def test_complex(self):
     # Complex b and c
     c = np.array([1+2j, -3, 4j, 5])
     b = np.arange(8).reshape(4, 2) + 0.5j
     x = solve_circulant(c, b)
     y = solve(circulant(c), b)
     assert_allclose(x, y)

 def test_basic3(self):
     # b is a 3-d matrix.
     c = np.array([1, 2, -3, -5])
     b = np.arange(24).reshape(4, 3, 2)
     x = solve_circulant(c, b)
     y = solve(circulant(c), b)
     assert_allclose(x, y)

 def test_singular(self):
     # c gives a singular circulant matrix.
     c = np.array([1, 1, 0, 0])
     b = np.array([1, 2, 3, 4])
     x = solve_circulant(c, b, singular='lstsq')
     y, res, rnk, s = lstsq(circulant(c), b)
     assert_allclose(x, y)
     assert_raises(LinAlgError, solve_circulant, x, y)

 def test_random_b_and_c(self):
     # Random b and c
     np.random.seed(54321)
     c = np.random.randn(50)
     b = np.random.randn(50)
     x = solve_circulant(c, b)
     y = solve(circulant(c), b)
     assert_allclose(x, y)

    def test_axis_args(self):
        # Test use of caxis, baxis and outaxis.

        # c has shape (2, 1, 4)
        c = np.array([[[-1, 2.5, 3, 3.5]], [[1, 6, 6, 6.5]]])

        # b has shape (3, 4)
        b = np.array([[0, 0, 1, 1], [1, 1, 0, 0], [1, -1, 0, 0]])

        x = solve_circulant(c, b, baxis=1)
        assert_equal(x.shape, (4, 2, 3))
        expected = np.empty_like(x)
        expected[:, 0, :] = solve(circulant(c[0]), b.T)
        expected[:, 1, :] = solve(circulant(c[1]), b.T)
        assert_allclose(x, expected)

        x = solve_circulant(c, b, baxis=1, outaxis=-1)
        assert_equal(x.shape, (2, 3, 4))
        assert_allclose(np.rollaxis(x, -1), expected)

        # np.swapaxes(c, 1, 2) has shape (2, 4, 1); b.T has shape (4, 3).
        x = solve_circulant(np.swapaxes(c, 1, 2), b.T, caxis=1)
        assert_equal(x.shape, (4, 2, 3))
        assert_allclose(x, expected)

 def test_basic1(self):
     c = np.array([1, 2, 3, 5])
     b = np.array([1, -1, 1, 0])
     x = solve_circulant(c, b)
     y = solve(circulant(c), b)
     assert_allclose(x, y)