cherab.imas.math.functions.fourier_bezier.py_fourier_mode¶

cherab.imas.math.functions.fourier_bezier.py_fourier_mode(phi, index, periodicity=1) → float¶

Calculate the value of a Fourier mode at a given angle \(\varphi\).

Note

This is the python wrapper for the Cython function fourier_mode(). If you are using this function in a loop, consider using the Cython function directly.

Fourier modes \(Z_l(\varphi)\) corresponding to the different mode indices \(l\) with \(n_\mathrm{p}\) as periodicity of the simulation are defined as:

\[\begin{split}Z_l(\varphi) = \begin{cases} 1 & \text{if } l = 0, \\ \sin\left(\displaystyle\frac{l}{2}n_\mathrm{p} \varphi\right) & \text{if } l \text{ is even}, \\ \cos\left(\displaystyle\frac{l + 1}{2}n_\mathrm{p} \varphi\right) & \text{if } l \text{ is odd}. \end{cases}\end{split}\]

Parameters:

phi : float¶

Angle \(\varphi\) at which to evaluate the Fourier mode in degree.

index : int¶

Index \(l\) of the Fourier mode.

periodicity : int, optional¶

Periodicity \(n_\mathrm{p}\) of the simulation, by default 1.

Returns:

float – Value of the Fourier mode at the given angle \(\varphi\).