Python theano.tensor.sin() Examples
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Example #1
Source File: pendulum.py From ilqr with GNU General Public License v3.0 | 6 votes |
def reduce_state(cls, state): """Reduces a non-angular state into an angular state by replacing sin(theta) and cos(theta) with theta. In this case, it converts: [sin(theta), cos(theta), theta'] -> [theta, theta'] Args: state: Augmented state vector [state_size]. Returns: Reduced state size [reducted_state_size]. """ if state.ndim == 1: sin_theta, cos_theta, theta_dot = state else: sin_theta = state[..., 0].reshape(-1, 1) cos_theta = state[..., 1].reshape(-1, 1) theta_dot = state[..., 2].reshape(-1, 1) theta = np.arctan2(sin_theta, cos_theta) return np.hstack([theta, theta_dot])
Example #2
Source File: utils_.py From kusanagi with MIT License | 6 votes |
def gTrig_np(x, angi): ''' Replaces angle dimensions with their complex representation ''' if isinstance(x, list): x = np.array(x) if x.ndim == 1: x = x[None, :] D = x.shape[1] Da = 2*len(angi) n = x.shape[0] xang = np.zeros((n, Da)) xi = x[:, angi] xang[:, ::2] = np.sin(xi) xang[:, 1::2] = np.cos(xi) na_dims = list(set(range(D)).difference(angi)) xnang = x[:, na_dims] m = np.concatenate([xnang, xang], axis=1) return m
Example #3
Source File: test_vm.py From attention-lvcsr with MIT License | 6 votes |
def test_no_leak_many_graphs(): # Verify no memory leaks when creating and deleting a lot of functions # This isn't really a unit test, you have to run it and look at top to # see if there's a leak for i in xrange(10000): x = tensor.vector() z = x for d in range(10): z = tensor.sin(-z + 1) f = function([x], z, mode=Mode(optimizer=None, linker='cvm')) if not i % 100: print(gc.collect()) sys.stdout.flush() gc.collect() if 1: f([2.0]) f([3.0]) f([4.0]) f([5.0])
Example #4
Source File: core.py From starry with MIT License | 6 votes |
def compute_ortho_grid_inc_obl(self, res, inc, obl): """Compute the polynomial basis on the plane of the sky, accounting for the map inclination and obliquity.""" # See NOTE on tt.mgrid bug in `compute_ortho_grid` dx = 2.0 / (res - 0.01) y, x = tt.mgrid[-1:1:dx, -1:1:dx] z = tt.sqrt(1 - x ** 2 - y ** 2) y = tt.set_subtensor(y[tt.isnan(z)], np.nan) x = tt.reshape(x, [1, -1]) y = tt.reshape(y, [1, -1]) z = tt.reshape(z, [1, -1]) Robl = self.RAxisAngle(tt.as_tensor_variable([0.0, 0.0, 1.0]), -obl) Rinc = self.RAxisAngle( tt.as_tensor_variable([tt.cos(obl), tt.sin(obl), 0.0]), -(0.5 * np.pi - inc), ) R = tt.dot(Robl, Rinc) xyz = tt.dot(R, tt.concatenate((x, y, z))) x = tt.reshape(xyz[0], [1, -1]) y = tt.reshape(xyz[1], [1, -1]) z = tt.reshape(xyz[2], [1, -1]) lat = tt.reshape(0.5 * np.pi - tt.arccos(y), [1, -1]) lon = tt.reshape(tt.arctan2(x, z), [1, -1]) return tt.concatenate((lat, lon)), tt.concatenate((x, y, z))
Example #5
Source File: cartpole.py From ilqr with GNU General Public License v3.0 | 6 votes |
def reduce_state(cls, state): """Reduces a non-angular state into an angular state by replacing sin(theta) and cos(theta) with theta. In this case, it converts: [x, x', sin(theta), cos(theta), theta'] -> [x, x', theta, theta'] Args: state: Augmented state vector [state_size]. Returns: Reduced state size [reducted_state_size]. """ if state.ndim == 1: x, x_dot, sin_theta, cos_theta, theta_dot = state else: x = state[..., 0].reshape(-1, 1) x_dot = state[..., 1].reshape(-1, 1) sin_theta = state[..., 2].reshape(-1, 1) cos_theta = state[..., 3].reshape(-1, 1) theta_dot = state[..., 4].reshape(-1, 1) theta = np.arctan2(sin_theta, cos_theta) return np.hstack([x, x_dot, theta, theta_dot])
Example #6
Source File: cartpole.py From ilqr with GNU General Public License v3.0 | 6 votes |
def augment_state(cls, state): """Augments angular state into a non-angular state by replacing theta with sin(theta) and cos(theta). In this case, it converts: [x, x', theta, theta'] -> [x, x', sin(theta), cos(theta), theta'] Args: state: State vector [reducted_state_size]. Returns: Augmented state size [state_size]. """ if state.ndim == 1: x, x_dot, theta, theta_dot = state else: x = state[..., 0].reshape(-1, 1) x_dot = state[..., 1].reshape(-1, 1) theta = state[..., 2].reshape(-1, 1) theta_dot = state[..., 3].reshape(-1, 1) return np.hstack([x, x_dot, np.sin(theta), np.cos(theta), theta_dot])
Example #7
Source File: pendulum.py From ilqr with GNU General Public License v3.0 | 6 votes |
def augment_state(cls, state): """Augments angular state into a non-angular state by replacing theta with sin(theta) and cos(theta). In this case, it converts: [theta, theta'] -> [sin(theta), cos(theta), theta'] Args: state: State vector [reducted_state_size]. Returns: Augmented state size [state_size]. """ if state.ndim == 1: theta, theta_dot = state else: theta = state[..., 0].reshape(-1, 1) theta_dot = state[..., 1].reshape(-1, 1) return np.hstack([np.sin(theta), np.cos(theta), theta_dot])
Example #8
Source File: core.py From starry with MIT License | 6 votes |
def compute_rect_grid(self, res): """Compute the polynomial basis on a rectangular lat/lon grid.""" # See NOTE on tt.mgrid bug in `compute_ortho_grid` dx = np.pi / (res - 0.01) lat, lon = tt.mgrid[ -np.pi / 2 : np.pi / 2 : dx, -3 * np.pi / 2 : np.pi / 2 : 2 * dx ] x = tt.reshape(tt.cos(lat) * tt.cos(lon), [1, -1]) y = tt.reshape(tt.cos(lat) * tt.sin(lon), [1, -1]) z = tt.reshape(tt.sin(lat), [1, -1]) R = self.RAxisAngle(tt.as_tensor_variable([1.0, 0.0, 0.0]), -np.pi / 2) return ( tt.concatenate( ( tt.reshape(lat, [1, -1]), tt.reshape(lon + 0.5 * np.pi, [1, -1]), ) ), tt.dot(R, tt.concatenate((x, y, z))), )
Example #9
Source File: test_vm.py From D-VAE with MIT License | 6 votes |
def test_no_leak_many_graphs(): # Verify no memory leaks when creating and deleting a lot of functions # This isn't really a unit test, you have to run it and look at top to # see if there's a leak for i in xrange(10000): x = tensor.vector() z = x for d in range(10): z = tensor.sin(-z + 1) f = function([x], z, mode=Mode(optimizer=None, linker='cvm')) if not i % 100: print(gc.collect()) sys.stdout.flush() gc.collect() if 1: f([2.0]) f([3.0]) f([4.0]) f([5.0])
Example #10
Source File: mujoco_costs.py From adversarial-policies with MIT License | 6 votes |
def __init__(self): def f(x, u, i, terminal): if terminal: ctrl_cost = T.zeros_like(x[..., 0]) else: ctrl_cost = T.square(u).sum(axis=-1) # x: (batch_size, 8) # x[..., 0:4]: qpos # x[..., 4:8]: qvel, time derivatives of qpos, not used in the cost. theta = x[..., 0] # qpos[0]: angle of joint 0 phi = x[..., 1] # qpos[1]: angle of joint 1 target_xpos = x[..., 2:4] # qpos[2:4], target x & y coordinate body1_xpos = 0.1 * T.stack([T.cos(theta), T.sin(theta)], axis=1) tip_xpos_incr = 0.11 * T.stack([T.cos(phi), T.sin(phi)], axis=1) tip_xpos = body1_xpos + tip_xpos_incr delta = tip_xpos - target_xpos state_cost = T.sqrt(T.sum(delta * delta, axis=-1)) cost = state_cost + ctrl_cost return cost super().__init__(f, state_size=8, action_size=2)
Example #11
Source File: rotconv.py From u24_lymphocyte with BSD 3-Clause "New" or "Revised" License | 5 votes |
def rot_filters(self, theta): fsize = self.filter_size[0]; ind = T.as_tensor_variable(np.indices((fsize, fsize)) - (fsize - 1.0) / 2.0); rotate = T.stack(T.cos(theta), -T.sin(theta), T.sin(theta), T.cos(theta)).reshape((2, 2)); ind_rot = T.tensordot(rotate, ind, axes=((0, 0))) + (fsize - 1.0) / 2.0; transy = T.clip(ind_rot[0], 0, fsize - 1 - .00001); transx = T.clip(ind_rot[1], 0, fsize - 1 - .00001); vert = T.iround(transy); horz = T.iround(transx); return self.W[:, :, vert, horz];
Example #12
Source File: rotconv.py From u24_lymphocyte with BSD 3-Clause "New" or "Revised" License | 5 votes |
def rot_filters(self, theta): fsize = self.filter_size[0]; ind = T.as_tensor_variable(np.indices((fsize, fsize)) - (fsize - 1.0) / 2.0); rotate = T.stack(T.cos(theta), -T.sin(theta), T.sin(theta), T.cos(theta)).reshape((2, 2)); ind_rot = T.tensordot(rotate, ind, axes=((0, 0))) + (fsize - 1.0) / 2.0; transy = T.clip(ind_rot[0], 0, fsize - 1 - .00001); transx = T.clip(ind_rot[1], 0, fsize - 1 - .00001); vert = T.iround(transy); horz = T.iround(transx); return self.W[:, :, vert, horz];
Example #13
Source File: rotconv.py From u24_lymphocyte with BSD 3-Clause "New" or "Revised" License | 5 votes |
def rot_filters(self, theta): fsize = self.filter_size[0]; ind = T.as_tensor_variable(np.indices((fsize, fsize)) - (fsize - 1.0) / 2.0); rotate = T.stack(T.cos(theta), -T.sin(theta), T.sin(theta), T.cos(theta)).reshape((2, 2)); ind_rot = T.tensordot(rotate, ind, axes=((0, 0))) + (fsize - 1.0) / 2.0; transy = T.clip(ind_rot[0], 0, fsize - 1 - .00001); transx = T.clip(ind_rot[1], 0, fsize - 1 - .00001); vert = T.iround(transy); horz = T.iround(transx); return self.W[:, :, vert, horz];
Example #14
Source File: rotconv.py From u24_lymphocyte with BSD 3-Clause "New" or "Revised" License | 5 votes |
def rot_filters(self, theta): fsize = self.filter_size[0]; ind = T.as_tensor_variable(np.indices((fsize, fsize)) - (fsize - 1.0) / 2.0); rotate = T.stack(T.cos(theta), -T.sin(theta), T.sin(theta), T.cos(theta)).reshape((2, 2)); ind_rot = T.tensordot(rotate, ind, axes=((0, 0))) + (fsize - 1.0) / 2.0; transy = T.clip(ind_rot[0], 0, fsize - 1 - .00001); transx = T.clip(ind_rot[1], 0, fsize - 1 - .00001); vert = T.iround(transy); horz = T.iround(transx); return self.W[:, :, vert, horz];
Example #15
Source File: rotconv.py From u24_lymphocyte with BSD 3-Clause "New" or "Revised" License | 5 votes |
def rot_filters(self, theta): fsize = self.filter_size[0]; ind = T.as_tensor_variable(np.indices((fsize, fsize)) - (fsize - 1.0) / 2.0); rotate = T.stack(T.cos(theta), -T.sin(theta), T.sin(theta), T.cos(theta)).reshape((2, 2)); ind_rot = T.tensordot(rotate, ind, axes=((0, 0))) + (fsize - 1.0) / 2.0; transy = T.clip(ind_rot[0], 0, fsize - 1 - .00001); transx = T.clip(ind_rot[1], 0, fsize - 1 - .00001); vert = T.iround(transy); horz = T.iround(transx); return self.W[:, :, vert, horz];
Example #16
Source File: rotconv.py From u24_lymphocyte with BSD 3-Clause "New" or "Revised" License | 5 votes |
def rot_filters(self, theta): fsize = self.filter_size[0]; ind = T.as_tensor_variable(np.indices((fsize, fsize)) - (fsize - 1.0) / 2.0); rotate = T.stack(T.cos(theta), -T.sin(theta), T.sin(theta), T.cos(theta)).reshape((2, 2)); ind_rot = T.tensordot(rotate, ind, axes=((0, 0))) + (fsize - 1.0) / 2.0; transy = T.clip(ind_rot[0], 0, fsize - 1 - .00001); transx = T.clip(ind_rot[1], 0, fsize - 1 - .00001); vert = T.iround(transy); horz = T.iround(transx); return self.W[:, :, vert, horz];
Example #17
Source File: distributions_T.py From MJHMC with GNU General Public License v2.0 | 5 votes |
def dEdX_val(self, X): sinX = T.sin(X*2*np.pi/self.scale2) dEdX = X/self.scale1**2 + -sinX*2*np.pi/self.scale2 return dEdX
Example #18
Source File: s3c.py From TextDetector with GNU General Public License v3.0 | 5 votes |
def rotate_towards(old_W, new_W, new_coeff): """ .. todo:: WRITEME properly For each column, rotates old_w toward new_w by new_coeff * theta, where theta is the angle between them Parameters ---------- old_W : WRITEME every column is a unit vector new_W : WRITEME new_coeff : WRITEME """ norms = theano_norms(new_W) # update, scaled back onto unit sphere scal_points = new_W / norms.dimshuffle('x',0) # dot product between scaled update and current W dot_update = (old_W * scal_points).sum(axis=0) theta = T.arccos(dot_update) rot_amt = new_coeff * theta new_basis_dir = scal_points - dot_update * old_W new_basis_norms = theano_norms(new_basis_dir) new_basis = new_basis_dir / new_basis_norms rval = T.cos(rot_amt) * old_W + T.sin(rot_amt) * new_basis return rval
Example #19
Source File: theano_backend.py From deepQuest with BSD 3-Clause "New" or "Revised" License | 5 votes |
def sin(x): return T.sin(x)
Example #20
Source File: theano_backend.py From DeepLearning_Wavelet-LSTM with MIT License | 5 votes |
def sin(x): return T.sin(x)
Example #21
Source File: theano_backend.py From KerasNeuralFingerprint with MIT License | 5 votes |
def sin(x): return T.sin(x)
Example #22
Source File: images2D_carrier.py From lddmm-ot with MIT License | 5 votes |
def _dirac_truncated_rfft(self, point) : """ Returns the truncated real FFT of a dirac at position 'point', as a (2+1)-d array of size "K.shape//2+1" + (4,),. See real_fft._irfft_2d to understand the format of the output. The code may seem quite circonvoluted but hey, it's not my fault if theano forces us to use real-valued FFT... """ su, di = self._phase_shifts(point) re_re = T.cos(di) + T.cos(su) # 2 cos(a)cos(b) = cos(a-b) + cos(a+b) re_im = T.sin(su) + T.sin(di) # 2 sin(a)cos(b) = sin(a+b) + sin(a-b) im_re = T.sin(su) - T.sin(di) # 2 cos(a)sin(b) = sin(a+b) - sin(a-b) im_im = T.cos(di) - T.cos(su) # 2 sin(a)sin(b) = cos(a-b) - cos(a+b) return .5 * T.stack([re_re, re_im, im_re, im_im], axis=2) # Don't forget the .5 !
Example #23
Source File: theano_graph_pro.py From gempy with GNU Lesser General Public License v3.0 | 5 votes |
def b_vector(self, dip_angles=None, azimuth=None, polarity=None): """ Creation of the independent vector b to solve the kriging system Args: verbose: -deprecated- Returns: theano.tensor.vector: independent vector """ length_of_C = self.matrices_shapes()[-1] if dip_angles is None: dip_angles = self.dip_angles if azimuth is None: azimuth = self.azimuth if polarity is None: polarity = self.polarity # ===================== # Creation of the gradients G vector # Calculation of the cartesian components of the dips assuming the unit module G_x = T.sin(T.deg2rad(dip_angles)) * T.sin(T.deg2rad(azimuth)) * polarity G_y = T.sin(T.deg2rad(dip_angles)) * T.cos(T.deg2rad(azimuth)) * polarity G_z = T.cos(T.deg2rad(dip_angles)) * polarity G = T.concatenate((G_x, G_y, G_z)) # Creation of the Dual Kriging vector b = T.zeros((length_of_C,)) b = T.set_subtensor(b[0:G.shape[0]], G) if str(sys._getframe().f_code.co_name) in self.verbose: b = theano.printing.Print('b vector')(b) # Add name to the theano node b.name = 'b vector' return b
Example #24
Source File: theano_kriging.py From gempy with GNU Lesser General Public License v3.0 | 5 votes |
def b_vector(self): """ Creation of the independent vector b to solve the kriging system Args: verbose: -deprecated- Returns: theano.tensor.vector: independent vector """ length_of_C = self.matrices_shapes()[-1] # ===================== # Creation of the gradients G vector # Calculation of the cartesian components of the dips assuming the unit module G_x = T.sin(T.deg2rad(self.dip_angles)) * T.sin(T.deg2rad(self.azimuth)) * self.polarity G_y = T.sin(T.deg2rad(self.dip_angles)) * T.cos(T.deg2rad(self.azimuth)) * self.polarity G_z = T.cos(T.deg2rad(self.dip_angles)) * self.polarity G = T.concatenate((G_x, G_y, G_z)) # Creation of the Dual Kriging vector b = T.zeros((length_of_C,)) b = T.set_subtensor(b[0:G.shape[0]], G) if str(sys._getframe().f_code.co_name) in self.verbose: b = theano.printing.Print('b vector')(b) # Add name to the theano node b.name = 'b vector' return b
Example #25
Source File: theano_graph.py From gempy with GNU Lesser General Public License v3.0 | 5 votes |
def b_vector(self): """ Creation of the independent vector b to solve the kriging system Args: verbose: -deprecated- Returns: theano.tensor.vector: independent vector """ length_of_C = self.matrices_shapes()[-1] # ===================== # Creation of the gradients G vector # Calculation of the cartesian components of the dips assuming the unit module G_x = T.sin(T.deg2rad(self.dip_angles)) * T.sin(T.deg2rad(self.azimuth)) * self.polarity G_y = T.sin(T.deg2rad(self.dip_angles)) * T.cos(T.deg2rad(self.azimuth)) * self.polarity G_z = T.cos(T.deg2rad(self.dip_angles)) * self.polarity G = T.concatenate((G_x, G_y, G_z)) # Creation of the Dual Kriging vector b = T.zeros((length_of_C,)) b = T.set_subtensor(b[0:G.shape[0]], G) if str(sys._getframe().f_code.co_name) in self.verbose: b = theano.printing.Print('b vector')(b) # Add name to the theano node b.name = 'b vector' return b
Example #26
Source File: core.py From starry with MIT License | 5 votes |
def compute_moll_grid(self, res): """Compute the polynomial basis on a Mollweide grid.""" # See NOTE on tt.mgrid bug in `compute_ortho_grid` dx = 2 * np.sqrt(2) / (res - 0.01) y, x = tt.mgrid[ -np.sqrt(2) : np.sqrt(2) : dx, -2 * np.sqrt(2) : 2 * np.sqrt(2) : 2 * dx, ] # Make points off-grid nan a = np.sqrt(2) b = 2 * np.sqrt(2) y = tt.where((y / a) ** 2 + (x / b) ** 2 <= 1, y, np.nan) # https://en.wikipedia.org/wiki/Mollweide_projection theta = tt.arcsin(y / np.sqrt(2)) lat = tt.arcsin((2 * theta + tt.sin(2 * theta)) / np.pi) lon0 = 3 * np.pi / 2 lon = lon0 + np.pi * x / (2 * np.sqrt(2) * tt.cos(theta)) # Back to Cartesian, this time on the *sky* x = tt.reshape(tt.cos(lat) * tt.cos(lon), [1, -1]) y = tt.reshape(tt.cos(lat) * tt.sin(lon), [1, -1]) z = tt.reshape(tt.sin(lat), [1, -1]) R = self.RAxisAngle(tt.as_tensor_variable([1.0, 0.0, 0.0]), -np.pi / 2) return ( tt.concatenate( ( tt.reshape(lat, (1, -1)), tt.reshape(lon - 1.5 * np.pi, (1, -1)), ) ), tt.dot(R, tt.concatenate((x, y, z))), )
Example #27
Source File: core.py From starry with MIT License | 5 votes |
def RAxisAngle(self, axis=[0, 1, 0], theta=0): """Wigner axis-angle rotation matrix.""" def compute(axis=[0, 1, 0], theta=0): axis = tt.as_tensor_variable(axis) axis /= axis.norm(2) cost = tt.cos(theta) sint = tt.sin(theta) return tt.reshape( tt.as_tensor_variable( [ cost + axis[0] * axis[0] * (1 - cost), axis[0] * axis[1] * (1 - cost) - axis[2] * sint, axis[0] * axis[2] * (1 - cost) + axis[1] * sint, axis[1] * axis[0] * (1 - cost) + axis[2] * sint, cost + axis[1] * axis[1] * (1 - cost), axis[1] * axis[2] * (1 - cost) - axis[0] * sint, axis[2] * axis[0] * (1 - cost) - axis[1] * sint, axis[2] * axis[1] * (1 - cost) + axis[0] * sint, cost + axis[2] * axis[2] * (1 - cost), ] ), [3, 3], ) # If theta is a vector, this is a tensor! if hasattr(theta, "ndim") and theta.ndim > 0: fn = lambda theta, axis: compute(axis=axis, theta=theta) R, _ = theano.scan(fn=fn, sequences=[theta], non_sequences=[axis]) return R else: return compute(axis=axis, theta=theta)
Example #28
Source File: pymc3.py From bilby with MIT License | 5 votes |
def _sine_prior(self, key): """ Map the bilby Sine prior to a PyMC3 style function """ # check prior is a Sine pymc3, STEP_METHODS, floatX = self._import_external_sampler() theano, tt, as_op = self._import_theano() if isinstance(self.priors[key], Sine): class Pymc3Sine(pymc3.Continuous): def __init__(self, lower=0., upper=np.pi): if lower >= upper: raise ValueError("Lower bound is above upper bound!") # set the mode self.lower = lower = tt.as_tensor_variable(floatX(lower)) self.upper = upper = tt.as_tensor_variable(floatX(upper)) self.norm = (tt.cos(lower) - tt.cos(upper)) self.mean = \ (tt.sin(upper) + lower * tt.cos(lower) - tt.sin(lower) - upper * tt.cos(upper)) / self.norm transform = pymc3.distributions.transforms.interval(lower, upper) super(Pymc3Sine, self).__init__(transform=transform) def logp(self, value): upper = self.upper lower = self.lower return pymc3.distributions.dist_math.bound( tt.log(tt.sin(value) / self.norm), lower <= value, value <= upper) return Pymc3Sine(key, lower=self.priors[key].minimum, upper=self.priors[key].maximum) else: raise ValueError("Prior for '{}' is not a Sine".format(key))
Example #29
Source File: pymc3.py From bilby with MIT License | 5 votes |
def _cosine_prior(self, key): """ Map the bilby Cosine prior to a PyMC3 style function """ # check prior is a Cosine pymc3, STEP_METHODS, floatX = self._import_external_sampler() theano, tt, as_op = self._import_theano() if isinstance(self.priors[key], Cosine): class Pymc3Cosine(pymc3.Continuous): def __init__(self, lower=-np.pi / 2., upper=np.pi / 2.): if lower >= upper: raise ValueError("Lower bound is above upper bound!") self.lower = lower = tt.as_tensor_variable(floatX(lower)) self.upper = upper = tt.as_tensor_variable(floatX(upper)) self.norm = (tt.sin(upper) - tt.sin(lower)) self.mean = \ (upper * tt.sin(upper) + tt.cos(upper) - lower * tt.sin(lower) - tt.cos(lower)) / self.norm transform = pymc3.distributions.transforms.interval(lower, upper) super(Pymc3Cosine, self).__init__(transform=transform) def logp(self, value): upper = self.upper lower = self.lower return pymc3.distributions.dist_math.bound( tt.log(tt.cos(value) / self.norm), lower <= value, value <= upper) return Pymc3Cosine(key, lower=self.priors[key].minimum, upper=self.priors[key].maximum) else: raise ValueError("Prior for '{}' is not a Cosine".format(key))
Example #30
Source File: theano_backend.py From keras-lambda with MIT License | 5 votes |
def sin(x): return T.sin(x)