Source code for pytential.linalg.utils

__copyright__ = "Copyright (C) 2018-2021 Alexandru Fikl"

__license__ = """
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"""

from dataclasses import dataclass
from typing import Any, Optional, Tuple

import numpy as np

from arraycontext import PyOpenCLArrayContext
from pytools import memoize_in, memoize_method

__doc__ = """
Misc
~~~~

.. currentmodule:: pytential.linalg

.. autoclass:: BlockIndexRanges
.. autoclass:: MatrixBlockIndexRanges

.. autofunction:: make_block_index_from_array
.. autofunction:: make_index_blockwise_product
"""


# {{{ block index handling

[docs]@dataclass(frozen=True) class BlockIndexRanges: """Convenience class for working with subsets (blocks) of an array. .. attribute:: nblocks .. attribute:: indices An :class:`~numpy.ndarray` of not necessarily continuous or increasing integers representing the indices of a global array. The individual blocks are delimited using :attr:`ranges`. .. attribute:: ranges An :class:`~numpy.ndarray` of size ``(nblocks + 1,)`` consisting of nondecreasing integers used to index into :attr:`indices`. A block :math:`i` can be retrieved using ``indices[ranges[i]:ranges[i + 1]]``. .. automethod:: block_size .. automethod:: block_indices .. automethod:: block_take """ indices: np.ndarray ranges: np.ndarray @property def nblocks(self) -> int: return self.ranges.size - 1
[docs] def block_size(self, i: int) -> int: if not (0 <= i < self.nblocks): raise IndexError(f"block {i} is out of bounds for {self.nblocks} blocks") return self.ranges[i + 1] - self.ranges[i]
[docs] def block_indices(self, i: int) -> np.ndarray: """ :returns: a view into the :attr:`indices` array for the range corresponding to block *i*. """ if not (0 <= i < self.nblocks): raise IndexError(f"block {i} is out of bounds for {self.nblocks} blocks") return self.indices[self.ranges[i]:self.ranges[i + 1]]
[docs] def block_take(self, x: np.ndarray, i: int) -> np.ndarray: """ :returns: a subset of *x* corresponding to the indices in block *i*. The returned array is a copy (not a view) of the elements of *x*. """ if not (0 <= i < self.nblocks): raise IndexError(f"block {i} is out of bounds for {self.nblocks} blocks") return x[self.block_indices(i)]
[docs]@dataclass(frozen=True) class MatrixBlockIndexRanges: """Convenience class for working with subsets (blocks) of a matrix. .. attribute:: nblocks .. attribute:: row A :class:`BlockIndexRanges` encapsulating row block indices. .. attribute:: col A :class:`BlockIndexRanges` encapsulating column block indices. .. automethod:: block_shape .. automethod:: block_indices .. automethod:: block_take """ row: BlockIndexRanges col: BlockIndexRanges def __post_init__(self): if self.row.nblocks != self.col.nblocks: raise ValueError("row and column must have the same number of blocks: " f"got {self.row.nblocks} row blocks " f"and {self.col.nblocks} column blocks") @property def nblocks(self): return self.row.nblocks @property @memoize_method def _total_size(self) -> int: """ :returns: sum of all the diagonal block sizes. """ return sum( self.row.block_size(i) * self.col.block_size(i) for i in range(self.nblocks)) @property @memoize_method def _block_ranges(self): return np.cumsum([0] + [ self.row.block_size(i) * self.col.block_size(i) for i in range(self.nblocks) ])
[docs] def block_shape(self, i: int, j: int) -> Tuple[int, int]: r""" :returns: the shape of the block ``(i, j)``, where *i* indexes into the :attr:`row`\ s and *j* into the :attr:`col`\ s. """ return (self.row.block_size(i), self.col.block_size(j))
[docs] def block_indices(self, i: int, j: int) -> Tuple[np.ndarray, np.ndarray]: """ :returns: a view into the indices that make up the block ``(i, j)``. """ return (self.row.block_indices(i), self.col.block_indices(j))
[docs] def block_take(self, x: np.ndarray, i: int, j: int) -> np.ndarray: """ :returns: a subset of the matrix *x* corresponding to the indices in the block ``(i, j)``. The returned array is a copy of the elements of *x*. """ irow, icol = self.block_indices(i, j) return x[np.ix_(irow, icol)]
[docs]def make_block_index_from_array( indices: np.ndarray, ranges: Optional[np.ndarray] = None) -> BlockIndexRanges: """Wrap a ``(indices, ranges)`` tuple into a ``BlockIndexRanges``. :param ranges: if *None*, then *indices* is expected to be an object array of indices, so that the ranges can be reconstructed. """ if ranges is None: ranges = np.cumsum([0] + [r.size for r in indices]) indices = np.hstack(indices) else: if ranges[-1] != indices.size: raise ValueError("size of 'indices' does not match 'ranges' endpoint; " f"expected {indices.size}, but got {ranges[-1]}") return BlockIndexRanges(indices=indices, ranges=ranges)
[docs]def make_index_blockwise_product( actx: PyOpenCLArrayContext, idx: MatrixBlockIndexRanges) -> Tuple[Any, Any]: """Constructs a block by block Cartesian product of all the indices in *idx*. The indices in the resulting arrays are laid out in *C* order. Retrieving two-dimensional data for a block diagonal :math:`i` using the resulting index arrays can be done as follows .. code:: python offsets = np.cumsum([0] + [ idx.row.block_size(i) * idx.col.block_size(i) for i in range(idx.nblocks) ]) istart = offsets[i] iend = offsets[i + 1] block_1d = x[rowindices[istart:iend], colindices[istart:iend]] block_2d = block_1d.reshape(*idx.block_shape(i, i)) assert np.allclose(block_2d, idx.block_take(x, i, i)) The result is equivalent to :meth:`~MatrixBlockIndexRanges.block_take`, which takes the Cartesian product as well. :returns: a :class:`tuple` containing ``(rowindices, colindices)``, where the type of the arrays is the base array type of *actx*. """ @memoize_in(actx, (make_index_blockwise_product, "index_set_product_knl")) def prg(): import loopy as lp from loopy.version import MOST_RECENT_LANGUAGE_VERSION knl = lp.make_kernel([ "{[irange]: 0 <= irange < nranges}", "{[i, j]: 0 <= i < nrows and 0 <= j < ncols}" ], """ for irange <> nrows = rowranges[irange + 1] - rowranges[irange] <> ncols = colranges[irange + 1] - colranges[irange] for i, j rowproduct[offsets[irange] + ncols * i + j] = \ rowindices[rowranges[irange] + i] \ {id_prefix=write_index} colproduct[offsets[irange] + ncols * i + j] = \ colindices[colranges[irange] + j] \ {id_prefix=write_index} end end """, [ lp.GlobalArg("offsets", None, shape="nranges + 1"), lp.GlobalArg("rowproduct", None, shape="nresults"), lp.GlobalArg("colproduct", None, shape="nresults"), lp.ValueArg("nresults", np.int64), ... ], name="index_set_product_knl", default_offset=lp.auto, assumptions="nranges>=1", silenced_warnings="write_race(write_index*)", lang_version=MOST_RECENT_LANGUAGE_VERSION) knl = lp.split_iname(knl, "irange", 128, outer_tag="g.0") return knl @memoize_in(idx, (make_index_blockwise_product, "index_set_product")) def _product(): _, (rowindices, colindices) = prg()(actx.queue, rowindices=actx.from_numpy(idx.row.indices), rowranges=actx.from_numpy(idx.row.ranges), colindices=actx.from_numpy(idx.col.indices), colranges=actx.from_numpy(idx.col.ranges), offsets=actx.from_numpy(idx._block_ranges), nresults=idx._total_size, ) return actx.freeze(rowindices), actx.freeze(colindices) return _product()
def make_block_diag( mat: np.ndarray, idx: MatrixBlockIndexRanges) -> np.ndarray: """ :param mat: a one-dimensional :class:`~numpy.ndarray` that has a one-to-one correspondence to the index sets constructed by :func:`make_index_blockwise_product` for *idx*. :returns: a block diagonal object :class:`~numpy.ndarray`, where each diagonal element :math:`(i, i)` is the reshaped slice of *mat* that corresponds to the block :math:`i`. """ ranges = idx._block_ranges blk = np.full((idx.nblocks, idx.nblocks), 0, dtype=object) for i in range(idx.nblocks): blk[i, i] = mat[ranges[i]:ranges[i + 1]].reshape(idx.block_shape(i, i)) return blk # }}}