def th_dihedral_angle(r0,r1,r2,r3, shift=0.):
bxa = thcross(r2 - r1, r1 - r0)
bxa /= bxa.norm(2)
cxb = thcross(r3 - r2, r2 - r1)
cxb /= cxb.norm(2)
angle = th.arccos(th.dot(bxa, cxb))
return angle + shift
def loss(lv1, lv2):
""" Contrastive cosine distance optimization target """
# number of samples in batch
n = lv1.shape[0]
# compute cosine distance
D = lv1.dot(lv2.T)
# compute arcus cosinus -> converts similarity into distance
D = T.arccos(D)
# distance between matching pairs
d = D.diagonal().reshape((-1, 1))
# distance between non-matching pairs
M = T.identity_like(D)
O = D[(M <= 0).nonzero()].reshape((n, n - 1))
# max margin hinge loss
L = gamma + d
L = T.repeat(L, n - 1, 1)
L -= O
L = T.clip(L, 0, 1000)
# compute batch mean
loss = L.mean()
return weight * loss
def th_dihedral_angle_rec(r0,r1,r2,r3, shift=0.):
# reciprocal of the angle
bxa = thcross(r2 - r1, r1 - r0)
bxa /= bxa.norm(2)
cxb = thcross(r3 - r2, r2 - r1)
cxb /= cxb.norm(2)
angle = 2*sp.pi - th.arccos(th.dot(bxa, cxb))
return angle + shift
def generator(self, u):
if u.ndim == 1:
u = u[None, :]
z, n = u[:, :self.z_dim], u[:, self.z_dim:self.z_dim + self.x_dim]
loc, scale = self.x_gvn_z(z)
alpha = 2 * scale / (1 + scale**2)
phi = tt.arccos((tt.cos(2 * np.pi * n) + alpha) /
(1 + alpha * tt.cos(2 * np.pi * n))) + loc
return tt.switch(n < 0.5, phi, 2 * np.pi - phi)
def log(self, X, Y):
V = self.proj(X, Y - X)
dists = tensor.arccos((X * Y).sum(0))
norms = tensor.sqrt((V ** 2).sum(0)).real
factors = dists / norms
# For very close points, dists is almost equal to norms, but because
# they are both almost zero, the division above can return NaN's. To
# avoid that, we force those ratios to 1.
factors[dists <= 1e-6] = 1
return V * factors
def loss(self, y, output):
print 'Calling SentenceLSTMLayers.loss()...'
# y is a single output. No support for minibatches as of yet.
W_dist, W_angle = 0.5, 0.5
assert output.ndim == 1
y_ = assert_op(y, T.eq(y.shape[0], output.shape[0]), T.eq(y.shape[1], 1))
loss = T.mean((output - y_[:, 0])**2) + T.arccos(T.dot(output, y[:, 0])/(absolute(output)*absolute(y[:, 0])))
loss_ = assert_op(loss, T.eq(loss.ndim, 0))
print 'The dimensions of loss is', loss.ndim
print 'SentenceLSTMLayers.loss() call successful'
return loss_
def calctheta(self, vec):
try:
return self.CALCTHETA(vec)
except: # Else build function
VEC = T.vector()
calctheta = T.arccos(
T.clip(VEC[2] / T.sqrt(VEC[0]**2 + VEC[1]**2 + VEC[2]**2),
-1.0, 1.0))
self.CALCTHETA = theano.function(
[VEC], calctheta) # function is compiled to calculate theta
return self.CALCTHETA(vec)
def localdepth(self, theta, phi):
try: # If depth function has been compiled
return self.DEPTH(theta, phi)
except:
############################################################################
########################## Define depth function ###########################
############################################################################
print "Setting up and compiling intrinsic surface function... sit tight.\n"
self.depth = (
(self.MAG * T.exp(-self.BETA * T.arccos(
T.clip(T.dot(self.Si, [self.refX, self.refY, self.refZ]),
-1.0, 1.0))**2)).sum() /
(T.exp(-self.BETA * T.arccos(
T.clip(T.dot(self.Si, [self.refX, self.refY, self.refZ]),
-1.0, 1.0))**2)).sum())
self.DEPTH = theano.function(
[self.THETA, self.PHI],
self.depth) # depth function is compiled here
return self.DEPTH(theta, phi)
def get_arc_cosine_penalty(self):
"""Calculate the arccosine distance in [0, 1].
0: the two vectors are very similar. (have the same orientation)
1: the two vectors are very disimilar (have the opposite orientation).
The cosine similarity does not take in consideration the magnitude
of the vectors. It considers only thier orientation (angle).
Therefore, two vectors are similar if they have the same angle.
See: https://en.wikipedia.org/wiki/Cosine_similarity
"""
# tiny value:
# tiny = sharedX_value(np.finfo(dtype=theano.config.floatX).tiny,
# name="tiny")
# the gradient of sqrt at 0 is undefinded (nan).
# use a tiny value instead of 0.
# OLD SOLUTION
# denom = T.sqrt(
# T.sum(self.output1**2, axis=1) * T.sum(self.output2**2, axis=1))
# nomin = (self.output1 * self.output2).sum(1)
# cosine = nomin/denom # the cosine betwen the two vectors
# pi = sharedX_value(np.pi, name="pi")
# minus1 = sharedX_value(-1., name="minus1")
# plus1 = sharedX_value(1. - np.finfo(dtype=theano.config.floatX).eps,
# name="plus1")
# # Need to be clipped. accos() gives nan when sin is close to 1.
# angle = T.arccos(T.clip(
# cosine, minus1.get_value(), plus1.get_value()))/pi
# OLD SOLUTION
# plus1 = sharedX_value(1. - np.finfo(dtype=theano.config.floatX).eps,
# name="plus1")
pi = sharedX_value(np.pi, name="pi")
cosine = T.clip(
((self.output1 * self.output2).sum(axis=1) /
(self._magnitude(self.output1) * self._magnitude(self.output2))),
-1, 1 - 1e-7)
angle = T.clip(T.arccos(cosine) / pi, 0, 1)
return angle
def get_model(parallax=None):
with pm.Model() as model:
if parallax is None:
# Without an actual parallax measurement, we can model the orbit in units of arcseconds
# by providing a fake_parallax and conversion constant
plx = 1 # arcsec
else:
# Below we will run a version of this model where a measurement of parallax is provided
# The measurement is in milliarcsec
m_plx = pm.Bound(pm.Normal, lower=0, upper=100)(
"m_plx", mu=parallax[0], sd=parallax[1], testval=parallax[0]
)
plx = pm.Deterministic("plx", 1e-3 * m_plx)
a_ang = pm.Uniform("a_ang", 0.1, 1.0, testval=0.324)
a = pm.Deterministic("a", a_ang / plx)
# We expect the period to be somewhere in the range of 25 years,
# so we'll set a broad prior on logP
logP = pm.Normal(
"logP", mu=np.log(25 * yr), sd=10.0, testval=np.log(28.8 * yr)
)
P = pm.Deterministic("P", tt.exp(logP))
# For astrometric-only fits, it's generally better to fit in
# p = (Omega + omega)/2 and m = (Omega - omega)/2 instead of omega and Omega
# directly
omega0 = 251.6 * deg - np.pi
Omega0 = 159.6 * deg
p = Angle("p", testval=0.5 * (Omega0 + omega0))
m = Angle("m", testval=0.5 * (Omega0 - omega0))
omega = pm.Deterministic("omega", p - m)
Omega = pm.Deterministic("Omega", p + m)
# For these orbits, it can also be better to fit for a phase angle
# (relative to a reference time) instead of the time of periasteron
# passage directly
phase = Angle("phase", testval=0.0)
tperi = pm.Deterministic("tperi", T0 + P * phase / (2 * np.pi))
# Geometric uiform prior on cos(incl)
cos_incl = pm.Uniform(
"cos_incl", lower=-1, upper=1, testval=np.cos(96.0 * deg)
)
incl = pm.Deterministic("incl", tt.arccos(cos_incl))
ecc = pm.Uniform("ecc", lower=0.0, upper=1.0, testval=0.798)
# Set up the orbit
orbit = xo.orbits.KeplerianOrbit(
a=a * au_to_R_sun,
t_periastron=tperi,
period=P,
incl=incl,
ecc=ecc,
omega=omega,
Omega=Omega,
)
if parallax is not None:
pm.Deterministic("M_tot", orbit.m_total)
# Compute the model in rho and theta
rho_model, theta_model = orbit.get_relative_angles(astro_jds, plx)
pm.Deterministic("rho_model", rho_model)
pm.Deterministic("theta_model", theta_model)
# Add jitter terms to both separation and position angle
log_rho_s = pm.Normal(
"log_rho_s", mu=np.log(np.median(rho_err)), sd=5.0
)
log_theta_s = pm.Normal(
"log_theta_s", mu=np.log(np.median(theta_err)), sd=5.0
)
rho_tot_err = tt.sqrt(rho_err ** 2 + tt.exp(2 * log_rho_s))
theta_tot_err = tt.sqrt(theta_err ** 2 + tt.exp(2 * log_theta_s))
# define the likelihood function, e.g., a Gaussian on both rho and theta
pm.Normal("rho_obs", mu=rho_model, sd=rho_tot_err, observed=rho_data)
# We want to be cognizant of the fact that theta wraps so the following is equivalent to
# pm.Normal("obs_theta", mu=theta_model, observed=theta_data, sd=theta_tot_err)
# but takes into account the wrapping. Thanks to Rob de Rosa for the tip.
theta_diff = tt.arctan2(
tt.sin(theta_model - theta_data), tt.cos(theta_model - theta_data)
)
pm.Normal("theta_obs", mu=theta_diff, sd=theta_tot_err, observed=0.0)
# Set up predicted orbits for later plotting
rho_dense, theta_dense = orbit.get_relative_angles(t_fine, plx)
rho_save = pm.Deterministic("rho_save", rho_dense)
theta_save = pm.Deterministic("theta_save", theta_dense)
# Optimize to find the initial parameters
map_soln = model.test_point
map_soln = xo.optimize(map_soln, vars=[log_rho_s, log_theta_s])
map_soln = xo.optimize(map_soln, vars=[phase])
map_soln = xo.optimize(map_soln, vars=[p, m, ecc])
map_soln = xo.optimize(map_soln, vars=[logP, a_ang, phase])
map_soln = xo.optimize(map_soln)
return model, map_soln
import numpy as np
import scipy.signal as ss
import argparse
import theano
import theano.tensor as T
# Theano functions
# QEA function
x0, x1, x2 = (T.zvector('x0'),T.zvector('x1'), T.zvector('x2'))
IF_FUN = T.arccos((x2 + x0) / (2 * x1 + 1e-16)) / np.pi / 2
QEA_FUN = theano.function([x0, x1, x2], IF_FUN)
def floatx(np_data):
return np.asarray(np_data, dtype=theano.config.floatX)
def qea(im):
"""
Quasi-eigen approximation function
Input
- im : 1d vector that contains a time series
Ouput
- ia : instantaneous amplitude
- ip : instantaneous phase
- ifeq: instantaneous frequency
"""
im = floatx(im.ravel())
# computes analytic signal
H = ss.hilbert(im)
H = im+1j*H
def build_model(self):
print('Building the model')
self.pm_model = pm.Model()
with self.pm_model:
# Mode locations
numax = pm.Normal('numax', mu = self.init['numax'], sigma = 10., testval = self.init['numax'])
alpha = pm.Lognormal('alpha', mu = np.log(self.init['alpha']), sigma = 0.01, testval = self.init['alpha'])
epsilon = pm.Normal('epsilon', mu = self.init['epsilon'], sigma = 1., testval = self.init['epsilon'])
d01 = pm.Lognormal('d01', mu = np.log(self.init['d01']), sigma = 0.1, testval = self.init['d01'])
d02 = pm.Lognormal('d02', mu = np.log(self.init['d02']), sigma = 0.1, testval = self.init['d02'])
sigma0 = pm.HalfCauchy('sigma0', beta = 2., testval = self.init['sigma0'])
sigma1 = pm.HalfCauchy('sigma1', beta = 2., testval = self.init['sigma1'])
sigma2 = pm.HalfCauchy('sigma2', beta = 2., testval = self.init['sigma2'])
f0 = pm.Normal('f0', mu = self.mod.f0([numax, alpha, epsilon, d01, d02]), sigma = sigma0, shape=len(self.mod.n0))
f1 = pm.Normal('f1', mu = self.mod.f1([numax, alpha, epsilon, d01, d02]), sigma = sigma1, shape=len(self.mod.n1))
f2 = pm.Normal('f2', mu = self.mod.f2([numax, alpha, epsilon, d01, d02]), sigma = sigma2, shape=len(self.mod.n2))
# Mode Linewidths
m = pm.Normal('m', self.init['m'], 1., testval = self.init['m'])
c = pm.Normal('c', self.init['c'], 1., testval = self.init['c'])
rho = pm.Lognormal('rho', mu = np.log(self.init['rho']), sigma = 0.1, testval = self.init['rho'])
# ls = pm.TruncatedNormal('ls', mu = np.log(self.init['L']), sigma = 0.1, lower=0., testval = self.init['L'])
mu = pm.gp.mean.Linear(coeffs = m, intercept = c)
cov = tt.sqr(rho) * pm.gp.cov.ExpQuad(1, ls = self.init['L'])
gp = pm.gp.Latent(cov_func = cov, mean_func = mu)
lng = gp.prior('lng', X = self.nf_)
g0 = pm.Deterministic('g0', tt.exp(lng)[0:len(f0_)])
g1 = pm.Deterministic('g1', tt.exp(lng)[len(f0_):len(f0_)+len(f1_)])
g2 = pm.Deterministic('g2', tt.exp(lng)[len(f0_)+len(f1_):])
# Mode Amplitude & Height
w = pm.Lognormal('w', mu = np.log(self.init['w']), sigma = 10., testval=self.init['w'])
A = pm.Lognormal('A', mu = np.log(self.init['A']), sigma = 1., testval=self.init['A'])
V1 = pm.Lognormal('V1', mu = np.log(self.init['V1']), sigma = 0.1, testval=self.init['V1'])
V2 = pm.Lognormal('V2', mu = np.log(self.init['V2']), sigma = 0.1, testval=self.init['V2'])
sigmaA = pm.HalfCauchy('sigmaA', beta = 1., testval = self.init['sigmaA'])
Da0 = pm.Normal('Da0', mu = 0., sigma = 1., shape=len(self.mod.n0))
Da1 = pm.Normal('Da1', mu = 0., sigma = 1., shape=len(self.mod.n1))
Da2 = pm.Normal('Da2', mu = 0., sigma = 1., shape=len(self.mod.n2))
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.Lognormal('xsplit', mu = np.log(self.init['xsplit']), sigma= 0.75, testval = self.init['xsplit'])
cosi = pm.Uniform('cosi', 0., 1., testval = self.init['cosi'])
i = pm.Deterministic('i', tt.arccos(cosi))
split = pm.Deterministic('split', xsplit/tt.sin(i))
# Background treatment
phi = pm.MvNormal('phi', mu=self.phi_, chol=self.phi_cholesky, testval=self.phi_, shape=len(self.phi_))
# Construct model
fit = mod.model([f0, f1, f2, g0, g1, g2, h0, h1, h2, split, i, phi])
like = pm.Gamma('like', alpha=1., beta=1./fit, observed=self.p)
def _get_compiled_theano_functions(N_QUAD_PTS):
# resonance j and k
j, k = T.lscalars('jk')
s = (j - k) / k
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
eta1 = mstar + m1
eta2 = mstar + m2
beta1 = mu1 * T.sqrt(eta1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(eta2 / mstar) / (mu1 + mu2)
# Angle variable for averaging over
psi = T.dvector('psi')
# Dynamical variables:
dyvars = T.vector()
y1, y2, phi1, x1, x2, J1, amd = [dyvars[i] for i in range(7)]
I1 = (y1 * y1 + x1 * x1) / 2
I2 = (y2 * y2 + x2 * x2) / 2
sigma1 = T.arctan2(y1, x1)
sigma2 = T.arctan2(y2, x2)
# Quadrature weights
quad_weights = T.dvector('w')
# Set l=0
l = T.constant(0.)
l1 = l - k * psi / 2
l2 = l + k * psi / 2
pomega1 = (1 + s) * l2 - s * l1 - sigma1
pomega2 = (1 + s) * l2 - s * l1 - sigma2
Gamma1 = I1
Gamma2 = I2
# Resonant semi-major axis ratio
a20 = T.constant(1.0)
a10 = (eta1 / eta2)**(1 / 3) * ((j - k) / j)**(2 / 3) * a20
Lambda20 = beta2 * T.sqrt(a20)
Lambda10 = beta1 * T.sqrt(a10)
Ltot = Lambda10 + Lambda20
Psi0 = 0.5 * k * (Lambda20 - Lambda10)
Psi = Psi0 - k * (s + 1 / 2) * amd
L1 = Ltot / 2 + J1 / 2 - Psi / k - s * (I1 + I2)
L2 = Ltot / 2 + J1 / 2 + Psi / k + (1 + s) * (I1 + I2)
# Choose z axis along direction of total angular momentum
r2_by_r1 = (L2 - L1 - Gamma2 + Gamma1) / (L1 + L2 - Gamma1 - Gamma2 - J1)
rho1 = 0.5 * J1 * (1 + r2_by_r1)
rho2 = 0.5 * J1 * (1 - r2_by_r1)
G1 = L1 - Gamma1
G2 = L2 - Gamma1
a1 = (L1 / beta1)**2
e1 = T.sqrt(1 - (1 - (Gamma1 / L1))**2)
a2 = (L2 / beta2)**2
e2 = T.sqrt(1 - (1 - (Gamma2 / L2))**2)
cos_inc1 = 1 - rho1 / G1
cos_inc2 = 1 - rho2 / G2
inc1 = T.arccos(cos_inc1)
inc2 = T.arccos(cos_inc2)
Omega1 = l - np.pi / 2 - phi1
Omega2 = l + np.pi / 2 - phi1
omega1 = pomega1 - Omega1
omega2 = pomega2 - Omega2
Hkep = -0.5 * T.sqrt(eta1) * beta1 / a1 - 0.5 * T.sqrt(eta2) * beta2 / a2
ko = KeplerOp()
M1 = l1 - pomega1
M2 = l2 - pomega2
sinf1, cosf1 = ko(M1, e1 + T.zeros_like(M1))
sinf2, cosf2 = ko(M2, e2 + T.zeros_like(M2))
#
n1 = T.sqrt(eta1 / mstar) * a1**(-3 / 2)
n2 = T.sqrt(eta2 / mstar) * a2**(-3 / 2)
Hint_dir, Hint_ind = calc_Hint_components_sinf_cosf(
a1, a2, e1, e2, inc1, inc2, omega1, omega2, Omega1, Omega2, n1, n2,
sinf1, cosf1, sinf2, cosf2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar * a20)
Hpert = (Hint_dir + Hint_ind / mstar).dot(quad_weights)
Htot = Hkep + eps * Hpert
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes, weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(psi, nodes), (quad_weights, weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2, j, k]
ins = [dyvars] + extra_ins
orbels = [
a1, e1, inc1, sigma1 * k, Omega1, a2, e2, inc2, sigma2 * k, Omega2
]
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
Jtens = T.as_tensor(np.pad(_get_Omega_matrix(3), (0, 1), 'constant'))
H_flow_vec = Jtens.dot(gradHtot)
H_flow_jac = Jtens.dot(hessHtot)
##########################
# Compile Theano functions
##########################
actions_fn = theano.function(
inputs=ins,
outputs={'L1':L1,'L1':L2,'Gamma1':Gamma1,'Gamma2':Gamma2,\
'Q1':rho1,'Q2':rho2,'Psi':Psi,'Psi0':Psi0},
givens=givens,
on_unused_input='ignore'
)
orbels_fn = theano.function(inputs=ins,
outputs=orbels,
givens=givens,
on_unused_input='ignore')
Htot_fn = theano.function(inputs=ins,
outputs=Htot,
givens=givens,
on_unused_input='ignore')
Hpert_fn = theano.function(inputs=ins,
outputs=Hpert,
givens=givens,
on_unused_input='ignore')
H_flow_vec_fn = theano.function(inputs=ins,
outputs=H_flow_vec,
givens=givens,
on_unused_input='ignore')
H_flow_jac_fn = theano.function(inputs=ins,
outputs=H_flow_jac,
givens=givens,
on_unused_input='ignore')
return dict({
'orbital_elements': orbels_fn,
'actions': actions_fn,
'Hamiltonian': Htot_fn,
'Hpert': Hpert_fn,
'Hamiltonian_flow': H_flow_vec_fn,
'Hamiltonian_flow_jacobian': H_flow_jac_fn
})
def get_camera_image(self, state, camera_name):
# get camera image
# do ray-sphere and ray-plane intersections
# find cube by using 6 planes, throwing away the irrelevant intersections
# step 1: generate list of rays (1 per pixel)
# focal_point (3,)
# ray_dir (px_hor, px_ver, 3)
# ray_offset (px_hor, px_ver, 3)
camera = self.cameras[camera_name]
positions, velocities, rotations = state.positions, state.velocities, state.rotations
ray_dir = camera["ray_direction"]
ray_offset = camera["ray_offset"]
parent = camera["parent"]
px_ver = ray_dir.shape[0]
px_hor = ray_dir.shape[1]
# WORKPOINT
if parent:
pid = self.objects[parent]
# rotate and move the camera according to its parent
ray_dir = theano_convert_model_to_world_coordinate_no_bias(
ray_dir, rotations[:, pid, :, :])
ray_offset = theano_convert_model_to_world_coordinate(
ray_offset, rotations[:, pid, :, :], positions[:, pid, :])
else:
ray_dir = ray_dir[None, :, :, :]
ray_offset = ray_offset[None, :, :, :]
# step 2a: intersect the rays with all the spheres
has_spheres = (0 != len(self.sphere_parent))
#s_relevant = np.ones(shape=(self.batch_size, px_ver, px_hor, self.sphere_parent.shape[0]))
if has_spheres:
s_pos_vectors = positions[:, None, None, self.sphere_parent, :]
s_rot_matrices = rotations[:, self.sphere_parent, :, :]
L = s_pos_vectors - ray_offset[:, :, :, None, :]
tca = T.sum(L * ray_dir[:, :, :, None, :],
axis=4) # L.dotProduct(ray_dir)
#// if (tca < 0) return false;
d2 = T.sum(L * L, axis=4) - tca * tca
r2 = self.sphere_radius**2
#if (d2 > radius2) return false;
s_relevant = (tca > 0) * (d2[:, :, :, :] < r2[None, None, None, :])
float_s_relevant = T.cast(s_relevant, 'float32')
thc = T.sqrt(
(r2[None, None, None, :] - float_s_relevant * d2[:, :, :, :]))
s_t0 = tca - thc
Phit = ray_offset[:, :, :,
None, :] + s_t0[:, :, :, :,
None] * ray_dir[:, :, :, None, :]
N = (Phit - s_pos_vectors) / self.sphere_radius[None, None,
None, :, None]
N = theano_convert_world_to_model_coordinate_no_bias(
N, s_rot_matrices[:, None, None, :, :, :])
# tex_y en tex_x in [-1,1]
s_tex_x = T.arctan2(N[:, :, :, :, 2], N[:, :, :, :, 0]) / np.pi
s_tex_y = -1. + (2. - eps) * T.arccos(
T.clip(N[:, :, :, :, 1], -1.0, 1.0)) / np.pi
# step 2b: intersect the rays with the cubes (cubes=planes)
# step 2c: intersect the rays with the planes
has_faces = (0 != len(self.face_parent))
if has_faces:
hasparent = [
i for i, par in enumerate(self.face_parent) if par is not None
]
hasnoparent = [
i for i, par in enumerate(self.face_parent) if par is None
]
parents = [
parent for parent in self.face_parent if parent is not None
]
static_fn = numpy_repeat_new_axis(self.face_normal[hasnoparent, :],
self.batch_size)
static_fp = numpy_repeat_new_axis(self.face_point[hasnoparent, :],
self.batch_size)
static_ftx = numpy_repeat_new_axis(
self.face_texture_x[hasnoparent, :], self.batch_size)
static_fty = numpy_repeat_new_axis(
self.face_texture_y[hasnoparent, :], self.batch_size)
if hasparent:
fn = theano_convert_model_to_world_coordinate_no_bias(
self.face_normal[None, hasparent, :],
rotations[:, parents, :, :])
fn = T.concatenate([static_fn, fn], axis=1)
fp = theano_convert_model_to_world_coordinate(
self.face_point[None, hasparent, :],
rotations[:, parents, :, :], positions[:, parents, :])
fp = T.concatenate([static_fp, fp], axis=1)
ftx = theano_convert_model_to_world_coordinate_no_bias(
self.face_texture_x[None, hasparent, :],
rotations[:, parents, :, :])
ftx = T.concatenate([static_ftx, ftx], axis=1)
fty = theano_convert_model_to_world_coordinate_no_bias(
self.face_texture_y[None, hasparent, :],
rotations[:, parents, :, :])
fty = T.concatenate([static_fty, fty], axis=1)
else:
fn = static_fn
fp = static_fp
ftx = static_ftx
fty = static_fty
# reshuffle the face_texture_indexes to match the reshuffling we did above
face_indices = hasnoparent + hasparent
face_texture_index = self.face_texture_index[face_indices]
face_texture_limited = self.face_texture_limited[face_indices]
face_colors = self.face_colors[face_indices, :]
denom = T.sum(fn[:, None, None, :, :] * ray_dir[:, :, :, None, :],
axis=4)
p0l0 = fp[:, None, None, :, :] - ray_offset[:, :, :, None, :]
p_t0 = T.sum(p0l0 * fn[:, None, None, :, :],
axis=4) / (denom + 1e-9)
Phit = ray_offset[:, :, :,
None, :] + p_t0[:, :, :, :,
None] * ray_dir[:, :, :, None, :]
pd = Phit - fp[:, None, None, :, :]
p_tex_x = T.sum(ftx[:, None, None, :, :] * pd, axis=4)
p_tex_y = T.sum(fty[:, None, None, :, :] * pd, axis=4)
# the following only on limited textures
p_relevant = (p_t0 > 0) * (1 -
(1 - (-1 < p_tex_x) * (p_tex_x < 1) *
(-1 < p_tex_y) *
(p_tex_y < 1)) * face_texture_limited)
p_tex_x = ((p_tex_x + 1) % 2.) - 1
p_tex_y = ((p_tex_y + 1) % 2.) - 1
# step 3: find the closest point of intersection for all objects (z-culling)
if has_spheres and has_faces:
relevant = T.concatenate([s_relevant, p_relevant],
axis=3).astype('float32')
tex_x = T.concatenate([s_tex_x, p_tex_x], axis=3)
tex_y = T.concatenate([s_tex_y, p_tex_y], axis=3)
tex_t = np.concatenate(
[self.sphere_texture_index, face_texture_index], axis=0)
t = T.concatenate([s_t0, p_t0], axis=3)
elif has_spheres:
relevant = s_relevant.astype('float32')
tex_x = s_tex_x
tex_y = s_tex_y
tex_t = self.sphere_texture_index
t = s_t0
elif has_faces:
relevant = p_relevant.astype('float32')
tex_x = p_tex_x
tex_y = p_tex_y
tex_t = face_texture_index
t = p_t0
else:
raise NotImplementedError()
mint = T.min(t * relevant + (1. - relevant) * np.float32(1e9), axis=3)
relevant *= (t <= mint[:, :, :, None]) #only use the closest object
# step 4: go into the object's texture and get the corresponding value (see image transform)
x_size, y_size = self.textures.shape[1] - 1, self.textures.shape[2] - 1
tex_x = (tex_x + 1) * x_size / 2.
tex_y = (tex_y + 1) * y_size / 2.
x_idx = T.floor(tex_x)
x_wgh = tex_x - x_idx
y_idx = T.floor(tex_y)
y_wgh = tex_y - y_idx
# if the following are -2,147,483,648 or -9,223,372,036,854,775,808, you have NaN's
x_idx, y_idx = T.cast(x_idx, 'int64'), T.cast(y_idx, 'int64')
textures = T.TensorConstant(type=T.ftensor4,
data=self.textures.astype('float32'),
name='textures')
sample= ( x_wgh * y_wgh )[:,:,:,:,None] * textures[tex_t[None,None,None,:],x_idx+1,y_idx+1,:] + \
( x_wgh * (1-y_wgh))[:,:,:,:,None] * textures[tex_t[None,None,None,:],x_idx+1,y_idx ,:] + \
((1-x_wgh) * y_wgh )[:,:,:,:,None] * textures[tex_t[None,None,None,:],x_idx ,y_idx+1,:] + \
((1-x_wgh) * (1-y_wgh))[:,:,:,:,None] * textures[tex_t[None,None,None,:],x_idx ,y_idx ,:]
# multiply with color of object
colors = np.concatenate([self.sphere_colors, face_colors], axis=0)
if np.min(colors) != 1.: # if the colors are actually used
sample = colors[None, None, None, :, :] * sample
# step 5: return this value
image = T.sum(sample * relevant[:, :, :, :, None], axis=3)
background_color = camera["background_color"]
if background_color is not None:
# find the rays for which no object was relevant. Make them background color
background = background_color[None, None, None, :] * (
1 - T.max(relevant[:, :, :, :], axis=3))[:, :, :, None]
image += background
# do a dimshuffle to closer match the deep learning conventions
image = T.unbroadcast(image, 0, 1, 2, 3).dimshuffle(0, 3, 2, 1)
return image
def _get_compiled_theano_functions(N_QUAD_PTS):
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
eta1 = mstar + m1
eta2 = mstar + m2
beta1 = mu1 * T.sqrt(eta1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(eta2 / mstar) / (mu1 + mu2)
j, k = T.lscalars('jk')
s = (j - k) / k
# Angle variable for averaging over
psi = T.dvector('psi')
# Quadrature weights
quad_weights = T.dvector('w')
# Dynamical variables:
Ndof = 3
Nconst = 1
dyvars = T.vector()
s1, s2, phi, I1, I2, Phi, dRtilde = [
dyvars[i] for i in range(2 * Ndof + Nconst)
]
a20 = T.constant(1.)
a10 = ((j - k) / j)**(2 / 3) * (eta1 / eta2)**(1 / 3) * a20
L10 = beta1 * T.sqrt(a10)
L20 = beta2 * T.sqrt(a20)
Psi = s * L20 + (1 + s) * L10
Rtilde = dRtilde - L10 - L20
####
# angles
####
rtilde = T.constant(0.)
Omega = -1 * rtilde
l1 = phi + k * (1 + s) * psi + Omega
l2 = phi + k * s * psi + Omega
gamma1 = s1 - phi - Omega
gamma2 = s2 - phi - Omega
q1 = 0.5 * np.pi - Omega
q2 = -0.5 * np.pi - Omega
pomega1 = -1 * gamma1
pomega2 = -1 * gamma2
Omega1 = -1 * q1
Omega2 = -1 * q2
omega1 = pomega1 - Omega1
omega2 = pomega2 - Omega2
###
# actions
###
Gamma1 = I1
Gamma2 = I2
L1 = Psi / k - s * (I1 + I2) - s * Phi
L2 = -1 * Psi / k + (1 + s) * (I1 + I2) + (1 + s) * Phi
Cz = -1 * Rtilde
R = L1 + L2 - Gamma1 - Gamma2 - Cz
G1 = L1 - Gamma1
G2 = L2 - Gamma2
r2_by_r1 = (L2 - L1 - Gamma2 + Gamma1) / (L1 + L2 - Gamma1 - Gamma2 - R)
rho1 = 0.5 * R * (1 + r2_by_r1)
rho2 = 0.5 * R * (1 - r2_by_r1)
a1 = (L1 / beta1)**2
e1 = T.sqrt(1 - (1 - (Gamma1 / L1))**2)
a2 = (L2 / beta2)**2
e2 = T.sqrt(1 - (1 - (Gamma2 / L2))**2)
cos_inc1 = 1 - rho1 / G1
cos_inc2 = 1 - rho2 / G2
inc1 = T.arccos(cos_inc1)
inc2 = T.arccos(cos_inc2)
Hkep = -0.5 * T.sqrt(eta1) * beta1 / a1 - 0.5 * T.sqrt(eta2) * beta2 / a2
ko = KeplerOp()
M1 = l1 - pomega1
M2 = l2 - pomega2
sinf1, cosf1 = ko(M1, e1 + T.zeros_like(M1))
sinf2, cosf2 = ko(M2, e2 + T.zeros_like(M2))
#
n1 = T.sqrt(eta1 / mstar) * a1**(-3 / 2)
n2 = T.sqrt(eta2 / mstar) * a2**(-3 / 2)
Hint_dir, Hint_ind, r1, r2, v1, v2 = calc_Hint_components_sinf_cosf(
a1, a2, e1, e2, inc1, inc2, omega1, omega2, Omega1, Omega2, n1, n2,
sinf1, cosf1, sinf2, cosf2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hint_dir + Hint_ind / mstar)
Hpert_av = Hpert.dot(quad_weights)
Htot = Hkep + eps * Hpert_av
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes, weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(psi, nodes), (quad_weights, weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2, j, k]
ins = [dyvars] + extra_ins
orbels = [a1, e1, inc1, k * s1, a2, e2, inc2, k * s2, phi, Omega]
orbels_dict = dict(
zip([
'a1', 'e1', 'inc1', 'theta1', 'a2', 'e2', 'inc2', 'theta2', 'phi'
], orbels))
actions = [L1, L2, Gamma1, Gamma2, rho1, rho2]
actions_dict = dict(
zip(['L1', 'L2', 'Gamma1', 'Gamma2', 'Q1', 'Q2'], actions))
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
Jtens = T.as_tensor(
np.pad(_get_Omega_matrix(Ndof), (0, Nconst), 'constant'))
H_flow_vec = Jtens.dot(gradHtot)
H_flow_jac = Jtens.dot(hessHtot)
##########################
# Compile Theano functions
##########################
orbels_fn = theano.function(inputs=ins,
outputs=orbels_dict,
givens=givens,
on_unused_input='ignore')
actions_fn = theano.function(inputs=ins,
outputs=actions_dict,
givens=givens,
on_unused_input='ignore')
Rtilde_fn = theano.function(inputs=ins,
outputs=Rtilde,
givens=givens,
on_unused_input='ignore')
Htot_fn = theano.function(inputs=ins,
outputs=Htot,
givens=givens,
on_unused_input='ignore')
Hpert_fn = theano.function(inputs=ins,
outputs=Hpert_av,
givens=givens,
on_unused_input='ignore')
Hpert_components_fn = theano.function(
inputs=ins,
outputs=[Hint_dir.dot(quad_weights),
Hint_ind.dot(quad_weights)],
givens=givens,
on_unused_input='ignore')
H_flow_vec_fn = theano.function(inputs=ins,
outputs=H_flow_vec,
givens=givens,
on_unused_input='ignore')
H_flow_jac_fn = theano.function(inputs=ins,
outputs=H_flow_jac,
givens=givens,
on_unused_input='ignore')
return dict({
'orbital_elements': orbels_fn,
'actions': actions_fn,
'Rtilde': Rtilde_fn,
'Hamiltonian': Htot_fn,
'Hpert': Hpert_fn,
'Hpert_components': Hpert_components_fn,
'Hamiltonian_flow': H_flow_vec_fn,
'Hamiltonian_flow_jacobian': H_flow_jac_fn
})
return vals[0], variance # T.maximum(T.var(s, axis=0), eps) # Should eps be here?!
# return T.mean(s, axis=0), variance # T.maximum(T.var(s, axis=0), eps) # Should eps be here?!
def bound_loss(x, tnp = np) :
eps = 1e-9
loss = tnp.maximum(tnp.maximum(eps,x-1), tnp.maximum(eps,-x)) + eps
return tnp.maximum(loss, eps) + eps
params_plus1 = shared(np.random.rand(nbatch, 2))
params_plus2 = shared(np.random.rand(nbatch, 2))
a = Print('invplus(x, params_plus1')(invplus(x, params_plus1))
b = Print('invplus(x, params_plus2')(invplus(y, params_plus2))
eps = 1e-9
a2 = T.arccos(T.clip(a, eps, 1))
b2 = T.arcsin(T.clip(b, eps, 1))
bl1 = bound_loss(a, tnp = T)
bl2 = bound_loss(b, tnp = T)
theta1_group = []
theta2_group = []
theta3_group = []
theta1_group.append(a2[:, 0])
theta1_group.append(b2[:, 0])
delta_group = []
delta_group.append(a2[:, 1])
delta_group.append(b2[:, 1])
delta_single, delta_var = singular(delta_group, name = 'delta')
def __graph_output(self, epoch):
self.update_learning_stats_fn()
######## Learning statistic associated with optimized parameters
for param in self.params:
last_update = self.last_batch_update[param]
this_update = self.this_batch_update[param]
init = self.init[param]
sp = self.subplots[param]
name = str(param)
if param.ndim == 1:
data = param.get_value()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 0].hist(remove=True, x=data, bins=35)
sp[0, 0].set_title('{} at epoch {}'.format(param, epoch),
fontsize=10)
sp[1, 0].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
data = (param - init).eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 1].hist(remove=True, x=data, bins=35)
sp[0, 1].set_title('{}-initial'.format(param), fontsize=10)
sp[1, 1].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
data = this_update.get_value()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 2].hist(remove=True, x=data, bins=35)
sp[0, 2].set_title('{} gradient update'.format(param),
fontsize=10)
sp[1, 2].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
elif param.ndim > 1:
if param.ndim == 2:
param = param.T
last_update = last_update.T
this_update = this_update.T
init = init.T
param = param.flatten(2)
last_update = last_update.flatten(2)
this_update = this_update.flatten(2)
init = init.flatten(2)
# Norms
nrm = T.sqrt((param**2).sum(1))
data = nrm.eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 0].hist(remove=True, x=data, bins=35)
sp[0, 0].set_title(
r'$\Vert w_i \Vert \/ i \in [1,{}]$ at epoch {}'.format(
len(data), epoch),
fontsize=10)
sp[1, 0].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
# Orthonormality
param_nrm = param / nrm[:, None]
data = T.dot(param_nrm, param_nrm.T).flatten().eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 1].hist(remove=True, x=data, bins=60)
sp[0, 1].set_yscale('log', nonposy='clip')
sp[0, 1].set_title(
r'$ {{ \frac{{ {{w_i}}^\intercal w_j }}{{ \Vert w_i \Vert \Vert w_j \Vert }} }} {{\vert}}_{{(t={})}} \/ i,j \in [1,{}] $'
.format(epoch, int(sqrt(len(data)))),
fontsize=10)
sp[1, 1].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
# Rotations with respect to initial state
cos = (param * init).sum(1)
nrm = T.sqrt((param**2).sum(1))
nrm_init = T.sqrt((init**2).sum(1))
fac = cast_x(180. / np.pi)
data = (T.arccos(cos / (nrm * nrm_init)) *
fac).flatten().eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 2].hist(remove=True, x=data, bins=35)
sp[0, 2].set_title(
r'$ \measuredangle ( w^{{(t={})}}_i, w^{{(t=0)}}_i ) \/ i \in [1,{}] $'
.format(epoch, len(data)),
fontsize=10)
sp[1, 2].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
# Update norm
data = T.sqrt((this_update**2).sum(1)).eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 3].hist(remove=True, x=data, bins=35)
sp[0, 3].set_title(
r'$\Vert u_i \Vert \/ i \in [1,{}]$ at epoch {}'.format(
len(data), epoch),
fontsize=10)
sp[1, 3].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
# Update rotation with respect to weight vectors
cos = (param * this_update).sum(1)
nrm = T.sqrt((param**2).sum(1))
nrm_init = T.sqrt((this_update**2).sum(1))
fac = cast_x(180. / np.pi)
data = (T.arccos(cos / (nrm * nrm_init)) *
fac).flatten().eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
try:
sp[0, 4].hist(remove=True, x=data, bins=35)
except:
print(param)
print(data.shape)
raise
sp[0, 4].set_title(
r'$ \measuredangle ( w^{{(t={})}}_i, u^{{(t={})}}_i ) \/ i \in [1,{}] $'
.format(epoch, epoch, len(data)),
fontsize=10)
sp[1, 4].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
# Update rotation if this update with respect to the last
cos = (this_update * last_update).sum(1)
nrm_this = T.sqrt((last_update**2).sum(1))
nrm_last = T.sqrt((this_update**2).sum(1))
fac = cast_x(180. / np.pi)
data = (T.arccos(cos / (nrm_this * nrm_last)) *
fac).flatten().eval()
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 5].hist(remove=True, x=data, bins=35)
sp[0, 5].set_title(
r'$ \measuredangle ( u^{{(t={})}}_i, u^{{(t={})}}_i ) \/ i \in [1,{}] $'
.format(epoch, epoch - 1, len(data)),
fontsize=10)
sp[1, 5].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()))
else:
continue
sp.savefig(join(
self.output_path, '{}_{}_learning_stats_{}.png'.format({
0:
'unsupervised',
1:
'supervised'
}[self.supervised], self.model_id, name)),
dpi=100)
######## Learning statistic associated with optimized parameters
if self.debug_nodes:
outputs = self.debug_fn()
for (name, node), data in zip(list(self.debug_nodes.items()),
outputs):
sp = self.subplots[node]
data = data.flatten()
nonzeros = float((data != 0).mean())
p005, median, p995 = np.percentile(data, [0.5, 50, 99.5])
sp[0, 0].hist(remove=True, x=data, bins=60)
sp[0, 0].set_yscale('log', nonposy='clip')
sp[0, 0].set_title('{} at t={}'.format(name, epoch),
fontsize=6)
sp[1, 0].add_point(p005=(epoch, p005),
median=(epoch, median),
p995=(epoch, p995),
std=(epoch, data.std()),
nonzero=(epoch, nonzeros))
sp[1,
0].set_title('Non-zero = {:0.4f}%'.format(nonzeros * 100),
fontsize=8)
sp.savefig(join(self.output_path, name + '.png'), dpi=100)
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.kepler_op = KeplerOp(**kwargs)
# 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
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
# The Jacobian for the transform cos(i) -> b
self.dcosidb = 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 = tt.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 = tt.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 = tt.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 = 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.t0
self.sin_incl = tt.sin(self.incl)
##### print(f"start position of real C_alpha trace within loaded protein: {rand}")
##### cas_real = cas_real[rand: rand+n] #####################################
# Vertical stack to concatenate list of lists of coordinates into np array
cas_real_array = np.vstack(cas_real)
cas_real_array_centered = center(cas_real_array)
M_obs = cas_real_array_centered
###########
with pm.Model() as inner_model:
### 1. prior over mean M
x1 = pm.Uniform("x1", 0, 1, shape=n)
theta = 2 * np.pi * x1
x2 = pm.Uniform("x2", 0, 1, shape=n)
phi = tt.arccos(1 - 2 * x2)
x = tt.sin(phi) * tt.cos(theta)
y = tt.sin(phi) * tt.sin(theta)
z = tt.cos(phi)
# stack the 3 coordinate-column-vectors horizontally to get the n*3 matrix of all C_alpha positions
# adjust length of unit vectors to 3.8 A (average C_alpha distance)
cas = pm.Deterministic("cas", 3.8 * tt.stack([x, y, z], axis=1))
# make a C_alpha-trace out of the C_alpha positions lying on the sphere with radius 3.8
cas_trace = tt.extra_ops.cumsum(cas, axis=0)
# Move center of mass of C_alpha trace to origin
M = cas_trace - tt.mean(cas_trace, axis=0)
def acos(x): return T.arccos(x)
logP_inner = pm.Uniform("logP_inner",
lower=0,
upper=np.log(50.0),
testval=np.log(34.879)) # days
P_inner = pm.Deterministic("P_inner", tt.exp(logP_inner))
e_inner = pm.Uniform("e_inner", lower=0, upper=1, testval=0.63)
omega_inner = Angle("omega_inner", testval=1.42) # omega_Aa
Omega_inner = Angle("Omega_inner", testval=1.99)
cos_incl_inner = pm.Uniform("cos_incl_inner",
lower=-1.0,
upper=1.0,
testval=0.67)
incl_inner = pm.Deterministic("incl_inner", tt.arccos(cos_incl_inner))
MAb = pm.Normal("MAb", mu=0.29, sd=0.5) # solar masses
t_periastron_inner = pm.Uniform("t_periastron_inner",
lower=4050.0,
upper=4100.0,
testval=4073.0) # + 2400000 + jd0
orbit_inner = xo.orbits.KeplerianOrbit(
a=a_inner * au_to_R_sun,
period=P_inner,
ecc=e_inner,
t_periastron=t_periastron_inner,
omega=omega_inner,
Omega=Omega_inner,
def _get_compiled_theano_functions():
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
eta1 = mstar + m1
eta2 = mstar + m2
beta1 = mu1 * T.sqrt(eta1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(eta2 / mstar) / (mu1 + mu2)
# Dynamical variables:
dyvars = T.vector()
l1, l2, y1, y2, Omega, L1, L2, x1, x2, Rtilde = [
dyvars[i] for i in range(10)
]
Gamma1 = 0.5 * (x1 * x1 + y1 * y1)
Gamma2 = 0.5 * (x2 * x2 + y2 * y2)
gamma1 = T.arctan2(y1, x1)
gamma2 = T.arctan2(y2, x2)
Cz = -1 * Rtilde
R1 = Gamma1
R2 = Gamma2
R = L1 + L2 - R1 - R2 - Cz
G1 = L1 - Gamma1
G2 = L2 - Gamma2
r2_by_r1 = (L2 - L1 - R2 + R1) / (L1 + L2 - R1 - R2 - R)
rho1 = 0.5 * R * (1 + r2_by_r1)
rho2 = 0.5 * R * (1 - r2_by_r1)
a1 = (L1 / beta1)**2
e1 = T.sqrt(1 - (1 - (Gamma1 / L1))**2)
a2 = (L2 / beta2)**2
e2 = T.sqrt(1 - (1 - (Gamma2 / L2))**2)
cos_inc1 = 1 - rho1 / G1
cos_inc2 = 1 - rho2 / G2
inc1 = T.arccos(cos_inc1)
inc2 = T.arccos(cos_inc2)
l1_r = l1 - Omega
l2_r = l2 - Omega
Omega1_r = T.constant(np.pi / 2) - Omega
Omega2_r = Omega1_r - T.constant(np.pi)
pomega1 = -1 * gamma1
pomega2 = -1 * gamma2
pomega1_r = pomega1 - Omega
pomega2_r = pomega2 - Omega
omega1 = pomega1_r - Omega1_r
omega2 = pomega2_r - Omega2_r
Hkep = -0.5 * T.sqrt(eta1) * beta1 / a1 - 0.5 * T.sqrt(eta2) * beta2 / a2
ko = KeplerOp()
M1 = l1_r - pomega1_r
M2 = l2_r - pomega2_r
sinf1, cosf1 = ko(M1, e1 + T.zeros_like(M1))
sinf2, cosf2 = ko(M2, e2 + T.zeros_like(M2))
#
n1 = T.sqrt(eta1 / mstar) * a1**(-3 / 2)
n2 = T.sqrt(eta2 / mstar) * a2**(-3 / 2)
Hint_dir, Hint_ind, r1, r2, v1, v2 = calc_Hint_components_sinf_cosf(
a1, a2, e1, e2, inc1, inc2, omega1, omega2, Omega1_r, Omega2_r, n1, n2,
sinf1, cosf1, sinf2, cosf2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hint_dir + Hint_ind / mstar)
Htot = Hkep + eps * Hpert
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2]
givens = []
ins = [dyvars] + extra_ins
orbels = [
a1, e1, inc1, l1_r, pomega1_r, Omega1_r, a2, e2, inc2, l2_r, pomega2_r,
Omega2_r
]
orbels_dict = dict(
zip([
'a1', 'e1', 'inc1', 'l1', 'pomega1', 'Omega1', 'a2', 'e2', 'inc2',
'l2', 'pomega2', 'Omega2'
], orbels))
actions = [L1, L2, Gamma1, Gamma2, rho1, rho2]
actions_dict = dict(
zip(['L1', 'L2', 'Gamma1', 'Gamma2', 'Q1', 'Q2'], actions))
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
Jtens = T.as_tensor(_get_Omega_matrix(5))
H_flow_vec = Jtens.dot(gradHtot)
H_flow_jac = Jtens.dot(hessHtot)
##########################
# Compile Theano functions
##########################
orbels_fn = theano.function(inputs=ins,
outputs=orbels_dict,
givens=givens,
on_unused_input='ignore')
actions_fn = theano.function(inputs=ins,
outputs=actions_dict,
givens=givens,
on_unused_input='ignore')
rv1_fn = theano.function(inputs=ins,
outputs=r1 + v1,
givens=givens,
on_unused_input='ignore')
rv2_fn = theano.function(inputs=ins,
outputs=r2 + v2,
givens=givens,
on_unused_input='ignore')
Htot_fn = theano.function(inputs=ins,
outputs=Htot,
givens=givens,
on_unused_input='ignore')
Hpert_fn = theano.function(inputs=ins,
outputs=Hpert,
givens=givens,
on_unused_input='ignore')
Hpert_components_fn = theano.function(inputs=ins,
outputs=[Hint_dir, Hint_ind],
givens=givens,
on_unused_input='ignore')
H_flow_vec_fn = theano.function(inputs=ins,
outputs=H_flow_vec,
givens=givens,
on_unused_input='ignore')
H_flow_jac_fn = theano.function(inputs=ins,
outputs=H_flow_jac,
givens=givens,
on_unused_input='ignore')
return dict({
'orbital_elements': orbels_fn,
'actions': actions_fn,
'Hamiltonian': Htot_fn,
'Hpert': Hpert_fn,
'Hpert_components': Hpert_components_fn,
'Hamiltonian_flow': H_flow_vec_fn,
'Hamiltonian_flow_jacobian': H_flow_jac_fn,
'positions_and_velocities1': rv1_fn,
'positions_and_velocities2': rv2_fn
})
def cos_loss(x1, x2, types, angular=False):
cossim = cos(x1, x2)
if angular:
cossim = 1 - 2 * T.arccos(cossim - 1e-6) / np.pi
cos_cost = T.switch(types, 1 - cossim, cossim)
return cos_cost
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)
def __init__(self,
period=None, a=None, t0=0.0,
incl=None, b=None, duration=None,
ecc=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.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.t0 = tt.as_tensor_variable(t0)
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()
# 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)
self.tref = self.t0 - self.M0 / 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)
self.tref = self.t0 - self.M0 / self.n
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
self.sin_incl = tt.sin(self.incl)
testval=np.log(34.87846)) # days
P = pm.Deterministic("P", tt.exp(logP))
e = pm.Uniform("e", lower=0, upper=1, testval=0.62)
omega = Angle("omega", testval=80.5 * deg) # omega_Aa
Omega = Angle("Omega", testval=110.0 *
deg) # - pi to pi # estimated assuming same as CB disk
gamma = pm.Uniform("gamma", lower=0, upper=20, testval=10.1) # km/s
# uniform on cos incl. testpoint assuming same as CB disk.
cos_incl = pm.Uniform("cosIncl",
lower=0.0,
upper=1.0,
testval=np.cos(48.0 *
deg)) # radians, 0 to 180 degrees
incl = pm.Deterministic("incl", tt.arccos(cos_incl))
# Since we're doing an RV + astrometric fit, M2 now becomes a parameter of the model
# use a bounded normal to enforce positivity
PosNormal = pm.Bound(pm.Normal, lower=0.0)
MAb = PosNormal("MAb", mu=0.3, sd=0.5, testval=0.3) # solar masses
t_periastron = pm.Uniform("tPeri",
lower=1130.0,
upper=1170.0,
testval=1159.00) # + 2400000 days
orbit = xo.orbits.KeplerianOrbit(
a=a * au_to_R_sun,
period=P,
ecc=e,
def make_model(A_re_data,
A_im_data,
E_re_data,
E_im_data,
Tobs,
f0,
fdot,
fddot,
sigma,
hbin,
lnAlow,
lnAhigh,
N,
start_pt={}):
f0_mean = f0
fdot_mean = fdot
fddot_mean = fddot
with pm.Model() as model:
_ = pm.Data('sigma', sigma)
_ = pm.Data('hbin', hbin)
_ = pm.Data('Tobs', Tobs)
_ = pm.Data('N', N)
A_re_data = pm.Data('A_re_data', A_re_data)
A_im_data = pm.Data('A_im_data', A_im_data)
E_re_data = pm.Data('E_re_data', E_re_data)
E_im_data = pm.Data('E_im_data', E_im_data)
n_phi = pm.Normal('n_phi',
mu=zeros(2),
sigma=ones(2),
shape=(2, ),
testval=start_pt.get('n_phi', randn(2)))
phi0 = pm.Deterministic('phi0', tt.arctan2(n_phi[1], n_phi[0]))
dphi_f0 = pm.Normal('dphi_f0', mu=0, sigma=pi, testval=0)
dphi_fdot = pm.Normal('dphi_fdot', mu=0, sigma=pi, testval=0)
dphi_fddot = pm.Normal('dphi_fddot', mu=0, sigma=pi, testval=0)
f0 = pm.Deterministic('f0', f0_mean + dphi_f0 / (2 * pi * Tobs))
fdot = pm.Deterministic('fdot',
fdot_mean + dphi_fdot / (pi * Tobs * Tobs))
fddot = pm.Deterministic(
'fddot', fddot_mean + 3.0 * dphi_fddot / (pi * Tobs * Tobs * Tobs))
cos_iota = pm.Uniform('cos_iota',
lower=-1,
upper=1,
testval=start_pt.get(
'cos_iota', np.random.uniform(low=-1,
high=1)))
iota = pm.Deterministic('iota', tt.arccos(cos_iota))
# This 2-vector gives 2*psi
n_2psi = pm.Normal('n_2psi',
mu=zeros(2),
sigma=ones(2),
shape=(2, ),
testval=start_pt.get('n_2psi', randn(2)))
psi = pm.Deterministic('psi', tt.arctan2(n_2psi[1], n_2psi[0]) / 2)
n_ra_dec = pm.Normal('n_ra_dec',
mu=zeros(3),
sigma=ones(3),
shape=(3, ),
testval=start_pt.get('nhat', randn(3)))
nhat = pm.Deterministic(
'nhat',
n_ra_dec / pmm.sqrt(tt.tensordot(n_ra_dec, n_ra_dec, axes=1)))
_ = pm.Deterministic('phi', tt.arctan2(n_ra_dec[1], n_ra_dec[0]))
_ = pm.Deterministic('theta', tt.arccos(nhat[2]))
lnA = pm.Uniform('lnA',
lower=lnAlow,
upper=lnAhigh,
testval=start_pt.get(
'lnA', np.random.uniform(low=lnAlow,
high=lnAhigh)))
A = pm.Deterministic('A', pmm.exp(lnA))
y_re, y_im = y_fd(Tobs, f0, fdot, fddot, phi0, nhat, cos_iota, psi,
hbin, N)
((X_re, X_im), (Y_re, Y_im),
(Z_re, Z_im)) = XYZ_freq(y_re, y_im, Tobs, hbin, N)
((A_re, A_im), (E_re, E_im),
(T_re, T_im)) = AET_XYZ(X_re, X_im, Y_re, Y_im, Z_re, Z_im)
A_re = pm.Deterministic('A_re', A * A_re)
A_im = pm.Deterministic('A_im', A * A_im)
E_re = pm.Deterministic('E_re', A * E_re)
E_im = pm.Deterministic('E_im', A * E_im)
snr = pm.Deterministic(
'SNR',
tt.sqrt(
tt.sum(tt.square(A_re / sigma)) +
tt.sum(tt.square(A_im / sigma)) +
tt.sum(tt.square(E_re / sigma)) +
tt.sum(tt.square(E_im / sigma))))
_ = pm.Normal('A_re_obs', mu=A_re, sigma=sigma, observed=A_re_data)
_ = pm.Normal('A_im_obs', mu=A_im, sigma=sigma, observed=A_im_data)
_ = pm.Normal('E_re_obs', mu=E_re, sigma=sigma, observed=E_re_data)
_ = pm.Normal('E_im_obs', mu=E_im, sigma=sigma, observed=E_im_data)
return model
lower=np.log(20),
upper=np.log(50.0),
testval=np.log(34.88)) # days
P_inner = pm.Deterministic("PInner", tt.exp(logP_inner))
e_inner = pm.Uniform("eInner", lower=0, upper=1, testval=0.63)
omega_inner = Angle("omegaInner", testval=1.415) # omega_Aa
Omega_inner = Angle("OmegaInner", testval=1.821)
# constrained to be i > 90
cos_incl_inner = pm.Uniform("cosInclInner",
lower=-1.0,
upper=0.0,
testval=-0.659)
incl_inner = pm.Deterministic("inclInner", tt.arccos(cos_incl_inner))
MAb = pm.Normal("MAb", mu=0.29, sd=0.5, testval=0.241) # solar masses
t_periastron_inner = pm.Uniform("tPeriastronInner",
lower=1140.0,
upper=1180.0,
testval=1159.57) # + 2400000 + jd0
orbit_inner = xo.orbits.KeplerianOrbit(
a=a_inner * au_to_R_sun,
period=P_inner,
ecc=e_inner,
t_periastron=t_periastron_inner,
omega=omega_inner,
Omega=Omega_inner,
def evaluate(self, state, dt, motor_signals):
positions, velocities, rotations = state.positions, state.velocities, state.rotations
# ALL CONSTRAINTS CAN BE TRANSFORMED TO VELOCITY CONSTRAINTS!
##################
# --- Step 1 --- #
##################
# First, we integrate the applied force F_a acting of each rigid body (like gravity, ...) and
# we obtain some new velocities newv that tend to violate the constraints.
# TODO: integrate other forces
totalforce = np.array(
[0, 0, 0, 0, 0, 0], dtype='float32'
) # total force acting on body outside of constraints
acceleration = np.array(
[0, 0, -9.81, 0, 0, 0],
dtype='float32') # acceleration of the default frame
newv = velocities + dt * acceleration[None, None, :]
originalv = newv
##################
# --- Step 2 --- #
##################
# now enforce the constraints by having corrective impulses
# convert mass matrices to world coordinates
# changes every timestep
M00 = self.lower_inertia_inv
M01 = T.zeros(shape=(self.batch_size, self.num_moving_bodies, 3, 3))
M10 = M01
M11 = T.sum(rotations[:, :, :, None, :, None] *
self.upper_inertia_inv[:, :, :, :, None, None] *
rotations[:, :, None, :, None, :],
axis=(2, 3))
M0 = T.concatenate([M00, M01], axis=3)
M1 = T.concatenate([M10, M11], axis=3)
M = T.concatenate([M0, M1], axis=2)
# constraints are first dimension! We will need to stack them afterwards!
J = [
np.zeros((self.batch_size, 6), dtype="float32")
for _ in xrange(2 * self.num_constraints)
] # 0 constraints x 0 bodies x 2 objects x 6 velocities
b_res = [
np.zeros((self.batch_size, ), dtype="float32")
for _ in xrange(self.num_constraints)
] # 0 constraints x 0 bodies
b_error = [
np.zeros((self.batch_size, ), dtype="float32")
for _ in xrange(self.num_constraints)
] # 0 constraints x 0 bodies
C = [
np.zeros((self.batch_size, ), dtype="float32")
for _ in xrange(self.num_constraints)
] # 0 constraints x 0 bodies
c_idx = 0
for constraint, references, parameters in self.constraints:
idx1 = references[0]
idx2 = references[1]
follows_Newtons_third_law = (idx1 is not None) and (idx2
is not None)
# If connected to universe, idx2 is None
if idx2 is None:
idx1, idx2 = idx1, idx1
if idx1 is None:
idx1, idx2 = idx2, idx2
if constraint == "ball-and-socket" or constraint == "hinge" or constraint == "fixed":
r1 = parameters["joint_in_model1_coordinates"][None, :].astype(
'float32')
r2 = parameters["joint_in_model2_coordinates"][None, :]
r1x = theano_convert_model_to_world_coordinate_no_bias(
r1, rotations[:, idx1, :, :])
r2x = theano_convert_model_to_world_coordinate_no_bias(
r2, rotations[:, idx2, :, :])
ss_r1x = single_skew_symmetric(r1x)
ss_r2x = single_skew_symmetric(r2x)
batched_eye = numpy_repeat_new_axis(np.eye(3, dtype='float32'),
self.batch_size)
complete_J1 = T.concatenate([-batched_eye, ss_r1x], axis=1)
complete_J2 = T.concatenate([batched_eye, -ss_r2x], axis=1)
error = positions[:, idx2, :] + r2x - positions[:,
idx1, :] - r1x
for i in xrange(3):
J[2 * (c_idx + i) + 0] = complete_J1[:, :, i]
J[2 * (c_idx + i) + 1] = complete_J2[:, :, i]
b_error[c_idx + i] = error[:, i]
c_idx += 3
if constraint == "parallel" or constraint == "plane" or constraint == "slider" or constraint == "fixed":
batched_eye = numpy_repeat_new_axis(np.eye(3, dtype='float32'),
self.batch_size)
batched_zeros = numpy_repeat_new_axis(
np.zeros((3, 3), dtype='float32'), self.batch_size)
complete_J1 = np.concatenate([batched_zeros, -batched_eye],
axis=1)
complete_J2 = np.concatenate([batched_zeros, batched_eye],
axis=1)
for i in xrange(3):
J[2 * (c_idx + i) + 0] = complete_J1[:, :, i]
J[2 * (c_idx + i) + 1] = complete_J2[:, :, i]
#TODO: this is np?
#rot_current = theano_dot_last_dimension_matrices(rotations[:,idx2,:,:], rotations[:,idx1,:,:].dimshuffle(0,2,1))
#rot_diff = np.dot(rot_current, parameters['rot_init'].T)
#cross = rot_diff.T - rot_diff
# TODO: add stabilization of this constraint
b_error[c_idx] = np.zeros(
shape=(self.batch_size, )) #cross[1,2]
b_error[c_idx + 1] = np.zeros(
shape=(self.batch_size, )) #cross[2,0]
b_error[c_idx + 2] = np.zeros(
shape=(self.batch_size, )) #cross[0,1]
c_idx += 3
if constraint == "plane" or constraint == "slider":
if follows_Newtons_third_law:
n1 = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis1_in_model1_coordinates'],
rotations[:, idx1, :, :])
else:
n1 = parameters['axis1_in_model1_coordinates']
n1 = numpy_repeat_new_axis(n1, self.batch_size)
complete_J1 = T.concatenate(
[-n1, T.zeros(shape=(self.batch_size, 3))], axis=1)
complete_J2 = -complete_J1
if follows_Newtons_third_law:
J[2 * c_idx + 0] = complete_J1
J[2 * c_idx + 1] = complete_J2
if follows_Newtons_third_law:
orig_error = theano_convert_model_to_world_coordinate_no_bias(
parameters['trans_init_in_model2'],
rotations[:, idx2, :, :])
pos_error = positions[:,
idx2, :] - positions[:,
idx1, :] - orig_error
else:
orig_error = parameters['trans_init']
orig_error = numpy_repeat_new_axis(orig_error,
self.batch_size)
pos_error = positions[:, idx2, :] - orig_error
b_error[c_idx] = theano_dot_last_dimension_vectors(
pos_error, n1)
c_idx += 1
if constraint == "slider":
if follows_Newtons_third_law:
n2 = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis2_in_model1_coordinates'],
rotations[:, idx1, :, :])
else:
n2 = parameters['axis2_in_model1_coordinates']
n2 = numpy_repeat_new_axis(n2, self.batch_size)
complete_J1 = T.concatenate(
[-n2, T.zeros(shape=(self.batch_size, 3))], axis=1)
complete_J2 = -complete_J1
if follows_Newtons_third_law:
J[2 * c_idx + 0] = complete_J1
J[2 * c_idx + 1] = complete_J2
if follows_Newtons_third_law:
orig_error = theano_convert_model_to_world_coordinate_no_bias(
parameters['trans_init_in_model2'],
rotations[:, idx2, :, :])
pos_error = positions[:,
idx2, :] - positions[:,
idx1, :] - orig_error
else:
orig_error = parameters['trans_init']
orig_error = numpy_repeat_new_axis(orig_error,
self.batch_size)
pos_error = positions[:, idx2, :] - orig_error
b_error[c_idx] = theano_dot_last_dimension_vectors(
pos_error, n2)
c_idx += 1
if constraint == "hinge":
a2x = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis_in_model2_coordinates'][None, :],
rotations[:, idx2, :, :])
b1x = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis1_in_model1_coordinates'][None, :],
rotations[:, idx1, :, :])
c1x = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis2_in_model1_coordinates'][None, :],
rotations[:, idx1, :, :])
ss_a2x = single_skew_symmetric(a2x)
batched_zeros = numpy_repeat_new_axis(
np.zeros((3, ), dtype='float32'), self.batch_size)
J[2 * (c_idx + 0) + 0] = T.concatenate([
batched_zeros,
-theano_dot_last_dimension_vector_matrix(b1x, ss_a2x)
],
axis=1)
J[2 * (c_idx + 0) + 1] = T.concatenate([
batched_zeros,
theano_dot_last_dimension_vector_matrix(b1x, ss_a2x)
],
axis=1)
J[2 * (c_idx + 1) + 0] = T.concatenate([
batched_zeros,
-theano_dot_last_dimension_vector_matrix(c1x, ss_a2x)
],
axis=1)
J[2 * (c_idx + 1) + 1] = T.concatenate([
batched_zeros,
theano_dot_last_dimension_vector_matrix(c1x, ss_a2x)
],
axis=1)
b_error[c_idx + 0] = theano_dot_last_dimension_vectors(
a2x, b1x)
b_error[c_idx + 1] = theano_dot_last_dimension_vectors(
a2x, c1x)
c_idx += 2
if constraint == "angular motor":
ac = parameters['axis_in_model2_coordinates'][None, :]
a = theano_convert_model_to_world_coordinate_no_bias(
ac, rotations[:, idx2, :, :])
# TODO: remove dimshuffle(0,2,1) by using batched_dot
rot_current = theano_dot_last_dimension_matrices(
rotations[:, idx2, :, :],
rotations[:, idx1, :, :].dimshuffle(0, 2, 1))
rot_init = numpy_repeat_new_axis(parameters['rot_init'].T,
self.batch_size)
rot_diff = theano_dot_last_dimension_matrices(
rot_current, rot_init)
traces = rot_diff[:, 0, 0] + rot_diff[:, 1, 1] + rot_diff[:, 2,
2]
# grad when x=-1 or x=1 does not exist for arccos
theta2 = T.arccos(T.clip(0.5 * (traces - 1), -1 + eps,
1 - eps))
cross = rot_diff.dimshuffle(0, 2, 1) - rot_diff
dot2 = cross[:, 1,
2] * ac[:,
0] + cross[:, 2,
0] * ac[:,
1] + cross[:, 0,
1] * ac[:,
2]
theta = ((dot2 > 0) * 2 - 1) * theta2
batched_zeros = numpy_repeat_new_axis(
np.zeros((3, ), dtype='float32'), self.batch_size)
J[2 * c_idx + 0] = T.concatenate([batched_zeros, -a], axis=1)
J[2 * c_idx + 1] = T.concatenate([batched_zeros, a], axis=1)
motor_signal = motor_signals[:, parameters["motor_id"]]
if "min" in parameters and "max" in parameters:
motor_min = (parameters["min"] / 180. * np.pi)
motor_max = (parameters["max"] / 180. * np.pi)
motor_signal = T.clip(motor_signal, motor_min,
motor_max).astype('float32')
def smallestSignedAngleBetween(x, y):
a1 = (x - y) % np.float32(2 * np.pi)
b1 = (y - x) % np.float32(2 * np.pi)
return T.minimum(a1, b1) * ((a1 > b1) * 2 - 1)
error_signal = -smallestSignedAngleBetween(theta, motor_signal)
if parameters["type"] == "velocity":
b_error[c_idx] = motor_signal
elif parameters["type"] == "position":
if "delta" in parameters and "motor_velocity" in parameters:
velocity = parameters["motor_velocity"] / 180. * np.pi
b_error[c_idx] = dt * T.clip(
(abs(error_signal) > parameters["delta"]) *
error_signal * parameters["motor_gain"], -velocity,
velocity)
else:
b_error[c_idx] = dt * error_signal * parameters[
"motor_gain"]
c_idx += 1
if constraint == "linear motor":
ac = parameters['axis_in_model2_coordinates'][None, :]
a = theano_convert_model_to_world_coordinate_no_bias(
ac, rotations[:, idx2, :, :])
batched_zeros = numpy_repeat_new_axis(
np.zeros((3, ), dtype='float32'), self.batch_size)
if follows_Newtons_third_law:
J[2 * c_idx + 0] = T.concatenate([-a, batched_zeros],
axis=1)
J[2 * c_idx + 1] = T.concatenate([a, batched_zeros], axis=1)
if follows_Newtons_third_law:
position = positions[:,
idx2, :] - positions[:,
idx1, :] - parameters[
'pos_init']
else:
position = positions[:, idx2, :] - parameters['pos_init']
motor_signal = motor_signals[:, parameters["motor_id"]]
if "min" in parameters and "max" in parameters:
motor_min = parameters["min"]
motor_max = parameters["max"]
motor_signal = T.clip(motor_signal, motor_min, motor_max)
error_signal = theano_dot_last_dimension_vectors(
position, a) - motor_signal
if parameters["servo"] == "velocity":
b_error[c_idx] = motor_signal
elif parameters["servo"] == "position":
if "delta" in parameters and "motor_velocity" in parameters:
velocity = parameters["motor_velocity"]
b_error[c_idx] = dt * T.clip(
(abs(error_signal) > parameters["delta"]) *
error_signal * parameters["motor_gain"], -velocity,
velocity)
else:
b_error[c_idx] = dt * error_signal * parameters[
"motor_gain"]
c_idx += 1
if constraint == "angular limit":
angle = parameters["angle"] / 180. * np.pi
ac = parameters['axis_in_model2_coordinates'][None, :]
a = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis_in_model2_coordinates'],
rotations[:, idx2, :, :])
rot_current = theano_dot_last_dimension_matrices(
rotations[:, idx2, :, :],
rotations[:, idx1, :, :].dimshuffle(0, 2, 1))
rot_init = parameters['rot_init'].T
rot_diff = theano_dot_last_dimension_matrices(
rot_current, rot_init)
traces = rot_diff[:, 0, 0] + rot_diff[:, 1, 1] + rot_diff[:, 2,
2]
theta2 = T.arccos(T.clip(0.5 * (traces - 1), -1 + eps,
1 - eps))
cross = rot_diff.dimshuffle(0, 2, 1) - rot_diff
dot2 = cross[:, 1,
2] * ac[:,
0] + cross[:, 2,
0] * ac[:,
1] + cross[:, 0,
1] * ac[:,
2]
theta = ((dot2 > 0) * 2 - 1) * theta2
batched_zeros = numpy_repeat_new_axis(
np.zeros((3, ), dtype='float32'), self.batch_size)
if parameters["angle"] < 0:
if follows_Newtons_third_law:
J[2 * c_idx + 0] = T.concatenate([batched_zeros, -a])
J[2 * c_idx + 1] = T.concatenate([batched_zeros, a])
else:
if follows_Newtons_third_law:
J[2 * c_idx + 0] = T.concatenate([batched_zeros, a])
J[2 * c_idx + 1] = T.concatenate([batched_zeros, -a])
b_error[c_idx] = T.abs_(angle - theta)
if parameters["angle"] > 0:
b_error[c_idx] = angle - theta
self.C[c_idx] = (theta > angle)
else:
b_error[c_idx] = theta - angle
self.C[c_idx] = (theta < angle)
c_idx += 1
if constraint == "linear limit":
offset = parameters["offset"]
if follows_Newtons_third_law:
ac = parameters['axis_in_model1_coordinates'][None, :]
a = theano_convert_model_to_world_coordinate_no_bias(
ac, rotations[:, idx1, :, :])
else:
a = parameters['axis_in_model1_coordinates'][None, :]
if offset < 0:
if follows_Newtons_third_law:
J[2 * c_idx + 0] = T.concatenate([-a, batched_zeros])
J[2 * c_idx + 1] = T.concatenate([a, batched_zeros])
else:
if follows_Newtons_third_law:
J[2 * c_idx + 0] = T.concatenate([a, batched_zeros])
J[2 * c_idx + 1] = T.concatenate([-a, batched_zeros])
if follows_Newtons_third_law:
position = positions[:,
idx2, :] - positions[:,
idx1, :] - parameters[
'pos_init']
else:
position = positions[:, idx2, :] - parameters['pos_init']
current_offset = theano_dot_last_dimension_vectors(position, a)
if parameters["offset"] > 0:
b_error[c_idx] = offset - current_offset
self.C[c_idx] = (current_offset > offset)
else:
b_error[c_idx] = offset - current_offset
self.C[c_idx] = (current_offset < offset)
c_idx += 1
if constraint == "ground":
r = self.radii[idx1].astype('float32')
J[2 * c_idx + 0] = numpy_repeat_new_axis(
np.array([0, 0, 1, 0, 0, 0], dtype='float32'),
self.batch_size)
J[2 * c_idx + 1] = numpy_repeat_new_axis(
np.array([0, 0, 0, 0, 0, 0], dtype='float32'),
self.batch_size)
# TODO: use T.maximum
b_error[c_idx] = T.clip(
positions[:, idx1, Z] - r + parameters["delta"],
np.finfo('float32').min, 0)
b_res[c_idx] = parameters["alpha"] * newv[:, idx1, Z]
C[c_idx] = positions[:, idx1, Z] - r
c_idx += 1
if constraint == "ground" and parameters["mu"] != 0:
r = self.radii[idx1].astype('float32')
for i in xrange(2):
if i == 0:
J[2 * (c_idx + i) + 0] = numpy_repeat_new_axis(
np.array([0, 1, 0, -r, 0, 0], dtype='float32'),
self.batch_size)
else:
J[2 * (c_idx + i) + 0] = numpy_repeat_new_axis(
np.array([1, 0, 0, 0, r, 0], dtype='float32'),
self.batch_size)
J[2 * (c_idx + i) + 1] = numpy_repeat_new_axis(
np.array([0, 0, 0, 0, 0, 0], dtype='float32'),
self.batch_size)
C[c_idx + i] = positions[:, idx1, Z] - r
c_idx += 2
if constraint == "ground" and parameters[
"torsional_friction"] and parameters["mu"] != 0:
r = self.radii[idx1].astype('float32')
J[2 * c_idx + 0] = numpy_repeat_new_axis(
np.array([0, 0, 0, 0, 0, r], dtype='float32'),
self.batch_size)
J[2 * c_idx + 1] = numpy_repeat_new_axis(
np.array([0, 0, 0, 0, 0, 0], dtype='float32'),
self.batch_size)
C[c_idx] = positions[:, idx1, Z] - r
c_idx += 1
zipped_indices = [
j for i in zip(self.zero_index, self.one_index) for j in i
]
mass_matrix = M[:, zipped_indices, :, :].reshape(
shape=(self.batch_size, self.num_constraints, 2, 6, 6))
J = theano_stack_batched_integers_mixed_numpy(
J, expected_shape=(self.num_constraints, 2, self.batch_size,
6)).dimshuffle(2, 0, 1, 3)
C = theano_stack_batched_integers_mixed_numpy(
C, expected_shape=(self.num_constraints,
self.batch_size)).dimshuffle(1, 0)
b_res = theano_stack_batched_integers_mixed_numpy(
b_res, expected_shape=(self.num_constraints,
self.batch_size)).dimshuffle(1, 0)
b_error = theano_stack_batched_integers_mixed_numpy(
b_error, expected_shape=(self.num_constraints,
self.batch_size)).dimshuffle(1, 0)
self.impulses_P = self.warm_start * self.impulses_P
# TODO: batch-dot-product
m_eff = 1. / T.sum(
T.sum(J[:, :, :, None, :] * mass_matrix, axis=4) * J, axis=(2, 3))
k = m_eff * (self.w**2)
c = m_eff * 2 * self.zeta * self.w
CFM = 1. / (c + dt * k)
ERP = dt * k / (c + dt * k)
m_c = 1. / (1. / m_eff + CFM)
b = ERP / dt * b_error + b_res
for iteration in xrange(self.projected_gauss_seidel_iterations):
# this changes every iteration
v = newv[:, zipped_indices, :].reshape(shape=(self.batch_size,
self.num_constraints,
2, 6))
lamb = -m_c * (T.sum(J * v, axis=(2, 3)) + CFM * self.impulses_P +
b)
self.impulses_P += lamb
if self.do_impulse_clipping:
if self.do_friction_clipping:
clipping_force = self.impulses_P[:, self.clipping_idx]
clipping_limit = abs(self.clipping_a * clipping_force +
self.clipping_b * dt)
else:
clipping_limit = self.clipping_b * dt
self.impulses_P = T.clip(self.impulses_P, -clipping_limit,
clipping_limit)
if self.has_conditional_constraints:
applicable = (1.0 * (C <= 0)) * (1 - (self.only_when_positive *
(self.impulses_P <= 0)))
self.impulses_P = self.impulses_P * applicable
# TODO: batch-dot-product
result = T.sum(mass_matrix * J[:, :, :, None, :],
axis=4) * self.impulses_P[:, :, None, None]
result = result.reshape(
(self.batch_size, 2 * self.num_constraints, 6))
r = []
for constraint in self.map_object_to_constraint:
idx_list = np.array(constraint,
dtype='int64') # deal with empty lists
delta_v = T.sum(result[:, idx_list, :], axis=1)
r.append(delta_v)
newv = newv + T.stack(r, axis=1)
#print
#print theano.printing.debugprint(newv)
return newv
def _get_compiled_theano_functions():
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
eta1 = mstar + m1
eta2 = mstar + m2
beta1 = mu1 * T.sqrt(eta1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(eta2 / mstar) / (mu1 + mu2)
j, k = T.lscalars('jk')
s = (j - k) / k
# Dynamical variables:
dyvars = T.vector()
s1, s2, psi, phi, Omega, I1, I2, Psi, Phi, Rtilde = [
dyvars[i] for i in range(10)
]
l1 = phi - 0.5 * k * psi
l2 = phi + 0.5 * k * psi
gamma1 = s1 - (1 + s) * l2 + s * l1
gamma2 = s2 - (1 + s) * l2 + s * l1
Gamma1 = I1
Gamma2 = I2
L1 = Phi / 2 - Psi / k - s * (I1 + I2)
L2 = Phi / 2 + Psi / k + (s + 1) * (I1 + I2)
Cz = -1 * Rtilde
R = L1 + L2 - Gamma1 - Gamma2 - Cz
G1 = L1 - Gamma1
G2 = L2 - Gamma2
r2_by_r1 = (L2 - L1 - Gamma2 + Gamma1) / (L1 + L2 - Gamma1 - Gamma2 - R)
rho1 = 0.5 * R * (1 + r2_by_r1)
rho2 = 0.5 * R * (1 - r2_by_r1)
a1 = (L1 / beta1)**2
e1 = T.sqrt(1 - (1 - (Gamma1 / L1))**2)
a2 = (L2 / beta2)**2
e2 = T.sqrt(1 - (1 - (Gamma2 / L2))**2)
cos_inc1 = 1 - rho1 / G1
cos_inc2 = 1 - rho2 / G2
inc1 = T.arccos(cos_inc1)
inc2 = T.arccos(cos_inc2)
l1_r = l1 - Omega
l2_r = l2 - Omega
Omega1_r = T.constant(np.pi / 2) - Omega
Omega2_r = Omega1_r - T.constant(np.pi)
pomega1 = -1 * gamma1
pomega2 = -1 * gamma2
pomega1_r = pomega1 - Omega
pomega2_r = pomega2 - Omega
omega1 = pomega1_r - Omega1_r
omega2 = pomega2_r - Omega2_r
Hkep = -0.5 * T.sqrt(eta1) * beta1 / a1 - 0.5 * T.sqrt(eta2) * beta2 / a2
ko = KeplerOp()
M1 = l1_r - pomega1_r
M2 = l2_r - pomega2_r
sinf1, cosf1 = ko(M1, e1 + T.zeros_like(M1))
sinf2, cosf2 = ko(M2, e2 + T.zeros_like(M2))
#
n1 = T.sqrt(eta1 / mstar) * a1**(-3 / 2)
n2 = T.sqrt(eta2 / mstar) * a2**(-3 / 2)
Hint_dir, Hint_ind, r1, r2, v1, v2 = calc_Hint_components_sinf_cosf(
a1, a2, e1, e2, inc1, inc2, omega1, omega2, Omega1_r, Omega2_r, n1, n2,
sinf1, cosf1, sinf2, cosf2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hint_dir + Hint_ind / mstar)
Htot = Hkep + eps * Hpert
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2, j, k]
givens = []
ins = [dyvars] + extra_ins
orbels = [
a1, e1, inc1, l1_r, pomega1_r, Omega1_r, a2, e2, inc2, l2_r, pomega2_r,
Omega2_r
]
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
Jtens = T.as_tensor(_get_Omega_matrix(5))
H_flow_vec = Jtens.dot(gradHtot)
H_flow_jac = Jtens.dot(hessHtot)
##########################
# Compile Theano functions
##########################
orbels_fn = theano.function(inputs=ins,
outputs=orbels,
givens=givens,
on_unused_input='ignore')
rv1_fn = theano.function(inputs=ins,
outputs=r1 + v1,
givens=givens,
on_unused_input='ignore')
rv2_fn = theano.function(inputs=ins,
outputs=r2 + v2,
givens=givens,
on_unused_input='ignore')
Htot_fn = theano.function(inputs=ins,
outputs=Htot,
givens=givens,
on_unused_input='ignore')
Hpert_fn = theano.function(inputs=ins,
outputs=Hpert,
givens=givens,
on_unused_input='ignore')
Hpert_components_fn = theano.function(inputs=ins,
outputs=[Hint_dir, Hint_ind],
givens=givens,
on_unused_input='ignore')
H_flow_vec_fn = theano.function(inputs=ins,
outputs=H_flow_vec,
givens=givens,
on_unused_input='ignore')
H_flow_jac_fn = theano.function(inputs=ins,
outputs=H_flow_jac,
givens=givens,
on_unused_input='ignore')
return dict({
'orbital_elements': orbels_fn,
'Hamiltonian': Htot_fn,
'Hpert': Hpert_fn,
'Hpert_components': Hpert_components_fn,
'Hamiltonian_flow': H_flow_vec_fn,
'Hamiltonian_flow_jacobian': H_flow_jac_fn,
'positions_and_velocities1': rv1_fn,
'positions_and_velocities2': rv2_fn
})
def dist(self, X, Y):
XY = tensor.sum((X * Y), axis=0)
XY[XY > 1] = 1
U = tensor.arccos(XY)
return U.norm()
def evaluate(self, dt, positions, velocities, rot_matrices, motor_signals):
# ALL CONSTRAINTS CAN BE TRANSFORMED TO VELOCITY CONSTRAINTS!
##################
# --- Step 1 --- #
##################
# First, we integrate the applied force F_a acting of each rigid body (like gravity, ...) and
# we obtain some new velocities v2' that tends to violate the constraints.
totalforce = np.array(
[0, 0, 0, 0, 0, 0], dtype='float32'
) # total force acting on body outside of constraints
acceleration = np.array(
[0, 0, -9.81, 0, 0, 0],
dtype='float32') # acceleration of the default frame
newv = velocities + dt * acceleration[None, :]
originalv = newv
##################
# --- Step 2 --- #
##################
# now enforce the constraints by having corrective impulses
# convert mass matrices to world coordinates
M = T.zeros(shape=(self.massMatrices.shape[0], 6, 6))
M00 = self.lower_inertia_inv
M01 = T.zeros(shape=(self.massMatrices.shape[0], 3, 3))
M10 = M01
M11 = T.sum(rot_matrices.dimshuffle(0, 1, 'x', 2, 'x') *
self.upper_inertia_inv.dimshuffle(0, 1, 2, 'x', 'x') *
rot_matrices.dimshuffle(0, 'x', 1, 'x', 2),
axis=(1, 2))
M0 = T.concatenate([M00, M01], axis=2)
M1 = T.concatenate([M10, M11], axis=2)
M = T.concatenate([M0, M1], axis=1)
#self.P = np.zeros((self.num_constraints,))# constant
# changes every timestep
J = [np.zeros((1, 6)) for _ in xrange(2 * self.num_constraints)
] # 0 constraints x 2 objects x 6 states
b_res = [0 for _ in xrange(self.num_constraints)] # 0 constraints
b_error = [0 for _ in xrange(self.num_constraints)] # 0 constraints
C = [0 for _ in xrange(self.num_constraints)] # 0 constraints
c_idx = 0
for constraint, references, parameters in self.constraints:
idx1 = references[0]
if references[1] is not None:
idx2 = references[1]
else:
idx2 = None
if constraint == "ball-and-socket" or constraint == "hinge" or constraint == "fixed":
r1x = theano_convert_model_to_world_coordinate_no_bias(
parameters["joint_in_model1_coordinates"],
rot_matrices[idx1, :, :])
r2x = theano_convert_model_to_world_coordinate_no_bias(
parameters["joint_in_model2_coordinates"],
rot_matrices[idx2, :, :])
ss_r1x = single_skew_symmetric(r1x)
ss_r2x = single_skew_symmetric(r2x)
complete_J1 = T.concatenate(
[-np.eye(3, dtype='float32'), ss_r1x])
complete_J2 = T.concatenate(
[np.eye(3, dtype='float32'), -ss_r2x])
error = positions[idx2, :] + r2x - positions[idx1, :] - r1x
for i in xrange(3):
J[2 * (c_idx + i) + 0] = complete_J1[:, i]
J[2 * (c_idx + i) + 1] = complete_J2[:, i]
b_error[c_idx + i] = error[i]
c_idx += 3
if constraint == "slider" or constraint == "fixed":
complete_J1 = np.concatenate([np.zeros((3, 3)),
-np.eye(3)]).astype('float32')
complete_J2 = np.concatenate([np.zeros((3, 3)),
np.eye(3)]).astype('float32')
for i in xrange(3):
J[2 * (c_idx + i) + 0] = complete_J1[:, i]
J[2 * (c_idx + i) + 1] = complete_J2[:, i]
rot_current = np.dot(rot_matrices[idx2, :, :],
rot_matrices[idx1, :, :].T)
rot_diff = np.dot(rot_current, parameters['rot_init'].T)
cross = rot_diff.T - rot_diff
# TODO: add stabilization of this constraint
b_error[c_idx] = 0 #cross[1,2]
b_error[c_idx + 1] = 0 #cross[2,0]
b_error[c_idx + 2] = 0 #cross[0,1]
c_idx += 3
if constraint == "hinge":
a2x = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis_in_model2_coordinates'],
rot_matrices[idx2, :, :])
b1x = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis1_in_model1_coordinates'],
rot_matrices[idx1, :, :])
c1x = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis2_in_model1_coordinates'],
rot_matrices[idx1, :, :])
ss_a2x = single_skew_symmetric(a2x)
J[2 * (c_idx + 0) + 0] = T.concatenate(
[np.zeros((3, ), dtype='float32'), -T.dot(b1x, ss_a2x)])
J[2 * (c_idx + 0) + 1] = T.concatenate(
[np.zeros((3, ), dtype='float32'),
T.dot(b1x, ss_a2x)])
J[2 * (c_idx + 1) + 0] = T.concatenate(
[np.zeros((3, ), dtype='float32'), -T.dot(c1x, ss_a2x)])
J[2 * (c_idx + 1) + 1] = T.concatenate(
[np.zeros((3, ), dtype='float32'),
T.dot(c1x, ss_a2x)])
b_error[c_idx + 0] = T.sum(a2x * b1x)
b_error[c_idx + 1] = T.sum(a2x * c1x)
c_idx += 2
if constraint == "limit":
angle = parameters["angle"] / 180. * np.pi
a = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis_in_model1_coordinates'],
rot_matrices[idx1, :, :])
rot_current = np.dot(rot_matrices[idx2, :, :],
rot_matrices[idx1, :, :].T)
rot_diff = np.dot(rot_current,
quat_to_rot_matrix(parameters['rot_init']).T)
theta2 = np.arccos(0.5 * (np.trace(rot_diff) - 1))
cross = rot_diff.T - rot_diff
dot2 = cross[1, 2] * a[0] + cross[2, 0] * a[1] + cross[
0, 1] * a[2]
theta = ((dot2 > 0) * 2 - 1) * theta2
if parameters["angle"] < 0:
J[2 * c_idx + 0] = np.concatenate(
[np.zeros((3, ), dtype='float32'), -a])
J[2 * c_idx + 1] = np.concatenate(
[np.zeros((3, ), dtype='float32'), a])
else:
J[2 * c_idx + 0] = np.concatenate(
[np.zeros((3, ), dtype='float32'), a])
J[2 * c_idx + 1] = np.concatenate(
[np.zeros((3, ), dtype='float32'), -a])
b_error[c_idx] = np.abs(angle - theta)
if parameters["angle"] > 0:
b_error[c_idx] = angle - theta
C[c_idx] = (theta > angle)
else:
b_error[c_idx] = theta - angle
C[c_idx] = (theta < angle)
c_idx += 1
if constraint == "motor":
a = theano_convert_model_to_world_coordinate_no_bias(
parameters['axis_in_model1_coordinates'],
rot_matrices[idx1, :, :])
rot_current = T.dot(rot_matrices[idx2, :, :],
rot_matrices[idx1, :, :].T)
rot_diff = T.dot(rot_current, parameters['rot_init'].T)
theta2 = T.arccos(
T.clip(0.5 * (T.nlinalg.trace(rot_diff) - 1), -1 + eps,
1 - eps))
cross = rot_diff.T - rot_diff
dot2 = cross[1, 2] * a[0] + cross[2, 0] * a[1] + cross[
0, 1] * a[2]
theta = ((dot2 > 0) * 2 - 1) * theta2
J[2 * c_idx + 0] = T.concatenate(
[np.zeros((3, ), dtype='float32'), -a])
J[2 * c_idx + 1] = T.concatenate(
[np.zeros((3, ), dtype='float32'), a])
motor_signal = motor_signals[parameters["motor_id"]]
motor_min = parameters["min"] / 180. * np.pi
motor_max = parameters["max"] / 180. * np.pi
motor_signal = T.clip(motor_signal, motor_min, motor_max)
if parameters["type"] == "velocity":
b_error[c_idx] = motor_signal
elif parameters["type"] == "position":
if "delta" in parameters and parameters["delta"] > 0:
b_error[c_idx] = dt * (
abs(theta - motor_signal) > parameters["delta"]
) * (theta -
motor_signal) * parameters["motor_velocity"]
else:
b_error[c_idx] = dt * (theta - motor_signal
) * parameters["motor_velocity"]
#print c_idx
c_idx += 1
if constraint == "ground":
r = self.radii[idx1].astype('float32')
J[2 * c_idx + 0] = np.array([0, 0, 1, 0, 0, 0],
dtype='float32')
J[2 * c_idx + 1] = np.array([0, 0, 0, 0, 0, 0],
dtype='float32')
b_error[c_idx] = T.clip(
positions[idx1, Z] - r + parameters["delta"],
np.finfo('float32').min, 0)
b_res[c_idx] = parameters["alpha"] * newv[idx1, Z]
C[c_idx] = positions[idx1, Z] - r
c_idx += 1
if constraint == "ground" and parameters["mu"] != 0:
r = self.radii[idx1].astype('float32')
for i in xrange(2):
if i == 0:
J[2 * (c_idx + i) + 0] = np.array([0, 1, 0, -r, 0, 0],
dtype='float32')
else:
J[2 * (c_idx + i) + 0] = np.array([1, 0, 0, 0, r, 0],
dtype='float32')
J[2 * (c_idx + i) + 1] = np.array([0, 0, 0, 0, 0, 0],
dtype='float32')
C[c_idx + i] = positions[idx1, Z] - r
c_idx += 2
if constraint == "ground" and parameters[
"torsional_friction"] and parameters["mu"] != 0:
r = self.radii[idx1].astype('float32')
J[2 * c_idx + 0] = np.array([0, 0, 0, 0, 0, r],
dtype='float32')
J[2 * c_idx + 1] = np.array([0, 0, 0, 0, 0, 0],
dtype='float32')
C[c_idx] = positions[idx1, Z] - r
c_idx += 1
mass_matrix = T.concatenate(
(T.stack([M[i, None, :, :] for i in self.zero_index], axis=0),
T.stack([M[i, None, :, :] for i in self.one_index], axis=0)),
axis=1)
J = T.stack(J, axis=0).reshape(shape=(self.num_constraints, 2, 6))
C = theano_stack_integers_mixed_numpy(C)
#v = np.zeros((self.num_constraints,2,6)) # 0 constraints x 2 objects x 6 states
b_res = theano_stack_integers_mixed_numpy(b_res)
b_error = theano_stack_integers_mixed_numpy(b_error)
for iteration in xrange(self.num_iterations):
# changes every iteration
v = T.concatenate(
(T.stack([newv[i, None, :] for i in self.zero_index], axis=0),
T.stack([newv[j, None, :] for j in self.one_index], axis=0)),
axis=1)
m_eff = 1. / T.sum(
T.sum(J[:, :, None, :] * mass_matrix, axis=3) * J, axis=(1, 2))
k = m_eff * (self.w**2)
c = m_eff * 2 * self.zeta * self.w
CFM = 1. / (c + dt * k)
ERP = dt * k / (c + dt * k)
m_c = 1. / (1. / m_eff + CFM)
b = ERP / dt * b_error + b_res
#theano_to_print.extend([b[i] for i in [3,7,11,15]])
lamb = -m_c * (T.sum(J * v, axis=(1, 2)) + CFM * self.P + b)
self.P += lamb
#print J[[39,61,65,69],:]
#print np.sum(lamb**2), np.sum(self.P**2)
clipping_force = T.concatenate(
[self.P[j].dimshuffle('x') for j in self.clipping_idx], axis=0)
clipping_limit = abs(self.clipping_a * clipping_force +
self.clipping_b * dt)
self.P = T.clip(self.P, -clipping_limit, clipping_limit)
applicable = (1 - (self.only_when_positive *
(1 - (self.P >= 0)))) * (C <= 0)
result = T.sum(mass_matrix * J[:, :, None, :],
axis=3) * self.P[:, None,
None] * applicable[:, None, None]
#theano_to_print.extend([T.sum(abs(result[i]),axis=(-1,-2)) for i in [3,7,11,15]])
result = result.reshape((2 * self.num_constraints, 6))
#theano_to_print.extend([T.sum(abs(result[i]),axis=(-1)) for i in [6,14,22,30]])
r = []
for i in xrange(len(self.map_object_to_constraint)):
delta_v = T.sum(T.stack(
[result[j, :] for j in self.map_object_to_constraint[i]],
axis=0),
axis=0)
r.append(delta_v)
#theano_to_print.extend([T.sum(abs(newv[i]),axis=(-1)) for i in [4,3,5,11]])
delta_v = T.stack(r, axis=0)
#newv = originalv + delta_v
newv = newv + delta_v
#print
return newv
def __init__(self,
numpy_rng,
theano_rng=None,
n_ins=40 * 3,
layers_types=[ReLU, ReLU, ReLU, ReLU, ReLU],
layers_sizes=[1024, 1024, 1024, 1024],
n_outs=100,
n_embs=2,
loss='cos2',
rho=0.9,
eps=1.E-6,
max_norm=0.,
debugprint=False):
self.layers = []
self.params = []
self.n_layers = len(layers_types)
self.layers_types = layers_types
assert self.n_layers > 0
self.max_norm = max_norm
self._rho = rho # ``momentum'' for adadelta
self._eps = eps # epsilon for adadelta
self._accugrads = [] # for adadelta
self._accudeltas = [] # for adadelta
if theano_rng == None:
theano_rng = RandomStreams(numpy_rng.randint(2**30))
self.x1 = T.fmatrix('x1')
self.x2 = T.fmatrix('x2')
self.x3 = T.fmatrix('x3')
self.y12s = [T.ivector('y12') for _ in n_embs]
self.y13s = [T.ivector('y13') for _ in n_embs]
self.n_embs = n_embs
self.layers_ins = [n_ins] + layers_sizes[:-1]
self.layers_outs = layers_sizes
layer_input1 = self.x1
layer_input2 = self.x2
layer_input3 = self.x3
layer_embs1 = [None for _ in n_embs]
layer_embs2 = [None for _ in n_embs]
layer_embs3 = [None for _ in n_embs]
for layer_ind, (layer_type, n_in, n_out) in enumerate(
zip(layers_types[:-1], self.layers_ins, self.layers_outs)):
this_layer1 = layer_type(rng=numpy_rng,
input=layer_input1,
n_in=n_in,
n_out=n_out) #, cap=6.)
assert hasattr(this_layer1, 'output')
layer_input1 = this_layer1.output
self.params.extend(this_layer1.params)
self._accugrads.extend([
build_shared_zeros(t.shape.eval(), 'accugrad')
for t in this_layer1.params
])
self._accudeltas.extend([
build_shared_zeros(t.shape.eval(), 'accudelta')
for t in this_layer1.params
])
self.layers.append(this_layer1)
this_layer2 = layer_type(rng=numpy_rng,
input=layer_input2,
n_in=n_in,
n_out=n_out,
W=this_layer1.W,
b=this_layer1.b) #, cap=6.)
assert hasattr(this_layer2, 'output')
this_layer3 = layer_type(rng=numpy_rng,
input=layer_input2,
n_in=n_in,
n_out=n_out,
W=this_layer1.W,
b=this_layer1.b) #, cap=6.)
assert hasattr(this_layer3, 'output')
layer_input2 = this_layer2.output
self.layers.append(this_layer2)
layer_input3 = this_layer3.output
self.layers.append(this_layer3)
for i_emb in xrange(n_embs):
emb_layer_type = layers_types[-1]
n_in = layers_sizes[-1]
n_out = n_outs
this_emb_layer1 = emb_layer_type(rng=numpy_rng,
input=layer_input1,
n_in=n_in,
n_out=n_out) #, cap=6.)
assert hasattr(this_emb_layer1, 'output')
layer_embs1[i_emb] = this_emb_layer1.output
self.params.extend(this_emb_layer1.params)
self._accugrads.extend([
build_shared_zeros(t.shape.eval(), 'accugrad')
for t in this_emb_layer1.params
])
self._accudeltas.extend([
build_shared_zeros(t.shape.eval(), 'accudelta')
for t in this_emb_layer1.params
])
this_emb_layer2 = emb_layer_type(rng=numpy_rng,
input=layer_input2,
n_in=n_in,
n_out=n_out,
W=this_emb_layer1.W,
b=this_emb_layer1.b) #, cap=6.)
assert hasattr(this_emb_layer2, 'output')
layer_embs2[i_emb] = this_emb_layer2.output
this_emb_layer3 = emb_layer_type(rng=numpy_rng,
input=layer_input3,
n_in=n_in,
n_out=n_out,
W=this_emb_layer1.W,
b=this_emb_layer1.b) #, cap=6.)
assert hasattr(this_emb_layer3, 'output')
layer_embs3[i_emb] = this_emb_layer3.output
self.layers.append(this_emb_layer1)
self.layers.append(this_emb_layer2)
self.layers.append(this_emb_layer3)
L2 = 0.
for param in self.params:
L2 += T.sum(param**2)
L1 = 0.
for param in self.params:
L1 += T.sum(abs(param))
self.cos2_costs = []
self.acos_costs = []
for i_emb in xrange(n_embs):
y12 = self.y12s[i_emb]
y13 = self.y13s[i_emb]
self.cos_sim_12 = (T.sum(layer_input1 * layer_input2, axis=-1) /
(layer_input1.norm(2, axis=-1) *
layer_input2.norm(2, axis=-1)))
self.cos_sim_13 = (T.sum(layer_input1 * layer_input3, axis=-1) /
(layer_input1.norm(2, axis=-1) *
layer_input3.norm(2, axis=-1)))
self.acos_sim_12 = T.arccos(self.cos_sim_12)
self.acos_sim_13 = T.arccos(self.cos_sim_13)
self.cos2_sim_12 = self.cos_sim_12**2
self.cos2_sim_13 = self.cos_sim_13**2
cos2_sim_cost = (y12+y13)*1. +\
T.switch(y12, self.cos2_sim_12, -self.cos2_sim_12) +\
T.switch(y13, self.cos2_sim_13, -self.cos2_sim_13)
acos_sim_cost = (y12+y13)*1. +\
T.switch(y12, self.acos_sim_12, -self.acos_sim_12) +\
T.switch(y13, self.acos_sim_13, -self.acos_sim_13)
self.cos2_costs.append(cos2_sim_cost)
self.acos_costs.append(acos_sim_cost)
# TODO HERE
self.cos2_sim_cost = T.sum(self.cos2_costs)
self.mean_cos2_sim_cost = T.mean(self.cos2_sim_cost)
self.sum_cos2_sim_cost = T.sum(self.cos2_sim_cost)
self.acos_sim_cost = T.sum(self.acos_costs)
self.mean_acos_sim_cost = T.mean(self.acos_sim_cost)
self.sum_acos_sim_cost = T.sum(self.acos_sim_cost)
if loss == 'cos2':
self.cost = self.sum_cos_cos2_sim_cost
self.mean_cost = self.mean_cos_cos2_sim_cost
elif loss == 'acos':
self.cost = self.sum_cos_sim_cost
self.mean_cost = self.mean_cos_sim_cost
else:
print >> sys.stderr, "NO COST FUNCTION"
sys.exit(-1)
if debugprint:
theano.printing.debugprint(self.cost)
if hasattr(self, 'cost'):
self.cost_training = self.cost
if hasattr(self, 'mean_cost'):
self.mean_cost_training = self.mean_cost
a_ang_inner = tt.dscalar("a_ang_inner") # milliarcsec
# the semi-major axis in au
a_inner = 1e-3 * a_ang_inner / parallax # au
logP_inner = tt.dscalar("logP_inner") # days
P_inner = tt.exp(logP_inner)
e_inner = tt.dscalar("e_inner")
omega_inner = tt.dscalar("omega_inner") # omega_Aa
Omega_inner = tt.dscalar("Omega_inner")
cos_incl_inner = tt.dscalar("cos_incl_inner")
incl_inner = tt.arccos(cos_incl_inner)
MAb = tt.dscalar("MAb")
t_periastron_inner = tt.dscalar("t_periastron_inner")
orbit_inner = xo.orbits.KeplerianOrbit(
a=a_inner * au_to_R_sun,
period=P_inner,
ecc=e_inner,
t_periastron=t_periastron_inner,
omega=omega_inner,
Omega=Omega_inner,
incl=incl_inner,
m_planet=MAb,
)
def __init__(
self,
numpy_rng,
theano_rng=None,
n_ins=40 * 3,
layers_types=[ReLU, ReLU, ReLU, ReLU, ReLU],
layers_sizes=[1024, 1024, 1024, 1024],
n_outs=100,
n_embs=2,
loss="cos2",
rho=0.9,
eps=1.0e-6,
max_norm=0.0,
debugprint=False,
):
self.layers = []
self.params = []
self.n_layers = len(layers_types)
self.layers_types = layers_types
assert self.n_layers > 0
self.max_norm = max_norm
self._rho = rho # ``momentum'' for adadelta
self._eps = eps # epsilon for adadelta
self._accugrads = [] # for adadelta
self._accudeltas = [] # for adadelta
if theano_rng == None:
theano_rng = RandomStreams(numpy_rng.randint(2 ** 30))
self.x1 = T.fmatrix("x1")
self.x2 = T.fmatrix("x2")
self.x3 = T.fmatrix("x3")
self.y12s = [T.ivector("y12") for _ in n_embs]
self.y13s = [T.ivector("y13") for _ in n_embs]
self.n_embs = n_embs
self.layers_ins = [n_ins] + layers_sizes[:-1]
self.layers_outs = layers_sizes
layer_input1 = self.x1
layer_input2 = self.x2
layer_input3 = self.x3
layer_embs1 = [None for _ in n_embs]
layer_embs2 = [None for _ in n_embs]
layer_embs3 = [None for _ in n_embs]
for layer_ind, (layer_type, n_in, n_out) in enumerate(
zip(layers_types[:-1], self.layers_ins, self.layers_outs)
):
this_layer1 = layer_type(rng=numpy_rng, input=layer_input1, n_in=n_in, n_out=n_out) # , cap=6.)
assert hasattr(this_layer1, "output")
layer_input1 = this_layer1.output
self.params.extend(this_layer1.params)
self._accugrads.extend([build_shared_zeros(t.shape.eval(), "accugrad") for t in this_layer1.params])
self._accudeltas.extend([build_shared_zeros(t.shape.eval(), "accudelta") for t in this_layer1.params])
self.layers.append(this_layer1)
this_layer2 = layer_type(
rng=numpy_rng, input=layer_input2, n_in=n_in, n_out=n_out, W=this_layer1.W, b=this_layer1.b
) # , cap=6.)
assert hasattr(this_layer2, "output")
this_layer3 = layer_type(
rng=numpy_rng, input=layer_input2, n_in=n_in, n_out=n_out, W=this_layer1.W, b=this_layer1.b
) # , cap=6.)
assert hasattr(this_layer3, "output")
layer_input2 = this_layer2.output
self.layers.append(this_layer2)
layer_input3 = this_layer3.output
self.layers.append(this_layer3)
for i_emb in xrange(n_embs):
emb_layer_type = layers_types[-1]
n_in = layers_sizes[-1]
n_out = n_outs
this_emb_layer1 = emb_layer_type(rng=numpy_rng, input=layer_input1, n_in=n_in, n_out=n_out) # , cap=6.)
assert hasattr(this_emb_layer1, "output")
layer_embs1[i_emb] = this_emb_layer1.output
self.params.extend(this_emb_layer1.params)
self._accugrads.extend([build_shared_zeros(t.shape.eval(), "accugrad") for t in this_emb_layer1.params])
self._accudeltas.extend([build_shared_zeros(t.shape.eval(), "accudelta") for t in this_emb_layer1.params])
this_emb_layer2 = emb_layer_type(
rng=numpy_rng, input=layer_input2, n_in=n_in, n_out=n_out, W=this_emb_layer1.W, b=this_emb_layer1.b
) # , cap=6.)
assert hasattr(this_emb_layer2, "output")
layer_embs2[i_emb] = this_emb_layer2.output
this_emb_layer3 = emb_layer_type(
rng=numpy_rng, input=layer_input3, n_in=n_in, n_out=n_out, W=this_emb_layer1.W, b=this_emb_layer1.b
) # , cap=6.)
assert hasattr(this_emb_layer3, "output")
layer_embs3[i_emb] = this_emb_layer3.output
self.layers.append(this_emb_layer1)
self.layers.append(this_emb_layer2)
self.layers.append(this_emb_layer3)
L2 = 0.0
for param in self.params:
L2 += T.sum(param ** 2)
L1 = 0.0
for param in self.params:
L1 += T.sum(abs(param))
self.cos2_costs = []
self.acos_costs = []
for i_emb in xrange(n_embs):
y12 = self.y12s[i_emb]
y13 = self.y13s[i_emb]
self.cos_sim_12 = T.sum(layer_input1 * layer_input2, axis=-1) / (
layer_input1.norm(2, axis=-1) * layer_input2.norm(2, axis=-1)
)
self.cos_sim_13 = T.sum(layer_input1 * layer_input3, axis=-1) / (
layer_input1.norm(2, axis=-1) * layer_input3.norm(2, axis=-1)
)
self.acos_sim_12 = T.arccos(self.cos_sim_12)
self.acos_sim_13 = T.arccos(self.cos_sim_13)
self.cos2_sim_12 = self.cos_sim_12 ** 2
self.cos2_sim_13 = self.cos_sim_13 ** 2
cos2_sim_cost = (
(y12 + y13) * 1.0
+ T.switch(y12, self.cos2_sim_12, -self.cos2_sim_12)
+ T.switch(y13, self.cos2_sim_13, -self.cos2_sim_13)
)
acos_sim_cost = (
(y12 + y13) * 1.0
+ T.switch(y12, self.acos_sim_12, -self.acos_sim_12)
+ T.switch(y13, self.acos_sim_13, -self.acos_sim_13)
)
self.cos2_costs.append(cos2_sim_cost)
self.acos_costs.append(acos_sim_cost)
# TODO HERE
self.cos2_sim_cost = T.sum(self.cos2_costs)
self.mean_cos2_sim_cost = T.mean(self.cos2_sim_cost)
self.sum_cos2_sim_cost = T.sum(self.cos2_sim_cost)
self.acos_sim_cost = T.sum(self.acos_costs)
self.mean_acos_sim_cost = T.mean(self.acos_sim_cost)
self.sum_acos_sim_cost = T.sum(self.acos_sim_cost)
if loss == "cos2":
self.cost = self.sum_cos_cos2_sim_cost
self.mean_cost = self.mean_cos_cos2_sim_cost
elif loss == "acos":
self.cost = self.sum_cos_sim_cost
self.mean_cost = self.mean_cos_sim_cost
else:
print >>sys.stderr, "NO COST FUNCTION"
sys.exit(-1)
if debugprint:
theano.printing.debugprint(self.cost)
if hasattr(self, "cost"):
self.cost_training = self.cost
if hasattr(self, "mean_cost"):
self.mean_cost_training = self.mean_cost
def bound_loss(x, tnp=np):
eps = 1e-9
loss = tnp.maximum(tnp.maximum(eps, x - 1), tnp.maximum(eps, -x)) + eps
return tnp.maximum(loss, eps) + eps
params_plus1 = shared(np.random.rand(nbatch, 2))
params_plus2 = shared(np.random.rand(nbatch, 2))
a = Print("invplus(x, params_plus1")(invplus(x, params_plus1))
b = Print("invplus(x, params_plus2")(invplus(y, params_plus2))
eps = 1e-9
a2 = T.arccos(T.clip(a, eps, 1 - eps))
b2 = T.arcsin(T.clip(b, eps, 1 - eps))
bl1 = bound_loss(a, tnp=T)
bl2 = bound_loss(b, tnp=T)
phi1_group = []
phi2_group = []
phi3_group = []
phi1_group.append(a2[:, 0])
phi1_group.append(b2[:, 0])
delta_group = []
delta_group.append(a2[:, 1])
delta_group.append(b2[:, 1])
delta_single, delta_var = singular(delta_group, name="delta")
def _get_compiled_theano_functions(N_QUAD_PTS):
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
Mstar1 = mstar + m1
Mstar2 = mstar + m2
beta1 = mu1 * T.sqrt(Mstar1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(Mstar2 / mstar) / (mu1 + mu2)
j, k = T.lscalars('jk')
s = (j - k) / k
# Angle variable for averaging over
psi = T.dvector()
# Quadrature weights
quad_weights = T.dvector('w')
# Dynamical variables:
Ndof = 3
Nconst = 1
dyvars = T.vector()
y1, y2, y_inc, x1, x2, x_inc, amd = [
dyvars[i] for i in range(2 * Ndof + Nconst)
]
a20 = T.constant(1.)
a10 = ((j - k) / j)**(2 / 3) * (Mstar1 / Mstar2)**(1 / 3)
L10 = beta1 * T.sqrt(a10)
L20 = beta2 * T.sqrt(a20)
Ltot = L10 + L20
f = L10 / L20
L2res = (Ltot + amd) / (1 + f)
Psi = -k * (s * L2res + (1 + s) * f * L2res)
###
# actions
###
I1 = 0.5 * (x1 * x1 + y1 * y1)
I2 = 0.5 * (x2 * x2 + y2 * y2)
Phi = 0.5 * (x_inc * x_inc + y_inc * y_inc)
L1 = -s * Ltot - Psi / k - s * (I1 + I2 + Phi)
L2 = (1 + s) * Ltot + Psi / k + (1 + s) * (I1 + I2 + Phi)
# Set lambda2=0
l2 = T.constant(0.)
l1 = -1 * k * psi
theta_res = (1 + s) * l2 - s * l1
cos_theta_res = T.cos(theta_res)
sin_theta_res = T.sin(theta_res)
kappa1 = x1 * cos_theta_res + y1 * sin_theta_res
eta1 = y1 * cos_theta_res - x1 * sin_theta_res
kappa2 = x2 * cos_theta_res + y2 * sin_theta_res
eta2 = y2 * cos_theta_res - x2 * sin_theta_res
sigma = x_inc * cos_theta_res + y_inc * sin_theta_res
rho = y_inc * cos_theta_res - x_inc * sin_theta_res
# y = (sigma-i*rho)/sqrt(2)
# = sqrt(Phi) * exp[i (Omega1+Omega2) / 2]
# Malige+ 2002, Eqs 20 and 21
r2byr1 = (L2 - L1 - I2 + I1) / Ltot
sigma1 = rho * T.sqrt(1 + r2byr1) / T.sqrt(2)
sigma2 = -rho * T.sqrt(1 - r2byr1) / T.sqrt(2)
rho1 = -sigma * T.sqrt(1 + r2byr1) / T.sqrt(2)
rho2 = sigma * T.sqrt(1 - r2byr1) / T.sqrt(2)
Xre1 = kappa1 / T.sqrt(L1)
Xim1 = -eta1 / T.sqrt(L1)
Yre1 = 0.5 * sigma1 / T.sqrt(L1)
Yim1 = -0.5 * rho1 / T.sqrt(L1)
Xre2 = kappa2 / T.sqrt(L2)
Xim2 = -eta2 / T.sqrt(L2)
Yre2 = 0.5 * sigma2 / T.sqrt(L2)
Yim2 = -0.5 * rho2 / T.sqrt(L2)
absX1_sq = 2 * I1 / L1
absX2_sq = 2 * I2 / L2
X_to_z1 = T.sqrt(1 - absX1_sq / 4)
X_to_z2 = T.sqrt(1 - absX2_sq / 4)
Y_to_zeta1 = 1 / T.sqrt(1 - absX1_sq / 2)
Y_to_zeta2 = 1 / T.sqrt(1 - absX2_sq / 2)
a1 = (L1 / beta1)**2
k1 = Xre1 * X_to_z1
h1 = Xim1 * X_to_z1
q1 = Yre1 * Y_to_zeta1
p1 = Yim1 * Y_to_zeta1
e1 = T.sqrt(absX1_sq) * X_to_z1
inc1 = 2 * T.arcsin(T.sqrt(p1 * p1 + q1 * q1))
a2 = (L2 / beta2)**2
k2 = Xre2 * X_to_z2
h2 = Xim2 * X_to_z2
q2 = Yre2 * Y_to_zeta2
p2 = Yim2 * Y_to_zeta2
e2 = T.sqrt(absX2_sq) * X_to_z2
inc2 = 2 * T.arcsin(T.sqrt(p2 * p2 + q2 * q2))
beta1p = T.sqrt(Mstar1) * beta1
beta2p = T.sqrt(Mstar2) * beta2
Hkep = -0.5 * beta1p / a1 - 0.5 * beta2p / a2
Hdir, Hind = calc_Hint_components_spatial(a1, a2, l1, l2, h1, k1, h2, k2,
p1, q1, p2, q2, Mstar1, Mstar2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hdir + Hind / mstar)
Hpert_av = Hpert.dot(quad_weights)
Htot = Hkep + eps * Hpert_av
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes, weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(psi, nodes), (quad_weights, weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2, j, k]
ins = [dyvars] + extra_ins
Stilde = Phi * (L2 - I2 - L1 + I1) / (Ltot)
Q1 = 0.5 * (Phi + Stilde)
Q2 = 0.5 * (Phi - Stilde)
inc1 = T.arccos(1 - Q1 / (L1 - I1))
inc2 = T.arccos(1 - Q2 / (L2 - I2))
orbels = [
a1, e1, inc1, k * T.arctan2(y1, x1), a2, e2, inc2,
k * T.arctan2(y2, x2),
T.arctan2(y_inc, x_inc)
]
orbels_dict = dict(
zip([
'a1', 'e1', 'inc1', 'theta1', 'a2', 'e2', 'inc2', 'theta2', 'phi'
], orbels))
actions = [L1, L2, I1, I2, Q1, Q2]
actions_dict = dict(
zip(['L1', 'L2', 'Gamma1', 'Gamma2', 'Q1', 'Q2'], actions))
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
gradHpert = T.grad(Hpert_av, wrt=dyvars)
gradHkep = T.grad(Hkep, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
hessHpert = theano.gradient.hessian(Hpert_av, wrt=dyvars)
hessHkep = theano.gradient.hessian(Hkep, wrt=dyvars)
Jtens = T.as_tensor(np.pad(getOmegaMatrix(Ndof), (0, Nconst), 'constant'))
H_flow_vec = Jtens.dot(gradHtot)
Hpert_flow_vec = Jtens.dot(gradHpert)
Hkep_flow_vec = Jtens.dot(gradHkep)
H_flow_jac = Jtens.dot(hessHtot)
Hpert_flow_jac = Jtens.dot(hessHpert)
Hkep_flow_jac = Jtens.dot(hessHkep)
##########################
# Compile Theano functions
##########################
func_dict = {
# Hamiltonians
'H': Htot,
#'Hpert':Hpert_av,
#'Hkep':Hkep,
## Hamiltonian flows
'H_flow': H_flow_vec,
#'Hpert_flow':Hpert_flow_vec,
#'Hkep_flow':Hkep_flow_vec,
## Hamiltonian flow Jacobians
'H_flow_jac': H_flow_jac,
#'Hpert_flow_jac':Hpert_flow_jac,
#'Hkep_flow_jac':Hkep_flow_jac,
## Extras
'orbital_elements': orbels_dict,
'actions': actions_dict
}
compiled_func_dict = dict()
with tqdm(func_dict.items()) as t:
for key, val in t:
t.set_description("Compiling '{}'".format(key))
if key is 'timescales':
inputs = extra_ins
else:
inputs = ins
cf = theano.function(inputs=inputs,
outputs=val,
givens=givens,
on_unused_input='ignore')
compiled_func_dict[key] = cf
return compiled_func_dict
def evaluate(self, dt, positions, velocities, rot_matrices, motor_signals):
# ALL CONSTRAINTS CAN BE TRANSFORMED TO VELOCITY CONSTRAINTS!
##################
# --- Step 1 --- #
##################
# First, we integrate the applied force F_a acting of each rigid body (like gravity, ...) and
# we obtain some new velocities v2' that tends to violate the constraints.
totalforce = np.array([0,0,0,0,0,0], dtype='float32') # total force acting on body outside of constraints
acceleration = np.array([0,0,-9.81,0,0,0], dtype='float32') # acceleration of the default frame
newv = velocities + dt * acceleration[None,None,:]
originalv = newv
##################
# --- Step 2 --- #
##################
# now enforce the constraints by having corrective impulses
# convert mass matrices to world coordinates
M = T.zeros(shape=(self.batch_size,self.num_bodies,6,6))
M00 = self.lower_inertia_inv
M01 = T.zeros(shape=(self.batch_size,self.num_bodies,3,3))
M10 = M01
M11 = T.sum(rot_matrices[:,:,:,None,:,None] * self.upper_inertia_inv[:,:,:,:,None,None] * rot_matrices[:,:,None,:,None,:], axis=(2,3))
M0 = T.concatenate([M00,M01],axis=3)
M1 = T.concatenate([M10,M11],axis=3)
M = T.concatenate([M0,M1],axis=2)
# changes every timestep
# constraints are first dimension! We will need to stack them afterwards!
J = [np.zeros((self.batch_size,6), dtype="float32") for _ in xrange(2 * self.num_constraints)] # 0 constraints x 0 bodies x 2 objects x 6 states
b_res = [np.zeros((self.batch_size,), dtype="float32") for _ in xrange(self.num_constraints)] # 0 constraints x 0 bodies
b_error = [np.zeros((self.batch_size,), dtype="float32") for _ in xrange(self.num_constraints)] # 0 constraints x 0 bodies
C = [np.zeros((self.batch_size,), dtype="float32") for _ in xrange(self.num_constraints)] # 0 constraints x 0 bodies
c_idx = 0
for constraint,references,parameters in self.constraints:
idx1 = references[0]
if references[1] is not None:
idx2 = references[1]
else:
idx2 = None
if constraint == "universe":
batched_J = numpy_repeat_new_axis(np.concatenate([-np.eye(3), np.zeros((3,3))]), self.batch_size).astype('float32')
for i in xrange(3):
J[2*(c_idx+i)+0] = batched_J[:,:,i]
#J[c_idx+i,1,:] = np.concatenate([ np.eye(3), np.zeros((3,3))])[:,i]
b_error[c_idx+i] = -positions[:,idx1,i]
c_idx += 3
batched_J = numpy_repeat_new_axis(np.concatenate([np.zeros((3,3)),-np.eye(3)]), self.batch_size).astype('float32')
for i in xrange(3):
J[2*(c_idx+i)+0] = batched_J[:,:,i]
#J[c_idx+i,1,:] = np.concatenate([np.zeros((3,3), dtype=DTYPE), np.eye(3)])[:,i]
b_error[c_idx+i] = np.zeros(shape=(self.batch_size,))
c_idx += 3
if constraint == "ball-and-socket" or constraint == "hinge" or constraint == "fixed":
r1x = theano_convert_model_to_world_coordinate_no_bias(parameters["joint_in_model1_coordinates"][None,:], rot_matrices[:,idx1,:,:])
r2x = theano_convert_model_to_world_coordinate_no_bias(parameters["joint_in_model2_coordinates"][None,:], rot_matrices[:,idx2,:,:])
ss_r1x = single_skew_symmetric(r1x)
ss_r2x = single_skew_symmetric(r2x)
batched_eye = numpy_repeat_new_axis(np.eye(3, dtype='float32'), self.batch_size)
complete_J1 = T.concatenate([-batched_eye, ss_r1x],axis=1)
complete_J2 = T.concatenate([ batched_eye,-ss_r2x],axis=1)
error = positions[:,idx2,:]+r2x-positions[:,idx1,:]-r1x
for i in xrange(3):
J[2*(c_idx+i)+0] = complete_J1[:,:,i]
J[2*(c_idx+i)+1] = complete_J2[:,:,i]
b_error[c_idx+i] = error[:,i]
c_idx += 3
if constraint == "slider" or constraint == "fixed":
batched_eye = numpy_repeat_new_axis(np.eye(3, dtype='float32'), self.batch_size)
batched_zeros = numpy_repeat_new_axis(np.zeros((3,3), dtype='float32'), self.batch_size)
complete_J1 = np.concatenate([batched_zeros,-batched_eye],axis=1)
complete_J2 = np.concatenate([batched_zeros, batched_eye],axis=1)
for i in xrange(3):
J[2*(c_idx+i)+0] = complete_J1[:,:,i]
J[2*(c_idx+i)+1] = complete_J2[:,:,i]
rot_current = np.dot(rot_matrices[idx2,:,:], rot_matrices[idx1,:,:].T)
rot_diff = np.dot(rot_current, parameters['rot_init'].T)
cross = rot_diff.T - rot_diff
# TODO: add stabilization of this constraint
b_error[c_idx] = np.zeros(shape=(self.batch_size,))#cross[1,2]
b_error[c_idx+1] = np.zeros(shape=(self.batch_size,))#cross[2,0]
b_error[c_idx+2] = np.zeros(shape=(self.batch_size,))#cross[0,1]
c_idx += 3
if constraint == "hinge":
a2x = theano_convert_model_to_world_coordinate_no_bias(parameters['axis_in_model2_coordinates'][None,:], rot_matrices[:,idx2,:,:])
b1x = theano_convert_model_to_world_coordinate_no_bias(parameters['axis1_in_model1_coordinates'][None,:], rot_matrices[:,idx1,:,:])
c1x = theano_convert_model_to_world_coordinate_no_bias(parameters['axis2_in_model1_coordinates'][None,:], rot_matrices[:,idx1,:,:])
ss_a2x = single_skew_symmetric(a2x)
batched_zeros = numpy_repeat_new_axis(np.zeros((3,), dtype='float32'), self.batch_size)
J[2*(c_idx+0)+0] = T.concatenate([batched_zeros,-theano_dot_last_dimension_vector_matrix(b1x,ss_a2x)],axis=1)
J[2*(c_idx+0)+1] = T.concatenate([batched_zeros, theano_dot_last_dimension_vector_matrix(b1x,ss_a2x)],axis=1)
J[2*(c_idx+1)+0] = T.concatenate([batched_zeros,-theano_dot_last_dimension_vector_matrix(c1x,ss_a2x)],axis=1)
J[2*(c_idx+1)+1] = T.concatenate([batched_zeros, theano_dot_last_dimension_vector_matrix(c1x,ss_a2x)],axis=1)
b_error[c_idx+0] = theano_dot_last_dimension_vectors(a2x,b1x)
b_error[c_idx+1] = theano_dot_last_dimension_vectors(a2x,c1x)
c_idx += 2
"""
if constraint == "limit":
#TODO: move to Theano...
angle = parameters["angle"]/180. * np.pi
a = theano_convert_model_to_world_coordinate_no_bias(parameters['axis_in_model1_coordinates'], rot_matrices[:,idx1,:,:])
rot_current = theano_dot_last_dimension_matrices(rot_matrices[:,idx2,:,:], rot_matrices[idx1,:,:].dimshuffle(0,2,1))
rot_diff = theano_dot_last_dimension_matrices(rot_current, quat_to_rot_matrix(parameters['rot_init']).dimshuffle(0,2,1))
theta2 = np.arccos(0.5*(np.trace(rot_diff)-1))
cross = rot_diff.T - rot_diff
dot2 = cross[1,2] * a[0] + cross[2,0] * a[1] + cross[0,1] * a[2]
theta = ((dot2>0) * 2 - 1) * theta2
if parameters["angle"] < 0:
J[2*c_idx+0] = np.concatenate([np.zeros((3,), dtype='float32'),-a])
J[2*c_idx+1] = np.concatenate([np.zeros((3,), dtype='float32'), a])
else:
J[2*c_idx+0] = np.concatenate([np.zeros((3,), dtype='float32'), a])
J[2*c_idx+1] = np.concatenate([np.zeros((3,), dtype='float32'),-a])
b_error[c_idx] = np.abs(angle - theta)
if parameters["angle"] > 0:
b_error[c_idx] = angle - theta
C[c_idx] = (theta > angle)
else:
b_error[c_idx] = theta - angle
C[c_idx] = (theta < angle)
c_idx += 1
"""
if constraint == "motor":
ac = parameters['axis_in_model2_coordinates'][None,:]
a = theano_convert_model_to_world_coordinate_no_bias(ac, rot_matrices[:,idx2,:,:])
# TODO: remove dimshuffle(0,2,1) by using batched_dot
rot_current = theano_dot_last_dimension_matrices(rot_matrices[:,idx2,:,:], rot_matrices[:,idx1,:,:].dimshuffle(0,2,1))
rot_init = numpy_repeat_new_axis(parameters['rot_init'].T, self.batch_size)
rot_diff = theano_dot_last_dimension_matrices(rot_current, rot_init)
traces = rot_diff[:,0,0] + rot_diff[:,1,1] + rot_diff[:,2,2]
# grad when x=-1 or x=1 does not exist for arccos
theta2 = T.arccos(T.clip(0.5*(traces-1),-1+eps,1-eps))
cross = rot_diff.dimshuffle(0,2,1) - rot_diff
dot2 = cross[:,1,2] * ac[:,0] + cross[:,2,0] * ac[:,1] + cross[:,0,1] * ac[:,2]
theta = ((dot2>0) * 2 - 1) * theta2
batched_zeros = numpy_repeat_new_axis(np.zeros((3,), dtype='float32'), self.batch_size)
J[2*c_idx+0] = T.concatenate([batched_zeros,-a],axis=1)
J[2*c_idx+1] = T.concatenate([batched_zeros, a],axis=1)
motor_signal = motor_signals[:,parameters["motor_id"]]
if "min" in parameters and "max" in parameters:
motor_min = (parameters["min"]/180. * np.pi)
motor_max = (parameters["max"]/180. * np.pi)
motor_signal = T.clip(motor_signal, motor_min, motor_max).astype('float32')
def smallestSignedAngleBetween(x, y):
a1 = (x - y) % np.float32(2*np.pi)
b1 = (y - x) % np.float32(2*np.pi)
return T.minimum(a1,b1)*((a1>b1)*2-1)
error_signal = -smallestSignedAngleBetween(theta, motor_signal)
if parameters["type"] == "velocity":
b_error[c_idx] = motor_signal
elif parameters["type"] == "position":
if "delta" in parameters and "motor_velocity" in parameters:
velocity = parameters["motor_velocity"] / 180. * np.pi
b_error[c_idx] = dt * T.clip((abs(error_signal) > parameters["delta"]) * error_signal * parameters["motor_gain"], -velocity, velocity)
else:
b_error[c_idx] = dt * error_signal * parameters["motor_gain"]
c_idx += 1
if constraint == "ground":
r = self.radii[idx1].astype('float32')
J[2*c_idx+0] = numpy_repeat_new_axis(np.array([0,0,1,0,0,0], dtype='float32'), self.batch_size)
J[2*c_idx+1] = numpy_repeat_new_axis(np.array([0,0,0,0,0,0], dtype='float32'), self.batch_size)
b_error[c_idx] = T.clip(positions[:,idx1,Z] - r + parameters["delta"], np.finfo('float32').min, 0)
b_res[c_idx] = parameters["alpha"] * newv[:,idx1,Z]
C[c_idx] = positions[:,idx1,Z] - r
c_idx += 1
if constraint == "ground" and parameters["mu"]!=0:
r = self.radii[idx1].astype('float32')
for i in xrange(2):
if i==0:
J[2*(c_idx+i)+0] = numpy_repeat_new_axis(np.array([0,1,0,-r,0,0], dtype='float32'), self.batch_size)
else:
J[2*(c_idx+i)+0] = numpy_repeat_new_axis(np.array([1,0,0,0,r,0], dtype='float32'), self.batch_size)
J[2*(c_idx+i)+1] = numpy_repeat_new_axis(np.array([0,0,0,0,0,0], dtype='float32'), self.batch_size)
C[c_idx+i] = positions[:,idx1,Z] - r
c_idx += 2
if constraint == "ground" and parameters["torsional_friction"] and parameters["mu"]!=0:
r = self.radii[idx1].astype('float32')
J[2*c_idx+0] = numpy_repeat_new_axis(np.array([0,0,0,0,0,r], dtype='float32'), self.batch_size)
J[2*c_idx+1] = numpy_repeat_new_axis(np.array([0,0,0,0,0,0], dtype='float32'), self.batch_size)
C[c_idx] = positions[:,idx1,Z] - r
c_idx += 1
zipped_indices = [j for i in zip(self.zero_index,self.one_index) for j in i]
mass_matrix = M[:,zipped_indices,:,:].reshape(shape=(self.batch_size, self.num_constraints, 2, 6, 6))
#mass_matrix = T.concatenate((M[:,self.zero_index,None,:,:], M[:,self.one_index,None,:,:]), axis=2)
#mass_matrix = T.concatenate((
# T.stack([M[:,i,None,:,:] for i in self.zero_index], axis=1),
# T.stack([M[:,j,None,:,:] for j in self.one_index], axis=1)
# ), axis=2)
#J = T.stack(J, axis=0).reshape(shape=(self.num_constraints,2,self.batch_size,6)).dimshuffle(2,0,1,3)
J = theano_stack_batched_integers_mixed_numpy(J, expected_shape=(self.num_constraints,2,self.batch_size,6)).dimshuffle(2,0,1,3)
C = theano_stack_batched_integers_mixed_numpy(C, expected_shape=(self.num_constraints,self.batch_size)).dimshuffle(1,0)
b_res = theano_stack_batched_integers_mixed_numpy(b_res, expected_shape=(self.num_constraints,self.batch_size)).dimshuffle(1,0)
b_error = theano_stack_batched_integers_mixed_numpy(b_error, expected_shape=(self.num_constraints,self.batch_size)).dimshuffle(1,0)
#v = np.zeros((self.num_constraints,2,6)) # 0 constraints x 2 objects x 6 states
self.P = self.warm_start * self.P
for iteration in xrange(self.projected_gauss_seidel_iterations):
# changes every iteration
v = newv[:,zipped_indices,:].reshape(shape=(self.batch_size, self.num_constraints, 2, 6))
#v = T.concatenate((newv[self.zero_index,None,:],newv[self.one_index,None,:]),axis=1)
#v = T.concatenate((
# T.stack([newv[:,i,None,:] for i in self.zero_index], axis=1),
# T.stack([newv[:,j,None,:] for j in self.one_index], axis=1)
#),axis=2)
# TODO: batch-dot-product
m_eff = 1./T.sum(T.sum(J[:,:,:,None,:]*mass_matrix, axis=4)*J, axis=(2,3))
#m_eff = 1./T.sum(T.sum(J[:,:,None,:]*mass_matrix, axis=-1)*J, axis=(-1,-2))
k = m_eff * (self.w**2)
c = m_eff * 2*self.zeta*self.w
CFM = 1./(c+dt*k)
ERP = dt*k/(c+dt*k)
m_c = 1./(1./m_eff + CFM)
b = ERP/dt * b_error + b_res
lamb = - m_c * (T.sum(J*v, axis=(2,3)) + CFM * self.P + b)
self.P += lamb
#print J[[39,61,65,69],:]
#print np.sum(lamb**2), np.sum(self.P**2)
#clipping_force = T.concatenate([self.P[:,j].dimshuffle(0,'x') for j in self.clipping_idx],axis=1)
clipping_force = self.P[:,self.clipping_idx]
clipping_limit = abs(self.clipping_a * clipping_force + self.clipping_b * dt)
self.P = T.clip(self.P,-clipping_limit, clipping_limit)
applicable = (1.0*(C<=0)) * (1-(self.only_when_positive*(self.P<=0)))
# TODO: batch-dot-product
result = T.sum(mass_matrix*J[:,:,:,None,:], axis=4) * (self.P * applicable)[:,:,None,None]
#result = theano_dot_last_dimension_matrix_vector(mass_matrix,J) * (self.P * applicable)[:,:,None,None]
result = result.reshape((self.batch_size, 2*self.num_constraints, 6))
r = []
for i in xrange(len(self.map_object_to_constraint)):
delta_v = T.sum(result[:,self.map_object_to_constraint[i],:], axis=1)
r.append(delta_v)
newv = newv + T.stack(r, axis=1)
#print
return newv
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)
# generate Omega_disk from range of samples
Omega_disk = pm.Uniform(
"OmegaDisk",
lower=np.min(Omega_samples),
upper=np.max(Omega_samples),
testval=np.mean(Omega_samples),
)
disk_observed = tt.as_tensor_variable([MA, i_disk, Omega_disk])
pm.MvNormal("obs_disk", mu=disk_mu, cov=disk_cov, observed=disk_observed)
# calculate the mutual inclination as well
theta = pm.Deterministic(
"thetaADisk",
tt.arccos(
tt.cos(i_disk) * tt.cos(incl) +
tt.sin(i_disk) * tt.sin(incl) * tt.cos(Omega_disk - Omega)))
# 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)
]
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 & model
xsplit = pm.HalfNormal('xsplit',
sigma=2.0,
testval=init_m[9] * np.sin(init_m[10]))
cosi = pm.Uniform('cosi', 0., 1., testval=np.cos(init_m[10]))
i = pm.Deterministic('i', tt.arccos(cosi))
split = pm.Deterministic('split', xsplit / tt.sin(i))
b = BNormal('b', mu=1., sigma=.1, testval=1.)
fit = mod.model([f0, f1, f2, g0, g1, g2, h0, h1, h2, split, i, b])
like = pm.Gamma('like', alpha=1., beta=1. / fit, observed=p)
# In[20]:
with pm_model:
trace = pm.sample(chains=4, target_accept=.99)
# In[21]:
def pred(self, output):
W1 = 0.5
W2 = 0.5
pred = T.argmin(W1 * T.arccos(T.dot(output, mappings_vec.T)/(absolute(output)*absolute(mappings_vec, axis=1))) +
W2 * (absolute(mappings_vec, axis=1) - absolute(output)))
return pred
