def test_kronecker():
np.random.seed(1)
# Create random matrices
[a, b, c] = [np.random.rand(3, 3 + i) for i in range(3)]
custom = kronecker(a, b, c) # Custom version
nested = tt.slinalg.kron(a, tt.slinalg.kron(b, c))
np.testing.assert_array_almost_equal(custom.eval(), nested.eval()) # Standard nested version
def test_kronecker():
np.random.seed(1)
# Create random matrices
[a, b, c] = [np.random.rand(3, 3+i) for i in range(3)]
custom = kronecker(a, b, c) # Custom version
nested = tt.slinalg.kron(a, tt.slinalg.kron(b, c))
np.testing.assert_array_almost_equal(
custom.eval(),
nested.eval() # Standard nested version
)
def test_kron_dot():
np.random.seed(1)
# Create random matrices
Ks = [np.random.rand(3, 3) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([k.shape[1] for k in Ks])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then multiply
big = kronecker(*Ks)
slow_ans = at.dot(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_dot(Ks, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())
def test_kron_solve_lower():
np.random.seed(1)
# Create random matrices
Ls = [np.tril(np.random.rand(3, 3)) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([L.shape[1] for L in Ls])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then solve
big = kronecker(*Ls)
slow_ans = at.slinalg.solve_lower_triangular(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_solve_lower(Ls, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())
def test_kron_solve_lower():
np.random.seed(1)
# Create random matrices
Ls = [np.tril(np.random.rand(3, 3)) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([L.shape[1] for L in Ls])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then solve
big = kronecker(*Ls)
slow_ans = tt.slinalg.solve_lower_triangular(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_solve_lower(Ls, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())
def test_kron_dot():
np.random.seed(1)
# Create random matrices
Ks = [np.random.rand(3, 3) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([k.shape[1] for k in Ks])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then multiply
big = kronecker(*Ks)
slow_ans = tt.dot(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_dot(Ks, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())
def test_multiops(self):
X1 = np.linspace(0, 1, 3)[:, None]
X21 = np.linspace(0, 1, 5)[:, None]
X22 = np.linspace(0, 1, 4)[:, None]
X2 = cartesian(X21, X22)
X = cartesian(X1, X21, X22)
with pm.Model() as model:
cov1 = (
3
+ pm.gp.cov.ExpQuad(1, 0.1)
+ pm.gp.cov.ExpQuad(1, 0.1) * pm.gp.cov.ExpQuad(1, 0.1)
)
cov2 = pm.gp.cov.ExpQuad(1, 0.1) * pm.gp.cov.ExpQuad(2, 0.1)
cov = pm.gp.cov.Kron([cov1, cov2])
K_true = kronecker(theano.function([], cov1(X1))(), theano.function([], cov2(X2))()).eval()
K = theano.function([], cov(X))()
npt.assert_allclose(K_true, K)
