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# Copyright (C) 2023-2024 Matthew Scroggs and Garth N. Wells
#
# This file is part of Basix (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: MIT
"""Interpolation."""
import numpy.typing as npt
from basix._basixcpp import (
compute_interpolation_operator as _compute_interpolation_operator,
)
from basix.finite_element import FiniteElement
def compute_interpolation_operator(
e0: FiniteElement,
e1: FiniteElement,
) -> npt.NDArray:
"""Compute a matrix that represents the interpolation between two elements.
If the two elements have the same value size, this function returns
the interpolation between them.
If element_from has value size 1 and element_to has value size > 1,
then this function returns a matrix to interpolate from a blocked
element_from (ie multiple copies of element_from) into element_to.
If element_to has value size 1 and element_from has value size > 1,
then this function returns a matrix that interpolates the components
of element_from into copies of element_to.
Note:
If the elements have different value sizes and both are
greater than 1, this function throws a runtime error
In order to interpolate functions between finite element spaces on
arbitrary cells, the functions must be pulled back to the reference
element (this pull back includes applying DOF transformations). The
matrix that this function returns can then be applied, then the
result pushed forward to the cell. If element_from and element_to
have the same map type, then only the DOF transformations need to be
applied, as the pull back and push forward cancel each other out.
Args:
e0: The element to interpolate from
e1: The element to interpolate to
Returns:
Matrix operator that maps the 'from' degrees-of-freedom to
the 'to' degrees-of-freedom. Shape is (ndofs(element_to),
ndofs(element_from))
"""
return _compute_interpolation_operator(e0._e, e1._e) # type: ignore
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