def func(theta, i):
# ith eigenvalue of K
K = np.zeros((n, n))
_ratematrix.build_ratemat(np.exp(theta), n, None, K)
w = np.real(scipy.linalg.eigvals(K))
w = np.sort(w)
return w[i]
def func(theta, i):
# ith eigenvalue of K
K = np.zeros((n, n))
_ratematrix.build_ratemat(theta, n, K)
w = np.real(scipy.linalg.eigvals(K))
w = np.sort(w)
return w[i]
def g(i):
h = 1e-7
e = np.zeros_like(exp_sp)
e[i] = h
K1 = np.zeros((n, n))
K2 = np.zeros((n, n))
_ratematrix.build_ratemat(exp_sp, n, inds_sp, K1)
_ratematrix.build_ratemat(np.exp(np.log(exp_sp) + e), n, inds_sp, K2)
return np.sum(np.multiply(A, (K2 - K1) / h))
def g(i):
h = 1e-7
e = np.zeros_like(exptheta)
e[i] = h
K1 = np.zeros((n, n))
K2 = np.zeros((n, n))
_ratematrix.build_ratemat(exptheta, n, None, K1)
_ratematrix.build_ratemat(np.exp(np.log(exptheta) + e), n, None, K2)
return np.sum(np.multiply(A, (K2 - K1) / h)), (K2 - K1) / h
def test_build_ratemat_1():
# test build_ratemat in sparse mode vs. dense mode
n = 4
exptheta = dense_exptheta(n)
u = np.arange(n*(n-1)/2 + n).astype(np.intp)
K1 = np.zeros((n, n))
K2 = np.zeros((n, n))
_ratematrix.build_ratemat(exptheta, n, u, K1)
_ratematrix.build_ratemat(exptheta, n, None, K2)
np.testing.assert_array_equal(K1, K2)
def test_build_ratemat_2():
# test build_ratemat in sparse mode vs. dense mode
n = 4
exp_d, exp_sp, inds_sp = sparse_exptheta(n)
K1 = np.zeros((n, n))
K2 = np.zeros((n, n))
_ratematrix.build_ratemat(exp_sp, n, inds_sp, K1)
_ratematrix.build_ratemat(exp_d, n, None, K2)
np.testing.assert_array_equal(K1, K2)
def test_build_ratemat_1():
# test build_ratemat
n = 4
theta = example_theta(n)
K = np.zeros((n, n))
_ratematrix.build_ratemat(theta, n, K)
# diagonal entries are negative
assert np.all(np.diag(K) < 0)
# off diagonal entries are non-negative
assert np.all(np.extract(1-np.eye(n), K) >= 0)
# row-sums are 0
np.testing.assert_array_almost_equal(np.sum(K, axis=1), 0)
def test_build_ratemat():
# test build_ratemat
n = 4
theta = example_theta(n)
K = np.zeros((n, n))
_ratematrix.build_ratemat(theta, n, K)
# diagonal entries are negative
assert np.all(np.diag(K) < 0)
# off diagonal entries are non-negative
assert np.all(np.extract(1 - np.eye(n), K) >= 0)
# row-sums are 0
np.testing.assert_array_almost_equal(np.sum(K, axis=1), 0)
def grad(theta, i):
# gradient of the ith eigenvalue of K with respect to theta
K = np.zeros((n, n))
_ratematrix.build_ratemat(np.exp(theta), n, None, 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_A(np.exp(theta), n, u, None, 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
def func(x, i, j):
# (i,j) entry of the rate matrix
K = np.zeros((n, n))
_ratematrix.build_ratemat(x, n, K)
return K[i, j]
def func(x, i, j):
# (i,j) entry of the rate matrix
K = np.zeros((n, n))
_ratematrix.build_ratemat(x, n, K)
return K[i, j]
