def rte_mu(x):
mu = x.reshape(n_layer, n_frequency)
rTE = rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
_, _, J_mu = rTE_gradient(frequencies, lamb, sigma, mu, thicknesses)
def J(y):
y = y.reshape(n_layer, n_frequency)
# do summation over layers, broadcast over frequencies only
return np.einsum('i...k,i...', J_mu, y)
return rTE, J
def rte_h(x):
thicknesses = x
rTE = rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
_, J_h, _ = rTE_gradient(frequencies, lamb, sigma, mu, thicknesses)
def J(y):
#(J_h.T@y).T
out = np.einsum('i...,i', J_h, y)
# do sum over n_layer, broadcast over all others
return out
return rTE, J
def rte_sigma(x):
sigma = x.reshape(n_layer, n_frequency)
rTE = rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
J_sigma, _, _ = rTE_gradient(frequencies, lamb, sigma, mu, thicknesses)
def J(y):
y = y.reshape(n_layer, n_frequency)
# do summation over layers, broadcast over frequencies only
# equivalent to:
# out = np.empty_like(rTE)
# for i in range(n_frequency):
# out[i] = J_sigma[:, i, :]).T@y[:, i]
return np.einsum('i...k,i...', J_sigma, y)
return rTE, J
def setUp(self):
"""Test to make sure numpy and compiled give same results"""
n_layer = 11
n_frequency = 5
n_lambda = 8
frequencies = np.logspace(-4, -2, n_frequency)
thicknesses = np.ones(n_layer-1)
lamb = np.logspace(-5, -3, n_lambda)
np.random.seed(123)
sigma = 1E-1 * (1 + 1.0/(n_layer*n_frequency) * np.arange(n_layer*n_frequency).reshape(n_layer, n_frequency))
mu = mu_0 * (1 + 1.0/(n_layer*n_frequency) * np.arange(n_layer*n_frequency).reshape(n_layer, n_frequency))
self.rTE1 = rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
self.rTE2 = _rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
self.rTE1_dsigma, self.rTE1_dh, self.rTE1_dmu = rTE_gradient(frequencies, lamb, sigma, mu, thicknesses)
self.rTE2_dsigma, self.rTE2_dh, self.rTE2_dmu = _rTE_gradient(frequencies, lamb, sigma, mu, thicknesses)
def test_rTE(self):
"""Test to make sure numpy and compiled give same results"""
n_layer = 11
n_frequency = 5
n_lambda = 8
frequencies = np.logspace(1, 4, 5)
thicknesses = np.ones(n_layer - 1)
lamb = np.logspace(0, 3, n_lambda)
sigma = np.random.rand(n_layer, n_frequency)
mu = np.random.rand(n_layer, n_frequency)
rTE1 = rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
rTE2 = _rTE_forward(frequencies, lamb, sigma, mu, thicknesses)
assert_allclose(rTE1, rTE1)
rTE1_dsigma, rTE1_dh, rTE1_dmu = rTE_gradient(frequencies, lamb, sigma,
mu, thicknesses)
rTE2_dsigma, rTE2_dh, rTE2_dmu = _rTE_gradient(frequencies, lamb,
sigma, mu, thicknesses)
assert_allclose(rTE1_dsigma, rTE2_dsigma)
assert_allclose(rTE1_dh, rTE2_dh)
assert_allclose(rTE1_dmu, rTE2_dmu)