/
coo.py
507 lines (416 loc) · 17.8 KB
/
coo.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
""" A sparse matrix in COOrdinate or 'triplet' format"""
from __future__ import division, print_function, absolute_import
__docformat__ = "restructuredtext en"
__all__ = ['coo_matrix', 'isspmatrix_coo']
from warnings import warn
import numpy as np
from scipy._lib.six import zip as izip
from ._sparsetools import coo_tocsr, coo_todense, coo_matvec
from .base import isspmatrix, SparseEfficiencyWarning, spmatrix
from .data import _data_matrix, _minmax_mixin
from .sputils import (upcast, upcast_char, to_native, isshape, getdtype,
get_index_dtype, downcast_intp_index)
class coo_matrix(_data_matrix, _minmax_mixin):
"""
A sparse matrix in COOrdinate format.
Also known as the 'ijv' or 'triplet' format.
This can be instantiated in several ways:
coo_matrix(D)
with a dense matrix D
coo_matrix(S)
with another sparse matrix S (equivalent to S.tocoo())
coo_matrix((M, N), [dtype])
to construct an empty matrix with shape (M, N)
dtype is optional, defaulting to dtype='d'.
coo_matrix((data, (i, j)), [shape=(M, N)])
to construct from three arrays:
1. data[:] the entries of the matrix, in any order
2. i[:] the row indices of the matrix entries
3. j[:] the column indices of the matrix entries
Where ``A[i[k], j[k]] = data[k]``. When shape is not
specified, it is 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
COO format data array of the matrix
row
COO format row index array of the matrix
col
COO format column index array of the matrix
Notes
-----
Sparse matrices can be used in arithmetic operations: they support
addition, subtraction, multiplication, division, and matrix power.
Advantages of the COO format
- facilitates fast conversion among sparse formats
- permits duplicate entries (see example)
- very fast conversion to and from CSR/CSC formats
Disadvantages of the COO format
- does not directly support:
+ arithmetic operations
+ slicing
Intended Usage
- COO is a fast format for constructing sparse matrices
- Once a matrix has been constructed, convert to CSR or
CSC format for fast arithmetic and matrix vector operations
- By default when converting to CSR or CSC format, duplicate (i,j)
entries will be summed together. This facilitates efficient
construction of finite element matrices and the like. (see example)
Examples
--------
>>> from scipy.sparse import coo_matrix
>>> coo_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, 3, 1, 0])
>>> col = np.array([0, 3, 1, 2])
>>> data = np.array([4, 5, 7, 9])
>>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
array([[4, 0, 9, 0],
[0, 7, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 5]])
>>> # example with duplicates
>>> row = np.array([0, 0, 1, 3, 1, 0, 0])
>>> col = np.array([0, 2, 1, 3, 1, 0, 0])
>>> data = np.array([1, 1, 1, 1, 1, 1, 1])
>>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
array([[3, 0, 1, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
"""
format = 'coo'
def __init__(self, arg1, shape=None, dtype=None, copy=False):
_data_matrix.__init__(self)
if isinstance(arg1, tuple):
if isshape(arg1):
M, N = arg1
self.shape = (M,N)
idx_dtype = get_index_dtype(maxval=max(M, N))
self.row = np.array([], dtype=idx_dtype)
self.col = np.array([], dtype=idx_dtype)
self.data = np.array([], getdtype(dtype, default=float))
self.has_canonical_format = True
else:
try:
obj, (row, col) = arg1
except (TypeError, ValueError):
raise TypeError('invalid input format')
if shape is None:
if len(row) == 0 or len(col) == 0:
raise ValueError('cannot infer dimensions from zero '
'sized index arrays')
M = np.max(row) + 1
N = np.max(col) + 1
self.shape = (M, N)
else:
# Use 2 steps to ensure shape has length 2.
M, N = shape
self.shape = (M, N)
idx_dtype = get_index_dtype(maxval=max(self.shape))
self.row = np.array(row, copy=copy, dtype=idx_dtype)
self.col = np.array(col, copy=copy, dtype=idx_dtype)
self.data = np.array(obj, copy=copy)
self.has_canonical_format = False
else:
if isspmatrix(arg1):
if isspmatrix_coo(arg1) and copy:
self.row = arg1.row.copy()
self.col = arg1.col.copy()
self.data = arg1.data.copy()
self.shape = arg1.shape
else:
coo = arg1.tocoo()
self.row = coo.row
self.col = coo.col
self.data = coo.data
self.shape = coo.shape
self.has_canonical_format = False
else:
#dense argument
M = np.atleast_2d(np.asarray(arg1))
if M.ndim != 2:
raise TypeError('expected dimension <= 2 array or matrix')
else:
self.shape = M.shape
self.row, self.col = M.nonzero()
self.data = M[self.row, self.col]
self.has_canonical_format = True
if dtype is not None:
self.data = self.data.astype(dtype, copy=False)
self._check()
def getnnz(self, axis=None):
if axis is None:
nnz = len(self.data)
if nnz != len(self.row) or nnz != len(self.col):
raise ValueError('row, column, and data array must all be the '
'same length')
if self.data.ndim != 1 or self.row.ndim != 1 or \
self.col.ndim != 1:
raise ValueError('row, column, and data arrays must be 1-D')
return int(nnz)
if axis < 0:
axis += 2
if axis == 0:
return np.bincount(downcast_intp_index(self.col),
minlength=self.shape[1])
elif axis == 1:
return np.bincount(downcast_intp_index(self.row),
minlength=self.shape[0])
else:
raise ValueError('axis out of bounds')
getnnz.__doc__ = spmatrix.getnnz.__doc__
def _check(self):
""" Checks data structure for consistency """
# index arrays should have integer data types
if self.row.dtype.kind != 'i':
warn("row index array has non-integer dtype (%s) "
% self.row.dtype.name)
if self.col.dtype.kind != 'i':
warn("col index array has non-integer dtype (%s) "
% self.col.dtype.name)
idx_dtype = get_index_dtype(maxval=max(self.shape))
self.row = np.asarray(self.row, dtype=idx_dtype)
self.col = np.asarray(self.col, dtype=idx_dtype)
self.data = to_native(self.data)
if self.nnz > 0:
if self.row.max() >= self.shape[0]:
raise ValueError('row index exceeds matrix dimensions')
if self.col.max() >= self.shape[1]:
raise ValueError('column index exceeds matrix dimensions')
if self.row.min() < 0:
raise ValueError('negative row index found')
if self.col.min() < 0:
raise ValueError('negative column index found')
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
return coo_matrix((self.data, (self.col, self.row)),
shape=(N, M), copy=copy)
transpose.__doc__ = spmatrix.transpose.__doc__
def toarray(self, order=None, out=None):
"""See the docstring for `spmatrix.toarray`."""
B = self._process_toarray_args(order, out)
fortran = int(B.flags.f_contiguous)
if not fortran and not B.flags.c_contiguous:
raise ValueError("Output array must be C or F contiguous")
M,N = self.shape
coo_todense(M, N, self.nnz, self.row, self.col, self.data,
B.ravel('A'), fortran)
return B
def tocsc(self, copy=False):
"""Convert this matrix to Compressed Sparse Column format
Duplicate entries will be summed together.
Examples
--------
>>> from numpy import array
>>> from scipy.sparse import coo_matrix
>>> row = array([0, 0, 1, 3, 1, 0, 0])
>>> col = array([0, 2, 1, 3, 1, 0, 0])
>>> data = array([1, 1, 1, 1, 1, 1, 1])
>>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsc()
>>> A.toarray()
array([[3, 0, 1, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
"""
from .csc import csc_matrix
if self.nnz == 0:
return csc_matrix(self.shape, dtype=self.dtype)
else:
M,N = self.shape
self.sum_duplicates()
idx_dtype = get_index_dtype((self.col, self.row),
maxval=max(self.nnz, M))
row = self.row.astype(idx_dtype, copy=False)
col = self.col.astype(idx_dtype, copy=False)
indptr = np.empty(N + 1, dtype=idx_dtype)
indices = np.empty_like(row, dtype=idx_dtype)
data = np.empty_like(self.data, dtype=upcast(self.dtype))
coo_tocsr(N, M, self.nnz, col, row, self.data,
indptr, indices, data)
return csc_matrix((data, indices, indptr), shape=self.shape)
def tocsr(self, copy=False):
"""Convert this matrix to Compressed Sparse Row format
Duplicate entries will be summed together.
Examples
--------
>>> from numpy import array
>>> from scipy.sparse import coo_matrix
>>> row = array([0, 0, 1, 3, 1, 0, 0])
>>> col = array([0, 2, 1, 3, 1, 0, 0])
>>> data = array([1, 1, 1, 1, 1, 1, 1])
>>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsr()
>>> A.toarray()
array([[3, 0, 1, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
"""
from .csr import csr_matrix
if self.nnz == 0:
return csr_matrix(self.shape, dtype=self.dtype)
else:
M,N = self.shape
self.sum_duplicates()
idx_dtype = get_index_dtype((self.row, self.col),
maxval=max(self.nnz, N))
row = self.row.astype(idx_dtype, copy=False)
col = self.col.astype(idx_dtype, copy=False)
indptr = np.empty(M + 1, dtype=idx_dtype)
indices = np.empty_like(col, dtype=idx_dtype)
data = np.empty_like(self.data, dtype=upcast(self.dtype))
coo_tocsr(M, N, self.nnz, row, col, self.data,
indptr, indices, data)
return csr_matrix((data, indices, indptr), shape=self.shape)
def tocoo(self, copy=False):
if copy:
return self.copy()
else:
return self
tocoo.__doc__ = spmatrix.tocoo.__doc__
def todia(self, copy=False):
from .dia import dia_matrix
self.sum_duplicates()
ks = self.col - self.row # the diagonal for each nonzero
diags, diag_idx = np.unique(ks, return_inverse=True)
if len(diags) > 100:
# probably undesired, should todia() have a maxdiags parameter?
warn("Constructing a DIA matrix with %d diagonals "
"is inefficient" % len(diags), SparseEfficiencyWarning)
#initialize and fill in data array
if self.data.size == 0:
data = np.zeros((0, 0), dtype=self.dtype)
else:
data = np.zeros((len(diags), self.col.max()+1), dtype=self.dtype)
data[diag_idx, self.col] = self.data
return dia_matrix((data,diags), shape=self.shape)
todia.__doc__ = spmatrix.todia.__doc__
def todok(self, copy=False):
from .dok import dok_matrix
self.sum_duplicates()
dok = dok_matrix((self.shape), dtype=self.dtype)
dok.update(izip(izip(self.row,self.col),self.data))
return dok
todok.__doc__ = spmatrix.todok.__doc__
def diagonal(self):
diag = np.zeros(min(self.shape), dtype=self.dtype)
diag_mask = self.row == self.col
if self.has_canonical_format:
row = self.row[diag_mask]
data = self.data[diag_mask]
else:
row, _, data = self._sum_duplicates(self.row[diag_mask],
self.col[diag_mask],
self.data[diag_mask])
diag[row] = data
return diag
diagonal.__doc__ = _data_matrix.diagonal.__doc__
def _setdiag(self, values, k):
M, N = self.shape
if values.ndim and not len(values):
return
idx_dtype = self.row.dtype
# Determine which triples to keep and where to put the new ones.
full_keep = self.col - self.row != k
if k < 0:
max_index = min(M+k, N)
if values.ndim:
max_index = min(max_index, len(values))
keep = np.logical_or(full_keep, self.col >= max_index)
new_row = np.arange(-k, -k + max_index, dtype=idx_dtype)
new_col = np.arange(max_index, dtype=idx_dtype)
else:
max_index = min(M, N-k)
if values.ndim:
max_index = min(max_index, len(values))
keep = np.logical_or(full_keep, self.row >= max_index)
new_row = np.arange(max_index, dtype=idx_dtype)
new_col = np.arange(k, k + max_index, dtype=idx_dtype)
# Define the array of data consisting of the entries to be added.
if values.ndim:
new_data = values[:max_index]
else:
new_data = np.empty(max_index, dtype=self.dtype)
new_data[:] = values
# Update the internal structure.
self.row = np.concatenate((self.row[keep], new_row))
self.col = np.concatenate((self.col[keep], new_col))
self.data = np.concatenate((self.data[keep], new_data))
self.has_canonical_format = False
# 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 index arrays
(i.e. .row and .col) are copied.
"""
if copy:
return coo_matrix((data, (self.row.copy(), self.col.copy())),
shape=self.shape, dtype=data.dtype)
else:
return coo_matrix((data, (self.row, self.col)),
shape=self.shape, dtype=data.dtype)
def sum_duplicates(self):
"""Eliminate duplicate matrix entries by adding them together
This is an *in place* operation
"""
if self.has_canonical_format:
return
summed = self._sum_duplicates(self.row, self.col, self.data)
self.row, self.col, self.data = summed
self.has_canonical_format = True
def _sum_duplicates(self, row, col, data):
# Assumes (data, row, col) not in canonical format.
if len(data) == 0:
return row, col, data
order = np.lexsort((row, col))
row = row[order]
col = col[order]
data = data[order]
unique_mask = ((row[1:] != row[:-1]) |
(col[1:] != col[:-1]))
unique_mask = np.append(True, unique_mask)
row = row[unique_mask]
col = col[unique_mask]
unique_inds, = np.nonzero(unique_mask)
data = np.add.reduceat(data, unique_inds, dtype=self.dtype)
return row, col, data
def eliminate_zeros(self):
"""Remove zero entries from the matrix
This is an *in place* operation
"""
mask = self.data != 0
self.data = self.data[mask]
self.row = self.row[mask]
self.col = self.col[mask]
###########################
# Multiplication handlers #
###########################
def _mul_vector(self, other):
#output array
result = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
other.dtype.char))
coo_matvec(self.nnz, self.row, self.col, self.data, other, result)
return result
def _mul_multivector(self, other):
result = np.zeros((other.shape[1], self.shape[0]),
dtype=upcast_char(self.dtype.char, other.dtype.char))
for i, col in enumerate(other.T):
coo_matvec(self.nnz, self.row, self.col, self.data, col, result[i])
return result.T.view(type=type(other))
def isspmatrix_coo(x):
return isinstance(x, coo_matrix)