def __fitComplete2pMLE(self):
# initial guess:
shape = 1.2
scale = self.failures.mean()
parameters = jnp.array([shape, scale])
J = jacfwd(self.__logLikelihood2pComp)
H = jacfwd(jacrev(self.__logLikelihood2pComp))
epoch = 0
total = 1
while not (total < 0.01 or epoch > 200):
epoch += 1
grads = J(parameters)
hess = linalg.inv(H(parameters))
# Q is a coefficient to reduce gradient ascent step for high delta
q = 1 / (1 + jnp.sqrt(abs(grads / 800)))
# Newton-Raphson maximisation
parameters -= q * hess @ grads
total = abs(grads[0]) + abs(grads[1])
if epoch < 200:
self.converged = True
self.shape = parameters[0]
self.scale = parameters[1]
self.method = '2pComplete'
# Fisher Matrix confidence bound
self.variance = [abs(hess[0][0]), abs(hess[1][1])]
self.beta_eta_covar = [abs(hess[1][0])]
else:
# if more than 200 epoch it would be considered that fit is not converged
self.converged = False
self.shape = 0.0
self.scale = 0.0
self.method = Method.MLEComplete2p
def derivative(self, wrt):
if isinstance(wrt, str):
wrt_tuple = wrt,
return self.derivative(wrt_tuple)
# Trivial case, i.e., 0-th derivative
if wrt == ():
return self.fun
# Return the registered derivative, if it exists
try:
return self.derivatives[wrt]
except KeyError:
pass
# Compute the derivative
assert len(wrt) >= 1
fun = self.derivative(wrt[1:])
argnum = self.argnum(wrt[0])
deriv = jax.jacrev(fun, argnum)
# Save it and return
self.derivatives[wrt] = deriv
return deriv
def __fitTypeICensored2pMLE(self):
# initial guess:
shape = 1.2
scale = (self.failures.mean() + self.censored.mean()) / 2
parameters = jnp.array([shape, scale])
J = jacfwd(self.__logLikelihood2pTypeICensored)
H = jacfwd(jacrev(self.__logLikelihood2pTypeICensored))
epoch = 0
total = 1
while not (total < 0.09 or epoch > 200):
epoch += 1
grads = J(parameters)
hess = linalg.inv(H(parameters))
q = 1 / (
1 + jnp.sqrt(abs(grads / 8))
) # Q is a coefficient to reduce gradient ascent step for high delta
parameters -= q * hess @ grads # Newton-Raphson maximisation
total = abs(grads[0]) + abs(grads[1])
if epoch < 200:
self.converged = True
self.shape = parameters[0]
self.scale = parameters[1]
self.method = Method.MLECensored2p
self.variance = [abs(hess[0][0]), abs(hess[1][1])]
self.beta_eta_covar = [abs(hess[1][0])]
else:
# if more than 200 epoch it would be considered that fit is not converged
self.converged = False
self.shape = None
self.scale = None
self.method = Method.MLECensored2p
print('no')
def __init__(self, g=10.0):
self.max_speed = 20.
#self.max_torque=1.
self.max_torque = 3. # INCREASED TORQUE
self.dt = .05
self.g = g
self.action_space = (1, )
self.observation_space = (2, )
self.n, self.m = 2, 1
@jax.jit
def angle_normalize(x):
x = np.where(x > np.pi, x - 2 * np.pi, x)
x = np.where(x < -np.pi, x + 2 * np.pi, x)
return x
self.angle_normalize = angle_normalize
@jax.jit
def _dynamics(x, u):
th, th_dot = x
g = self.g
m = 1.
l = 1.
dt = self.dt
u = np.clip(u, -self.max_torque, self.max_torque)[0]
th_dot_dot = (-3. * g) / (2. * l) * np.sin(th + np.pi) + 3. / (
m * l**2) * u
new_th = self.angle_normalize(th + th_dot * dt)
new_th_dot = th_dot + th_dot_dot * dt
new_th_dot = np.clip(new_th_dot, -self.max_speed, self.max_speed)
return np.array([new_th, new_th_dot])
self._dynamics = _dynamics
jacobian = jax.jacrev(self._dynamics, argnums=(0, 1))
self.dynamics_jacobian = jax.jit(lambda x, u: jacobian(x, u))
def hessian(f, argnums=0):
return jax.jacfwd(jax.jacrev(f, argnums), argnums)
@jax.jit
def single_step_loss(theta, x, t_current, T):
L = 0
g = loss_grad(x)
lr = jnp.exp(theta[0]) * (T - t_current) / T + jnp.exp(
theta[1]) * t_current / T
x_new = x - lr * g
L += loss(x_new) * (t_current < T)
return L
compute_dL_dstate_old = jax.jit(jax.grad(single_step_loss, argnums=1))
compute_dL_dtheta_direct = jax.jit(jax.grad(single_step_loss, argnums=0))
compute_d_state_new_d_state_old = jax.jit(jax.jacrev(single_step, argnums=1))
compute_d_state_new_d_theta_direct = jax.jit(jax.jacrev(single_step,
argnums=0))
def rtrl_grad(theta, x, t0, T, K, dstate_dtheta=None):
t_current = t0
mystate = x
total_loss = 0.0
if dstate_dtheta is None:
dstate_dtheta = jnp.zeros((len(mystate), len(theta)))
total_theta_grad = 0
total_loss = 0.0
a0, a1, b0, b1 = c[i:i + 4]
alpha_n = 1 - a0**2 + a1 * (1 - a0) * jnp.cos(w)
beta_n = a0**2 + a1**2 + 1 + 2 * a0 * 1 * (
2 * jnp.cos(w)**2 - 1) + 2 * a1 * (a0 + 1) * jnp.cos(w)
alpha_d = 1 - b0**2 + b1 * (1 - b0) * jnp.cos(w)
beta_d = b0**2 + b1**2 + 1 + 2 * b0 * 1 * (
2 * jnp.cos(w)**2 - 1) + 2 * b1 * (b0 + 1) * jnp.cos(w)
group_delay += -alpha_n / beta_n + alpha_d / beta_d
return group_delay
group_delay_gradient = jax.jacrev(_group_delay)
def _group_delay_deviation(x, w):
"""
Calculates the group delay deviation for filter with coefficients x for the given frequencies in w
parameters
----------
x: ndarray
list of all coefficients of all seconds order stages and tau, the group delay optimization variable:
[c tau]
w: ndarray
frequency bins in the range [0, π] to evaluate the group delay on
def initialize_functions(hyper_params, phi, psi, g, get_params_from_opt, opt_update):
psi_z = jacrev(psi, argnums=1)
psi = jit(psi)
g = jit(g)
phi_x = jacrev(phi, argnums=1)
def l1_regularization(params, penalty):
val = 0.0
for layer in params:
for param in layer:
val += jnp.sum(jnp.abs(param))
return val * penalty
def l2_regularization(params, penalty):
val = 0.0
for layer in params:
for param in layer:
val += jnp.sum(param ** 2)
return val * penalty
def T(params_all, x, dx, z_ref):
params_phi = params_all[:hyper_params['n_phi']]
params_psi = params_all[hyper_params['n_phi']:hyper_params['n_phi'] + hyper_params['n_psi']]
params_g = params_all[hyper_params['n_phi'] + hyper_params['n_psi']:]
z_opt = phi(params_phi, x)
dz_g = g(params_g, z_opt, z_ref)
dx_recon = jnp.dot(psi_z(params_psi, z_opt, z_ref), dz_g)
z_opt_x = phi_x(params_phi, x)
x_loss = jnp.sum((x - psi(params_psi, z_opt, z_ref)) ** 2)
dx_loss = hyper_params['eta1'] * jnp.sum((dx - dx_recon) ** 2)
dz_loss = hyper_params['eta2'] * jnp.sum((jnp.dot(z_opt_x, dx) - dz_g) ** 2)
regul = l2_regularization(params_g, hyper_params['eta3'])
loss = x_loss + dx_loss + dz_loss + regul
return loss
def T_seperate(params_all, x, dx, z_ref):
params_phi = params_all[:hyper_params['n_phi']]
params_psi = params_all[hyper_params['n_phi']:hyper_params['n_phi'] + hyper_params['n_psi']]
params_g = params_all[hyper_params['n_phi'] + hyper_params['n_psi']:]
z_opt = phi(params_phi, x)
dz_g = g(params_g, z_opt, z_ref)
dx_recon = jnp.dot(psi_z(params_psi, z_opt, z_ref), dz_g)
z_opt_x = phi_x(params_phi, x)
x_loss = jnp.sum((x - psi(params_psi, z_opt, z_ref)) ** 2)
dx_loss = hyper_params['eta1'] * jnp.sum((dx - dx_recon) ** 2)
dz_loss = hyper_params['eta2'] * jnp.sum((jnp.dot(z_opt_x, dx) - dz_g) ** 2)
regul = l2_regularization(params_g, hyper_params['eta3'])
loss = x_loss + dx_loss + dz_loss + regul
return loss, x_loss, dx_loss, dz_loss, dx_recon, regul
T_params = grad(T, argnums=0)
# vectorized functions
psi_vec = jit(vmap(psi, (None, 0, 0)))
phi_vec = jit(vmap(phi, (None, 0)))
T_seperate_vec = jit(vmap(T_seperate, (None, 0, 0, 0)))
T_params_vec = jit(vmap(T_params, (None, 0, 0, 0)))
@jit
def update(i, opt_state, x, dx, z_ref):
params = get_params_from_opt(opt_state)
grads = T_params_vec(params, x, dx, z_ref)
grads_mean = []
for i, layer in enumerate(grads):
if (len(layer) == 0):
grads_mean.append(())
else:
grads_mean.append(tuple([jnp.mean(weight, axis=0) for weight in layer]))
return opt_update(i, grads_mean, opt_state)
return update, T_seperate_vec, phi_vec, psi_vec, phi, T, T_params, g
def hessian(f): return jacfwd(jacrev(f))
return (aa * bb).mean()
random_features_kernel, grad_random_features_kernel = get_mapped_kernel_grad(
random_features_kernel_basic, n_params=3)
def matrix_valued_kernel_basic(a, b, Q, h):
diff = (a - b)
return np.linalg.inv(Q) * np.exp(-0.5 / h * diff.T @ Q @ diff)
mv = vmap(matrix_valued_kernel_basic, (0, None, None, None), 0)
matrix_valued_kernel = jit(vmap(mv, (None, 0, None, None), 1))
jac_exp = jacrev(matrix_valued_kernel_basic)
def grad_update(a, b, Q, h, g, repulsion):
K = matrix_valued_kernel_basic(a, b, Q, h)
K_der = jac_exp(a, b, Q, h)
res = np.zeros(a.shape[-1])
for l in range(res.shape[-1]):
x = 0
for m in range(Q.shape[-1]):
x += K[l, m] * g[m] + repulsion * K_der[l, m, m]
res = index_update(res, index[l], x)
return res
mv = vmap(grad_update, (0, None, None, None, 0, None), 0)
def test_logdet_hess_da(self):
self.check_logdet_jac(lambda f: jax.jacfwd(jax.jacrev(f)),
hess=True,
da=True)
def test_quad_matrix_matrix_hess_da(self):
self.check_quad_jac(lambda f: jax.jacfwd(jax.jacrev(f)),
self.randmat,
self.randmat,
hess=True,
da=True)
def test_solve_matrix_hess_da(self):
self.check_solve_jac(self.randmat,
lambda f: jax.jacfwd(jax.jacrev(f)),
hess=True,
da=True)
normaly = dzdphi * dxdtheta - dxdphi * dzdtheta
normalz = dxdphi * dydtheta - dydphi * dxdtheta
norm_normal = jnp.sqrt(normalx * normalx + normaly * normaly +
normalz * normalz)
area = nfp * dtheta * dphi * jnp.sum(norm_normal)
# Compute plasma volume using \int (1/2) R^2 dZ dphi
# = \int (1/2) R^2 (dZ/dtheta) dtheta dphi
volume = 0.5 * nfp * dtheta * dphi * jnp.sum(r * r * dzdtheta)
return jnp.array([area, volume])
# area_volume_pure(rc, rs, zc, zs, stellsym, nfp, mpol, ntor, ntheta, nphi)
# jit_area_volume_pure = jit(area_volume_pure, static_argnums=(4, 5, 6, 7, 8, 9))
# jit_area_volume_pure = jit(area_volume_pure, static_argnums=(8, 9))
jit_area_volume_pure = area_volume_pure
darea_volume_pure = jacrev(area_volume_pure, argnums=(0, 1, 2, 3))
jit_dataset_area_volume = dataset_area_volume
class Surface(abc.ABC):
"""
Surface is a base class for various representations of toroidal
surfaces in simsopt.
"""
def __init__(self, nfp=1, stellsym=True):
#if not isinstance(nfp, int):
# raise TypeError('nfp must be an integer')
#if not isbool(stellsym):
# raise TypeError('stellsym must be a bool')
self.nfp = nfp
def __init__(self, neglog, d, metric_fun):
self.__neglog = neglog
self.__hessian_fun = jax.jit(jax.jacfwd(jax.jacrev(self.__neglog)))
self.__metric_fun = metric_fun
self.__d = d
self.__softabs_const = 1e0
def dlZ_dm(self, y, x, w, cav_mean, cav_var, power):
return jacrev(self.log_expected_likelihood,
argnums=3)(y, x, w, cav_mean, cav_var, power)
def jacobian(self, func, state, action):
return jax.jacrev(func, argnums=(0, 1))(state, action)
phi_vars = np.array([np.pi / 2., np.pi / 3.])
# phi_vars = np.array([np.pi/2.])
loc = 1.0
print(encode_point(loc, phi_vars))
print("")
print(grad_encode_point_x(loc, phi_vars))
print("")
print(grad_encode_point_phis(loc, phi_vars))
print("")
assert False
# trying it with a batch dimension
batch_encode_point = vmap(encode_point, (0, None))
grad_encode_point_x = vmap(jacrev(encode_point, argnums=0), (0, None))
grad_encode_point_phis = vmap(jacrev(encode_point, argnums=1), (0, None))
loc = numpy.array([
[0.0],
[1.2],
[1.4],
[1.5],
])
# phi_vars = numpy.array([
# [np.pi/2., np.pi/3.],
# [np.pi/2., np.pi/3.],
# [np.pi/8., 1.0],
# [-np.pi/7., np.pi/4.],
# ])
def __init__(self, **kwargs):
self.rollout_controller = None
self.gravity = 9.8
self.masscart = 1.0
self.masspole = 0.1
self.total_mass = (self.masspole + self.masscart)
self.length = 0.5 # actually half the pole's length
self.polemass_length = (self.masspole * self.length)
self.force_mag = 10.0
self.tau = 0.02 # seconds between state updates
# Angle at which to fail the episode
self.theta_threshold_radians = 15 * 2 * np.pi / 360
self.x_threshold = 2.4
self.action_space = (1, )
self.observation_space = (4, )
self.n, self.m = 4, 1
self.viewer = None
self._state = None
def _dynamics(x_0, u): # dynamics
# x_0, u = np.squeeze(x_0, axis=1), np.squeeze(u, axis=1)
x, x_dot, theta, theta_dot = np.split(x_0, 4)
force = self.force_mag * np.clip(
u, -1.0,
1.0) # iLQR may struggle with clipping due to lack of gradient
costh = np.cos(theta)
sinth = np.sin(theta)
temp = (force + self.polemass_length * theta_dot * theta_dot *
sinth) / self.total_mass
thetaacc = (self.gravity * sinth - costh * temp) / (
self.length *
(4.0 / 3.0 - self.masspole * costh * costh / self.total_mass))
xacc = temp - self.polemass_length * thetaacc * costh / self.total_mass
x = x + self.tau * x_dot # use euler integration by default
x_dot = x_dot + self.tau * xacc
theta = theta + self.tau * theta_dot
theta_dot = theta_dot + self.tau * thetaacc
state = np.hstack((x, x_dot, theta, theta_dot))
return state
self._dynamics = jax.jit(
_dynamics
) # MUST store as self._dynamics for default rollout implementation to work
# C_x, C_u = (np.diag(np.array([0.2, 0.05, 1.0, 0.05])), np.diag(np.array([0.05])))
# self._loss = jax.jit(lambda x, u: x.T @ C_x @ x + u.T @ C_u @ u) # MUST store as self._loss
self._loss = kwargs.get('loss')
# stack the jacobians of environment dynamics gradient
jacobian = jax.jacrev(self._dynamics, argnums=(0, 1))
# jacobian[0], jacobian[1] = np.squeeze(jacobian[0], axis=(1,3)), np.squeeze(jacobian[1], axis=(1,3))
self._dynamics_jacobian = jax.jit(
lambda x, u: np.hstack(jacobian(x, u)))
'''
def dyn_jac_aux(x,u):
j = jacobian(x,u)
return np.hstack((np.squeeze(j[0], axis=(1,3)), np.squeeze(j[1], axis=(1,3))))
self._dynamics_jacobian = jax.jit(dyn_jac_aux)'''
# stack the gradients of environment loss
loss_grad = jax.grad(self._loss, argnums=(0, 1))
self._loss_grad = jax.jit(lambda x, u: np.hstack(loss_grad(x, u)))
# block the hessian of environment loss
block_hessian = lambda A: np.vstack(
[np.hstack([A[0][0], A[0][1]]),
np.hstack([A[1][0], A[1][1]])])
hessian = jax.hessian(self._loss, argnums=(0, 1))
self._loss_hessian = jax.jit(lambda x, u: block_hessian(hessian(x, u)))
'''
from tfc.utils import TFCDict, Latex
# Initial solution
X0 = TFCDict({
'x': np.array([2. / 3.]),
'y': np.array([1. / 3.]),
'z': np.array([1. / 3.])
})
# Create function, Jacobian, and Hessian
f = lambda X: np.squeeze(X['x'] * X['y'] * (X['x'] * X['y'] + 6. * X[
'y'] - 8. * X['x'] - 48.) + X['z']**2 - 8. * X['z'] + 9. * X['y']**2 - 72.
* X['y'] + 16. * X['x']**2 + 96. * X['x'] + 160)
J = lambda X: np.hstack([val for val in jacfwd(f)(X).values()])
H = lambda X: np.hstack([val for val in jacrev(J)(X).values()])
# Equality constraint
A = np.array([[1., 2., -1.], [1., 0., 1.]])
b = np.array([[1.], [1.]])
N = sp.linalg.null_space(A)
# Iterate to find the solution (use a jax for loop)
X = X0
val = {'s': np.array([0.]), 'X0': X0, 'X': X, 'N': N}
def body(k, val):
val['s'] += np.linalg.multi_dot([
np.linalg.inv(np.linalg.multi_dot([val['N'].T,
H(val['X']), val['N']])),
else:
model = pystan.StanModel(file=path + model_name + '.stan')
with open(path + model_name + '.pkl', 'wb') as file:
pickle.dump(model, file)
# load hmc warmup
inv_metric = pickle.load(open('stan_traces/inv_metric.pkl', 'rb'))
stepsize = pickle.load(open('stan_traces/step_size.pkl', 'rb'))
last_pos = pickle.load(open('stan_traces/last_pos.pkl', 'rb'))
# define MPC cost, gradient and hessian function and prepare to commpile
cost = jit(log_barrier_cosine_cost,
static_argnums=(11, 12, 13, 14, 15)) # static argnums means it will recompile if N changes
gradient = jit(grad(log_barrier_cosine_cost, argnums=0), static_argnums=(
11, 12, 13, 14, 15)) # get compiled function to return gradients with respect to z (uc, s)
hessian = jit(jacfwd(jacrev(log_barrier_cosine_cost, argnums=0)), static_argnums=(11, 12, 13, 14, 15))
mu = 1e4
gamma = 1
delta = 0.05
max_iter = 5000
# declare some variables for storing the ongoing resutls
xt_est_save = np.zeros((Ns, Nx, T))
theta_est_save = np.zeros((Ns, 6, T))
q_est_save = np.zeros((Ns, 4, T))
r_est_save = np.zeros((Ns, 3, T))
uc_save = np.zeros((1, Nh, T))
mpc_result_save = []
hmc_traces_save = []
accept_rates = []
def hessian(fun):
return jit(jacfwd(jacrev(fun)))
temp = np.sin(np.power(np.subtract(var[0], args[:, 0]), 3))
ele1 = np.sum(temp)
# sin(var[1]**3 - var[2]**2) * args[:,1]
temp = np.sin(np.subtract(np.power(var[1], 3), np.power(var[2], 2)))
ele2 = np.sum(np.dot(temp, args[:, 1]))
# log(args[:,1]*args[:,2]*var[0]*var[1]*var[2])
temp = np.multiply(args[:, 1], args[:, 2])
ele3 = np.sum(
np.log(1 + np.abs(np.dot(var[0] * var[1] * var[2], temp))))
# print("\n\n", ele1, "\n", ele2, "\n", ele3)
# print(res, type(res))
return ele1 + ele2 + ele3
# print("-------------Reverse mode---------------")
# jax.jit(func)
grad = jax.jit(jax.jacrev(func))
for j in range(10):
f.write("\tSubstep " + str(j + 1) + "\n")
var = np.array([0.001 * j, 0.001 * 2 * j, 0.001 * 3 * j])
print("\tSubstep:", str(j))
start = time.time()
gradient = grad(var)
end = time.time()
f.write("\t\t" + str(gradient) + "\n")
print("\t\tGradient:", gradient)
print("\t\tExecution time:", float(end - start))
# for ele in exetime:
# for x in ele:
# f.write(str(x)+" ")
def test_autodiff(self, get, same_inputs, phi):
x1 = np.cos(random.normal(random.PRNGKey(1), (3, 1, 2, 3)))
if same_inputs is None:
x2 = None
elif same_inputs is True:
x2 = x1
else:
x2 = np.cos(random.normal(random.PRNGKey(2), (4, 1, 2, 3)))
name = phi.__name__
if name == 'LeakyRelu':
phi = phi(0.1)
elif name == 'ElementwiseNumerical':
phi = phi(fn=np.cos, deg=25)
else:
phi = phi()
_, _, kernel_fn = stax.serial(stax.Dense(1, 2., 0.01), phi,
stax.Dense(1, 2., 0.01), phi)
def k(x1, x2):
return kernel_fn(x1, x2, get)
dx1 = random.normal(random.PRNGKey(3), x1.shape) * 0.01
if x2 is None:
dx2 = None
else:
dx2 = random.normal(random.PRNGKey(4), x2.shape) * 0.01
def dk(x1, x2):
return jvp(k, (x1, x2), (dx1, dx2))[1]
def d2k(x1, x2):
return jvp(dk, (x1, x2), (dx1, dx2))[1]
_dk = dk(x1, x2)
_d2k = d2k(x1, x2)
if same_inputs is not False and get == 'ntk' and 'Relu' in name:
tol = 8e-3
else:
tol = 2e-3 if name == 'ElementwiseNumerical' else 1e-4
def assert_close(x, y, tol=3e-5):
if default_backend() == 'tpu':
# TODO(romann): understand why TPUs have high errors.
tol = 0.21
self.assertLess(
np.max(np.abs(x - y)) / (np.mean(np.abs(x)) + np.mean(np.abs(y))),
tol)
# k(x + dx) ~ k(x) + dk(x) dx + dx^T d2k(x) dx
assert_close(k(x1 + dx1, None if same_inputs is None else x2 + dx2),
k(x1, x2) + _dk + _d2k / 2,
tol=tol)
# d/dx1
k_fwd_0 = jacfwd(k)(x1, x2)
k_rev_0 = jacrev(k)(x1, x2)
assert_close(k_fwd_0, k_rev_0)
if same_inputs is not None:
# d/dx2
k_fwd_1 = jacfwd(k, 1)(x1, x2)
k_rev_1 = jacrev(k, 1)(x1, x2)
assert_close(k_fwd_1, k_rev_1)
# dk(x2, x1)/dx2 = dk(x1, x2)/dx1
k_fwd_01 = jacfwd(k, 1)(x2, x1)
k_rev_01 = jacrev(k, 1)(x2, x1)
assert_close(np.moveaxis(k_fwd_0, (0, 2, 4), (1, 3, 5)), k_fwd_01)
assert_close(np.moveaxis(k_rev_0, (0, 2, 4), (1, 3, 5)), k_rev_01)
# dk(x2, x1)/dx1 = dk(x1, x2)/dx2
k_fwd_10 = jacfwd(k)(x2, x1)
k_rev_10 = jacrev(k)(x2, x1)
assert_close(np.moveaxis(k_fwd_1, (0, 2, 4), (1, 3, 5)), k_fwd_10)
assert_close(np.moveaxis(k_rev_1, (0, 2, 4), (1, 3, 5)), k_rev_10)
def test_complex_output_jacrev_raises_error(self):
self.assertRaises(TypeError, lambda: jacrev(lambda x: np.sin(x))
(1 + 2j))
def fn1(th):
xi = jp.einsum('ii...->i...', jax.jacrev(Ls)(th))
_, prod = jax.jvp(Ls, (th,), (xi,))
return prod
def lagrangian_grad_real_flat(x, u, H):
z = real2comp(x).reshape(K, M)
gg = jax.jacrev(lagrangian)
grad = gg(z, u, H).conj()
return comp2real(grad.reshape(K * M, ))
def fn1(th):
xi = jp.lax.stop_gradient(jp.einsum('ii...->i...', jax.jacrev(Ls)(th)))
_, prod = jax.jvp(Ls, (th,), (xi,))
return (prod - jp.einsum('ij,ij->i', xi, xi))
xf = index_update(xf, index[1:-1], np.exp(1.j * phis[0, :]))
xf = index_update(xf, index[-1], 1)
yf = np.zeros((dim, ), dtype='complex64')
yf = index_update(yf, index[0], 1)
yf = index_update(yf, index[1:-1], np.exp(1.j * phis[1, :]))
yf = index_update(yf, index[-1], 1)
# jax version of irfft assumes there is a nyquist frequency
# they have not implemented it for odd dimensions
ret = np.fft.irfft(xf**pos[0] * yf**pos[1])
return ret
# grad_encode_point_x = grad(encode_2d_point_even, argnums=0)
# grad_encode_point_phis = grad(encode_2d_point_even, argnums=1)
grad_encode_point_x = jacrev(encode_2d_point_even, argnums=0)
grad_encode_point_phis = jacrev(encode_2d_point_even, argnums=1)
#print(encode_point(2., np.array([np.pi/2., np.pi/3.])))
#print(grad_encode_point_x(2., np.array([np.pi/2., np.pi/3.])))
#print(grad_encode_point_phis(2., np.array([np.pi/2., np.pi/3.])))
phi_vars = np.array([
[np.pi / 2., 0.],
[0., np.pi / 3.],
])
# phi_vars = np.array([np.pi/2.])
loc = (1.0, 0.5)
print(encode_2d_point_even(loc, phi_vars))
print("")
def cost_func_jacrev(bb, u):
direcmat = jax.jacrev(cost_func, argnums=(0, ))(bb, u)
return direcmat[0]