def test__solve_triangular_banded(self, its=100):
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, transposed=False)
chol_data = chol_bm.data
depth = chol_bm.l + chol_bm.u
lower = (chol_bm.u == 0)
if size > 0 and rand_bool() and rand_bool():
badFrame = randint(size)
chol_data[0 if lower else depth, badFrame] = 0.0
else:
badFrame = None
transposed = rand_bool()
overwrite_b = rand_bool()
chol_full = chol_bm.full()
b_arg = b.copy()
if badFrame is not None:
msg = (
'singular matrix: resolution failed at diagonal %d' %
badFrame
)
msgRe = '^' + re.escape(msg) + '$'
with self.assertRaisesRegexp(la.LinAlgError, msgRe):
bla._solve_triangular_banded(
chol_data, b_arg, transposed=transposed, lower=lower,
overwrite_b=overwrite_b
)
with self.assertRaisesRegexp(la.LinAlgError, msgRe):
sla.solve_triangular(
chol_full, b, trans=transposed, lower=lower
)
else:
x = bla._solve_triangular_banded(
chol_data, b_arg, transposed=transposed, lower=lower,
overwrite_b=overwrite_b
)
if transposed:
assert_allclose(bm.dot_mv(chol_bm.T, x), b)
else:
assert_allclose(bm.dot_mv(chol_bm, x), b)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.solve_triangular(
chol_full, b, trans=transposed, lower=lower
)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, chol_data)
if size > 0:
self.assertEquals(
np.may_share_memory(x, b_arg),
overwrite_b
)
if not overwrite_b:
assert np.all(b_arg == b)
def test__solve_triangular_banded(self, its=100):
for it in range(its):
size = random.choice([0, 1, randint(0, 10), randint(0, 100)])
b = randn(size)
chol_bm = gen_chol_factor_BandMat(size, transposed=False)
chol_data = chol_bm.data
depth = chol_bm.l + chol_bm.u
lower = (chol_bm.u == 0)
if size > 0 and rand_bool() and rand_bool():
badFrame = randint(size)
chol_data[0 if lower else depth, badFrame] = 0.0
else:
badFrame = None
transposed = rand_bool()
overwrite_b = rand_bool()
chol_full = chol_bm.full()
b_arg = b.copy()
if badFrame is not None:
msg = (
'singular matrix: resolution failed at diagonal %d' %
badFrame
)
msgRe = '^' + re.escape(msg) + '$'
with self.assertRaisesRegexp(la.LinAlgError, msgRe):
bla._solve_triangular_banded(
chol_data, b_arg, transposed=transposed, lower=lower,
overwrite_b=overwrite_b
)
with self.assertRaisesRegexp(la.LinAlgError, msgRe):
sla.solve_triangular(
chol_full, b, trans=transposed, lower=lower
)
else:
x = bla._solve_triangular_banded(
chol_data, b_arg, transposed=transposed, lower=lower,
overwrite_b=overwrite_b
)
if transposed:
assert_allclose(bm.dot_mv(chol_bm.T, x), b)
else:
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, trans=transposed, lower=lower
)
assert_allclose(x, x_good)
assert not np.may_share_memory(x, chol_data)
if size > 0:
self.assertEquals(
np.may_share_memory(x, b_arg),
overwrite_b
)
if not overwrite_b:
assert np.all(b_arg == b)
def smooth(a, Phat, N, lambda_1, lambda_2):
"""
a: (N,) number of measurements at that timestep
Phat: (N, 3) sum of measurements at that timestep
N: num time steps
lambda_1, lambda_2: regularization parameters
solves the optimization problem (over P \in R^{Tx3}):
minimize ||diag(a)*P-Phat||^2 + lambda_1/N*||D_2*P||^2 + lambda_2/N*||D_3*P||^2
returns:
- P: (N, 3) matrix with full trajectory
"""
# A in Banded Matrix form
A = bm.diag(1. * a)
# D_2 and D_3 in Banded Matrix form transposed
D_2_bm_T = bm.BandMat(
1, 1,
np.hstack([
np.zeros((3, 1)),
np.repeat([[1.], [-2.], [1.]], N - 2, axis=1),
np.zeros((3, 1))
]))
D_3_bm_T = bm.BandMat(
2, 2,
np.hstack([
np.zeros((5, 2)),
np.repeat([[-1.], [2.], [0.], [-2.], [1.]], N - 4, axis=1),
np.zeros((5, 2))
]))
# XP=B normal equations
X = bm.dot_mm(A, A) + lambda_1 / N * bm.dot_mm(
D_2_bm_T, D_2_bm_T.T) + lambda_2 / N * bm.dot_mm(D_3_bm_T, D_3_bm_T.T)
l_and_u = (X.l, X.u) # lower and upper band bounds
B = np.hstack([
np.expand_dims(bm.dot_mv(A, Phat[:, 0]), -1),
np.expand_dims(bm.dot_mv(A, Phat[:, 1]), -1),
np.expand_dims(bm.dot_mv(A, Phat[:, 2]), -1)
])
# solve normal equations
P = solve_banded(l_and_u, X.data, B)
return P
def test_cho_solve(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.cho_solve(chol_bm, b)
assert_allclose(
bm.dot_mv(chol_lower_bm, bm.dot_mv(chol_lower_bm.T, x)), b)
if size == 0:
x_good = np.zeros((size, ))
else:
x_good = sla.cho_solve((chol_full, lower), b)
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_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_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_cho_solve(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.cho_solve(chol_bm, b)
assert_allclose(
bm.dot_mv(chol_lower_bm, bm.dot_mv(chol_lower_bm.T, x)),
b
)
if size == 0:
x_good = np.zeros((size,))
else:
x_good = sla.cho_solve((chol_full, lower), b)
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_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_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_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_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)