How to use the uncertainties.unumpy.matrix function in uncertainties

def test_matrix():
    "Matrices of numbers with uncertainties"
    # Matrix inversion:

    # Matrix with a mix of Variable objects and regular
    # Python numbers:

    m = unumpy.matrix([[ufloat((10, 1)), -3.1],
                       [0, ufloat((3, 0))]])
    m_nominal_values = unumpy.nominal_values(m)

    # Test of the nominal_value attribute:
    assert numpy.all(m_nominal_values == m.nominal_values)

    assert type(m[0, 0]) == uncertainties.Variable

    # Test of scalar multiplication, both sides:
    3*m
    m*3

def test_component_extraction():
    "Extracting the nominal values and standard deviations from an array"

    arr = unumpy.uarray(([1, 2], [0.1, 0.2]))

    assert numpy.all(unumpy.nominal_values(arr) == [1, 2])
    assert numpy.all(unumpy.std_devs(arr) == [0.1, 0.2])

    # unumpy matrices, in addition, should have nominal_values that
    # are simply numpy matrices (not unumpy ones, because they have no
    # uncertainties):
    mat = unumpy.matrix(arr)
    assert numpy.all(unumpy.nominal_values(mat) == [1, 2])
    assert numpy.all(unumpy.std_devs(mat) == [0.1, 0.2])
    assert type(unumpy.nominal_values(mat)) == numpy.matrix

# Checks of the numerical values: the diagonal elements of the
    # inverse should be the inverses of the diagonal elements of
    # m (because we started with a triangular matrix):
    assert _numbers_close(1/m_nominal_values[0, 0],
                          m_inv_uncert[0, 0].nominal_value), "Wrong value"

    assert _numbers_close(1/m_nominal_values[1, 1],
                          m_inv_uncert[1, 1].nominal_value), "Wrong value"


    ####################

    # Checks of the covariances between elements:
    x = ufloat((10, 1))
    m = unumpy.matrix([[x, x],
                       [0, 3+2*x]])

    m_inverse = m.I

    # Check of the properties of the inverse:
    m_double_inverse = m_inverse.I
    # The initial matrix should be recovered, including its
    # derivatives, which define covariances:
    assert _numbers_close(m_double_inverse[0, 0].nominal_value,
                          m[0, 0].nominal_value)
    assert _numbers_close(m_double_inverse[0, 0].std_dev(),
                          m[0, 0].std_dev())

    assert matrices_close(m_double_inverse, m)

    # Partial test:

def test_pseudo_inverse():
    "Tests of the pseudo-inverse"

    # Numerical version of the pseudo-inverse:
    pinv_num = core.wrap_array_func(numpy.linalg.pinv)

    ##########
    # Full rank rectangular matrix:
    m = unumpy.matrix([[ufloat((10, 1)), -3.1],
                       [0, ufloat((3, 0))],
                       [1, -3.1]])

    # Numerical and package (analytical) pseudo-inverses: they must be
    # the same:
    rcond = 1e-8  # Test of the second argument to pinv()
    m_pinv_num = pinv_num(m, rcond)
    m_pinv_package = core._pinv(m, rcond)
    assert matrices_close(m_pinv_num, m_pinv_package)

    ##########
    # Example with a non-full rank rectangular matrix:
    vector = [ufloat((10, 1)), -3.1, 11]
    m = unumpy.matrix([vector, vector])
    m_pinv_num = pinv_num(m, rcond)
    m_pinv_package = core._pinv(m, rcond)

x = ufloat((1, 0.1))
    y = ufloat((2, 0.1))
    mat = unumpy.matrix([[x, x], [y, 0]])

    # Internal consistency: the inverse and the pseudo-inverse yield
    # the same result on square matrices:
    assert matrices_close(mat.I, unumpy.ulinalg.pinv(mat), 1e-4)
    assert matrices_close(unumpy.ulinalg.inv(mat),
                          # Support for the optional pinv argument is
                          # tested:
                          unumpy.ulinalg.pinv(mat, 1e-15), 1e-4)

    # Non-square matrices:
    x = ufloat((1, 0.1))
    y = ufloat((2, 0.1))
    mat1 = unumpy.matrix([[x, y]])  # "Long" matrix
    mat2 = unumpy.matrix([[x, y], [1, 3+x], [y, 2*x]])  # "Tall" matrix

    # Internal consistency:
    assert matrices_close(mat1.I, unumpy.ulinalg.pinv(mat1, 1e-10))
    assert matrices_close(mat2.I, unumpy.ulinalg.pinv(mat2, 1e-8))

def test_list_pseudo_inverse():
    "Test of the pseudo-inverse"

    x = ufloat((1, 0.1))
    y = ufloat((2, 0.1))
    mat = unumpy.matrix([[x, x], [y, 0]])

    # Internal consistency: the inverse and the pseudo-inverse yield
    # the same result on square matrices:
    assert matrices_close(mat.I, unumpy.ulinalg.pinv(mat), 1e-4)
    assert matrices_close(unumpy.ulinalg.inv(mat),
                          # Support for the optional pinv argument is
                          # tested:
                          unumpy.ulinalg.pinv(mat, 1e-15), 1e-4)

    # Non-square matrices:
    x = ufloat((1, 0.1))
    y = ufloat((2, 0.1))
    mat1 = unumpy.matrix([[x, y]])  # "Long" matrix
    mat2 = unumpy.matrix([[x, y], [1, 3+x], [y, 2*x]])  # "Tall" matrix

    # Internal consistency:

'''
    num = range(len(slopes))
    allComb = cartesian((num, num))
    comb = []
    # remove doubles
    for row in allComb:
        if row[0] != row[1]:
            comb.append(row)
    comb = np.array(comb)

    # initialize the matrix to store the line intersections
    lineX = np.zeros((len(comb), 2), dtype='object')
    # for each line intersection...
    for j, row in enumerate(comb):
        sl = np.array([slopes[row[0]], slopes[row[1]]])
        a = unumpy.matrix(np.vstack((-sl, np.ones((2)))).T)
        b = np.array([intercepts[row[0]], intercepts[row[1]]])
        lineX[j] = np.dot(a.I, b)
    com = np.mean(lineX, axis=0)

    return com[0], com[1]

'''
    num = range(len(slopes))
    allComb = cartesian((num, num))
    comb = []
    # remove doubles
    for row in allComb:
        if row[0] != row[1]:
            comb.append(row)
    comb = np.array(comb)

    # initialize the matrix to store the line intersections
    lineX = np.zeros((len(comb), 2), dtype='object')
    # for each line intersection...
    for j, row in enumerate(comb):
        sl = np.array([slopes[row[0]], slopes[row[1]]])
        a = unumpy.matrix(np.vstack((-sl, np.ones((2)))).T)
        b = np.array([intercepts[row[0]], intercepts[row[1]]])
        lineX[j] = np.dot(a.I, b)
    com = np.mean(lineX, axis=0)

    return com[0], com[1]