res_hess_voigt

TRXASprefitpack.res.res_hess_voigt()

Compute hessian of 1/2*chi(C(theta), theta) defined in seperation scheme section

Parameters:

• x0 –

  initial parameter

  • i th: peak position e0_i for i th voigt component

  • \({num}_{voigt}+i\) th: fwhm_G of i th voigt component

  • \(2{num}_{voigt}+i\) th: fwhm_L of i th voigt component

  if edge is not None:

  • \(3{num}_{voigt}+i\) th: ith edge position

  • \(3{num}_{voigt}+{num}_{edge}+i\) th: fwhm of ith edge function

• num_voigt – number of voigt component

• edge ({'g', 'l'}) – type of edge shape function if edge is not set, it does not include edge function.

• num_edge – number of edge component

• base_order (int) – polynomial order of baseline function if base_order is not set, it does not include baseline function.

• e – 1d array of energy points of data (n,)

• intensity – intensity of static data (n,)

• eps – estimated error of data (n,)

Returns:

Hessian of scalar residual function \((\frac{1}{2}\sum_i {res}^2_i)\) based on the seperation scheme

Note

• If fwhm_G of ith voigt component is zero then it is treated as lorenzian function with fwhm_L

• If fwhm_L of ith voigt component is zero then it is treated as gaussian function with fwhm_G