spectrax._inverse_transform

Inverse Hermite–Fourier transform utilities.

This module reconstructs the phase-space distribution function f(x, v) from Hermite–Fourier coefficients. The implementation is written for JAX and uses orthax.hermite.hermval to evaluate Hermite polynomials efficiently.

Functions

inverse_HF_transform(Ck, Nn, Nm, Np, xi_x, xi_y, xi_z)

Reconstruct f(x, v) from Hermite–Fourier coefficients.

Module Contents

spectrax._inverse_transform.inverse_HF_transform(Ck, Nn, Nm, Np, xi_x, xi_y, xi_z)

Reconstruct f(x, v) from Hermite–Fourier coefficients.

Parameters:

  • Ck (jnp.ndarray) – Hermite-Fourier coefficients for (one or more) species/moments. The inverse FFT is applied along the last three axes.

  • Nn (int) – Number of Hermite modes retained along each velocity-space axis.

  • Nm (int) – Number of Hermite modes retained along each velocity-space axis.

  • Np (int) – Number of Hermite modes retained along each velocity-space axis.

  • xi_x (jnp.ndarray) – Normalized velocity-space coordinates (typically (v - u)/alpha) used to evaluate Hermite polynomials and the Gaussian weight.

  • xi_y (jnp.ndarray) – Normalized velocity-space coordinates (typically (v - u)/alpha) used to evaluate Hermite polynomials and the Gaussian weight.

  • xi_z (jnp.ndarray) – Normalized velocity-space coordinates (typically (v - u)/alpha) used to evaluate Hermite polynomials and the Gaussian weight.

Returns:

The reconstructed distribution function evaluated on (t, x, y, z, xi_x, xi_y, xi_z).

Return type:

jnp.ndarray