def test_dK_dtheta_5():
n = 4
theta = np.array([
2.59193443e-02, 0.00000000e+00, 6.83797216e-07, 3.08837678e-03,
0.00000000e+00, 2.56956907e-02, -1.48051536e+00, -1.51759911e+00,
-1.34983215e+00, -1.22431771e+00
])
size = len(theta)
dK1 = np.zeros((size, n, n))
dK2 = np.zeros((size, n, n))
dK3 = np.zeros((size, n, n))
for u in range(size):
_ratematrix.dK_dtheta_ij(theta, n, u, A=None, out=dK1[u, :, :])
for i in range(n):
for j in range(n):
_ratematrix.dK_dtheta_u(theta, n, i, j, out=dK2[:, i, j])
for i in range(n):
for j in range(n):
dKij = np.zeros(size)
_ratematrix.dK_dtheta_u(theta, n, i, j, out=dKij)
dK3[:, i, j] = dKij
np.testing.assert_almost_equal(dK1, dK2)
np.testing.assert_almost_equal(dK1, dK3)
np.testing.assert_almost_equal(dK2, dK3)
def test_dK_dtheta_5():
n = 4
theta = np.array(
[ 2.59193443e-02, 0.00000000e+00, 6.83797216e-07, 3.08837678e-03,
0.00000000e+00, 2.56956907e-02, -1.48051536e+00, -1.51759911e+00,
-1.34983215e+00, -1.22431771e+00])
size = len(theta)
dK1 = np.zeros((size, n, n))
dK2 = np.zeros((size, n, n))
dK3 = np.zeros((size, n, n))
for u in range(size):
_ratematrix.dK_dtheta_ij(theta, n, u, A=None, out=dK1[u, :, :])
for i in range(n):
for j in range(n):
_ratematrix.dK_dtheta_u(theta, n, i, j, out=dK2[:, i, j])
for i in range(n):
for j in range(n):
dKij = np.zeros(size)
_ratematrix.dK_dtheta_u(theta, n, i, j, out=dKij)
dK3[:, i, j] = dKij
np.testing.assert_almost_equal(dK1, dK2)
np.testing.assert_almost_equal(dK1, dK3)
np.testing.assert_almost_equal(dK2, dK3)
def grad(x, i, j):
# gradient of the (i,j) entry of the rate matrix w.r.t. theta
dKu = np.zeros((n, n))
g = np.zeros(len(x))
for u in range(len(x)):
_ratematrix.dK_dtheta_ij(x, n, u, None, dKu)
g[u] = dKu[i, j]
return g
def grad(x, i, j):
# gradient of the (i,j) entry of the rate matrix w.r.t. theta
dKu = np.zeros((n, n))
g = np.zeros(len(x))
for u in range(len(x)):
_ratematrix.dK_dtheta_ij(x, n, u, None, dKu)
g[u] = dKu[i, j]
return g
def test_dK_dtheta_2():
# test function `dK_dtheta_A` to make sure that the part that hadamards
# the matrix against A is correct.
n = 4
A = random.randn(4, 4)
theta = example_theta(n)
for u in range(len(theta)):
dKu = np.zeros((n, n))
_ratematrix.dK_dtheta_ij(theta, n, u, None, dKu)
value1 = (dKu * A).sum()
dKu = np.zeros((n, n))
value2 = _ratematrix.dK_dtheta_ij(theta, n, u, A, dKu)
value3 = _ratematrix.dK_dtheta_ij(theta, n, u, A)
np.testing.assert_approx_equal(value1, value2)
np.testing.assert_approx_equal(value1, value3)
def test_dK_dtheta_2():
# test function `dK_dtheta_A` to make sure that the part that hadamards
# the matrix against A is correct.
n = 4
A = random.randn(4, 4)
theta = example_theta(n)
for u in range(len(theta)):
dKu = np.zeros((n, n))
_ratematrix.dK_dtheta_ij(theta, n, u, None, dKu)
value1 = (dKu * A).sum()
dKu = np.zeros((n, n))
value2 = _ratematrix.dK_dtheta_ij(theta, n, u, A, dKu)
value3 = _ratematrix.dK_dtheta_ij(theta, n, u, A)
np.testing.assert_approx_equal(value1, value2)
np.testing.assert_approx_equal(value1, value3)
def test_dK_dtheta_3():
# test dK_dtheta_ij vs dK_dtheta_u. both return slices of the same 3D
# tensor, so by repeated calls to both functions we can build the whole
# tensor using both approaches and check that they're equal.
for n in [3, 4]:
theta = example_theta(n)
dKuij1 = np.zeros((len(theta), n, n))
dKuij2 = np.zeros((len(theta), n, n))
for u in range(len(theta)):
_ratematrix.dK_dtheta_ij(theta, n, u, None, dKuij1[u])
for i in range(n):
for j in range(n):
_ratematrix.dK_dtheta_u(theta, n, i, j, out=dKuij2[:, i, j])
np.testing.assert_array_almost_equal(dKuij1, dKuij2)
def test_dK_dtheta_3():
# test dK_dtheta_ij vs dK_dtheta_u. both return slices of the same 3D
# tensor, so by repeated calls to both functions we can build the whole
# tensor using both approaches and check that they're equal.
for n in [3, 4]:
theta = example_theta(n)
dKuij1 = np.zeros((len(theta), n, n))
dKuij2 = np.zeros((len(theta), n, n))
for u in range(len(theta)):
_ratematrix.dK_dtheta_ij(theta, n, u, None, dKuij1[u])
for i in range(n):
for j in range(n):
_ratematrix.dK_dtheta_u(theta, n, i, j, out=dKuij2[:, i, j])
np.testing.assert_array_almost_equal(dKuij1, dKuij2)
def grad(theta, i):
# gradient of the ith eigenvalue of K with respect to theta
K = np.zeros((n, n))
_ratematrix.build_ratemat(theta, n, K)
w, V = scipy.linalg.eig(K)
order = np.argsort(np.real(w))
V = np.real(np.ascontiguousarray(V[:, order]))
U = np.ascontiguousarray(scipy.linalg.inv(V).T)
g = np.zeros(len(theta))
for u in range(len(theta)):
dKu = np.zeros((n, n))
_ratematrix.dK_dtheta_ij(theta, n, u, None, dKu)
out = np.zeros(n)
temp = np.zeros(n)
_ratematrix.dw_du(dKu, U, V, n, temp, out)
g[u] = out[i]
return g
def grad(theta, i):
# gradient of the ith eigenvalue of K with respect to theta
K = np.zeros((n, n))
_ratematrix.build_ratemat(theta, n, K)
w, V = scipy.linalg.eig(K)
order = np.argsort(np.real(w))
V = np.real(np.ascontiguousarray(V[:, order]))
U = np.ascontiguousarray(scipy.linalg.inv(V).T)
g = np.zeros(len(theta))
for u in range(len(theta)):
dKu = np.zeros((n, n))
_ratematrix.dK_dtheta_ij(theta, n, u, None, dKu)
out = np.zeros(n)
temp = np.zeros(n)
_ratematrix.dw_du(dKu, U, V, n, temp, out)
g[u] = out[i]
return g