def test_svd_test_case():
    # a test case from Golub and Reinsch
    #  (see wilkinson/reinsch: handbook for auto. comp., vol ii-linear algebra, 134-151(1971).)

    eps = mp.exp(0.8 * mp.log(mp.eps))

    a = [[22, 10,  2,   3,  7],
         [14,  7, 10,   0,  8],
         [-1, 13, -1, -11,  3],
         [-3, -2, 13,  -2,  4],
         [ 9,  8,  1,  -2,  4],
         [ 9,  1, -7,   5, -1],
         [ 2, -6,  6,   5,  1],
         [ 4,  5,  0,  -2,  2]]

    a = mp.matrix(a)
    b = mp.matrix([mp.sqrt(1248), 20, mp.sqrt(384), 0, 0])

    S = mp.svd_r(a, compute_uv = False)
    S -= b
    assert mp.mnorm(S) < eps

    S = mp.svd_c(a, compute_uv = False)
    S -= b
    assert mp.mnorm(S) < eps
示例#2
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def test_svd_test_case():
    # a test case from Golub and Reinsch
    #  (see wilkinson/reinsch: handbook for auto. comp., vol ii-linear algebra, 134-151(1971).)

    eps = mp.exp(0.8 * mp.log(mp.eps))

    a = [[22, 10, 2, 3, 7], [14, 7, 10, 0, 8], [-1, 13, -1, -11, 3],
         [-3, -2, 13, -2, 4], [9, 8, 1, -2, 4], [9, 1, -7, 5, -1],
         [2, -6, 6, 5, 1], [4, 5, 0, -2, 2]]

    a = mp.matrix(a)
    b = mp.matrix([mp.sqrt(1248), 20, mp.sqrt(384), 0, 0])

    S = mp.svd_r(a, compute_uv=False)
    S -= b
    assert mp.mnorm(S) < eps

    S = mp.svd_c(a, compute_uv=False)
    S -= b
    assert mp.mnorm(S) < eps
示例#3
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def run_svd_c(A, full_matrices=False, verbose=True):

    m, n = A.rows, A.cols

    eps = mp.exp(0.8 * mp.log(mp.eps))

    if verbose:
        print("original matrix:\n", str(A))
        print("full", full_matrices)

    U, S0, V = mp.svd_c(A, full_matrices=full_matrices)

    S = mp.zeros(U.cols, V.rows)
    for j in xrange(min(m, n)):
        S[j, j] = S0[j]

    if verbose:
        print("U:\n", str(U))
        print("S:\n", str(S0))
        print("V:\n", str(V))

    C = U * S * V - A
    err = mp.mnorm(C)
    if verbose:
        print("C\n", str(C), "\n", err)
    assert err < eps

    D = V * V.transpose_conj() - mp.eye(V.rows)
    err = mp.mnorm(D)
    if verbose:
        print("D:\n", str(D), "\n", err)
    assert err < eps

    E = U.transpose_conj() * U - mp.eye(U.cols)
    err = mp.mnorm(E)
    if verbose:
        print("E:\n", str(E), "\n", err)
    assert err < eps
def run_svd_c(A, full_matrices = False, verbose = True):

    m, n = A.rows, A.cols

    eps = mp.exp(0.8 * mp.log(mp.eps))

    if verbose:
        print("original matrix:\n", str(A))
        print("full", full_matrices)

    U, S0, V = mp.svd_c(A, full_matrices = full_matrices)

    S = mp.zeros(U.cols, V.rows)
    for j in xrange(min(m, n)):
        S[j,j] = S0[j]

    if verbose:
        print("U:\n", str(U))
        print("S:\n", str(S0))
        print("V:\n", str(V))

    C = U * S * V - A
    err = mp.mnorm(C)
    if verbose:
        print("C\n", str(C), "\n", err)
    assert err  < eps

    D = V * V.transpose_conj() - mp.eye(V.rows)
    err = mp.mnorm(D)
    if verbose:
        print("D:\n", str(D), "\n", err)
    assert err < eps

    E = U.transpose_conj() * U - mp.eye(U.cols)
    err = mp.mnorm(E)
    if verbose:
        print("E:\n", str(E), "\n", err)
    assert err < eps