log_non_central_chi

Import in python using from mcutils.utils.noise import log_non_central_chi

mcutils.utils.noise.log_non_central_chi(observed, signal, noise_var, ncoils, derivative='None', log_bessel='approximate')

Models the noise as a non-central chi distribution

Parameters

• observed – observed signal

• signal – model signal

• noise_var – variance of the noise

• ncoils – number of coils (equal to degrees of freedom divided by 2)

• derivative –

  set to one of:

  • ”None”: no derivative

  • ”signal”: add derivatives wrt signal

  • ”noise_var”: add derivative wrt noise variance

  • ”both”: add derivatives wrt signal and noise variance

• log_bessel –

  method to evaluate the log-bessel function; one of:

  • ”approximate”: Uses scipy if possible and approximations if too small or large (error of up to 1%, but typically much smaller)

  • ”scipy”: uses the default scipy interpretation, which will return -np.inf or np.inf if too small/large

  • ”precise”: Uses mpmath to precisely evaluate the value. This is very slow

  • ”interpolate”: use cubic interpolation between pre-computed “precise” values. Will become slow if values vary too much.

Returns

log(P) of the non-central chi distribution and its derivatives if set