def gaussian(x, cen=0, sigma=1):
"""1 dimensional gaussian:
gaussian(x, cen, sigma)
"""
cen = param_value(cen)
sig = param_value(sigma)
return (1./(s2pi*sig)) * exp(-(1.0*x-cen)**2 /(2*sig**2))
def gaussian(x, cen=0, sigma=1):
"""1 dimensional gaussian:
gaussian(x, cen, sigma)
"""
cen = param_value(cen)
sigma = param_value(sigma)
return (sqrt(log2/pi)/sigma) * exp(-log2 * (1.0*x-cen) **2 / sigma**2)
def lorentzian(x, cen=0, sigma=1):
"""1 dimensional lorentzian
lorentzian(x, cen, sigma)
"""
cen = param_value(cen)
sigma = param_value(sigma)
return (1. / (1 + ((1.0 * x - cen) / sigma)**2)) / (pi * sigma)
def lorentzian(x, cen=0, sigma=1):
"""1 dimensional lorentzian
lorentzian(x, cen, sigma)
"""
cen = param_value(cen)
sigma = param_value(sigma)
return (1. / (1 + ((1.0*x-cen)/sigma)**2) ) / (pi*sigma)
def gaussian(x, cen=0, sigma=1):
"""1 dimensional gaussian:
gaussian(x, cen, sigma)
"""
cen = param_value(cen)
sig = param_value(sigma)
return (1. / (s2pi * sig)) * exp(-(1.0 * x - cen)**2 / (2 * sig**2))
def lognormal(x, cen=0, sigma=1):
"""log-normal function
lognormal(x, cen, sigma)
= (1/x) * exp(-(ln(x) - cen)/ (2* sigma**2))
"""
cen = param_value(cen)
sig = param_value(sigma)
return (1./(x*sig*s2pi)) * exp(-(log(x) - cen)**2/ (2* sig**2))
def lognormal(x, cen=0, sigma=1):
"""log-normal function
lognormal(x, cen, sigma)
= (1/x) * exp(-(ln(x) - cen)/ (2* sigma**2))
"""
cen = param_value(cen)
sig = param_value(sigma)
return (1. / (x * sig * s2pi)) * exp(-(log(x) - cen)**2 / (2 * sig**2))
def pearson7(x, cen=0, sigma=1, expon=0.5):
"""pearson7 lineshape, according to NIST StRD
though it seems wikpedia gives a different formula...
pearson7(x, cen, sigma, expon)
"""
cen = param_value(cen)
sigma = param_value(sigma)
expon = param_value(expon)
scale = gamma(expon) * sqrt((2**(1/expon) -1)) / (gamma(expon-0.5)) / (sigma*spi)
return scale / (1 + ( ((1.0*x-cen)/sigma)**2) * (2**(1/expon) -1) )**expon
def pvoigt(x, cen=0, sigma=1, frac=0.5):
"""1 dimensional pseudo-voigt:
pvoigt(x, cen, sigma, frac)
= (1-frac)*gaussion(x,cen,sigma) + frac*lorentzian(x,cen, sigma)
"""
cen = param_value(cen)
sigma = param_value(sigma)
frac = param_value(frac)
return ((1-frac)*gaussian(x, cen=cen, sigma=sigma) +
frac*lorentzian(x, cen=cen, sigma=sigma))
def pvoigt(x, cen=0, sigma=1, frac=0.5):
"""1 dimensional pseudo-voigt:
pvoigt(x, cen, sigma, frac)
= (1-frac)*gaussion(x,cen,sigma) + frac*lorentzian(x,cen, sigma)
"""
cen = param_value(cen)
sigma = param_value(sigma)
frac = param_value(frac)
return ((1 - frac) * gaussian(x, cen=cen, sigma=sigma) +
frac * lorentzian(x, cen=cen, sigma=sigma))
def voigt(x, cen=0, sigma=1, gamma=None):
"""1 dimensional voigt function.
see http://en.wikipedia.org/wiki/Voigt_profile
"""
if gamma is None:
gamma = sigma
cen = param_value(cen)
sigma = param_value(sigma)
gamma = param_value(gamma)
z = (x - cen + 1j * gamma) / (sigma * s2)
return wofz(z).real / (sigma * s2pi)
def pearson7(x, cen=0, sigma=1, expon=0.5):
"""pearson7 lineshape, according to NIST StRD
though it seems wikpedia gives a different formula...
pearson7(x, cen, sigma, expon)
"""
cen = param_value(cen)
sigma = param_value(sigma)
expon = param_value(expon)
scale = gamma(expon) * sqrt(
(2**(1 / expon) - 1)) / (gamma(expon - 0.5)) / (sigma * spi)
return scale / (1 + (((1.0 * x - cen) / sigma)**2) *
(2**(1 / expon) - 1))**expon
def voigt(x, cen=0, sigma=1, gamma=None):
"""1 dimensional voigt function.
see http://en.wikipedia.org/wiki/Voigt_profile
"""
if gamma is None:
gamma = sigma
cen = param_value(cen)
sigma = param_value(sigma)
gamma = param_value(gamma)
z = (x-cen + 1j*gamma)/ (sigma*s2)
return wofz(z).real / (sigma*s2pi)
def _pathparams(self, paramgroup=None, **kws):
"""evaluate path parameter value
"""
# degen, s02, e0, ei, deltar, sigma2, third, fourth
if (paramgroup is not None and
self._larch.symtable.isgroup(paramgroup)):
self._larch.symtable._sys.paramGroup = paramgroup
self._larch.symtable._fix_searchGroups()
# put 'reff' and '_feffdat' into the paramGroup so that
# 'reff' can be used in constraint expressions and
# '_feffdat' can be used inside Debye and Eins functions
stable = self._larch.symtable
if stable.isgroup(stable._sys.paramGroup):
stable._sys.paramGroup.reff = self._feffdat.reff
stable._sys.paramGroup._feffdat = self._feffdat
out = []
for param in ('degen', 's02', 'e0', 'ei',
'deltar', 'sigma2', 'third', 'fourth'):
val = getattr(self, param)
if param in kws:
if kws[param] is not None:
val = kws[param]
if isinstance(val, six.string_types):
thispar = Parameter(expr=val, _larch=self._larch)
#if isinstance(thispar, Parameter):
# thispar = thispar.value
setattr(self, param, thispar)
val = getattr(self, param)
out.append(param_value(val))
return out
def _pathparams(self, paramgroup=None, **kws):
"""evaluate path parameter value
"""
# degen, s02, e0, ei, deltar, sigma2, third, fourth
if (paramgroup is not None
and self._larch.symtable.isgroup(paramgroup)):
self._larch.symtable._sys.paramGroup = paramgroup
self._larch.symtable._fix_searchGroups()
# put 'reff' and '_feffdat' into the paramGroup so that
# 'reff' can be used in constraint expressions and
# '_feffdat' can be used inside Debye and Eins functions
stable = self._larch.symtable
if stable.isgroup(stable._sys.paramGroup):
stable._sys.paramGroup.reff = self._feffdat.reff
stable._sys.paramGroup._feffdat = self._feffdat
out = []
for param in ('degen', 's02', 'e0', 'ei', 'deltar', 'sigma2', 'third',
'fourth'):
val = getattr(self, param)
if param in kws:
if kws[param] is not None:
val = kws[param]
if isinstance(val, six.string_types):
thispar = Parameter(expr=val, _larch=self._larch)
#if isinstance(thispar, Parameter):
# thispar = thispar.value
setattr(self, param, thispar)
val = getattr(self, param)
out.append(param_value(val))
return out
def _peakparams(self, paramgroup=None, **kws):
"""evaluate peak parameter values """
# sigma, amplitude, center
out = []
for parname in ('amplitude', 'sigma', 'center'):
val = getattr(self, parname)
if parname in kws:
if kws[parname] is not None:
val = kws[parname]
if isinstance(val, six.string_types):
thispar = Parameter(expr=val, _larch=self._larch)
setattr(self, parname, thispar)
val = getattr(self, parname)
out.append(param_value(val))
return out
def _peakparams(self, paramgroup=None, **kws):
"""evaluate peak parameter values """
# sigma, amplitude, center
if (paramgroup is not None
and self._larch.symtable.isgroup(paramgroup)):
self._larch.symtable._sys.paramGroup = paramgroup
self._larch.symtable._fix_searchGroups()
out = []
for parname in ('amplitude', 'sigma', 'center'):
val = getattr(self, parname)
if parname in kws:
if kws[parname] is not None:
val = kws[parname]
if isinstance(val, (str, unicode)):
thispar = Parameter(expr=val, _larch=self._larch)
setattr(self, parname, thispar)
val = getattr(self, parname)
out.append(param_value(val))
return out
def _peakparams(self, paramgroup=None, **kws):
"""evaluate peak parameter values """
# sigma, amplitude, center
if (paramgroup is not None and
self._larch.symtable.isgroup(paramgroup)):
self._larch.symtable._sys.paramGroup = paramgroup
self._larch.symtable._fix_searchGroups()
out = []
for parname in ('amplitude', 'sigma', 'center'):
val = getattr(self, parname)
if parname in kws:
if kws[parname] is not None:
val = kws[parname]
if isinstance(val, six.string_types):
thispar = Parameter(expr=val, _larch=self._larch)
setattr(self, parname, thispar)
val = getattr(self, parname)
out.append(param_value(val))
return out
