'''
exp_conv_irf:
submodule for fitting data with sum of exponential decay convolved with irf
:copyright: 2021 by pistack (Junho Lee).
:license: LGPL3.
'''
from typing import Union, Optional
import numpy as np
import scipy.linalg as LA
from .A_matrix import make_A_matrix_cauchy
from .A_matrix import make_A_matrix_gau, make_A_matrix_pvoigt
[docs]def model_n_comp_conv(t: np.ndarray,
fwhm: Union[float, np.ndarray],
tau: np.ndarray,
c: np.ndarray,
base: Optional[bool] = True,
irf: Optional[str] = 'g',
eta: Optional[float] = None
) -> np.ndarray:
'''
Constructs the model for the convolution of n exponential and
instrumental response function
Supported instrumental response function are
irf
* g: gaussian distribution
* c: cauchy distribution
* pv: pseudo voigt profile
Args:
t: time
fwhm: full width at half maximum of instrumental response function
tau: life time for each component
c: coefficient for each component
base: whether or not include baseline [default: True]
irf: shape of instrumental
response function [default: g]
* 'g': normalized gaussian distribution,
* 'c': normalized cauchy distribution,
* 'pv': pseudo voigt profile :math:`(1-\\eta)g + \\eta c`
eta: mixing parameter for pseudo voigt profile
(only needed for pseudo voigt profile,
default value is guessed according to
Journal of Applied Crystallography. 33 (6): 1311–1316.)
Returns:
Convolution of the sum of n exponential decays and instrumental
response function.
Note:
1. *fwhm* For gaussian and cauchy distribution,
only one value of fwhm is needed,
so fwhm is assumed to be float
However, for pseudo voigt profile,
it needs two value of fwhm, one for gaussian part and
the other for cauchy part.
So, in this case,
fwhm is assumed to be numpy.ndarray with size 2.
2. *c* size of c is assumed to be
num_comp+1 when base is set to true.
Otherwise, it is assumed to be num_comp.
'''
k = 1/tau
if base:
k = np.concatenate((k, np.array([0])))
if irf == 'g':
A = make_A_matrix_gau(t, fwhm, k)
elif irf == 'c':
A = make_A_matrix_cauchy(t, fwhm, k)
elif irf == 'pv':
if eta is None:
f = fwhm[0]**5+2.69269*fwhm[0]**4*fwhm[1] + \
2.42843*fwhm[0]**3*fwhm[1]**2 + \
4.47163*fwhm[0]**2*fwhm[1]**3 + \
0.07842*fwhm[0]*fwhm[1]**4 + \
fwhm[1]**5
f = f**(1/5)
x = fwhm[1]/f
eta = 1.36603*x-0.47719*x**2+0.11116*x**3
A = make_A_matrix_pvoigt(t, fwhm[0], fwhm[1],
eta, k)
y = c@A
return y
[docs]def fact_anal_exp_conv(t: np.ndarray,
fwhm: Union[float, np.ndarray],
tau: np.ndarray,
base: Optional[bool] = True,
irf: Optional[str] = 'g',
eta: Optional[float] = None,
data: Optional[np.ndarray] = None,
eps: Optional[np.ndarray] = None
) -> np.ndarray:
'''
Estimate the best coefficiets when full width at half maximum fwhm
and life constant tau are given
When you fits your model to tscan data, you need to have
good initial guess for not only life time of
each component but also coefficients. To help this it solves
linear least square problem to find best coefficients when fwhm and
tau are given.
Supported instrumental response functions are
irf
1. 'g': gaussian distribution
2. 'c': cauchy distribution
3. 'pv': pseudo voigt profile
Args:
t: time
fwhm: full width at half maximum of instrumental response function
tau: life time for each component
base: whether or not include baseline [default: True]
irf: shape of instrumental
response function [default: g]
* 'g': normalized gaussian distribution,
* 'c': normalized cauchy distribution,
* 'pv': pseudo voigt profile :math:`(1-\\eta)g + \\eta c`
eta: mixing parameter for pseudo voigt profile
(only needed for pseudo voigt profile,
default value is guessed according to
Journal of Applied Crystallography. 33 (6): 1311–1316.)
data: time scan data to fit
eps: standard error of data
Returns:
Best coefficient for given fwhm and tau, if base is set to `True` then
size of coefficient is `num_comp + 1`, otherwise is `num_comp`.
Note:
data should not contain time range and
the dimension of the data must be one.
'''
k = 1/tau
if base:
k = np.concatenate((k, np.array([0])))
if irf == 'g':
A = make_A_matrix_gau(t, fwhm, k)
elif irf == 'c':
A = make_A_matrix_cauchy(t, fwhm, k)
elif irf == 'pv':
if eta is None:
f = fwhm[0]**5+2.69269*fwhm[0]**4*fwhm[1] + \
2.42843*fwhm[0]**3*fwhm[1]**2 + \
4.47163*fwhm[0]**2*fwhm[1]**3 + \
0.07842*fwhm[0]*fwhm[1]**4 + \
fwhm[1]**5
f = f**(1/5)
x = fwhm[1]/f
eta = 1.36603*x-0.47719*x**2+0.11116*x**3
A = make_A_matrix_pvoigt(t, fwhm[0], fwhm[1], eta, k)
if eps is not None:
y = data/eps
for i in range(k.shape[0]):
A[i, :] = A[i, :]/eps
else:
y = data
c, _, _, _ = LA.lstsq(A.T, y)
return c