def test_dimensions_mismatch():
    # Regression test for GH #3493. Check that setting up a PDF with a mean of
    # length M and a covariance matrix of size (N, N), where M != N, raises a
    # ValueError with an informative error message.

    mu = np.array([0.0, 0.0])
    sigma = np.array([[1.0]])

    assert_raises(ValueError, multivariate_normal, mu, sigma)

    # A simple check that the right error message was passed along. Checking
    # that the entire message is there, word for word, would be somewhat
    # fragile, so we just check for the leading part.
    try:
        multivariate_normal(mu, sigma)
    except ValueError as e:
        msg = "Dimension mismatch"
        assert_equal(str(e)[:len(msg)], msg)
Ejemplo n.º 2
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def test_dimensions_mismatch():
    # Regression test for GH #3493. Check that setting up a PDF with a mean of
    # length M and a covariance matrix of size (N, N), where M != N, raises a
    # ValueError with an informative error message.

    mu = np.array([0.0, 0.0])
    sigma = np.array([[1.0]])

    assert_raises(ValueError, multivariate_normal, mu, sigma)

    # A simple check that the right error message was passed along. Checking
    # that the entire message is there, word for word, would be somewhat
    # fragile, so we just check for the leading part.
    try:
        multivariate_normal(mu, sigma)
    except ValueError as e:
        msg = "Dimension mismatch"
        assert_equal(str(e)[:len(msg)], msg)
def test_rank():
    # Check that the rank is detected correctly.
    np.random.seed(1234)
    n = 4
    mean = np.random.randn(n)
    for expected_rank in range(1, n + 1):
        s = np.random.randn(n, expected_rank)
        cov = np.dot(s, s.T)
        distn = multivariate_normal(mean, cov, allow_singular=True)
        assert_equal(distn.cov_info.rank, expected_rank)
def test_frozen():
    # The frozen distribution should agree with the regular one
    np.random.seed(1234)
    x = np.random.randn(5)
    mean = np.random.randn(5)
    cov = np.abs(np.random.randn(5))
    norm_frozen = multivariate_normal(mean, cov)
    assert_allclose(norm_frozen.pdf(x), multivariate_normal.pdf(x, mean, cov))
    assert_allclose(norm_frozen.logpdf(x),
                    multivariate_normal.logpdf(x, mean, cov))
Ejemplo n.º 5
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def test_rank():
    # Check that the rank is detected correctly.
    np.random.seed(1234)
    n = 4
    mean = np.random.randn(n)
    for expected_rank in range(1, n + 1):
        s = np.random.randn(n, expected_rank)
        cov = np.dot(s, s.T)
        distn = multivariate_normal(mean, cov, allow_singular=True)
        assert_equal(distn.cov_info.rank, expected_rank)
Ejemplo n.º 6
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def test_frozen():
    # The frozen distribution should agree with the regular one
    np.random.seed(1234)
    x = np.random.randn(5)
    mean = np.random.randn(5)
    cov = np.abs(np.random.randn(5))
    norm_frozen = multivariate_normal(mean, cov)
    assert_allclose(norm_frozen.pdf(x), multivariate_normal.pdf(x, mean, cov))
    assert_allclose(norm_frozen.logpdf(x),
                    multivariate_normal.logpdf(x, mean, cov))
def test_degenerate_distributions():
    for n in range(1, 5):
        x = np.random.randn(n)
        for k in range(1, n + 1):
            # Sample a small covariance matrix.
            s = np.random.randn(k, k)
            cov_kk = np.dot(s, s.T)

            # Embed the small covariance matrix into a larger low rank matrix.
            cov_nn = np.zeros((n, n))
            cov_nn[:k, :k] = cov_kk

            # Define a rotation of the larger low rank matrix.
            u = _sample_orthonormal_matrix(n)
            cov_rr = np.dot(u, np.dot(cov_nn, u.T))
            y = np.dot(u, x)

            # Check some identities.
            distn_kk = multivariate_normal(np.zeros(k),
                                           cov_kk,
                                           allow_singular=True)
            distn_nn = multivariate_normal(np.zeros(n),
                                           cov_nn,
                                           allow_singular=True)
            distn_rr = multivariate_normal(np.zeros(n),
                                           cov_rr,
                                           allow_singular=True)
            assert_equal(distn_kk.cov_info.rank, k)
            assert_equal(distn_nn.cov_info.rank, k)
            assert_equal(distn_rr.cov_info.rank, k)
            pdf_kk = distn_kk.pdf(x[:k])
            pdf_nn = distn_nn.pdf(x)
            pdf_rr = distn_rr.pdf(y)
            assert_allclose(pdf_kk, pdf_nn)
            assert_allclose(pdf_kk, pdf_rr)
            logpdf_kk = distn_kk.logpdf(x[:k])
            logpdf_nn = distn_nn.logpdf(x)
            logpdf_rr = distn_rr.logpdf(y)
            assert_allclose(logpdf_kk, logpdf_nn)
            assert_allclose(logpdf_kk, logpdf_rr)
Ejemplo n.º 8
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def test_degenerate_distributions():
    for n in range(1, 5):
        x = np.random.randn(n)
        for k in range(1, n + 1):
            # Sample a small covariance matrix.
            s = np.random.randn(k, k)
            cov_kk = np.dot(s, s.T)

            # Embed the small covariance matrix into a larger low rank matrix.
            cov_nn = np.zeros((n, n))
            cov_nn[:k, :k] = cov_kk

            # Define a rotation of the larger low rank matrix.
            u = _sample_orthonormal_matrix(n)
            cov_rr = np.dot(u, np.dot(cov_nn, u.T))
            y = np.dot(u, x)

            # Check some identities.
            distn_kk = multivariate_normal(np.zeros(k), cov_kk,
                                           allow_singular=True)
            distn_nn = multivariate_normal(np.zeros(n), cov_nn,
                                           allow_singular=True)
            distn_rr = multivariate_normal(np.zeros(n), cov_rr,
                                           allow_singular=True)
            assert_equal(distn_kk.cov_info.rank, k)
            assert_equal(distn_nn.cov_info.rank, k)
            assert_equal(distn_rr.cov_info.rank, k)
            pdf_kk = distn_kk.pdf(x[:k])
            pdf_nn = distn_nn.pdf(x)
            pdf_rr = distn_rr.pdf(y)
            assert_allclose(pdf_kk, pdf_nn)
            assert_allclose(pdf_kk, pdf_rr)
            logpdf_kk = distn_kk.logpdf(x[:k])
            logpdf_nn = distn_nn.logpdf(x)
            logpdf_rr = distn_rr.logpdf(y)
            assert_allclose(logpdf_kk, logpdf_nn)
            assert_allclose(logpdf_kk, logpdf_rr)
def test_rvs_shape():
    # Check that rvs parses the mean and covariance correctly, and returns
    # an array of the right shape
    N = 300
    d = 4
    sample = multivariate_normal.rvs(mean=np.zeros(d), cov=1, size=N)
    assert_equal(sample.shape, (N, d))

    sample = multivariate_normal.rvs(mean=None,
                                     cov=np.array([[2, .1], [.1, 1]]),
                                     size=N)
    assert_equal(sample.shape, (N, 2))

    u = multivariate_normal(mean=0, cov=1)
    sample = u.rvs(N)
    assert_equal(sample.shape, (N, ))
Ejemplo n.º 10
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def test_rvs_shape():
    # Check that rvs parses the mean and covariance correctly, and returns
    # an array of the right shape
    N = 300
    d = 4
    sample = multivariate_normal.rvs(mean=np.zeros(d), cov=1, size=N)
    assert_equal(sample.shape, (N, d))

    sample = multivariate_normal.rvs(mean=None,
                                     cov=np.array([[2, .1], [.1, 1]]),
                                     size=N)
    assert_equal(sample.shape, (N, 2))

    u = multivariate_normal(mean=0, cov=1)
    sample = u.rvs(N)
    assert_equal(sample.shape, (N, ))
def test_entropy():
    np.random.seed(2846)

    n = 3
    mean = np.random.randn(n)
    M = np.random.randn(n, n)
    cov = np.dot(M, M.T)

    rv = multivariate_normal(mean, cov)

    # Check that frozen distribution agrees with entropy function
    assert_almost_equal(rv.entropy(), multivariate_normal.entropy(mean, cov))
    # Compare entropy with manually computed expression involving
    # the sum of the logs of the eigenvalues of the covariance matrix
    eigs = np.linalg.eig(cov)[0]
    desired = 1 / 2 * (n * (np.log(2 * np.pi) + 1) + np.sum(np.log(eigs)))
    assert_almost_equal(desired, rv.entropy())
Ejemplo n.º 12
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def test_entropy():
    np.random.seed(2846)

    n = 3
    mean = np.random.randn(n)
    M = np.random.randn(n, n)
    cov = np.dot(M, M.T)

    rv = multivariate_normal(mean, cov)

    # Check that frozen distribution agrees with entropy function
    assert_almost_equal(rv.entropy(), multivariate_normal.entropy(mean, cov))
    # Compare entropy with manually computed expression involving
    # the sum of the logs of the eigenvalues of the covariance matrix
    eigs = np.linalg.eig(cov)[0]
    desired = 1 / 2 * (n * (np.log(2 * np.pi) + 1) + np.sum(np.log(eigs)))
    assert_almost_equal(desired, rv.entropy())
def test_multivariate_normal_rvs_zero_covariance():
    mean = np.zeros(2)
    covariance = np.zeros((2, 2))
    model = multivariate_normal(mean, covariance, allow_singular=True)
    sample = model.rvs()
    assert_equal(sample, [0, 0])
Ejemplo n.º 14
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def test_multivariate_normal_rvs_zero_covariance():
    mean = np.zeros(2)
    covariance = np.zeros((2, 2))
    model = multivariate_normal(mean, covariance, allow_singular=True)
    sample = model.rvs()
    assert_equal(sample, [0, 0])