def multifit(x=None,
y=None,
epsil=None,
wid=None,
ang=0,
mix=None,
opti='lbf',
yerr=None,
smooth=None,
dierep=0,
ifit=None,
nfit_lays=0,
lims=None):
'''fitting thickness of multiple layers / mixing ratios in
dierep: fitting complete dielectric function
uses tabulated values of dielec. function (given in epsil)
additional parameters to fit can produce polynomial shift of diel. fun
(layer adjusted is specified by global "mod_layer" parameter)
ADDed:
smoothing option to reduce sensitivity to fast variations
floating_norm global parameter (in the case of smoothing)
global setting
non_uniform: accounts for spread of widths over illuminated area (large diaphragm)
'''
global idix, fit
#if ang>0: print 'incidence at %.1f deg '%ang
if opti == 'tnc':
from scipy.optimize import tnc as optimod
mizer = optimod.fmin_tnc
else:
from scipy.optimize import lbfgsb as optimod
mizer = optimod.fmin_l_bfgs_b
from numpy import array, all, conj, sqrt, ones
if wid[0] == 0: #no assumptions about initial parameters
from spectra import fitting
out = fitting(x, y)
wid[0] = per_conv[0] / (
(out[0][3] - per_conv[1]) * sqrt(epsil[0].real.mean()))
#wid[0]=per_conv/(out[3]*sqrt(epsil[0].real.mean()))
print('estimated principal layer width %f' % wid[0])
if yerr != None and all(yerr.real > 0):
weight = 1 / yerr.real
if all(yerr.imag > 0): weight += 1j / yerr.imag
if ifit == None: #no fit functions entered
r, sh, psi = plate(x, epsil, wid, ang=ang, rep=-1)
from numpy import convolve, polyfit, polyval
if smooth != None:
y = convolve(y, smooth)[len(smooth):-len(smooth)]
print('data shape %i' % y.shape)
def fit(spars, rep=0):
global idix
#print spars
slate = convolve(
abs(
friter([t.copy() for t in r],
[sh[i] * spars[i] for i in range(len(sh))],
psi))**2, smooth)[len(smooth):-len(smooth)]
#slate=convolve(plate(x,epsil,list(spars),meth=0,ang=ang,rep=dierep),smooth)[len(smooth):-len(smooth)]
if floating_norm > 0:
idix = polyfit(slate, y, floating_norm)
dif = y - polyval(idix, slate)
else:
dif = y - slate
if yerr != None: dif *= weight
if rep == 1: return dif
return sum((dif * conj(dif)).real)
else:
def fit(spars, rep=0):
global idix
#print spars
rlays = [t.copy() for t in r]
shlays = [
sh[i] * spars[i] for i in range(min(len(sh), len(spars)))
]
if len(spars) < len(sh):
shlays.extend(sh[len(spars):])
elif len(spars) > len(sh):
prof = polyval(spars[:len(sh) - 1:-1], x)
rlays[mod_layer] *= prof
shlays[mod_layer] *= prof
if non_uniform:
dif = y - wid_spread(
rlays,
shlays,
psi, [1 - abs(non_uniform), 1 + abs(non_uniform)],
wind=non_uniform_layer,
ang=ang,
rep=-2)
if floating_norm >= 0:
slate = abs(friter(rlays, shlays, psi))**2
if floating_norm == 0:
from extra import rob_polyfit
a, c = rob_polyfit(slate, y, wei=-1)
if c > 0.6: # minimal correlation to do renormalization
idix = rob_polyfit(slate, y, wei=2)
dif = y - polyval(idix, slate)
else:
dif = y - slate
else:
idix = polyfit(slate, y, floating_norm)
dif = y - polyval(idix, slate)
else:
dif = y - abs(friter(rlays, shlays, psi))**2
#dif=y-plate(x,epsil,list(spars),meth=0,ang=ang,rep=dierep)
if yerr != None: dif *= weight
if rep == 1: return dif
return sum((dif * conj(dif)).real)
if dierep == -2: return fit
else: fit = ifit
if nfit_lays == 0: nfit_lays = len(wid)
if lims:
out = mizer(fit,
ones(nfit_lays),
None,
args=(),
approx_grad=True,
bounds=array(lims))
else:
out = mizer(fit, ones(nfit_lays), None, args=(), approx_grad=True)
return out, wid
def multifit(x=None,y=None,epsil=None,wid=None,ang=0,mix=None,opti='lbf',yerr=None,smooth=None,dierep=0,ifit=None,nfit_lays=0,lims=None):
'''fitting thickness of multiple layers / mixing ratios in
dierep: fitting complete dielectric function
uses tabulated values of dielec. function (given in epsil)
additional parameters to fit can produce polynomial shift of diel. fun
(layer adjusted is specified by global "mod_layer" parameter)
ADDed:
smoothing option to reduce sensitivity to fast variations
floating_norm global parameter (in the case of smoothing)
global setting
non_uniform: accounts for spread of widths over illuminated area (large diaphragm)
'''
global idix,fit
#if ang>0: print 'incidence at %.1f deg '%ang
if opti=='tnc':
from scipy.optimize import tnc as optimod
mizer=optimod.fmin_tnc
else:
from scipy.optimize import lbfgsb as optimod
mizer=optimod.fmin_l_bfgs_b
from numpy import array,all,conj,sqrt,ones
if wid[0]==0: #no assumptions about initial parameters
from spectra import fitting
out=fitting(x,y)
wid[0]=per_conv[0]/((out[0][3]-per_conv[1])*sqrt(epsil[0].real.mean()))
#wid[0]=per_conv/(out[3]*sqrt(epsil[0].real.mean()))
print('estimated principal layer width %f'%wid[0])
if yerr!=None and all(yerr.real>0):
weight=1/yerr.real
if all(yerr.imag>0): weight+=1j/yerr.imag
if ifit==None: #no fit functions entered
r,sh,psi=plate(x,epsil,wid,ang=ang,rep=-1)
from numpy import convolve,polyfit,polyval
if smooth!=None:
y=convolve(y,smooth)[len(smooth):-len(smooth)]
print('data shape %i'%y.shape)
def fit(spars,rep=0):
global idix
#print spars
slate=convolve(abs(friter([t.copy() for t in r],[sh[i]*spars[i] for i in range(len(sh))],psi))**2,smooth)[len(smooth):-len(smooth)]
#slate=convolve(plate(x,epsil,list(spars),meth=0,ang=ang,rep=dierep),smooth)[len(smooth):-len(smooth)]
if floating_norm>0:
idix=polyfit(slate,y,floating_norm)
dif=y-polyval(idix,slate)
else: dif=y-slate
if yerr!=None: dif*=weight
if rep==1: return dif
return sum((dif*conj(dif)).real)
else:
def fit(spars,rep=0):
global idix
#print spars
rlays=[t.copy() for t in r]
shlays=[sh[i]*spars[i] for i in range(min(len(sh),len(spars)))]
if len(spars)<len(sh):
shlays.extend(sh[len(spars):])
elif len(spars)>len(sh):
prof=polyval(spars[:len(sh)-1:-1],x)
rlays[mod_layer]*=prof
shlays[mod_layer]*=prof
if non_uniform:
dif=y-wid_spread(rlays,shlays,psi,[1-abs(non_uniform),1+abs(non_uniform)],wind=non_uniform_layer,ang=ang,rep=-2)
if floating_norm>=0:
slate=abs(friter(rlays,shlays,psi))**2
if floating_norm==0:
from extra import rob_polyfit
a,c=rob_polyfit(slate,y,wei=-1)
if c>0.6: # minimal correlation to do renormalization
idix=rob_polyfit(slate,y,wei=2)
dif=y-polyval(idix,slate)
else: dif=y-slate
else:
idix=polyfit(slate,y,floating_norm)
dif=y-polyval(idix,slate)
else:
dif=y-abs(friter(rlays,shlays,psi))**2
#dif=y-plate(x,epsil,list(spars),meth=0,ang=ang,rep=dierep)
if yerr!=None: dif*=weight
if rep==1: return dif
return sum((dif*conj(dif)).real)
if dierep==-2: return fit
else: fit=ifit
if nfit_lays==0:nfit_lays=len(wid)
if lims: out=mizer(fit,ones(nfit_lays),None,args=(),approx_grad=True,bounds=array(lims))
else: out=mizer(fit,ones(nfit_lays),None,args=(),approx_grad=True)
return out,wid
def dofit(x,
y,
pars,
lims=[[1e-2, 1e6], [1, 4000.], [0.001, 100.]],
yerr=None,
einf=1.,
drude=None,
rep=1,
opti='lbf',
fix=None,
args=()):
'''fitting reflectivity/transmissivity with N-resonator model
pars is a 2-d array (ampl,freq,absorb)
errors not yet implemented
fitting method either TNC, light BFGS or Cobyla ('tnc/lbf/cob')
'''
global gang, fit
extrapars = {}
if opti == 'tnc':
from scipy.optimize import tnc as optimod
mizer = optimod.fmin_tnc
extrapars = {'messages': 0}
else:
from scipy.optimize import lbfgsb as optimod
mizer = optimod.fmin_l_bfgs_b
from numpy import array
if fit == None: #no fit functions entered
dierep = -1
if len(y.shape) == 2 and y.shape[1] == 2:
y = y[:, 0] + 1j * y[:, 1]
if yerr != None: weight = 1 / yerr[:, 0] + 1j / yerr[:, 1]
print("fitting complex numbers: ellipsometry")
#dierep=
elif str(y.dtype)[:7] == 'complex':
dierep = 0 # calculating in complex plane
if yerr != None: weight = 1 / yerr.real + 1j / yerr.imag
print("fitting complex numbers")
else:
if yerr != None: weight = 1 / yerr
if drude != None:
def fit(spars):
ospars = array(spars[3:]).reshape((len(spars) - 3) // 3,
3) #oscilator parameters
dif = y.copy()
if dierep == 0:
dif -= dielect(x, spars[0], ospars, drude=spars[1:3])
else:
dif -= rdielect(x,
spars[0],
ospars,
drude=spars[1:3],
ang=gang)
if yerr != None: dif *= weight
return sum(abs(dif)**2) #dif*conj(dif))
else:
def fit(spars):
ospars = array(spars[1:]).reshape((len(spars) - 1) // 3, 3)
dif = y.copy()
if dierep == 0: dif -= dielect(x, spars[0], ospars)
else: dif -= rdielect(x, spars[0], ospars, ang=gang)
if yerr != None: dif *= weight
return sum(abs(dif)**2) #sum(dif*conj(dif))
if rep == -3: return fit
#def fit(spars,args):
# return sum((args[1]-dielect(args[0],spars[0],array(spars[1:]).reshape((len(spars)-1)//3,3)))**2)
if type(pars) == list: pars = array(pars)
if len(pars.shape) == 2: pars = pars.reshape(pars.shape + (1, ))
if einf == None: ipars = [1.]
else: ipars = type(einf) == list and einf[:1] or [einf]
if drude != None: ipars += list(drude)
ipars += list(pars[:, :, 0].flat)
if rep == -2: return ipars
if lims != None:
if len(lims) == len(ipars): blims = lims
else:
blims = [elims]
if drude != None: blims += [[0.1, 100], [0.1, 100.]]
if len(lims) == len(ipars) - 1: blims += lims
elif len(lims) == 3:
print('setting limits')
for i in range(len(pars)):
for j in range(3):
if lims[j][0] < 0:
blims.append([pars[i, j, 0] + a for a in lims[j]])
else:
blims.append(lims[j])
#if type(lims[0]==list)
if rep == -1: return blims
blims = array(blims)
else:
blims = None
if opti == 'cob':
from scipy.optimize import fmin_cobyla as mizer
par_con = [
lambda p: (p[i] - blims[i][0]) * (blims[i][1] - p[i])
for i in range(len(blims))
]
out = mizer(fit, array(ipars), par_con, args=args)
else:
out = mizer(fit,
array(ipars),
None,
args=args,
approx_grad=True,
bounds=blims,
**extrapars)
return out
def dofit(x,y,pars,lims=[[1e-2,1e6],[1,4000.],[0.001,100.]],yerr=None,einf=1.,drude=None,rep=1,opti='lbf',fix=None,args=()):
'''fitting reflectivity/transmissivity with N-resonator model
pars is a 2-d array (ampl,freq,absorb)
errors not yet implemented
fitting method either TNC, light BFGS or Cobyla ('tnc/lbf/cob')
'''
global gang,fit
extrapars={}
if opti=='tnc':
from scipy.optimize import tnc as optimod
mizer=optimod.fmin_tnc
extrapars={'messages':0}
else:
from scipy.optimize import lbfgsb as optimod
mizer=optimod.fmin_l_bfgs_b
from numpy import array
if fit==None: #no fit functions entered
dierep=-1
if len(y.shape)==2 and y.shape[1]==2:
y=y[:,0]+1j*y[:,1]
if yerr!=None: weight=1/yerr[:,0]+1j/yerr[:,1]
print("fitting complex numbers: ellipsometry")
#dierep=
elif str(y.dtype)[:7]=='complex':
dierep=0 # calculating in complex plane
if yerr!=None: weight=1/yerr.real+1j/yerr.imag
print("fitting complex numbers")
else:
if yerr!=None: weight=1/yerr
if drude!=None:
def fit(spars):
ospars=array(spars[3:]).reshape((len(spars)-3)//3,3) #oscilator parameters
dif=y.copy()
if dierep==0: dif-=dielect(x,spars[0],ospars,drude=spars[1:3])
else: dif-=rdielect(x,spars[0],ospars,drude=spars[1:3],ang=gang)
if yerr!=None: dif*=weight
return sum(abs(dif)**2)#dif*conj(dif))
else:
def fit(spars):
ospars=array(spars[1:]).reshape((len(spars)-1)//3,3)
dif=y.copy()
if dierep==0: dif-=dielect(x,spars[0],ospars)
else: dif-=rdielect(x,spars[0],ospars,ang=gang)
if yerr!=None: dif*=weight
return sum(abs(dif)**2)#sum(dif*conj(dif))
if rep==-3: return fit
#def fit(spars,args):
# return sum((args[1]-dielect(args[0],spars[0],array(spars[1:]).reshape((len(spars)-1)//3,3)))**2)
if type(pars)==list: pars=array(pars)
if len(pars.shape)==2: pars=pars.reshape(pars.shape+(1,))
if einf==None: ipars=[1.]
else: ipars=type(einf)==list and einf[:1] or [einf]
if drude!=None: ipars+=list(drude)
ipars+=list(pars[:,:,0].flat)
if rep==-2: return ipars
if lims!=None:
if len(lims)==len(ipars): blims=lims
else:
blims=[elims]
if drude!=None: blims+=[[0.1,100],[0.1,100.]]
if len(lims)==len(ipars)-1: blims+=lims
elif len(lims)==3:
print('setting limits')
for i in range(len(pars)):
for j in range(3):
if lims[j][0]<0: blims.append([pars[i,j,0]+a for a in lims[j]])
else: blims.append(lims[j])
#if type(lims[0]==list)
if rep==-1: return blims
blims=array(blims)
else:
blims=None
if opti=='cob':
from scipy.optimize import fmin_cobyla as mizer
par_con=[lambda p:(p[i]-blims[i][0])*(blims[i][1]-p[i]) for i in range(len(blims))]
out=mizer(fit,array(ipars),par_con,args=args)
else:
out=mizer(fit,array(ipars),None,args=args,approx_grad=True,bounds=blims,**extrapars)
return out
