deriv_exp_sum_conv_cauchy

TRXASprefitpack.mathfun.deriv_exp_sum_conv_cauchy(t: ndarray, fwhm: float, k: ndarray, c: ndarray, base: bool | None = True) → ndarray

Compute derivative of sum of exponential 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)

• c – coefficient

• base – include baseline (i.e. k=0)

Returns:

Derivative of Convolution of normalized cauchy distribution and sum of exponential decay \((\exp(-kt))\).

Note

• 1st column: df/dt

• 2nd column: df/d(fwhm)

• 2+i th column: df/dk_i