chaosmagpy.coordinate_utils.synth_rotate_gauss(time, frequency, spectrum, scaled=None)[source]

Compute time-dependent matrices that transform spherical harmonic expansion from the given Fourier coefficients.

The function computes matrices that transform the spherical harmonic expansion of a time-dependent reference system (e.g. GSM, SM) to GEO using Fourier expansion of the transformation coefficients.

timendarray, shape (…)

Time given as modified Julian date, i.e. with respect to the date 0h00 January 1, 2000 (mjd2000).

frequencyndarray, shape (k,) or (k, m, n)

Vector of positive frequencies given in oscillations per day.

spectrumndarray, shape (k, m, n)

Fourier components of the matrices (reside in the last two dimensions).

scaledbool, optional (defaults to False)

If True, the function expects scaled Fourier coefficients, i.e. the non-bias term (all non-zero frequency terms) have been multiplied by a factor of 2. Hence, taking the real part of the spectrum multiplied with the complex exponentials results in the correctly scaled and time-shifted real-valued harmonics.

matrixndarray, shape (…, m, n)