hess_exp_conv_cauchy

TRXASprefitpack.mathfun.hess_exp_conv_cauchy(t: float | ndarray, fwhm: float, k: float) → float | ndarray

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

Parameters:

• t – time

• fwhm – full width at half maximum of cauchy distribution

• k – rate constant (inverse of life time)

Returns:

Hessian of convolution of normalized cauchy distribution and exponential decay \((\exp(-kt))\).

Note

• 1st column: d^2f/dt^2

• 2nd column: d^2f/dtd(fwhm)

• 3rd column: d^2f/dtdk

• 4th column: d^2f/d(fwhm)^2

• 5th column: d^2f/d(fwhm)dk

• 6th column: d^2f/dk^2