def convolution(simulated, resolution, expdata, convolved, dak=None, norm2one=False):
"""Convolve a simulated S(Q,E) with a resolution file
Arguments:
simulated: Nexus file containing S(Q,E) from a simulation
resolution: Nexus file containing the resolution. This will be used to produce a elastic line.
convolved: Output Nexus file containing the convolution of the simulated S(Q,E) with the model beamline.
expdata: Optional, experimental nexus file. Convolved will be binned as expdata.
Returns:
workspace for the convolution
"""
from mantid.simpleapi import (LoadNexus, Rebin, ConvertToHistogram, NormaliseToUnity, SaveNexus, SaveAscii, AddSampleLog)
wss=LoadNexus(Filename=simulated,OutputWorkspace='simulated')
width=wss.readX(0)[1]-wss.readX(0)[0] # rebin resolution as simulated
wsr=LoadNexus(Filename=resolution,OutputWorkspace='resolution')
#symmetrize the domain of the resolution function. Otherwise the
#convolution results in a function with its peak shifted from the origin
min=wsr.readX(0)[0]
max=wsr.readX(0)[-1]
delta=min+max
if delta<0:
wsr=Rebin(wsr, Params=(-max,width,max))
elif delta>0:
wsr=Rebin(wsr, Params=(min,width,-min))
else:
wsr=Rebin(wsr, Params=(min,width,max))
# convolve now, overwriting simulateds
for i in range(wss.getNumberHistograms()):
v=wsr.readY(i)
w=wss.readY(i)
x=camm_convolve(w,v,mode='same')
wss.setY(i,x)
wse=LoadNexus(Filename=expdata,OutputWorkspace='expdata')
width=wse.readX(0)[1]-wse.readX(0)[0] # rebin simulated as expdata
Rebin(InputWorkspace='simulated', Params=(wse.readX(0)[0],width,wse.readX(0)[-1]), OutputWorkspace='convolved')
ConvertToHistogram(InputWorkspace='convolved', OutputWorkspace='convolved') # remember that output from sassena are point-data
if norm2one:
wsc=NormaliseToUnity(InputWorkspace='convolved', OutputWorkspace='convolved')
AddSampleLog(Workspace='convolved',LogName='NormaliseToUnity',LogText=str(float(norm2one)),LogType='Number')
if dak:
dakota_vals = getParams(dak) # read in Dakota params file
AddSampleLog(Workspace='convolved',LogName='FF1',LogText=str(dakota_vals["FF1"]),LogType='Number')
from mantid.simpleapi import mtd
SaveNexus(InputWorkspace='convolved', Filename=convolved)
return
def modelB_EC_C(model, resolution, convolved, qvalues, assembled, expdata=None, costfile=None):
"""Assemble the Background, Elastic line and Convolution of the resolution with the simulated S(Q,E)
This is a hard-coded model consisting of a linear background, and elastic line, and a convolution:
b0+b1*E + +EC(Q)*e0*exp(-e1*Q^2)*Elastic(E) + c0*Resolution(E)xSimulated(Q,E)
We load Resolution(E)xSimulated(Q,E) as Convolved(Q,E)
EC(Q) is a fit to the Q-dependence of the integrated intensity of the empty can
EC(Q) = 2.174495971 - 2.065826056*Q + 0.845367259*Q^2
Arguments:
model: beamline model file is a single line, e.g,
b0=1.3211; b1=0.00 e0=0.99; e1=1.9; c0=2.3
resolution: Nexus file containing the resolution. This will be used to produce a elastic line.
convolved: Nexus file containing the convolution of the simulated S(Q,E) with the resolution.
qvalues: single-column file containing list of Q-values
assembled: output Nexus file containing the assembled S(Q,E) of the beamline model and the simulated S(Q,E)
expdata: Optional, experimental nexus file. If passed, output convolved will be binned as expdata.
costfile: Optional, file to store cost. If passed, the cost of comparing convolved and expdata will be saved.
Returns:
workspace containing the assembled S(Q,E)
"""
import numpy
from mantid.simpleapi import (LoadNexus, ScaleX, ConvertToPointData, SaveNexus, DakotaChiSquared)
EC = lambda Q: 2.174495971 - 2.065826056*Q + 0.845367259*Q*Q
Q=[float(q) for q in open(qvalues,'r').read().split('\n')]
p={}
for pair in open(model,'r').readline().split(';'):
key,val=pair.split('=')
p[key.strip()]=float(val.strip())
wsr=LoadNexus(Filename=resolution,OutputWorkspace='resolution')
wsr=ConvertToPointData(wsr)
E=wsr.readX(0)
wse=ScaleX(InputWorkspace=wsr, OutputWorkspace='elastic',factor=-1) # elastic line
wsc=LoadNexus(Filename=convolved,OutputWorkspace='convolved')
for i in range(wsc.getNumberHistograms()):
elastic=wse.readY(i) # elastic spectrum at a given Q
convolved=wsc.readY(i) # convolved spectrum at a given Q
wsc.setY(i, (p['b0']+p['b1']*E) + (EC(Q[i])*p['e0']*numpy.exp(-p['e1']*Q[i])*elastic) + (p['c0']*convolved) ) # overwrite spectrum
SaveNexus(InputWorkspace=wsc, Filename=assembled)
if expdata and costfile:
DakotaChiSquared(DataFile=assembled,CalculatedFile=expdata,OutputFile=costfile)
return wsc
def modelB_freeE_C(modeltpl, elastic, convolved, expdata, initparfile=None):
"""Estimate initial beamline parameters for the modelB_freeE_C
This is a hard-coded model consisting of a linear background, and elastic line, and a convolution:
b0+b1*E + +e0(Q)*Elastic(E) + c0*Resolution(E)xSimulated(Q,E)
We load Resolution(E)xSimulated(Q,E) as Convolved(Q,E)
e0(Q) are a set of fitting parameters, one for each Q
Initial values are estimated as follows:
b0:0.0
b1:0.0
Evaluation of the model at E=0:
e0*elastic(Q,0) + c0*convolved(Q,0) ~ experiment(Q,0) {Eq.1},
with 'convolved' the convolution of the experimental resolution and the Fourier transform
of the simulated intermediate structure factor
For the lowest Q, we assume contributions fromt the elastic line and simuation are equal. Thus:
c0*convolved(Qmin,0) ~ 1/2*experiment(Qmin,0) ---> provides estimation for c0
e0(Qmin)*elastic(Qmin,0) ~ 1/2*experiment(Qmin,0) ---> provides estimation for e0
For the remaining Q, we use {Eq.1} substituting the c0 found above.
Finally, eshift:0.0
Arguments:
model: beamline template model file (xml format)
elastic: Nexus file containing the elastic line
convolved: Nexus file containing convolution of the resolution and simulated structure factor
expdata: Nexus file containing the experimental data
[initparfile]: Output the initial parameters as a string in file with name initparfile
Returns:
initparms: string with initial values for the parameters
"""
from simulation.src.molmec.ffupdate.ff_update import loadFFtpl,updateTemplate
from mantid.simpleapi import LoadNexus
wse=LoadNexus(Filename=elastic,OutputWorkspace='elastic')
wsc=LoadNexus(Filename=convolved,OutputWorkspace='convolved')
wsx=LoadNexus(Filename=expdata,OutputWorkspace='experiment')
parl,template=loadFFtpl(modeltpl)
pard={}
for par in parl: pard[par._name]=par
nhist=wsx.getNumberHistograms()
le=len(wsx.readX(0))
for ws in wse,wsc:
if ws.getNumberHistograms()!=nhist or len(ws.readX(0))!=le:
error_message='%s %d histograms of length %d do not conform to those of experiment'%(ws.getName(),ws.getNumberHistograms(),len(ws.readX(0)))
ws.getName()+' histograms do not conform to those of experiment'
g_log.error(error_message)
raise StandardError(error_message)
pard['b0'].setValue(1e-10) # needs to be positive
pard['b1'].setValue(0.)
ezero=le/2 # assume E=0 in the middle of the histogram span
pard['c0'].setValue(0.5*wsx.readY(0)[ezero]/wsc.readY(0)[ezero])
pard['e0.0'].setValue(0.5*wsx.readY(0)[ezero]/wse.readY(0)[ezero])
trace()
for ihist in range(1,nhist):
pard['e0.'+str(ihist)].setValue((wsx.readY(ihist)[ezero] - pard['c0']._value*wsc.readY(ihist)[ezero]) / wse.readY(ihist)[ezero])
pard['eshift'].setValue(0.)
template=updateTemplate(template,parl)
if initparfile: open(initparfile,'w').write(template)
return template
def modelB_freeE_C(model, resolution, convolved, assembled, expdata=None, costfile=None, derivdata=None, derivexclude=[], doshift=None):
"""Assemble the Background, Elastic line and Convolution of the resolution with the simulated S(Q,E)
This is a hard-coded model consisting of a linear background, and elastic line, and a convolution:
b0+b1*E + +e0(Q)*Elastic(E) + c0*Resolution(E)xSimulated(Q,E)
We load Resolution(E)xSimulated(Q,E) as Convolved(Q,E)
e0(Q) are a set of fitting parameters, one for each Q
Arguments:
model: beamline model file is a single line, e.g,
b0=1.3211; b1=0.00; e0.0=0.99; e0.1=0.99; e0.2=0.99;...e0.N=0.99; e1=1.9; c0=2.3
resolution: Nexus file containing the resolution. This will be used to produce a elastic line.
convolved: Nexus file containing the convolution of the simulated S(Q,E) with the resolution.
assembled: output Nexus file containing the assembled S(Q,E) of the beamline model and the simulated S(Q,E)
expdata: Optional, experimental nexus file. If passed, output convolved will be binned as expdata.
costfile: Optional, file to store cost. If passed, residuals and (optionally) partial derivatives will be stored
derivdata: Optional, perform analytic derivatives (store in costfile if provided)
derivexclude: list of fitting parameters for which partial derivatives will not be computed
doshift: Optional, perform the shift of the model function
Returns:
wsm: workspace containing the assembled S(Q,E)
gradients: dictionary of partial derivatives with respect to model parameters
"""
import numpy
from copy import copy,deepcopy
from mantid.simpleapi import (LoadNexus, ScaleX, ConvertToPointData, SaveNexus, DakotaChiSquared, AddSampleLog)
from math import sqrt
def shiftalongX(*kargs,**kwargs):
""" Function to do the shift along the E-axis. By default, does nothing """
pass
import interpX
if doshift: # replace the dummy function with the real thing
if doshift in dir(interpX):
shiftalongX=getattr(__import__('interpX'), doshift)
else:
shiftalongX = getattr(__import__('interpX'), 'itp_simple')
def computemodel(p,wse,wsc):
"""Assemble the model
Arguments
p: dictionary with parameter values
wse: Mantid workspace holding the elastic line
wsc: Mantid workspace holding the convolution of the resolution and the simulation
Returns:
wsm: Mantid workspace holding the resulting model
"""
from mantid.simpleapi import CloneWorkspace
wsm=CloneWorkspace(wsc)
E=wse.readX(0) # energy values, bins boundary values
Eshifted=(E[1:]+E[:-1])/2 # energy values, center bin values
for i in range(wsc.getNumberHistograms()):
elastic=wse.readY(i) # elastic spectrum at a given Q
convolved=wsc.readY(i) # convolved spectrum at a given Q
wsm.setY(i, p['b0']+p['b1']*Eshifted + p['e0.'+str(i)]*elastic + p['c0']*convolved) # overwrite spectrum
return wsm
# init list of parameters names for which analytical derivative exists, same order as in the input model file
derivparnames=[] # filled only if derivdata different than None
p={}
for pair in open(model,'r').readline().split(';'):
key,val=[x.strip() for x in pair.split('=')]
if derivdata and key not in derivexclude: derivparnames.append(key)
p[key]=float(val)
# read various inputs
wsr=LoadNexus(Filename=resolution,OutputWorkspace='resolution')
wse=ScaleX(InputWorkspace=wsr, OutputWorkspace='elastic',factor=-1) # elastic line
wsc=LoadNexus(Filename=convolved,OutputWorkspace='convolved')
E=wsr.readX(0) # energy values, bins boundary values
de=E[1]-E[0] # assume all bins have same bin width
Eshifted=(E[1:]+E[:-1])/2 # energy values, center bin values
nhist=wsc.getNumberHistograms()
nrsl=len(Eshifted)*nhist # number of residuals
# calculate partial numerical derivative with respect to eshift
gradients={}
if 'eshift' in derivparnames:
wsm=computemodel(p,wse,wsc)
eshiftderiv=(shiftalongX(wsm,p['eshift']+0.5*de,newWorkspace='wsplus') - shiftalongX(wsm,p['eshift']-0.5*de,newWorkspace='wsminus')) / de # forward-backward difference with a 0.5*de step
gradients['eshift']=numpy.zeros(0)
for i in range(eshiftderiv.getNumberHistograms()): gradients['eshift'] = numpy.concatenate([gradients['eshift'], eshiftderiv.readY(i)])
# do eshift of component workspaces
if doshift: Eshifted-=p['eshift']
wse=shiftalongX(wse,p['eshift']) # shift the spectrum, does nothing if shiftalongX is the dummy function
wsc=shiftalongX(wsc,p['eshift']) # shift the spectrum, does nothing if shiftalongX is the dummy function
# find difference in convolutions with FF1 changed
if 'FF1' not in derivexclude:
derivparnames.append('FF1')
# difference in FF1 workspaces
convolvedf=convolved.replace('.nxs','_1.nxs')
wscf=LoadNexus(Filename=convolvedf,OutputWorkspace='convolvedf')
convolvedb=convolved.replace('.nxs','_0.nxs')
wscb=LoadNexus(Filename=convolvedb,OutputWorkspace='convolvedb')
wksp_diff=wscf-wscb
# calculate analytic partial derivatives with respect to the fit parameters
if derivparnames:
gradients['b0']=numpy.ones(nrsl)
gradients['b1']=numpy.zeros(0)
gradients['c0']=numpy.zeros(0)
gradients['FF1']=numpy.zeros(0)
for i in range(nhist):
gradients['b1'] = numpy.concatenate([gradients['b1'], Eshifted])
gradients['c0'] = numpy.concatenate([gradients['c0'], wsc.readY(i)])
if 'FF1' not in derivexclude:
gradients['FF1'] = numpy.concatenate([gradients['FF1'], wksp_diff.readY(i)])
gradients['e0.'+str(i)]=numpy.zeros(0)
for j in range(nhist):
if i==j:
gradients['e0.'+str(i)] = numpy.concatenate([gradients['e0.'+str(i)], wse.readY(i)])
else:
gradients['e0.'+str(i)] = numpy.concatenate([gradients['e0.'+str(i)], numpy.zeros(len(Eshifted))])
if 'FF1' not in derivexclude:
FF1_f=wscf.getRun().getLogData('FF1').value
FF1_b=wscb.getRun().getLogData('FF1').value
gradients['FF1'] *= p['c0']/(FF1_f-FF1_b)
# save model to file
wsm=computemodel(p,wse,wsc)
# add all parameters to assembled file
for pair in open(model,'r').readline().split(';'):
key,val=[x.strip() for x in pair.split('=')]
AddSampleLog(Workspace=wsm,LogName=key,LogText=str(p[key]),LogType='Number')
print key, "=", p[key]
print "FF1 =", wsm.getRun().getLogData('FF1').value
SaveNexus(InputWorkspace=wsm, Filename=assembled)
# save residuals and partial derivatives
buf=''
if expdata and costfile:
wex=LoadNexus(Filename=expdata,OutputWorkspace='experiment')
chisq,wR=DakotaChiSquared(DataFile=expdata,CalculatedFile=assembled,OutputFile=costfile,ResidualsWorkspace='wR')
Xe=numpy.zeros(0) # list of errors for each residual
for i in range(nhist):
Xe = numpy.concatenate([Xe, wex.readE(i)])
Ry=wR.readY(i)
for j in range(len(Ry)):
buf+=str(Ry[j])+" least_sq_term_"+str(i*len(Ry)+j+1)+"\n"
for parname in derivparnames: gradients[parname]/=numpy.where(Xe>0,Xe,1) # divide by experimental error (with non-positive elements replaced by one)
if derivparnames:
for i in range(nrsl):
buf+="["
for parname in derivparnames: buf+=" %.10e"%(-gradients[parname][i])
buf+=" ]\n"
open(costfile,'w').write(buf)
AddSampleLog(Workspace=wsm,LogName="chisq",LogText=str(chisq),LogType='Number')
norm_chisq=chisq/(len(Ry)-len(derivparnames))
print costfile, " R = ", sqrt(norm_chisq)
AddSampleLog(Workspace=wsm,LogName="norm_chisq",LogText=str(norm_chisq),LogType='Number')
AddSampleLog(Workspace=wsm,LogName="norm_chi",LogText=str(sqrt(norm_chisq)),LogType='Number')
SaveNexus(InputWorkspace=wsm, Filename=assembled)
return {'model':wsm, 'gradients':gradients}
