You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
490 lines
16 KiB
Python
490 lines
16 KiB
Python
6 years ago
|
"""Compressed Sparse Row matrix format"""
|
||
|
|
|
||
|
|
from __future__ import division, print_function, absolute_import
|
||
|
|
|
||
|
|
__docformat__ = "restructuredtext en"
|
||
|
|
|
||
|
|
__all__ = ['csr_matrix', 'isspmatrix_csr']
|
||
|
|
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy._lib.six import xrange
|
||
|
|
|
||
|
|
from .base import spmatrix
|
||
|
|
|
||
|
|
from ._sparsetools import csr_tocsc, csr_tobsr, csr_count_blocks, \
|
||
|
|
get_csr_submatrix, csr_sample_values
|
||
|
|
from .sputils import (upcast, isintlike, IndexMixin, issequence,
|
||
|
|
get_index_dtype, ismatrix)
|
||
|
|
|
||
|
|
from .compressed import _cs_matrix
|
||
|
|
|
||
|
|
|
||
|
|
class csr_matrix(_cs_matrix, IndexMixin):
|
||
|
|
"""
|
||
|
|
Compressed Sparse Row matrix
|
||
|
|
|
||
|
|
This can be instantiated in several ways:
|
||
|
|
csr_matrix(D)
|
||
|
|
with a dense matrix or rank-2 ndarray D
|
||
|
|
|
||
|
|
csr_matrix(S)
|
||
|
|
with another sparse matrix S (equivalent to S.tocsr())
|
||
|
|
|
||
|
|
csr_matrix((M, N), [dtype])
|
||
|
|
to construct an empty matrix with shape (M, N)
|
||
|
|
dtype is optional, defaulting to dtype='d'.
|
||
|
|
|
||
|
|
csr_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
|
||
|
|
where ``data``, ``row_ind`` and ``col_ind`` satisfy the
|
||
|
|
relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
|
||
|
|
|
||
|
|
csr_matrix((data, indices, indptr), [shape=(M, N)])
|
||
|
|
is the standard CSR representation where the column indices for
|
||
|
|
row i are stored in ``indices[indptr[i]:indptr[i+1]]`` and their
|
||
|
|
corresponding 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
|
||
|
|
CSR format data array of the matrix
|
||
|
|
indices
|
||
|
|
CSR format index array of the matrix
|
||
|
|
indptr
|
||
|
|
CSR format index pointer array 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.
|
||
|
|
|
||
|
|
Advantages of the CSR format
|
||
|
|
- efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
|
||
|
|
- efficient row slicing
|
||
|
|
- fast matrix vector products
|
||
|
|
|
||
|
|
Disadvantages of the CSR format
|
||
|
|
- slow column slicing operations (consider CSC)
|
||
|
|
- changes to the sparsity structure are expensive (consider LIL or DOK)
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from scipy.sparse import csr_matrix
|
||
|
|
>>> csr_matrix((3, 4), dtype=np.int8).toarray()
|
||
|
|
array([[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])
|
||
|
|
>>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
|
||
|
|
array([[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])
|
||
|
|
>>> csr_matrix((data, indices, indptr), shape=(3, 3)).toarray()
|
||
|
|
array([[1, 0, 2],
|
||
|
|
[0, 0, 3],
|
||
|
|
[4, 5, 6]])
|
||
|
|
|
||
|
|
As an example of how to construct a CSR matrix incrementally,
|
||
|
|
the following snippet builds a term-document matrix from texts:
|
||
|
|
|
||
|
|
>>> docs = [["hello", "world", "hello"], ["goodbye", "cruel", "world"]]
|
||
|
|
>>> indptr = [0]
|
||
|
|
>>> indices = []
|
||
|
|
>>> data = []
|
||
|
|
>>> vocabulary = {}
|
||
|
|
>>> for d in docs:
|
||
|
|
... for term in d:
|
||
|
|
... index = vocabulary.setdefault(term, len(vocabulary))
|
||
|
|
... indices.append(index)
|
||
|
|
... data.append(1)
|
||
|
|
... indptr.append(len(indices))
|
||
|
|
...
|
||
|
|
>>> csr_matrix((data, indices, indptr), dtype=int).toarray()
|
||
|
|
array([[2, 1, 0, 0],
|
||
|
|
[0, 1, 1, 1]])
|
||
|
|
|
||
|
|
"""
|
||
|
|
format = 'csr'
|
||
|
|
|
||
|
|
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."))
|
||
|
|
|
||
|
|
M, N = self.shape
|
||
|
|
|
||
|
|
from .csc import csc_matrix
|
||
|
|
return csc_matrix((self.data, self.indices,
|
||
|
|
self.indptr), shape=(N, M), copy=copy)
|
||
|
|
|
||
|
|
transpose.__doc__ = spmatrix.transpose.__doc__
|
||
|
|
|
||
|
|
def tolil(self, copy=False):
|
||
|
|
from .lil import lil_matrix
|
||
|
|
lil = lil_matrix(self.shape,dtype=self.dtype)
|
||
|
|
|
||
|
|
self.sum_duplicates()
|
||
|
|
ptr,ind,dat = self.indptr,self.indices,self.data
|
||
|
|
rows, data = lil.rows, lil.data
|
||
|
|
|
||
|
|
for n in xrange(self.shape[0]):
|
||
|
|
start = ptr[n]
|
||
|
|
end = ptr[n+1]
|
||
|
|
rows[n] = ind[start:end].tolist()
|
||
|
|
data[n] = dat[start:end].tolist()
|
||
|
|
|
||
|
|
return lil
|
||
|
|
|
||
|
|
tolil.__doc__ = spmatrix.tolil.__doc__
|
||
|
|
|
||
|
|
def tocsr(self, copy=False):
|
||
|
|
if copy:
|
||
|
|
return self.copy()
|
||
|
|
else:
|
||
|
|
return self
|
||
|
|
|
||
|
|
tocsr.__doc__ = spmatrix.tocsr.__doc__
|
||
|
|
|
||
|
|
def tocsc(self, copy=False):
|
||
|
|
idx_dtype = get_index_dtype((self.indptr, self.indices),
|
||
|
|
maxval=max(self.nnz, self.shape[0]))
|
||
|
|
indptr = np.empty(self.shape[1] + 1, dtype=idx_dtype)
|
||
|
|
indices = np.empty(self.nnz, dtype=idx_dtype)
|
||
|
|
data = np.empty(self.nnz, dtype=upcast(self.dtype))
|
||
|
|
|
||
|
|
csr_tocsc(self.shape[0], self.shape[1],
|
||
|
|
self.indptr.astype(idx_dtype),
|
||
|
|
self.indices.astype(idx_dtype),
|
||
|
|
self.data,
|
||
|
|
indptr,
|
||
|
|
indices,
|
||
|
|
data)
|
||
|
|
|
||
|
|
from .csc import csc_matrix
|
||
|
|
A = csc_matrix((data, indices, indptr), shape=self.shape)
|
||
|
|
A.has_sorted_indices = True
|
||
|
|
return A
|
||
|
|
|
||
|
|
tocsc.__doc__ = spmatrix.tocsc.__doc__
|
||
|
|
|
||
|
|
def tobsr(self, blocksize=None, copy=True):
|
||
|
|
from .bsr import bsr_matrix
|
||
|
|
|
||
|
|
if blocksize is None:
|
||
|
|
from .spfuncs import estimate_blocksize
|
||
|
|
return self.tobsr(blocksize=estimate_blocksize(self))
|
||
|
|
|
||
|
|
elif blocksize == (1,1):
|
||
|
|
arg1 = (self.data.reshape(-1,1,1),self.indices,self.indptr)
|
||
|
|
return bsr_matrix(arg1, shape=self.shape, copy=copy)
|
||
|
|
|
||
|
|
else:
|
||
|
|
R,C = blocksize
|
||
|
|
M,N = self.shape
|
||
|
|
|
||
|
|
if R < 1 or C < 1 or M % R != 0 or N % C != 0:
|
||
|
|
raise ValueError('invalid blocksize %s' % blocksize)
|
||
|
|
|
||
|
|
blks = csr_count_blocks(M,N,R,C,self.indptr,self.indices)
|
||
|
|
|
||
|
|
idx_dtype = get_index_dtype((self.indptr, self.indices),
|
||
|
|
maxval=max(N//C, blks))
|
||
|
|
indptr = np.empty(M//R+1, dtype=idx_dtype)
|
||
|
|
indices = np.empty(blks, dtype=idx_dtype)
|
||
|
|
data = np.zeros((blks,R,C), dtype=self.dtype)
|
||
|
|
|
||
|
|
csr_tobsr(M, N, R, C,
|
||
|
|
self.indptr.astype(idx_dtype),
|
||
|
|
self.indices.astype(idx_dtype),
|
||
|
|
self.data,
|
||
|
|
indptr, indices, data.ravel())
|
||
|
|
|
||
|
|
return bsr_matrix((data,indices,indptr), shape=self.shape)
|
||
|
|
|
||
|
|
tobsr.__doc__ = spmatrix.tobsr.__doc__
|
||
|
|
|
||
|
|
# these functions are used by the parent class (_cs_matrix)
|
||
|
|
# to remove redudancy between csc_matrix and csr_matrix
|
||
|
|
def _swap(self, x):
|
||
|
|
"""swap the members of x if this is a column-oriented matrix
|
||
|
|
"""
|
||
|
|
return x
|
||
|
|
|
||
|
|
def __getitem__(self, key):
|
||
|
|
def asindices(x):
|
||
|
|
try:
|
||
|
|
x = np.asarray(x)
|
||
|
|
|
||
|
|
# Check index contents to avoid creating 64bit arrays needlessly
|
||
|
|
idx_dtype = get_index_dtype((x,), check_contents=True)
|
||
|
|
if idx_dtype != x.dtype:
|
||
|
|
x = x.astype(idx_dtype)
|
||
|
|
except Exception:
|
||
|
|
raise IndexError('invalid index')
|
||
|
|
else:
|
||
|
|
return x
|
||
|
|
|
||
|
|
def check_bounds(indices, N):
|
||
|
|
if indices.size == 0:
|
||
|
|
return (0, 0)
|
||
|
|
|
||
|
|
max_indx = indices.max()
|
||
|
|
if max_indx >= N:
|
||
|
|
raise IndexError('index (%d) out of range' % max_indx)
|
||
|
|
|
||
|
|
min_indx = indices.min()
|
||
|
|
if min_indx < -N:
|
||
|
|
raise IndexError('index (%d) out of range' % (N + min_indx))
|
||
|
|
|
||
|
|
return min_indx, max_indx
|
||
|
|
|
||
|
|
def extractor(indices,N):
|
||
|
|
"""Return a sparse matrix P so that P*self implements
|
||
|
|
slicing of the form self[[1,2,3],:]
|
||
|
|
"""
|
||
|
|
indices = asindices(indices).copy()
|
||
|
|
|
||
|
|
min_indx, max_indx = check_bounds(indices, N)
|
||
|
|
|
||
|
|
if min_indx < 0:
|
||
|
|
indices[indices < 0] += N
|
||
|
|
|
||
|
|
indptr = np.arange(len(indices)+1, dtype=indices.dtype)
|
||
|
|
data = np.ones(len(indices), dtype=self.dtype)
|
||
|
|
shape = (len(indices),N)
|
||
|
|
|
||
|
|
return csr_matrix((data,indices,indptr), shape=shape,
|
||
|
|
dtype=self.dtype, copy=False)
|
||
|
|
|
||
|
|
row, col = self._unpack_index(key)
|
||
|
|
|
||
|
|
# First attempt to use original row optimized methods
|
||
|
|
# [1, ?]
|
||
|
|
if isintlike(row):
|
||
|
|
# [i, j]
|
||
|
|
if isintlike(col):
|
||
|
|
return self._get_single_element(row, col)
|
||
|
|
# [i, 1:2]
|
||
|
|
elif isinstance(col, slice):
|
||
|
|
return self._get_row_slice(row, col)
|
||
|
|
# [i, [1, 2]]
|
||
|
|
elif issequence(col):
|
||
|
|
P = extractor(col,self.shape[1]).T
|
||
|
|
return self[row, :] * P
|
||
|
|
elif isinstance(row, slice):
|
||
|
|
# [1:2,??]
|
||
|
|
if ((isintlike(col) and row.step in (1, None)) or
|
||
|
|
(isinstance(col, slice) and
|
||
|
|
col.step in (1, None) and
|
||
|
|
row.step in (1, None))):
|
||
|
|
# col is int or slice with step 1, row is slice with step 1.
|
||
|
|
return self._get_submatrix(row, col)
|
||
|
|
elif issequence(col):
|
||
|
|
# row is slice, col is sequence.
|
||
|
|
P = extractor(col,self.shape[1]).T # [1:2,[1,2]]
|
||
|
|
sliced = self
|
||
|
|
if row != slice(None, None, None):
|
||
|
|
sliced = sliced[row,:]
|
||
|
|
return sliced * P
|
||
|
|
|
||
|
|
elif issequence(row):
|
||
|
|
# [[1,2],??]
|
||
|
|
if isintlike(col) or isinstance(col,slice):
|
||
|
|
P = extractor(row, self.shape[0]) # [[1,2],j] or [[1,2],1:2]
|
||
|
|
extracted = P * self
|
||
|
|
if col == slice(None, None, None):
|
||
|
|
return extracted
|
||
|
|
else:
|
||
|
|
return extracted[:,col]
|
||
|
|
|
||
|
|
elif ismatrix(row) and issequence(col):
|
||
|
|
if len(row[0]) == 1 and isintlike(row[0][0]):
|
||
|
|
# [[[1],[2]], [1,2]], outer indexing
|
||
|
|
row = asindices(row)
|
||
|
|
P_row = extractor(row[:,0], self.shape[0])
|
||
|
|
P_col = extractor(col, self.shape[1]).T
|
||
|
|
return P_row * self * P_col
|
||
|
|
|
||
|
|
if not (issequence(col) and issequence(row)):
|
||
|
|
# Sample elementwise
|
||
|
|
row, col = self._index_to_arrays(row, col)
|
||
|
|
|
||
|
|
row = asindices(row)
|
||
|
|
col = asindices(col)
|
||
|
|
if row.shape != col.shape:
|
||
|
|
raise IndexError('number of row and column indices differ')
|
||
|
|
assert row.ndim <= 2
|
||
|
|
|
||
|
|
num_samples = np.size(row)
|
||
|
|
if num_samples == 0:
|
||
|
|
return csr_matrix(np.atleast_2d(row).shape, dtype=self.dtype)
|
||
|
|
check_bounds(row, self.shape[0])
|
||
|
|
check_bounds(col, self.shape[1])
|
||
|
|
|
||
|
|
val = np.empty(num_samples, dtype=self.dtype)
|
||
|
|
csr_sample_values(self.shape[0], self.shape[1],
|
||
|
|
self.indptr, self.indices, self.data,
|
||
|
|
num_samples, row.ravel(), col.ravel(), val)
|
||
|
|
if row.ndim == 1:
|
||
|
|
# row and col are 1d
|
||
|
|
return np.asmatrix(val)
|
||
|
|
return self.__class__(val.reshape(row.shape))
|
||
|
|
|
||
|
|
def __iter__(self):
|
||
|
|
indptr = np.zeros(2, dtype=self.indptr.dtype)
|
||
|
|
shape = (1, self.shape[1])
|
||
|
|
i0 = 0
|
||
|
|
for i1 in self.indptr[1:]:
|
||
|
|
indptr[1] = i1 - i0
|
||
|
|
indices = self.indices[i0:i1]
|
||
|
|
data = self.data[i0:i1]
|
||
|
|
yield csr_matrix((data, indices, indptr), shape=shape, copy=True)
|
||
|
|
i0 = i1
|
||
|
|
|
||
|
|
def getrow(self, i):
|
||
|
|
"""Returns a copy of row i of the matrix, as a (1 x n)
|
||
|
|
CSR matrix (row vector).
|
||
|
|
"""
|
||
|
|
M, N = self.shape
|
||
|
|
i = int(i)
|
||
|
|
if i < 0:
|
||
|
|
i += M
|
||
|
|
if i < 0 or i >= M:
|
||
|
|
raise IndexError('index (%d) out of range' % i)
|
||
|
|
idx = slice(*self.indptr[i:i+2])
|
||
|
|
data = self.data[idx].copy()
|
||
|
|
indices = self.indices[idx].copy()
|
||
|
|
indptr = np.array([0, len(indices)], dtype=self.indptr.dtype)
|
||
|
|
return csr_matrix((data, indices, indptr), shape=(1, N),
|
||
|
|
dtype=self.dtype, copy=False)
|
||
|
|
|
||
|
|
def getcol(self, i):
|
||
|
|
"""Returns a copy of column i of the matrix, as a (m x 1)
|
||
|
|
CSR matrix (column vector).
|
||
|
|
"""
|
||
|
|
return self._get_submatrix(slice(None), i)
|
||
|
|
|
||
|
|
def _get_row_slice(self, i, cslice):
|
||
|
|
"""Returns a copy of row self[i, cslice]
|
||
|
|
"""
|
||
|
|
M, N = self.shape
|
||
|
|
|
||
|
|
if i < 0:
|
||
|
|
i += M
|
||
|
|
|
||
|
|
if i < 0 or i >= M:
|
||
|
|
raise IndexError('index (%d) out of range' % i)
|
||
|
|
|
||
|
|
start, stop, stride = cslice.indices(N)
|
||
|
|
|
||
|
|
if stride == 1:
|
||
|
|
# for stride == 1, get_csr_submatrix is faster
|
||
|
|
row_indptr, row_indices, row_data = get_csr_submatrix(
|
||
|
|
M, N, self.indptr, self.indices, self.data, i, i + 1,
|
||
|
|
start, stop)
|
||
|
|
else:
|
||
|
|
# other strides need new code
|
||
|
|
row_indices = self.indices[self.indptr[i]:self.indptr[i + 1]]
|
||
|
|
row_data = self.data[self.indptr[i]:self.indptr[i + 1]]
|
||
|
|
|
||
|
|
if stride > 0:
|
||
|
|
ind = (row_indices >= start) & (row_indices < stop)
|
||
|
|
else:
|
||
|
|
ind = (row_indices <= start) & (row_indices > stop)
|
||
|
|
|
||
|
|
if abs(stride) > 1:
|
||
|
|
ind &= (row_indices - start) % stride == 0
|
||
|
|
|
||
|
|
row_indices = (row_indices[ind] - start) // stride
|
||
|
|
row_data = row_data[ind]
|
||
|
|
row_indptr = np.array([0, len(row_indices)])
|
||
|
|
|
||
|
|
if stride < 0:
|
||
|
|
row_data = row_data[::-1]
|
||
|
|
row_indices = abs(row_indices[::-1])
|
||
|
|
|
||
|
|
shape = (1, int(np.ceil(float(stop - start) / stride)))
|
||
|
|
return csr_matrix((row_data, row_indices, row_indptr), shape=shape,
|
||
|
|
dtype=self.dtype, copy=False)
|
||
|
|
|
||
|
|
def _get_submatrix(self, row_slice, col_slice):
|
||
|
|
"""Return a submatrix of this matrix (new matrix is created)."""
|
||
|
|
|
||
|
|
def process_slice(sl, num):
|
||
|
|
if isinstance(sl, slice):
|
||
|
|
i0, i1, stride = sl.indices(num)
|
||
|
|
if stride != 1:
|
||
|
|
raise ValueError('slicing with step != 1 not supported')
|
||
|
|
elif isintlike(sl):
|
||
|
|
if sl < 0:
|
||
|
|
sl += num
|
||
|
|
i0, i1 = sl, sl + 1
|
||
|
|
else:
|
||
|
|
raise TypeError('expected slice or scalar')
|
||
|
|
|
||
|
|
if not (0 <= i0 <= num) or not (0 <= i1 <= num) or not (i0 <= i1):
|
||
|
|
raise IndexError(
|
||
|
|
"index out of bounds: 0 <= %d <= %d, 0 <= %d <= %d,"
|
||
|
|
" %d <= %d" % (i0, num, i1, num, i0, i1))
|
||
|
|
return i0, i1
|
||
|
|
|
||
|
|
M,N = self.shape
|
||
|
|
i0, i1 = process_slice(row_slice, M)
|
||
|
|
j0, j1 = process_slice(col_slice, N)
|
||
|
|
|
||
|
|
indptr, indices, data = get_csr_submatrix(
|
||
|
|
M, N, self.indptr, self.indices, self.data, i0, i1, j0, j1)
|
||
|
|
|
||
|
|
shape = (i1 - i0, j1 - j0)
|
||
|
|
return self.__class__((data, indices, indptr), shape=shape,
|
||
|
|
dtype=self.dtype, copy=False)
|
||
|
|
|
||
|
|
|
||
|
|
def isspmatrix_csr(x):
|
||
|
|
"""Is x of csr_matrix type?
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x
|
||
|
|
object to check for being a csr matrix
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
bool
|
||
|
|
True if x is a csr matrix, False otherwise
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.sparse import csr_matrix, isspmatrix_csr
|
||
|
|
>>> isspmatrix_csr(csr_matrix([[5]]))
|
||
|
|
True
|
||
|
|
|
||
|
|
>>> from scipy.sparse import csc_matrix, csr_matrix, isspmatrix_csc
|
||
|
|
>>> isspmatrix_csr(csc_matrix([[5]]))
|
||
|
|
False
|
||
|
|
"""
|
||
|
|
return isinstance(x, csr_matrix)
|