722 lines
25 KiB
Python
722 lines
25 KiB
Python
"""Compressed Block Sparse Row matrix format"""
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__docformat__ = "restructuredtext en"
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__all__ = ['bsr_matrix', 'isspmatrix_bsr']
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from warnings import warn
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import numpy as np
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from ._data import _data_matrix, _minmax_mixin
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from ._compressed import _cs_matrix
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from ._base import isspmatrix, _formats, spmatrix
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from ._sputils import (isshape, getdtype, getdata, to_native, upcast,
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get_index_dtype, check_shape)
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from . import _sparsetools
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from ._sparsetools import (bsr_matvec, bsr_matvecs, csr_matmat_maxnnz,
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bsr_matmat, bsr_transpose, bsr_sort_indices,
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bsr_tocsr)
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class bsr_matrix(_cs_matrix, _minmax_mixin):
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"""Block Sparse Row matrix
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This can be instantiated in several ways:
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bsr_matrix(D, [blocksize=(R,C)])
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where D is a dense matrix or 2-D ndarray.
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bsr_matrix(S, [blocksize=(R,C)])
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with another sparse matrix S (equivalent to S.tobsr())
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bsr_matrix((M, N), [blocksize=(R,C), dtype])
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to construct an empty matrix with shape (M, N)
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dtype is optional, defaulting to dtype='d'.
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bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
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where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
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bsr_matrix((data, indices, indptr), [shape=(M, N)])
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is the standard BSR representation where the block column
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indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
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and their corresponding block values are stored in
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``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
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supplied, the matrix dimensions are inferred from the index arrays.
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Attributes
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----------
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dtype : dtype
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Data type of the matrix
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shape : 2-tuple
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Shape of the matrix
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ndim : int
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Number of dimensions (this is always 2)
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nnz
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Number of stored values, including explicit zeros
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data
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Data array of the matrix
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indices
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BSR format index array
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indptr
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BSR format index pointer array
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blocksize
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Block size of the matrix
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has_sorted_indices
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Whether indices are sorted
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Notes
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-----
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Sparse matrices can be used in arithmetic operations: they support
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addition, subtraction, multiplication, division, and matrix power.
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**Summary of BSR format**
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The Block Compressed Row (BSR) format is very similar to the Compressed
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Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
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sub matrices like the last example below. Block matrices often arise in
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vector-valued finite element discretizations. In such cases, BSR is
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considerably more efficient than CSR and CSC for many sparse arithmetic
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operations.
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**Blocksize**
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The blocksize (R,C) must evenly divide the shape of the matrix (M,N).
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That is, R and C must satisfy the relationship ``M % R = 0`` and
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``N % C = 0``.
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If no blocksize is specified, a simple heuristic is applied to determine
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an appropriate blocksize.
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Examples
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--------
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>>> from scipy.sparse import bsr_matrix
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>>> import numpy as np
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>>> bsr_matrix((3, 4), dtype=np.int8).toarray()
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array([[0, 0, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 0]], dtype=int8)
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>>> row = np.array([0, 0, 1, 2, 2, 2])
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>>> col = np.array([0, 2, 2, 0, 1, 2])
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>>> data = np.array([1, 2, 3 ,4, 5, 6])
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>>> bsr_matrix((data, (row, col)), shape=(3, 3)).toarray()
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array([[1, 0, 2],
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[0, 0, 3],
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[4, 5, 6]])
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>>> indptr = np.array([0, 2, 3, 6])
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>>> indices = np.array([0, 2, 2, 0, 1, 2])
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>>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
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>>> bsr_matrix((data,indices,indptr), shape=(6, 6)).toarray()
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array([[1, 1, 0, 0, 2, 2],
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[1, 1, 0, 0, 2, 2],
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[0, 0, 0, 0, 3, 3],
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[0, 0, 0, 0, 3, 3],
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[4, 4, 5, 5, 6, 6],
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[4, 4, 5, 5, 6, 6]])
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"""
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format = 'bsr'
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def __init__(self, arg1, shape=None, dtype=None, copy=False, blocksize=None):
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_data_matrix.__init__(self)
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if isspmatrix(arg1):
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if isspmatrix_bsr(arg1) and copy:
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arg1 = arg1.copy()
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else:
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arg1 = arg1.tobsr(blocksize=blocksize)
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self._set_self(arg1)
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elif isinstance(arg1,tuple):
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if isshape(arg1):
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# it's a tuple of matrix dimensions (M,N)
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self._shape = check_shape(arg1)
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M,N = self.shape
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# process blocksize
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if blocksize is None:
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blocksize = (1,1)
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else:
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if not isshape(blocksize):
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raise ValueError('invalid blocksize=%s' % blocksize)
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blocksize = tuple(blocksize)
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self.data = np.zeros((0,) + blocksize, getdtype(dtype, default=float))
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R,C = blocksize
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if (M % R) != 0 or (N % C) != 0:
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raise ValueError('shape must be multiple of blocksize')
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# Select index dtype large enough to pass array and
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# scalar parameters to sparsetools
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idx_dtype = get_index_dtype(maxval=max(M//R, N//C, R, C))
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self.indices = np.zeros(0, dtype=idx_dtype)
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self.indptr = np.zeros(M//R + 1, dtype=idx_dtype)
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elif len(arg1) == 2:
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# (data,(row,col)) format
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self._set_self(
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self._coo_container(arg1, dtype=dtype, shape=shape).tobsr(
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blocksize=blocksize
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)
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)
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elif len(arg1) == 3:
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# (data,indices,indptr) format
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(data, indices, indptr) = arg1
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# Select index dtype large enough to pass array and
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# scalar parameters to sparsetools
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maxval = 1
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if shape is not None:
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maxval = max(shape)
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if blocksize is not None:
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maxval = max(maxval, max(blocksize))
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idx_dtype = get_index_dtype((indices, indptr), maxval=maxval,
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check_contents=True)
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self.indices = np.array(indices, copy=copy, dtype=idx_dtype)
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self.indptr = np.array(indptr, copy=copy, dtype=idx_dtype)
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self.data = getdata(data, copy=copy, dtype=dtype)
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if self.data.ndim != 3:
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raise ValueError(
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'BSR data must be 3-dimensional, got shape=%s' % (
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self.data.shape,))
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if blocksize is not None:
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if not isshape(blocksize):
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raise ValueError('invalid blocksize=%s' % (blocksize,))
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if tuple(blocksize) != self.data.shape[1:]:
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raise ValueError('mismatching blocksize=%s vs %s' % (
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blocksize, self.data.shape[1:]))
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else:
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raise ValueError('unrecognized bsr_matrix constructor usage')
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else:
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# must be dense
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try:
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arg1 = np.asarray(arg1)
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except Exception as e:
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raise ValueError("unrecognized form for"
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" %s_matrix constructor" % self.format) from e
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arg1 = self._coo_container(
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arg1, dtype=dtype
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).tobsr(blocksize=blocksize)
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self._set_self(arg1)
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if shape is not None:
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self._shape = check_shape(shape)
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else:
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if self.shape is None:
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# shape not already set, try to infer dimensions
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try:
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M = len(self.indptr) - 1
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N = self.indices.max() + 1
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except Exception as e:
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raise ValueError('unable to infer matrix dimensions') from e
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else:
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R,C = self.blocksize
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self._shape = check_shape((M*R,N*C))
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if self.shape is None:
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if shape is None:
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# TODO infer shape here
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raise ValueError('need to infer shape')
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else:
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self._shape = check_shape(shape)
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if dtype is not None:
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self.data = self.data.astype(dtype, copy=False)
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self.check_format(full_check=False)
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def check_format(self, full_check=True):
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"""check whether the matrix format is valid
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*Parameters*:
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full_check:
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True - rigorous check, O(N) operations : default
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False - basic check, O(1) operations
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"""
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M,N = self.shape
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R,C = self.blocksize
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# index arrays should have integer data types
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if self.indptr.dtype.kind != 'i':
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warn("indptr array has non-integer dtype (%s)"
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% self.indptr.dtype.name)
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if self.indices.dtype.kind != 'i':
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warn("indices array has non-integer dtype (%s)"
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% self.indices.dtype.name)
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idx_dtype = get_index_dtype((self.indices, self.indptr))
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self.indptr = np.asarray(self.indptr, dtype=idx_dtype)
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self.indices = np.asarray(self.indices, dtype=idx_dtype)
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self.data = to_native(self.data)
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# check array shapes
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if self.indices.ndim != 1 or self.indptr.ndim != 1:
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raise ValueError("indices, and indptr should be 1-D")
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if self.data.ndim != 3:
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raise ValueError("data should be 3-D")
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# check index pointer
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if (len(self.indptr) != M//R + 1):
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raise ValueError("index pointer size (%d) should be (%d)" %
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(len(self.indptr), M//R + 1))
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if (self.indptr[0] != 0):
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raise ValueError("index pointer should start with 0")
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# check index and data arrays
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if (len(self.indices) != len(self.data)):
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raise ValueError("indices and data should have the same size")
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if (self.indptr[-1] > len(self.indices)):
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raise ValueError("Last value of index pointer should be less than "
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"the size of index and data arrays")
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self.prune()
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if full_check:
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# check format validity (more expensive)
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if self.nnz > 0:
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if self.indices.max() >= N//C:
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raise ValueError("column index values must be < %d (now max %d)" % (N//C, self.indices.max()))
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if self.indices.min() < 0:
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raise ValueError("column index values must be >= 0")
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if np.diff(self.indptr).min() < 0:
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raise ValueError("index pointer values must form a "
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"non-decreasing sequence")
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# if not self.has_sorted_indices():
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# warn('Indices were not in sorted order. Sorting indices.')
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# self.sort_indices(check_first=False)
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def _get_blocksize(self):
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return self.data.shape[1:]
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blocksize = property(fget=_get_blocksize)
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def getnnz(self, axis=None):
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if axis is not None:
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raise NotImplementedError("getnnz over an axis is not implemented "
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"for BSR format")
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R,C = self.blocksize
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return int(self.indptr[-1] * R * C)
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getnnz.__doc__ = spmatrix.getnnz.__doc__
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def __repr__(self):
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format = _formats[self.getformat()][1]
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return ("<%dx%d sparse matrix of type '%s'\n"
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"\twith %d stored elements (blocksize = %dx%d) in %s format>" %
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(self.shape + (self.dtype.type, self.nnz) + self.blocksize +
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(format,)))
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def diagonal(self, k=0):
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rows, cols = self.shape
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if k <= -rows or k >= cols:
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return np.empty(0, dtype=self.data.dtype)
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R, C = self.blocksize
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y = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
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dtype=upcast(self.dtype))
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_sparsetools.bsr_diagonal(k, rows // R, cols // C, R, C,
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self.indptr, self.indices,
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np.ravel(self.data), y)
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return y
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diagonal.__doc__ = spmatrix.diagonal.__doc__
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##########################
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# NotImplemented methods #
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##########################
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def __getitem__(self,key):
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raise NotImplementedError
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def __setitem__(self,key,val):
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raise NotImplementedError
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######################
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# Arithmetic methods #
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######################
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def _add_dense(self, other):
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return self.tocoo(copy=False)._add_dense(other)
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def _mul_vector(self, other):
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M,N = self.shape
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R,C = self.blocksize
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result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
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bsr_matvec(M//R, N//C, R, C,
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self.indptr, self.indices, self.data.ravel(),
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other, result)
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return result
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def _mul_multivector(self,other):
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R,C = self.blocksize
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M,N = self.shape
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n_vecs = other.shape[1] # number of column vectors
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result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype))
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bsr_matvecs(M//R, N//C, n_vecs, R, C,
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self.indptr, self.indices, self.data.ravel(),
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other.ravel(), result.ravel())
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return result
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def _mul_sparse_matrix(self, other):
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M, K1 = self.shape
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K2, N = other.shape
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R,n = self.blocksize
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# convert to this format
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if isspmatrix_bsr(other):
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C = other.blocksize[1]
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else:
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C = 1
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from ._csr import isspmatrix_csr
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if isspmatrix_csr(other) and n == 1:
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other = other.tobsr(blocksize=(n,C), copy=False) # lightweight conversion
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else:
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other = other.tobsr(blocksize=(n,C))
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idx_dtype = get_index_dtype((self.indptr, self.indices,
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other.indptr, other.indices))
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bnnz = csr_matmat_maxnnz(M//R, N//C,
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self.indptr.astype(idx_dtype),
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self.indices.astype(idx_dtype),
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other.indptr.astype(idx_dtype),
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other.indices.astype(idx_dtype))
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idx_dtype = get_index_dtype((self.indptr, self.indices,
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other.indptr, other.indices),
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maxval=bnnz)
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indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
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indices = np.empty(bnnz, dtype=idx_dtype)
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data = np.empty(R*C*bnnz, dtype=upcast(self.dtype,other.dtype))
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bsr_matmat(bnnz, M//R, N//C, R, C, n,
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self.indptr.astype(idx_dtype),
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self.indices.astype(idx_dtype),
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np.ravel(self.data),
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other.indptr.astype(idx_dtype),
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other.indices.astype(idx_dtype),
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np.ravel(other.data),
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indptr,
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indices,
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data)
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data = data.reshape(-1,R,C)
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# TODO eliminate zeros
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return self._bsr_container(
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(data, indices, indptr), shape=(M, N), blocksize=(R, C)
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)
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######################
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# Conversion methods #
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######################
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def tobsr(self, blocksize=None, copy=False):
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"""Convert this matrix into Block Sparse Row Format.
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With copy=False, the data/indices may be shared between this
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matrix and the resultant bsr_matrix.
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If blocksize=(R, C) is provided, it will be used for determining
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block size of the bsr_matrix.
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"""
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if blocksize not in [None, self.blocksize]:
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return self.tocsr().tobsr(blocksize=blocksize)
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if copy:
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return self.copy()
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else:
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return self
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def tocsr(self, copy=False):
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M, N = self.shape
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R, C = self.blocksize
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nnz = self.nnz
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idx_dtype = get_index_dtype((self.indptr, self.indices),
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maxval=max(nnz, N))
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indptr = np.empty(M + 1, dtype=idx_dtype)
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indices = np.empty(nnz, dtype=idx_dtype)
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data = np.empty(nnz, dtype=upcast(self.dtype))
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bsr_tocsr(M // R, # n_brow
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N // C, # n_bcol
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R, C,
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self.indptr.astype(idx_dtype, copy=False),
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self.indices.astype(idx_dtype, copy=False),
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self.data,
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indptr,
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indices,
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data)
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return self._csr_container((data, indices, indptr), shape=self.shape)
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tocsr.__doc__ = spmatrix.tocsr.__doc__
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def tocsc(self, copy=False):
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return self.tocsr(copy=False).tocsc(copy=copy)
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tocsc.__doc__ = spmatrix.tocsc.__doc__
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def tocoo(self, copy=True):
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"""Convert this matrix to COOrdinate format.
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When copy=False the data array will be shared between
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this matrix and the resultant coo_matrix.
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"""
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M,N = self.shape
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R,C = self.blocksize
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indptr_diff = np.diff(self.indptr)
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if indptr_diff.dtype.itemsize > np.dtype(np.intp).itemsize:
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# Check for potential overflow
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indptr_diff_limited = indptr_diff.astype(np.intp)
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if np.any(indptr_diff_limited != indptr_diff):
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raise ValueError("Matrix too big to convert")
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indptr_diff = indptr_diff_limited
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row = (R * np.arange(M//R)).repeat(indptr_diff)
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row = row.repeat(R*C).reshape(-1,R,C)
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row += np.tile(np.arange(R).reshape(-1,1), (1,C))
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row = row.reshape(-1)
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col = (C * self.indices).repeat(R*C).reshape(-1,R,C)
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col += np.tile(np.arange(C), (R,1))
|
|
col = col.reshape(-1)
|
|
|
|
data = self.data.reshape(-1)
|
|
|
|
if copy:
|
|
data = data.copy()
|
|
|
|
return self._coo_container(
|
|
(data, (row, col)), shape=self.shape
|
|
)
|
|
|
|
def toarray(self, order=None, out=None):
|
|
return self.tocoo(copy=False).toarray(order=order, out=out)
|
|
|
|
toarray.__doc__ = spmatrix.toarray.__doc__
|
|
|
|
def transpose(self, axes=None, copy=False):
|
|
if axes is not None:
|
|
raise ValueError(("Sparse matrices do not support "
|
|
"an 'axes' parameter because swapping "
|
|
"dimensions is the only logical permutation."))
|
|
|
|
R, C = self.blocksize
|
|
M, N = self.shape
|
|
NBLK = self.nnz//(R*C)
|
|
|
|
if self.nnz == 0:
|
|
return self._bsr_container((N, M), blocksize=(C, R),
|
|
dtype=self.dtype, copy=copy)
|
|
|
|
indptr = np.empty(N//C + 1, dtype=self.indptr.dtype)
|
|
indices = np.empty(NBLK, dtype=self.indices.dtype)
|
|
data = np.empty((NBLK, C, R), dtype=self.data.dtype)
|
|
|
|
bsr_transpose(M//R, N//C, R, C,
|
|
self.indptr, self.indices, self.data.ravel(),
|
|
indptr, indices, data.ravel())
|
|
|
|
return self._bsr_container((data, indices, indptr),
|
|
shape=(N, M), copy=copy)
|
|
|
|
transpose.__doc__ = spmatrix.transpose.__doc__
|
|
|
|
##############################################################
|
|
# methods that examine or modify the internal data structure #
|
|
##############################################################
|
|
|
|
def eliminate_zeros(self):
|
|
"""Remove zero elements in-place."""
|
|
|
|
if not self.nnz:
|
|
return # nothing to do
|
|
|
|
R,C = self.blocksize
|
|
M,N = self.shape
|
|
|
|
mask = (self.data != 0).reshape(-1,R*C).sum(axis=1) # nonzero blocks
|
|
|
|
nonzero_blocks = mask.nonzero()[0]
|
|
|
|
self.data[:len(nonzero_blocks)] = self.data[nonzero_blocks]
|
|
|
|
# modifies self.indptr and self.indices *in place*
|
|
_sparsetools.csr_eliminate_zeros(M//R, N//C, self.indptr,
|
|
self.indices, mask)
|
|
self.prune()
|
|
|
|
def sum_duplicates(self):
|
|
"""Eliminate duplicate matrix entries by adding them together
|
|
|
|
The is an *in place* operation
|
|
"""
|
|
if self.has_canonical_format:
|
|
return
|
|
self.sort_indices()
|
|
R, C = self.blocksize
|
|
M, N = self.shape
|
|
|
|
# port of _sparsetools.csr_sum_duplicates
|
|
n_row = M // R
|
|
nnz = 0
|
|
row_end = 0
|
|
for i in range(n_row):
|
|
jj = row_end
|
|
row_end = self.indptr[i+1]
|
|
while jj < row_end:
|
|
j = self.indices[jj]
|
|
x = self.data[jj]
|
|
jj += 1
|
|
while jj < row_end and self.indices[jj] == j:
|
|
x += self.data[jj]
|
|
jj += 1
|
|
self.indices[nnz] = j
|
|
self.data[nnz] = x
|
|
nnz += 1
|
|
self.indptr[i+1] = nnz
|
|
|
|
self.prune() # nnz may have changed
|
|
self.has_canonical_format = True
|
|
|
|
def sort_indices(self):
|
|
"""Sort the indices of this matrix *in place*
|
|
"""
|
|
if self.has_sorted_indices:
|
|
return
|
|
|
|
R,C = self.blocksize
|
|
M,N = self.shape
|
|
|
|
bsr_sort_indices(M//R, N//C, R, C, self.indptr, self.indices, self.data.ravel())
|
|
|
|
self.has_sorted_indices = True
|
|
|
|
def prune(self):
|
|
""" Remove empty space after all non-zero elements.
|
|
"""
|
|
|
|
R,C = self.blocksize
|
|
M,N = self.shape
|
|
|
|
if len(self.indptr) != M//R + 1:
|
|
raise ValueError("index pointer has invalid length")
|
|
|
|
bnnz = self.indptr[-1]
|
|
|
|
if len(self.indices) < bnnz:
|
|
raise ValueError("indices array has too few elements")
|
|
if len(self.data) < bnnz:
|
|
raise ValueError("data array has too few elements")
|
|
|
|
self.data = self.data[:bnnz]
|
|
self.indices = self.indices[:bnnz]
|
|
|
|
# utility functions
|
|
def _binopt(self, other, op, in_shape=None, out_shape=None):
|
|
"""Apply the binary operation fn to two sparse matrices."""
|
|
|
|
# Ideally we'd take the GCDs of the blocksize dimensions
|
|
# and explode self and other to match.
|
|
other = self.__class__(other, blocksize=self.blocksize)
|
|
|
|
# e.g. bsr_plus_bsr, etc.
|
|
fn = getattr(_sparsetools, self.format + op + self.format)
|
|
|
|
R,C = self.blocksize
|
|
|
|
max_bnnz = len(self.data) + len(other.data)
|
|
idx_dtype = get_index_dtype((self.indptr, self.indices,
|
|
other.indptr, other.indices),
|
|
maxval=max_bnnz)
|
|
indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
|
|
indices = np.empty(max_bnnz, dtype=idx_dtype)
|
|
|
|
bool_ops = ['_ne_', '_lt_', '_gt_', '_le_', '_ge_']
|
|
if op in bool_ops:
|
|
data = np.empty(R*C*max_bnnz, dtype=np.bool_)
|
|
else:
|
|
data = np.empty(R*C*max_bnnz, dtype=upcast(self.dtype,other.dtype))
|
|
|
|
fn(self.shape[0]//R, self.shape[1]//C, R, C,
|
|
self.indptr.astype(idx_dtype),
|
|
self.indices.astype(idx_dtype),
|
|
self.data,
|
|
other.indptr.astype(idx_dtype),
|
|
other.indices.astype(idx_dtype),
|
|
np.ravel(other.data),
|
|
indptr,
|
|
indices,
|
|
data)
|
|
|
|
actual_bnnz = indptr[-1]
|
|
indices = indices[:actual_bnnz]
|
|
data = data[:R*C*actual_bnnz]
|
|
|
|
if actual_bnnz < max_bnnz/2:
|
|
indices = indices.copy()
|
|
data = data.copy()
|
|
|
|
data = data.reshape(-1,R,C)
|
|
|
|
return self.__class__((data, indices, indptr), shape=self.shape)
|
|
|
|
# needed by _data_matrix
|
|
def _with_data(self,data,copy=True):
|
|
"""Returns a matrix with the same sparsity structure as self,
|
|
but with different data. By default the structure arrays
|
|
(i.e. .indptr and .indices) are copied.
|
|
"""
|
|
if copy:
|
|
return self.__class__((data,self.indices.copy(),self.indptr.copy()),
|
|
shape=self.shape,dtype=data.dtype)
|
|
else:
|
|
return self.__class__((data,self.indices,self.indptr),
|
|
shape=self.shape,dtype=data.dtype)
|
|
|
|
# # these functions are used by the parent class
|
|
# # to remove redudancy between bsc_matrix and bsr_matrix
|
|
# def _swap(self,x):
|
|
# """swap the members of x if this is a column-oriented matrix
|
|
# """
|
|
# return (x[0],x[1])
|
|
|
|
|
|
def isspmatrix_bsr(x):
|
|
"""Is x of a bsr_matrix type?
|
|
|
|
Parameters
|
|
----------
|
|
x
|
|
object to check for being a bsr matrix
|
|
|
|
Returns
|
|
-------
|
|
bool
|
|
True if x is a bsr matrix, False otherwise
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy.sparse import bsr_matrix, isspmatrix_bsr
|
|
>>> isspmatrix_bsr(bsr_matrix([[5]]))
|
|
True
|
|
|
|
>>> from scipy.sparse import bsr_matrix, csr_matrix, isspmatrix_bsr
|
|
>>> isspmatrix_bsr(csr_matrix([[5]]))
|
|
False
|
|
"""
|
|
from ._arrays import bsr_array
|
|
return isinstance(x, bsr_matrix) or isinstance(x, bsr_array)
|