TRXASprefitpack.mathfun package

Module contents

TRXASprefitpack.mathfun Package

mathfun: subpackage for the mathematical functions for TRXASprefitpack

copyright

2021-2022 by pistack (Junho Lee).

license

LGPL3.

Functions

voigt(e, fwhm_G, fwhm_L)

voigt: evaluates voigt profile function with full width at half maximum of gaussian part is fwhm_G and full width at half maximum of lorenzian part is fwhm_L

edge_gaussian(e, fwhm_G)

Gaussian type edge function :math:(frac{1}{2}left(1+{erf}left(frac{x}{sigmasqrt{2}}right)right))

edge_lorenzian(e, fwhm_L)

Lorenzian type edge function :math:(0.5+frac{1}{pi}{arctan}left(frac{x}{gamma}right))

voigt_thy(e, thy_peak, fwhm_G, fwhm_L, ...)

Calculates normalized voigt broadened theoretically calculated lineshape spectrum

deriv_voigt(e, fwhm_G, fwhm_L)

deriv_voigt: derivative of voigt profile with respect to (e, fwhm_G, fwhm_L)

deriv_edge_gaussian(e, fwhm_G)

derivative of gaussian type edge

deriv_edge_lorenzian(e, fwhm_L)

derivative of lorenzian type edge

deriv_voigt_thy(e, thy_peak, fwhm_G, fwhm_L, ...)

Calculates derivative of normalized voigt broadened theoretically calculated lineshape spectrum

gau_irf(t, fwhm)

Compute gaussian shape irf function

cauchy_irf(t, fwhm)

Compute lorenzian shape irf function

pvoigt_irf(t, fwhm, eta)

Compute pseudo voight shape irf function (i.e.

calc_eta(fwhm_G, fwhm_L)

Calculate eta of pseudo voigt profile with fwhm_G, fwhm_L based on Journal of Applied Crystallography.

calc_fwhm(fwhm_G, fwhm_L)

Calculate uniform fwhm of both gaussian and cauchy component of pseudo voigt profile with fwhm_G, fwhm_L based on Journal of Applied Crystallography.

deriv_eta(fwhm_G, fwhm_L)

Calculate gradient of eta of pseudo voigt profile with fwhm_G, fwhm_L based on Journal of Applied Crystallography.

deriv_fwhm(fwhm_G, fwhm_L)

Computes gradient of uniform fwhm parameter of pseudo voigt approximation based on Journal of Applied Crystallography.

exp_conv_gau(t, fwhm, k)

Compute exponential function convolved with normalized gaussian distribution

exp_conv_cauchy(t, fwhm, k)

Compute exponential function convolved with normalized cauchy distribution

exp_conv_pvoigt(t, fwhm, eta, k)

Compute exponential function convolved with normalized pseudo voigt profile (i.e.

deriv_exp_conv_gau(t, fwhm, k)

Compute derivative of exponential function convolved with normalized gaussian distribution

deriv_exp_conv_cauchy(t, fwhm, k)

Compute derivative of the convolution of exponential function and normalized cauchy distribution

deriv_exp_sum_conv_gau(t, fwhm, k, c[, base])

Compute derivative of sum of exponential function convolved with normalized gaussian distribution

deriv_exp_sum_conv_cauchy(t, fwhm, k, c[, base])

Compute derivative of sum of exponential function convolved with normalized cauchy distribution

dmp_osc_conv_gau(t, fwhm, k, T, phase)

Compute damped oscillation convolved with normalized gaussian distribution

dmp_osc_conv_cauchy(t, fwhm, k, T, phase)

Compute damped oscillation convolved with normalized cauchy distribution

dmp_osc_conv_pvoigt(t, fwhm, eta, k, T, phase)

Compute damped oscillation convolved with normalized pseudo voigt profile (i.e.

deriv_dmp_osc_conv_gau(t, fwhm, k, T, phase)

Compute derivative of the convolution of damped oscillation and normalized gaussian distribution

deriv_dmp_osc_conv_cauchy(t, fwhm, k, T, phase)

Compute derivative of convolution of damped oscillation and normalized cauchy distribution

solve_model(equation, y0)

Solve system of first order rate equation

solve_seq_model(tau, y0)

Solve sequential decay model

solve_l_model(equation, y0)

Solve system of first order rate equation where the rate equation matrix is lower triangle

compute_model(t, eigval, V, c)

Compute solution of the system of rate equations solved by solve_model Note: eigval, V, c should be obtained from solve_model

compute_signal_gau(t, fwhm, eigval, V, c)

Compute solution of the system of rate equations solved by solve_model convolved with normalized gaussian distribution

compute_signal_cauchy(t, fwhm, eigval, V, c)

Compute solution of the system of rate equations solved by solve_model convolved with normalized cauchy distribution

compute_signal_pvoigt(t, fwhm, eta, eigval, V, c)

Compute solution of the system of rate equations solved by solve_model convolved with normalized pseudo voigt profile

exp_conv(t, fwhm, tau, c[, base, irf, eta])

Constructs the model for the convolution of n exponential and instrumental response function Supported instrumental response function are

fact_anal_exp_conv(t, fwhm, tau[, base, ...])

Estimate the best coefficiets when full width at half maximum fwhm and life constant tau are given

rate_eq_conv(t, fwhm, abs, eigval, V, c[, ...])

Constructs signal model rate equation with instrumental response function Supported instrumental response function are

fact_anal_rate_eq_conv(t, fwhm, eigval, V, c)

Estimate the best coefficiets when full width at half maximum fwhm and eigenvector and eigenvalue of rate equation matrix are given

dmp_osc_conv(t, fwhm, tau, T, phase, c[, ...])

Constructs convolution of sum of damped oscillation and instrumental response function Supported instrumental response function are

fact_anal_dmp_osc_conv(t, fwhm, tau, T[, ...])

Estimate the best coefficiets and phase factor when full width at half maximum fwhm , life constant tau and period of vibration T are given

sum_exp_dmp_osc_conv(t, fwhm, tau, tau_osc, ...)

Constructs convolution of sum of exponential decay and damped oscillation and instrumental response function Supported instrumental response function are

fact_anal_sum_exp_dmp_osc_conv(t, fwhm, tau, ...)

Estimate the best coefficiets and phase factor of oscillation part when full width at half maximum fwhm , lifetime constant of decay component tau, lifetime constant of oscillation component tau_osc and period of vibration T are given