deriv) derivatives of pseudopotential with respect to 5 atom
crystallographic xyz coordinates.
'''
deriv = np.zeros((len(XYZ),3))
dx = 0.00001
for j,xyz in enumerate(XYZ):
for i,x in enumerate(np.array([[dx,0,0],[0,dx,0],[0,0,dx]])):
XYZ[j] -= x
phi,psi = getRestRama(XYZ,Amat)
p1,d1 = calcRamaEnergy(phi,psi,Coeff)
XYZ[j] += 2*x
phi,psi = getRestRama(XYZ,Amat)
p2,d2 = calcRamaEnergy(phi,psi,Coeff)
XYZ[j] -= x
deriv[j][i] = (p2-p1)/(2*dx)
return deriv.flatten()
[docs]def getRestPolefig(ODFln,SamSym,Grid):
'''default doc string
:param type name: description
:returns: type name: description
'''
X,Y = np.meshgrid(np.linspace(1.,-1.,Grid),np.linspace(-1.,1.,Grid))
R,P = np.sqrt(X**2+Y**2).flatten(),atan2d(Y,X).flatten()
R = np.where(R <= 1.,2.*atand(R),0.0)
Z = np.zeros_like(R)
Z = G2lat.polfcal(ODFln,SamSym,R,P)
Z = np.reshape(Z,(Grid,Grid))
return np.reshape(R,(Grid,Grid)),np.reshape(P,(Grid,Grid)),Z
[docs]def getRestPolefigDerv(HKL,Grid,SHCoeff):
'''default doc string
:param type name: description
:returns: type name: description
'''
pass
[docs]def getDistDerv(Oxyz,Txyz,Amat,Tunit,Top,SGData):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcDist(Ox,Tx,U,inv,C,M,T,Amat):
TxT = inv*(np.inner(M,Tx)+T)+C+U
return np.sqrt(np.sum(np.inner(Amat,(TxT-Ox))**2))
inv = Top/abs(Top)
cent = abs(Top)//100
op = abs(Top)%100-1
M,T = SGData['SGOps'][op]
C = SGData['SGCen'][cent]
dx = .00001
deriv = np.zeros(6)
for i in [0,1,2]:
Oxyz[i] -= dx
d0 = calcDist(Oxyz,Txyz,Tunit,inv,C,M,T,Amat)
Oxyz[i] += 2*dx
deriv[i] = (calcDist(Oxyz,Txyz,Tunit,inv,C,M,T,Amat)-d0)/(2.*dx)
Oxyz[i] -= dx
Txyz[i] -= dx
d0 = calcDist(Oxyz,Txyz,Tunit,inv,C,M,T,Amat)
Txyz[i] += 2*dx
deriv[i+3] = (calcDist(Oxyz,Txyz,Tunit,inv,C,M,T,Amat)-d0)/(2.*dx)
Txyz[i] -= dx
return deriv
def getAngleDerv(Oxyz,Axyz,Bxyz,Amat,Tunit,symNo,SGData):
def calcAngle(Oxyz,ABxyz,Amat,Tunit,symNo,SGData):
vec = np.zeros((2,3))
for i in range(2):
inv = 1
if symNo[i] < 0:
inv = -1
cen = inv*symNo[i]//100
op = inv*symNo[i]%100-1
M,T = SGData['SGOps'][op]
D = T*inv+SGData['SGCen'][cen]
D += Tunit[i]
ABxyz[i] = np.inner(M*inv,ABxyz[i])+D
vec[i] = np.inner(Amat,(ABxyz[i]-Oxyz))
dist = np.sqrt(np.sum(vec[i]**2))
if not dist:
return 0.
vec[i] /= dist
angle = acosd(np.sum(vec[0]*vec[1]))
# GSASIIpath.IPyBreak()
return angle
dx = .00001
deriv = np.zeros(9)
for i in [0,1,2]:
Oxyz[i] -= dx
a0 = calcAngle(Oxyz,[Axyz,Bxyz],Amat,Tunit,symNo,SGData)
Oxyz[i] += 2*dx
deriv[i] = (calcAngle(Oxyz,[Axyz,Bxyz],Amat,Tunit,symNo,SGData)-a0)/(2.*dx)
Oxyz[i] -= dx
Axyz[i] -= dx
a0 = calcAngle(Oxyz,[Axyz,Bxyz],Amat,Tunit,symNo,SGData)
Axyz[i] += 2*dx
deriv[i+3] = (calcAngle(Oxyz,[Axyz,Bxyz],Amat,Tunit,symNo,SGData)-a0)/(2.*dx)
Axyz[i] -= dx
Bxyz[i] -= dx
a0 = calcAngle(Oxyz,[Axyz,Bxyz],Amat,Tunit,symNo,SGData)
Bxyz[i] += 2*dx
deriv[i+6] = (calcAngle(Oxyz,[Axyz,Bxyz],Amat,Tunit,symNo,SGData)-a0)/(2.*dx)
Bxyz[i] -= dx
return deriv
[docs]def getAngSig(VA,VB,Amat,SGData,covData={}):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcVec(Ox,Tx,U,inv,C,M,T,Amat):
TxT = inv*(np.inner(M,Tx)+T)+C+U
return np.inner(Amat,(TxT-Ox))
def calcAngle(Ox,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat):
VecA = calcVec(Ox,TxA,unitA,invA,CA,MA,TA,Amat)
VecA /= np.sqrt(np.sum(VecA**2))
VecB = calcVec(Ox,TxB,unitB,invB,CB,MB,TB,Amat)
VecB /= np.sqrt(np.sum(VecB**2))
edge = VecB-VecA
edge = np.sum(edge**2)
angle = (2.-edge)/2.
angle = max(angle,-1.)
return acosd(angle)
OxAN,OxA,TxAN,TxA,unitA,TopA = VA
OxBN,OxB,TxBN,TxB,unitB,TopB = VB
invA = invB = 1
invA = TopA//abs(TopA)
invB = TopB//abs(TopB)
centA = abs(TopA)//100
centB = abs(TopB)//100
opA = abs(TopA)%100-1
opB = abs(TopB)%100-1
MA,TA = SGData['SGOps'][opA]
MB,TB = SGData['SGOps'][opB]
CA = SGData['SGCen'][centA]
CB = SGData['SGCen'][centB]
if 'covMatrix' in covData:
covMatrix = covData['covMatrix']
varyList = covData['varyList']
AngVcov = getVCov(OxAN+TxAN+TxBN,varyList,covMatrix)
dx = .00001
dadx = np.zeros(9)
Ang = calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)
for i in [0,1,2]:
OxA[i] -= dx
a0 = calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)
OxA[i] += 2*dx
dadx[i] = (calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)-a0)/(2*dx)
OxA[i] -= dx
TxA[i] -= dx
a0 = calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)
TxA[i] += 2*dx
dadx[i+3] = (calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)-a0)/(2*dx)
TxA[i] -= dx
TxB[i] -= dx
a0 = calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)
TxB[i] += 2*dx
dadx[i+6] = (calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat)-a0)/(2*dx)
TxB[i] -= dx
sigAng = np.sqrt(np.inner(dadx,np.inner(AngVcov,dadx)))
if sigAng < 0.01:
sigAng = 0.0
return Ang,sigAng
else:
return calcAngle(OxA,TxA,TxB,unitA,unitB,invA,CA,MA,TA,invB,CB,MB,TB,Amat),0.0
[docs]def GetDistSig(Oatoms,Atoms,Amat,SGData,covData={}):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcDist(Atoms,SyOps,Amat):
XYZ = []
for i,atom in enumerate(Atoms):
Inv,M,T,C,U = SyOps[i]
XYZ.append(np.array(atom[1:4]))
XYZ[-1] = Inv*(np.inner(M,np.array(XYZ[-1]))+T)+C+U
XYZ[-1] = np.inner(Amat,XYZ[-1]).T
V1 = XYZ[1]-XYZ[0]
return np.sqrt(np.sum(V1**2))
SyOps = []
names = []
for i,atom in enumerate(Oatoms):
names += atom[-1]
Op,unit = Atoms[i][-1]
inv = Op//abs(Op)
m,t = SGData['SGOps'][abs(Op)%100-1]
c = SGData['SGCen'][abs(Op)//100]
SyOps.append([inv,m,t,c,unit])
Dist = calcDist(Oatoms,SyOps,Amat)
sig = -0.001
if 'covMatrix' in covData:
dx = .00001
dadx = np.zeros(6)
for i in range(6):
ia = i//3
ix = i%3
Oatoms[ia][ix+1] += dx
a0 = calcDist(Oatoms,SyOps,Amat)
Oatoms[ia][ix+1] -= 2*dx
dadx[i] = (calcDist(Oatoms,SyOps,Amat)-a0)/(2.*dx)
covMatrix = covData['covMatrix']
varyList = covData['varyList']
DistVcov = getVCov(names,varyList,covMatrix)
sig = np.sqrt(np.inner(dadx,np.inner(DistVcov,dadx)))
if sig < 0.001:
sig = -0.001
return Dist,sig
[docs]def GetAngleSig(Oatoms,Atoms,Amat,SGData,covData={}):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcAngle(Atoms,SyOps,Amat):
XYZ = []
for i,atom in enumerate(Atoms):
Inv,M,T,C,U = SyOps[i]
XYZ.append(np.array(atom[1:4]))
XYZ[-1] = Inv*(np.inner(M,np.array(XYZ[-1]))+T)+C+U
XYZ[-1] = np.inner(Amat,XYZ[-1]).T
V1 = XYZ[1]-XYZ[0]
V1 /= np.sqrt(np.sum(V1**2))
V2 = XYZ[1]-XYZ[2]
V2 /= np.sqrt(np.sum(V2**2))
V3 = V2-V1
cang = min(1.,max((2.-np.sum(V3**2))/2.,-1.))
return acosd(cang)
SyOps = []
names = []
for i,atom in enumerate(Oatoms):
names += atom[-1]
Op,unit = Atoms[i][-1]
inv = Op//abs(Op)
m,t = SGData['SGOps'][abs(Op)%100-1]
c = SGData['SGCen'][abs(Op)//100]
SyOps.append([inv,m,t,c,unit])
Angle = calcAngle(Oatoms,SyOps,Amat)
sig = -0.01
if 'covMatrix' in covData:
dx = .00001
dadx = np.zeros(9)
for i in range(9):
ia = i//3
ix = i%3
Oatoms[ia][ix+1] += dx
a0 = calcAngle(Oatoms,SyOps,Amat)
Oatoms[ia][ix+1] -= 2*dx
dadx[i] = (calcAngle(Oatoms,SyOps,Amat)-a0)/(2.*dx)
covMatrix = covData['covMatrix']
varyList = covData['varyList']
AngVcov = getVCov(names,varyList,covMatrix)
sig = np.sqrt(np.inner(dadx,np.inner(AngVcov,dadx)))
if sig < 0.01:
sig = -0.01
return Angle,sig
[docs]def GetTorsionSig(Oatoms,Atoms,Amat,SGData,covData={}):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcTorsion(Atoms,SyOps,Amat):
XYZ = []
for i,atom in enumerate(Atoms):
Inv,M,T,C,U = SyOps[i]
XYZ.append(np.array(atom[1:4]))
XYZ[-1] = Inv*(np.inner(M,np.array(XYZ[-1]))+T)+C+U
XYZ[-1] = np.inner(Amat,XYZ[-1]).T
V1 = XYZ[1]-XYZ[0]
V2 = XYZ[2]-XYZ[1]
V3 = XYZ[3]-XYZ[2]
V1 /= np.sqrt(np.sum(V1**2))
V2 /= np.sqrt(np.sum(V2**2))
V3 /= np.sqrt(np.sum(V3**2))
M = np.array([V1,V2,V3])
D = nl.det(M)
P12 = np.dot(V1,V2)
P13 = np.dot(V1,V3)
P23 = np.dot(V2,V3)
Tors = acosd((P12*P23-P13)/(np.sqrt(1.-P12**2)*np.sqrt(1.-P23**2)))*D/abs(D)
return Tors
SyOps = []
names = []
for i,atom in enumerate(Oatoms):
names += atom[-1]
Op,unit = Atoms[i][-1]
inv = Op//abs(Op)
m,t = SGData['SGOps'][abs(Op)%100-1]
c = SGData['SGCen'][abs(Op)//100]
SyOps.append([inv,m,t,c,unit])
Tors = calcTorsion(Oatoms,SyOps,Amat)
sig = -0.01
if 'covMatrix' in covData:
dx = .00001
dadx = np.zeros(12)
for i in range(12):
ia = i//3
ix = i%3
Oatoms[ia][ix+1] -= dx
a0 = calcTorsion(Oatoms,SyOps,Amat)
Oatoms[ia][ix+1] += 2*dx
dadx[i] = (calcTorsion(Oatoms,SyOps,Amat)-a0)/(2.*dx)
Oatoms[ia][ix+1] -= dx
covMatrix = covData['covMatrix']
varyList = covData['varyList']
TorVcov = getVCov(names,varyList,covMatrix)
sig = np.sqrt(np.inner(dadx,np.inner(TorVcov,dadx)))
if sig < 0.01:
sig = -0.01
return Tors,sig
[docs]def GetDATSig(Oatoms,Atoms,Amat,SGData,covData={}):
'''default doc string
:param type name: description
:returns: type name: description
'''
def calcDist(Atoms,SyOps,Amat):
XYZ = []
for i,atom in enumerate(Atoms):
Inv,M,T,C,U = SyOps[i]
XYZ.append(np.array(atom[1:4]))
XYZ[-1] = Inv*(np.inner(M,np.array(XYZ[-1]))+T)+C+U
XYZ[-1] = np.inner(Amat,XYZ[-1]).T
V1 = XYZ[1]-XYZ[0]
return np.sqrt(np.sum(V1**2))
def calcAngle(Atoms,SyOps,Amat):
XYZ = []
for i,atom in enumerate(Atoms):
Inv,M,T,C,U = SyOps[i]
XYZ.append(np.array(atom[1:4]))
XYZ[-1] = Inv*(np.inner(M,np.array(XYZ[-1]))+T)+C+U
XYZ[-1] = np.inner(Amat,XYZ[-1]).T
V1 = XYZ[1]-XYZ[0]
V1 /= np.sqrt(np.sum(V1**2))
V2 = XYZ[1]-XYZ[2]
V2 /= np.sqrt(np.sum(V2**2))
V3 = V2-V1
cang = min(1.,max((2.-np.sum(V3**2))/2.,-1.))
return acosd(cang)
def calcTorsion(Atoms,SyOps,Amat):
XYZ = []
for i,atom in enumerate(Atoms):
Inv,M,T,C,U = SyOps[i]
XYZ.append(np.array(atom[1:4]))
XYZ[-1] = Inv*(np.inner(M,np.array(XYZ[-1]))+T)+C+U
XYZ[-1] = np.inner(Amat,XYZ[-1]).T
V1 = XYZ[1]-XYZ[0]
V2 = XYZ[2]-XYZ[1]
V3 = XYZ[3]-XYZ[2]
V1 /= np.sqrt(np.sum(V1**2))
V2 /= np.sqrt(np.sum(V2**2))
V3 /= np.sqrt(np.sum(V3**2))
M = np.array([V1,V2,V3])
D = nl.det(M)
P12 = np.dot(V1,V2)
P13 = np.dot(V1,V3)
P23 = np.dot(V2,V3)
Tors = acosd((P12*P23-P13)/(np.sqrt(1.-P12**2)*np.sqrt(1.-P23**2)))*D/abs(D)
return Tors
SyOps = []
names = []
for i,atom in enumerate(Oatoms):
names += atom[-1]
Op,unit = Atoms[i][-1]
inv = Op//abs(Op)
m,t = SGData['SGOps'][abs(Op)%100-1]
c = SGData['SGCen'][abs(Op)//100]
SyOps.append([inv,m,t,c,unit])
M = len(Oatoms)
if M == 2:
Val = calcDist(Oatoms,SyOps,Amat)
elif M == 3:
Val = calcAngle(Oatoms,SyOps,Amat)
else:
Val = calcTorsion(Oatoms,SyOps,Amat)
sigVals = [-0.001,-0.01,-0.01]
sig = sigVals[M-3]
if 'covMatrix' in covData:
dx = .00001
N = M*3
dadx = np.zeros(N)
for i in range(N):
ia = i//3
ix = i%3
Oatoms[ia][ix+1] += dx
if M == 2:
a0 = calcDist(Oatoms,SyOps,Amat)
elif M == 3:
a0 = calcAngle(Oatoms,SyOps,Amat)
else:
a0 = calcTorsion(Oatoms,SyOps,Amat)
Oatoms[ia][ix+1] -= 2*dx
if M == 2:
dadx[i] = (calcDist(Oatoms,SyOps,Amat)-a0)/(2.*dx)
elif M == 3:
dadx[i] = (calcAngle(Oatoms,SyOps,Amat)-a0)/(2.*dx)
else:
dadx[i] = (calcTorsion(Oatoms,SyOps,Amat)-a0)/(2.*dx)
covMatrix = covData['covMatrix']
varyList = covData['varyList']
Vcov = getVCov(names,varyList,covMatrix)
sig = np.sqrt(np.inner(dadx,np.inner(Vcov,dadx)))
if sig < sigVals[M-3]:
sig = sigVals[M-3]
return Val,sig
[docs]def ValEsd(value,esd=0,nTZ=False):
'''Format a floating point number with a given level of precision or
with in crystallographic format with a "esd", as value(esd). If esd is
negative the number is formatted with the level of significant figures
appropriate if abs(esd) were the esd, but the esd is not included.
if the esd is zero, approximately 6 significant figures are printed.
nTZ=True causes "extra" zeros to be removed after the decimal place.
for example:
* "1.235(3)" for value=1.2346 & esd=0.003
* "1.235(3)e4" for value=12346. & esd=30
* "1.235(3)e6" for value=0.12346e7 & esd=3000
* "1.235" for value=1.2346 & esd=-0.003
* "1.240" for value=1.2395 & esd=-0.003
* "1.24" for value=1.2395 & esd=-0.003 with nTZ=True
* "1.23460" for value=1.2346 & esd=0.0
:param float value: number to be formatted
:param float esd: uncertainty or if esd < 0, specifies level of
precision to be shown e.g. esd=-0.01 gives 2 places beyond decimal
:param bool nTZ: True to remove trailing zeros (default is False)
:returns: value(esd) or value as a string
'''
# Note: this routine is Python 3 compatible -- I think
cutoff = 3.16228 #=(sqrt(10); same as old GSAS was 1.95
if math.isnan(value): # invalid value, bail out
return '?'
if math.isnan(esd): # invalid esd, treat as zero
esd = 0
esdoff = 5
# if esd < 1.e-5:
# esd = 0
# esdoff = 5
elif esd != 0:
# transform the esd to a one or two digit integer
l = math.log10(abs(esd)) % 1.
if l < math.log10(cutoff): l+= 1.
intesd = int(round(10**l)) # esd as integer
# determine the number of digits offset for the esd
esdoff = int(round(math.log10(intesd*1./abs(esd))))
else:
esdoff = 5
valoff = 0
if abs(value) < abs(esdoff): # value is effectively zero
pass
elif esdoff < 0 or abs(value) > 1.0e6 or abs(value) < 1.0e-4: # use scientific notation
# where the digit offset is to the left of the decimal place or where too many
# digits are needed
if abs(value) > 1:
valoff = int(math.log10(abs(value)))
elif abs(value) > 0:
valoff = int(math.log10(abs(value))-0.9999999)
else:
valoff = 0
if esd != 0:
if valoff+esdoff < 0:
valoff = esdoff = 0
out = ("{:."+str(valoff+esdoff)+"f}").format(value/10**valoff) # format the value
elif valoff != 0: # esd = 0; exponential notation ==> esdoff decimal places
out = ("{:."+str(esdoff)+"f}").format(value/10**valoff) # format the value
else: # esd = 0; non-exponential notation ==> esdoff+1 significant digits
if abs(value) > 0:
extra = -math.log10(abs(value))
else:
extra = 0
if extra > 0: extra += 1
out = ("{:."+str(max(0,esdoff+int(extra)))+"f}").format(value) # format the value
if esd > 0:
out += ("({:d})").format(intesd) # add the esd
elif nTZ and '.' in out:
out = out.rstrip('0') # strip zeros to right of decimal
out = out.rstrip('.') # and decimal place when not needed
if valoff != 0:
out += ("e{:d}").format(valoff) # add an exponent, when needed
return out
###############################################################################
#### Protein validation - "ERRATV2" analysis
###############################################################################
def validProtein(Phase,old):
def sumintact(intact):
return {'CC':intact['CC'],'NN':intact['NN'],'OO':intact['OO'],
'CN':(intact['CN']+intact['NC']),'CO':(intact['CO']+intact['OC']),
'NO':(intact['NO']+intact['ON'])}
resNames = ['ALA','ARG','ASN','ASP','CYS','GLN','GLU','GLY','HIS','ILE',
'LEU','LYS','MET','PHE','PRO','SER','THR','TRP','TYR','VAL','MSE']
# data from errat.f
b1_old = np.array([
[1154.343, 600.213, 1051.018, 1132.885, 960.738],
[600.213, 1286.818, 1282.042, 957.156, 612.789],
[1051.018, 1282.042, 3519.471, 991.974, 1226.491],
[1132.885, 957.156, 991.974, 1798.672, 820.355],
[960.738, 612.789, 1226.491, 820.355, 2428.966]
])
avg_old = np.array([ 0.225, 0.281, 0.071, 0.237, 0.044]) #Table 1 3.5A Obsd. Fr. p 1513
# data taken from erratv2.ccp
b1 = np.array([
[5040.279078850848200, 3408.805141583649400, 4152.904423767300600, 4236.200004171890200, 5054.781210204625500],
[3408.805141583648900, 8491.906094010220800, 5958.881777877950300, 1521.387352718486200, 4304.078200827221700],
[4152.904423767301500, 5958.881777877952100, 7637.167089335050100, 6620.715738223072500, 5287.691183798410700],
[4236.200004171890200, 1521.387352718486200, 6620.715738223072500, 18368.343774298410000, 4050.797811118806700],
[5054.781210204625500, 4304.078200827220800, 5287.691183798409800, 4050.797811118806700, 6666.856740479164700]])
avg = np.array([0.192765509919262, 0.195575208778518, 0.275322406824210, 0.059102357035642, 0.233154192767480])
General = Phase['General']
Amat,Bmat = G2lat.cell2AB(General['Cell'][1:7])
cx,ct,cs,cia = getAtomPtrs(Phase)
Atoms = Phase['Atoms']
cartAtoms = []
xyzmin = 999.*np.ones(3)
xyzmax = -999.*np.ones(3)
#select residue atoms,S,Se --> O make cartesian
for atom in Atoms:
if atom[1] in resNames:
cartAtoms.append(atom[:cx+3])
if atom[4].strip() in ['S','Se']:
if not old:
continue #S,Se skipped for erratv2?
cartAtoms[-1][3] = 'Os'
cartAtoms[-1][4] = 'O'
cartAtoms[-1][cx:cx+3] = np.inner(Amat,cartAtoms[-1][cx:cx+3])
cartAtoms[-1].append(atom[cia+8])
XYZ = np.array([atom[cx:cx+3] for atom in cartAtoms])
xyzmin = np.array([np.min(XYZ.T[i]) for i in [0,1,2]])
xyzmax = np.array([np.max(XYZ.T[i]) for i in [0,1,2]])
nbox = list(np.array(np.ceil((xyzmax-xyzmin)/4.),dtype=int))+[15,]
Boxes = np.zeros(nbox,dtype=int)
iBox = np.array([np.trunc((XYZ.T[i]-xyzmin[i])/4.) for i in [0,1,2]],dtype=int).T
for ib,box in enumerate(iBox): #put in a try for too many atoms in box (IndexError)?
try:
Boxes[box[0],box[1],box[2],0] += 1
Boxes[box[0],box[1],box[2],Boxes[box[0],box[1],box[2],0]] = ib
except IndexError:
G2fil.G2Print('Error: too many atoms in box' )
continue
#Box content checks with errat.f $ erratv2.cpp ibox1 arrays
indices = (-1,0,1)
Units = np.array([[h,k,l] for h in indices for k in indices for l in indices])
dsmax = 3.75**2
if old:
dsmax = 3.5**2
chains = []
resIntAct = []
chainIntAct = []
res = []
resNames = []
resIDs = {}
resname = []
resID = {}
newChain = True
intact = {'CC':0,'CN':0,'CO':0,'NN':0,'NO':0,'OO':0,'NC':0,'OC':0,'ON':0}
for ia,atom in enumerate(cartAtoms):
jntact = {'CC':0,'CN':0,'CO':0,'NN':0,'NO':0,'OO':0,'NC':0,'OC':0,'ON':0}
if atom[2] not in chains: #get chain id & save residue sequence from last chain
chains.append(atom[2])
if len(resIntAct):
resIntAct.append(sumintact(intact))
chainIntAct.append(resIntAct)
resNames += resname
resIDs.update(resID)
res = []
resname = []
resID = {}
resIntAct = []
intact = {'CC':0,'CN':0,'CO':0,'NN':0,'NO':0,'OO':0,'NC':0,'OC':0,'ON':0}
newChain = True
if atom[0] not in res: #new residue, get residue no.
if res and int(res[-1]) != int(atom[0])-1: #a gap in chain - not new chain
intact = {'CC':0,'CN':0,'CO':0,'NN':0,'NO':0,'OO':0,'NC':0,'OC':0,'ON':0}
ires = int(res[-1])
for i in range(int(atom[0])-ires-1):
res.append(str(ires+i+1))
resname.append('')
resIntAct.append(sumintact(intact))
res.append(atom[0])
name = '%s-%s%s'%(atom[2],atom[0],atom[1])
resname.append(name)
resID[name] = atom[-1]
if not newChain:
resIntAct.append(sumintact(intact))
intact = {'CC':0,'CN':0,'CO':0,'NN':0,'NO':0,'OO':0,'NC':0,'OC':0,'ON':0}
newChain = False
ibox = iBox[ia] #box location of atom
tgts = []
for unit in Units: #assemble list of all possible target atoms
jbox = ibox+unit
if np.all(jbox>=0) and np.all((jbox-nbox[:3])<0):
tgts += list(Boxes[jbox[0],jbox[1],jbox[2]])
tgts = list(set(tgts))
tgts = [tgt for tgt in tgts if atom[:3] != cartAtoms[tgt][:3]] #exclude same residue
tgts = [tgt for tgt in tgts if np.sum((XYZ[ia]-XYZ[tgt])**2) < dsmax]
ires = int(atom[0])
if old:
if atom[3].strip() == 'C':
tgts = [tgt for tgt in tgts if not (cartAtoms[tgt][3].strip() == 'N' and int(cartAtoms[tgt][0]) in [ires-1,ires+1])]
elif atom[3].strip() == 'N':
tgts = [tgt for tgt in tgts if not (cartAtoms[tgt][3].strip() in ['C','CA'] and int(cartAtoms[tgt][0]) in [ires-1,ires+1])]
elif atom[3].strip() == 'CA':
tgts = [tgt for tgt in tgts if not (cartAtoms[tgt][3].strip() == 'N' and int(cartAtoms[tgt][0]) in [ires-1,ires+1])]
else:
tgts = [tgt for tgt in tgts if not int(cartAtoms[tgt][0]) in [ires+1,ires+2,ires+3,ires+4,ires+5,ires+6,ires+7,ires+8]]
if atom[3].strip() == 'C':
tgts = [tgt for tgt in tgts if not (cartAtoms[tgt][3].strip() == 'N' and int(cartAtoms[tgt][0]) == ires+1)]
elif atom[3].strip() == 'N':
tgts = [tgt for tgt in tgts if not (cartAtoms[tgt][3].strip() == 'C' and int(cartAtoms[tgt][0]) == ires-1)]
for tgt in tgts:
dsqt = np.sqrt(np.sum((XYZ[ia]-XYZ[tgt])**2))
mult = 1.0
if dsqt > 3.25 and not old:
mult = 2.*(3.75-dsqt)
intype = atom[4].strip()+cartAtoms[tgt][4].strip()
if 'S' not in intype:
intact[intype] += mult
jntact[intype] += mult
# print ia,atom[0]+atom[1]+atom[3],tgts,jntact['CC'],jntact['CN']+jntact['NC'],jntact['CO']+jntact['OC'],jntact['NN'],jntact['NO']+jntact['ON']
resNames += resname
resIDs.update(resID)
resIntAct.append(sumintact(intact))
chainIntAct.append(resIntAct)
chainProb = []
for ich,chn in enumerate(chains):
IntAct = chainIntAct[ich]
nRes = len(IntAct)
Probs = [0.,0.,0.,0.] #skip 1st 4 residues in chain
for i in range(4,nRes-4):
if resNames[i]:
mtrx = np.zeros(5)
summ = 0.
for j in range(i-4,i+5):
summ += np.sum(np.array(list(IntAct[j].values())))
if old:
mtrx[0] += IntAct[j]['CC']
mtrx[1] += IntAct[j]['CO']
mtrx[2] += IntAct[j]['NN']
mtrx[3] += IntAct[j]['NO']
mtrx[4] += IntAct[j]['OO']
else:
mtrx[0] += IntAct[j]['CC']
mtrx[1] += IntAct[j]['CN']
mtrx[2] += IntAct[j]['CO']
mtrx[3] += IntAct[j]['NN']
mtrx[4] += IntAct[j]['NO']
mtrx /= summ
# print i+1,mtrx*summ
if old:
mtrx -= avg_old
prob = np.inner(np.inner(mtrx,b1_old),mtrx)
else:
mtrx -= avg
prob = np.inner(np.inner(mtrx,b1),mtrx)
else: #skip the gaps
prob = 0.0
Probs.append(prob)
Probs += 4*[0.,] #skip last 4 residues in chain
chainProb += Probs
return resNames,chainProb,resIDs
################################################################################
#### Texture fitting stuff
################################################################################
def FitTexture(General,Gangls,refData,keyList,pgbar):
import pytexture as ptx
ptx.pyqlmninit() #initialize fortran arrays for spherical harmonics
def printSpHarm(textureData,SHtextureSig):
Tindx = 1.0
Tvar = 0.0
print ('\n Spherical harmonics texture: Order:' + str(textureData['Order']))
names = ['omega','chi','phi']
namstr = ' names :'
ptstr = ' values:'
sigstr = ' esds :'
for name in names:
namstr += '%12s'%('Sample '+name)
ptstr += '%12.3f'%(textureData['Sample '+name][1])
if 'Sample '+name in SHtextureSig:
sigstr += '%12.3f'%(SHtextureSig['Sample '+name])
else:
sigstr += 12*' '
print (namstr)
print (ptstr)
print (sigstr)
print ('\n Texture coefficients:')
SHcoeff = textureData['SH Coeff'][1]
SHkeys = list(SHcoeff.keys())
nCoeff = len(SHcoeff)
nBlock = nCoeff//10+1
iBeg = 0
iFin = min(iBeg+10,nCoeff)
for block in range(nBlock):
namstr = ' names :'
ptstr = ' values:'
sigstr = ' esds :'
for name in SHkeys[iBeg:iFin]:
if 'C' in name:
l = 2.0*eval(name.strip('C'))[0]+1
Tindx += SHcoeff[name]**2/l
namstr += '%12s'%(name)
ptstr += '%12.3f'%(SHcoeff[name])
if name in SHtextureSig:
Tvar += (2.*SHcoeff[name]*SHtextureSig[name]/l)**2
sigstr += '%12.3f'%(SHtextureSig[name])
else:
sigstr += 12*' '
print (namstr)
print (ptstr)
print (sigstr)
iBeg += 10
iFin = min(iBeg+10,nCoeff)
print(' Texture index J = %.3f(%d)'%(Tindx,int(1000*np.sqrt(Tvar))))
def Dict2Values(parmdict, varylist):
'''Use before call to leastsq to setup list of values for the parameters
in parmdict, as selected by key in varylist'''
return [parmdict[key] for key in varylist]
def Values2Dict(parmdict, varylist, values):
''' Use after call to leastsq to update the parameter dictionary with
values corresponding to keys in varylist'''
parmdict.update(list(zip(varylist,values)))
def errSpHarm(values,SGData,cell,Gangls,shModel,refData,parmDict,varyList,pgbar):
parmDict.update(list(zip(varyList,values)))
Mat = np.empty(0)
sumObs = 0
Sangls = [parmDict['Sample '+'omega'],parmDict['Sample '+'chi'],parmDict['Sample '+'phi']]
for hist in Gangls.keys():
Refs = refData[hist]
Refs[:,5] = np.where(Refs[:,5]>0.,Refs[:,5],0.)
wt = 1./np.sqrt(np.fmax(Refs[:,4],.25))
# wt = 1./np.max(Refs[:,4],.25)
sumObs += np.sum(wt*Refs[:,5])
Refs[:,6] = 1.
H = Refs[:,:3]
phi,beta = G2lat.CrsAng(H,cell,SGData)
psi,gam,x,x = G2lat.SamAng(Refs[:,3]/2.,Gangls[hist],Sangls,False) #assume not Bragg-Brentano!
for item in parmDict:
if 'C' in item:
L,M,N = eval(item.strip('C'))
Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta)
Ksl,x,x = G2lat.GetKsl(L,M,shModel,psi,gam)
Lnorm = G2lat.Lnorm(L)
Refs[:,6] += parmDict[item]*Lnorm*Kcl*Ksl
mat = wt*(Refs[:,5]-Refs[:,6])
Mat = np.concatenate((Mat,mat))
sumD = np.sum(np.abs(Mat))
R = min(100.,100.*sumD/sumObs)
pgbar.Raise()
pgbar.Update(R,newmsg='Residual = %5.2f'%(R))
print (' Residual: %.3f%%'%(R))
return Mat
def dervSpHarm(values,SGData,cell,Gangls,shModel,refData,parmDict,varyList,pgbar):
Mat = np.empty(0)
Sangls = [parmDict['Sample omega'],parmDict['Sample chi'],parmDict['Sample phi']]
for hist in Gangls.keys():
mat = np.zeros((len(varyList),len(refData[hist])))
Refs = refData[hist]
H = Refs[:,:3]
wt = 1./np.sqrt(np.fmax(Refs[:,4],.25))
# wt = 1./np.max(Refs[:,4],.25)
phi,beta = G2lat.CrsAng(H,cell,SGData)
psi,gam,dPdA,dGdA = G2lat.SamAng(Refs[:,3]/2.,Gangls[hist],Sangls,False) #assume not Bragg-Brentano!
for j,item in enumerate(varyList):
if 'C' in item:
L,M,N = eval(item.strip('C'))
Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta)
Ksl,dKdp,dKdg = G2lat.GetKsl(L,M,shModel,psi,gam)
Lnorm = G2lat.Lnorm(L)
mat[j] = -wt*Lnorm*Kcl*Ksl
for k,itema in enumerate(['Sample omega','Sample chi','Sample phi']):
try:
l = varyList.index(itema)
mat[l] -= parmDict[item]*wt*Lnorm*Kcl*(dKdp*dPdA[k]+dKdg*dGdA[k])
except ValueError:
pass
if len(Mat):
Mat = np.concatenate((Mat,mat.T))
else:
Mat = mat.T
print ('deriv')
return Mat
print (' Fit texture for '+General['Name'])
SGData = General['SGData']
cell = General['Cell'][1:7]
Texture = General['SH Texture']
if not Texture['Order']:
return 'No spherical harmonics coefficients'
varyList = []
parmDict = copy.copy(Texture['SH Coeff'][1])
for item in ['Sample omega','Sample chi','Sample phi']:
parmDict[item] = Texture[item][1]
if Texture[item][0]:
varyList.append(item)
if Texture['SH Coeff'][0]:
varyList += list(Texture['SH Coeff'][1].keys())
while True:
begin = time.time()
values = np.array(Dict2Values(parmDict, varyList))
result = so.leastsq(errSpHarm,values,Dfun=dervSpHarm,full_output=True,ftol=1.e-6,
args=(SGData,cell,Gangls,Texture['Model'],refData,parmDict,varyList,pgbar))
ncyc = int(result[2]['nfev']//2)
if ncyc:
runtime = time.time()-begin
chisq = np.sum(result[2]['fvec']**2)
Values2Dict(parmDict, varyList, result[0])
GOF = chisq/(len(result[2]['fvec'])-len(varyList)) #reduced chi^2
G2fil.G2Print ('Number of function calls: %d Number of observations: %d Number of parameters: %d'%(result[2]['nfev'],len(result[2]['fvec']),len(varyList)))
G2fil.G2Print ('refinement time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc))
try:
sig = np.sqrt(np.diag(result[1])*GOF)
if np.any(np.isnan(sig)):
G2fil.G2Print ('*** Least squares aborted - some invalid esds possible ***', mode='error')
break #refinement succeeded - finish up!
except ValueError: #result[1] is None on singular matrix
G2fil.G2Print ('**** Refinement failed - singular matrix ****', mode='error')
return None
else:
break
if ncyc:
for parm in parmDict:
if 'C' in parm:
Texture['SH Coeff'][1][parm] = parmDict[parm]
else:
Texture[parm][1] = parmDict[parm]
sigDict = dict(zip(varyList,sig))
printSpHarm(Texture,sigDict)
return None
################################################################################
#### Fourier & charge flip stuff
################################################################################
[docs]def adjHKLmax(SGData,Hmax):
'''default doc string
:param type name: description
:returns: type name: description
'''
if SGData['SGLaue'] in ['3','3m1','31m','6/m','6/mmm']:
Hmax[0] = int(math.ceil(Hmax[0]/6.))*6
Hmax[1] = int(math.ceil(Hmax[1]/6.))*6
Hmax[2] = int(math.ceil(Hmax[2]/4.))*4
else:
Hmax[0] = int(math.ceil(Hmax[0]/4.))*4
Hmax[1] = int(math.ceil(Hmax[1]/4.))*4
Hmax[2] = int(math.ceil(Hmax[2]/4.))*4
[docs]def OmitMap(data,reflDict,pgbar=None):
'''default doc string
:param type name: description
:returns: type name: description
'''
generalData = data['General']
if not generalData['Map']['MapType']:
G2fil.G2Print ('**** ERROR - Fourier map not defined')
return
mapData = generalData['Map']
dmin = mapData['GridStep']*2.
SGData = generalData['SGData']
SGMT = np.array([ops[0].T for ops in SGData['SGOps']])
SGT = np.array([ops[1] for ops in SGData['SGOps']])
cell = generalData['Cell'][1:8]
A = G2lat.cell2A(cell[:6])
Hmax = np.asarray(G2lat.getHKLmax(dmin,SGData,A),dtype='i')+1
adjHKLmax(SGData,Hmax)
Fhkl = np.zeros(shape=2*Hmax,dtype='c16')
time0 = time.time()
for iref,ref in enumerate(reflDict['RefList']):
if ref[4] >= dmin:
Fosq,Fcsq,ph = ref[8:11]
Uniq = np.inner(ref[:3],SGMT)
Phi = np.inner(ref[:3],SGT)
for i,hkl in enumerate(Uniq): #uses uniq
hkl = np.asarray(hkl,dtype='i')
dp = 360.*Phi[i] #and phi
a = cosd(ph+dp)
b = sind(ph+dp)
phasep = complex(a,b)
phasem = complex(a,-b)
if '2Fo-Fc' in mapData['MapType']:
F = 2.*np.sqrt(Fosq)-np.sqrt(Fcsq)
else:
F = np.sqrt(Fosq)
h,k,l = hkl+Hmax
Fhkl[h,k,l] = F*phasep
h,k,l = -hkl+Hmax
Fhkl[h,k,l] = F*phasem
rho0 = fft.fftn(fft.fftshift(Fhkl))/cell[6]
M = np.mgrid[0:4,0:4,0:4]
blkIds = np.array(list(zip(M[0].flatten(),M[1].flatten(),M[2].flatten())))
iBeg = blkIds*rho0.shape//4
iFin = (blkIds+1)*rho0.shape//4
rho_omit = np.zeros_like(rho0)
nBlk = 0
for iB,iF in zip(iBeg,iFin):
rho1 = np.copy(rho0)
rho1[iB[0]:iF[0],iB[1]:iF[1],iB[2]:iF[2]] = 0.
Fnew = fft.ifftshift(fft.ifftn(rho1))
Fnew = np.where(Fnew,Fnew,1.0) #avoid divide by zero
phase = Fnew/np.absolute(Fnew)
OFhkl = np.absolute(Fhkl)*phase
rho1 = np.real(fft.fftn(fft.fftshift(OFhkl)))*(1.+0j)
rho_omit[iB[0]:iF[0],iB[1]:iF[1],iB[2]:iF[2]] = np.copy(rho1[iB[0]:iF[0],iB[1]:iF[1],iB[2]:iF[2]])
nBlk += 1
pgbar.Raise()
pgbar.Update(nBlk)
mapData['rho'] = np.real(rho_omit)/cell[6]
mapData['rhoMax'] = max(np.max(mapData['rho']),-np.min(mapData['rho']))
mapData['minmax'] = [np.max(mapData['rho']),np.min(mapData['rho'])]
G2fil.G2Print ('Omit map time: %.4f no. elements: %d dimensions: %s'%(time.time()-time0,Fhkl.size,str(Fhkl.shape)))
return mapData
[docs]def FourierMap(data,reflDict):
'''default doc string
:param type name: description
:returns: type name: description
'''
generalData = data['General']
mapData = generalData['Map']
dmin = mapData['GridStep']*2.
SGData = generalData['SGData']
SGMT = np.array([ops[0].T for ops in SGData['SGOps']])
SGT = np.array([ops[1] for ops in SGData['SGOps']])
cell = generalData['Cell'][1:8]
A = G2lat.cell2A(cell[:6])
Hmax = np.asarray(G2lat.getHKLmax(dmin,SGData,A),dtype='i')+1
adjHKLmax(SGData,Hmax)
Fhkl = np.zeros(shape=2*Hmax,dtype='c16')
# Fhkl[0,0,0] = generalData['F000X']
time0 = time.time()
for iref,ref in enumerate(reflDict['RefList']):
if ref[4] > dmin:
Fosq,Fcsq,ph = ref[8:11]
Uniq = np.inner(ref[:3],SGMT)
Phi = np.inner(ref[:3],SGT)
for i,hkl in enumerate(Uniq): #uses uniq
hkl = np.asarray(hkl,dtype='i')
dp = 360.*Phi[i] #and phi
a = cosd(ph+dp)
b = sind(ph+dp)
phasep = complex(a,b)
phasem = complex(a,-b)
if 'Fobs' in mapData['MapType']:
F = np.where(Fosq>0.,np.sqrt(Fosq),0.)
h,k,l = hkl+Hmax
Fhkl[h,k,l] = F*phasep
h,k,l = -hkl+Hmax
Fhkl[h,k,l] = F*phasem
elif 'Fcalc' in mapData['MapType']:
F = np.sqrt(Fcsq)
h,k,l = hkl+Hmax
Fhkl[h,k,l] = F*phasep
h,k,l = -hkl+Hmax
Fhkl[h,k,l] = F*phasem
elif 'delt-F' in mapData['MapType']:
dF = np.where(Fosq>0.,np.sqrt(Fosq),0.)-np.sqrt(Fcsq)
h,k,l = hkl+Hmax
Fhkl[h,k,l] = dF*phasep
h,k,l = -hkl+Hmax
Fhkl[h,k,l] = dF*phasem
elif '2*Fo-Fc' in mapData['MapType']:
F = 2.*np.where(Fosq>0.,np.sqrt(Fosq),0.)-np.sqrt(Fcsq)
h,k,l = hkl+Hmax
Fhkl[h,k,l] = F*phasep
h,k,l = -hkl+Hmax
Fhkl[h,k,l] = F*phasem
elif 'Patterson' in mapData['MapType']:
h,k,l = hkl+Hmax
Fhkl[h,k,l] = complex(Fosq,0.)
h,k,l = -hkl+Hmax
Fhkl[h,k,l] = complex(Fosq,0.)
rho = fft.fftn(fft.fftshift(Fhkl))/cell[6]
G2fil.G2Print ('Fourier map time: %.4f no. elements: %d dimensions: %s'%(time.time()-time0,Fhkl.size,str(Fhkl.shape)))
mapData['Type'] = reflDict['Type']
mapData['rho'] = np.real(rho)
mapData['rhoMax'] = max(np.max(mapData['rho']),-np.min(mapData['rho']))
mapData['minmax'] = [np.max(mapData['rho']),np.min(mapData['rho'])]
[docs]def Fourier4DMap(data,reflDict):
'''default doc string
:param type name: description
:returns: type name: description
'''
generalData = data['General']
map4DData = generalData['4DmapData']
mapData = generalData['Map']
dmin = mapData['GridStep']*2.
SGData = generalData['SGData']
SSGData = generalData['SSGData']
SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']])
SSGT = np.array([ops[1] for ops in SSGData['SSGOps']])
cell = generalData['Cell'][1:8]
A = G2lat.cell2A(cell[:6])
maxM = 4
Hmax = G2lat.getHKLmax(dmin,SGData,A)+[maxM,]
adjHKLmax(SGData,Hmax)
Hmax = np.asarray(Hmax,dtype='i')+1
Fhkl = np.zeros(shape=2*Hmax,dtype='c16')
time0 = time.time()
for iref,ref in enumerate(reflDict['RefList']):
if ref[5] > dmin:
Fosq,Fcsq,ph = ref[9:12]
Fosq = np.where(Fosq>0.,Fosq,0.) #can't use Fo^2 < 0
Uniq = np.inner(ref[:4],SSGMT)
Phi = np.inner(ref[:4],SSGT)
for i,hkl in enumerate(Uniq): #uses uniq
hkl = np.asarray(hkl,dtype='i')
dp = 360.*Phi[i] #and phi
a = cosd(ph+dp)
b = sind(ph+dp)
phasep = complex(a,b)
phasem = complex(a,-b)
if 'Fobs' in mapData['MapType']:
F = np.sqrt(Fosq)
h,k,l,m = hkl+Hmax
Fhkl[h,k,l,m] = F*phasep
h,k,l,m = -hkl+Hmax
Fhkl[h,k,l,m] = F*phasem
elif 'Fcalc' in mapData['MapType']:
F = np.sqrt(Fcsq)
h,k,l,m = hkl+Hmax
Fhkl[h,k,l,m] = F*phasep
h,k,l,m = -hkl+Hmax
Fhkl[h,k,l,m] = F*phasem
elif 'delt-F' in mapData['MapType']:
dF = np.sqrt(Fosq)-np.sqrt(Fcsq)
h,k,l,m = hkl+Hmax
Fhkl[h,k,l,m] = dF*phasep
h,k,l,m = -hkl+Hmax
Fhkl[h,k,l,m] = dF*phasem
SSrho = fft.fftn(fft.fftshift(Fhkl))/cell[6] #4D map
rho = fft.fftn(fft.fftshift(Fhkl[:,:,:,maxM+1]))/cell[6] #3D map
map4DData['rho'] = np.real(SSrho)
map4DData['rhoMax'] = max(np.max(map4DData['rho']),-np.min(map4DData['rho']))
map4DData['minmax'] = [np.max(map4DData['rho']),np.min(map4DData['rho'])]
map4DData['Type'] = reflDict['Type']
mapData['Type'] = reflDict['Type']
mapData['rho'] = np.real(rho)
mapData['rhoMax'] = max(np.max(mapData['rho']),-np.min(mapData['rho']))
mapData['minmax'] = [np.max(mapData['rho']),np.min(mapData['rho'])]
G2fil.G2Print ('Fourier map time: %.4f no. elements: %d dimensions: %s'%(time.time()-time0,Fhkl.size,str(Fhkl.shape)))
# map printing for testing purposes
[docs]def printRho(SGLaue,rho,rhoMax):
'''default doc string
:param type name: description
:returns: type name: description
'''
dim = len(rho.shape)
if dim == 2:
ix,jy = rho.shape
for j in range(jy):
line = ''
if SGLaue in ['3','3m1','31m','6/m','6/mmm']:
line += (jy-j)*' '
for i in range(ix):
r = int(100*rho[i,j]/rhoMax)
line += '%4d'%(r)
print (line+'\n')
else:
ix,jy,kz = rho.shape
for k in range(kz):
print ('k = %d'%k)
for j in range(jy):
line = ''
if SGLaue in ['3','3m1','31m','6/m','6/mmm']:
line += (jy-j)*' '
for i in range(ix):
r = int(100*rho[i,j,k]/rhoMax)
line += '%4d'%(r)
print (line+'\n')
## keep this
[docs]def findOffset(SGData,A,Fhkl):
'''default doc string
:param type name: description
:returns: type name: description
'''
if SGData['SpGrp'] == 'P 1':
return [0,0,0]
hklShape = Fhkl.shape
hklHalf = np.array(hklShape)//2
sortHKL = np.argsort(Fhkl.flatten())
Fdict = {}
for hkl in sortHKL:
HKL = np.unravel_index(hkl,hklShape)
F = Fhkl[HKL[0]][HKL[1]][HKL[2]]
if F == 0.:
break
Fdict['%.6f'%(np.absolute(F))] = hkl
Flist = np.flipud(np.sort(list(Fdict.keys())))
F = str(1.e6)
i = 0
DH = []
Dphi = []
Hmax = 2*np.asarray(G2lat.getHKLmax(3.5,SGData,A),dtype='i')
for F in Flist:
hkl = np.unravel_index(Fdict[F],hklShape)
if np.any(np.abs(hkl-hklHalf)-Hmax > 0):
continue
iabsnt,mulp,Uniq,Phi = G2spc.GenHKLf(list(hkl-hklHalf),SGData)
Uniq = np.array(Uniq,dtype='i')
Phi = np.array(Phi)
Uniq = np.concatenate((Uniq,-Uniq))+hklHalf # put in Friedel pairs & make as index to Farray
Phi = np.concatenate((Phi,-Phi)) # and their phase shifts
Fh0 = Fhkl[hkl[0],hkl[1],hkl[2]]
ang0 = np.angle(Fh0,deg=True)/360.
for H,phi in list(zip(Uniq,Phi))[1:]:
ang = (np.angle(Fhkl[int(H[0]),int(H[1]),int(H[2])],deg=True)/360.-phi)
dH = H-hkl
dang = ang-ang0
DH.append(dH)
Dphi.append((dang+.5) % 1.0)
if i > 20 or len(DH) > 30:
break
i += 1
DH = np.array(DH)
G2fil.G2Print (' map offset no.of terms: %d from %d reflections'%(len(DH),len(Flist)))
Dphi = np.array(Dphi)
steps = np.array(hklShape)
X,Y,Z = np.meshgrid(np.linspace(0,1,steps[0]),np.linspace(0,1,steps[1]),np.linspace(0,1,steps[2]))
XYZ = np.array(list(zip(X.flatten(),Y.flatten(),Z.flatten())))
Dang = (np.dot(XYZ,DH.T)+.5)%1.-Dphi
Mmap = np.reshape(np.sum((Dang)**2,axis=1),newshape=steps)/len(DH)
hist,bins = np.histogram(Mmap,bins=1000)
chisq = np.min(Mmap)
DX = -np.array(np.unravel_index(np.argmin(Mmap),Mmap.shape))
ptext = ' map offset chi**2: %.3f, map offset: %d %d %d'%(chisq,DX[0],DX[1],DX[2])
G2fil.G2Print(ptext)
return DX,ptext
[docs]def ChargeFlip(data,reflDict,pgbar):
'''default doc string
:param type name: description
:returns: type name: description
'''
generalData = data['General']
mapData = generalData['Map']
flipData = generalData['Flip']
FFtable = {}
if 'None' not in flipData['Norm element']:
normElem = flipData['Norm element'].upper()
FFs = G2el.GetFormFactorCoeff(normElem.split('+')[0].split('-')[0])
for ff in FFs:
if ff['Symbol'] == normElem:
FFtable.update(ff)
dmin = flipData['GridStep']*2.
SGData = generalData['SGData']
SGMT = np.array([ops[0].T for ops in SGData['SGOps']])
SGT = np.array([ops[1] for ops in SGData['SGOps']])
cell = generalData['Cell'][1:8]
A = G2lat.cell2A(cell[:6])
Vol = cell[6]
im = 0
if generalData['Modulated'] == True:
im = 1
Hmax = np.asarray(G2lat.getHKLmax(dmin,SGData,A),dtype='i')+1
adjHKLmax(SGData,Hmax)
Ehkl = np.zeros(shape=2*Hmax,dtype='c16') #2X64bits per complex no.
time0 = time.time()
for iref,ref in enumerate(reflDict['RefList']):
dsp = ref[4+im]
if im and ref[3]: #skip super lattice reflections - result is 3D projection
continue
if dsp > dmin:
ff = 0.1*Vol #est. no. atoms for ~10A**3/atom
if FFtable:
SQ = 0.25/dsp**2
ff *= G2el.ScatFac(FFtable,SQ)[0]
if ref[8+im] > 0.: #use only +ve Fobs**2
E = np.sqrt(ref[8+im])/ff
else:
E = 0.
ph = ref[10]
ph = rn.uniform(0.,360.)
Uniq = np.inner(ref[:3],SGMT)
Phi = np.inner(ref[:3],SGT)
for i,hkl in enumerate(Uniq): #uses uniq
hkl = np.asarray(hkl,dtype='i')
dp = 360.*Phi[i] #and phi
a = cosd(ph+dp)
b = sind(ph+dp)
phasep = complex(a,b)
phasem = complex(a,-b)
h,k,l = hkl+Hmax
Ehkl[h,k,l] = E*phasep
h,k,l = -hkl+Hmax
Ehkl[h,k,l] = E*phasem
# Ehkl[Hmax] = 0.00001 #this to preserve F[0,0,0]
testHKL = np.array(flipData['testHKL'])+Hmax
CEhkl = copy.copy(Ehkl)
MEhkl = ma.array(Ehkl,mask=(Ehkl==0.0))
Emask = ma.getmask(MEhkl)
sumE = np.sum(ma.array(np.absolute(CEhkl),mask=Emask))
Ncyc = 0
old = np.seterr(all='raise')
twophases = []
while True:
CErho = np.real(fft.fftn(fft.fftshift(CEhkl)))*(1.+0j)
CEsig = np.std(CErho)
CFrho = np.where(np.real(CErho) >= flipData['k-factor']*CEsig,CErho,-CErho)
CFrho = np.where(np.real(CErho) <= flipData['k-Max']*CEsig,CFrho,-CFrho) #solves U atom problem!
CFhkl = fft.ifftshift(fft.ifftn(CFrho))
CFhkl = np.where(CFhkl,CFhkl,1.0) #avoid divide by zero
phase = CFhkl/np.absolute(CFhkl)
twophases.append([np.angle(phase[h,k,l]) for h,k,l in testHKL])
CEhkl = np.absolute(Ehkl)*phase
Ncyc += 1
sumCF = np.sum(ma.array(np.absolute(CFhkl),mask=Emask))
DEhkl = np.absolute(np.absolute(Ehkl)/sumE-np.absolute(CFhkl)/sumCF)
Rcf = min(100.,np.sum(ma.array(DEhkl,mask=Emask)*100.))
if Rcf < 5.:
break
GoOn = pgbar.Update(Rcf,newmsg='%s%8.3f%s\n%s %d'%('Residual Rcf =',Rcf,'%','No.cycles = ',Ncyc))[0]
if not GoOn or Ncyc > 10000:
break
np.seterr(**old)
G2fil.G2Print (' Charge flip time: %.4f'%(time.time()-time0),'no. elements: %d'%(Ehkl.size))
CErho = np.real(fft.fftn(fft.fftshift(CEhkl)))/10. #? to get on same scale as e-map
ctext = ' No.cycles = %d Residual Rcf =%8.3f%s Map size: %s'%(Ncyc,Rcf,'%',str(CErho.shape))
G2fil.G2Print (ctext)
roll,ptext = findOffset(SGData,A,CEhkl) #CEhkl needs to be just the observed set, not the full set!
mapData['Rcf'] = Rcf
mapData['rho'] = np.roll(np.roll(np.roll(CErho,roll[0],axis=0),roll[1],axis=1),roll[2],axis=2)
mapData['rhoMax'] = max(np.max(mapData['rho']),-np.min(mapData['rho']))
mapData['minmax'] = [np.max(mapData['rho']),np.min(mapData['rho'])]
mapData['Type'] = reflDict['Type']
return mapData,twophases,ptext,ctext
[docs]def findSSOffset(SGData,SSGData,A,Fhklm):
'''default doc string
:param type name: description
:returns: type name: description
'''
if SGData['SpGrp'] == 'P 1':
return [0,0,0,0]
hklmShape = Fhklm.shape
hklmHalf = np.array(hklmShape)/2
sortHKLM = np.argsort(Fhklm.flatten())
Fdict = {}
for hklm in sortHKLM:
HKLM = np.unravel_index(hklm,hklmShape)
F = Fhklm[HKLM[0]][HKLM[1]][HKLM[2]][HKLM[3]]
if F == 0.:
break
Fdict['%.6f'%(np.absolute(F))] = hklm
Flist = np.flipud(np.sort(list(Fdict.keys())))
F = str(1.e6)
i = 0
DH = []
Dphi = []
SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']])
SSGT = np.array([ops[1] for ops in SSGData['SSGOps']])
Hmax = 2*np.asarray(G2lat.getHKLmax(3.5,SGData,A),dtype='i')
for F in Flist:
hklm = np.unravel_index(Fdict[F],hklmShape)
if np.any(np.abs(hklm-hklmHalf)[:3]-Hmax > 0):
continue
Uniq = np.inner(hklm-hklmHalf,SSGMT)
Phi = np.inner(hklm-hklmHalf,SSGT)
Uniq = np.concatenate((Uniq,-Uniq))+hklmHalf # put in Friedel pairs & make as index to Farray
Phi = np.concatenate((Phi,-Phi)) # and their phase shifts
Fh0 = Fhklm[hklm[0],hklm[1],hklm[2],hklm[3]]
ang0 = np.angle(Fh0,deg=True)/360.
for H,phi in list(zip(Uniq,Phi))[1:]:
H = np.array(H,dtype=int)
ang = (np.angle(Fhklm[H[0],H[1],H[2],H[3]],deg=True)/360.-phi)
dH = H-hklm
dang = ang-ang0
DH.append(dH)
Dphi.append((dang+.5) % 1.0)
if i > 20 or len(DH) > 30:
break
i += 1
DH = np.array(DH)
G2fil.G2Print (' map offset no.of terms: %d from %d reflections'%(len(DH),len(Flist)))
Dphi = np.array(Dphi)
steps = np.array(hklmShape)
X,Y,Z,T = np.mgrid[0:1:1./steps[0],0:1:1./steps[1],0:1:1./steps[2],0:1:1./steps[3]]
XYZT = np.array(list(zip(X.flatten(),Y.flatten(),Z.flatten(),T.flatten())))
Dang = (np.dot(XYZT,DH.T)+.5)%1.-Dphi
Mmap = np.reshape(np.sum((Dang)**2,axis=1),newshape=steps)/len(DH)
hist,bins = np.histogram(Mmap,bins=1000)
chisq = np.min(Mmap)
DX = -np.array(np.unravel_index(np.argmin(Mmap),Mmap.shape))
ptext = ' map offset chi**2: %.3f, map offset: %d %d %d %d'%(chisq,DX[0],DX[1],DX[2],DX[3])
G2fil.G2Print(ptext)
return DX,ptext
[docs]def SSChargeFlip(data,reflDict,pgbar):
'''default doc string
:param type name: description
:returns: type name: description
'''
generalData = data['General']
mapData = generalData['Map']
map4DData = {}
flipData = generalData['Flip']
FFtable = {}
if 'None' not in flipData['Norm element']:
normElem = flipData['Norm element'].upper()
FFs = G2el.GetFormFactorCoeff(normElem.split('+')[0].split('-')[0])
for ff in FFs:
if ff['Symbol'] == normElem:
FFtable.update(ff)
dmin = flipData['GridStep']*2.
SGData = generalData['SGData']
SSGData = generalData['SSGData']
SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']])
SSGT = np.array([ops[1] for ops in SSGData['SSGOps']])
cell = generalData['Cell'][1:8]
A = G2lat.cell2A(cell[:6])
Vol = cell[6]
maxM = 4
Hmax = np.asarray(G2lat.getHKLmax(dmin,SGData,A)+[maxM,],dtype='i')+1
adjHKLmax(SGData,Hmax)
Ehkl = np.zeros(shape=2*Hmax,dtype='c16') #2X64bits per complex no.
time0 = time.time()
for iref,ref in enumerate(reflDict['RefList']):
dsp = ref[5]
if dsp > dmin:
ff = 0.1*Vol #est. no. atoms for ~10A**3/atom
if FFtable:
SQ = 0.25/dsp**2
ff *= G2el.ScatFac(FFtable,SQ)[0]
if ref[9] > 0.: #use only +ve Fobs**2
E = np.sqrt(ref[9])/ff
else:
E = 0.
ph = ref[11]
ph = rn.uniform(0.,360.)
Uniq = np.inner(ref[:4],SSGMT)
Phi = np.inner(ref[:4],SSGT)
for i,hklm in enumerate(Uniq): #uses uniq
hklm = np.asarray(hklm,dtype='i')
dp = 360.*Phi[i] #and phi
a = cosd(ph+dp)
b = sind(ph+dp)
phasep = complex(a,b)
phasem = complex(a,-b)
h,k,l,m = hklm+Hmax
Ehkl[h,k,l,m] = E*phasep
h,k,l,m = -hklm+Hmax #Friedel pair refl.
Ehkl[h,k,l,m] = E*phasem
# Ehkl[Hmax] = 0.00001 #this to preserve F[0,0,0]
CEhkl = copy.copy(Ehkl)
MEhkl = ma.array(Ehkl,mask=(Ehkl==0.0))
Emask = ma.getmask(MEhkl)
sumE = np.sum(ma.array(np.absolute(CEhkl),mask=Emask))
Ncyc = 0
old = np.seterr(all='raise')
while True:
CErho = np.real(fft.fftn(fft.fftshift(CEhkl)))*(1.+0j)
CEsig = np.std(CErho)
CFrho = np.where(np.real(CErho) >= flipData['k-factor']*CEsig,CErho,-CErho)
CFrho = np.where(np.real(CErho) <= flipData['k-Max']*CEsig,CFrho,-CFrho) #solves U atom problem!
CFhkl = fft.ifftshift(fft.ifftn(CFrho))
CFhkl = np.where(CFhkl,CFhkl,1.0) #avoid divide by zero
phase = CFhkl/np.absolute(CFhkl)
CEhkl = np.absolute(Ehkl)*phase
Ncyc += 1
sumCF = np.sum(ma.array(np.absolute(CFhkl),mask=Emask))
DEhkl = np.absolute(np.absolute(Ehkl)/sumE-np.absolute(CFhkl)/sumCF)
Rcf = min(100.,np.sum(ma.array(DEhkl,mask=Emask)*100.))
if Rcf < 5.:
break
GoOn = pgbar.Update(Rcf,newmsg='%s%8.3f%s\n%s %d'%('Residual Rcf =',Rcf,'%','No.cycles = ',Ncyc))[0]
if not GoOn or Ncyc > 10000:
break
np.seterr(**old)
G2fil.G2Print (' Charge flip time: %.4f no. elements: %d'%(time.time()-time0,Ehkl.size))
CErho = np.real(fft.fftn(fft.fftshift(CEhkl[:,:,:,maxM+1])))/10. #? to get on same scale as e-map
SSrho = np.real(fft.fftn(fft.fftshift(CEhkl)))/10. #? ditto
ctext = ' No.cycles = %d Residual Rcf =%8.3f%s Map size: %s'%(Ncyc,Rcf,'%',str(CErho.shape))
G2fil.G2Print (ctext)
roll,ptext = findSSOffset(SGData,SSGData,A,CEhkl) #CEhkl needs to be just the observed set, not the full set!
mapData['Rcf'] = Rcf
mapData['rho'] = np.roll(np.roll(np.roll(CErho,roll[0],axis=0),roll[1],axis=1),roll[2],axis=2)
mapData['rhoMax'] = max(np.max(mapData['rho']),-np.min(mapData['rho']))
mapData['minmax'] = [np.max(mapData['rho']),np.min(mapData['rho'])]
mapData['Type'] = reflDict['Type']
map4DData['Rcf'] = Rcf
map4DData['rho'] = np.real(np.roll(np.roll(np.roll(np.roll(SSrho,roll[0],axis=0),roll[1],axis=1),roll[2],axis=2),roll[3],axis=3))
map4DData['rhoMax'] = max(np.max(map4DData['rho']),-np.min(map4DData['rho']))
map4DData['minmax'] = [np.max(map4DData['rho']),np.min(map4DData['rho'])]
map4DData['Type'] = reflDict['Type']
return mapData,map4DData,ptext,ctext
[docs]def getRho(xyz,mapData):
''' get scattering density at a point by 8-point interpolation
param xyz: coordinate to be probed
param: mapData: dict of map data
:returns: density at xyz
'''
rollMap = lambda rho,roll: np.roll(np.roll(np.roll(rho,roll[0],axis=0),roll[1],axis=1),roll[2],axis=2)
if not len(mapData):
return 0.0
rho = copy.copy(mapData['rho']) #don't mess up original
if not len(rho):
return 0.0
mapShape = np.array(rho.shape)
mapStep = 1./mapShape
X = np.array(xyz)%1. #get into unit cell
I = np.array(X*mapShape,dtype='int')
D = X-I*mapStep #position inside map cell
D12 = D[0]*D[1]
D13 = D[0]*D[2]
D23 = D[1]*D[2]
D123 = np.prod(D)
Rho = rollMap(rho,-I) #shifts map so point is in corner
R = Rho[0,0,0]*(1.-np.sum(D))+Rho[1,0,0]*D[0]+Rho[0,1,0]*D[1]+Rho[0,0,1]*D[2]+ \
Rho[1,1,1]*D123+Rho[0,1,1]*(D23-D123)+Rho[1,0,1]*(D13-D123)+Rho[1,1,0]*(D12-D123)+ \
Rho[0,0,0]*(D12+D13+D23-D123)-Rho[0,0,1]*(D13+D23-D123)- \
Rho[0,1,0]*(D23+D12-D123)-Rho[1,0,0]*(D13+D12-D123)
return R
[docs]def getRhos(XYZ,rho):
''' get scattering density at an array of point by 8-point interpolation
this is faster than gerRho which is only used for single points. However, getRhos is
replaced by scipy.ndimage.interpolation.map_coordinates which does a better job & is just as fast.
Thus, getRhos is unused in GSAS-II at this time.
param xyz: array coordinates to be probed Nx3
param: rho: array copy of map (NB: don't use original!)
:returns: density at xyz
'''
def getBoxes(rho,I):
Rhos = np.zeros((2,2,2))
Mx,My,Mz = rho.shape
Ix,Iy,Iz = I
Rhos = np.array([[[rho[Ix%Mx,Iy%My,Iz%Mz],rho[Ix%Mx,Iy%My,(Iz+1)%Mz]],
[rho[Ix%Mx,(Iy+1)%My,Iz%Mz],rho[Ix%Mx,(Iy+1)%My,(Iz+1)%Mz]]],
[[rho[(Ix+1)%Mx,Iy%My,Iz%Mz],rho[(Ix+1)%Mx,Iy%My,(Iz+1)%Mz]],
[rho[(Ix+1)%Mx,(Iy+1)%My,Iz%