def advanced_indexing(volume, *indices_list, **kwargs):
""" Performs advanced indexing on `volume`.
This function exists because in Theano<=0.9 advanced indexing is
only supported along the first dimension.
Notes
-----
Assuming `volume` is C contiguous.
"""
strides = kwargs.get("strides")
if strides is None:
shapes = T.cast(volume.shape[:len(indices_list)],
dtype=theano.config.floatX)
strides = T.concatenate([T.ones(
(1, )), T.cumprod(shapes[::-1])[:-1]],
axis=0)[::-1]
shapes = T.cast(volume.shape, dtype=theano.config.floatX)
indices = T.maximum(
0, T.minimum(indices_list[-1], shapes[len(indices_list) - 1] - 1))
for i in range(len(indices_list) - 1):
clipped_idx = T.maximum(0, T.minimum(indices_list[i], shapes[i] - 1))
indices += clipped_idx * strides[i]
# indices = T.sum(T.stack(indices_list, axis=1)*strides[:len(indices_list)], axis=1)
indices = T.cast(indices, dtype="int32")
return volume.reshape((-1, volume.shape[-1]))[indices]
def test_trilinear_interpolation():
trk = nib.streamlines.load(
os.path.abspath(pjoin(__file__, '..', 'data', 'CA.trk')))
trk.tractogram.apply_affine(np.linalg.inv(trk.affine))
dwi = nib.load(os.path.abspath(pjoin(__file__, '..', 'data',
'dwi.nii.gz')))
expected = eval_volume_at_3d_coordinates(dwi.get_data().astype('float32'),
trk.streamlines._data)
coords = T.matrix("coords")
coords.tag.test_value = trk.streamlines._data
volume = T.tensor3("image")
volume.tag.test_value = dwi.get_data()[..., 0]
fct = theano.function([volume, coords],
eval_volume_at_3d_coordinates_in_theano(
volume, coords))
# theano.printing.pydotprint(fct, 'interpolation_vol3d', with_ids=True)
# Process directly multiple 3D volumes then concatenate the results.
values = []
for i in range(dwi.shape[-1]):
values_tmp = fct(dwi.get_data()[..., i], trk.streamlines._data)
values.append(values_tmp)
values = np.array(values).T
assert_array_almost_equal(values, expected, decimal=4)
# Process directly the 4D volume.
volume = theano.shared(dwi.get_data())
coords = theano.shared(trk.streamlines._data)
# Precompute strides that will be used in the interpolation.
shapes = T.cast(volume.shape[:-1], dtype=theano.config.floatX)
strides = T.concatenate([T.ones(
(1, )), T.cumprod(shapes[::-1])[:-1]],
axis=0)[::-1]
volume_strides = strides.eval()
values = eval_volume_at_3d_coordinates_in_theano(
volume, coords, strides=volume_strides).eval()
assert_array_almost_equal(values, expected, decimal=4)
# fct = theano.function([], eval_volume_at_3d_coordinates_in_theano(volume, coords, strides=volume_strides))
# theano.printing.pydotprint(fct, 'interpolation_vol4d', with_ids=True)
# Test tahat coordinates outside the volume are clipped.
coords = coords * np.max(dwi.shape).astype('float32')
expected = eval_volume_at_3d_coordinates(dwi.get_data().astype('float32'),
coords.eval())
values = eval_volume_at_3d_coordinates_in_theano(
volume, coords, strides=volume_strides).eval()
assert_array_almost_equal(values, expected, decimal=4)
coords = -coords
expected = eval_volume_at_3d_coordinates(dwi.get_data().astype('float32'),
coords.eval())
values = eval_volume_at_3d_coordinates_in_theano(
volume, coords, strides=volume_strides).eval()
assert_array_almost_equal(values, expected, decimal=4)
def advanced_indexing(volume, *indices_list, **kwargs):
""" Performs advanced indexing on `volume`.
This function exists because in Theano<=0.9 advanced indexing is
only supported along the first dimension.
Notes
-----
Assuming `volume` is C contiguous.
"""
strides = kwargs.get("strides")
if strides is None:
shapes = T.cast(volume.shape[:len(indices_list)], dtype=theano.config.floatX)
strides = T.concatenate([T.ones((1,)), T.cumprod(shapes[::-1])[:-1]], axis=0)[::-1]
shapes = T.cast(volume.shape, dtype=theano.config.floatX)
indices = T.maximum(0, T.minimum(indices_list[-1], shapes[len(indices_list)-1]-1))
for i in range(len(indices_list)-1):
clipped_idx = T.maximum(0, T.minimum(indices_list[i], shapes[i]-1))
indices += clipped_idx * strides[i]
# indices = T.sum(T.stack(indices_list, axis=1)*strides[:len(indices_list)], axis=1)
indices = T.cast(indices, dtype="int32")
return volume.reshape((-1, volume.shape[-1]))[indices]
def sym_pemb(P, order, roughness):
# embed precision matrix (symbolic operation)
k = -T.ones(order)
d = T.arange(order)
k = k**d
d = d * 2
x = roughness * T.sqrt(2)
r = T.zeros(order)
r = T.join(0, [T.cumprod(1 - d) / (x**d), np.zeros(order)]).T
r = r.flatten(1)[:-1]
R = T.join(0, [r[i:i + order] for i in range(order)])
R = R * k.reshape((1, order))
R = T.nlinalg.matrix_inverse(R)
return T.cast(sym_kron(R, P), theano.config.floatX)
def test_trilinear_interpolation():
trk = nib.streamlines.load(os.path.abspath(pjoin(__file__, '..', 'data', 'CA.trk')))
trk.tractogram.apply_affine(np.linalg.inv(trk.affine))
dwi = nib.load(os.path.abspath(pjoin(__file__, '..', 'data', 'dwi.nii.gz')))
expected = eval_volume_at_3d_coordinates(dwi.get_data().astype('float32'), trk.streamlines._data)
coords = T.matrix("coords")
coords.tag.test_value = trk.streamlines._data
volume = T.tensor3("image")
volume.tag.test_value = dwi.get_data()[..., 0]
fct = theano.function([volume, coords], eval_volume_at_3d_coordinates_in_theano(volume, coords))
# theano.printing.pydotprint(fct, 'interpolation_vol3d', with_ids=True)
# Process directly multiple 3D volumes then concatenate the results.
values = []
for i in range(dwi.shape[-1]):
values_tmp = fct(dwi.get_data()[..., i], trk.streamlines._data)
values.append(values_tmp)
values = np.array(values).T
assert_array_almost_equal(values, expected, decimal=4)
# Process directly the 4D volume.
volume = theano.shared(dwi.get_data())
coords = theano.shared(trk.streamlines._data)
# Precompute strides that will be used in the interpolation.
shapes = T.cast(volume.shape[:-1], dtype=theano.config.floatX)
strides = T.concatenate([T.ones((1,)), T.cumprod(shapes[::-1])[:-1]], axis=0)[::-1]
volume_strides = strides.eval()
values = eval_volume_at_3d_coordinates_in_theano(volume, coords, strides=volume_strides).eval()
assert_array_almost_equal(values, expected, decimal=4)
# fct = theano.function([], eval_volume_at_3d_coordinates_in_theano(volume, coords, strides=volume_strides))
# theano.printing.pydotprint(fct, 'interpolation_vol4d', with_ids=True)
# Test tahat coordinates outside the volume are clipped.
coords = coords * np.max(dwi.shape).astype('float32')
expected = eval_volume_at_3d_coordinates(dwi.get_data().astype('float32'), coords.eval())
values = eval_volume_at_3d_coordinates_in_theano(volume, coords, strides=volume_strides).eval()
assert_array_almost_equal(values, expected, decimal=4)
coords = -coords
expected = eval_volume_at_3d_coordinates(dwi.get_data().astype('float32'), coords.eval())
values = eval_volume_at_3d_coordinates_in_theano(volume, coords, strides=volume_strides).eval()
assert_array_almost_equal(values, expected, decimal=4)
def _initialize_reps(self):
self._reps = {}
if self.nonparametric:
# nu_aux = np.array([2.]+[-1.]*(self.nlatfeats-1))
nu_aux = np.array([0.]*self.nlatfeats)
self._reps['nu'] = shared(nu_aux, name='nu')
self._nu = T.nnet.sigmoid(self._reps['nu'])
self._mu = T.cumprod(self._nu)
verbreps_aux = np.random.normal(0., 1e-2, size=[self.data.n('verb')-self.data.n('clausetype'),
self.nlatfeats])
projection_aux = np.random.normal(0., 1e-2, size=[self.nlatfeats, self.data.n('feature')])
verbfeatprob_aux = np.zeros([self.data.n('verb')-self.data.n('clausetype'), self.nlatfeats])-4.
if self.data.n('clausetype'):
try:
assert self.data.n('clausetype') <= self.nlatfeats
except AssertionError:
raise ValueError('nlatfeats must be greater than or equal to the number of clausetypes')
ctype_ident = (1.-1e-10)*np.eye(self.data.n('clausetype'))
ct_aux_vr = np.log(ctype_ident)-np.log(1.-ctype_ident)
ct_aux_vr = np.concatenate([ct_aux_vr, -np.inf*np.ones([self.data.n('clausetype'),
self.nlatfeats-self.data.n('clausetype')])],
axis=1)
ct_aux_vfp = np.inf*np.ones([self.data.n('clausetype'), self.nlatfeats])
verbreps_aux = np.concatenate([ct_aux_vr, verbreps_aux])
verbfeatprob_aux = np.concatenate([ct_aux_vfp, verbfeatprob_aux])
self._reps['verbreps'] = shared(verbreps_aux, name='verbreps')
self._reps['projection'] = shared(projection_aux, name='projection')
self._reps['verbfeatprob'] = shared(verbfeatprob_aux, name='verbfeatprob')
self._verbreps = T.nnet.sigmoid(self._reps['verbreps'])
self._projection = T.nnet.sigmoid(self._reps['projection'])
self._verbfeatprob = T.nnet.sigmoid(self._reps['verbfeatprob'])
softand = self._verbfeatprob[:,:,None]*self._verbreps[:,:,None]*self._projection[None,:,:]
self._featureprob = 1.-T.prod(1.-softand, axis=1)
def step(x_t, y_t, o_tm1, A, B, dodA, dodB, dodotm1):
# the model itself
o_t = T.dot(x_t, A) + T.dot(o_tm1, B)
mse = T.mean(T.sum(T.square(y_t - o_t), axis=0))
# gradient of o_t w.r.t. A is x_t, w.r.t. B is o_tm1, w.r.t. o_tm1 is B
dodA_t = T.repeat(T.shape_padright(T.mean(x_t, axis=0)),
repeats=n_out,
axis=1)
dodA_up = T.concatenate([T.shape_padleft(dodA_t), dodA[:-1]], axis=0)
dodB_t = T.repeat(T.shape_padright(T.mean(o_tm1, axis=0)),
repeats=n_out,
axis=1)
dodB_up = T.concatenate([T.shape_padleft(dodB_t), dodB[:-1]], axis=0)
dodotm1_t = B
dodotm1_up = T.concatenate([T.shape_padleft(dodotm1_t), dodotm1[:-1]],
axis=0)
# deltaE: update component from current error
# take mean over batch index
# and padleft so size is 1 x n_out
deltaE = T.shape_padleft(T.mean(T.grad(mse, o_t),
axis=0)) # mean over the batch index
# deltaR: update components over time from recurrence
# cumulative product effectively does backprop
# size is bptt_limit x n_out x n_out
deltaR = T.cumprod(dodotm1_up, axis=0)
# updates
# dA = T.dot(deltaE,T.sum(T.batched_dot(deltaR,dodA_up),axis=0))
dA = deltaE * T.sum(T.batched_dot(deltaR, dodA_up), axis=0)
dB = deltaE * T.sum(T.batched_dot(deltaR, dodB_up), axis=0)
updates = OrderedDict()
updates[A] = A - learning_rate * dA
updates[B] = B - learning_rate * dB
updates[dodA] = dodA_up
updates[dodB] = dodB_up
updates[dodotm1] = dodotm1_up
return [o_t, mse, dA], updates