deriv_exp_sum_conv_cauchy

TRXASprefitpack.mathfun.deriv_exp_sum_conv_cauchy(t: ndarray, fwhm: float, k: ndarray, c: ndarray, base: Optional[bool] = True) → ndarray[source]

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