Interface Methods

All different solvers can be generated using the interface class. Note that if you specify the gpu interface, but your system does not support it (or you did not install it), you will only get a cpu solver.

static FIMPY.create_fim_solver(points: numpy.ndarray, elems: numpy.ndarray, metrics: typing.Optional[numpy.ndarray] = None, precision=<class 'numpy.float32'>, device='gpu', use_active_list=True) → fimpy.fim_base.FIMBase

Creates a Fast Iterative Method solver for solving the anisotropic eikonal equation

\[\begin{split}\left\{ \begin{array}{rll} \left<\nabla \phi, D \nabla \phi \right> &= 1 \quad &\text{on} \; \Omega \\ \phi(\mathbf{x}_0) &= g(\mathbf{x}_0) \quad &\text{on} \; \Gamma \end{array} \right. .\end{split}\]
Parameters

  • points (Union[np.ndarray (float), cp.ndarray (float)]) – Array of points, \(n \times d\)

  • elems (Union[np.ndarray (int), cp.ndarray (int)]) – Array of elements, \(m \times d_e\)

  • metrics (Union[np.ndarray (float), cp.ndarray (float)], optional) – Specifies the initial \(D \in \mathbb{R}^{d \times d}\) tensors. If not specified, you later need to provide them in comp_fim, by default None

  • precision (np.dtype, optional) – precision of all calculations and the final result, by default np.float32

  • device (str, optional) – Specifies the target device for the computations. One of [cpu, gpu], by default ‘gpu’

  • use_active_list (bool, optional) – If set to true, you will get an active list solver that only computes the necessary subset of points in each iteration. If set to false, a Jacobi solver will be returned that updates all points of the mesh in each iteration. By default True

Returns

Returns a Fast Iterative Method solver

Return type

FIMBase

Computing the anisotropic eikonal equation can be easily achieved by calling fimpy.fim_base.FIMBase.comp_fim() on the returned solver.

FIMBase.comp_fim(x0, x0_vals, metrics=None, max_iterations=10000000000)

Computes the solution \(\phi\) to the anisotropic eikonal equation

\[\begin{split}\left\{ \begin{array}{rll} \left<\nabla \phi, D \nabla \phi \right> &= 1 \quad &\text{on} \; \Omega \\ \phi(\mathbf{x}_0) &= g(\mathbf{x}_0) \quad &\text{on} \; \Gamma \end{array} \right. .\end{split}\]
Parameters

  • x0 (ndarray (int)) – Array of [k] discrete point indices of the mesh where we prescribe initial values \(\mathbf{x}_0\).

  • x0_vals (ndarray (float)) – Array of [k] discrete prescribed initial values that prescribe \(g(\mathbf{x}_0)\).

  • metrics (np.ndarray(float), optional) – Specifies the tensor \(D\) of the anisotropic eikonal equation as a discrete [m, d, d] array. This is optional only if you specified the metrics already at construction time (FIMBase), by default None

  • max_iterations (int, optional) – Maximum number of iterations before aborting the algorithm. If the algorithm stops before reaching convergence, some vertices might still be set to undef_val. By default int(1e10)

Returns

The solution to the anisotropic eikonal equation, \(\phi\) as a [n] array.

Return type

ndarray (float, cupy or numpy)

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