def test_extract_overlapping_m_chunked(self, its=50):
for it in range(its):
num_subs = random.choice([0, 1, randint(10), randint(100)])
step = random.choice([1, randint(1, 10)])
width = step + random.choice([0, 1, randint(10)])
depth = width - 1
assert depth >= 0
overlap = width - step
mat_size = num_subs * step + overlap
chunk_size = random.choice([1, randint(1, 10), randint(1, 10)])
mat_bm = gen_BandMat(mat_size, l=depth, u=depth)
indices_remaining = set(range(num_subs))
submats_all = np.empty((num_subs, width, width))
for start, end, submats in bmo.extract_overlapping_m_chunked(
mat_bm, chunk_size, step=step):
assert end >= start + 1
for index in range(start, end):
assert index in indices_remaining
indices_remaining.remove(index)
submats_all[start:end] = submats
submats_good = bmo.extract_overlapping_m(mat_bm, step=step)
assert_allclose(submats_all, submats_good)
def test_dot_mm_partial(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
l = random.choice([0, 1, randint(0, 10)])
u = random.choice([0, 1, randint(0, 10)])
diag = None if rand_bool() else randn(size)
diag_value = np.ones((size,)) if diag is None else diag
a_full = a_bm.full()
b_full = b_bm.full()
c_bm = bm.dot_mm_partial(l, u, a_bm, b_bm, diag=diag)
c_full = fl.band_ec(
l, u,
np.dot(np.dot(a_full, np.diag(diag_value)), b_full)
)
assert c_bm.l == l
assert c_bm.u == u
assert c_bm.size == size
assert_allclose(c_bm.full(), c_full)
assert not np.may_share_memory(c_bm.data, a_bm.data)
assert not np.may_share_memory(c_bm.data, b_bm.data)
if diag is not None:
assert not np.may_share_memory(c_bm.data, diag)
def test_dot_mm_plus_equals(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
c_bm = gen_BandMat(size)
diag = None if rand_bool() else randn(size)
diag_value = np.ones((size,)) if diag is None else diag
a_full = a_bm.full()
b_full = b_bm.full()
c_full = c_bm.full()
l = c_bm.l
u = c_bm.u
array_mem = get_array_mem(a_bm.data, b_bm.data, c_bm.data)
if diag is not None:
diag_mem = get_array_mem(diag)
bm.dot_mm_plus_equals(a_bm, b_bm, c_bm, diag=diag)
c_full += fl.band_ec(
l, u,
np.dot(np.dot(a_full, np.diag(diag_value)), b_full)
)
assert_allclose(c_bm.full(), c_full)
assert get_array_mem(a_bm.data, b_bm.data, c_bm.data) == array_mem
if diag is not None:
assert get_array_mem(diag) == diag_mem
def test_band_e_linear(self, its=100):
"""Checks band_e is linear."""
for it in range(its):
l = random.choice([0, 1, randint(0, 10)])
u = random.choice([0, 1, randint(0, 10)])
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
# check additive
mat_full1 = randn(size, size)
mat_full2 = randn(size, size)
assert_allclose(
fl.band_e(l, u, mat_full1 + mat_full2),
fl.band_e(l, u, mat_full1) + fl.band_e(l, u, mat_full2)
)
# check homogeneous
mat_full = randn(size, size)
mult = random.choice([0.0, randn(), randn(), randn()])
assert_allclose(
fl.band_e(l, u, mat_full * mult),
fl.band_e(l, u, mat_full) * mult
)
# check output is a newly-created array
mat_rect = fl.band_e(l, u, mat_full)
assert not np.may_share_memory(mat_rect, mat_full)
def test_BandMat_isub(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
a_full = a_bm.full()
b_full = b_bm.full()
array_mem = get_array_mem(a_bm.data, b_bm.data)
if a_bm.l >= b_bm.l and a_bm.u >= b_bm.u:
a_bm -= b_bm
a_full -= b_full
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data, b_bm.data) == array_mem
else:
with self.assertRaises(AssertionError):
a_bm -= b_bm
a_bm -= 0
a_full -= 0
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data, b_bm.data) == array_mem
with self.assertRaises(TypeError):
a_bm -= 1.0
def test_extract_overlapping_m_chunked(self, its=50):
for it in range(its):
num_subs = random.choice([0, 1, randint(10), randint(100)])
step = random.choice([1, randint(1, 10)])
width = step + random.choice([0, 1, randint(10)])
depth = width - 1
assert depth >= 0
overlap = width - step
mat_size = num_subs * step + overlap
chunk_size = random.choice([1, randint(1, 10), randint(1, 10)])
mat_bm = gen_BandMat(mat_size, l=depth, u=depth)
indices_remaining = set(range(num_subs))
submats_all = np.empty((num_subs, width, width))
for start, end, submats in bmo.extract_overlapping_m_chunked(
mat_bm, chunk_size, step=step
):
assert end >= start + 1
for index in range(start, end):
assert index in indices_remaining
indices_remaining.remove(index)
submats_all[start:end] = submats
submats_good = bmo.extract_overlapping_m(mat_bm, step=step)
assert_allclose(submats_all, submats_good)
def test_BandMat_isub(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
a_full = a_bm.full()
b_full = b_bm.full()
array_mem = get_array_mem(a_bm.data, b_bm.data)
if a_bm.l >= b_bm.l and a_bm.u >= b_bm.u:
a_bm -= b_bm
a_full -= b_full
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data, b_bm.data) == array_mem
else:
with self.assertRaises(AssertionError):
a_bm -= b_bm
a_bm -= 0
a_full -= 0
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data, b_bm.data) == array_mem
with self.assertRaises(TypeError):
a_bm -= 1.0
def test_band_e_linear(self, its=100):
"""Checks band_e is linear."""
for it in range(its):
l = random.choice([0, 1, randint(0, 10)])
u = random.choice([0, 1, randint(0, 10)])
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
# check additive
mat_full1 = randn(size, size)
mat_full2 = randn(size, size)
assert_allclose(
fl.band_e(l, u, mat_full1 + mat_full2),
fl.band_e(l, u, mat_full1) + fl.band_e(l, u, mat_full2)
)
# check homogeneous
mat_full = randn(size, size)
mult = random.choice([0.0, randn(), randn(), randn()])
assert_allclose(
fl.band_e(l, u, mat_full * mult),
fl.band_e(l, u, mat_full) * mult
)
# check output is a newly-created array
mat_rect = fl.band_e(l, u, mat_full)
assert not np.may_share_memory(mat_rect, mat_full)
def test_BandMat_neg(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = -a_bm
b_full = -a_full
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
def test_BandMat_neg(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = -a_bm
b_full = -a_full
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
def test_trace_dot(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
a_full = a_bm.full()
b_full = b_bm.full()
c = bm.trace_dot(a_bm, b_bm)
c_good = np.trace(np.dot(a_full.T, b_full))
assert_allclose(c, c_good)
def test_assert_allclose(self):
a0 = np.array([2.0, 3.0, 4.0])
a1 = np.array([2.0, 3.0, 4.0])
a2 = np.array([2.0, 3.0])
a3 = np.array([2.0, 3.0, 5.0])
a4 = np.array([[2.0, 3.0, 4.0]])
th.assert_allclose(a0, a0)
th.assert_allclose(a0, a1)
self.assertRaises(AssertionError, th.assert_allclose, a0, a2)
self.assertRaises(AssertionError, th.assert_allclose, a0, a3)
self.assertRaises(AssertionError, th.assert_allclose, a0, a4)
def test_trace_dot(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
a_full = a_bm.full()
b_full = b_bm.full()
c = bm.trace_dot(a_bm, b_bm)
c_good = np.trace(np.dot(a_full.T, b_full))
assert_allclose(c, c_good)
def test_cholesky_banded_upper_scipy_test(self):
"""Basic test copied from scipy.linalg.tests.test_decomp_cholesky."""
# Symmetric positive definite banded matrix `a`
a = np.array([[4.0, 1.0, 0.0, 0.0], [1.0, 4.0, 0.5, 0.0],
[0.0, 0.5, 4.0, 0.2], [0.0, 0.0, 0.2, 4.0]])
# Banded storage form of `a`.
ab = np.array([[-1.0, 1.0, 0.5, 0.2], [4.0, 4.0, 4.0, 4.0]])
c = bla._cholesky_banded(ab, lower=False)
ufac = np.zeros_like(a)
ufac[range(4), range(4)] = c[-1]
ufac[(0, 1, 2), (1, 2, 3)] = c[0, 1:]
assert_allclose(a, np.dot(ufac.T, ufac))
def test_dot_mv(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b = randn(size)
a_full = a_bm.full()
c = bm.dot_mv(a_bm, b)
c_good = np.dot(a_full, b)
assert_allclose(c, c_good)
assert not np.may_share_memory(c, a_bm.data)
assert not np.may_share_memory(c, b)
def test_BandMat_reverse_view(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = a_bm.reverse_view()
b_full = a_full[::-1, ::-1]
assert_allclose(b_bm.full(), b_full)
assert b_bm.data.base is a_bm.data
if size > 0:
assert np.may_share_memory(b_bm.data, a_bm.data)
def test_BandMat_reverse_view(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = a_bm.reverse_view()
b_full = a_full[::-1, ::-1]
assert_allclose(b_bm.full(), b_full)
assert b_bm.data.base is a_bm.data
if size > 0:
assert np.may_share_memory(b_bm.data, a_bm.data)
def test_band_e_bm_common(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
num_bms = randint(5)
mat_bms = [ gen_BandMat(size) for _ in range(num_bms) ]
if num_bms > 0:
l = max([ mat_bm.l for mat_bm in mat_bms ])
u = max([ mat_bm.u for mat_bm in mat_bms ])
mat_rects = bm.band_e_bm_common(*mat_bms)
for mat_bm, mat_rect in zip(mat_bms, mat_rects):
assert_allclose(mat_rect, bm.band_e_bm(l, u, mat_bm))
def test_cholesky_banded_lower_scipy_test(self):
"""Basic test copied from scipy.linalg.tests.test_decomp_cholesky."""
# Symmetric positive definite banded matrix `a`
a = np.array([[4.0, 1.0, 0.0, 0.0], [1.0, 4.0, 0.5, 0.0],
[0.0, 0.5, 4.0, 0.2], [0.0, 0.0, 0.2, 4.0]])
# Banded storage form of `a`.
ab = np.array([[4.0, 4.0, 4.0, 4.0], [1.0, 0.5, 0.2, -1.0]])
c = bla._cholesky_banded(ab, lower=True)
lfac = np.zeros_like(a)
lfac[range(4), range(4)] = c[0]
lfac[(1, 2, 3), (0, 1, 2)] = c[1, :3]
assert_allclose(a, np.dot(lfac, lfac.T))
def test_dot_mv(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b = randn(size)
a_full = a_bm.full()
c = bm.dot_mv(a_bm, b)
c_good = np.dot(a_full, b)
assert_allclose(c, c_good)
assert not np.may_share_memory(c, a_bm.data)
assert not np.may_share_memory(c, b)
def test_band_e_bm_common(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
num_bms = randint(5)
mat_bms = [gen_BandMat(size) for _ in range(num_bms)]
if num_bms > 0:
l = max([mat_bm.l for mat_bm in mat_bms])
u = max([mat_bm.u for mat_bm in mat_bms])
mat_rects = bm.band_e_bm_common(*mat_bms)
for mat_bm, mat_rect in zip(mat_bms, mat_rects):
assert_allclose(mat_rect, bm.band_e_bm(l, u, mat_bm))
def test_BandMat_various_divs(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = a_bm // mult
b_full = a_full // mult
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
b_bm = a_bm / mult
b_full = a_full / mult
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
b_bm = a_bm.__floordiv__(mult)
b_full = a_full.__floordiv__(mult)
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
# __div__ does not exist in python3
if sys.version_info[0] < 3:
b_bm = a_bm.__div__(mult)
b_full = a_full.__div__(mult)
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
b_bm = a_bm.__truediv__(mult)
b_full = a_full.__truediv__(mult)
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
with self.assertRaises(TypeError):
a_bm // a_bm
with self.assertRaises(TypeError):
a_bm / a_bm
with self.assertRaises(TypeError):
1.0 // a_bm
with self.assertRaises(TypeError):
1.0 / a_bm
def test_BandMat_various_divs(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = a_bm // mult
b_full = a_full // mult
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
b_bm = a_bm / mult
b_full = a_full / mult
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
b_bm = a_bm.__floordiv__(mult)
b_full = a_full.__floordiv__(mult)
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
# __div__ does not exist in python3
if sys.version_info[0] < 3:
b_bm = a_bm.__div__(mult)
b_full = a_full.__div__(mult)
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
b_bm = a_bm.__truediv__(mult)
b_full = a_full.__truediv__(mult)
assert b_bm.l == a_bm.l
assert b_bm.u == a_bm.u
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
with self.assertRaises(TypeError):
a_bm // a_bm
with self.assertRaises(TypeError):
a_bm / a_bm
with self.assertRaises(TypeError):
1.0 // a_bm
with self.assertRaises(TypeError):
1.0 / a_bm
def test_BandMat_sum(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
num_terms = randint(10)
a_bms = [ gen_BandMat(size) for _ in range(num_terms) ]
a_fulls = [ a_bm.full() for a_bm in a_bms ]
b_bm = sum(a_bms)
b_full = sum(a_fulls)
if num_terms > 0:
assert_allclose(b_bm.full(), b_full)
for a_bm in a_bms:
assert not np.may_share_memory(b_bm.data, a_bm.data)
def test_BandMat_sum(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
num_terms = randint(10)
a_bms = [gen_BandMat(size) for _ in range(num_terms)]
a_fulls = [a_bm.full() for a_bm in a_bms]
b_bm = sum(a_bms)
b_full = sum(a_fulls)
if num_terms > 0:
assert_allclose(b_bm.full(), b_full)
for a_bm in a_bms:
assert not np.may_share_memory(b_bm.data, a_bm.data)
def test_band_of_inverse(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mat_bm = gen_pos_def_BandMat(size)
depth = mat_bm.l
band_of_inv_bm = bla.band_of_inverse(mat_bm)
assert not np.may_share_memory(band_of_inv_bm.data, mat_bm.data)
band_of_inv_full_good = fl.band_ec(
depth, depth,
np.eye(0, 0) if size == 0 else la.inv(mat_bm.full()))
assert_allclose(band_of_inv_bm.full(), band_of_inv_full_good)
def test_BandMat_various_idivs(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm //= mult
a_full //= mult
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm /= mult
a_full /= mult
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm.__ifloordiv__(mult)
a_full.__ifloordiv__(mult)
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
# __idiv__ does not exist in python3
if sys.version_info[0] < 3:
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm.__idiv__(mult)
a_full.__idiv__(mult)
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm.__itruediv__(mult)
a_full.__itruediv__(mult)
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
with self.assertRaises(TypeError):
a_bm //= a_bm
with self.assertRaises(TypeError):
a_bm /= a_bm
def test_BandMat_various_idivs(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm //= mult
a_full //= mult
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm /= mult
a_full /= mult
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm.__ifloordiv__(mult)
a_full.__ifloordiv__(mult)
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
# __idiv__ does not exist in python3
if sys.version_info[0] < 3:
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm.__idiv__(mult)
a_full.__idiv__(mult)
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm.__itruediv__(mult)
a_full.__itruediv__(mult)
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
with self.assertRaises(TypeError):
a_bm //= a_bm
with self.assertRaises(TypeError):
a_bm /= a_bm
def test_dot_mv_plus_equals(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b = randn(size)
c = randn(size)
a_full = a_bm.full()
c_good = c.copy()
array_mem = get_array_mem(a_bm.data, b, c)
bm.dot_mv_plus_equals(a_bm, b, c)
c_good += np.dot(a_full, b)
assert_allclose(c, c_good)
assert get_array_mem(a_bm.data, b, c) == array_mem
def test_band_of_inverse(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mat_bm = gen_pos_def_BandMat(size)
depth = mat_bm.l
band_of_inv_bm = bla.band_of_inverse(mat_bm)
assert not np.may_share_memory(band_of_inv_bm.data, mat_bm.data)
band_of_inv_full_good = fl.band_ec(
depth, depth,
np.eye(0, 0) if size == 0 else la.inv(mat_bm.full())
)
assert_allclose(band_of_inv_bm.full(), band_of_inv_full_good)
def test_dot_mv_plus_equals(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b = randn(size)
c = randn(size)
a_full = a_bm.full()
c_good = c.copy()
array_mem = get_array_mem(a_bm.data, b, c)
bm.dot_mv_plus_equals(a_bm, b, c)
c_good += np.dot(a_full, b)
assert_allclose(c, c_good)
assert get_array_mem(a_bm.data, b, c) == array_mem
def test_BandMat_imul(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm *= mult
a_full *= mult
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
with self.assertRaises(TypeError):
a_bm *= a_bm
def test_BandMat_plus_equals_band_of(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
target_bm = gen_BandMat(size)
mat_bm = gen_BandMat(size)
target_full = target_bm.full()
mat_full = mat_bm.full()
array_mem = get_array_mem(target_bm.data, mat_bm.data)
target_bm.plus_equals_band_of(mat_bm, mult)
target_full += (fl.band_ec(target_bm.l, target_bm.u, mat_full) *
mult)
assert_allclose(target_bm.full(), target_full)
assert get_array_mem(target_bm.data, mat_bm.data) == array_mem
def test_BandMat_embed_as_sub_matrix(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
start = randint(size + 1)
end = randint(size + 1)
if start > end:
start, end = end, start
a_bm = gen_BandMat(end - start)
a_full = a_bm.full()
b_bm = a_bm.embed_as_sub_matrix(start, size)
b_full = np.zeros((size, size))
b_full[start:end, start:end] = a_full
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
def test_BandMat_embed_as_sub_matrix(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
start = randint(size + 1)
end = randint(size + 1)
if start > end:
start, end = end, start
a_bm = gen_BandMat(end - start)
a_full = a_bm.full()
b_bm = a_bm.embed_as_sub_matrix(start, size)
b_full = np.zeros((size, size))
b_full[start:end, start:end] = a_full
assert_allclose(b_bm.full(), b_full)
assert not np.may_share_memory(b_bm.data, a_bm.data)
def test_band_of_inverse_from_chol(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
chol_bm = gen_chol_factor_BandMat(size)
depth = chol_bm.l + chol_bm.u
band_of_inv_bm = bla.band_of_inverse_from_chol(chol_bm)
assert not np.may_share_memory(band_of_inv_bm.data, chol_bm.data)
mat_bm = (bm.dot_mm(chol_bm, chol_bm.T)
if chol_bm.u == 0 else bm.dot_mm(chol_bm.T, chol_bm))
band_of_inv_full_good = fl.band_ec(
depth, depth,
np.eye(0, 0) if size == 0 else la.inv(mat_bm.full()))
assert_allclose(band_of_inv_bm.full(), band_of_inv_full_good)
def test_cholesky_banded_lower_scipy_test(self):
"""Basic test copied from scipy.linalg.tests.test_decomp_cholesky."""
# Symmetric positive definite banded matrix `a`
a = np.array([[4.0, 1.0, 0.0, 0.0],
[1.0, 4.0, 0.5, 0.0],
[0.0, 0.5, 4.0, 0.2],
[0.0, 0.0, 0.2, 4.0]])
# Banded storage form of `a`.
ab = np.array([[4.0, 4.0, 4.0, 4.0],
[1.0, 0.5, 0.2, -1.0]])
c = bla._cholesky_banded(ab, lower=True)
lfac = np.zeros_like(a)
lfac[range(4), range(4)] = c[0]
lfac[(1, 2, 3), (0, 1, 2)] = c[1, :3]
assert_allclose(a, np.dot(lfac, lfac.T))
def test_cholesky_banded_upper_scipy_test(self):
"""Basic test copied from scipy.linalg.tests.test_decomp_cholesky."""
# Symmetric positive definite banded matrix `a`
a = np.array([[4.0, 1.0, 0.0, 0.0],
[1.0, 4.0, 0.5, 0.0],
[0.0, 0.5, 4.0, 0.2],
[0.0, 0.0, 0.2, 4.0]])
# Banded storage form of `a`.
ab = np.array([[-1.0, 1.0, 0.5, 0.2],
[4.0, 4.0, 4.0, 4.0]])
c = bla._cholesky_banded(ab, lower=False)
ufac = np.zeros_like(a)
ufac[range(4), range(4)] = c[-1]
ufac[(0, 1, 2), (1, 2, 3)] = c[0, 1:]
assert_allclose(a, np.dot(ufac.T, ufac))
def test_BandMat_imul(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
a_bm = gen_BandMat(size)
a_full = a_bm.full()
array_mem = get_array_mem(a_bm.data)
a_bm *= mult
a_full *= mult
assert_allclose(a_bm.full(), a_full)
assert get_array_mem(a_bm.data) == array_mem
with self.assertRaises(TypeError):
a_bm *= a_bm
def test_BandMat_sub_matrix_view(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
start = randint(size + 1)
end = randint(size + 1)
if start > end:
start, end = end, start
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = a_bm.sub_matrix_view(start, end)
b_full = a_full[start:end, start:end]
assert_allclose(b_bm.full(), b_full)
assert b_bm.data.base is a_bm.data
if end > start:
assert np.may_share_memory(b_bm.data, a_bm.data)
def test_BandMat_plus_equals_band_of(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mult = randn()
target_bm = gen_BandMat(size)
mat_bm = gen_BandMat(size)
target_full = target_bm.full()
mat_full = mat_bm.full()
array_mem = get_array_mem(target_bm.data, mat_bm.data)
target_bm.plus_equals_band_of(mat_bm, mult)
target_full += (
fl.band_ec(target_bm.l, target_bm.u, mat_full) * mult
)
assert_allclose(target_bm.full(), target_full)
assert get_array_mem(target_bm.data, mat_bm.data) == array_mem
def test_solveh(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
b = randn(size)
a_bm = gen_pos_def_BandMat(size)
a_full = a_bm.full()
x = bla.solveh(a_bm, b)
assert_allclose(bm.dot_mv(a_bm, x), b)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.solve(a_full, b, sym_pos=True)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, a_bm.data)
assert not np.may_share_memory(x, b)
def test_BandMat_sub_matrix_view(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
start = randint(size + 1)
end = randint(size + 1)
if start > end:
start, end = end, start
a_bm = gen_BandMat(size)
a_full = a_bm.full()
b_bm = a_bm.sub_matrix_view(start, end)
b_full = a_full[start:end, start:end]
assert_allclose(b_bm.full(), b_full)
assert b_bm.data.base is a_bm.data
if end > start:
assert np.may_share_memory(b_bm.data, a_bm.data)
def test_solveh(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
b = randn(size)
a_bm = gen_pos_def_BandMat(size)
a_full = a_bm.full()
x = bla.solveh(a_bm, b)
assert_allclose(bm.dot_mv(a_bm, x), b)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.solve(a_full, b, sym_pos=True)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, a_bm.data)
assert not np.may_share_memory(x, b)
def test_band_of_inverse_from_chol(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
chol_bm = gen_chol_factor_BandMat(size)
depth = chol_bm.l + chol_bm.u
band_of_inv_bm = bla.band_of_inverse_from_chol(chol_bm)
assert not np.may_share_memory(band_of_inv_bm.data, chol_bm.data)
mat_bm = (bm.dot_mm(chol_bm, chol_bm.T) if chol_bm.u == 0
else bm.dot_mm(chol_bm.T, chol_bm))
band_of_inv_full_good = fl.band_ec(
depth, depth,
np.eye(0, 0) if size == 0 else la.inv(mat_bm.full())
)
assert_allclose(band_of_inv_bm.full(), band_of_inv_full_good)
def test_band_of_outer_plus_equals(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_vec = randn(size)
b_vec = randn(size)
mult = randn()
mat_bm = gen_BandMat(size)
mat_full = mat_bm.full()
l = mat_bm.l
u = mat_bm.u
array_mem = get_array_mem(a_vec, b_vec, mat_bm.data)
bm.band_of_outer_plus_equals(a_vec, b_vec, mat_bm, mult=mult)
mat_full += fl.band_ec(l, u, np.outer(a_vec, b_vec) * mult)
assert_allclose(mat_bm.full(), mat_full)
assert get_array_mem(a_vec, b_vec, mat_bm.data) == array_mem
def test_band_of_outer_plus_equals(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_vec = randn(size)
b_vec = randn(size)
mult = randn()
mat_bm = gen_BandMat(size)
mat_full = mat_bm.full()
l = mat_bm.l
u = mat_bm.u
array_mem = get_array_mem(a_vec, b_vec, mat_bm.data)
bm.band_of_outer_plus_equals(a_vec, b_vec, mat_bm, mult=mult)
mat_full += fl.band_ec(l, u, np.outer(a_vec, b_vec) * mult)
assert_allclose(mat_bm.full(), mat_full)
assert get_array_mem(a_vec, b_vec, mat_bm.data) == array_mem
def test_sum_overlapping_m(self, its=50):
for it in range(its):
num_contribs = random.choice([0, 1, randint(10), randint(100)])
step = random.choice([1, randint(2), randint(10)])
width = max(step, 1) + random.choice([0, 1, randint(10)])
depth = width - 1
assert depth >= 0
overlap = width - step
mat_size = num_contribs * step + overlap
contribs = randn(num_contribs, width, width)
target_bm = gen_BandMat(mat_size, l=depth, u=depth)
target_bm_orig = target_bm.copy()
mat_bm = bmo.sum_overlapping_m(contribs, step=step)
assert mat_bm.size == mat_size
assert mat_bm.l == mat_bm.u == depth
# check target-based version adds to target_bm correctly
bmo.sum_overlapping_m(contribs, step=step, target_bm=target_bm)
assert_allclose(*cc(target_bm, target_bm_orig + mat_bm))
if num_contribs == 0:
# check action for no contributions
assert_allequal(mat_bm.full(), np.zeros((overlap, overlap)))
elif num_contribs == 1:
# check action for a single contribution
assert_allequal(mat_bm.full(), contribs[0])
else:
# check action under splitting list of contributions in two
split_pos = randint(num_contribs + 1)
mat_bm_again = bm.zeros(depth, depth, mat_size)
bmo.sum_overlapping_m(
contribs[:split_pos],
step=step,
target_bm=mat_bm_again.sub_matrix_view(
0, split_pos * step + overlap
)
)
bmo.sum_overlapping_m(
contribs[split_pos:],
step=step,
target_bm=mat_bm_again.sub_matrix_view(
split_pos * step, mat_size
)
)
assert_allclose(*cc(mat_bm, mat_bm_again))
def test_solve(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
b = randn(size)
# the below tries to ensure the matrix is well-conditioned
a_bm = gen_BandMat(size) + bm.diag(np.ones((size,)) * 10.0)
a_full = a_bm.full()
x = bla.solve(a_bm, b)
assert_allclose(bm.dot_mv(a_bm, x), b)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.solve(a_full, b)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, a_bm.data)
assert not np.may_share_memory(x, b)
def test_fancy_plus_equals(self, its=100):
for it in range(its):
source_size = random.choice([0, 1, randint(10), randint(100)])
target_size = random.choice([1, randint(1, 10), randint(1, 100)])
source = randn(source_size)
target = randn(target_size)
target_index_seq = randint(target_size, size=source_size)
array_mem = get_array_mem(target_index_seq, source, target)
target_good = target.copy()
for source_index, target_index in enumerate(target_index_seq):
target_good[target_index] += source[source_index]
fancy_plus_equals(target_index_seq, source, target)
assert_allclose(target, target_good)
assert get_array_mem(target_index_seq, source, target) == array_mem
def test__cholesky_banded(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
if rand_bool():
mat_bm = gen_pos_def_BandMat(size, transposed=False)
else:
mat_bm = gen_symmetric_BandMat(size, transposed=False)
# make it a bit more likely to be pos def
bm.diag(mat_bm)[:] = np.abs(bm.diag(mat_bm)) + 0.1
depth = mat_bm.l
lower = rand_bool()
if lower:
mat_half_data = mat_bm.data[depth:]
else:
mat_half_data = mat_bm.data[:(depth + 1)]
overwrite = rand_bool()
mat_half_data_arg = mat_half_data.copy()
try:
chol_data = bla._cholesky_banded(
mat_half_data_arg, overwrite_ab=overwrite, lower=lower
)
except la.LinAlgError as e:
# First part of the message is e.g. "2-th leading minor".
msgRe = (r'^' + re.escape(str(e)[:15]) +
r'.*not positive definite$')
with self.assertRaisesRegexp(la.LinAlgError, msgRe):
sla.cholesky(mat_bm.full(), lower=lower)
else:
assert np.shape(chol_data) == (depth + 1, size)
if lower:
chol_bm = bm.BandMat(depth, 0, chol_data)
mat_bm_again = bm.dot_mm(chol_bm, chol_bm.T)
else:
chol_bm = bm.BandMat(0, depth, chol_data)
mat_bm_again = bm.dot_mm(chol_bm.T, chol_bm)
assert_allclose(mat_bm_again.full(), mat_bm.full())
if size > 0:
self.assertEqual(
np.may_share_memory(chol_data, mat_half_data_arg),
overwrite
)
if not overwrite:
assert np.all(mat_half_data_arg == mat_half_data)
def test_fancy_plus_equals(self, its=100):
for it in range(its):
source_size = random.choice([0, 1, randint(10), randint(100)])
target_size = random.choice([1, randint(1, 10), randint(1, 100)])
source = randn(source_size)
target = randn(target_size)
target_index_seq = randint(target_size, size=source_size)
array_mem = get_array_mem(target_index_seq, source, target)
target_good = target.copy()
for source_index, target_index in enumerate(target_index_seq):
target_good[target_index] += source[source_index]
fancy_plus_equals(target_index_seq, source, target)
assert_allclose(target, target_good)
assert get_array_mem(target_index_seq, source, target) == array_mem
def test_solve(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
b = randn(size)
# the below tries to ensure the matrix is well-conditioned
a_bm = gen_BandMat(size) + bm.diag(np.ones((size,)) * 10.0)
a_full = a_bm.full()
x = bla.solve(a_bm, b)
assert_allclose(bm.dot_mv(a_bm, x), b)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.solve(a_full, b)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, a_bm.data)
assert not np.may_share_memory(x, b)
def test__cholesky_banded(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
if rand_bool():
mat_bm = gen_pos_def_BandMat(size, transposed=False)
else:
mat_bm = gen_symmetric_BandMat(size, transposed=False)
# make it a bit more likely to be pos def
bm.diag(mat_bm)[:] = np.abs(bm.diag(mat_bm)) + 0.1
depth = mat_bm.l
lower = rand_bool()
if lower:
mat_half_data = mat_bm.data[depth:]
else:
mat_half_data = mat_bm.data[:(depth + 1)]
overwrite = rand_bool()
mat_half_data_arg = mat_half_data.copy()
try:
chol_data = bla._cholesky_banded(mat_half_data_arg,
overwrite_ab=overwrite,
lower=lower)
except la.LinAlgError as e:
# First part of the message is e.g. "2-th leading minor".
msgRe = (r'^' + re.escape(str(e)[:15]) +
r'.*not positive definite$')
with self.assertRaisesRegexp(la.LinAlgError, msgRe):
sla.cholesky(mat_bm.full(), lower=lower)
else:
assert np.shape(chol_data) == (depth + 1, size)
if lower:
chol_bm = bm.BandMat(depth, 0, chol_data)
mat_bm_again = bm.dot_mm(chol_bm, chol_bm.T)
else:
chol_bm = bm.BandMat(0, depth, chol_data)
mat_bm_again = bm.dot_mm(chol_bm.T, chol_bm)
assert_allclose(mat_bm_again.full(), mat_bm.full())
if size > 0:
self.assertEqual(
np.may_share_memory(chol_data, mat_half_data_arg),
overwrite)
if not overwrite:
assert np.all(mat_half_data_arg == mat_half_data)
def test_sum_overlapping_v_chunked(self, its=50):
for it in range(its):
num_contribs = random.choice([0, 1, randint(10), randint(100)])
step = random.choice([1, randint(2), randint(10)])
width = step + random.choice([0, 1, randint(10)])
overlap = width - step
vec_size = num_contribs * step + overlap
contribs = randn(num_contribs, width)
contribs_chunks = chunk_randomly(contribs)
target = randn(vec_size)
target_orig = target.copy()
bmo.sum_overlapping_v_chunked(
contribs_chunks, width, target, step=step
)
vec_good = bmo.sum_overlapping_v(contribs, step=step)
assert_allclose(target, target_orig + vec_good)
def test_cholesky(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
mat_bm = gen_pos_def_BandMat(size)
depth = mat_bm.l
lower = rand_bool()
alternative = rand_bool()
chol_bm = bla.cholesky(mat_bm, lower=lower,
alternative=alternative)
assert chol_bm.l == (depth if lower else 0)
assert chol_bm.u == (0 if lower else depth)
assert not np.may_share_memory(chol_bm.data, mat_bm.data)
if lower != alternative:
mat_bm_again = bm.dot_mm(chol_bm, chol_bm.T)
else:
mat_bm_again = bm.dot_mm(chol_bm.T, chol_bm)
assert_allclose(mat_bm_again.full(), mat_bm.full())
def test_solve_triangular(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
b = randn(size)
chol_bm = gen_chol_factor_BandMat(size)
depth = chol_bm.l + chol_bm.u
lower = (chol_bm.u == 0)
chol_lower_bm = chol_bm if lower else chol_bm.T
chol_full = chol_bm.full()
x = bla.solve_triangular(chol_bm, b)
assert_allclose(bm.dot_mv(chol_bm, x), b)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.solve_triangular(chol_full, b, lower=lower)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, chol_bm.data)
assert not np.may_share_memory(x, b)
def test_sum_overlapping_v_chunked(self, its=50):
for it in range(its):
num_contribs = random.choice([0, 1, randint(10), randint(100)])
step = random.choice([1, randint(2), randint(10)])
width = step + random.choice([0, 1, randint(10)])
overlap = width - step
vec_size = num_contribs * step + overlap
contribs = randn(num_contribs, width)
contribs_chunks = chunk_randomly(contribs)
target = randn(vec_size)
target_orig = target.copy()
bmo.sum_overlapping_v_chunked(contribs_chunks,
width,
target,
step=step)
vec_good = bmo.sum_overlapping_v(contribs, step=step)
assert_allclose(target, target_orig + vec_good)
def test_dot_mm(self, its=50):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
a_bm = gen_BandMat(size)
b_bm = gen_BandMat(size)
diag = None if rand_bool() else randn(size)
diag_value = np.ones((size, )) if diag is None else diag
a_full = a_bm.full()
b_full = b_bm.full()
c_bm = bm.dot_mm(a_bm, b_bm, diag=diag)
c_full = np.dot(np.dot(a_full, np.diag(diag_value)), b_full)
assert c_bm.l == a_bm.l + b_bm.l
assert c_bm.u == a_bm.u + b_bm.u
assert c_bm.size == size
assert_allclose(c_bm.full(), c_full)
assert not np.may_share_memory(c_bm.data, a_bm.data)
assert not np.may_share_memory(c_bm.data, b_bm.data)
if diag is not None:
assert not np.may_share_memory(c_bm.data, diag)