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| Original file line number | Diff line number | Diff line change |
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| """Abstract base class for basis.""" | ||
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| from __future__ import annotations | ||
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| from typing import Any, Tuple, TypeVar | ||
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| import multimethod | ||
| import numpy as np | ||
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| from ...typing._numpy import NDArrayFloat | ||
| from .._functional_data import FData | ||
| from ..grid import FDataGrid | ||
| from ._basis import Basis | ||
| from ._fdatabasis import FDataBasis | ||
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| T = TypeVar("T", bound="CustomBasis") | ||
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| class CustomBasis(Basis): | ||
| """Basis composed of custom functions. | ||
| Defines a basis composed of the functions in the :class: `FData` object | ||
| passed as argument. | ||
| The functions must be linearly independent, otherwise | ||
| an exception is raised. | ||
| Parameters: | ||
| fdata: Functions that define the basis. | ||
| """ | ||
|
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| def __init__( | ||
| self, | ||
| *, | ||
| fdata: FData, | ||
| ) -> None: | ||
| """Basis constructor.""" | ||
| super().__init__( | ||
| domain_range=fdata.domain_range, | ||
| n_basis=fdata.n_samples, | ||
| ) | ||
| self._check_linearly_independent(fdata) | ||
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| self.fdata = fdata | ||
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| @multimethod.multidispatch | ||
| def _check_linearly_independent(self, fdata: FData) -> None: | ||
| raise ValueError("Unexpected type of functional data object.") | ||
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| @_check_linearly_independent.register | ||
| def _check_linearly_independent_grid(self, fdata: FDataGrid) -> None: | ||
| # Reshape to a bidimensional matrix. This only affects FDataGrids | ||
| # whose codomain is not 1-dimensional and it can be done because | ||
| # checking linear independence in (R^n)^k is equivalent to doing | ||
| # it in R^(nk). | ||
| coord_matrix = fdata.data_matrix.reshape( | ||
| fdata.data_matrix.shape[0], | ||
| -1, | ||
| ) | ||
| return self._check_linearly_independent_matrix(coord_matrix) | ||
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| @_check_linearly_independent.register | ||
| def _check_linearly_independent_basis(self, fdata: FDataBasis) -> None: | ||
| return self._check_linearly_independent_matrix(fdata.coefficients) | ||
|
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| def _check_linearly_independent_matrix(self, matrix: NDArrayFloat) -> None: | ||
| """Check if the functions are linearly independent.""" | ||
| if matrix.shape[0] > matrix.shape[1]: | ||
| raise ValueError( | ||
| "There are more functions than the maximum dimension of the " | ||
| "space that they could generate.", | ||
| ) | ||
|
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| rank = np.linalg.matrix_rank(matrix) | ||
| if rank != matrix.shape[0]: | ||
| raise ValueError( | ||
| "There are only {rank} linearly independent " | ||
| "functions".format( | ||
| rank=rank, | ||
| ), | ||
| ) | ||
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| def _derivative_basis_and_coefs( | ||
| self: T, | ||
| coefs: NDArrayFloat, | ||
| order: int = 1, | ||
| ) -> Tuple[T, NDArrayFloat]: | ||
| deriv_fdata = self.fdata.derivative(order=order) | ||
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| return self._create_subspace_basis_coef(deriv_fdata, coefs) | ||
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| @multimethod.multidispatch | ||
| def _create_subspace_basis_coef( | ||
| self: T, | ||
| fdata: FData, | ||
| coefs: np.ndarray, | ||
| ) -> Tuple[T, NDArrayFloat]: | ||
| """ | ||
| Create a basis of the subspace generated by the given functions. | ||
| Args: | ||
| fdata: The resulting basis will span the subspace generated | ||
| by these functions. | ||
| coefs: Coefficients of some functions in the given fdata. | ||
| These coefficients will be transformed into the coefficients | ||
| of the same functions in the resulting basis. | ||
| """ | ||
| raise ValueError( | ||
| "Unexpected type of functional data object: {type}.".format( | ||
| type=type(fdata), | ||
| ), | ||
| ) | ||
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| @_create_subspace_basis_coef.register | ||
| def _create_subspace_basis_coef_grid( | ||
| self: T, | ||
| fdata: FDataGrid, | ||
| coefs: np.ndarray, | ||
| ) -> Tuple[T, NDArrayFloat]: | ||
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| # Reshape to a bidimensional matrix. This can be done because | ||
| # working in (R^n)^k is equivalent to working in R^(nk) when | ||
| # it comes to linear independence and basis. | ||
| data_matrix_reshaped = fdata.data_matrix.reshape( | ||
| fdata.data_matrix.shape[0], | ||
| -1, | ||
| ) | ||
| # If the basis formed by the derivatives has maximum rank, | ||
| # we can just return that | ||
| rank = np.linalg.matrix_rank(data_matrix_reshaped) | ||
| if rank == fdata.n_samples: | ||
| return type(self)(fdata=fdata), coefs | ||
|
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| # Otherwise, we need to find the basis of the subspace generated | ||
| # by the functions | ||
| q, r = np.linalg.qr(data_matrix_reshaped.T) | ||
|
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| # Go back from R^(nk) to (R^n)^k | ||
| fdata.data_matrix = q.T.reshape( | ||
| -1, | ||
| *fdata.data_matrix.shape[1:], | ||
| ) | ||
|
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| new_basis = type(self)(fdata=fdata) | ||
|
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| # Since the QR decomponsition yields an orthonormal basis, | ||
| # the coefficients are just the projections of values of | ||
| # the functions in every point (coefs @ data_matrix_reshaped) | ||
| # in the new basis (q). | ||
| # Note that to simply the calculations, we use both the data_matrix | ||
| # and the basis matrix in R^(nk) instead of the original space | ||
| values_in_eval_points = coefs @ data_matrix_reshaped | ||
| coefs = values_in_eval_points @ q | ||
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| return new_basis, coefs | ||
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| @_create_subspace_basis_coef.register | ||
| def _create_subspace_basis_coef_basis( | ||
| self: T, | ||
| fdata: FDataBasis, | ||
| coefs: np.ndarray, | ||
| ) -> Tuple[T, NDArrayFloat]: | ||
|
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| # If the basis formed by the derivatives has maximum rank, | ||
| # we can just return that | ||
| rank = np.linalg.matrix_rank(fdata.coefficients) | ||
| if rank == fdata.n_samples: | ||
| return type(self)(fdata=fdata), coefs | ||
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| q, r = np.linalg.qr(fdata.coefficients.T) | ||
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| fdata.coefficients = q.T | ||
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| new_basis = type(self)(fdata=fdata) | ||
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| # Since the QR decomponsition yields an orthonormal basis, | ||
| # the coefficients are just the result of projecting the | ||
| # coefficients in the underlying basis of the FDataBasis onto | ||
| # the new basis (q) | ||
| coefs_wrt_underlying_fdata_basis = coefs @ fdata.coefficients | ||
| coefs = coefs_wrt_underlying_fdata_basis @ q | ||
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| return new_basis, coefs | ||
|
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| def _coordinate_nonfull( | ||
| self, | ||
| coefs: NDArrayFloat, | ||
| key: int | slice, | ||
| ) -> Tuple[Basis, NDArrayFloat]: | ||
| return CustomBasis(fdata=self.fdata.coordinates[key]), coefs | ||
|
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| def _evaluate( | ||
| self, | ||
| eval_points: NDArrayFloat, | ||
| ) -> NDArrayFloat: | ||
| return self.fdata(eval_points) | ||
|
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| def __len__(self) -> int: | ||
| return self.n_basis | ||
|
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| @property | ||
| def dim_codomain(self) -> int: | ||
| return self.fdata.dim_codomain | ||
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| def __eq__(self, other: Any) -> bool: | ||
| return super().__eq__(other) and all(self.fdata == other.fdata) | ||
|
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| def __ne__(self, other: Any) -> bool: | ||
| return not self.__eq__(other) | ||
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| def __repr__(self) -> str: | ||
| """Representation of a CustomBasis object.""" | ||
| return "{super}, fdata={fdata}".format( | ||
| super=super().__repr__(), | ||
| fdata=self.fdata, | ||
| ) | ||
|
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| def __hash__(self) -> int: | ||
| return hash(self.fdata) |
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