pyissm.tools.interp

Interpolation functions for ISSM

This module contains various interpolation functions that can be used in conjunction with ISSM models.

Functions

averaging(md, data, iterations[, layer])

Smooth input data over a mesh using area/volume-weighted nodal averaging.

element_to_vertex(md, values[, layer])

Transfer element-defined values to vertices.

vertex_to_element(md, values[, method])

Transfer vertex-defined values to mesh elements.
pyissm.tools.interp.averaging(md, data, iterations, layer=0)

Smooth input data over a mesh using area/volume-weighted nodal averaging.

This function performs an iterative smoothing of data defined either on mesh elements or on mesh vertices. For element-defined data, it first distributes element values to nodes using element areas/volumes as weights. For vertex- defined data, it uses the provided nodal values as the starting point. Each iteration computes element-averaged values from current nodal values and then recomputes nodal values as the area/volume-weighted average of adjacent element averages. The algorithm supports 2-D meshes, full 3-D meshes (using element volumes), and extraction of a single 2-D layer from a 3-D mesh.

Parameters:

  • md (ISSM model object)

  • data (array_like) – 1-D array-like of scalar values defined either on elements or on vertices. Its length must be equal to either: - md.mesh.numberofelements (data on elements), or - md.mesh.numberofvertices (data on vertices). If layer is provided for a 3-D mesh, the vertex-based length should be md.mesh.numberofvertices2d and element-based length md.mesh.numberofelements2d.

  • iterations (int) – Number of smoothing iterations to perform. Must be a non-negative integer. A value of 0 will still perform the initial element->node distribution if data is provided on elements.

  • layer (int, optional) – Layer index to extract when working with a 3-D mesh. Default is 0, meaning operate on the full mesh. If non-zero, it must satisfy 1 <= layer <= md.mesh.numberoflayers and the function will operate on the corresponding 2-D layer (using mesh.elements2d, x2d, y2d, etc.).

Returns:

average – Dense column vector containing the smoothed nodal values. The length n is md.mesh.numberofvertices when layer == 0, or md.mesh.numberofvertices2d when a 2-D layer is extracted.

Return type:

numpy.ndarray, shape (n, 1)

Raises:

  • Exception – If the length of data does not match the expected number of elements or vertices for the mesh/layer combination.

  • ValueError – If a non-zero layer is provided for a 3-D mesh but is outside the valid range (not in 1..md.mesh.numberoflayers).

Notes

  • Weighting: element areas (2-D) or volumes (3-D) are used to weight the contribution of each element to its corner nodes when distributing element values to nodes and when recomputing nodal values from element averages.

  • Indexing: mesh connectivity arrays are expected to be 1-based in the model and are converted to 0-based indices internally.

  • Output is returned as a dense array (not a sparse matrix) for compatibility with downstream code (e.g. C routines) that expect full arrays.

Examples

>>> # Smooth element data on a 2-D mesh for 5 iterations
>>> avg = averaging(md, element_data, iterations=5)
>>> # Smooth nodal data on layer 2 of a 3-D mesh
>>> avg2d = averaging(md, vertex_data_2d, iterations=3, layer=2)
pyissm.tools.interp.element_to_vertex(md, values, layer=0)

Transfer element-defined values to vertices.

Parameters:

  • md (pyissm.model) – ISSM model object containing mesh connectivity in md.mesh.elements and vertex count in md.mesh.numberofvertices.

  • values (numpy.ndarray) – Element-defined field of shape (md.mesh.numberofelements,).

  • layer (int, optional) – Layer index to extract when working with a 3-D mesh. Default is 0, meaning operate on the full mesh. If non-zero, it must satisfy 1 <= layer <= md.mesh.numberoflayers and the function will operate on the corresponding 2-D layer (using mesh.elements2d, x2d, y2d, etc.).

Returns:

Vertex-defined field of shape (md.mesh.numberofvertices,).

Return type:

numpy.ndarray

pyissm.tools.interp.vertex_to_element(md, values, method='mean')

Transfer vertex-defined values to mesh elements.

Parameters:

  • md (pyissm.model) – ISSM model object containing mesh connectivity in md.mesh.elements and vertex count in md.mesh.numberofvertices.

  • values (array_like) – Vertex-defined field of shape (md.mesh.numberofvertices,).

  • method (str, optional) –

    Aggregation method used to combine vertex values within each element. Available options: "mean", "min", "max". Default is "mean".

    • "mean": Compute the average of vertex values for each element.

    • "min": Take the minimum vertex value for each element.

    • "max": Take the maximum vertex value for each element.

Returns:

Element-defined field of shape (md.mesh.numberofelements,).

Return type:

numpy.ndarray

Raises:

ValueError – If values is not vertex-defined for the mesh or if method is unsupported.