626 lines
24 KiB
Python
626 lines
24 KiB
Python
# Authors: Olivier Grisel <olivier.grisel@ensta.org>
|
|
# Mathieu Blondel <mathieu@mblondel.org>
|
|
# Denis Engemann <denis-alexander.engemann@inria.fr>
|
|
#
|
|
# License: BSD 3 clause
|
|
|
|
import numpy as np
|
|
from scipy import sparse
|
|
from scipy import linalg
|
|
from scipy import stats
|
|
|
|
from sklearn.utils.testing import assert_equal
|
|
from sklearn.utils.testing import assert_almost_equal
|
|
from sklearn.utils.testing import assert_array_equal
|
|
from sklearn.utils.testing import assert_array_almost_equal
|
|
from sklearn.utils.testing import assert_true
|
|
from sklearn.utils.testing import assert_false
|
|
from sklearn.utils.testing import assert_greater
|
|
from sklearn.utils.testing import assert_warns
|
|
from sklearn.utils.testing import assert_warns_message
|
|
from sklearn.utils.testing import skip_if_32bit
|
|
from sklearn.utils.testing import SkipTest
|
|
from sklearn.utils.testing import ignore_warnings
|
|
from sklearn.utils.fixes import np_version
|
|
|
|
from sklearn.utils.extmath import density
|
|
from sklearn.utils.extmath import logsumexp
|
|
from sklearn.utils.extmath import norm, squared_norm
|
|
from sklearn.utils.extmath import randomized_svd
|
|
from sklearn.utils.extmath import row_norms
|
|
from sklearn.utils.extmath import weighted_mode
|
|
from sklearn.utils.extmath import cartesian
|
|
from sklearn.utils.extmath import log_logistic
|
|
from sklearn.utils.extmath import svd_flip
|
|
from sklearn.utils.extmath import _incremental_mean_and_var
|
|
from sklearn.utils.extmath import _deterministic_vector_sign_flip
|
|
from sklearn.utils.extmath import softmax
|
|
from sklearn.utils.extmath import stable_cumsum
|
|
from sklearn.datasets.samples_generator import make_low_rank_matrix
|
|
|
|
|
|
def test_density():
|
|
rng = np.random.RandomState(0)
|
|
X = rng.randint(10, size=(10, 5))
|
|
X[1, 2] = 0
|
|
X[5, 3] = 0
|
|
X_csr = sparse.csr_matrix(X)
|
|
X_csc = sparse.csc_matrix(X)
|
|
X_coo = sparse.coo_matrix(X)
|
|
X_lil = sparse.lil_matrix(X)
|
|
|
|
for X_ in (X_csr, X_csc, X_coo, X_lil):
|
|
assert_equal(density(X_), density(X))
|
|
|
|
|
|
def test_uniform_weights():
|
|
# with uniform weights, results should be identical to stats.mode
|
|
rng = np.random.RandomState(0)
|
|
x = rng.randint(10, size=(10, 5))
|
|
weights = np.ones(x.shape)
|
|
|
|
for axis in (None, 0, 1):
|
|
mode, score = stats.mode(x, axis)
|
|
mode2, score2 = weighted_mode(x, weights, axis)
|
|
|
|
assert_array_equal(mode, mode2)
|
|
assert_array_equal(score, score2)
|
|
|
|
|
|
def test_random_weights():
|
|
# set this up so that each row should have a weighted mode of 6,
|
|
# with a score that is easily reproduced
|
|
mode_result = 6
|
|
|
|
rng = np.random.RandomState(0)
|
|
x = rng.randint(mode_result, size=(100, 10))
|
|
w = rng.random_sample(x.shape)
|
|
|
|
x[:, :5] = mode_result
|
|
w[:, :5] += 1
|
|
|
|
mode, score = weighted_mode(x, w, axis=1)
|
|
|
|
assert_array_equal(mode, mode_result)
|
|
assert_array_almost_equal(score.ravel(), w[:, :5].sum(1))
|
|
|
|
|
|
@ignore_warnings # Test deprecated backport to be removed in 0.21
|
|
def test_logsumexp():
|
|
# Try to add some smallish numbers in logspace
|
|
x = np.array([1e-40] * 1000000)
|
|
logx = np.log(x)
|
|
assert_almost_equal(np.exp(logsumexp(logx)), x.sum())
|
|
|
|
X = np.vstack([x, x])
|
|
logX = np.vstack([logx, logx])
|
|
assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
|
|
assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
|
|
|
|
|
|
def check_randomized_svd_low_rank(dtype):
|
|
# Check that extmath.randomized_svd is consistent with linalg.svd
|
|
n_samples = 100
|
|
n_features = 500
|
|
rank = 5
|
|
k = 10
|
|
decimal = 5 if dtype == np.float32 else 7
|
|
dtype = np.dtype(dtype)
|
|
|
|
# generate a matrix X of approximate effective rank `rank` and no noise
|
|
# component (very structured signal):
|
|
X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
|
|
effective_rank=rank, tail_strength=0.0,
|
|
random_state=0).astype(dtype, copy=False)
|
|
assert_equal(X.shape, (n_samples, n_features))
|
|
|
|
# compute the singular values of X using the slow exact method
|
|
U, s, V = linalg.svd(X, full_matrices=False)
|
|
|
|
# Convert the singular values to the specific dtype
|
|
U = U.astype(dtype, copy=False)
|
|
s = s.astype(dtype, copy=False)
|
|
V = V.astype(dtype, copy=False)
|
|
|
|
for normalizer in ['auto', 'LU', 'QR']: # 'none' would not be stable
|
|
# compute the singular values of X using the fast approximate method
|
|
Ua, sa, Va = randomized_svd(
|
|
X, k, power_iteration_normalizer=normalizer, random_state=0)
|
|
|
|
# If the input dtype is float, then the output dtype is float of the
|
|
# same bit size (f32 is not upcast to f64)
|
|
# But if the input dtype is int, the output dtype is float64
|
|
if dtype.kind == 'f':
|
|
assert Ua.dtype == dtype
|
|
assert sa.dtype == dtype
|
|
assert Va.dtype == dtype
|
|
else:
|
|
assert Ua.dtype == np.float64
|
|
assert sa.dtype == np.float64
|
|
assert Va.dtype == np.float64
|
|
|
|
assert_equal(Ua.shape, (n_samples, k))
|
|
assert_equal(sa.shape, (k,))
|
|
assert_equal(Va.shape, (k, n_features))
|
|
|
|
# ensure that the singular values of both methods are equal up to the
|
|
# real rank of the matrix
|
|
assert_almost_equal(s[:k], sa, decimal=decimal)
|
|
|
|
# check the singular vectors too (while not checking the sign)
|
|
assert_almost_equal(np.dot(U[:, :k], V[:k, :]), np.dot(Ua, Va),
|
|
decimal=decimal)
|
|
|
|
# check the sparse matrix representation
|
|
X = sparse.csr_matrix(X)
|
|
|
|
# compute the singular values of X using the fast approximate method
|
|
Ua, sa, Va = \
|
|
randomized_svd(X, k, power_iteration_normalizer=normalizer,
|
|
random_state=0)
|
|
if dtype.kind == 'f':
|
|
assert Ua.dtype == dtype
|
|
assert sa.dtype == dtype
|
|
assert Va.dtype == dtype
|
|
else:
|
|
assert Ua.dtype.kind == 'f'
|
|
assert sa.dtype.kind == 'f'
|
|
assert Va.dtype.kind == 'f'
|
|
|
|
assert_almost_equal(s[:rank], sa[:rank], decimal=decimal)
|
|
|
|
|
|
def test_randomized_svd_low_rank_all_dtypes():
|
|
for dtype in (np.int32, np.int64, np.float32, np.float64):
|
|
yield check_randomized_svd_low_rank, dtype
|
|
|
|
|
|
@ignore_warnings # extmath.norm is deprecated to be removed in 0.21
|
|
def test_norm_squared_norm():
|
|
X = np.random.RandomState(42).randn(50, 63)
|
|
X *= 100 # check stability
|
|
X += 200
|
|
|
|
assert_almost_equal(np.linalg.norm(X.ravel()), norm(X))
|
|
assert_almost_equal(norm(X) ** 2, squared_norm(X), decimal=6)
|
|
assert_almost_equal(np.linalg.norm(X), np.sqrt(squared_norm(X)), decimal=6)
|
|
# Check the warning with an int array and np.dot potential overflow
|
|
assert_warns_message(
|
|
UserWarning, 'Array type is integer, np.dot may '
|
|
'overflow. Data should be float type to avoid this issue',
|
|
squared_norm, X.astype(int))
|
|
|
|
|
|
def test_row_norms():
|
|
X = np.random.RandomState(42).randn(100, 100)
|
|
for dtype in (np.float32, np.float64):
|
|
if dtype is np.float32:
|
|
precision = 4
|
|
else:
|
|
precision = 5
|
|
|
|
X = X.astype(dtype)
|
|
sq_norm = (X ** 2).sum(axis=1)
|
|
|
|
assert_array_almost_equal(sq_norm, row_norms(X, squared=True),
|
|
precision)
|
|
assert_array_almost_equal(np.sqrt(sq_norm), row_norms(X), precision)
|
|
|
|
Xcsr = sparse.csr_matrix(X, dtype=dtype)
|
|
assert_array_almost_equal(sq_norm, row_norms(Xcsr, squared=True),
|
|
precision)
|
|
assert_array_almost_equal(np.sqrt(sq_norm), row_norms(Xcsr), precision)
|
|
|
|
|
|
def test_randomized_svd_low_rank_with_noise():
|
|
# Check that extmath.randomized_svd can handle noisy matrices
|
|
n_samples = 100
|
|
n_features = 500
|
|
rank = 5
|
|
k = 10
|
|
|
|
# generate a matrix X wity structure approximate rank `rank` and an
|
|
# important noisy component
|
|
X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
|
|
effective_rank=rank, tail_strength=0.1,
|
|
random_state=0)
|
|
assert_equal(X.shape, (n_samples, n_features))
|
|
|
|
# compute the singular values of X using the slow exact method
|
|
_, s, _ = linalg.svd(X, full_matrices=False)
|
|
|
|
for normalizer in ['auto', 'none', 'LU', 'QR']:
|
|
# compute the singular values of X using the fast approximate
|
|
# method without the iterated power method
|
|
_, sa, _ = randomized_svd(X, k, n_iter=0,
|
|
power_iteration_normalizer=normalizer,
|
|
random_state=0)
|
|
|
|
# the approximation does not tolerate the noise:
|
|
assert_greater(np.abs(s[:k] - sa).max(), 0.01)
|
|
|
|
# compute the singular values of X using the fast approximate
|
|
# method with iterated power method
|
|
_, sap, _ = randomized_svd(X, k,
|
|
power_iteration_normalizer=normalizer,
|
|
random_state=0)
|
|
|
|
# the iterated power method is helping getting rid of the noise:
|
|
assert_almost_equal(s[:k], sap, decimal=3)
|
|
|
|
|
|
def test_randomized_svd_infinite_rank():
|
|
# Check that extmath.randomized_svd can handle noisy matrices
|
|
n_samples = 100
|
|
n_features = 500
|
|
rank = 5
|
|
k = 10
|
|
|
|
# let us try again without 'low_rank component': just regularly but slowly
|
|
# decreasing singular values: the rank of the data matrix is infinite
|
|
X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
|
|
effective_rank=rank, tail_strength=1.0,
|
|
random_state=0)
|
|
assert_equal(X.shape, (n_samples, n_features))
|
|
|
|
# compute the singular values of X using the slow exact method
|
|
_, s, _ = linalg.svd(X, full_matrices=False)
|
|
for normalizer in ['auto', 'none', 'LU', 'QR']:
|
|
# compute the singular values of X using the fast approximate method
|
|
# without the iterated power method
|
|
_, sa, _ = randomized_svd(X, k, n_iter=0,
|
|
power_iteration_normalizer=normalizer)
|
|
|
|
# the approximation does not tolerate the noise:
|
|
assert_greater(np.abs(s[:k] - sa).max(), 0.1)
|
|
|
|
# compute the singular values of X using the fast approximate method
|
|
# with iterated power method
|
|
_, sap, _ = randomized_svd(X, k, n_iter=5,
|
|
power_iteration_normalizer=normalizer)
|
|
|
|
# the iterated power method is still managing to get most of the
|
|
# structure at the requested rank
|
|
assert_almost_equal(s[:k], sap, decimal=3)
|
|
|
|
|
|
def test_randomized_svd_transpose_consistency():
|
|
# Check that transposing the design matrix has limited impact
|
|
n_samples = 100
|
|
n_features = 500
|
|
rank = 4
|
|
k = 10
|
|
|
|
X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
|
|
effective_rank=rank, tail_strength=0.5,
|
|
random_state=0)
|
|
assert_equal(X.shape, (n_samples, n_features))
|
|
|
|
U1, s1, V1 = randomized_svd(X, k, n_iter=3, transpose=False,
|
|
random_state=0)
|
|
U2, s2, V2 = randomized_svd(X, k, n_iter=3, transpose=True,
|
|
random_state=0)
|
|
U3, s3, V3 = randomized_svd(X, k, n_iter=3, transpose='auto',
|
|
random_state=0)
|
|
U4, s4, V4 = linalg.svd(X, full_matrices=False)
|
|
|
|
assert_almost_equal(s1, s4[:k], decimal=3)
|
|
assert_almost_equal(s2, s4[:k], decimal=3)
|
|
assert_almost_equal(s3, s4[:k], decimal=3)
|
|
|
|
assert_almost_equal(np.dot(U1, V1), np.dot(U4[:, :k], V4[:k, :]),
|
|
decimal=2)
|
|
assert_almost_equal(np.dot(U2, V2), np.dot(U4[:, :k], V4[:k, :]),
|
|
decimal=2)
|
|
|
|
# in this case 'auto' is equivalent to transpose
|
|
assert_almost_equal(s2, s3)
|
|
|
|
|
|
def test_randomized_svd_power_iteration_normalizer():
|
|
# randomized_svd with power_iteration_normalized='none' diverges for
|
|
# large number of power iterations on this dataset
|
|
rng = np.random.RandomState(42)
|
|
X = make_low_rank_matrix(100, 500, effective_rank=50, random_state=rng)
|
|
X += 3 * rng.randint(0, 2, size=X.shape)
|
|
n_components = 50
|
|
|
|
# Check that it diverges with many (non-normalized) power iterations
|
|
U, s, V = randomized_svd(X, n_components, n_iter=2,
|
|
power_iteration_normalizer='none')
|
|
A = X - U.dot(np.diag(s).dot(V))
|
|
error_2 = linalg.norm(A, ord='fro')
|
|
U, s, V = randomized_svd(X, n_components, n_iter=20,
|
|
power_iteration_normalizer='none')
|
|
A = X - U.dot(np.diag(s).dot(V))
|
|
error_20 = linalg.norm(A, ord='fro')
|
|
assert_greater(np.abs(error_2 - error_20), 100)
|
|
|
|
for normalizer in ['LU', 'QR', 'auto']:
|
|
U, s, V = randomized_svd(X, n_components, n_iter=2,
|
|
power_iteration_normalizer=normalizer,
|
|
random_state=0)
|
|
A = X - U.dot(np.diag(s).dot(V))
|
|
error_2 = linalg.norm(A, ord='fro')
|
|
|
|
for i in [5, 10, 50]:
|
|
U, s, V = randomized_svd(X, n_components, n_iter=i,
|
|
power_iteration_normalizer=normalizer,
|
|
random_state=0)
|
|
A = X - U.dot(np.diag(s).dot(V))
|
|
error = linalg.norm(A, ord='fro')
|
|
assert_greater(15, np.abs(error_2 - error))
|
|
|
|
|
|
def test_svd_flip():
|
|
# Check that svd_flip works in both situations, and reconstructs input.
|
|
rs = np.random.RandomState(1999)
|
|
n_samples = 20
|
|
n_features = 10
|
|
X = rs.randn(n_samples, n_features)
|
|
|
|
# Check matrix reconstruction
|
|
U, S, V = linalg.svd(X, full_matrices=False)
|
|
U1, V1 = svd_flip(U, V, u_based_decision=False)
|
|
assert_almost_equal(np.dot(U1 * S, V1), X, decimal=6)
|
|
|
|
# Check transposed matrix reconstruction
|
|
XT = X.T
|
|
U, S, V = linalg.svd(XT, full_matrices=False)
|
|
U2, V2 = svd_flip(U, V, u_based_decision=True)
|
|
assert_almost_equal(np.dot(U2 * S, V2), XT, decimal=6)
|
|
|
|
# Check that different flip methods are equivalent under reconstruction
|
|
U_flip1, V_flip1 = svd_flip(U, V, u_based_decision=True)
|
|
assert_almost_equal(np.dot(U_flip1 * S, V_flip1), XT, decimal=6)
|
|
U_flip2, V_flip2 = svd_flip(U, V, u_based_decision=False)
|
|
assert_almost_equal(np.dot(U_flip2 * S, V_flip2), XT, decimal=6)
|
|
|
|
|
|
def test_randomized_svd_sign_flip():
|
|
a = np.array([[2.0, 0.0], [0.0, 1.0]])
|
|
u1, s1, v1 = randomized_svd(a, 2, flip_sign=True, random_state=41)
|
|
for seed in range(10):
|
|
u2, s2, v2 = randomized_svd(a, 2, flip_sign=True, random_state=seed)
|
|
assert_almost_equal(u1, u2)
|
|
assert_almost_equal(v1, v2)
|
|
assert_almost_equal(np.dot(u2 * s2, v2), a)
|
|
assert_almost_equal(np.dot(u2.T, u2), np.eye(2))
|
|
assert_almost_equal(np.dot(v2.T, v2), np.eye(2))
|
|
|
|
|
|
def test_randomized_svd_sign_flip_with_transpose():
|
|
# Check if the randomized_svd sign flipping is always done based on u
|
|
# irrespective of transpose.
|
|
# See https://github.com/scikit-learn/scikit-learn/issues/5608
|
|
# for more details.
|
|
def max_loading_is_positive(u, v):
|
|
"""
|
|
returns bool tuple indicating if the values maximising np.abs
|
|
are positive across all rows for u and across all columns for v.
|
|
"""
|
|
u_based = (np.abs(u).max(axis=0) == u.max(axis=0)).all()
|
|
v_based = (np.abs(v).max(axis=1) == v.max(axis=1)).all()
|
|
return u_based, v_based
|
|
|
|
mat = np.arange(10 * 8).reshape(10, -1)
|
|
|
|
# Without transpose
|
|
u_flipped, _, v_flipped = randomized_svd(mat, 3, flip_sign=True)
|
|
u_based, v_based = max_loading_is_positive(u_flipped, v_flipped)
|
|
assert_true(u_based)
|
|
assert_false(v_based)
|
|
|
|
# With transpose
|
|
u_flipped_with_transpose, _, v_flipped_with_transpose = randomized_svd(
|
|
mat, 3, flip_sign=True, transpose=True)
|
|
u_based, v_based = max_loading_is_positive(
|
|
u_flipped_with_transpose, v_flipped_with_transpose)
|
|
assert_true(u_based)
|
|
assert_false(v_based)
|
|
|
|
|
|
def test_cartesian():
|
|
# Check if cartesian product delivers the right results
|
|
|
|
axes = (np.array([1, 2, 3]), np.array([4, 5]), np.array([6, 7]))
|
|
|
|
true_out = np.array([[1, 4, 6],
|
|
[1, 4, 7],
|
|
[1, 5, 6],
|
|
[1, 5, 7],
|
|
[2, 4, 6],
|
|
[2, 4, 7],
|
|
[2, 5, 6],
|
|
[2, 5, 7],
|
|
[3, 4, 6],
|
|
[3, 4, 7],
|
|
[3, 5, 6],
|
|
[3, 5, 7]])
|
|
|
|
out = cartesian(axes)
|
|
assert_array_equal(true_out, out)
|
|
|
|
# check single axis
|
|
x = np.arange(3)
|
|
assert_array_equal(x[:, np.newaxis], cartesian((x,)))
|
|
|
|
|
|
def test_logistic_sigmoid():
|
|
# Check correctness and robustness of logistic sigmoid implementation
|
|
def naive_log_logistic(x):
|
|
return np.log(1 / (1 + np.exp(-x)))
|
|
|
|
x = np.linspace(-2, 2, 50)
|
|
assert_array_almost_equal(log_logistic(x), naive_log_logistic(x))
|
|
|
|
extreme_x = np.array([-100., 100.])
|
|
assert_array_almost_equal(log_logistic(extreme_x), [-100, 0])
|
|
|
|
|
|
def test_incremental_variance_update_formulas():
|
|
# Test Youngs and Cramer incremental variance formulas.
|
|
# Doggie data from http://www.mathsisfun.com/data/standard-deviation.html
|
|
A = np.array([[600, 470, 170, 430, 300],
|
|
[600, 470, 170, 430, 300],
|
|
[600, 470, 170, 430, 300],
|
|
[600, 470, 170, 430, 300]]).T
|
|
idx = 2
|
|
X1 = A[:idx, :]
|
|
X2 = A[idx:, :]
|
|
|
|
old_means = X1.mean(axis=0)
|
|
old_variances = X1.var(axis=0)
|
|
old_sample_count = X1.shape[0]
|
|
final_means, final_variances, final_count = \
|
|
_incremental_mean_and_var(X2, old_means, old_variances,
|
|
old_sample_count)
|
|
assert_almost_equal(final_means, A.mean(axis=0), 6)
|
|
assert_almost_equal(final_variances, A.var(axis=0), 6)
|
|
assert_almost_equal(final_count, A.shape[0])
|
|
|
|
|
|
@skip_if_32bit
|
|
def test_incremental_variance_numerical_stability():
|
|
# Test Youngs and Cramer incremental variance formulas.
|
|
|
|
def np_var(A):
|
|
return A.var(axis=0)
|
|
|
|
# Naive one pass variance computation - not numerically stable
|
|
# https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
|
|
def one_pass_var(X):
|
|
n = X.shape[0]
|
|
exp_x2 = (X ** 2).sum(axis=0) / n
|
|
expx_2 = (X.sum(axis=0) / n) ** 2
|
|
return exp_x2 - expx_2
|
|
|
|
# Two-pass algorithm, stable.
|
|
# We use it as a benchmark. It is not an online algorithm
|
|
# https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Two-pass_algorithm
|
|
def two_pass_var(X):
|
|
mean = X.mean(axis=0)
|
|
Y = X.copy()
|
|
return np.mean((Y - mean)**2, axis=0)
|
|
|
|
# Naive online implementation
|
|
# https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm
|
|
# This works only for chunks for size 1
|
|
def naive_mean_variance_update(x, last_mean, last_variance,
|
|
last_sample_count):
|
|
updated_sample_count = (last_sample_count + 1)
|
|
samples_ratio = last_sample_count / float(updated_sample_count)
|
|
updated_mean = x / updated_sample_count + last_mean * samples_ratio
|
|
updated_variance = last_variance * samples_ratio + \
|
|
(x - last_mean) * (x - updated_mean) / updated_sample_count
|
|
return updated_mean, updated_variance, updated_sample_count
|
|
|
|
# We want to show a case when one_pass_var has error > 1e-3 while
|
|
# _batch_mean_variance_update has less.
|
|
tol = 200
|
|
n_features = 2
|
|
n_samples = 10000
|
|
x1 = np.array(1e8, dtype=np.float64)
|
|
x2 = np.log(1e-5, dtype=np.float64)
|
|
A0 = x1 * np.ones((n_samples // 2, n_features), dtype=np.float64)
|
|
A1 = x2 * np.ones((n_samples // 2, n_features), dtype=np.float64)
|
|
A = np.vstack((A0, A1))
|
|
|
|
# Older versions of numpy have different precision
|
|
# In some old version, np.var is not stable
|
|
if np.abs(np_var(A) - two_pass_var(A)).max() < 1e-6:
|
|
stable_var = np_var
|
|
else:
|
|
stable_var = two_pass_var
|
|
|
|
# Naive one pass var: >tol (=1063)
|
|
assert_greater(np.abs(stable_var(A) - one_pass_var(A)).max(), tol)
|
|
|
|
# Starting point for online algorithms: after A0
|
|
|
|
# Naive implementation: >tol (436)
|
|
mean, var, n = A0[0, :], np.zeros(n_features), n_samples // 2
|
|
for i in range(A1.shape[0]):
|
|
mean, var, n = \
|
|
naive_mean_variance_update(A1[i, :], mean, var, n)
|
|
assert_equal(n, A.shape[0])
|
|
# the mean is also slightly unstable
|
|
assert_greater(np.abs(A.mean(axis=0) - mean).max(), 1e-6)
|
|
assert_greater(np.abs(stable_var(A) - var).max(), tol)
|
|
|
|
# Robust implementation: <tol (177)
|
|
mean, var, n = A0[0, :], np.zeros(n_features), n_samples // 2
|
|
for i in range(A1.shape[0]):
|
|
mean, var, n = \
|
|
_incremental_mean_and_var(A1[i, :].reshape((1, A1.shape[1])),
|
|
mean, var, n)
|
|
assert_equal(n, A.shape[0])
|
|
assert_array_almost_equal(A.mean(axis=0), mean)
|
|
assert_greater(tol, np.abs(stable_var(A) - var).max())
|
|
|
|
|
|
def test_incremental_variance_ddof():
|
|
# Test that degrees of freedom parameter for calculations are correct.
|
|
rng = np.random.RandomState(1999)
|
|
X = rng.randn(50, 10)
|
|
n_samples, n_features = X.shape
|
|
for batch_size in [11, 20, 37]:
|
|
steps = np.arange(0, X.shape[0], batch_size)
|
|
if steps[-1] != X.shape[0]:
|
|
steps = np.hstack([steps, n_samples])
|
|
|
|
for i, j in zip(steps[:-1], steps[1:]):
|
|
batch = X[i:j, :]
|
|
if i == 0:
|
|
incremental_means = batch.mean(axis=0)
|
|
incremental_variances = batch.var(axis=0)
|
|
# Assign this twice so that the test logic is consistent
|
|
incremental_count = batch.shape[0]
|
|
sample_count = batch.shape[0]
|
|
else:
|
|
result = _incremental_mean_and_var(
|
|
batch, incremental_means, incremental_variances,
|
|
sample_count)
|
|
(incremental_means, incremental_variances,
|
|
incremental_count) = result
|
|
sample_count += batch.shape[0]
|
|
|
|
calculated_means = np.mean(X[:j], axis=0)
|
|
calculated_variances = np.var(X[:j], axis=0)
|
|
assert_almost_equal(incremental_means, calculated_means, 6)
|
|
assert_almost_equal(incremental_variances,
|
|
calculated_variances, 6)
|
|
assert_equal(incremental_count, sample_count)
|
|
|
|
|
|
def test_vector_sign_flip():
|
|
# Testing that sign flip is working & largest value has positive sign
|
|
data = np.random.RandomState(36).randn(5, 5)
|
|
max_abs_rows = np.argmax(np.abs(data), axis=1)
|
|
data_flipped = _deterministic_vector_sign_flip(data)
|
|
max_rows = np.argmax(data_flipped, axis=1)
|
|
assert_array_equal(max_abs_rows, max_rows)
|
|
signs = np.sign(data[range(data.shape[0]), max_abs_rows])
|
|
assert_array_equal(data, data_flipped * signs[:, np.newaxis])
|
|
|
|
|
|
def test_softmax():
|
|
rng = np.random.RandomState(0)
|
|
X = rng.randn(3, 5)
|
|
exp_X = np.exp(X)
|
|
sum_exp_X = np.sum(exp_X, axis=1).reshape((-1, 1))
|
|
assert_array_almost_equal(softmax(X), exp_X / sum_exp_X)
|
|
|
|
|
|
def test_stable_cumsum():
|
|
if np_version < (1, 9):
|
|
raise SkipTest("Sum is as unstable as cumsum for numpy < 1.9")
|
|
assert_array_equal(stable_cumsum([1, 2, 3]), np.cumsum([1, 2, 3]))
|
|
r = np.random.RandomState(0).rand(100000)
|
|
assert_warns(RuntimeWarning, stable_cumsum, r, rtol=0, atol=0)
|
|
|
|
# test axis parameter
|
|
A = np.random.RandomState(36).randint(1000, size=(5, 5, 5))
|
|
assert_array_equal(stable_cumsum(A, axis=0), np.cumsum(A, axis=0))
|
|
assert_array_equal(stable_cumsum(A, axis=1), np.cumsum(A, axis=1))
|
|
assert_array_equal(stable_cumsum(A, axis=2), np.cumsum(A, axis=2))
|