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"""Compressed Block Sparse Row matrix format"""
from __future__ import division, print_function, absolute_import
__docformat__ = "restructuredtext en"
__all__ = ['bsr_matrix', 'isspmatrix_bsr']
from warnings import warn
import numpy as np
from .data import _data_matrix, _minmax_mixin
from .compressed import _cs_matrix
from .base import isspmatrix, _formats
from .sputils import isshape, getdtype, to_native, upcast
from . import sparsetools
from .sparsetools import bsr_matvec, bsr_matvecs, csr_matmat_pass1, \
bsr_matmat_pass2, bsr_transpose, bsr_sort_indices
class bsr_matrix(_cs_matrix, _minmax_mixin):
"""Block Sparse Row matrix
This can be instantiated in several ways:
bsr_matrix(D, [blocksize=(R,C)])
with a dense matrix or rank-2 ndarray D
bsr_matrix(S, [blocksize=(R,C)])
with another sparse matrix S (equivalent to S.tobsr())
bsr_matrix((M, N), [blocksize=(R,C), dtype])
to construct an empty matrix with shape (M, N)
dtype is optional, defaulting to dtype='d'.
bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
bsr_matrix((data, indices, indptr), [shape=(M, N)])
is the standard BSR representation where the block column
indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
and their corresponding block values are stored in
``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
supplied, the matrix dimensions are inferred from the index arrays.
Attributes
----------
dtype : dtype
Data type of the matrix
shape : 2-tuple
Shape of the matrix
ndim : int
Number of dimensions (this is always 2)
nnz
Number of nonzero elements
data
Data array of the matrix
indices
BSR format index array
indptr
BSR format index pointer array
blocksize
Block size of the matrix
has_sorted_indices
Whether indices are sorted
Notes
-----
Sparse matrices can be used in arithmetic operations: they support
addition, subtraction, multiplication, division, and matrix power.
**Summary of BSR format**
The Block Compressed Row (BSR) format is very similar to the Compressed
Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
sub matrices like the last example below. Block matrices often arise in
vector-valued finite element discretizations. In such cases, BSR is
considerably more efficient than CSR and CSC for many sparse arithmetic
operations.
**Blocksize**
The blocksize (R,C) must evenly divide the shape of the matrix (M,N).
That is, R and C must satisfy the relationship ``M % R = 0`` and
``N % C = 0``.
If no blocksize is specified, a simple heuristic is applied to determine
an appropriate blocksize.
Examples
--------
>>> from scipy.sparse import bsr_matrix
>>> bsr_matrix((3,4), dtype=np.int8).todense()
matrix([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]], dtype=int8)
>>> row = np.array([0,0,1,2,2,2])
>>> col = np.array([0,2,2,0,1,2])
>>> data = np.array([1,2,3,4,5,6])
>>> bsr_matrix((data, (row,col)), shape=(3,3)).todense()
matrix([[1, 0, 2],
[0, 0, 3],
[4, 5, 6]])
>>> indptr = np.array([0,2,3,6])
>>> indices = np.array([0,2,2,0,1,2])
>>> data = np.array([1,2,3,4,5,6]).repeat(4).reshape(6,2,2)
>>> bsr_matrix((data,indices,indptr), shape=(6,6)).todense()
matrix([[1, 1, 0, 0, 2, 2],
[1, 1, 0, 0, 2, 2],
[0, 0, 0, 0, 3, 3],
[0, 0, 0, 0, 3, 3],
[4, 4, 5, 5, 6, 6],
[4, 4, 5, 5, 6, 6]])
"""
def __init__(self, arg1, shape=None, dtype=None, copy=False, blocksize=None):
_data_matrix.__init__(self)
if isspmatrix(arg1):
if isspmatrix_bsr(arg1) and copy:
arg1 = arg1.copy()
else:
arg1 = arg1.tobsr(blocksize=blocksize)
self._set_self(arg1)
elif isinstance(arg1,tuple):
if isshape(arg1):
# it's a tuple of matrix dimensions (M,N)
self.shape = arg1
M,N = self.shape
# process blocksize
if blocksize is None:
blocksize = (1,1)
else:
if not isshape(blocksize):
raise ValueError('invalid blocksize=%s' % blocksize)
blocksize = tuple(blocksize)
self.data = np.zeros((0,) + blocksize, getdtype(dtype, default=float))
self.indices = np.zeros(0, dtype=np.intc)
R,C = blocksize
if (M % R) != 0 or (N % C) != 0:
raise ValueError('shape must be multiple of blocksize')
self.indptr = np.zeros(M//R + 1, dtype=np.intc)
elif len(arg1) == 2:
# (data,(row,col)) format
from .coo import coo_matrix
self._set_self(coo_matrix(arg1, dtype=dtype).tobsr(blocksize=blocksize))
elif len(arg1) == 3:
# (data,indices,indptr) format
(data, indices, indptr) = arg1
self.indices = np.array(indices, copy=copy)
self.indptr = np.array(indptr, copy=copy)
self.data = np.array(data, copy=copy, dtype=getdtype(dtype, data))
else:
raise ValueError('unrecognized bsr_matrix constructor usage')
else:
# must be dense
try:
arg1 = np.asarray(arg1)
except:
raise ValueError("unrecognized form for"
" %s_matrix constructor" % self.format)
from .coo import coo_matrix
arg1 = coo_matrix(arg1, dtype=dtype).tobsr(blocksize=blocksize)
self._set_self(arg1)
if shape is not None:
self.shape = shape # spmatrix will check for errors
else:
if self.shape is None:
# shape not already set, try to infer dimensions
try:
M = len(self.indptr) - 1
N = self.indices.max() + 1
except:
raise ValueError('unable to infer matrix dimensions')
else:
R,C = self.blocksize
self.shape = (M*R,N*C)
if self.shape is None:
if shape is None:
# TODO infer shape here
raise ValueError('need to infer shape')
else:
self.shape = shape
if dtype is not None:
self.data = self.data.astype(dtype)
self.check_format(full_check=False)
def check_format(self, full_check=True):
"""check whether the matrix format is valid
*Parameters*:
full_check:
True - rigorous check, O(N) operations : default
False - basic check, O(1) operations
"""
M,N = self.shape
R,C = self.blocksize
# index arrays should have integer data types
if self.indptr.dtype.kind != 'i':
warn("indptr array has non-integer dtype (%s)"
% self.indptr.dtype.name)
if self.indices.dtype.kind != 'i':
warn("indices array has non-integer dtype (%s)"
% self.indices.dtype.name)
# only support 32-bit ints for now
self.indptr = np.asarray(self.indptr, np.intc)
self.indices = np.asarray(self.indices, np.intc)
self.data = to_native(self.data)
# check array shapes
if np.rank(self.indices) != 1 or np.rank(self.indptr) != 1:
raise ValueError("indices, and indptr should be rank 1")
if np.rank(self.data) != 3:
raise ValueError("data should be rank 3")
# check index pointer
if (len(self.indptr) != M//R + 1):
raise ValueError("index pointer size (%d) should be (%d)" %
(len(self.indptr), M//R + 1))
if (self.indptr[0] != 0):
raise ValueError("index pointer should start with 0")
# check index and data arrays
if (len(self.indices) != len(self.data)):
raise ValueError("indices and data should have the same size")
if (self.indptr[-1] > len(self.indices)):
raise ValueError("Last value of index pointer should be less than "
"the size of index and data arrays")
self.prune()
if full_check:
# check format validity (more expensive)
if self.nnz > 0:
if self.indices.max() >= N//C:
raise ValueError("column index values must be < %d (now max %d)" % (N//C, self.indices.max()))
if self.indices.min() < 0:
raise ValueError("column index values must be >= 0")
if np.diff(self.indptr).min() < 0:
raise ValueError("index pointer values must form a "
"non-decreasing sequence")
# if not self.has_sorted_indices():
# warn('Indices were not in sorted order. Sorting indices.')
# self.sort_indices(check_first=False)
def _get_blocksize(self):
return self.data.shape[1:]
blocksize = property(fget=_get_blocksize)
def getnnz(self):
R,C = self.blocksize
return int(self.indptr[-1] * R * C)
nnz = property(fget=getnnz)
def __repr__(self):
nnz = self.getnnz()
format = self.getformat()
return "<%dx%d sparse matrix of type '%s'\n" \
"\twith %d stored elements (blocksize = %dx%d) in %s format>" % \
(self.shape + (self.dtype.type, nnz) + self.blocksize +
(_formats[format][1],))
def diagonal(self):
"""Returns the main diagonal of the matrix
"""
M,N = self.shape
R,C = self.blocksize
y = np.empty(min(M,N), dtype=upcast(self.dtype))
sparsetools.bsr_diagonal(M//R, N//C, R, C,
self.indptr, self.indices, np.ravel(self.data), y)
return y
##########################
# NotImplemented methods #
##########################
def getdata(self,ind):
raise NotImplementedError
def __getitem__(self,key):
raise NotImplementedError
def __setitem__(self,key,val):
raise NotImplementedError
######################
# Arithmetic methods #
######################
def matvec(self, other):
return self * other
def matmat(self, other):
return self * other
def _mul_vector(self, other):
M,N = self.shape
R,C = self.blocksize
result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
bsr_matvec(M//R, N//C, R, C,
self.indptr, self.indices, self.data.ravel(),
other, result)
return result
def _mul_multivector(self,other):
R,C = self.blocksize
M,N = self.shape
n_vecs = other.shape[1] # number of column vectors
result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype))
bsr_matvecs(M//R, N//C, n_vecs, R, C,
self.indptr, self.indices, self.data.ravel(),
other.ravel(), result.ravel())
return result
def _mul_sparse_matrix(self, other):
M, K1 = self.shape
K2, N = other.shape
indptr = np.empty_like(self.indptr)
R,n = self.blocksize
# convert to this format
if isspmatrix_bsr(other):
C = other.blocksize[1]
else:
C = 1
from .csr import isspmatrix_csr
if isspmatrix_csr(other) and n == 1:
other = other.tobsr(blocksize=(n,C), copy=False) # lightweight conversion
else:
other = other.tobsr(blocksize=(n,C))
csr_matmat_pass1(M//R, N//C,
self.indptr, self.indices,
other.indptr, other.indices,
indptr)
bnnz = indptr[-1]
indices = np.empty(bnnz, dtype=np.intc)
data = np.empty(R*C*bnnz, dtype=upcast(self.dtype,other.dtype))
bsr_matmat_pass2(M//R, N//C, R, C, n,
self.indptr, self.indices, np.ravel(self.data),
other.indptr, other.indices, np.ravel(other.data),
indptr, indices, data)
data = data.reshape(-1,R,C)
# TODO eliminate zeros
return bsr_matrix((data,indices,indptr),shape=(M,N),blocksize=(R,C))
######################
# Conversion methods #
######################
def tobsr(self,blocksize=None,copy=False):
if blocksize not in [None, self.blocksize]:
return self.tocsr().tobsr(blocksize=blocksize)
if copy:
return self.copy()
else:
return self
def tocsr(self):
return self.tocoo(copy=False).tocsr()
# TODO make this more efficient
def tocsc(self):
return self.tocoo(copy=False).tocsc()
def tocoo(self,copy=True):
"""Convert this matrix to COOrdinate format.
When copy=False the data array will be shared between
this matrix and the resultant coo_matrix.
"""
M,N = self.shape
R,C = self.blocksize
row = (R * np.arange(M//R)).repeat(np.diff(self.indptr))
row = row.repeat(R*C).reshape(-1,R,C)
row += np.tile(np.arange(R).reshape(-1,1), (1,C))
row = row.reshape(-1)
col = (C * self.indices).repeat(R*C).reshape(-1,R,C)
col += np.tile(np.arange(C), (R,1))
col = col.reshape(-1)
data = self.data.reshape(-1)
if copy:
data = data.copy()
from .coo import coo_matrix
return coo_matrix((data,(row,col)), shape=self.shape)
def transpose(self):
R,C = self.blocksize
M,N = self.shape
NBLK = self.nnz//(R*C)
if self.nnz == 0:
return bsr_matrix((N,M), blocksize=(C,R))
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 bsr_matrix((data,indices,indptr), shape=(N,M))
##############################################################
# methods that examine or modify the internal data structure #
##############################################################
def eliminate_zeros(self):
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]
if len(nonzero_blocks) == 0:
return # nothing to do
self.data[:len(nonzero_blocks)] = self.data[nonzero_blocks]
from .csr import csr_matrix
# modifies self.indptr and self.indices *in place*
proxy = csr_matrix((mask,self.indices,self.indptr),shape=(M//R,N//C))
proxy.eliminate_zeros()
self.prune()
def sum_duplicates(self):
raise NotImplementedError
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)
indptr = np.empty_like(self.indptr)
indices = np.empty(max_bnnz, dtype=np.intc)
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, self.indices, np.ravel(self.data),
other.indptr, other.indices, 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):
return isinstance(x, bsr_matrix)
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