def arc_distance_theano_broadcast_prepare(dtype='float64'):
"""
Calculates the pairwise arc distance between all points in vector a and b.
"""
a = tensor.matrix(dtype=str(dtype))
b = tensor.matrix(dtype=str(dtype))
theta_1 = a[:, 0][None, :]
theta_2 = b[:, 0][None, :]
phi_1 = a[:, 1][:, None]
phi_2 = b[:, 1][None, :]
temp = (tensor.sin((theta_2 - theta_1) / 2)**2
+
tensor.cos(theta_1) * tensor.cos(theta_2)
* tensor.sin((phi_2 - phi_1) / 2)**2)
distance_matrix = 2 * (tensor.arctan2(tensor.sqrt(temp),
tensor.sqrt(1 - temp)))
name = "arc_distance_theano_broadcast"
rval = theano.function([a, b],
distance_matrix,
name=name)
rval.__name__ = name
return rval
def poseDiff2D(startingPose, endingPose):
x1, y1, theta1 = endingPose[0], endingPose[1], endingPose[2]
x2, y2, theta2 = startingPose[0], startingPose[1], startingPose[2]
dx = (x1 - x2)*T.cos(theta2) + (y1 - y2)*T.sin(theta2)
dy = -(x1 - x2)*T.sin(theta2) + (y1 - y2)*T.cos(theta2)
dtheta = normalizeAngle(theta1 - theta2)
return dx, dy, dtheta
def arc_distance_theano_alloc_prepare(dtype='float64'):
"""
Calculates the pairwise arc distance between all points in vector a and b.
"""
a = tensor.matrix(dtype=str(dtype))
b = tensor.matrix(dtype=str(dtype))
# Theano don't implement all case of tile, so we do the equivalent with alloc.
#theta_1 = tensor.tile(a[:, 0], (b.shape[0], 1)).T
theta_1 = tensor.alloc(a[:, 0], b.shape[0], b.shape[0]).T
phi_1 = tensor.alloc(a[:, 1], b.shape[0], b.shape[0]).T
theta_2 = tensor.alloc(b[:, 0], a.shape[0], a.shape[0])
phi_2 = tensor.alloc(b[:, 1], a.shape[0], a.shape[0])
temp = (tensor.sin((theta_2 - theta_1) / 2)**2
+
tensor.cos(theta_1) * tensor.cos(theta_2)
* tensor.sin((phi_2 - phi_1) / 2)**2)
distance_matrix = 2 * (tensor.arctan2(tensor.sqrt(temp),
tensor.sqrt(1 - temp)))
name = "arc_distance_theano_alloc"
rval = theano.function([a, b],
distance_matrix,
name=name)
rval.__name__ = name
return rval
def get_celerite_matrices(self, x, diag):
x = tt.as_tensor_variable(x)
diag = tt.as_tensor_variable(diag)
ar, cr, ac, bc, cc, dc = self.coefficients
a = diag + tt.sum(ar) + tt.sum(ac)
U = tt.concatenate((
ar[None, :] + tt.zeros_like(x)[:, None],
ac[None, :] * tt.cos(dc[None, :] * x[:, None])
+ bc[None, :] * tt.sin(dc[None, :] * x[:, None]),
ac[None, :] * tt.sin(dc[None, :] * x[:, None])
- bc[None, :] * tt.cos(dc[None, :] * x[:, None]),
), axis=1)
V = tt.concatenate((
tt.zeros_like(ar)[None, :] + tt.ones_like(x)[:, None],
tt.cos(dc[None, :] * x[:, None]),
tt.sin(dc[None, :] * x[:, None]),
), axis=1)
dx = x[1:] - x[:-1]
P = tt.concatenate((
tt.exp(-cr[None, :] * dx[:, None]),
tt.exp(-cc[None, :] * dx[:, None]),
tt.exp(-cc[None, :] * dx[:, None]),
), axis=1)
return a, U, V, P
def get_uhs_operator(uhs, depth, n_hidden, rhos):
"""
:param uhs:
:param depth:
:param n_hidden:
:param rhos: can be shared variable or constant of shape (depth, )!!
:return:
"""
# Will use a Fourier matrix (will be O(n^2)...)
# Doesn't seem to slow things down much though!
exp_phases = [T.cos(uhs), T.sin(uhs)]
neg_exp_phases = [T.cos(uhs[:, ::-1]), -T.sin(uhs[:, ::-1])]
ones_ = [T.ones((depth, 1), dtype=theano.config.floatX), T.zeros((depth, 1), dtype=theano.config.floatX)]
rhos_reshaped = T.reshape(rhos, (depth, 1), ndim=2)
rhos_reshaped = T.addbroadcast(rhos_reshaped, 1)
eigvals_re = rhos_reshaped * T.concatenate((ones_[0], exp_phases[0], -ones_[0], neg_exp_phases[0]), axis=1)
eigvals_im = rhos_reshaped * T.concatenate((ones_[1], exp_phases[1], -ones_[1], neg_exp_phases[1]), axis=1)
phase_array = -2 * np.pi * np.outer(np.arange(n_hidden), np.arange(n_hidden)) / n_hidden
f_array_re_val = np.cos(phase_array) / n_hidden
f_array_im_val = np.sin(phase_array) / n_hidden
f_array_re = theano.shared(f_array_re_val.astype(theano.config.floatX), name="f_arr_re")
f_array_im = theano.shared(f_array_im_val.astype(theano.config.floatX), name="f_arr_im")
a_k = T.dot(eigvals_re, f_array_re) + T.dot(eigvals_im, f_array_im)
uhs_op = rep_vec(a_k, n_hidden, n_hidden) # shape (depth, 2 * n_hidden - 1)
return uhs_op
def get_output_for(self, inputs, **kwargs):
# see eq. (1) and sec 3.1 in [1]
input, para = inputs
num_batch, channels, height, width = input.shape
_w = T.cast(width, dtype = self.dtype)
_h = T.cast(height, dtype = self.dtype)
mat = T.zeros((num_batch, 3, 3), dtype = self.dtype)
mat = T.set_subtensor(mat[:, 0, 0], const(1.0))
mat = T.set_subtensor(mat[:, 1, 1], const(1.0))
mat = T.set_subtensor(mat[:, 2, 2], const(1.0))
if self.method == 'perspective':
mat = T.set_subtensor(mat[:, 2, 0], (para[:, 0] / 1e4 - 1e-3) * _w)
mat = T.set_subtensor(mat[:, 2, 1], (para[:, 1] / 1e4 - 1e-3) * _h)
elif self.method == 'angle':
angle = T.cast(T.argmax(para, axis = 1), dtype = self.dtype) * np.pi / 90 - np.pi / 3.0
# ss = np.sqrt(2.0)
mat = T.set_subtensor(mat[:, :, :], T.stacklists([
[T.cos(angle), T.sin(angle), -(T.cos(angle) * _w + T.sin(angle) * _h - _w) / (2.0 * _w)],
[-T.sin(angle), T.cos(angle), -(-T.sin(angle) * _w + T.cos(angle) * _h - _h) / (2.0 * _h)],
[constv(0, num_batch, self.dtype), constv(0, num_batch, self.dtype), constv(1, num_batch, self.dtype)]]).dimshuffle(2, 0, 1))
# return [mat, _w, _h]
elif self.method == 'all':
mat = T.reshape(para, [-1, 3, 3])
mat = T.set_subtensor(mat[:, 0, 2], mat[:, 0, 2] / T.cast(width, dtype))
mat = T.set_subtensor(mat[:, 1, 2], mat[:, 1, 2] / T.cast(height, dtype))
mat = T.set_subtensor(mat[:, 2, 0], mat[:, 2, 0] * T.cast(width, dtype))
mat = T.set_subtensor(mat[:, 2, 1], mat[:, 2, 1] * T.cast(height, dtype))
else:
raise Exception('method not understood.')
return transform_affine(mat, input, self.method, scale_factor = self.scale_factor)
def grad(self, inputs, gradients):
M, e = inputs
E, f = self(M, e)
bM = tt.zeros_like(M)
be = tt.zeros_like(M)
ecosE = e * tt.cos(E)
if not isinstance(gradients[0].type, theano.gradient.DisconnectedType):
# Backpropagate E_bar
bM = gradients[0] / (1 - ecosE)
be = tt.sin(E) * bM
if not isinstance(gradients[1].type, theano.gradient.DisconnectedType):
# Backpropagate f_bar
sinf2 = tt.sin(0.5*f)
cosf2 = tt.cos(0.5*f)
tanf2 = sinf2 / cosf2
e2 = e**2
ome2 = 1 - e2
ome = 1 - e
ope = 1 + e
cosf22 = cosf2**2
twoecosf22 = 2 * e * cosf22
factor = tt.sqrt(ope/ome)
inner = (twoecosf22+ome) * tt.as_tensor_variable(gradients[1])
bM += factor*(ome*tanf2**2+ope)*inner*cosf22/(ope*ome2)
be += -2*cosf22*tanf2/ome2**2*inner*(ecosE-2+e2)
return [bM, be]
def _getrz(self,d):
r=theano.shared(np.zeros((3,3),dtype='float32'))
r=T.set_subtensor(r[2,2],1.0)
r=T.set_subtensor(r[0,0],T.cos(d))
r=T.set_subtensor(r[0,1],-T.sin(d))
r=T.set_subtensor(r[1,0],T.sin(d))
r=T.set_subtensor(r[1,1],T.cos(d))
return r
def xyz(R1, theta, R2, phi):
theta_ = T.scalar('theta')
phi_ = T.scalar('phi')
x = R1 * T.cos(theta_) * R2 * T.cos(phi_)
y = R2 * T.sin(theta_) * R2 * T.cos(phi_)
z = R2 * T.sin(phi_)
func = function([theta_, phi_], [x, y, z], allow_input_downcast=True)
vals = func(theta, phi)
return vals[0].flatten(), vals[1].flatten(), vals[2].flatten()
def xyz2(theta, a, b, m, n1, n2, n3, rho, a2, b2, m2, n4, n5, n6):
theta_ = T.scalar('theta')
rho_ = T.scalar('rho')
R1 = R(theta, a, b, m, n1, n2, n3)
R2 = R(rho, a2, b2, m2, n4, n5, n6)
x = R1 * T.cos(theta_) * R2 * T.cos(rho_)
y = R1 * T.sin(theta_) * R2 * T.cos(rho_)
z = R2 * T.sin(rho_)
func = function([theta_, rho_], [x, y, z], allow_input_downcast=True)
vals = func(theta, rho)
return vals[0].flatten(), vals[1].flatten(), vals[2].flatten()
def get_output(self, train=False):
rnorm = self.omega / np.sqrt(2*np.pi)*self.kappa
val = - self.omega**2 / (8 * self.kappa**2)
dir1 = 4 * (self._outter(self.x, tensor.cos(self.theta)) +
self._outter(self.y, tensor.sin(self.theta)))**2
dir2 = (-self._outter(self.x, tensor.sin(self.theta)) +
self._outter(self.y, tensor.cos(self.theta)))**2
ex = 1j * (self.omega * self._outter(tensor.cos(self.theta), self.x) +
self.omega * self._outter(tensor.sin(self.theta), self.y))
output = rnorm * tensor.exp(val * (dir1 + dir2)) * (tensor.exp(ex)
- tensor.exp(-self.kappa**2 / 2))
return output
def theano_dynamics(self, x, u):
G, L1, L2, M1, M2 = self.extract_constants()
# TODO: this is just an approximation
dydx = T.alloc(0.0, 4)
dydx = T.set_subtensor(dydx[0], x[1])
del_ = x[2]-x[0]
den1 = (M1+M2)*L1 - M2*L1*T.cos(del_)*T.cos(del_)
dydx = T.set_subtensor(dydx[1],
( M2*L1 * x[1] * x[1] * T.sin(del_) * T.cos(del_)
+ M2*G * T.sin(x[2]) * T.cos(del_) +
M2*L2 * x[3] * x[3] * T.sin(del_)
- (M1+M2)*G * T.sin(x[0]))/den1 )
dydx = T.set_subtensor(dydx[2], x[3])
den2 = (L2/L1)*den1
dydx = T.set_subtensor(dydx[3], (-M2*L2 * x[3]*x[3]*T.sin(del_)*T.cos(del_)
+ (M1+M2)*G * T.sin(x[0])*T.cos(del_)
- (M1+M2)*L1 * x[1]*x[1]*T.sin(del_)
- (M1+M2)*G * T.sin(x[2]))/den2 + u )
return x + dydx * self.dt
def get_theano_func():
a = tt.dvector("a")
v = tt.dvector("v")
freq = tt.dscalar("freq")
t = tt.dscalar("t")
dt = tt.dscalar("dt")
tau = tt.dscalar("tau")
return theano.function(
[a, v, freq, t, dt, tau],
a * tt.sin(2.0 * freq * pi * t)
+ b
+ v * tt.exp(-dt / tau)
+ (-a * tt.sin(2.0 * freq * pi * t) - b) * tt.exp(-dt / tau),
)
def __init__(self, target, initial_phi, profile_s=None, A0=1.0):
self.target = target
self.n_pixels = int(target.shape[0] / 2) # target should be 512x512, but SLM pattern calculated should be 256x256.
self.intensity_calc = None
self.cost = None # placeholder for cost function.
if profile_s is None:
profile_s = np.ones((self.n_pixels, self.n_pixels))
assert profile_s.shape == (self.n_pixels, self.n_pixels), 'profile_s is wrong shape, should be ({n},{n})'.format(n=self.n_pixels)
self.profile_s_r = profile_s.real.astype('float64')
self.profile_s_i = profile_s.imag.astype('float64')
assert initial_phi.shape == (self.n_pixels**2,), "initial_phi must be a vector of phases of size N^2 (not (N,N)). Shape is " + str(initial_phi.shape)
self.A0 = A0
# Set zeros matrix:
self.zero_frame = np.zeros((2*self.n_pixels, 2*self.n_pixels), dtype='float64')
# Phi and its momentum for use in gradient descent with momentum:
self.phi = theano.shared(value=initial_phi.astype('float64'),
name='phi')
self.phi_rate = theano.shared(value=np.zeros_like(initial_phi).astype('float64'),
name='phi_rate')
self.S_r = theano.shared(value=self.profile_s_r,
name='s_r')
self.S_i = theano.shared(value=self.profile_s_i,
name='s_i')
self.zero_matrix = theano.shared(value=self.zero_frame,
name='zero_matrix')
# E_in: (n_pixels**2)
phi_reshaped = self.phi.reshape((self.n_pixels, self.n_pixels))
self.E_in_r = self.A0 * (self.S_r*T.cos(phi_reshaped) - self.S_i*T.sin(phi_reshaped))
self.E_in_i = self.A0 * (self.S_i*T.cos(phi_reshaped) + self.S_r*T.sin(phi_reshaped))
# E_in padded: (4n_pixels**2)
idx_0, idx_1 = get_centre_range(self.n_pixels)
self.E_in_r_pad = T.set_subtensor(self.zero_matrix[idx_0:idx_1,idx_0:idx_1], self.E_in_r)
self.E_in_i_pad = T.set_subtensor(self.zero_matrix[idx_0:idx_1,idx_0:idx_1], self.E_in_i)
# E_out:
self.E_out_r, self.E_out_i = fft(self.E_in_r_pad, self.E_in_i_pad)
# finally, the output intensity:
self.E_out_2 = T.add(T.pow(self.E_out_r, 2), T.pow(self.E_out_i, 2))
def hdist(a, b):
lat1 = a[:, 0] * deg2rad
lon1 = a[:, 1] * deg2rad
lat2 = b[:, 0] * deg2rad
lon2 = b[:, 1] * deg2rad
dlat = abs(lat1-lat2)
dlon = abs(lon1-lon2)
al = tensor.sin(dlat/2)**2 + tensor.cos(lat1) * tensor.cos(lat2) * (tensor.sin(dlon/2)**2)
d = tensor.arctan2(tensor.sqrt(al), tensor.sqrt(const(1)-al))
hd = const(2) * rearth * d
return tensor.switch(tensor.eq(hd, float('nan')), (a-b).norm(2, axis=1), hd)
def symbolic_call(self,x,u):
u = TT.clip(u, -self.max_force, self.max_force) #pylint: disable=E1111
dt = self.dt
z = TT.take(x,0,axis=x.ndim-1)
zdot = TT.take(x,1,axis=x.ndim-1)
th = TT.take(x,2,axis=x.ndim-1)
thdot = TT.take(x,3,axis=x.ndim-1)
u0 = TT.take(u,0,axis=u.ndim-1)
th1 = np.pi - th
g = 10.
mc = 1. # mass of cart
mp = .1 # mass of pole
muc = .0005 # coeff friction of cart
mup = .000002 # coeff friction of pole
l = 1. # length of pole
def sign(x):
return TT.switch(x>0, 1, -1)
thddot = -(-g*TT.sin(th1)
+ TT.cos(th1) * (-u0 - mp * l *thdot**2 * TT.sin(th1) + muc*sign(zdot))/(mc+mp)
- mup*thdot / (mp*l)) \
/ (l*(4/3. - mp*TT.cos(th1)**2 / (mc + mp)))
zddot = (u0 + mp*l*(thdot**2 * TT.sin(th1) - thddot * TT.cos(th1)) - muc*sign(zdot)) \
/ (mc+mp)
newzdot = zdot + dt*zddot
newz = z + dt*newzdot
newthdot = thdot + dt*thddot
newth = th + dt*newthdot
done = (z > self.max_cart_pos) | (z < -self.max_cart_pos) | (th > self.max_pole_angle) | (th < -self.max_pole_angle)
ucost = 1e-5*(u**2).sum(axis=u.ndim-1)
xcost = 1-TT.cos(th)
# notdone = TT.neg(done) #pylint: disable=W0612,E1111
notdone = 1-done
costs = TT.stack((done-1)*10., notdone*xcost, notdone*ucost).T #pylint: disable=E1103
newx = TT.stack(newz, newzdot, newth, newthdot).T #pylint: disable=E1103
return [newx,newx,costs,done]
def rotate(angle, axis):
"""Returns a transform to represent a rotation"""
angle = T.as_tensor_variable(angle)
axis = T.as_tensor_variable(axis)
a = axis
radians = angle*np.pi/180.0
s = T.sin(radians)
c = T.cos(radians)
m = T.alloc(0., 4, 4)
m = T.set_subtensor(m[0,0], a[0] * a[0] + (1. - a[0] * a[0]) * c)
m = T.set_subtensor(m[0,1], a[0] * a[1] * (1. - c) - a[2] * s)
m = T.set_subtensor(m[0,2], a[0] * a[2] * (1. - c) + a[1] * s)
m = T.set_subtensor(m[1,0], a[0] * a[1] * (1. - c) + a[2] * s)
m = T.set_subtensor(m[1,1], a[1] * a[1] + (1. - a[1] * a[1]) * c)
m = T.set_subtensor(m[1,2], a[1] * a[2] * (1. - c) - a[0] * s)
m = T.set_subtensor(m[2,0], a[0] * a[2] * (1. - c) - a[1] * s)
m = T.set_subtensor(m[2,1], a[1] * a[2] * (1. - c) + a[0] * s)
m = T.set_subtensor(m[2,2], a[2] * a[2] + (1. - a[2] * a[2]) * c)
m = T.set_subtensor(m[3,3], 1)
return Transform(m, m.T)
def get_output_for(self, input, **kwargs):
cosT = T.cos(self.Degree * 3.1415926 / 180.0)
sinT = T.sin(self.Degree * 3.1415926 / 180.0)
zeros = T.zeros_like(cosT)
# zeros = self.Translation
theta = T.stack([cosT, sinT, zeros, -sinT, cosT, zeros], axis = 1)
return transform_affine(theta, input)
def _step(self,xg_t, xo_t, xc_t, mask_tm1,h_tm1, c_tm1, u_g, u_o, u_c): h_mask_tm1 = mask_tm1 * h_tm1 c_mask_tm1 = mask_tm1 * c_tm1 act = T.tensordot( xg_t + h_mask_tm1, u_g , [[1],[2]]) gate = T.nnet.softmax(act.reshape((-1, act.shape[-1]))).reshape(act.shape) c_tilda = self.activation(xc_t + T.dot(h_mask_tm1, u_c)) sigma_se = self.k_parameters[0] sigma_per = self.k_parameters[1] sigma_b_lin = self.k_parameters[2] sigma_v_lin = self.k_parameters[3] sigma_rq = self.k_parameters[4] l_se = self.k_parameters[5] l_per = self.k_parameters[6] l_lin = self.k_parameters[7] l_rq = self.k_parameters[8] alpha_rq = self.k_parameters[9] p_per = self.k_parameters[10] k_se = T.pow(sigma_se,2) * T.exp( -T.pow(c_mask_tm1 - c_tilda,2) / (2* T.pow(l_se,2) + self.EPS)) k_per = T.pow(sigma_per,2) * T.exp( -2*T.pow(T.sin( math.pi*(c_mask_tm1 - c_tilda)/ (p_per + self.EPS) ),2) / ( T.pow(l_per,2) + self.EPS )) k_lin = T.pow(sigma_b_lin,2) + T.pow(sigma_v_lin,2) * (c_mask_tm1 - l_lin) * (c_tilda - l_lin ) k_rq = T.pow(sigma_rq,2) * T.pow( 1 + T.pow( (c_mask_tm1 - c_tilda),2) / ( 2 * alpha_rq * T.pow(l_rq,2) + self.EPS), -alpha_rq) ops = [c_mask_tm1,c_tilda,k_se, k_per, k_lin,k_rq] yshuff = T.as_tensor_variable( ops, name='yshuff').dimshuffle(1,2,0) c_t = (gate.reshape((-1,gate.shape[-1])) * yshuff.reshape((-1,yshuff.shape[-1]))).sum(axis = 1).reshape(gate.shape[:2]) o_t = self.inner_activation(xo_t + T.dot(h_mask_tm1, u_o)) h_t = o_t * self.activation(c_t) return h_t, c_t
def get_output_for(self, input, **kwargs):
cosT = T.cos(self.Degree * 3.1415926 / 180.0)
sinT = T.sin(self.Degree * 3.1415926 / 180.0)
zeros = T.zeros_like(cosT)
# zeros = self.Translation
finalResult = T.stack([cosT, sinT, zeros, -sinT, cosT, zeros], axis = 1)
return finalResult
def get_output_for(self, input, **kwargs):
cosT = T.cos(self.Degree[:, 0] * 3.1415926 / 180.0)
sinT = T.sin(self.Degree[:, 0] * 3.1415926 / 180.0)
ones = self.scaling[:, 0]
zeros = T.zeros_like(self.translation[:,0])
theta = T.stack([ones * cosT, sinT, self.translation[:,0], -sinT, ones * cosT, self.translation[:,1]], axis = 1)
return transform_affine(theta, input)
def create_transport_gradient(self):
HL2 = T.sqrt((self.search_direction ** 2).sum(axis=0,keepdims=True)) + np.spacing(np.single(1))
transported = self.last_G - (self.last_G*self.search_direction).sum(axis=0,keepdims=True)/(HL2**2) * \
(self.X*HL2 * T.sin(self.t_prev*HL2) + self.search_direction * (1.0-T.cos(self.t_prev*HL2)))
f = theano.function([],[],updates=[(self.last_G,transported)])
return f
def test_opt_gpujoin_joinvectors_elemwise_then_minusone():
# from a bug in gpu normal sampling
_a = numpy.asarray([1, 2, 3, 4], dtype='float32')
_b = numpy.asarray([5, 6, 7, 8], dtype='float32')
a = cuda.shared_constructor(_a)
b = cuda.shared_constructor(_b)
a_prime = tensor.cos(a)
b_prime = tensor.sin(b)
c = tensor.join(0, a_prime, b_prime)
d = c[:-1]
f = theano.function([], d, mode=mode_with_gpu)
graph_nodes = f.maker.fgraph.toposort()
assert isinstance(graph_nodes[-1].op, cuda.HostFromGpu)
assert isinstance(graph_nodes[-2].op, cuda.GpuSubtensor)
assert isinstance(graph_nodes[-3].op, cuda.GpuJoin)
concat = numpy.concatenate([numpy.cos(_a), numpy.sin(_b)], axis=0)
concat = concat[:-1]
assert numpy.allclose(numpy.asarray(f()), concat)
def For_MMD_Sub_class(self,target,data,omega,num_FF,Xlabel):
Num=T.sum(Xlabel,0)
D_num=Xlabel.shape[1]
N=data.shape[0]
F_times_Omega = T.dot(data, omega)#minibatch_size*n_rff
Phi = (self.sf2**0.5 /num_FF**0.5 ) * T.concatenate([T.cos(F_times_Omega), T.sin(F_times_Omega)],1)
#各RFFは２N_rffのたてベクトル
Phi_total=T.sum(Phi.T,-1)/N
#Domain_number*2N_rffの行列
Phi_each_domain, updates = theano.scan(fn=lambda a,b: T.switch(T.neq(b,0), Phi.T*a/b, 0),
sequences=[Xlabel.T,Num])
each_Phi=T.sum(Phi_each_domain,-1)
#まず自分自身との内積 結果はD次元のベクトル
each_domain_sum=T.sum(each_Phi*each_Phi,-1)
#全体の内積
tot_sum=T.dot(Phi_total,Phi_total)
#全体とドメインのクロス内積
tot_domain_sum, updates=theano.scan(fn=lambda a: a*Phi_total,
sequences=[each_Phi])
#MMDの計算
MMD_central=T.sum(each_domain_sum)+D_num*tot_sum-2*T.sum(tot_domain_sum)
return MMD_central
def get_output_for(self, input, **kwargs):
#self.translation = T.zeros((n, 2))
#ones = T.exp(self.scaling[:, 0])
ones = T.ones((self.n,))
zeros = T.zeros((self.n,))
cosTx = T.cos(self.DegreeX * 3.1415926 / 180.0)
sinTx = T.sin(self.DegreeX * 3.1415926 / 180.0)
cosTy = T.cos(self.DegreeY * 3.1415926 / 180.0)
sinTy = T.sin(self.DegreeY * 3.1415926 / 180.0)
cosTz = T.cos(self.DegreeZ * 3.1415926 / 180.0)
sinTz = T.sin(self.DegreeZ * 3.1415926 / 180.0)
thetaX = T.stack([ones, zeros, zeros, zeros, zeros, cosTx, -sinTx, zeros, zeros, sinTx, cosTx, zeros, zeros, zeros, zeros, ones], axis = 1)
thetaY = T.stack([cosTy, zeros, sinTy, zeros, zeros, ones, zeros, zeros, -sinTy, zeros, cosTy, zeros, zeros, zeros, zeros, ones], axis = 1)
thetaZ = T.stack([cosTz, -sinTz, zeros, zeros, sinTz, cosTz, zeros, zeros, zeros, zeros, ones, zeros, zeros, zeros, zeros, ones], axis = 1)
return transform_affine(thetaX, thetaY, thetaZ, input)
def beta_noise(rng, input):
srng = theano.tensor.shared_randomstreams.RandomStreams(rng.randint(999999))
# Beta(.5,.5) multiplicative noise
mask = T.cast(T.sin( (np.pi / 2.0) * srng.uniform(size=input.shape, low=0.0, high=1.0) )**2, theano.config.floatX)
return mask * input
def _get_position(self, a, t):
f = self._get_true_anomaly(t)
cosf = tt.cos(f)
if self.ecc is None:
r = a
else:
r = a * (1.0 - self.ecc**2) / (1 + self.ecc * cosf)
return self._rotate_vector(r * cosf, r * tt.sin(f))
def xyzt_2_param(xyzt):
# get individual xyz
dx = xyzt[:, 0] # x and y are already between -1 and 1
dy = xyzt[:, 1] # x and y are already between -1 and 1
z = xyzt[:, 2]
t = xyzt[:, 3]
# compute the resize from the largest scale image
dr = (np.cast[floatX](reduc_ratio) * np.cast[floatX]
(2.0)**z / np.cast[floatX](max_scale))
# dimshuffle before concatenate
params = [dr * T.cos(t), -dr * T.sin(t), dx, dr * T.sin(t),
dr * T.cos(t), dy]
params = [_p.flatten().dimshuffle(0, 'x') for _p in params]
# concatenate to have (1 0 0 0 1 0) when identity transform
return T.concatenate(params, axis=1)
def get_output_for(self, inputs, **kwargs):
input, degree = inputs
cosT = T.cos(degree)
sinT = T.sin(degree)
zeros = T.zeros_like(cosT)
# zeros = self.Translation
theta = T.stack([cosT, sinT, zeros, -sinT, cosT, zeros], axis = 1)
return transform_affine(theta, input)
def alpha_perfect(self, w, u):
alpha = sharedX(1.5)
beta = sharedX(0.5)
S_var = self.S(alpha,beta)
B_var = self.B(alpha,beta)
first = T.sin(alpha*(u+B_var)/(T.cos(u)**(1/alpha)))
second = T.cos(u-alpha*(u+B_var))/w
return S_var*first*(second**((1-alpha)/alpha))
def build_model(peaks, t, y=None, yerr=None, model=None):
model = pm.modelcontext(model)
n_planets = len(peaks)
if yerr is None:
yerr = np.random.uniform(0.01, 0.1, len(t))
if y is None:
y = yerr * np.random.randn(len(t))
trend = PolynomialTrend("trend", order=3)
logs = pm.Normal("logs", mu=-5.0, sd=5.0, testval=-5.0)
meanrv = pm.Normal("meanrv", mu=0.0, sd=10.0, testval=0.0)
dataset = RVDataset("data",
t,
y,
yerr,
logs=logs,
trend=trend,
meanrv=meanrv)
logamps = pm.Uniform("logamps",
lower=np.log(min_amp),
upper=np.log(max_amp),
shape=n_planets,
testval=np.log([
np.clip(peak["amp"], min_amp + 1e-2,
max_amp - 1e-2) for peak in peaks
]))
planets = []
for i, (peak, name) in enumerate(zip(peaks, string.ascii_lowercase[1:])):
logP = pm.Uniform(name + ":logP",
lower=np.log(min_period),
upper=np.log(max_period),
testval=np.log(peak["period"]))
logK = pm.Deterministic(name + ":logK", logamps[i])
eccen = pm.Beta(name + ":eccen",
alpha=0.867,
beta=3.03,
testval=peak["eccen"])
omegabase = pm.Uniform(name + ":omegabase",
-2 * np.pi,
2 * np.pi,
testval=peak["omega"])
omegavec = pm.Deterministic(
name + ":omegavec",
tt.stack([tt.cos(omegabase), tt.sin(omegabase)]))
phibase = pm.Uniform(name + ":phibase",
-2 * np.pi,
2 * np.pi,
testval=peak["phase"])
phivec = pm.Deterministic(name + ":phivec",
tt.stack([tt.cos(phibase),
tt.sin(phibase)]))
planets.append(
RVPlanet(name,
logP,
logK,
phivec=phivec,
eccen=eccen,
omegavec=omegavec))
rvmodel = RVModel("rv", dataset, planets)
pm.Deterministic("logp", model.logpt)
return rvmodel
def backward(self, y):
return tt.arctan2(tt.sin(y), tt.cos(y))
def _get_true_anomaly(self, t, _pad=True):
M = (self._warp_times(t, _pad=_pad) - self.tref) * self.n
if self.ecc is None:
return tt.sin(M), tt.cos(M)
sinf, cosf = kepler(M, self.ecc + tt.zeros_like(M))
return sinf, cosf
def f(x, u):
return tt.stacklists([
x[3] * tt.cos(x[2]), x[3] * tt.sin(x[2]), x[3] * u[0],
u[1] - x[3] * friction
])
def _get_true_anomaly(self, t):
M = (self._warp_times(t) - self.tref) * self.n
if self.ecc is None:
return tt.sin(M), tt.cos(M)
sinf, cosf = self.kepler_op(M, self.ecc + tt.zeros_like(M))
return sinf, cosf
def week_modulation(
new_cases_inferred,
week_modulation_type="abs_sine",
pr_mean_weekend_factor=0.7,
pr_sigma_weekend_factor=0.2,
week_end_days=(6, 7),
model=None,
save_in_trace=True,
):
"""
Parameters
----------
new_cases_inferred
week_modulation_type
pr_mean_weekend_factor
pr_sigma_weekend_factor
week_end_days
model
Returns
-------
"""
model = modelcontext(model)
shape_modulation = list(model.shape_sim)
diff_data_sim = model.diff_data_sim
shape_modulation[0] -= diff_data_sim
date_begin_sim = model.date_begin_sim
len_L2 = () if model.ndim_sim == 1 else model.shape_sim[1]
week_end_factor, _ = hierarchical_normal(
"weekend_factor",
"sigma_weekend_factor",
pr_mean=pr_mean_weekend_factor,
pr_sigma=pr_sigma_weekend_factor,
len_L2=len_L2,
)
if week_modulation_type == "step":
modulation = np.zeros(shape_modulation[0])
for i in range(shape_modulation[0]):
date_curr = date_begin_sim + datetime.timedelta(days=i +
diff_data_sim + 1)
if date_curr.isoweekday() in week_end_days:
modulation[i] = 1
elif week_modulation_type == "abs_sine":
offset_rad = pm.VonMises("offset_modulation_rad", mu=0, kappa=0.01)
offset = pm.Deterministic("offset_modulation",
offset_rad / (2 * np.pi) * 7)
t = np.arange(shape_modulation[0])
date_begin = date_begin_sim + datetime.timedelta(days=diff_data_sim +
1)
weekday_begin = date_begin.weekday()
t -= weekday_begin # Sunday is zero
modulation = 1 - tt.abs_(tt.sin(t / 7 * np.pi + offset_rad / 2))
if model.ndim_sim == 2:
modulation = tt.shape_padaxis(modulation, axis=-1)
multiplication_vec = np.ones(
shape_modulation) - (1 - week_end_factor) * modulation
new_cases_inferred_eff = new_cases_inferred * multiplication_vec
if save_in_trace:
pm.Deterministic("new_cases", new_cases_inferred_eff)
return new_cases_inferred_eff
# yをxに関して微分 gy2 = T.grad(cost=y, wrt=x) # 微分係数を求める関数を定義 f = theano.function(inputs=[x], outputs=gy2) print(theano.pp(f.maker.fgraph.outputs[0])) print(f(2)) print(f(3)) print(f(4)) # y = sin(x)を微分 # 微分される数式のシンボルを定義 y = T.sin(x) # yをxに関して微分 gy = T.grad(cost=y, wrt=x) # 微分係数を求める関数を定義 f = theano.function(inputs=[x], outputs=gy) print(theano.pp(f.maker.fgraph.outputs[0])) print(f(0)) print(f(np.pi / 2)) print(f(np.pi)) # y = (x-4)(x^2+6)を微分 y = (x - 4) * (x**2 + 6) gy = T.grad(cost=y, wrt=x)
def forward(self, x):
return tt.concatenate((
tt.shape_padleft(tt.sin(x)),
tt.shape_padleft(tt.cos(x))
), axis=0)
def get_apodization(self, nyquist):
x = (np.pi * self.f) / (2 * nyquist)
return tt.sqr((tt.sin(x)/x))
def gTrig2(m, v, angi, D=None):
'''
Replaces angle dimensions with their complex representation.
i.e. if x[i] is an angle ( i in angi ), then x[i] will be replaced
with cos[x[i]] and sin[x[i]].
Since the input is a gaussian distribution, the output mean and covariance
are computed via moment matching
'''
if D is None:
D = m.shape[0]
if isinstance(angi, list) or isinstance(angi, tuple):
angi = np.array(angi, dtype=np.int32)
idx = tt.arange(D)
na_dims = (1 - tt.eq(idx, angi[:, None])).prod(0).nonzero()[0]
Da = 2 * angi.size
Dna = na_dims.size
Ma = tt.zeros((Da, ))
Va = tt.zeros((Da, Da))
Ca = tt.zeros((D, Da))
# compute the mean
mi = m[angi]
vi = v[angi, :][:, angi]
vii = v[angi, angi]
exp_vii_h = tt.exp(-vii / 2)
Ma = tt.set_subtensor(Ma[::2], exp_vii_h * tt.sin(mi))
Ma = tt.set_subtensor(Ma[1::2], exp_vii_h * tt.cos(mi))
# compute the entries in the augmented covariance matrix
vii_c = vii.dimshuffle(0, 'x')
vii_r = vii.dimshuffle('x', 0)
lq = -0.5 * (vii_c + vii_r)
q = tt.exp(lq)
exp_lq_p_vi = tt.exp(lq + vi)
exp_lq_m_vi = tt.exp(lq - vi)
mi_c = mi.dimshuffle(0, 'x')
mi_r = mi.dimshuffle('x', 0)
U1 = (exp_lq_p_vi - q) * (tt.sin(mi_c - mi_r))
U2 = (exp_lq_m_vi - q) * (tt.sin(mi_c + mi_r))
U3 = (exp_lq_p_vi - q) * (tt.cos(mi_c - mi_r))
U4 = (exp_lq_m_vi - q) * (tt.cos(mi_c + mi_r))
Va = tt.set_subtensor(Va[::2, ::2], U3 - U4)
Va = tt.set_subtensor(Va[1::2, 1::2], U3 + U4)
U12 = U1 + U2
Va = tt.set_subtensor(Va[::2, 1::2], U12)
Va = tt.set_subtensor(Va[1::2, ::2], U12.T)
Va = 0.5 * Va
# inv times input output covariance
Is = 2 * tt.arange(angi.size)
Ic = Is + 1
Ca = tt.set_subtensor(Ca[angi, Is], Ma[1::2])
Ca = tt.set_subtensor(Ca[angi, Ic], -Ma[::2])
# construct mean vectors ( non angle dimensions come first,
# then angle dimensions)
Mna = m[na_dims]
M = tt.concatenate([Mna, Ma])
# construct the corresponding covariance matrices
# just the blocks for the non angle dimensions and the angle dimensions
# separately
V = tt.zeros((Dna + Da, Dna + Da))
Vna = v[na_dims, :][:, na_dims]
V = tt.set_subtensor(V[:Dna, :Dna], Vna)
V = tt.set_subtensor(V[Dna:, Dna:], Va)
# fill in the cross covariances
q = v.dot(Ca)[na_dims, :]
V = tt.set_subtensor(V[:Dna, Dna:], q)
V = tt.set_subtensor(V[Dna:, :Dna], q.T)
return [M, V, Ca]
mu=rv2_dupont,
observed=d.dupont2[1],
sd=get_err(d.dupont2[2], logjit_dupont),
)
# get the astrometric predictions
# since there is only one measurement no jitter
rho_model, theta_model = orbit.get_relative_angles(d.anthonioz[0],
parallax) # arcsec
# evaluate the astrometric likelihood functions
pm.Normal("obs_rho",
mu=rho_model,
observed=d.anthonioz[1],
sd=d.anthonioz[2])
theta_diff = tt.arctan2(tt.sin(theta_model - d.anthonioz[3]),
tt.cos(theta_model - d.anthonioz[3])) # wrap-safe
pm.Normal("obs_theta", mu=theta_diff, observed=0.0, sd=d.anthonioz[4])
# iterate through the list of free_RVs in the model to get things like
# ['logKAa_interval__', etc...] then use a regex to strip away
# the transformations (in this case, _interval__ and _angle__)
# \S corresponds to any character that is not whitespace
# https://docs.python.org/3/library/re.html
sample_vars = [re.sub("_\S*__", "", var.name) for var in model.free_RVs]
all_vars = [
var.name for var in model.unobserved_RVs
if ("_interval__" not in var.name) and ("_angle__" not in var.name) and (
"_lowerbound__" not in var.name)
]
import theano
import theano.tensor as tt
import numpy
x = tt.matrix('x')
y = tt.matrix('y')
z = tt.matrix('z')
output = (z.T * (tt.cos(x)**2 + tt.sin(x)**2)).sum(1)
f = theano.function([x, y, z], output)
print theano.printing.debugprint(f)
xx = numpy.ones((5, 5), dtype='float64')
print f(xx, xx, xx)
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)
def forward(self, inputtensor):
inputimage = inputtensor[0]
return (T.concatenate(
[T.sin(inputimage), T.cos(inputimage)], axis=1), )
C2 = 0.0
sin_omc = T.zeros(len(fixed_ephem))
elif local_trend_type[npl][ng-1] == "quadratic":
C2 = pm.Normal("C2", mu=0.0, sd=2*ttv_rms_amp[npl])
sin_omc = T.zeros(len(fixed_ephem))
elif local_trend_type[npl][ng-1] == "sinusoid":
C2 = 0.0
freq = pm.Normal("freq", mu=sin_priors[npl][0], sd=0.1*sin_priors[npl][0])
A = pm.Normal("A", mu=0, sd=ttv_rms_amp[npl], testval=sin_priors[npl][1])
B = pm.Normal("B", mu=0, sd=ttv_rms_amp[npl], testval=sin_priors[npl][2])
sin_omc = pm.Deterministic("sin_omc",
A*T.sin(2*pi*freq*fixed_ephem) +
B*T.cos(2*pi*freq*fixed_ephem))
else:
raise ValueError("local_trend_type must be 'linear', 'quadratic', or 'sinusoid'")
# hierarchical (hyper)parameters
if USE_HBM:
log_pop_var = pm.Normal('log_pop_var', mu=2*np.log(ttv_rms_amp[npl]),
sd=np.log(4))
pop_sd = pm.Deterministic('pop_sd', T.sqrt(T.exp(log_pop_var)))
else:
def forward(self, inputtensor):
inputimage = inputtensor[0]
return (T.sin(self.a[0] * inputimage), )
def __init__(self,
period=None,
a=None,
t0=None,
t_periastron=None,
incl=None,
b=None,
duration=None,
ecc=None,
omega=None,
sin_omega=None,
cos_omega=None,
Omega=None,
m_planet=0.0,
m_star=None,
r_star=None,
rho_star=None,
ror=None,
m_planet_units=None,
rho_star_units=None,
model=None,
contact_points_kwargs=None,
**kwargs):
add_citations_to_model(self.__citations__, model=model)
self.jacobians = defaultdict(lambda: defaultdict(None))
daordtau = None
if ecc is None and duration is not None:
if r_star is None:
r_star = as_tensor_variable(1.0)
if b is None:
raise ValueError(
"'b' must be provided for a circular orbit with a "
"'duration'")
aor, daordtau = get_aor_from_transit_duration(duration,
period,
b,
ror=ror)
a = r_star * aor
duration = None
# Parameters
if m_planet_units is not None:
warnings.warn(
"The `m_planet_units` argument has been deprecated. "
"Use `with_unit` instead.",
DeprecationWarning,
)
m_planet = with_unit(m_planet, m_planet_units)
if rho_star_units is not None:
warnings.warn(
"The `rho_star_units` argument has been deprecated. "
"Use `with_unit` instead.",
DeprecationWarning,
)
rho_star = with_unit(rho_star, rho_star_units)
inputs = _get_consistent_inputs(a, period, rho_star, r_star, m_star,
m_planet)
(
self.a,
self.period,
self.rho_star,
self.r_star,
self.m_star,
self.m_planet,
) = inputs
self.m_total = self.m_star + self.m_planet
self.n = 2 * np.pi / self.period
self.a_star = self.a * self.m_planet / self.m_total
self.a_planet = -self.a * self.m_star / self.m_total
# Track the Jacobian between the duration and a
if daordtau is not None:
dadtau = self.r_star * daordtau
self.jacobians["duration"]["a"] = dadtau
self.jacobians["duration"]["a_star"] = (dadtau * self.m_planet /
self.m_total)
self.jacobians["duration"]["a_planet"] = (-dadtau * self.m_star /
self.m_total)
# rho = 3 * pi * (a/R)**3 / (G * P**2)
# -> drho / d(a/R) = 9 * pi * (a/R)**2 / (G * P**2)
self.jacobians["duration"]["rho_star"] = (
9 * np.pi * (self.a / self.r_star)**2 * daordtau *
gcc_per_sun / (G_grav * self.period**2))
self.K0 = self.n * self.a / self.m_total
# Set up the contact points calculation
if contact_points_kwargs is None:
self.contact_points = contact_points
else:
self.contact_points = ContactPoints(**contact_points_kwargs)
if Omega is None:
self.Omega = None
else:
self.Omega = as_tensor_variable(Omega)
self.cos_Omega = tt.cos(self.Omega)
self.sin_Omega = tt.sin(self.Omega)
# Eccentricity
if ecc is None:
self.ecc = None
self.M0 = 0.5 * np.pi + tt.zeros_like(self.n)
incl_factor = 1
else:
self.ecc = as_tensor_variable(ecc)
if omega is not None:
if sin_omega is not None and cos_omega is not None:
raise ValueError(
"either 'omega' or 'sin_omega' and 'cos_omega' can be "
"provided")
self.omega = as_tensor_variable(omega)
self.cos_omega = tt.cos(self.omega)
self.sin_omega = tt.sin(self.omega)
elif sin_omega is not None and cos_omega is not None:
self.cos_omega = as_tensor_variable(cos_omega)
self.sin_omega = as_tensor_variable(sin_omega)
self.omega = tt.arctan2(self.sin_omega, self.cos_omega)
else:
raise ValueError("both e and omega must be provided")
opsw = 1 + self.sin_omega
E0 = 2 * tt.arctan2(
tt.sqrt(1 - self.ecc) * self.cos_omega,
tt.sqrt(1 + self.ecc) * opsw,
)
self.M0 = E0 - self.ecc * tt.sin(E0)
ome2 = 1 - self.ecc**2
self.K0 /= tt.sqrt(ome2)
incl_factor = (1 + self.ecc * self.sin_omega) / ome2
# The Jacobian for the transform cos(i) -> b
self.dcosidb = self.jacobians["b"]["cos_incl"] = (incl_factor *
self.r_star / self.a)
if b is not None:
if incl is not None or duration is not None:
raise ValueError(
"only one of 'incl', 'b', and 'duration' can be given")
self.b = as_tensor_variable(b)
self.cos_incl = self.dcosidb * self.b
self.incl = tt.arccos(self.cos_incl)
elif incl is not None:
if duration is not None:
raise ValueError(
"only one of 'incl', 'b', and 'duration' can be given")
self.incl = as_tensor_variable(incl)
self.cos_incl = tt.cos(self.incl)
self.b = self.cos_incl / self.dcosidb
elif duration is not None:
if self.ecc is None:
raise ValueError(
"fitting with duration only works for eccentric orbits")
self.duration = as_tensor_variable(to_unit(duration, u.day))
c = tt.sin(np.pi * self.duration * incl_factor / self.period)
c2 = c * c
aor = self.a_planet / self.r_star
esinw = self.ecc * self.sin_omega
self.b = tt.sqrt(
(aor**2 * c2 - 1) / (c2 * esinw**2 + 2 * c2 * esinw + c2 -
self.ecc**4 + 2 * self.ecc**2 - 1))
self.b *= 1 - self.ecc**2
self.cos_incl = self.dcosidb * self.b
self.incl = tt.arccos(self.cos_incl)
else:
zla = tt.zeros_like(self.a)
self.incl = 0.5 * np.pi + zla
self.cos_incl = zla
self.b = zla
if t0 is not None and t_periastron is not None:
raise ValueError("you can't define both t0 and t_periastron")
if t0 is None and t_periastron is None:
t0 = tt.zeros_like(self.period)
if t0 is None:
self.t_periastron = as_tensor_variable(t_periastron)
self.t0 = self.t_periastron + self.M0 / self.n
else:
self.t0 = as_tensor_variable(t0)
self.t_periastron = self.t0 - self.M0 / self.n
self.tref = self.t_periastron - self.t0
self.sin_incl = tt.sin(self.incl)
# -*- coding: utf-8 -*-
"""3.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/1usas99e-lvo-jD_7TDeg6fCoZ4qklog6
"""
import numpy
import theano
import theano.tensor as T
t = T.dscalar("t")
x1 = 5 * T.cos(2 * t) - 2
y1 = 5 * T.sin(2 * t)
x2 = 10 * T.cos(t) - 2
y2 = 10 * T.sin(t)
# ヘロンの公式
a = T.sqrt(x1**2 + y1**2)
b = T.sqrt(x2**2 + y2**2)
c = T.sqrt((x1 - x2)**2 + (y1 - y2)**2)
s = (a + b + c) / 2
S = T.sqrt(s * (s - a) * (s - b) * (s - c))
# tで微分
dS = T.grad(S, t)
f = theano.function([t], dS)
g = theano.function([t], S)
def normal(self,
size,
avg=0.0,
std=1.0,
ndim=None,
dtype=None,
nstreams=None):
"""
:param size: Can be a list of integers or Theano variables (ex: the
shape of another Theano Variable)
:param dtype: The output data type. If dtype is not specified, it will
be inferred from the dtype of low and high, but will be at least as
precise as floatX.
:param nstreams: Number of streams.
"""
# We need an even number of ]0,1[ samples. Then we split them
# in two halves. First half becomes our U1's for Box-Muller,
# second half our U2's. See Wikipedia page:
# http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
avg = as_tensor_variable(avg)
std = as_tensor_variable(std)
if dtype is None:
dtype = scal.upcast(config.floatX, avg.dtype, std.dtype)
avg = cast(avg, dtype)
std = cast(std, dtype)
evened = False
constant = False
if isinstance(size, tuple) and all(
[isinstance(i, (numpy.integer, int)) for i in size]):
constant = True
# Force dtype because it defaults to float when size is empty
n_samples = numpy.prod(size, dtype='int64')
if n_samples % 2 == 1:
n_samples += 1
evened = True
else:
#if even, don't change, if odd, +1
n_samples = prod(size) + (prod(size) % 2)
flattened = self.uniform(size=(n_samples, ),
dtype=dtype,
nstreams=nstreams)
if constant:
U1 = flattened[:n_samples // 2]
U2 = flattened[n_samples // 2:]
else:
U1 = flattened[:prod(flattened.shape) // 2]
U2 = flattened[prod(flattened.shape) // 2:]
#normal_samples = zeros_like(flattened)
sqrt_ln_U1 = sqrt(-2.0 * log(U1))
# TypeError: 'TensorVariable' object does not support item assignment
# so this doesn't work...
#normal_samples[:n_samples/2] = sqrt_ln_U1 * cos(2.0*numpy.pi*U2)
#normal_samples[n_samples/2:] = sqrt_ln_U1 * sin(2.0*numpy.pi*U2)
# so trying this instead
first_half = sqrt_ln_U1 * cos(
numpy.array(2.0 * numpy.pi, dtype=dtype) * U2)
second_half = sqrt_ln_U1 * sin(
numpy.array(2.0 * numpy.pi, dtype=dtype) * U2)
normal_samples = join(0, first_half, second_half)
final_samples = None
if evened:
final_samples = normal_samples[:-1]
elif constant:
final_samples = normal_samples
else:
final_samples = normal_samples[:prod(size)]
if not size:
# Force the dtype to be int64, otherwise reshape complains
size = tensor.constant(size, dtype='int64')
final_samples = final_samples.reshape(size)
final_samples = avg + std * final_samples
assert final_samples.dtype == dtype
return final_samples
#### LINEAR REGRESSION USING THEANO
import theano
import theano.tensor as T
import theano.tensor.nnet as nnet
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from matplotlib import colors
y_train = y2
X_train = x2
x = T.dscalar()
fx = T.exp(T.sin(x**2))
f = theano.function(inputs=[x], outputs=[fx])
fp = T.grad(fx, wrt=x)
fprime = theano.function([x], fp)
x = T.dvector()
y = T.dscalar()
def layer(x, w):
b = np.array([1], dtype=theano.config.floatX)
new_x = T.concatenate([x, b])
m = T.dot(w.T, new_x) #theta1: 3x3 * x: 3x1 = 3x1 ;;; theta2: 1x4 * 4x1
h = nnet.sigmoid(m)
return h
def __init__(self,
period=None,
a=None,
t0=None,
t_periastron=None,
incl=None,
b=None,
duration=None,
ecc=None,
omega=None,
Omega=None,
m_planet=0.0,
m_star=None,
r_star=None,
rho_star=None,
m_planet_units=None,
rho_star_units=None,
model=None,
contact_points_kwargs=None,
**kwargs):
add_citations_to_model(self.__citations__, model=model)
self.gcc_to_sun = ((constants.M_sun / constants.R_sun**3).to(
u.g / u.cm**3).value)
self.au_to_R_sun = (constants.au / constants.R_sun).value
self.G_grav = constants.G.to(u.R_sun**3 / u.M_sun / u.day**2).value
self.kepler_op = KeplerOp(**kwargs)
# Parameters
# self.period = tt.as_tensor_variable(period)
self.m_planet = tt.as_tensor_variable(m_planet)
if m_planet_units is not None:
self.m_planet *= (1 * m_planet_units).to(u.M_sun).value
self.a, self.period, self.rho_star, self.r_star, self.m_star = self._get_consistent_inputs(
a, period, rho_star, r_star, m_star, rho_star_units)
self.m_total = self.m_star + self.m_planet
self.n = 2 * np.pi / self.period
self.a_star = self.a * self.m_planet / self.m_total
self.a_planet = -self.a * self.m_star / self.m_total
self.K0 = self.n * self.a / self.m_total
# Set up the contact points calculation
if contact_points_kwargs is None:
contact_points_kwargs = dict()
if Omega is None:
self.Omega = None
else:
self.Omega = tt.as_tensor_variable(Omega)
self.cos_Omega = tt.cos(self.Omega)
self.sin_Omega = tt.sin(self.Omega)
# Eccentricity
self.contact_points_op = ContactPointsOp(**contact_points_kwargs)
if ecc is None:
self.ecc = None
self.M0 = 0.5 * np.pi + tt.zeros_like(self.n)
incl_factor = 1
else:
self.ecc = tt.as_tensor_variable(ecc)
if omega is None:
raise ValueError("both e and omega must be provided")
self.omega = tt.as_tensor_variable(omega)
self.cos_omega = tt.cos(self.omega)
self.sin_omega = tt.sin(self.omega)
opsw = 1 + self.sin_omega
E0 = 2 * tt.arctan2(
tt.sqrt(1 - self.ecc) * self.cos_omega,
tt.sqrt(1 + self.ecc) * opsw,
)
self.M0 = E0 - self.ecc * tt.sin(E0)
ome2 = 1 - self.ecc**2
self.K0 /= tt.sqrt(ome2)
incl_factor = (1 + self.ecc * self.sin_omega) / ome2
if b is not None:
if incl is not None or duration is not None:
raise ValueError("only one of 'incl', 'b', and 'duration' can "
"be given")
self.b = tt.as_tensor_variable(b)
self.cos_incl = incl_factor * self.b * self.r_star / self.a_planet
self.incl = tt.arccos(self.cos_incl)
elif incl is not None:
if duration is not None:
raise ValueError("only one of 'incl', 'b', and 'duration' can "
"be given")
self.incl = tt.as_tensor_variable(incl)
self.cos_incl = tt.cos(self.incl)
self.b = (self.a_planet * self.cos_incl /
(incl_factor * self.r_star))
elif duration is not None:
if self.ecc is None:
raise ValueError("fitting with duration only works for "
"eccentric orbits")
self.duration = tt.as_tensor_variable(duration)
c = tt.sin(np.pi * self.duration * incl_factor / self.period)
c2 = c * c
aor = self.a_planet / self.r_star
esinw = self.ecc * self.sin_omega
self.b = tt.sqrt(
(aor**2 * c2 - 1) / (c2 * esinw**2 + 2 * c2 * esinw + c2 -
self.ecc**4 + 2 * self.ecc**2 - 1))
self.b *= 1 - self.ecc**2
self.cos_incl = incl_factor * self.b * self.r_star / self.a_planet
self.incl = tt.arccos(self.cos_incl)
else:
zla = tt.zeros_like(self.a)
self.incl = 0.5 * np.pi + zla
self.cos_incl = zla
self.b = zla
if t0 is not None and t_periastron is not None:
raise ValueError("you can't define both t0 and t_periastron")
if t0 is None and t_periastron is None:
t0 = 0.0
if t0 is None:
self.t_periastron = tt.as_tensor_variable(t_periastron)
self.t0 = self.t_periastron + self.M0 / self.n
else:
self.t0 = tt.as_tensor_variable(t0)
self.t_periastron = self.t0 - self.M0 / self.n
self.tref = self.t_periastron
self.sin_incl = tt.sin(self.incl)
def bengio_RNN(n_input,
n_hidden,
n_output,
input_type='real',
out_every_t=False,
loss_function='CE'):
#Initialize states
#This is the matrix from input -> hidden
V = initialize_matrix(n_input, 2 * n_hidden, 'V')
print V
print V.get_value()
#Matrix from hidden -> out
U = initialize_matrix(2 * n_hidden, n_output, "U")
print U
#Now the output bias. No input bias?
U_bias_values = np.zeros((n_output, 1), dtype=theano.config.floatX)
U_bias = theano.shared(U_bias_values, name='U Bias')
#Now the hidden state
hidden_bias_mean = 0
#The hidden_to_hidden matrix is a list of the different weight matrices
hidden_bias, h_0, hidden_to_hidden_matrix = initialize_complex_RNN_layer(
n_hidden, 0, "H")
#Don't actually understand what this is for
swap_re_im = np.concatenate((np.arange(n_hidden,
2 * n_hidden), np.arange(n_hidden)))
print swap_re_im
theta = hidden_to_hidden_matrix[0]
reflection = hidden_to_hidden_matrix[1]
index_permute_long = hidden_to_hidden_matrix[2]
#This is the set of all params. h_0 is the initial parameters for h_0.
parameters = [V, U, hidden_bias, reflection, U_bias, theta, h_0]
#for i_layer in xrange(2,n_layers+1):
# Wvparams = initialize_unitary
#I am not doing multiple layers right now
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
#These are structued to be sequences, non-sequences
def recurrence(x_t, y_t, ymask_t, h_prev, cost_prev, acc_prev, V,
hidden_bias, out_bias, U, *argv):
# h_prev is of size n_batch x n_layers*2*n_hidden
Wparams = argv[0:3]
argv = argv[3:]
print "Testing recurrence..."
print n_hidden
#print h_prev.get_value()
h_prev_layer1 = h_prev[:, 0:2 * n_hidden]
hidden_lin_output = times_unitary(h_prev_layer1, n_hidden, swap_re_im,
Wparams)
msg = theano.printing.Print('T')(x_t)
#if (input_type=='categorical'):
data_lin_output = V[T.cast(x_t, 'int32')]
#else:
# data_lin_output = T.dot(x_t,V)
lin_output = data_lin_output
#Non linearity
modulus = T.sqrt(1e-5 + lin_output**2 + lin_output[:, swap_re_im]**2)
firstval = modulus + T.tile(hidden_bias, [2]).dimshuffle('x', 0)
rescale = T.maximum(firstval, 0.) / (modulus + 1e-5)
h_t = lin_output * rescale
if (out_every_t):
lin_output = T.dot(h_t, U) + out.bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, cost_t, acc_t, msg
h_0_batch = T.tile(h_0, [x.shape[1], 1])
non_sequences = [V, hidden_bias, U_bias, U] + hidden_to_hidden_matrix
if (out_every_t):
print "My x: ", x
print x.shape
sequences = [
x, y,
T.tile(theano.shared(np.ones((1, 1), dtype=theano.config.floatX)),
[x.shape[0], 1, 1])
]
else:
sequences = [
x,
T.tile(theano.shared(np.zeros((1, 1), dtype=theano.config.floatX)),
[x.shape[0], 1, 1]),
T.tile(theano.shared(np.ones((1, 1), dtype=theano.config.floatX)),
[x.shape[0], 1, 1])
]
#outputs_info = [h_0_batch,theano.shared(np.float32(0,0)),theano.shared(np.float32(0.0))]
outputs_info = [
h_0_batch,
theano.shared(np.float32(0.0)),
theano.shared(np.float32(0.0))
]
print "Ready for scan:"
print recurrence
print sequences
print non_sequences
print outputs_info
print "N Hidden: ", n_hidden
print "H prev: ", non_sequences[1].get_value()
[hidden_states, cost_steps,
acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info=outputs_info)
if (cost_transform == 'magTimesPhase'):
cosPhase = T.cos(lin_output)
sinPhase = T.sin(lin_output)
linMag = np.sqrt(10**(x / 10.0) - 1e-5)
yest_real = linMag * cosPhase
yest_imag = linMag * sinPhase
yest = T.concatenate([yest_real, yest_imag], axis=2)
mse = (yest - y)**2
cost_steps = T.mean(mse * ymask[:, :, 0].dimshuffle(0, 1, 'x'), axis=2)
elif cost_transform is not None:
# assume that cost_transform is an inverse DFT followed by synthesis windowing
lin_output_real = lin_output[:, :, :n_output]
lin_output_imag = lin_output[:, :, n_output:]
lin_output_sym_real = T.concatenate(
[lin_output_real, lin_output_real[:, :, n_output - 2:0:-1]],
axis=2)
lin_output_sym_imag = T.concatenate(
[-lin_output_imag, lin_output_imag[:, :, n_output - 2:0:-1]],
axis=2)
lin_output_sym = T.concatenate(
[lin_output_sym_real, lin_output_sym_imag], axis=2)
yest_xform = T.dot(lin_output_sym, cost_transform)
# apply synthesis window
yest_xform = yest_xform * cost_weight.dimshuffle('x', 'x', 0)
y_real = y[:, :, :n_output]
y_imag = y[:, :, n_output:]
y_sym_real = T.concatenate([y_real, y_real[:, :, n_output - 2:0:-1]],
axis=2)
y_sym_imag = T.concatenate([-y_imag, y_imag[:, :, n_output - 2:0:-1]],
axis=2)
y_sym = T.concatenate([y_sym_real, y_sym_imag], axis=2)
y_xform = T.dot(y_sym, cost_transform)
# apply synthesis window
y_xform = y_xform * cost_weight.dimshuffle('x', 'x', 0)
mse = (y_xform - yest_xform)**2
cost_steps = T.mean(mse * ymask[:, :, 0].dimshuffle(0, 1, 'x'), axis=2)
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return [x, y], parameters, costs
def build_graph(x, depth=5):
z = x
for d in range(depth):
z = tensor.sin(-z + 1)
return z
def passage(self,F,omega,W,num_FF):
F_times_Omega = T.dot(F, omega)#minibatch_size*n_rff
Phi = (self.sf2**0.5 /num_FF**0.5 ) * T.concatenate([T.cos(F_times_Omega), T.sin(F_times_Omega)],1)
F_next=T.dot(Phi,W)
return F_next
def SIR_with_change_points(new_cases_obs,
change_points_list,
date_begin_simulation,
num_days_sim,
diff_data_sim,
N,
priors_dict=None,
weekends_modulated=False,
weekend_modulation_type='step',
student_nu=4):
"""
Parameters
----------
new_cases_obs : list or array
Timeseries (day over day) of newly reported cases (not the total number)
change_points_list : list of dicts
List of dictionaries, each corresponding to one change point.
Each dict can have the following key-value pairs. If a pair is not provided,
the respective default is used.
* pr_mean_date_begin_transient : datetime.datetime, NO default
* pr_median_lambda : number, same as default priors, below
* pr_sigma_lambda : number, same as default priors, below
* pr_sigma_date_begin_transient : number, 3
* pr_median_transient_len : number, 3
* pr_sigma_transient_len : number, 0.3
date_begin_simulation: datetime.datetime
The begin of the simulation data
num_days_sim : integer
Number of days to forecast into the future
diff_data_sim : integer
Number of days that the simulation-begin predates the first data point in
`new_cases_obs`. This is necessary so the model can fit the reporting delay.
Set this parameter to a value larger than what you expect to find
for the reporting delay.
N : number
The population size. For Germany, we used 83e6
priors_dict : dict
Dictionary of the prior assumptions
Possible key-value pairs (and default values) are:
* pr_beta_I_begin : number, default = 100
* pr_median_lambda_0 : number, default = 0.4
* pr_sigma_lambda_0 : number, default = 0.5
* pr_median_mu : number, default = 1/8
* pr_sigma_mu : number, default = 0.2
* pr_median_delay : number, default = 8
* pr_sigma_delay : number, default = 0.2
* pr_beta_sigma_obs : number, default = 10
* week_end_days : tuple, default = (6,7)
* pr_mean_weekend_factor : number, default = 0.7
* pr_sigma_weekend_factor :number, default = 0.17
weekends_modulated : bool
Whether to add the prior that cases are less reported on week ends. Multiplies the new cases numbers on weekends
by a number between 0 and 1, given by a prior beta distribution. The beta distribution is parametrised
by pr_mean_weekend_factor and pr_sigma_weekend_factor
weekend_modulation_type : 'step' or 'abs_sine':
whether the weekends are modulated by a step function, which only multiplies the days given by week_end_days
by the week_end_factor, or whether the whole week is modulated by an abs(sin(x)) function, with an offset
with flat prior.
Returns
-------
: pymc3.Model
Returns an instance of pymc3 model with the change points
"""
if priors_dict is None:
priors_dict = dict()
default_priors = dict(pr_beta_I_begin=100,
pr_median_lambda_0=0.4,
pr_sigma_lambda_0=0.5,
pr_median_mu=1 / 8,
pr_sigma_mu=0.2,
pr_median_delay=8,
pr_sigma_delay=0.2,
pr_beta_sigma_obs=10,
week_end_days=(6, 7),
pr_mean_weekend_factor=0.7,
pr_sigma_weekend_factor=0.17)
default_priors_change_points = dict(
pr_median_lambda=default_priors["pr_median_lambda_0"],
pr_sigma_lambda=default_priors["pr_sigma_lambda_0"],
pr_sigma_date_begin_transient=3,
pr_median_transient_len=3,
pr_sigma_transient_len=0.3,
pr_mean_date_begin_transient=None,
)
if not weekends_modulated:
del default_priors['week_end_days']
del default_priors['pr_mean_weekend_factor']
del default_priors['pr_sigma_weekend_factor']
for prior_name in priors_dict.keys():
if prior_name not in default_priors:
raise RuntimeError(f"Prior with name {prior_name} not known")
for change_point in change_points_list:
for prior_name in change_point.keys():
if prior_name not in default_priors_change_points:
raise RuntimeError(f"Prior with name {prior_name} not known")
for prior_name, value in default_priors.items():
if prior_name not in priors_dict:
priors_dict[prior_name] = value
print(f"{prior_name} was set to default value {value}")
for prior_name, value in default_priors_change_points.items():
for i_cp, change_point in enumerate(change_points_list):
if prior_name not in change_point:
change_point[prior_name] = value
print(
f"{prior_name} of change point {i_cp} was set to default value {value}"
)
if (diff_data_sim < priors_dict["pr_median_delay"] + 3 *
priors_dict["pr_median_delay"] * priors_dict["pr_sigma_delay"]):
print(
"WARNING: diff_data_sim could be to small compared to the prior delay"
)
if num_days_sim < len(new_cases_obs) + diff_data_sim:
raise RuntimeError(
"Simulation ends before the end of the data. Increase num_days_sim."
)
# ------------------------------------------------------------------------------ #
# Model and prior implementation
# ------------------------------------------------------------------------------ #
with pm.Model() as model:
# all pm functions now apply on the model instance
# true cases at begin of loaded data but we do not know the real number
I_begin = pm.HalfCauchy(name="I_begin",
beta=priors_dict["pr_beta_I_begin"])
# fraction of people that are newly infected each day
lambda_list = []
lambda_list.append(
pm.Lognormal(
name="lambda_0",
mu=np.log(priors_dict["pr_median_lambda_0"]),
sigma=priors_dict["pr_sigma_lambda_0"],
))
for i, cp in enumerate(change_points_list):
lambda_list.append(
pm.Lognormal(
name=f"lambda_{i + 1}",
mu=np.log(cp["pr_median_lambda"]),
sigma=cp["pr_sigma_lambda"],
))
# list of start dates of the transient periods of the change points
tr_begin_list = []
dt_before = date_begin_simulation
for i, cp in enumerate(change_points_list):
dt_begin_transient = cp["pr_mean_date_begin_transient"]
if dt_before is not None and dt_before > dt_begin_transient:
raise RuntimeError(
"Dates of change points are not temporally ordered")
prior_mean = (
dt_begin_transient - date_begin_simulation
).days - 1 # convert the provided date format (argument) into days (a number)
tr_begin = pm.Normal(
name=f"transient_begin_{i}",
mu=prior_mean,
sigma=cp["pr_sigma_date_begin_transient"],
)
tr_begin_list.append(tr_begin)
dt_before = dt_begin_transient
# same for transient times
tr_len_list = []
for i, cp in enumerate(change_points_list):
tr_len = pm.Lognormal(
name=f"transient_len_{i}",
mu=np.log(cp["pr_median_transient_len"]),
sigma=cp["pr_sigma_transient_len"],
)
tr_len_list.append(tr_len)
# build the time-dependent spreading rate
lambda_t_list = [lambda_list[0] * tt.ones(num_days_sim)]
lambda_before = lambda_list[0]
for tr_begin, tr_len, lambda_after in zip(tr_begin_list, tr_len_list,
lambda_list[1:]):
lambda_t = smooth_step_function(
start_val=0,
end_val=1,
t_begin=tr_begin,
t_end=tr_begin + tr_len,
t_total=num_days_sim,
) * (lambda_after - lambda_before)
lambda_before = lambda_after
lambda_t_list.append(lambda_t)
lambda_t = sum(lambda_t_list)
# fraction of people that recover each day, recovery rate mu
mu = pm.Lognormal(
name="mu",
mu=np.log(priors_dict["pr_median_mu"]),
sigma=priors_dict["pr_sigma_mu"],
)
# delay in days between contracting the disease and being recorded
delay = pm.Lognormal(
name="delay",
mu=np.log(priors_dict["pr_median_delay"]),
sigma=priors_dict["pr_sigma_delay"],
)
# prior of the error of observed cases
sigma_obs = pm.HalfCauchy("sigma_obs",
beta=priors_dict["pr_beta_sigma_obs"])
# -------------------------------------------------------------------------- #
# training the model with loaded data provided as argument
# -------------------------------------------------------------------------- #
S_begin = N - I_begin
S, I, new_I = _SIR_model(lambda_t=lambda_t,
mu=mu,
S_begin=S_begin,
I_begin=I_begin,
N=N)
new_cases_inferred = delay_cases(
new_I_t=new_I,
len_new_I_t=num_days_sim,
len_out=num_days_sim - diff_data_sim,
delay=delay,
delay_diff=diff_data_sim,
)
if weekends_modulated:
week_end_factor = pm.Beta(
'weekend_factor',
mu=priors_dict['pr_mean_weekend_factor'],
sigma=priors_dict['pr_sigma_weekend_factor'])
if weekend_modulation_type == 'step':
modulation = np.zeros(num_days_sim - diff_data_sim)
for i in range(num_days_sim - diff_data_sim):
date_curr = date_begin_simulation + datetime.timedelta(
days=i + diff_data_sim + 1)
if date_curr.isoweekday() in priors_dict['week_end_days']:
modulation[i] = 1
elif weekend_modulation_type == 'abs_sine':
offset_rad = pm.VonMises('offset_modulation_rad',
mu=0,
kappa=0.01)
offset = pm.Deterministic('offset_modulation',
offset_rad / (2 * np.pi) * 7)
t = np.arange(num_days_sim - diff_data_sim)
date_begin = date_begin_simulation + datetime.timedelta(
days=diff_data_sim + 1)
weekday_begin = date_begin.weekday()
t -= weekday_begin # Sunday is zero
modulation = 1 - tt.abs_(
tt.sin(t / 7 * np.pi + offset_rad / 2))
multiplication_vec = np.ones(num_days_sim - diff_data_sim) - (
1 - week_end_factor) * modulation
new_cases_inferred_eff = new_cases_inferred * multiplication_vec
else:
new_cases_inferred_eff = new_cases_inferred
# likelihood of the model:
# observed cases are distributed following studentT around the model.
# we want to approximate a Poisson distribution of new cases.
# we choose nu=4 to get heavy tails and robustness to outliers.
# https://www.jstor.org/stable/2290063
num_days_data = new_cases_obs.shape[-1]
pm.StudentT(
name="_new_cases_studentT",
nu=student_nu,
mu=new_cases_inferred_eff[:num_days_data],
sigma=tt.abs_(new_cases_inferred[:num_days_data] + 1)**0.5 *
sigma_obs, # +1 and tt.abs to avoid nans
observed=new_cases_obs,
)
# add these observables to the model so we can extract a time series of them
# later via e.g. `model.trace['lambda_t']`
pm.Deterministic("lambda_t", lambda_t)
pm.Deterministic("new_cases", new_cases_inferred_eff)
pm.Deterministic("new_cases_raw", new_cases_inferred)
return model
def sin(x):
return T.sin(x)
def sin(var, name=None):
"""Implement element-wise sin"""
_tensor = T.sin(var.unwrap())
return Tensor(tensor=_tensor, shape=var.shape, name=name)
# -*- coding=utf8 -*-
"""
a simple example to show how to user theano
"""
import theano.tensor as T
from theano import function
x = T.dscalar('x')
y = 0.5 * x * x + x * T.sin(x)
dy = T.grad(y, x)
func = function(inputs=[x], outputs=dy)
start = 5.0
iter_num = 10000
rate = 0.01
for i in xrange(iter_num):
d = func(start)
if d < 0.005:
break
start -= rate * d
print start
def __init__(self, model):
#### theano params
learnrate=T.scalar('lr')
imgin=T.vector('imgin')
ang=T.vector('orient')
#### load model
sz=self.boxsz=model["boxsz"]
sym=str(model["sym"]).lower()
balls_pos=np.asarray(model["center"],dtype=theano.config.floatX)
balls_wt=np.asarray(model["weight"],dtype=theano.config.floatX)
ballzero = theano.shared(value=balls_pos, name='balls', borrow=True)
weight = theano.shared(value=balls_wt, name='wts', borrow=True)
wts=T.nnet.sigmoid(weight)
nballs=len(balls_pos)
### motion vector of the balls
mov_vec= np.zeros((nballs,3),dtype=theano.config.floatX)
movvec=theano.shared(value=mov_vec, name="move_vec", borrow=True)
cfval=np.array(0,dtype=theano.config.floatX)
conf=theano.shared(value=cfval, name="conf", borrow=True)
ball=ballzero+conf*movvec
### deal with symmetry.. painfully...
nsym=Transform.get_nsym(sym)
if sym!="c1":
if sym.startswith('d'):
asym=[]
for i in range(nsym/2):
a=6.28/(nsym/2)*i
asym.append(T.stacklists(
[ball[:,0]*T.cos(a)-ball[:,1]*T.sin(a),
ball[:,0]*T.sin(a)+ball[:,1]*T.cos(a),
ball[:,2]]))
asym.append(T.stacklists(
[ball[:,0]*T.cos(a)-ball[:,1]*T.sin(a),
-(ball[:,0]*T.sin(a)+ball[:,1]*T.cos(a)),
-ball[:,2]]))
#print asym[0].T.eval()
balls=T.concatenate(asym,axis=1).T
nballs*=nsym
if sym.startswith('c'):
asym=[]
for i in range(nsym):
a=6.28/(nsym)*i
asym.append(T.stacklists(
[ball[:,0]*T.cos(a)-ball[:,1]*T.sin(a),
ball[:,0]*T.sin(a)+ball[:,1]*T.cos(a),
ball[:,2]]))
#print asym[0].T.eval()
balls=T.concatenate(asym,axis=1).T
nballs*=nsym
ww=[wts for i in range(nsym)]
wtss=T.concatenate(ww,axis=0)
else:
balls=ball
wtss=wts
print(balls.shape.eval())
print(wtss.shape.eval())
#numpy2pdb(balls.eval(), "tmp.pdb")
#exit()
### get the 3d density map for initial tunning
ind_np=np.indices((sz,sz,sz)).astype(theano.config.floatX)
ind_np=np.transpose(ind_np,axes=(3,2,1,0))
ind=theano.shared(value=ind_np,borrow=True)
def make_3d(p,w,den,ind):
d=(ind-p)**2
v=w*T.exp(-T.sum(d,axis=3)/(model["width"]))
den+=v
return den
map_3d_all,update=theano.scan(fn=make_3d,
outputs_info=T.zeros((sz,sz,sz)),
sequences=[balls+sz/2,wtss],
non_sequences=ind,
)
map_3d=map_3d_all[-1]
#map_3d=map_3d.dimshuffle([2,1,0])
self.target_map=T.tensor3('tar_map')
self.map_err=T.sum((self.target_map-map_3d)**2)
map_grad_w=T.grad(self.map_err, weight)
self.map_update_w=[(weight,weight-map_grad_w*learnrate)]
map_grad_p=T.grad(self.map_err, ballzero)
self.map_update_p=[(ballzero,ballzero-map_grad_p*learnrate)]
### make rotation matrix
azp=ang[2]+3.14/2
altp=3.14-ang[1]
phip=6.28-ang[0]
matrix=[(T.cos(phip)*T.cos(azp) - T.cos(altp)*T.sin(azp)*T.sin(phip)),
(T.cos(phip)*T.sin(azp) + T.cos(altp)*T.cos(azp)*T.sin(phip)),
(T.sin(altp)*T.sin(phip)),
(-T.sin(phip)*T.cos(azp) - T.cos(altp)*T.sin(azp)*T.cos(phip)),
(-T.sin(phip)*T.sin(azp) + T.cos(altp)*T.cos(azp)*T.cos(phip)),
(T.sin(altp)*T.cos(phip)),
(T.sin(altp)*T.sin(azp)),
(-T.sin(altp)*T.cos(azp)),
T.cos(altp)]
mat=T.stacklists(matrix).T.reshape((3,3))
newpos=T.dot(balls,mat)#+sz/2
tx=ang[5]
ty=ang[4]
newpos=T.inc_subtensor(newpos[:,0],tx)
newpos=T.inc_subtensor(newpos[:,1],ty)
mirror=ang[3]
newpos=T.set_subtensor(newpos[:,1], newpos[:,1]*mirror)
newpos=newpos+sz/2
#newpos[:,1]+=ty
### gird for 2d images
grid_x =T.arange(sz).astype(theano.config.floatX)
grid_x=grid_x.repeat(sz,axis=0).reshape((sz,sz))
grid_y=grid_x.copy().T
### now make 2d projections
iy=T.arange(nballs)
def make_img(iy,r,x,y,pos, wt):
ret=r+ wt[iy] *T.exp((-(x-pos[iy,0])**2 -(y-pos[iy,1])**2)/(15))
return ret
img,update=theano.scan(fn=make_img,
outputs_info=T.zeros((sz,sz)),
sequences=[iy],
non_sequences=[grid_x,grid_y,newpos,wtss],
)
out=img[-1]#[:-1]
xx=out.flatten()
zz=imgin.flatten()
L = T.sum(xx*zz)/T.sqrt(T.sum(xx**2))/T.sqrt(T.sum(zz**2))
cost=-L#T.mean(L)
grad_conf=T.grad(cost, conf)
self.update_conf=[(conf, conf-learnrate*grad_conf)]
self.grad_ballpos=T.grad(cost, ballzero)
self.imgin=imgin
self.orientin=ang
self.balls=balls
self.cost=cost
self.learnrate=learnrate
self.map3d=map_3d
self.conf=conf
#self.updates=updates
#self.updates_ang=updates_ang
self.out=out
self.weight=weight
self.ballzero=ballzero
self.movvec=movvec
Da2 = pm.Normal('Da2',0, 1, shape=len(f2_))
a0 = pm.Deterministic('a0', sigmaA * Da0 + mod.A0(f0_, [numax, w, A, V1, V2]))
a1 = pm.Deterministic('a1', sigmaA * Da1 + mod.A1(f1_, [numax, w, A, V1, V2]))
a2 = pm.Deterministic('a2', sigmaA * Da2 + mod.A2(f2_, [numax, w, A, V1, V2]))
h0 = pm.Deterministic('h0', 2*tt.sqr(a0)/np.pi/g0)
h1 = pm.Deterministic('h1', 2*tt.sqr(a1)/np.pi/g1)
h2 = pm.Deterministic('h2', 2*tt.sqr(a2)/np.pi/g2)
# Mode splitting
xsplit = pm.HalfNormal('xsplit', sigma=2.0, testval = init['xsplit'])
cosi = pm.Uniform('cosi', 0., 1., testval = init['cosi'])
i = pm.Deterministic('i', tt.arccos(cosi))
split = pm.Deterministic('split', xsplit/tt.sin(i))
# Background treatment
aphi = pm.MvNormal('aphi', mu=aphi_, chol=aphi_cholesky, testval=aphi_, shape=len(aphi_))
bphi = pm.Normal('bphi', mu=bphi_, sigma=bphi_sigma, testval=bphi_, shape=len(bphi_))
# Construct model
fit = mod.model([f0, f1, f2, g0, g1, g2, h0, h1, h2, split, i, aphi, bphi])
like = pm.Gamma('like', alpha=1., beta=1./fit, observed=p)
# In[ ]:
for RV in pm_model.basic_RVs: