/
_construct.py
1401 lines (1149 loc) · 46.1 KB
/
_construct.py
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"""Functions to construct sparse matrices and arrays
"""
__docformat__ = "restructuredtext en"
__all__ = ['spdiags', 'eye', 'identity', 'kron', 'kronsum',
'hstack', 'vstack', 'bmat', 'rand', 'random', 'diags', 'block_diag',
'diags_array', 'block_array', 'eye_array', 'random_array']
import numbers
import math
import numpy as np
from scipy._lib._util import check_random_state, rng_integers
from ._sputils import upcast, get_index_dtype, isscalarlike
from ._sparsetools import csr_hstack
from ._bsr import bsr_matrix, bsr_array
from ._coo import coo_matrix, coo_array
from ._csc import csc_matrix, csc_array
from ._csr import csr_matrix, csr_array
from ._dia import dia_matrix, dia_array
from ._base import issparse, sparray
def spdiags(data, diags, m=None, n=None, format=None):
"""
Return a sparse matrix from diagonals.
Parameters
----------
data : array_like
Matrix diagonals stored row-wise
diags : sequence of int or an int
Diagonals to set:
* k = 0 the main diagonal
* k > 0 the kth upper diagonal
* k < 0 the kth lower diagonal
m, n : int, tuple, optional
Shape of the result. If `n` is None and `m` is a given tuple,
the shape is this tuple. If omitted, the matrix is square and
its shape is len(data[0]).
format : str, optional
Format of the result. By default (format=None) an appropriate sparse
matrix format is returned. This choice is subject to change.
.. warning::
This function returns a sparse matrix -- not a sparse array.
You are encouraged to use ``diags_array`` to take advantage
of the sparse array functionality.
See Also
--------
diags_array : more convenient form of this function
diags : matrix version of diags_array
dia_matrix : the sparse DIAgonal format.
Examples
--------
>>> import numpy as np
>>> from scipy.sparse import spdiags
>>> data = np.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
>>> diags = np.array([0, -1, 2])
>>> spdiags(data, diags, 4, 4).toarray()
array([[1, 0, 3, 0],
[1, 2, 0, 4],
[0, 2, 3, 0],
[0, 0, 3, 4]])
"""
if m is None and n is None:
m = n = len(data[0])
elif n is None:
m, n = m
return dia_matrix((data, diags), shape=(m, n)).asformat(format)
def diags_array(diagonals, /, *, offsets=0, shape=None, format=None, dtype=None):
"""
Construct a sparse array from diagonals.
Parameters
----------
diagonals : sequence of array_like
Sequence of arrays containing the array diagonals,
corresponding to `offsets`.
offsets : sequence of int or an int, optional
Diagonals to set:
- k = 0 the main diagonal (default)
- k > 0 the kth upper diagonal
- k < 0 the kth lower diagonal
shape : tuple of int, optional
Shape of the result. If omitted, a square array large enough
to contain the diagonals is returned.
format : {"dia", "csr", "csc", "lil", ...}, optional
Matrix format of the result. By default (format=None) an
appropriate sparse array format is returned. This choice is
subject to change.
dtype : dtype, optional
Data type of the array.
Notes
-----
The result from `diags_array` is the sparse equivalent of::
np.diag(diagonals[0], offsets[0])
+ ...
+ np.diag(diagonals[k], offsets[k])
Repeated diagonal offsets are disallowed.
.. versionadded:: 1.11
Examples
--------
>>> from scipy.sparse import diags_array
>>> diagonals = [[1, 2, 3, 4], [1, 2, 3], [1, 2]]
>>> diags_array(diagonals, offsets=[0, -1, 2]).toarray()
array([[1, 0, 1, 0],
[1, 2, 0, 2],
[0, 2, 3, 0],
[0, 0, 3, 4]])
Broadcasting of scalars is supported (but shape needs to be
specified):
>>> diags_array([1, -2, 1], offsets=[-1, 0, 1], shape=(4, 4)).toarray()
array([[-2., 1., 0., 0.],
[ 1., -2., 1., 0.],
[ 0., 1., -2., 1.],
[ 0., 0., 1., -2.]])
If only one diagonal is wanted (as in `numpy.diag`), the following
works as well:
>>> diags_array([1, 2, 3], offsets=1).toarray()
array([[ 0., 1., 0., 0.],
[ 0., 0., 2., 0.],
[ 0., 0., 0., 3.],
[ 0., 0., 0., 0.]])
"""
# if offsets is not a sequence, assume that there's only one diagonal
if isscalarlike(offsets):
# now check that there's actually only one diagonal
if len(diagonals) == 0 or isscalarlike(diagonals[0]):
diagonals = [np.atleast_1d(diagonals)]
else:
raise ValueError("Different number of diagonals and offsets.")
else:
diagonals = list(map(np.atleast_1d, diagonals))
offsets = np.atleast_1d(offsets)
# Basic check
if len(diagonals) != len(offsets):
raise ValueError("Different number of diagonals and offsets.")
# Determine shape, if omitted
if shape is None:
m = len(diagonals[0]) + abs(int(offsets[0]))
shape = (m, m)
# Determine data type, if omitted
if dtype is None:
dtype = np.common_type(*diagonals)
# Construct data array
m, n = shape
M = max([min(m + offset, n - offset) + max(0, offset)
for offset in offsets])
M = max(0, M)
data_arr = np.zeros((len(offsets), M), dtype=dtype)
K = min(m, n)
for j, diagonal in enumerate(diagonals):
offset = offsets[j]
k = max(0, offset)
length = min(m + offset, n - offset, K)
if length < 0:
raise ValueError("Offset %d (index %d) out of bounds" % (offset, j))
try:
data_arr[j, k:k+length] = diagonal[...,:length]
except ValueError as e:
if len(diagonal) != length and len(diagonal) != 1:
raise ValueError(
"Diagonal length (index %d: %d at offset %d) does not "
"agree with array size (%d, %d)." % (
j, len(diagonal), offset, m, n)) from e
raise
return dia_array((data_arr, offsets), shape=(m, n)).asformat(format)
def diags(diagonals, offsets=0, shape=None, format=None, dtype=None):
"""
Construct a sparse matrix from diagonals.
.. warning::
This function returns a sparse matrix -- not a sparse array.
You are encouraged to use ``diags_array`` to take advantage
of the sparse array functionality.
Parameters
----------
diagonals : sequence of array_like
Sequence of arrays containing the matrix diagonals,
corresponding to `offsets`.
offsets : sequence of int or an int, optional
Diagonals to set:
- k = 0 the main diagonal (default)
- k > 0 the kth upper diagonal
- k < 0 the kth lower diagonal
shape : tuple of int, optional
Shape of the result. If omitted, a square matrix large enough
to contain the diagonals is returned.
format : {"dia", "csr", "csc", "lil", ...}, optional
Matrix format of the result. By default (format=None) an
appropriate sparse matrix format is returned. This choice is
subject to change.
dtype : dtype, optional
Data type of the matrix.
See Also
--------
spdiags : construct matrix from diagonals
diags_array : construct sparse array instead of sparse matrix
Notes
-----
This function differs from `spdiags` in the way it handles
off-diagonals.
The result from `diags` is the sparse equivalent of::
np.diag(diagonals[0], offsets[0])
+ ...
+ np.diag(diagonals[k], offsets[k])
Repeated diagonal offsets are disallowed.
.. versionadded:: 0.11
Examples
--------
>>> from scipy.sparse import diags
>>> diagonals = [[1, 2, 3, 4], [1, 2, 3], [1, 2]]
>>> diags(diagonals, [0, -1, 2]).toarray()
array([[1, 0, 1, 0],
[1, 2, 0, 2],
[0, 2, 3, 0],
[0, 0, 3, 4]])
Broadcasting of scalars is supported (but shape needs to be
specified):
>>> diags([1, -2, 1], [-1, 0, 1], shape=(4, 4)).toarray()
array([[-2., 1., 0., 0.],
[ 1., -2., 1., 0.],
[ 0., 1., -2., 1.],
[ 0., 0., 1., -2.]])
If only one diagonal is wanted (as in `numpy.diag`), the following
works as well:
>>> diags([1, 2, 3], 1).toarray()
array([[ 0., 1., 0., 0.],
[ 0., 0., 2., 0.],
[ 0., 0., 0., 3.],
[ 0., 0., 0., 0.]])
"""
A = diags_array(diagonals, offsets=offsets, shape=shape, dtype=dtype)
return dia_matrix(A).asformat(format)
def identity(n, dtype='d', format=None):
"""Identity matrix in sparse format
Returns an identity matrix with shape (n,n) using a given
sparse format and dtype. This differs from `eye_array` in
that it has a square shape with ones only on the main diagonal.
It is thus the multiplicative identity. `eye_array` allows
rectangular shapes and the diagonal can be offset from the main one.
.. warning::
This function returns a sparse matrix -- not a sparse array.
You are encouraged to use ``eye_array`` to take advantage
of the sparse array functionality.
Parameters
----------
n : int
Shape of the identity matrix.
dtype : dtype, optional
Data type of the matrix
format : str, optional
Sparse format of the result, e.g., format="csr", etc.
Examples
--------
>>> import scipy as sp
>>> sp.sparse.identity(3).toarray()
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> sp.sparse.identity(3, dtype='int8', format='dia')
<3x3 sparse matrix of type '<class 'numpy.int8'>'
with 3 stored elements (1 diagonals) in DIAgonal format>
>>> sp.sparse.eye_array(3, dtype='int8', format='dia')
<3x3 sparse array of type '<class 'numpy.int8'>'
with 3 stored elements (1 diagonals) in DIAgonal format>
"""
return eye(n, n, dtype=dtype, format=format)
def eye_array(m, n=None, *, k=0, dtype=float, format=None):
"""Identity matrix in sparse array format
Return a sparse array with ones on diagonal.
Specifically a sparse array (m x n) where the kth diagonal
is all ones and everything else is zeros.
Parameters
----------
m : int or tuple of ints
Number of rows requested.
n : int, optional
Number of columns. Default: `m`.
k : int, optional
Diagonal to place ones on. Default: 0 (main diagonal).
dtype : dtype, optional
Data type of the array
format : str, optional (default: "dia")
Sparse format of the result, e.g., format="csr", etc.
Examples
--------
>>> import numpy as np
>>> import scipy as sp
>>> sp.sparse.eye_array(3).toarray()
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> sp.sparse.eye_array(3, dtype=np.int8)
<3x3 sparse array of type '<class 'numpy.int8'>'
with 3 stored elements (1 diagonals) in DIAgonal format>
"""
# TODO: delete next 15 lines [combine with _eye()] once spmatrix removed
return _eye(m, n, k, dtype, format)
def _eye(m, n, k, dtype, format, as_sparray=True):
if as_sparray:
csr_sparse = csr_array
csc_sparse = csc_array
coo_sparse = coo_array
diags_sparse = diags_array
else:
csr_sparse = csr_matrix
csc_sparse = csc_matrix
coo_sparse = coo_matrix
diags_sparse = diags
if n is None:
n = m
m, n = int(m), int(n)
if m == n and k == 0:
# fast branch for special formats
if format in ['csr', 'csc']:
idx_dtype = get_index_dtype(maxval=n)
indptr = np.arange(n+1, dtype=idx_dtype)
indices = np.arange(n, dtype=idx_dtype)
data = np.ones(n, dtype=dtype)
cls = {'csr': csr_sparse, 'csc': csc_sparse}[format]
return cls((data, indices, indptr), (n, n))
elif format == 'coo':
idx_dtype = get_index_dtype(maxval=n)
row = np.arange(n, dtype=idx_dtype)
col = np.arange(n, dtype=idx_dtype)
data = np.ones(n, dtype=dtype)
return coo_sparse((data, (row, col)), (n, n))
data = np.ones((1, max(0, min(m + k, n))), dtype=dtype)
return diags_sparse(data, offsets=[k], shape=(m, n), dtype=dtype).asformat(format)
def eye(m, n=None, k=0, dtype=float, format=None):
"""Sparse matrix with ones on diagonal
Returns a sparse matrix (m x n) where the kth diagonal
is all ones and everything else is zeros.
Parameters
----------
m : int
Number of rows in the matrix.
n : int, optional
Number of columns. Default: `m`.
k : int, optional
Diagonal to place ones on. Default: 0 (main diagonal).
dtype : dtype, optional
Data type of the matrix.
format : str, optional
Sparse format of the result, e.g., format="csr", etc.
.. warning::
This function returns a sparse matrix -- not a sparse array.
You are encouraged to use ``eye_array`` to take advantage
of the sparse array functionality.
Examples
--------
>>> import numpy as np
>>> import scipy as sp
>>> sp.sparse.eye(3).toarray()
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> sp.sparse.eye(3, dtype=np.int8)
<3x3 sparse matrix of type '<class 'numpy.int8'>'
with 3 stored elements (1 diagonals) in DIAgonal format>
"""
return _eye(m, n, k, dtype, format, False)
def kron(A, B, format=None):
"""kronecker product of sparse matrices A and B
Parameters
----------
A : sparse or dense matrix
first matrix of the product
B : sparse or dense matrix
second matrix of the product
format : str, optional (default: 'bsr' or 'coo')
format of the result (e.g. "csr")
If None, choose 'bsr' for relatively dense array and 'coo' for others
Returns
-------
kronecker product in a sparse format.
Returns a sparse matrix unless either A or B is a
sparse array in which case returns a sparse array.
Examples
--------
>>> import numpy as np
>>> import scipy as sp
>>> A = sp.sparse.csr_array(np.array([[0, 2], [5, 0]]))
>>> B = sp.sparse.csr_array(np.array([[1, 2], [3, 4]]))
>>> sp.sparse.kron(A, B).toarray()
array([[ 0, 0, 2, 4],
[ 0, 0, 6, 8],
[ 5, 10, 0, 0],
[15, 20, 0, 0]])
>>> sp.sparse.kron(A, [[1, 2], [3, 4]]).toarray()
array([[ 0, 0, 2, 4],
[ 0, 0, 6, 8],
[ 5, 10, 0, 0],
[15, 20, 0, 0]])
"""
# TODO: delete next 10 lines and replace _sparse with _array when spmatrix removed
if isinstance(A, sparray) or isinstance(B, sparray):
# convert to local variables
bsr_sparse = bsr_array
csr_sparse = csr_array
coo_sparse = coo_array
else: # use spmatrix
bsr_sparse = bsr_matrix
csr_sparse = csr_matrix
coo_sparse = coo_matrix
B = coo_sparse(B)
# B is fairly dense, use BSR
if (format is None or format == "bsr") and 2*B.nnz >= B.shape[0] * B.shape[1]:
A = csr_sparse(A,copy=True)
output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1])
if A.nnz == 0 or B.nnz == 0:
# kronecker product is the zero matrix
return coo_sparse(output_shape).asformat(format)
B = B.toarray()
data = A.data.repeat(B.size).reshape(-1,B.shape[0],B.shape[1])
data = data * B
return bsr_sparse((data,A.indices,A.indptr), shape=output_shape)
else:
# use COO
A = coo_sparse(A)
output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1])
if A.nnz == 0 or B.nnz == 0:
# kronecker product is the zero matrix
return coo_sparse(output_shape).asformat(format)
# expand entries of a into blocks
row = A.row.repeat(B.nnz)
col = A.col.repeat(B.nnz)
data = A.data.repeat(B.nnz)
if max(A.shape[0]*B.shape[0], A.shape[1]*B.shape[1]) > np.iinfo('int32').max:
row = row.astype(np.int64)
col = col.astype(np.int64)
row *= B.shape[0]
col *= B.shape[1]
# increment block indices
row,col = row.reshape(-1,B.nnz),col.reshape(-1,B.nnz)
row += B.row
col += B.col
row,col = row.reshape(-1),col.reshape(-1)
# compute block entries
data = data.reshape(-1,B.nnz) * B.data
data = data.reshape(-1)
return coo_sparse((data,(row,col)), shape=output_shape).asformat(format)
def kronsum(A, B, format=None):
"""kronecker sum of square sparse matrices A and B
Kronecker sum of two sparse matrices is a sum of two Kronecker
products kron(I_n,A) + kron(B,I_m) where A has shape (m,m)
and B has shape (n,n) and I_m and I_n are identity matrices
of shape (m,m) and (n,n), respectively.
Parameters
----------
A
square matrix
B
square matrix
format : str
format of the result (e.g. "csr")
Returns
-------
kronecker sum in a sparse matrix format
"""
# TODO: delete next 8 lines and replace _sparse with _array when spmatrix removed
if isinstance(A, sparray) or isinstance(B, sparray):
# convert to local variables
coo_sparse = coo_array
identity_sparse = eye_array
else:
coo_sparse = coo_matrix
identity_sparse = identity
A = coo_sparse(A)
B = coo_sparse(B)
if A.shape[0] != A.shape[1]:
raise ValueError('A is not square')
if B.shape[0] != B.shape[1]:
raise ValueError('B is not square')
dtype = upcast(A.dtype, B.dtype)
I_n = identity_sparse(A.shape[0], dtype=dtype)
I_m = identity_sparse(B.shape[0], dtype=dtype)
L = kron(I_m, A, format='coo')
R = kron(B, I_n, format='coo')
return (L + R).asformat(format)
def _compressed_sparse_stack(blocks, axis, return_spmatrix):
"""
Stacking fast path for CSR/CSC matrices or arrays
(i) vstack for CSR, (ii) hstack for CSC.
"""
other_axis = 1 if axis == 0 else 0
data = np.concatenate([b.data for b in blocks])
constant_dim = blocks[0].shape[other_axis]
idx_dtype = get_index_dtype(arrays=[b.indptr for b in blocks],
maxval=max(data.size, constant_dim))
indices = np.empty(data.size, dtype=idx_dtype)
indptr = np.empty(sum(b.shape[axis] for b in blocks) + 1, dtype=idx_dtype)
last_indptr = idx_dtype(0)
sum_dim = 0
sum_indices = 0
for b in blocks:
if b.shape[other_axis] != constant_dim:
raise ValueError(f'incompatible dimensions for axis {other_axis}')
indices[sum_indices:sum_indices+b.indices.size] = b.indices
sum_indices += b.indices.size
idxs = slice(sum_dim, sum_dim + b.shape[axis])
indptr[idxs] = b.indptr[:-1]
indptr[idxs] += last_indptr
sum_dim += b.shape[axis]
last_indptr += b.indptr[-1]
indptr[-1] = last_indptr
# TODO remove this if-structure when sparse matrices removed
if return_spmatrix:
if axis == 0:
return csr_matrix((data, indices, indptr),
shape=(sum_dim, constant_dim))
else:
return csc_matrix((data, indices, indptr),
shape=(constant_dim, sum_dim))
if axis == 0:
return csr_array((data, indices, indptr),
shape=(sum_dim, constant_dim))
else:
return csc_array((data, indices, indptr),
shape=(constant_dim, sum_dim))
def _stack_along_minor_axis(blocks, axis):
"""
Stacking fast path for CSR/CSC matrices along the minor axis
(i) hstack for CSR, (ii) vstack for CSC.
"""
n_blocks = len(blocks)
if n_blocks == 0:
raise ValueError('Missing block matrices')
if n_blocks == 1:
return blocks[0]
# check for incompatible dimensions
other_axis = 1 if axis == 0 else 0
other_axis_dims = {b.shape[other_axis] for b in blocks}
if len(other_axis_dims) > 1:
raise ValueError(f'Mismatching dimensions along axis {other_axis}: '
f'{other_axis_dims}')
constant_dim, = other_axis_dims
# Do the stacking
indptr_list = [b.indptr for b in blocks]
data_cat = np.concatenate([b.data for b in blocks])
# Need to check if any indices/indptr, would be too large post-
# concatenation for np.int32:
# - The max value of indices is the output array's stacking-axis length - 1
# - The max value in indptr is the number of non-zero entries. This is
# exceedingly unlikely to require int64, but is checked out of an
# abundance of caution.
sum_dim = sum(b.shape[axis] for b in blocks)
nnz = sum(len(b.indices) for b in blocks)
idx_dtype = get_index_dtype(maxval=max(sum_dim - 1, nnz))
stack_dim_cat = np.array([b.shape[axis] for b in blocks], dtype=idx_dtype)
if data_cat.size > 0:
indptr_cat = np.concatenate(indptr_list).astype(idx_dtype)
indices_cat = (np.concatenate([b.indices for b in blocks])
.astype(idx_dtype))
indptr = np.empty(constant_dim + 1, dtype=idx_dtype)
indices = np.empty_like(indices_cat)
data = np.empty_like(data_cat)
csr_hstack(n_blocks, constant_dim, stack_dim_cat,
indptr_cat, indices_cat, data_cat,
indptr, indices, data)
else:
indptr = np.zeros(constant_dim + 1, dtype=idx_dtype)
indices = np.empty(0, dtype=idx_dtype)
data = np.empty(0, dtype=data_cat.dtype)
if axis == 0:
return blocks[0]._csc_container((data, indices, indptr),
shape=(sum_dim, constant_dim))
else:
return blocks[0]._csr_container((data, indices, indptr),
shape=(constant_dim, sum_dim))
def hstack(blocks, format=None, dtype=None):
"""
Stack sparse matrices horizontally (column wise)
Parameters
----------
blocks
sequence of sparse matrices with compatible shapes
format : str
sparse format of the result (e.g., "csr")
by default an appropriate sparse matrix format is returned.
This choice is subject to change.
dtype : dtype, optional
The data-type of the output matrix. If not given, the dtype is
determined from that of `blocks`.
Returns
-------
new_array : sparse matrix or array
If any block in blocks is a sparse array, return a sparse array.
Otherwise return a sparse matrix.
If you want a sparse array built from blocks that are not sparse
arrays, use `block(hstack(blocks))` or convert one block
e.g. `blocks[0] = csr_array(blocks[0])`.
See Also
--------
vstack : stack sparse matrices vertically (row wise)
Examples
--------
>>> from scipy.sparse import coo_matrix, hstack
>>> A = coo_matrix([[1, 2], [3, 4]])
>>> B = coo_matrix([[5], [6]])
>>> hstack([A,B]).toarray()
array([[1, 2, 5],
[3, 4, 6]])
"""
blocks = np.asarray(blocks, dtype='object')
if any(isinstance(b, sparray) for b in blocks.flat):
return _block([blocks], format, dtype)
else:
return _block([blocks], format, dtype, return_spmatrix=True)
def vstack(blocks, format=None, dtype=None):
"""
Stack sparse arrays vertically (row wise)
Parameters
----------
blocks
sequence of sparse arrays with compatible shapes
format : str, optional
sparse format of the result (e.g., "csr")
by default an appropriate sparse array format is returned.
This choice is subject to change.
dtype : dtype, optional
The data-type of the output array. If not given, the dtype is
determined from that of `blocks`.
Returns
-------
new_array : sparse matrix or array
If any block in blocks is a sparse array, return a sparse array.
Otherwise return a sparse matrix.
If you want a sparse array built from blocks that are not sparse
arrays, use `block(vstack(blocks))` or convert one block
e.g. `blocks[0] = csr_array(blocks[0])`.
See Also
--------
hstack : stack sparse matrices horizontally (column wise)
Examples
--------
>>> from scipy.sparse import coo_array, vstack
>>> A = coo_array([[1, 2], [3, 4]])
>>> B = coo_array([[5, 6]])
>>> vstack([A, B]).toarray()
array([[1, 2],
[3, 4],
[5, 6]])
"""
blocks = np.asarray(blocks, dtype='object')
if any(isinstance(b, sparray) for b in blocks.flat):
return _block([[b] for b in blocks], format, dtype)
else:
return _block([[b] for b in blocks], format, dtype, return_spmatrix=True)
def bmat(blocks, format=None, dtype=None):
"""
Build a sparse array or matrix from sparse sub-blocks
Note: `block_array` is preferred over `bmat`. They are the same function
except that `bmat` can return a deprecated sparse matrix.
`bmat` returns a coo_matrix if none of the inputs are a sparse array.
.. warning::
This function returns a sparse matrix -- not a sparse array.
You are encouraged to use ``block_array`` to take advantage
of the sparse array functionality.
Parameters
----------
blocks : array_like
Grid of sparse matrices with compatible shapes.
An entry of None implies an all-zero matrix.
format : {'bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil'}, optional
The sparse format of the result (e.g. "csr"). By default an
appropriate sparse matrix format is returned.
This choice is subject to change.
dtype : dtype, optional
The data-type of the output matrix. If not given, the dtype is
determined from that of `blocks`.
Returns
-------
bmat : sparse matrix or array
If any block in blocks is a sparse array, return a sparse array.
Otherwise return a sparse matrix.
If you want a sparse array built from blocks that are not sparse
arrays, use `block_array()`.
See Also
--------
block_array
Examples
--------
>>> from scipy.sparse import coo_array, bmat
>>> A = coo_array([[1, 2], [3, 4]])
>>> B = coo_array([[5], [6]])
>>> C = coo_array([[7]])
>>> bmat([[A, B], [None, C]]).toarray()
array([[1, 2, 5],
[3, 4, 6],
[0, 0, 7]])
>>> bmat([[A, None], [None, C]]).toarray()
array([[1, 2, 0],
[3, 4, 0],
[0, 0, 7]])
"""
blocks = np.asarray(blocks, dtype='object')
if any(isinstance(b, sparray) for b in blocks.flat):
return _block(blocks, format, dtype)
else:
return _block(blocks, format, dtype, return_spmatrix=True)
def block_array(blocks, *, format=None, dtype=None):
"""
Build a sparse array from sparse sub-blocks
Parameters
----------
blocks : array_like
Grid of sparse arrays with compatible shapes.
An entry of None implies an all-zero array.
format : {'bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil'}, optional
The sparse format of the result (e.g. "csr"). By default an
appropriate sparse array format is returned.
This choice is subject to change.
dtype : dtype, optional
The data-type of the output array. If not given, the dtype is
determined from that of `blocks`.
Returns
-------
block : sparse array
See Also
--------
block_diag : specify blocks along the main diagonals
diags : specify (possibly offset) diagonals
Examples
--------
>>> from scipy.sparse import coo_array, block_array
>>> A = coo_array([[1, 2], [3, 4]])
>>> B = coo_array([[5], [6]])
>>> C = coo_array([[7]])
>>> block_array([[A, B], [None, C]]).toarray()
array([[1, 2, 5],
[3, 4, 6],
[0, 0, 7]])
>>> block_array([[A, None], [None, C]]).toarray()
array([[1, 2, 0],
[3, 4, 0],
[0, 0, 7]])
"""
return _block(blocks, format, dtype)
def _block(blocks, format, dtype, return_spmatrix=False):
blocks = np.asarray(blocks, dtype='object')
if blocks.ndim != 2:
raise ValueError('blocks must be 2-D')
M,N = blocks.shape
# check for fast path cases
if (format in (None, 'csr') and
all(issparse(b) and b.format == 'csr' for b in blocks.flat)
):
if N > 1:
# stack along columns (axis 1): must have shape (M, 1)
blocks = [[_stack_along_minor_axis(blocks[b, :], 1)] for b in range(M)]
blocks = np.asarray(blocks, dtype='object')
# stack along rows (axis 0):
A = _compressed_sparse_stack(blocks[:, 0], 0, return_spmatrix)
if dtype is not None:
A = A.astype(dtype)
return A
elif (format in (None, 'csc') and
all(issparse(b) and b.format == 'csc' for b in blocks.flat)
):
if M > 1:
# stack along rows (axis 0): must have shape (1, N)
blocks = [[_stack_along_minor_axis(blocks[:, b], 0) for b in range(N)]]
blocks = np.asarray(blocks, dtype='object')
# stack along columns (axis 1):
A = _compressed_sparse_stack(blocks[0, :], 1, return_spmatrix)
if dtype is not None:
A = A.astype(dtype)
return A
block_mask = np.zeros(blocks.shape, dtype=bool)
brow_lengths = np.zeros(M, dtype=np.int64)
bcol_lengths = np.zeros(N, dtype=np.int64)
# convert everything to COO format
for i in range(M):
for j in range(N):
if blocks[i,j] is not None:
A = coo_array(blocks[i,j])
blocks[i,j] = A
block_mask[i,j] = True
if brow_lengths[i] == 0:
brow_lengths[i] = A.shape[0]
elif brow_lengths[i] != A.shape[0]:
msg = (f'blocks[{i},:] has incompatible row dimensions. '
f'Got blocks[{i},{j}].shape[0] == {A.shape[0]}, '
f'expected {brow_lengths[i]}.')
raise ValueError(msg)
if bcol_lengths[j] == 0:
bcol_lengths[j] = A.shape[1]
elif bcol_lengths[j] != A.shape[1]:
msg = (f'blocks[:,{j}] has incompatible column '
f'dimensions. '
f'Got blocks[{i},{j}].shape[1] == {A.shape[1]}, '
f'expected {bcol_lengths[j]}.')
raise ValueError(msg)
nnz = sum(block.nnz for block in blocks[block_mask])
if dtype is None:
all_dtypes = [blk.dtype for blk in blocks[block_mask]]
dtype = upcast(*all_dtypes) if all_dtypes else None
row_offsets = np.append(0, np.cumsum(brow_lengths))
col_offsets = np.append(0, np.cumsum(bcol_lengths))
shape = (row_offsets[-1], col_offsets[-1])
data = np.empty(nnz, dtype=dtype)
idx_dtype = get_index_dtype(maxval=max(shape))
row = np.empty(nnz, dtype=idx_dtype)
col = np.empty(nnz, dtype=idx_dtype)
nnz = 0
ii, jj = np.nonzero(block_mask)
for i, j in zip(ii, jj):
B = blocks[i, j]
idx = slice(nnz, nnz + B.nnz)
data[idx] = B.data
np.add(B.row, row_offsets[i], out=row[idx], dtype=idx_dtype)
np.add(B.col, col_offsets[j], out=col[idx], dtype=idx_dtype)
nnz += B.nnz
if return_spmatrix:
return coo_matrix((data, (row, col)), shape=shape).asformat(format)
return coo_array((data, (row, col)), shape=shape).asformat(format)
def block_diag(mats, format=None, dtype=None):
"""
Build a block diagonal sparse matrix or array from provided matrices.
Parameters
----------
mats : sequence of matrices or arrays
Input matrices or arrays.
format : str, optional
The sparse format of the result (e.g., "csr"). If not given, the result
is returned in "coo" format.
dtype : dtype specifier, optional