def __init__(self,
incoming,
uvec=lasagne.init.Normal(1),
b=lasagne.init.Constant(0),
**kwargs):
super(OrthogonalFlow, self).__init__(incoming, **kwargs)
num_inputs = self.input_shape[1]
n = num_inputs
n_triu_entries = (n * (n + 1)) // 2
r = T.arange(n)
tmp_mat = r[np.newaxis, :] + (n_triu_entries - n -
(r * (r + 1)) // 2)[::-1, np.newaxis]
triu_index_matrix = T.tril(tmp_mat.T) - r[np.newaxis, :]
tmp_mat1 = T.tril(tmp_mat.T) - r[np.newaxis, :]
skew_index_mat = T.tril(tmp_mat1 - T.diag(T.diag(tmp_mat1)))
self.uvec = self.add_param(uvec,
((num_inputs - 1) * (num_inputs) / 2, ),
name='uvec')
vec0 = T.concatenate([T.zeros(1), self.uvec])
skw_matrix = vec0[skew_index_mat] - vec0[skew_index_mat].T
self.U = expm(skw_matrix)
self.b = self.add_param(b, (num_inputs, ), name='b') # scalar
def hky_transition_probs_expm(kappa, pi, t): Q_nodiag = make_tensor([ [0, kappa*pi[C], pi[A], pi[G]], [kappa*pi[T], 0, pi[A], pi[G]], [pi[T], pi[C], 0, kappa*pi[G]], [pi[T], pi[C], kappa*pi[A], 0] ]) Q_unnormalised = Q_nodiag - tt.diag(Q_nodiag.sum(axis = 1)) average_subs = -tt.nlinalg.trace(tt.dot(Q_unnormalised, tt.diag(pi))) return tsl.expm(Q * t / average_subs)
def test_expm():
scipy = pytest.importorskip("scipy")
rng = np.random.RandomState(utt.fetch_seed())
A = rng.randn(5, 5).astype(config.floatX)
ref = scipy.linalg.expm(A)
x = tensor.matrix()
m = expm(x)
expm_f = function([x], m)
val = expm_f(A)
np.testing.assert_array_almost_equal(val, ref)
def test_expm():
if not imported_scipy:
raise SkipTest("Scipy needed for the expm op.")
rng = np.random.RandomState(utt.fetch_seed())
A = rng.randn(5, 5).astype(config.floatX)
ref = scipy.linalg.expm(A)
x = tensor.matrix()
m = expm(x)
expm_f = function([x], m)
val = expm_f(A)
np.testing.assert_array_almost_equal(val, ref)
def test_expm():
if not imported_scipy:
raise SkipTest("Scipy needed for the expm op.")
rng = numpy.random.RandomState(utt.fetch_seed())
A = rng.randn(5, 5).astype(config.floatX)
ref = scipy.linalg.expm(A)
x = tensor.matrix()
m = expm(x)
expm_f = function([x], m)
val = expm_f(A)
numpy.testing.assert_array_almost_equal(val, ref)
deph2), TT.dot(m, conjU3ten[:, :, i])))) *
deph3)))) * inhom14
return (1j * 1j * 1j) * h1 * h2 * h3vec[i] * (
r1 + r2 + r3 + r4 - TT.conj(r1) - TT.conj(r2) - TT.conj(r3) -
TT.conj(r4))
response, updates = theano.scan(fn=resfunc,
outputs_info=None,
sequences=iscan,
non_sequences=[
xvec, y, h1, h2, h3vec, U1, U2,
U3ten, conjU1, conjU2, conjU3ten
])
# Theano time propagator expression
timeprop = TTslinalg.expm(-1j * w * (x - y))
#############################
# Declare theano functions
f_response = theano.function(
[xvec, y, h1, h2, h3vec, U1, U2, U3ten, conjU1, conjU2, conjU3ten],
response,
allow_input_downcast=True,
on_unused_input='warn')
f_timeprop = theano.function([x, y], timeprop)
#############################
# Calculate the time domain response function for single quantum excitation scans
U3array = np.zeros((n_states, n_states, NEmi), dtype=complex)
conjU3array = np.zeros((n_states, n_states, NEmi), dtype=complex)
h3temparray = np.zeros(NEmi, dtype=int)