deriv_dmp_osc_sum_conv_cauchy

TRXASprefitpack.mathfun.deriv_dmp_osc_sum_conv_cauchy(t: ndarray, fwhm: float, k: ndarray, T: ndarray, phase: ndarray, c: ndarray) → ndarray

Compute derivative of sum of damped oscillation function convolved with normalized cauchy distribution

Parameters:

• t – time

• fwhm – full width at half maximum of cauchy distribution

• k – rate constant (inverse of life time)

• T – period

• phase – phase factor

• c – coefficient

Returns:

Derivative of Convolution of normalized cauchy distribution and damped oscillation \((\exp(-kt)cos(2\pi t/T+phase))\).

Note

• 1st column: df/dt

• 2nd column: df/d(fwhm)

• 2+i th column: df/dk_i \((1 \leq i \leq {num}_{comp})\)

• 2+num_comp+i th column: df/dT_i \((1 \leq i \leq {num}_{comp})\)

• \(2+2{num}_{comp}+i\) th column: df/d(phase_i) \((1 \leq i \leq {num}_{comp})\)