def Overlap(W_i, W_ev, N):
"""
Computes the overlap between the evolved state and the initial state
with the Onishi Formula.
"""
#N = np.int(np.shape(W_i)[0]/2)
U_i = W_i[0:N, 0:N]
V_i = W_i[N:2 * N, 0:N]
#switch zero modes
P1 = np.diag(np.concatenate((np.array([0]), np.ones((N - 1)))))
P = np.concatenate((np.concatenate((P1, (np.identity(N) - P1)), axis=1),
np.concatenate(((np.identity(N) - P1), P1), axis=1)))
w_i = np.dot(W_i, P)
U_i2 = w_i[0:N, 0:N]
V_i2 = w_i[N:2 * N, 0:N]
U_ev = W_ev[0:N, 0:N]
V_ev = W_ev[N:2 * N, 0:N]
Overlap1 = np.abs(
np.linalg.det(
(np.dot(U_i.conj().T, U_ev) + np.dot(V_i.conj().T, V_ev))))
Overlap2 = np.abs(
np.linalg.det(
(np.dot(U_i2.conj().T, U_ev) + np.dot(V_i2.conj().T, V_ev))))
return np.max([Overlap1, Overlap2])
def final_fn(state, regularize=False):
"""
:param state: Current state of the scheme.
:param bool regularize: Whether to adjust diagonal for numerical stability.
:return: a triple of estimated covariance, the square root of precision, and
the inverse of that square root.
"""
mean, m2, n = state
# XXX it is not necessary to check for the case n=1
cov = m2 / (n - 1)
if regularize:
# Regularization from Stan
scaled_cov = (n / (n + 5)) * cov
shrinkage = 1e-3 * (5 / (n + 5))
if diagonal:
cov = scaled_cov + shrinkage
else:
cov = scaled_cov + shrinkage * jnp.identity(mean.shape[0])
if jnp.ndim(cov) == 2:
# copy the implementation of distributions.util.cholesky_of_inverse here
tril_inv = jnp.swapaxes(
jnp.linalg.cholesky(cov[..., ::-1, ::-1])[..., ::-1, ::-1], -2,
-1)
identity = jnp.identity(cov.shape[-1])
cov_inv_sqrt = solve_triangular(tril_inv, identity, lower=True)
else:
tril_inv = jnp.sqrt(cov)
cov_inv_sqrt = jnp.reciprocal(tril_inv)
return cov, cov_inv_sqrt, tril_inv
def initialize(self, n, m, x, T_0, K=None, Q=None, R=None):
"""
Description: Initialize the dynamics of the model
Args:
n (float/numpy.ndarray): dimension of the state
m (float/numpy.ndarray): dimension of the controls
x (postive int): initial state
T_0 (int): system identification time
K (float/numpy.ndarray): initial controller (optional)
Q, R (float/numpy.ndarray): cost matrices (c(x, u) = x^T Q x + u^T R u)
"""
self.initialized = True
self.n, self.m = n, m
self.x = x
self.T_0 = T_0
self.T = 0
Q = np.identity(n) if Q is None else Q
R = np.identity(m) if R is None else R
if K:
self.K = K
else:
X = scipy.linalg.solve_discrete_are(A, B, Q, R)
self.K = np.linalg.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
def __init__(self,
A: jnp.ndarray,
B: jnp.ndarray,
Q: jnp.ndarray = None,
R: jnp.ndarray = None) -> None:
"""
Description: Initialize the infinite-time horizon LQR.
Args:
A (jnp.ndarray): system dynamics
B (jnp.ndarray): system dynamics
Q (jnp.ndarray): cost matrices (i.e. cost = x^TQx + u^TRu)
R (jnp.ndarray): cost matrices (i.e. cost = x^TQx + u^TRu)
Returns:
None
"""
state_size, action_size = B.shape
if Q is None:
Q = jnp.identity(state_size, dtype=jnp.float32)
if R is None:
R = jnp.identity(action_size, dtype=jnp.float32)
# solve the ricatti equation
X = dare(A, B, Q, R)
# compute LQR gain
self.K = jnp.linalg.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
def __init__(
self,
A: jnp.ndarray,
B: jnp.ndarray,
T: jnp.ndarray,
Q: jnp.ndarray = None,
R: jnp.ndarray = None,
) -> None:
"""
Description: initializes the Hinf agent
Args:
A (jnp.ndarray):
B (jnp.ndarray):
T (jnp.ndarray):
Q (jnp.ndarray):
R (jnp.ndarray):
Returns:
None
"""
d_x, d_u = B.shape
if Q is None:
self.Q = jnp.identity(d_x, dtype=jnp.float32)
if R is None:
self.R = jnp.identity(d_u, dtype=jnp.float32)
# self.K, self.W = solve_hinf(A, B, Q, R, T)
self.t = 0
def update_C_prior(self, params):
sigma = params[0]
theta = params[1]
C_prior = np.identity(self.n_features) * 1 / theta
C_prior_inv = np.identity(self.n_features) * theta
return C_prior, C_prior_inv
def _randaugment_inner_for_loop(_, in_args):
"""
Loop body for for randougment.
Args:
i: loop iteration
in_args: loop body arguments
Returns:
updated loop arguments
"""
(image, geometric_transforms, random_key, available_ops, op_probs,
magnitude, cutout_const, translate_const, join_transforms,
default_replace_value) = in_args
random_keys = random.split(random_key, num=8)
random_key = random_keys[0] # keep for next iteration
op_to_select = random.choice(random_keys[1], available_ops, p=op_probs)
mask_value = jnp.where(default_replace_value > 0,
jnp.ones([image.shape[-1]]) * default_replace_value,
random.randint(random_keys[2],
[image.shape[-1]],
minval=-1, maxval=256))
random_magnitude = random.uniform(random_keys[3], [], minval=0.,
maxval=magnitude)
cutout_mask = color_transforms.get_random_cutout_mask(
random_keys[4],
image.shape,
cutout_const)
translate_vals = (random.uniform(random_keys[5], [], minval=0.0,
maxval=1.0) * translate_const,
random.uniform(random_keys[6], [], minval=0.0,
maxval=1.0) * translate_const)
negate = random.randint(random_keys[7], [], minval=0,
maxval=2).astype('bool')
args = level_to_arg(cutout_mask, translate_vals, negate,
random_magnitude, mask_value)
if DEBUG:
print(op_to_select, args[op_to_select])
image, geometric_transform = _apply_ops(image, args, op_to_select)
image, geometric_transform = jax.lax.cond(
jnp.logical_or(join_transforms, jnp.all(
jnp.not_equal(geometric_transform, jnp.identity(4)))),
lambda op: (op[0], op[1]),
lambda op: (transforms.apply_transform(op[0],
op[1],
mask_value=mask_value),
jnp.identity(4)),
(image, geometric_transform)
)
geometric_transforms = jnp.matmul(geometric_transforms, geometric_transform)
return(image, geometric_transforms, random_key, available_ops, op_probs,
magnitude, cutout_const, translate_const, join_transforms,
default_replace_value)
def test_mean_var(jax_dist, sp_dist, params):
n = 20000 if jax_dist in [dist.LKJ, dist.LKJCholesky] else 200000
d_jax = jax_dist(*params)
k = random.PRNGKey(0)
samples = d_jax.sample(k, sample_shape=(n,))
# check with suitable scipy implementation if available
if sp_dist and not _is_batched_multivariate(d_jax):
d_sp = sp_dist(*params)
try:
sp_mean = d_sp.mean()
except TypeError: # mvn does not have .mean() method
sp_mean = d_sp.mean
# for multivariate distns try .cov first
if d_jax.event_shape:
try:
sp_var = np.diag(d_sp.cov())
except TypeError: # mvn does not have .cov() method
sp_var = np.diag(d_sp.cov)
except AttributeError:
sp_var = d_sp.var()
else:
sp_var = d_sp.var()
assert_allclose(d_jax.mean, sp_mean, rtol=0.01, atol=1e-7)
assert_allclose(d_jax.variance, sp_var, rtol=0.01, atol=1e-7)
if np.all(np.isfinite(sp_mean)):
assert_allclose(np.mean(samples, 0), d_jax.mean, rtol=0.05, atol=1e-2)
if np.all(np.isfinite(sp_var)):
assert_allclose(np.std(samples, 0), np.sqrt(d_jax.variance), rtol=0.05, atol=1e-2)
elif jax_dist in [dist.LKJ, dist.LKJCholesky]:
if jax_dist is dist.LKJCholesky:
corr_samples = np.matmul(samples, np.swapaxes(samples, -2, -1))
else:
corr_samples = samples
dimension, concentration, _ = params
# marginal of off-diagonal entries
marginal = dist.Beta(concentration + 0.5 * (dimension - 2),
concentration + 0.5 * (dimension - 2))
# scale statistics due to linear mapping
marginal_mean = 2 * marginal.mean - 1
marginal_std = 2 * np.sqrt(marginal.variance)
expected_mean = np.broadcast_to(np.reshape(marginal_mean, np.shape(marginal_mean) + (1, 1)),
np.shape(marginal_mean) + d_jax.event_shape)
expected_std = np.broadcast_to(np.reshape(marginal_std, np.shape(marginal_std) + (1, 1)),
np.shape(marginal_std) + d_jax.event_shape)
# diagonal elements of correlation matrices are 1
expected_mean = expected_mean * (1 - np.identity(dimension)) + np.identity(dimension)
expected_std = expected_std * (1 - np.identity(dimension))
assert_allclose(np.mean(corr_samples, axis=0), expected_mean, atol=0.01)
assert_allclose(np.std(corr_samples, axis=0), expected_std, atol=0.01)
else:
if np.all(np.isfinite(d_jax.mean)):
assert_allclose(np.mean(samples, 0), d_jax.mean, rtol=0.05, atol=1e-2)
if np.all(np.isfinite(d_jax.variance)):
assert_allclose(np.std(samples, 0), np.sqrt(d_jax.variance), rtol=0.05, atol=1e-2)
def norm_project(self, y, A, c):
""" Project y using norm A on the convex set bounded by c. """
if np.any(np.isnan(y)) or np.all(np.absolute(y) <= c):
return y
y_shape = y.shape
y_reshaped = np.ravel(y)
dim_y = y_reshaped.shape[0]
P = matrix(self.numpyify(A))
q = matrix(self.numpyify(-np.dot(A, y_reshaped)))
G = matrix(self.numpyify(np.append(np.identity(dim_y), -np.identity(dim_y), axis=0)), tc='d')
h = matrix(self.numpyify(np.repeat(c, 2 * dim_y)), tc='d')
solution = np.array(onp.array(solvers.qp(P, q, G, h)['x'])).squeeze().reshape(y_shape)
return solution
def init_fn(z_info,
rng_key,
step_size=1.0,
inverse_mass_matrix=None,
mass_matrix_size=None):
"""
:param IntegratorState z_info: The initial integrator state.
:param jax.random.PRNGKey rng_key: Random key to be used as the source of randomness.
:param float step_size: Initial step size.
:param inverse_mass_matrix: Inverse of the initial mass matrix. If ``None``,
inverse of mass matrix will be an identity matrix with size is decided
by the argument `mass_matrix_size`.
:param int mass_matrix_size: Size of the mass matrix.
:return: initial state of the adapt scheme.
"""
rng_key, rng_key_ss = random.split(rng_key)
if inverse_mass_matrix is None:
assert mass_matrix_size is not None
if dense_mass:
inverse_mass_matrix = jnp.identity(mass_matrix_size)
else:
inverse_mass_matrix = jnp.ones(mass_matrix_size)
mass_matrix_sqrt = mass_matrix_sqrt_inv = inverse_mass_matrix
else:
if dense_mass:
mass_matrix_sqrt_inv = jnp.swapaxes(
jnp.linalg.cholesky(
inverse_mass_matrix[..., ::-1, ::-1])[..., ::-1, ::-1],
-2, -1)
identity = jnp.identity(inverse_mass_matrix.shape[-1])
mass_matrix_sqrt = solve_triangular(mass_matrix_sqrt_inv,
identity,
lower=True)
else:
mass_matrix_sqrt_inv = jnp.sqrt(inverse_mass_matrix)
mass_matrix_sqrt = jnp.reciprocal(mass_matrix_sqrt_inv)
if adapt_step_size:
step_size = find_reasonable_step_size(step_size,
inverse_mass_matrix, z_info,
rng_key_ss)
ss_state = ss_init(jnp.log(10 * step_size))
mm_state = mm_init(inverse_mass_matrix.shape[-1])
window_idx = 0
return HMCAdaptState(step_size, inverse_mass_matrix, mass_matrix_sqrt,
mass_matrix_sqrt_inv, ss_state, mm_state,
window_idx, rng_key)
def sample(N,
X=None,
prior_var=1.,
censorship_temp=10,
distance_threshold=.5,
distance_var=0.1):
"""Samples from the latent position model.
Args:
N: The number of latent positions.
prior: Either 'uniform' or 'gaussian', the form of the position prior.
prior_var: The variance for the position prior if it is Gaussian.
censorship_temp: The temperature of the sigmoid that defines the censorship
distribution, is multiplied by the covariates before they are exponentiated.
distance_threshold: The distance where the probability of censorship is 50%.
distance_var: The variance of the conditional distribution of distance given
the positions and censoring indicators.
Returns:
X: The positions.
C: The censorship indicators, a 2D numpy array of 0s and 1s
of length num_pos*(num_pos-1)/2. Is 0 if a distance was observed and 1 otherwise.
D: The pairwise distance matrix, flattened. Distances that were censored
are 0.
"""
if X is None:
X = onp.random.multivariate_normal(mean=[0.,0.], cov=prior_var*np.identity(2), size=[N])
distances = oscipy.spatial.distance.pdist(X)
censorship_probs = oscipy.special.expit(censorship_temp*(distances - distance_threshold))
C = onp.random.binomial(1, censorship_probs)
uncensored_D = onp.random.normal(loc=distances, scale=onp.sqrt(distance_var))
D = uncensored_D*(1-C)
return X, C, D
def system_id(self):
""" returns current estimate of hidden system dynamics """
assert self.T > 0
k = self.k if self.k else int(0.15 * self.T)
# transform eta and x
eta_np = np.array(self.eta)
x_np = np.array(self.x_history)
# prepare vectors and retrieve B
scan_len = self.T - k - 1 # need extra -1 because we iterate over j=0,..,k
N_j = np.array([
np.dot(x_np[j + 1:j + 1 + scan_len].T, eta_np[:scan_len])
for j in range(k + 1)
]) / scan_len
B = N_j[0] # np.dot(x_np[1:].T, eta_np[:-1]) / (self.T-1)
#B = np.dot(x_np[1:].T, eta_np[:-1]) / (self.T-1)
# retrieve A
C_0, C_1 = N_j[:-1], N_j[1:]
C_inv = np.linalg.inv(
np.tensordot(C_0, C_0, axes=([0, 2], [0, 2])) +
self.gamma * np.identity(self.n))
A = np.tensordot(C_1, C_0, axes=([0, 2], [0, 2])) @ C_inv + B @ self.K
return (A, B)
def kspring(self, kspring):
"""
Set new spring constant.
Arguments
---------
kspring:
A scalar, array length `N` or symmetric `N x N` matrix. Restraining spring constant.
"""
# Ensure array
kspring = np.asarray(kspring)
shape = kspring.shape
N = self._N
if len(shape) > 2:
raise RuntimeError(
f"Wrong kspring shape {shape} (expected scalar, 1D or 2D)")
elif len(shape) == 2:
if shape != (N, N):
raise RuntimeError(
f"2D kspring with wrong shape, expected ({N}, {N}), got {shape}"
)
if not np.allclose(kspring, kspring.T):
raise RuntimeError("Spring matrix is not symmetric")
self._kspring = kspring
else: # len(shape) == 0 or len(shape) == 1
n = kspring.size
if n != N and n != 1:
raise RuntimeError(
f"Wrong kspring size, expected 1 or {N}, got {n}.")
self._kspring = np.identity(N) * kspring
return self._kspring
def __init__(self,
loc=jnp.array([0.]),
cov=jnp.identity(1),
sl=jnp.array([0.])):
"""
Check dimensions compatibility and initialize the parameters.
Arguments:
- loc: location parameter
- cov: covariance matrix
- sl: slant parameter
"""
assert loc.shape[-1] == cov.shape[-1]
assert cov.shape[-1] == cov.shape[-2]
assert loc.shape[-1] == sl.shape[-1]
# assert (jnp.linalg.eigvalsh(cor - jnp.outer(skew, skew))).any() > 0
self.loc = loc
self.cov = cov
self.slant = sl
self.scale = jnp.sqrt(jnp.diag(cov))
self.cor = jnp.einsum('i,ij,j->ij', 1. / self.scale, self.cov,
1. / self.scale)
self.k = loc.shape[-1]
def kl_div(mu: np.ndarray,
A_chol: np.ndarray,
sigma_prior: float
) -> float:
"""
Computes the KL divergence between
- the approximated posterior distribution N(mu, Sigma)
- and the prior distribution on the parameters N(0, (sigma_prior ** 2) I)
Instead of working directly with the covariance matrix Sigma, we will only deal with its Cholesky matrix A:
It is the lower triangular matrix such that Sigma = A * A.T
:param mu: mean of the posterior distribution approximated by variational inference
:param A: Choleski matrix such that Sigma = A * A.T,
where Sigma is the coveriance of the posterior distribution approximated by variational inference.
:param sigma_prior: standard deviation of the prior on the parameters. We put the following prior on the parameters:
N(mean=0, variance=(sigma_prior**2) I)
:return: the value of the KL divergence
"""
# TODO
covariance_post = np.dot(A_chol,A_chol.T)
mean_post = mu
size = len(mu)
mean_prior = np.zeros(shape=(A_chol.shape[0],1))
covariance_prior = sigma_prior**2*np.identity(A_chol.shape[0])
cov_ratio = np.linalg.det(covariance_prior)/np.linalg.det(covariance_post) # get ratio of 2 covariance matrices
trace_matrices = np.trace(np.dot(np.linalg.inv(covariance_prior), covariance_post))
last_term = np.dot((mean_prior - mean_post).T, np.dot(np.linalg.inv(covariance_prior), (mean_prior - mean_post)))
kl = 0.5*(np.log(cov_ratio) - size + trace_matrices + last_term)
return kl[0][0]
def _get_posterior(self):
loc = numpyro.param('{}_loc'.format(self.prefix), self._init_latent)
scale_tril = numpyro.param('{}_scale_tril'.format(self.prefix),
jnp.identity(self.latent_dim) *
self._init_scale,
constraint=constraints.lower_cholesky)
return dist.MultivariateNormal(loc, scale_tril=scale_tril)
def _RuLSIF(self, x, y, alpha, s_sigma, s_lambda):
if len(s_sigma) == 1 and len(s_lambda) == 1:
sigma = s_sigma[0]
lambda_ = s_lambda[0]
else:
optimized_params = self._optimize_sigma_lambda(
x, y, alpha, s_sigma, s_lambda)
sigma = optimized_params['sigma']
lambda_ = optimized_params['lambda']
phi_x = self.__kernel(r=x, sigma=sigma)
phi_y = self.__kernel(r=y, sigma=sigma)
H = (1. -
alpha) * (np.dot(phi_y.T, phi_y) / self.__y_num_row) + alpha * (
np.dot(phi_x.T, phi_x) / self.__x_num_row) # Phi* Phi
h = np.average(phi_x, axis=0).T
weights = np.linalg.solve(H + lambda_ * np.identity(self.__kernel_num),
h).ravel()
# weights[weights < 0] = 0.
weights = jax.ops.index_update(weights, weights < 0, 0) # G2[G2<0]=0
self.__alpha = alpha
self.__weights = weights
self.__lambda = lambda_
self.__sigma = sigma
self.__phi_x = phi_x
self.__phi_y = phi_y
def covariance_matrix(self):
# TODO: find a better solution to create a diagonal matrix
new_diag = self.cov_diag[..., np.newaxis] * np.identity(
self.loc.shape[-1])
covariance_matrix = new_diag + np.matmul(
self.cov_factor, np.swapaxes(self.cov_factor, -1, -2))
return covariance_matrix
def test_lqr(steps=10, show_plot=True):
T = steps
n = 1 # dimension of the state x
m = 1 # control dimension
noise_magnitude = 0.2
noise_distribution = 'normal'
environment_id = "LDS"
environment_params = {
'n': n,
'm': m,
'noise_magnitude': noise_magnitude,
'noise_distribution': noise_distribution
}
C = np.identity(n + m) # quadratic cost
LQR_params = {'C': C, 'T': T}
LQR_results, LQR_norms, LQR_avg_results = get_trajectory((environment_id, environment_params), \
('LQR', LQR_params), T = T)
if (show_plot):
plt.plot(LQR_norms, label="LQR")
plt.title("LQR on LDS")
print("test_lqr passed")
return
def enumerate_support(self, expand=True):
n = self.event_shape[-1]
values = jnp.identity(n, dtype=canonicalize_dtype(self.dtype))
values = values.reshape((n,) + (1,) * len(self.batch_shape) + (n,))
if expand:
values = jnp.broadcast_to(values, (n,) + self.batch_shape + (n,))
return values
def _onion(self, key, size):
key_beta, key_normal = random.split(key)
# Now we generate w term in Algorithm 3.2 of [1].
beta_sample = self._beta.sample(key_beta, size)
# The following Normal distribution is used to create a uniform distribution on
# a hypershere (ref: http://mathworld.wolfram.com/HyperspherePointPicking.html)
normal_sample = random.normal(key_normal,
shape=size + self.batch_shape +
(self.dimension *
(self.dimension - 1) // 2, ))
normal_sample = vec_to_tril_matrix(normal_sample, diagonal=0)
u_hypershere = normal_sample / np.linalg.norm(
normal_sample, axis=-1, keepdims=True)
w = np.expand_dims(np.sqrt(beta_sample), axis=-1) * u_hypershere
# put w into the off-diagonal triangular part
cholesky = ops.index_add(
np.zeros(size + self.batch_shape + self.event_shape),
ops.index[..., 1:, :-1], w)
# correct the diagonal
# NB: we clip due to numerical precision
diag = np.sqrt(np.clip(1 - np.sum(cholesky**2, axis=-1), a_min=0.))
cholesky = cholesky + np.expand_dims(diag, axis=-1) * np.identity(
self.dimension)
return cholesky
def _get_transform(self):
loc = numpyro.param('{}_loc'.format(self.prefix), self._init_latent)
scale_tril = numpyro.param('{}_scale_tril'.format(self.prefix),
np.identity(self.latent_size) *
self._init_scale,
constraint=constraints.lower_cholesky)
return MultivariateAffineTransform(loc, scale_tril)
def init_fn(z, rng, step_size=1.0, inverse_mass_matrix=None, mass_matrix_size=None):
"""
:param z: Initial position of the integrator.
:param jax.random.PRNGKey rng: Random key to be used as the source of randomness.
:param float step_size: Initial step size.
:param inverse_mass_matrix: Inverse of the initial mass matrix. If ``None``,
inverse of mass matrix will be an identity matrix with size is decided
by the argument `mass_matrix_size`.
:param int mass_matrix_size: Size of the mass matrix.
:return: initial state of the adapt scheme.
"""
rng, rng_ss = random.split(rng)
if inverse_mass_matrix is None:
assert mass_matrix_size is not None
if dense_mass:
inverse_mass_matrix = np.identity(mass_matrix_size)
else:
inverse_mass_matrix = np.ones(mass_matrix_size)
mass_matrix_sqrt = inverse_mass_matrix
else:
if dense_mass:
mass_matrix_sqrt = cholesky_inverse(inverse_mass_matrix)
else:
mass_matrix_sqrt = np.sqrt(np.reciprocal(inverse_mass_matrix))
if adapt_step_size:
step_size = find_reasonable_step_size(inverse_mass_matrix, z, rng_ss, step_size)
ss_state = ss_init(np.log(10 * step_size))
mm_state = mm_init(inverse_mass_matrix.shape[-1])
window_idx = 0
return AdaptState(step_size, inverse_mass_matrix, mass_matrix_sqrt,
ss_state, mm_state, window_idx, rng)
def inv_vec_transform(y):
matrix = vec_to_tril_matrix(y, diagonal=-1)
if constraint is constraints.corr_matrix:
# fill the upper triangular part
matrix = matrix + np.swapaxes(
matrix, -2, -1) + np.identity(matrix.shape[-1])
return transform.inv(matrix)
def test_rot():
"""Tests the rot function and computation of its gradient"""
ket0 = jnp.array([1, 0], dtype=jnp.complex64)
evo = jnp.dot(rot([0.5, 0.7, 0.8]), ket0)
back_evo = jnp.dot(rot([0.5, 0.7, 0.8]), evo)
assert jnp.all(rot([0, 0, 0]) == jnp.identity(2, dtype="complex64"))
assert not jnp.all(jnp.equal(evo, back_evo))
def gamma_f(p: jnp.ndarray) -> jnp.ndarray:
gamma_f_arr = jnp.block([[zeros5],
[
jnp.identity(nn),
self.objective_object.final_weight(p),
zeros6
], [zeros51]])
return gamma_f_arr
def _get_posterior(self):
loc = numpyro.param("{}_loc".format(self.prefix), self._init_latent)
scale_tril = numpyro.param(
"{}_scale_tril".format(self.prefix),
jnp.identity(self.latent_dim) * self._init_scale,
constraint=self.scale_tril_constraint,
)
return dist.MultivariateNormal(loc, scale_tril=scale_tril)
def step(t, state, dt, space, t_h, parameters):
hamiltonian = init_hamiltonian(space, t + dt / 2, parameters, t_h)
I = np.identity(len(state))
H = 0.5j * hamiltonian * dt
# get the new state by solving a system of linear equations obtained by crank-nicolson
state = np.linalg.solve(I + H, (I - H).dot(state))
t += dt
return t, state
def cholesky_of_inverse(matrix):
# This formulation only takes the inverse of a triangular matrix
# which is more numerically stable.
# Refer to:
# https://nbviewer.jupyter.org/gist/fehiepsi/5ef8e09e61604f10607380467eb82006#Precision-to-scale_tril
tril_inv = jnp.swapaxes(jnp.linalg.cholesky(matrix[..., ::-1, ::-1])[..., ::-1, ::-1], -2, -1)
identity = jnp.broadcast_to(jnp.identity(matrix.shape[-1]), tril_inv.shape)
return solve_triangular(tril_inv, identity, lower=True)
def fill_cov(S, dim):
m, m = S.shape
S_eye = jnp.identity(dim - m)
S_fill = jnp.zeros((m, dim - m))
S_fill_left = jnp.vstack((S_fill, S_eye))
S_final = jnp.vstack((S, S_fill.T))
S_final = jnp.hstack((S_final, S_fill_left))
return S_final