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
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
|
# Authors: Mathieu Blondel
# Olivier Grisel
# Peter Prettenhofer
# Lars Buitinck
# Giorgio Patrini
#
# License: BSD 3 clause
#!python
from libc.math cimport fabs, sqrt
cimport numpy as cnp
import numpy as np
from cython cimport floating
from numpy.math cimport isnan
cnp.import_array()
ctypedef fused integral:
int
long long
ctypedef cnp.float64_t DOUBLE
def csr_row_norms(X):
"""L2 norm of each row in CSR matrix X."""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
return _csr_row_norms(X.data, X.shape, X.indices, X.indptr)
def _csr_row_norms(cnp.ndarray[floating, ndim=1, mode="c"] X_data,
shape,
cnp.ndarray[integral, ndim=1, mode="c"] X_indices,
cnp.ndarray[integral, ndim=1, mode="c"] X_indptr):
cdef:
unsigned long long n_samples = shape[0]
unsigned long long i
integral j
double sum_
norms = np.empty(n_samples, dtype=X_data.dtype)
cdef floating[::1] norms_view = norms
for i in range(n_samples):
sum_ = 0.0
for j in range(X_indptr[i], X_indptr[i + 1]):
sum_ += X_data[j] * X_data[j]
norms_view[i] = sum_
return norms
def csr_mean_variance_axis0(X, weights=None, return_sum_weights=False):
"""Compute mean and variance along axis 0 on a CSR matrix
Uses a np.float64 accumulator.
Parameters
----------
X : CSR sparse matrix, shape (n_samples, n_features)
Input data.
weights : ndarray of shape (n_samples,), dtype=floating, default=None
If it is set to None samples will be equally weighted.
.. versionadded:: 0.24
return_sum_weights : bool, default=False
If True, returns the sum of weights seen for each feature.
.. versionadded:: 0.24
Returns
-------
means : float array with shape (n_features,)
Feature-wise means
variances : float array with shape (n_features,)
Feature-wise variances
sum_weights : ndarray of shape (n_features,), dtype=floating
Returned if return_sum_weights is True.
"""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
if weights is None:
weights = np.ones(X.shape[0], dtype=X.dtype)
means, variances, sum_weights = _csr_mean_variance_axis0(
X.data, X.shape[0], X.shape[1], X.indices, X.indptr, weights)
if return_sum_weights:
return means, variances, sum_weights
return means, variances
def _csr_mean_variance_axis0(cnp.ndarray[floating, ndim=1, mode="c"] X_data,
unsigned long long n_samples,
unsigned long long n_features,
cnp.ndarray[integral, ndim=1] X_indices,
cnp.ndarray[integral, ndim=1] X_indptr,
cnp.ndarray[floating, ndim=1] weights):
# Implement the function here since variables using fused types
# cannot be declared directly and can only be passed as function arguments
cdef:
cnp.npy_intp i
unsigned long long row_ind
integral col_ind
cnp.float64_t diff
# means[j] contains the mean of feature j
cnp.ndarray[cnp.float64_t, ndim=1] means = np.zeros(n_features)
# variances[j] contains the variance of feature j
cnp.ndarray[cnp.float64_t, ndim=1] variances = np.zeros(n_features)
cnp.ndarray[cnp.float64_t, ndim=1] sum_weights = np.full(
fill_value=np.sum(weights, dtype=np.float64), shape=n_features)
cnp.ndarray[cnp.float64_t, ndim=1] sum_weights_nz = np.zeros(
shape=n_features)
cnp.ndarray[cnp.float64_t, ndim=1] correction = np.zeros(
shape=n_features)
cnp.ndarray[cnp.uint64_t, ndim=1] counts = np.full(
fill_value=weights.shape[0], shape=n_features, dtype=np.uint64)
cnp.ndarray[cnp.uint64_t, ndim=1] counts_nz = np.zeros(
shape=n_features, dtype=np.uint64)
for row_ind in range(len(X_indptr) - 1):
for i in range(X_indptr[row_ind], X_indptr[row_ind + 1]):
col_ind = X_indices[i]
if not isnan(X_data[i]):
means[col_ind] += <cnp.float64_t>(X_data[i]) * weights[row_ind]
# sum of weights where X[:, col_ind] is non-zero
sum_weights_nz[col_ind] += weights[row_ind]
# number of non-zero elements of X[:, col_ind]
counts_nz[col_ind] += 1
else:
# sum of weights where X[:, col_ind] is not nan
sum_weights[col_ind] -= weights[row_ind]
# number of non nan elements of X[:, col_ind]
counts[col_ind] -= 1
for i in range(n_features):
means[i] /= sum_weights[i]
for row_ind in range(len(X_indptr) - 1):
for i in range(X_indptr[row_ind], X_indptr[row_ind + 1]):
col_ind = X_indices[i]
if not isnan(X_data[i]):
diff = X_data[i] - means[col_ind]
# correction term of the corrected 2 pass algorithm.
# See "Algorithms for computing the sample variance: analysis
# and recommendations", by Chan, Golub, and LeVeque.
correction[col_ind] += diff * weights[row_ind]
variances[col_ind] += diff * diff * weights[row_ind]
for i in range(n_features):
if counts[i] != counts_nz[i]:
correction[i] -= (sum_weights[i] - sum_weights_nz[i]) * means[i]
correction[i] = correction[i]**2 / sum_weights[i]
if counts[i] != counts_nz[i]:
# only compute it when it's guaranteed to be non-zero to avoid
# catastrophic cancellation.
variances[i] += (sum_weights[i] - sum_weights_nz[i]) * means[i]**2
variances[i] = (variances[i] - correction[i]) / sum_weights[i]
if floating is float:
return (np.array(means, dtype=np.float32),
np.array(variances, dtype=np.float32),
np.array(sum_weights, dtype=np.float32))
else:
return means, variances, sum_weights
def csc_mean_variance_axis0(X, weights=None, return_sum_weights=False):
"""Compute mean and variance along axis 0 on a CSC matrix
Uses a np.float64 accumulator.
Parameters
----------
X : CSC sparse matrix, shape (n_samples, n_features)
Input data.
weights : ndarray of shape (n_samples,), dtype=floating, default=None
If it is set to None samples will be equally weighted.
.. versionadded:: 0.24
return_sum_weights : bool, default=False
If True, returns the sum of weights seen for each feature.
.. versionadded:: 0.24
Returns
-------
means : float array with shape (n_features,)
Feature-wise means
variances : float array with shape (n_features,)
Feature-wise variances
sum_weights : ndarray of shape (n_features,), dtype=floating
Returned if return_sum_weights is True.
"""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
if weights is None:
weights = np.ones(X.shape[0], dtype=X.dtype)
means, variances, sum_weights = _csc_mean_variance_axis0(
X.data, X.shape[0], X.shape[1], X.indices, X.indptr, weights)
if return_sum_weights:
return means, variances, sum_weights
return means, variances
def _csc_mean_variance_axis0(cnp.ndarray[floating, ndim=1, mode="c"] X_data,
unsigned long long n_samples,
unsigned long long n_features,
cnp.ndarray[integral, ndim=1] X_indices,
cnp.ndarray[integral, ndim=1] X_indptr,
cnp.ndarray[floating, ndim=1] weights):
# Implement the function here since variables using fused types
# cannot be declared directly and can only be passed as function arguments
cdef:
cnp.npy_intp i
unsigned long long col_ind
integral row_ind
cnp.float64_t diff
# means[j] contains the mean of feature j
cnp.ndarray[cnp.float64_t, ndim=1] means = np.zeros(n_features)
# variances[j] contains the variance of feature j
cnp.ndarray[cnp.float64_t, ndim=1] variances = np.zeros(n_features)
cnp.ndarray[cnp.float64_t, ndim=1] sum_weights = np.full(
fill_value=np.sum(weights, dtype=np.float64), shape=n_features)
cnp.ndarray[cnp.float64_t, ndim=1] sum_weights_nz = np.zeros(
shape=n_features)
cnp.ndarray[cnp.float64_t, ndim=1] correction = np.zeros(
shape=n_features)
cnp.ndarray[cnp.uint64_t, ndim=1] counts = np.full(
fill_value=weights.shape[0], shape=n_features, dtype=np.uint64)
cnp.ndarray[cnp.uint64_t, ndim=1] counts_nz = np.zeros(
shape=n_features, dtype=np.uint64)
for col_ind in range(n_features):
for i in range(X_indptr[col_ind], X_indptr[col_ind + 1]):
row_ind = X_indices[i]
if not isnan(X_data[i]):
means[col_ind] += <cnp.float64_t>(X_data[i]) * weights[row_ind]
# sum of weights where X[:, col_ind] is non-zero
sum_weights_nz[col_ind] += weights[row_ind]
# number of non-zero elements of X[:, col_ind]
counts_nz[col_ind] += 1
else:
# sum of weights where X[:, col_ind] is not nan
sum_weights[col_ind] -= weights[row_ind]
# number of non nan elements of X[:, col_ind]
counts[col_ind] -= 1
for i in range(n_features):
means[i] /= sum_weights[i]
for col_ind in range(n_features):
for i in range(X_indptr[col_ind], X_indptr[col_ind + 1]):
row_ind = X_indices[i]
if not isnan(X_data[i]):
diff = X_data[i] - means[col_ind]
# correction term of the corrected 2 pass algorithm.
# See "Algorithms for computing the sample variance: analysis
# and recommendations", by Chan, Golub, and LeVeque.
correction[col_ind] += diff * weights[row_ind]
variances[col_ind] += diff * diff * weights[row_ind]
for i in range(n_features):
if counts[i] != counts_nz[i]:
correction[i] -= (sum_weights[i] - sum_weights_nz[i]) * means[i]
correction[i] = correction[i]**2 / sum_weights[i]
if counts[i] != counts_nz[i]:
# only compute it when it's guaranteed to be non-zero to avoid
# catastrophic cancellation.
variances[i] += (sum_weights[i] - sum_weights_nz[i]) * means[i]**2
variances[i] = (variances[i] - correction[i]) / sum_weights[i]
if floating is float:
return (np.array(means, dtype=np.float32),
np.array(variances, dtype=np.float32),
np.array(sum_weights, dtype=np.float32))
else:
return means, variances, sum_weights
def incr_mean_variance_axis0(X, last_mean, last_var, last_n, weights=None):
"""Compute mean and variance along axis 0 on a CSR or CSC matrix.
last_mean, last_var are the statistics computed at the last step by this
function. Both must be initialized to 0.0. last_n is the
number of samples encountered until now and is initialized at 0.
Parameters
----------
X : CSR or CSC sparse matrix, shape (n_samples, n_features)
Input data.
last_mean : float array with shape (n_features,)
Array of feature-wise means to update with the new data X.
last_var : float array with shape (n_features,)
Array of feature-wise var to update with the new data X.
last_n : float array with shape (n_features,)
Sum of the weights seen so far (if weights are all set to 1
this will be the same as number of samples seen so far, before X).
weights : float array with shape (n_samples,) or None. If it is set
to None samples will be equally weighted.
Returns
-------
updated_mean : float array with shape (n_features,)
Feature-wise means
updated_variance : float array with shape (n_features,)
Feature-wise variances
updated_n : int array with shape (n_features,)
Updated number of samples seen
Notes
-----
NaNs are ignored during the computation.
References
----------
T. Chan, G. Golub, R. LeVeque. Algorithms for computing the sample
variance: recommendations, The American Statistician, Vol. 37, No. 3,
pp. 242-247
Also, see the non-sparse implementation of this in
`utils.extmath._batch_mean_variance_update`.
"""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
X_dtype = X.dtype
if weights is None:
weights = np.ones(X.shape[0], dtype=X_dtype)
elif weights.dtype not in [np.float32, np.float64]:
weights = weights.astype(np.float64, copy=False)
if last_n.dtype not in [np.float32, np.float64]:
last_n = last_n.astype(np.float64, copy=False)
return _incr_mean_variance_axis0(X.data,
np.sum(weights),
X.shape[1],
X.indices,
X.indptr,
X.format,
last_mean.astype(X_dtype, copy=False),
last_var.astype(X_dtype, copy=False),
last_n.astype(X_dtype, copy=False),
weights.astype(X_dtype, copy=False))
def _incr_mean_variance_axis0(cnp.ndarray[floating, ndim=1] X_data,
floating n_samples,
unsigned long long n_features,
cnp.ndarray[int, ndim=1] X_indices,
# X_indptr might be either in32 or int64
cnp.ndarray[integral, ndim=1] X_indptr,
str X_format,
cnp.ndarray[floating, ndim=1] last_mean,
cnp.ndarray[floating, ndim=1] last_var,
cnp.ndarray[floating, ndim=1] last_n,
# previous sum of the weights (ie float)
cnp.ndarray[floating, ndim=1] weights):
# Implement the function here since variables using fused types
# cannot be declared directly and can only be passed as function arguments
cdef:
cnp.npy_intp i
# last = stats until now
# new = the current increment
# updated = the aggregated stats
# when arrays, they are indexed by i per-feature
cdef:
cnp.ndarray[floating, ndim=1] new_mean
cnp.ndarray[floating, ndim=1] new_var
cnp.ndarray[floating, ndim=1] updated_mean
cnp.ndarray[floating, ndim=1] updated_var
if floating is float:
dtype = np.float32
else:
dtype = np.float64
new_mean = np.zeros(n_features, dtype=dtype)
new_var = np.zeros_like(new_mean, dtype=dtype)
updated_mean = np.zeros_like(new_mean, dtype=dtype)
updated_var = np.zeros_like(new_mean, dtype=dtype)
cdef:
cnp.ndarray[floating, ndim=1] new_n
cnp.ndarray[floating, ndim=1] updated_n
cnp.ndarray[floating, ndim=1] last_over_new_n
# Obtain new stats first
updated_n = np.zeros(shape=n_features, dtype=dtype)
last_over_new_n = np.zeros_like(updated_n, dtype=dtype)
# X can be a CSR or CSC matrix
if X_format == 'csr':
new_mean, new_var, new_n = _csr_mean_variance_axis0(
X_data, n_samples, n_features, X_indices, X_indptr, weights)
else: # X_format == 'csc'
new_mean, new_var, new_n = _csc_mean_variance_axis0(
X_data, n_samples, n_features, X_indices, X_indptr, weights)
# First pass
cdef bint is_first_pass = True
for i in range(n_features):
if last_n[i] > 0:
is_first_pass = False
break
if is_first_pass:
return new_mean, new_var, new_n
for i in range(n_features):
updated_n[i] = last_n[i] + new_n[i]
# Next passes
for i in range(n_features):
if new_n[i] > 0:
last_over_new_n[i] = dtype(last_n[i]) / dtype(new_n[i])
# Unnormalized stats
last_mean[i] *= last_n[i]
last_var[i] *= last_n[i]
new_mean[i] *= new_n[i]
new_var[i] *= new_n[i]
# Update stats
updated_var[i] = (
last_var[i] + new_var[i] +
last_over_new_n[i] / updated_n[i] *
(last_mean[i] / last_over_new_n[i] - new_mean[i])**2
)
updated_mean[i] = (last_mean[i] + new_mean[i]) / updated_n[i]
updated_var[i] /= updated_n[i]
else:
updated_var[i] = last_var[i]
updated_mean[i] = last_mean[i]
updated_n[i] = last_n[i]
return updated_mean, updated_var, updated_n
def inplace_csr_row_normalize_l1(X):
"""Inplace row normalize using the l1 norm"""
_inplace_csr_row_normalize_l1(X.data, X.shape, X.indices, X.indptr)
def _inplace_csr_row_normalize_l1(cnp.ndarray[floating, ndim=1] X_data,
shape,
cnp.ndarray[integral, ndim=1] X_indices,
cnp.ndarray[integral, ndim=1] X_indptr):
cdef unsigned long long n_samples = shape[0]
cdef unsigned long long n_features = shape[1]
# the column indices for row i are stored in:
# indices[indptr[i]:indices[i+1]]
# and their corresponding values are stored in:
# data[indptr[i]:indptr[i+1]]
cdef cnp.npy_intp i, j
cdef double sum_
for i in range(n_samples):
sum_ = 0.0
for j in range(X_indptr[i], X_indptr[i + 1]):
sum_ += fabs(X_data[j])
if sum_ == 0.0:
# do not normalize empty rows (can happen if CSR is not pruned
# correctly)
continue
for j in range(X_indptr[i], X_indptr[i + 1]):
X_data[j] /= sum_
def inplace_csr_row_normalize_l2(X):
"""Inplace row normalize using the l2 norm"""
_inplace_csr_row_normalize_l2(X.data, X.shape, X.indices, X.indptr)
def _inplace_csr_row_normalize_l2(cnp.ndarray[floating, ndim=1] X_data,
shape,
cnp.ndarray[integral, ndim=1] X_indices,
cnp.ndarray[integral, ndim=1] X_indptr):
cdef integral n_samples = shape[0]
cdef integral n_features = shape[1]
cdef cnp.npy_intp i, j
cdef double sum_
for i in range(n_samples):
sum_ = 0.0
for j in range(X_indptr[i], X_indptr[i + 1]):
sum_ += (X_data[j] * X_data[j])
if sum_ == 0.0:
# do not normalize empty rows (can happen if CSR is not pruned
# correctly)
continue
sum_ = sqrt(sum_)
for j in range(X_indptr[i], X_indptr[i + 1]):
X_data[j] /= sum_
def assign_rows_csr(X,
cnp.ndarray[cnp.npy_intp, ndim=1] X_rows,
cnp.ndarray[cnp.npy_intp, ndim=1] out_rows,
cnp.ndarray[floating, ndim=2, mode="c"] out):
"""Densify selected rows of a CSR matrix into a preallocated array.
Like out[out_rows] = X[X_rows].toarray() but without copying.
No-copy supported for both dtype=np.float32 and dtype=np.float64.
Parameters
----------
X : scipy.sparse.csr_matrix, shape=(n_samples, n_features)
X_rows : array, dtype=np.intp, shape=n_rows
out_rows : array, dtype=np.intp, shape=n_rows
out : array, shape=(arbitrary, n_features)
"""
cdef:
# npy_intp (np.intp in Python) is what np.where returns,
# but int is what scipy.sparse uses.
int i, ind, j
cnp.npy_intp rX
cnp.ndarray[floating, ndim=1] data = X.data
cnp.ndarray[int, ndim=1] indices = X.indices, indptr = X.indptr
if X_rows.shape[0] != out_rows.shape[0]:
raise ValueError("cannot assign %d rows to %d"
% (X_rows.shape[0], out_rows.shape[0]))
out[out_rows] = 0.
for i in range(X_rows.shape[0]):
rX = X_rows[i]
for ind in range(indptr[rX], indptr[rX + 1]):
j = indices[ind]
out[out_rows[i], j] = data[ind]
|
