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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
"""Functions for working with polynomials."""
import numpy as np
import numpy.typing as npt
from basix._basixcpp import PolynomialType, PolysetType
from basix._basixcpp import polynomials_dim as _pd
from basix._basixcpp import restriction as _restriction
from basix._basixcpp import superset as _superset
from basix._basixcpp import tabulate_polynomial_set as _tps
from basix._basixcpp import tabulate_polynomials as _tabulate_polynomials
from basix.cell import CellType
from basix.utils import index
__all__ = ["reshape_coefficients", "dim", "tabulate_polynomial_set"]
def reshape_coefficients(
poly_type: PolynomialType,
cell_type: CellType,
coefficients: npt.NDArray[np.float64],
value_size: int,
input_degree: int,
output_degree: int,
) -> npt.NDArray[np.float64]:
"""Reshape the coefficients.
Args:
poly_type: The polynomial type.
cell_type: The cell type
coefficients: The coefficients
value_size: The value size of the polynomials associated with
the coefficients.
input_degree: The maximum degree of polynomials associated with
the input coefficients.
output_degree: The maximum degree of polynomials associated with
the output coefficients.
Returns:
Coefficients representing the same coefficients as the input in
the set of polynomials of the output degree.
"""
if poly_type != PolynomialType.legendre:
raise NotImplementedError()
if output_degree < input_degree:
raise ValueError("Output degree must be greater than or equal to input degree")
if output_degree == input_degree:
return coefficients
pdim = dim(poly_type, cell_type, output_degree)
out = np.zeros((coefficients.shape[0], pdim * value_size))
indices: list[tuple[int, ...]] = []
if cell_type == CellType.interval:
indices = [(i,) for i in range(input_degree + 1)]
def idx(d, i):
return index(i[0])
elif cell_type == CellType.triangle:
indices = [(i, j) for i in range(input_degree + 1) for j in range(input_degree + 1 - i)]
def idx(d, i):
return index(i[1], i[0])
elif cell_type == CellType.tetrahedron:
indices = [
(i, j, k)
for i in range(input_degree + 1)
for j in range(input_degree + 1 - i)
for k in range(input_degree + 1 - i - j)
]
def idx(d, i):
return index(i[2], i[1], i[0])
elif cell_type == CellType.quadrilateral:
indices = [(i, j) for i in range(input_degree + 1) for j in range(input_degree + 1)]
def idx(d, i):
return (d + 1) * i[0] + i[1]
elif cell_type == CellType.hexahedron:
indices = [
(i, j, k)
for i in range(input_degree + 1)
for j in range(input_degree + 1)
for k in range(input_degree + 1)
]
def idx(d, i):
return (d + 1) ** 2 * i[0] + (d + 1) * i[1] + i[2]
elif cell_type == CellType.pyramid:
indices = [
(i, j, k)
for k in range(input_degree + 1)
for i in range(input_degree + 1 - k)
for j in range(input_degree + 1 - k)
]
def idx(d, i):
rv = d - i[2] + 1
r0 = i[2] * (d + 1) * (d - i[2] + 2) + (2 * i[2] - 1) * (i[2] - 1) * i[2] // 6
return r0 + i[0] * rv + i[1]
elif cell_type == CellType.prism:
indices = [
(i, j, k)
for i in range(input_degree + 1)
for j in range(input_degree + 1 - i)
for k in range(input_degree + 1)
]
def idx(d, i):
return (d + 1) * index(i[1], i[0]) + i[2]
else:
raise ValueError("Unsupported cell type")
pdim_in = dim(poly_type, cell_type, input_degree)
for v in range(value_size):
for i in indices:
out[:, v * pdim + idx(output_degree, i)] = coefficients[
:, v * pdim_in + idx(input_degree, i)
]
return out
def dim(ptype: PolynomialType, celltype: CellType, degree: int) -> int:
"""Dimension of a polynomial space.
Args:
ptype: The polynomial type
celltype: The cell type
degree: The polynomial degree
Returns:
The dimension of the polynomial space
"""
return _pd(ptype, celltype, degree)
def tabulate_polynomials(
ptype: PolynomialType, celltype: CellType, degree: int, pts: npt.NDArray
) -> npt.ArrayLike:
"""Tabulate a set of polynomials on a reference cell.
Args:
ptype: The polynomial type
celltype: The cell type
degree: The polynomial degree
pts: The points
Returns:
Tabulated polynomials
"""
return _tabulate_polynomials(ptype, celltype, degree, pts)
def restriction(ptype: PolysetType, cell: CellType, restriction_cell: CellType) -> PolysetType:
"""Get the polyset type that represents the restrictions of a type on a subentity.
Args:
ptype: The polynomial type
cell: The cell type
restriction_cell: The cell type if the subentity
Returns:
The restricted polyset type
"""
return _restriction(ptype, cell, restriction_cell)
def superset(cell: CellType, type1: PolysetType, type2: PolysetType) -> PolysetType:
"""Get the polyset type that is a superset of two types on the given cell.
Args:
cell: The cell type
type1: The first polyset type
type2: The second polyset type
Returns:
The superset type
"""
return _superset(cell, type1, type2)
def tabulate_polynomial_set(
celltype: CellType, ptype: PolysetType, degree: int, nderiv: int, pts: npt.NDArray
) -> npt.ArrayLike:
"""Tabulate a polynomial set.
Args:
celltype: The cell type
ptype: The polyset type
degree: The polynomial degree
nderiv: The number of derivatives
pts: The points to tabulat at
Returns:
Tabulated polynomial set
"""
return _tps(celltype, ptype, degree, nderiv, pts)
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