pyoculus.utils.convergence_domain

This module provides functions to make and plot a convergence domain.

For each pair in a grid of (x1, x2) points, it tries to find a cretain fixed point and the store the convergence behaviour.

authors:

Functions

compute_convergence_domain(map, x1s, x2s[, ...])

Compute where the FixedPoint solver converges to for each of the [x1, x2] point pair.

plot_convergence_domain(X1s, X2s, ...[, colors])

Plot the convergence domain for the FixedPoint solver in the X1s-X2s plane.
pyoculus.utils.convergence_domain.compute_convergence_domain(map: BaseMap, x1s: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str], x2s: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str], find_with_iota: bool = True, eps: float = 0.001, **kwargs) → tuple

Compute where the FixedPoint solver converges to for each of the [x1, x2] point pair. If a point converges, it is assigned a number which is the index corresponding to the equal first fixedpoint converging to the same place, otherwise it is assigned -1. The number corresponds to the index of the fixed point in the returned list of fixed points.

Parameters:

  • map (pyoculus.maps) – The problem to solve.

  • x1s (np.ndarray) – The x1 values of the meshgrid.

  • x2s (np.ndarray) – The x2 values of the meshgrid.

  • find_with_iota (bool, optional) – Whether to use the find_with_iota method. Defaults to True.

  • eps (float, optional) – The tolerance for the comparison with the fixed points. Defaults to 1e-3.

Keyword Arguments:

  • m (int) – The poloidal mode to use.

  • n (int) – The toroidal mode to use.

  • tol (float) – The tolerance of the fixed point finder.

  • t (float) – The parameter t for the find method.

  • nrestart (int) – The number of restarts for the fixed point finder.

  • niter (int) – The number of iterations for the fixed point finder.

Returns:

A tuple containing: - np.ndarray: The meshgrid of x1s and x2s, the assigned number for each point in the meshgrid, and the list of all fixed points objects convergent or not. - np.ndarray: The list of fixed points.

Return type:

tuple

pyoculus.utils.convergence_domain.plot_convergence_domain(X1s: array, X2s: array, assigned_to: array, fixed_points: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str], colors=None, **kwargs) → tuple

Plot the convergence domain for the FixedPoint solver in the X1s-X2s plane. If ax is None, a new figure is created, otherwise the plot is added to the existing figure.

Parameters:

  • X1s (np.ndarray) – The x1 values of the meshgrid.

  • X2s (np.ndarray) – The x2 values of the meshgrid.

  • assigned_to (np.ndarray) – The assigned number for each point in the meshgrid.

  • fixed_points (list) – The list of fixed points object (FixedPoint.OutputData).

  • colors (np.ndarray, optional) – The colors to use. Defaults to None. Should be of dimension (k, 3 or 4) for RGB/RGBA with k at least the number of fixed points plus one.

Keyword Arguments:

ax (matplotlib.axes.Axes, optional) – The axes to plot on. Defaults to None.

Returns:

A tuple containing:

  • fig (matplotlib.figure.Figure): The figure object.

  • ax (matplotlib.axes.Axes): The axes object.

Return type:

tuple