def test_diags_vs_diag(self):
# Check that
#
# diags([a, b, ...], [i, j, ...]) == diag(a, i) + diag(b, j) + ...
#
np.random.seed(1234)
for n_diags in [1, 2, 3, 4, 5, 10]:
n = 1 + n_diags // 2 + np.random.randint(0, 10)
offsets = np.arange(-n + 1, n - 1)
np.random.shuffle(offsets)
offsets = offsets[:n_diags]
diagonals = [np.random.rand(n - abs(q)) for q in offsets]
mat = construct.diags(diagonals, offsets)
dense_mat = sum(
[np.diag(x, j) for x, j in zip(diagonals, offsets)])
assert_array_almost_equal_nulp(mat.toarray(), dense_mat)
if len(offsets) == 1:
mat = construct.diags(diagonals[0], offsets[0])
dense_mat = np.diag(diagonals[0], offsets[0])
assert_array_almost_equal_nulp(mat.toarray(), dense_mat)
def test_diags(self):
a = array([1, 2, 3, 4, 5])
b = array([6, 7, 8, 9, 10])
c = array([11, 12, 13, 14, 15])
cases = []
cases.append((a[:1], 0, (1, 1), [[1]]))
cases.append(([a[:1]], [0], (1, 1), [[1]]))
cases.append(([a[:1]], [0], (2, 1), [[1], [0]]))
cases.append(([a[:1]], [0], (1, 2), [[1, 0]]))
cases.append(([a[:1]], [1], (1, 2), [[0, 1]]))
cases.append(([a[:2]], [0], (2, 2), [[1, 0], [0, 2]]))
cases.append(([a[:1]], [-1], (2, 2), [[0, 0], [1, 0]]))
cases.append(([a[:3]], [0], (3, 4), [[1, 0, 0, 0], [0, 2, 0, 0],
[0, 0, 3, 0]]))
cases.append(([a[:3]], [1], (3, 4), [[0, 1, 0, 0], [0, 0, 2, 0],
[0, 0, 0, 3]]))
cases.append(([a[:1]], [-2], (3, 5), [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0],
[1, 0, 0, 0, 0]]))
cases.append(([a[:2]], [-1], (3, 5), [[0, 0, 0, 0, 0], [1, 0, 0, 0, 0],
[0, 2, 0, 0, 0]]))
cases.append(([a[:3]], [0], (3, 5), [[1, 0, 0, 0, 0], [0, 2, 0, 0, 0],
[0, 0, 3, 0, 0]]))
cases.append(([a[:3]], [1], (3, 5), [[0, 1, 0, 0, 0], [0, 0, 2, 0, 0],
[0, 0, 0, 3, 0]]))
cases.append(([a[:3]], [2], (3, 5), [[0, 0, 1, 0, 0], [0, 0, 0, 2, 0],
[0, 0, 0, 0, 3]]))
cases.append(([a[:2]], [3], (3, 5), [[0, 0, 0, 1, 0], [0, 0, 0, 0, 2],
[0, 0, 0, 0, 0]]))
cases.append(([a[:1]], [4], (3, 5), [[0, 0, 0, 0, 1], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]]))
cases.append(([a[:1]], [-4], (5, 3), [[0, 0, 0], [0, 0, 0], [0, 0, 0],
[0, 0, 0], [1, 0, 0]]))
cases.append(([a[:2]], [-3], (5, 3), [[0, 0, 0], [0, 0, 0], [0, 0, 0],
[1, 0, 0], [0, 2, 0]]))
cases.append(([a[:3]], [-2], (5, 3), [[0, 0, 0], [0, 0, 0], [1, 0, 0],
[0, 2, 0], [0, 0, 3]]))
cases.append(([a[:3]], [-1], (5, 3), [[0, 0, 0], [1, 0, 0], [0, 2, 0],
[0, 0, 3], [0, 0, 0]]))
cases.append(([a[:3]], [0], (5, 3), [[1, 0, 0], [0, 2, 0], [0, 0, 3],
[0, 0, 0], [0, 0, 0]]))
cases.append(([a[:2]], [1], (5, 3), [[0, 1, 0], [0, 0, 2], [0, 0, 0],
[0, 0, 0], [0, 0, 0]]))
cases.append(([a[:1]], [2], (5, 3), [[0, 0, 1], [0, 0, 0], [0, 0, 0],
[0, 0, 0], [0, 0, 0]]))
cases.append(([a[:3], b[:1]], [0, 2], (3, 3), [[1, 0, 6], [0, 2, 0],
[0, 0, 3]]))
cases.append(([a[:2], b[:3]], [-1, 0], (3, 4), [[6, 0, 0, 0],
[1, 7, 0, 0],
[0, 2, 8, 0]]))
cases.append(([a[:4], b[:3]], [2, -3], (6, 6), [[0, 0, 1, 0, 0, 0],
[0, 0, 0, 2, 0, 0],
[0, 0, 0, 0, 3, 0],
[6, 0, 0, 0, 0, 4],
[0, 7, 0, 0, 0, 0],
[0, 0, 8, 0, 0, 0]]))
cases.append(([a[:4], b, c[:4]], [-1, 0, 1], (5, 5), [[6, 11, 0, 0, 0],
[1, 7, 12, 0, 0],
[0, 2, 8, 13, 0],
[0, 0, 3, 9, 14],
[0, 0, 0, 4,
10]]))
cases.append(([a[:2], b[:3], c], [-4, 2,
-1], (6, 5), [[0, 0, 6, 0, 0],
[11, 0, 0, 7, 0],
[0, 12, 0, 0, 8],
[0, 0, 13, 0, 0],
[1, 0, 0, 14, 0],
[0, 2, 0, 0, 15]]))
# too long arrays are OK
cases.append(([a], [0], (1, 1), [[1]]))
cases.append(([a[:3], b], [0, 2], (3, 3), [[1, 0, 6], [0, 2, 0],
[0, 0, 3]]))
cases.append((np.array([[1, 2, 3],
[4, 5, 6]]), [0, -1], (3, 3), [[1, 0, 0],
[4, 2, 0],
[0, 5, 3]]))
# scalar case: broadcasting
cases.append(([1, -2, 1], [1, 0, -1], (3, 3), [[-2, 1, 0], [1, -2, 1],
[0, 1, -2]]))
for d, o, shape, result in cases:
err_msg = "%r %r %r %r" % (d, o, shape, result)
assert_equal(construct.diags(d, o, shape=shape).toarray(),
result,
err_msg=err_msg)
if shape[0] == shape[1] and hasattr(
d[0], '__len__') and len(d[0]) <= max(shape):
# should be able to find the shape automatically
assert_equal(construct.diags(d, o).toarray(),
result,
err_msg=err_msg)
def test_diags_empty(self):
x = construct.diags([])
assert_equal(x.shape, (0, 0))
def test_diags_one_diagonal(self):
d = list(range(5))
for k in range(-5, 6):
assert_equal(
construct.diags(d, k).toarray(),
construct.diags([d], [k]).toarray())
def test_diags_dtype(self):
x = construct.diags([2.2], [0], shape=(2, 2), dtype=int)
assert_equal(x.dtype, int)
assert_equal(x.toarray(), [[2, 0], [0, 2]])
def test_diags_default(self):
a = array([1, 2, 3, 4, 5])
assert_equal(construct.diags(a).toarray(), np.diag(a))