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"""Tests for _sketches.py."""
import numpy as np
from numpy.testing import assert_, assert_equal
from scipy.linalg import clarkson_woodruff_transform
from scipy.linalg._sketches import cwt_matrix
from scipy.sparse import issparse, rand
from scipy.sparse.linalg import norm
class TestClarksonWoodruffTransform:
"""
Testing the Clarkson Woodruff Transform
"""
# set seed for generating test matrices
rng = np.random.default_rng(1179103485)
# Test matrix parameters
n_rows = 2000
n_cols = 100
density = 0.1
# Sketch matrix dimensions
n_sketch_rows = 200
# Seeds to test with
seeds = [1755490010, 934377150, 1391612830, 1752708722, 2008891431,
1302443994, 1521083269, 1501189312, 1126232505, 1533465685]
A_dense = rng.random((n_rows, n_cols))
A_csc = rand(
n_rows, n_cols, density=density, format='csc', random_state=rng,
)
A_csr = rand(
n_rows, n_cols, density=density, format='csr', random_state=rng,
)
A_coo = rand(
n_rows, n_cols, density=density, format='coo', random_state=rng,
)
# Collect the test matrices
test_matrices = [
A_dense, A_csc, A_csr, A_coo,
]
# Test vector with norm ~1
x = rng.random((n_rows, 1)) / np.sqrt(n_rows)
def test_sketch_dimensions(self):
for A in self.test_matrices:
for seed in self.seeds:
# seed to ensure backwards compatibility post SPEC7
sketch = clarkson_woodruff_transform(
A, self.n_sketch_rows, seed=seed
)
assert_(sketch.shape == (self.n_sketch_rows, self.n_cols))
def test_seed_returns_identical_transform_matrix(self):
for seed in self.seeds:
S1 = cwt_matrix(
self.n_sketch_rows, self.n_rows, rng=seed
).toarray()
S2 = cwt_matrix(
self.n_sketch_rows, self.n_rows, rng=seed
).toarray()
assert_equal(S1, S2)
def test_seed_returns_identically(self):
for A in self.test_matrices:
for seed in self.seeds:
sketch1 = clarkson_woodruff_transform(
A, self.n_sketch_rows, rng=seed
)
sketch2 = clarkson_woodruff_transform(
A, self.n_sketch_rows, rng=seed
)
if issparse(sketch1):
sketch1 = sketch1.toarray()
if issparse(sketch2):
sketch2 = sketch2.toarray()
assert_equal(sketch1, sketch2)
def test_sketch_preserves_frobenius_norm(self):
# Given the probabilistic nature of the sketches
# we run the test multiple times and check that
# we pass all/almost all the tries.
n_errors = 0
for A in self.test_matrices:
if issparse(A):
true_norm = norm(A)
else:
true_norm = np.linalg.norm(A)
for seed in self.seeds:
sketch = clarkson_woodruff_transform(
A, self.n_sketch_rows, rng=seed,
)
if issparse(sketch):
sketch_norm = norm(sketch)
else:
sketch_norm = np.linalg.norm(sketch)
if np.abs(true_norm - sketch_norm) > 0.1 * true_norm:
n_errors += 1
assert_(n_errors == 0)
def test_sketch_preserves_vector_norm(self):
n_errors = 0
n_sketch_rows = int(np.ceil(2. / (0.01 * 0.5**2)))
true_norm = np.linalg.norm(self.x)
for seed in self.seeds:
sketch = clarkson_woodruff_transform(
self.x, n_sketch_rows, rng=seed,
)
sketch_norm = np.linalg.norm(sketch)
if np.abs(true_norm - sketch_norm) > 0.5 * true_norm:
n_errors += 1
assert_(n_errors == 0)
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