Example #1
0
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)
Example #3
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    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)
Example #4
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    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)
Example #5
0
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
Example #6
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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)
Example #7
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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)
Example #8
0
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)
Example #9
0
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)
Example #10
0
    # 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()
Example #11
0
    # 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