def test_corrpsd_threshold():
x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]])
#print np.linalg.eigvalsh(x)
for threshold in [0, 1e-15, 1e-10, 1e-6]:
y = corr_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = corr_clipped(x, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
y = cov_nearest(x, method='nearest', n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
#print evals[0] / threshold - 1
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = cov_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
#print evals[0] / threshold - 1
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
def test_corrpsd_threshold():
x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]])
#print np.linalg.eigvalsh(x)
for threshold in [0, 1e-15, 1e-10, 1e-6]:
y = corr_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = corr_clipped(x, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
y = cov_nearest(x, method='nearest', n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
#print evals[0] / threshold - 1
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = cov_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
#print 'evals', evals, threshold
#print evals[0] / threshold - 1
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
def test_clipped(self):
x = self.x
res_r = self.res
y = corr_clipped(x, threshold=1e-7)
#print np.max(np.abs(x - y)), np.max(np.abs((x - y) / y))
assert_almost_equal(y, res_r.mat, decimal=1)
d = norm_f(x, y)
assert_allclose(d, res_r.normF, rtol=0.15)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals, res_r.eigenvalues[::-1], rtol=0.1, atol=1e-7)
assert_allclose(evals[0], 1e-7, rtol=0.02)
def test_clipped(self):
x = self.x
res_r = self.res
y = corr_clipped(x, threshold=1e-7)
#print np.max(np.abs(x - y)), np.max(np.abs((x - y) / y))
assert_almost_equal(y, res_r.mat, decimal=1)
d = norm_f(x, y)
assert_allclose(d, res_r.normF, rtol=0.15)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals, res_r.eigenvalues[::-1], rtol=0.1, atol=1e-7)
assert_allclose(evals[0], 1e-7, rtol=0.02)
def sample(): trained_generator = tf.keras.models.load_model(saved_model_name, compile=False) noise = tf.random.normal([1, n]) generated_image = trained_generator(noise, training=False) a, b = np.triu_indices(n, k=1) corr = np.array(generated_image[0,:,:,0]) np.fill_diagonal(corr, 1) corr[b, a] = corr[a, b] nearest_corr = corr_clipped(corr) np.fill_diagonal(nearest_corr, 1) nearest_corr[b, a] = nearest_corr[a, b] return nearest_corr
def test_corr_psd():
# test positive definite matrix is unchanged
x = np.array([[1, -0.2, -0.9], [-0.2, 1, -0.2], [-0.9, -0.2, 1]])
y = corr_nearest(x, n_fact=100)
#print np.max(np.abs(x - y))
assert_almost_equal(x, y, decimal=14)
y = corr_clipped(x)
assert_almost_equal(x, y, decimal=14)
y = cov_nearest(x, n_fact=100)
assert_almost_equal(x, y, decimal=14)
x2 = x + 0.001 * np.eye(3)
y = cov_nearest(x2, n_fact=100)
assert_almost_equal(x2, y, decimal=14)
def test_corr_psd():
# test positive definite matrix is unchanged
x = np.array([[1, -0.2, -0.9], [-0.2, 1, -0.2], [-0.9, -0.2, 1]])
y = corr_nearest(x, n_fact=100)
#print np.max(np.abs(x - y))
assert_almost_equal(x, y, decimal=14)
y = corr_clipped(x)
assert_almost_equal(x, y, decimal=14)
y = cov_nearest(x, n_fact=100)
assert_almost_equal(x, y, decimal=14)
x2 = x + 0.001 * np.eye(3)
y = cov_nearest(x2, n_fact=100)
assert_almost_equal(x2, y, decimal=14)
def test_corrpsd_threshold(threshold):
x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]])
y = corr_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = corr_clipped(x, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
y = cov_nearest(x, method='nearest', n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = cov_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
def test_corrpsd_threshold(threshold):
x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]])
y = corr_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = corr_clipped(x, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
y = cov_nearest(x, method='nearest', n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15)
y = cov_nearest(x, n_fact=100, threshold=threshold)
evals = np.linalg.eigvalsh(y)
assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15)
# x has negative eigenvalues, not definite
x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]])
#x = np.array([[1, 0.2, 0.2], [0.2, 1, 0.2], [0.2, 0.2, 1]])
n_fact = 2
print('evals original', np.linalg.eigvalsh(x))
y = corr_nearest(x, n_fact=100)
print('evals nearest', np.linalg.eigvalsh(y))
print(y)
y = corr_nearest(x, n_fact=100, threshold=1e-16)
print('evals nearest', np.linalg.eigvalsh(y))
print(y)
y = corr_clipped(x, threshold=1e-16)
print('evals clipped', np.linalg.eigvalsh(y))
print(y)
np.set_printoptions(precision=4)
print('\nMini Monte Carlo')
# we are simulating a uniformly distributed symmetric matrix
# and find close positive definite matrix
# original can be far away from positive definite,
# then original and converted matrices can be far apart in norm
# results are printed for visual inspection of different cases
k_vars = 5
diag_idx = np.arange(k_vars)
for ii in range(10):
print()
# x has negative eigenvalues, not definite
x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]])
#x = np.array([[1, 0.2, 0.2], [0.2, 1, 0.2], [0.2, 0.2, 1]])
n_fact = 2
print 'evals original', np.linalg.eigvalsh(x)
y = corr_nearest(x, n_fact=100)
print 'evals nearest', np.linalg.eigvalsh(y)
print y
y = corr_nearest(x, n_fact=100, threshold=1e-16)
print 'evals nearest', np.linalg.eigvalsh(y)
print y
y = corr_clipped(x, threshold=1e-16)
print 'evals clipped', np.linalg.eigvalsh(y)
print y
np.set_printoptions(precision=4)
print '\nMini Monte Carlo'
# we are simulating a uniformly distributed symmetric matrix
# and find close positive definite matrix
# original can be far away from positive definite,
# then original and converted matrices can be far apart in norm
# results are printed for visual inspection of different cases
k_vars = 5
diag_idx = np.arange(k_vars)
for ii in range(10):
print