def hessian(phi, R, Delta, t, N, regularized=False):
# Make sure phi is valid
if not all(np.isreal(phi)):
raise ControlledError('/hessian/ phi is not real: phi = %s' % phi)
if not all(np.isfinite(phi)):
raise ControlledError('/hessian/ phi is not finite: phi = %s' % phi)
# Make sure t is valid
if not np.isreal(t):
raise ControlledError('/hessian/ t is not real: t = %s' % t)
if not np.isfinite(t):
raise ControlledError('/hessian/ t is not finite: t = %s' % t)
# Make sure regularized is valid
if not isinstance(regularized, bool):
raise ControlledError(
'/hessian/ regularized must be a boolean: regularized = %s' %
type(regularized))
G = 1. * len(R)
quasiQ = utils.field_to_quasiprob(phi)
Delta_sparse = Delta.get_sparse_matrix()
H = sp.exp(-t) * Delta_sparse + G * diags(quasiQ, 0)
if regularized:
H += diags(np.ones(int(G)), 0) / (N * PHI_STD_REG**2)
# Make sure H is valid ?
return H
def gradient_per_datum_from_coeffs(coeffs, R, kernel, phi0=False,
regularized=True):
""" For optimizer. Computes gradient from coefficients. """
if not isinstance(phi0,np.ndarray):
phi0 = np.zeros(R.size)
else:
assert all(np.isreal(phi0))
phi = coeffs_to_field(coeffs, kernel)
quasiQ = utils.field_to_quasiprob(phi+phi0)
G = len(phi)
R_row = sp.mat(R) # 1 x G
quasiQ_row = sp.mat(quasiQ) # 1 x G
reg_row = (1./G)*sp.mat(phi)/(PHI_STD_REG**2) # 1 x G
kernel_mat = sp.mat(kernel) # G x kernel_dim
mu_R_row = R_row*kernel_mat # 1 x kernel_dim
mu_quasiQ_row = quasiQ_row*kernel_mat # 1 x kernel_dim
mu_reg_row = reg_row*kernel_mat
if regularized:
grad_row = mu_R_row - mu_quasiQ_row + mu_reg_row
else:
grad_row = mu_R_row - mu_quasiQ_row
return sp.array(grad_row).ravel() # Returns an array
def hessian_per_datum_from_coeffs(coeffs,
R,
kernel,
phi0=False,
regularized=False):
""" For optimizer. Computes hessian from coefficients. """
# Get number of gridpoints and dimension of kernel
G = kernel.shape[0]
kernel_dim = kernel.shape[1]
# Make sure coeffs is valid
if not (len(coeffs) == kernel_dim):
raise ControlledError(
'/hessian_per_datum_from_coeffs/ coeffs must have length %d: len(coeffs) = %d'
% (kernel_dim, len(coeffs)))
if not all(np.isreal(coeffs)):
raise ControlledError(
'/hessian_per_datum_from_coeffs/ coeffs is not real: coeffs = %s' %
coeffs)
if not all(np.isfinite(coeffs)):
raise ControlledError(
'/hessian_per_datum_from_coeffs/ coeffs is not finite: coeffs = %s'
% coeffs)
# Make sure phi0 is valid
if not isinstance(phi0, np.ndarray):
phi0 = np.zeros(G)
else:
if not all(np.isreal(phi0)):
raise ControlledError(
'/hessian_per_datum_from_coeffs/ phi0 is not real: phi0 = %s' %
phi0)
if not all(np.isfinite(phi0)):
raise ControlledError(
'/hessian_per_datum_from_coeffs/ phi0 is not finite: phi0 = %s'
% phi0)
# Make sure regularized is valid
if not isinstance(regularized, bool):
raise ControlledError(
'/hessian_per_datum_from_coeffs/ regularized must be a boolean: regularized = %s'
% type(regularized))
phi = coeffs_to_field(coeffs, kernel)
quasiQ = utils.field_to_quasiprob(phi + phi0)
kernel_mat = sp.mat(kernel) # G x kernel_dim
H = sp.mat(sp.diag(quasiQ)) # G x G
if regularized:
H += (1. / G) * sp.diag(np.ones(G)) / (PHI_STD_REG**2)
hessian_mat = kernel_mat.T * H * kernel_mat # kernel_dim x kernel_dim
# Make sure hessian_array is valid ?
return sp.array(hessian_mat) # Returns an array
def hessian(phi, R, Delta, t, regularized=False):
G = 1. * len(R)
quasiQ = utils.field_to_quasiprob(phi)
Delta_sparse = Delta.get_sparse_matrix()
H = sp.exp(-t) * Delta_sparse + G * diags(quasiQ, 0)
if regularized:
H += diags(np.ones(G), 0) / (PHI_STD_REG**2)
return H
def action(phi, R, Delta, t, N, phi_in_kernel=False, regularized=False):
# Make sure phi is valid
if not all(np.isreal(phi)):
raise ControlledError('/action/ phi is not real: phi = %s' % phi)
if not all(np.isfinite(phi)):
raise ControlledError('/action/ phi is not finite: phi = %s' % phi)
# Make sure t is valid
if not np.isreal(t):
raise ControlledError('/action/ t is not real: t = %s' % t)
# if not np.isfinite(t):
# raise ControlledError('/action/ t is not finite: t = %s' % t)
# Make sure phi_in_kernel is valid
if not isinstance(phi_in_kernel, bool):
raise ControlledError(
'/action/ phi_in_kernel must be a boolean: phi_in_kernel = %s' %
type(phi_in_kernel))
# Make sure regularized is valid
if not isinstance(regularized, bool):
raise ControlledError(
'/action/ regularized must be a boolean: regularized = %s' %
type(regularized))
G = 1. * len(R)
quasiQ = utils.field_to_quasiprob(phi)
quasiQ_col = sp.mat(quasiQ).T
Delta_sparse = Delta.get_sparse_matrix()
phi_col = sp.mat(phi).T
R_col = sp.mat(R).T
ones_col = sp.mat(sp.ones(int(G))).T
if phi_in_kernel:
S_mat = G * R_col.T * phi_col + G * ones_col.T * quasiQ_col
else:
S_mat = 0.5 * sp.exp(
-t
) * phi_col.T * Delta_sparse * phi_col + G * R_col.T * phi_col + G * ones_col.T * quasiQ_col
if regularized:
S_mat += 0.5 * (phi_col.T * phi_col) / (N * PHI_STD_REG**2)
S = S_mat[0, 0]
# Make sure S is valid
if not np.isreal(S):
raise ControlledError('/action/ S is not real at t = %s: S = %s' %
(t, S))
if not np.isfinite(S):
raise ControlledError('/action/ S is not finite at t = %s: S = %s' %
(t, S))
return S
def gradient(phi, R, Delta, t, regularized=False):
G = 1. * len(R)
quasiQ = utils.field_to_quasiprob(phi)
quasiQ_col = sp.mat(quasiQ).T
Delta_sparse = Delta.get_sparse_matrix()
phi_col = sp.mat(phi).T
R_col = sp.mat(R).T
grad_col = sp.exp(-t) * Delta_sparse * phi_col + G * R_col - G * quasiQ_col
if regularized:
grad_col += phi_col / (PHI_STD_REG**2)
grad = sp.array(grad_col).ravel()
assert all(np.isreal(grad))
return grad
def action_per_datum_from_coeffs(coeffs, R, kernel, phi0=False,
regularized=True):
""" For optimizer. Computes action from coefficients. """
if not isinstance(phi0,np.ndarray):
phi0 = np.zeros(R.size)
else:
assert all(np.isreal(phi0))
phi = coeffs_to_field(coeffs, kernel)
quasiQ = utils.field_to_quasiprob(phi+phi0)
current_term = sp.sum(R*phi)
nonlinear_term = sp.sum(quasiQ)
s = current_term + nonlinear_term
if regularized:
G = len(phi)
s += (.5/G)*sum(phi**2)/(PHI_STD_REG**2)
return s
def hessian_per_datum_from_coeffs(coeffs, R, kernel, phi0=False,
regularized=True):
""" For optimizer. Computes hessian from coefficients. """
if not isinstance(phi0,np.ndarray):
phi0 = np.zeros(R.size)
else:
assert all(np.isreal(phi0))
phi = coeffs_to_field(coeffs, kernel)
quasiQ = utils.field_to_quasiprob(phi+phi0)
kernel_mat = sp.mat(kernel) # G x kernel_dim matrix
H = sp.mat(sp.diag(quasiQ)) # G x G matrix
if regularized:
G = len(phi)
H += (1./G)*sp.diag(np.ones(G))/(PHI_STD_REG**2)
hessian_mat = kernel_mat.T*H*kernel_mat # kernel_dim^2 matrix
return sp.array(hessian_mat) # Returns an array
def gradient(phi, R, Delta, t, N, regularized=False):
# Make sure phi is valid
if not all(np.isreal(phi)):
raise ControlledError('/gradient/ phi is not real: phi = %s' % phi)
if not all(np.isfinite(phi)):
raise ControlledError('/gradient/ phi is not finite: phi = %s' % phi)
# Make sure t is valid
if not np.isreal(t):
raise ControlledError('/gradient/ t is not real: t = %s' % t)
if not np.isfinite(t):
raise ControlledError('/gradient/ t is not finite: t = %s' % t)
# Make sure regularized is valid
if not isinstance(regularized, bool):
raise ControlledError(
'/gradient/ regularized must be a boolean: regularized = %s' %
type(regularized))
G = 1. * len(R)
quasiQ = utils.field_to_quasiprob(phi)
quasiQ_col = sp.mat(quasiQ).T
Delta_sparse = Delta.get_sparse_matrix()
phi_col = sp.mat(phi).T
R_col = sp.mat(R).T
grad_col = sp.exp(-t) * Delta_sparse * phi_col + G * R_col - G * quasiQ_col
if regularized:
grad_col += phi_col / (N * PHI_STD_REG**2)
grad = sp.array(grad_col).ravel()
# Make sure grad is valid
if not all(np.isreal(grad)):
raise ControlledError(
'/gradient/ grad is not real at t = %s: grad = %s' % (t, grad))
if not all(np.isfinite(grad)):
raise ControlledError(
'/gradient/ grad is not finite at t = %s: grad = %s' % (t, grad))
return grad
def action(phi, R, Delta, t, phi_in_kernel=False, regularized=False):
G = 1. * len(R)
quasiQ = utils.field_to_quasiprob(phi)
quasiQ_col = sp.mat(quasiQ).T
Delta_sparse = Delta.get_sparse_matrix()
phi_col = sp.mat(phi).T
R_col = sp.mat(R).T
ones_col = sp.mat(sp.ones(G)).T
if phi_in_kernel:
S_mat = G * R_col.T * phi_col + G * ones_col.T * quasiQ_col
else:
S_mat = 0.5*sp.exp(-t)*phi_col.T*Delta_sparse*phi_col \
+ G*R_col.T*phi_col \
+ G*ones_col.T*quasiQ_col
if regularized:
S_mat += 0.5 * (phi_col.T * phi_col) / (PHI_STD_REG**2)
S = S_mat[0, 0]
assert np.isreal(S)
return S
def action_per_datum_from_coeffs(coeffs,
R,
kernel,
phi0=False,
regularized=False):
""" For optimizer. Computes action from coefficients. """
# Get number of gridpoints and dimension of kernel
G = kernel.shape[0]
kernel_dim = kernel.shape[1]
# Make sure coeffs is valid
if not (len(coeffs) == kernel_dim):
raise ControlledError(
'/action_per_datum_from_coeffs/ coeffs must have length %d: len(coeffs) = %d'
% (kernel_dim, len(coeffs)))
if not all(np.isreal(coeffs)):
raise ControlledError(
'/action_per_datum_from_coeffs/ coeffs is not real: coeffs = %s' %
coeffs)
if not all(np.isfinite(coeffs)):
raise ControlledError(
'/action_per_datum_from_coeffs/ coeffs is not finite: coeffs = %s'
% coeffs)
# Make sure phi0 is valid
if not isinstance(phi0, np.ndarray):
phi0 = np.zeros(G)
else:
if not all(np.isreal(phi0)):
raise ControlledError(
'/action_per_datum_from_coeffs/ phi0 is not real: phi0 = %s' %
phi0)
if not all(np.isfinite(phi0)):
raise ControlledError(
'/action_per_datum_from_coeffs/ phi0 is not finite: phi0 = %s'
% phi0)
# Make sure regularized is valid
if not isinstance(regularized, bool):
raise ControlledError(
'/action_per_datum_from_coeffs/ regularized must be a boolean: regularized = %s'
% type(regularized))
phi = coeffs_to_field(coeffs, kernel)
quasiQ = utils.field_to_quasiprob(phi + phi0)
current_term = sp.sum(R * phi)
nonlinear_term = sp.sum(quasiQ)
s = current_term + nonlinear_term
if regularized:
s += (.5 / G) * sum(phi**2) / (PHI_STD_REG**2)
# Make sure s is valid
if not np.isreal(s):
raise ControlledError(
'/action_per_datum_from_coeffs/ s is not real: s = %s' % s)
if not np.isfinite(s):
raise ControlledError(
'/action_per_datum_from_coeffs/ s is not finite: s = %s' % s)
return s
def gradient_per_datum_from_coeffs(coeffs,
R,
kernel,
phi0=False,
regularized=False):
""" For optimizer. Computes gradient from coefficients. """
# Get number of gridpoints and dimension of kernel
G = kernel.shape[0]
kernel_dim = kernel.shape[1]
# Make sure coeffs is valid
if not (len(coeffs) == kernel_dim):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ coeffs must have length %d: len(coeffs) = %d'
% (kernel_dim, len(coeffs)))
if not all(np.isreal(coeffs)):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ coeffs is not real: coeffs = %s'
% coeffs)
if not all(np.isfinite(coeffs)):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ coeffs is not finite: coeffs = %s'
% coeffs)
# Make sure phi0 is valid
if not isinstance(phi0, np.ndarray):
phi0 = np.zeros(G)
else:
if not all(np.isreal(phi0)):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ phi0 is not real: phi0 = %s'
% phi0)
if not all(np.isfinite(phi0)):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ phi0 is not finite: phi0 = %s'
% phi0)
# Make sure regularized is valid
if not isinstance(regularized, bool):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ regularized must be a boolean: regularized = %s'
% type(regularized))
phi = coeffs_to_field(coeffs, kernel)
quasiQ = utils.field_to_quasiprob(phi + phi0)
R_row = sp.mat(R) # 1 x G
quasiQ_row = sp.mat(quasiQ) # 1 x G
kernel_mat = sp.mat(kernel) # G x kernel_dim
mu_R_row = R_row * kernel_mat # 1 x kernel_dim
mu_quasiQ_row = quasiQ_row * kernel_mat # 1 x kernel_dim
grad_row = mu_R_row - mu_quasiQ_row # 1 x kernel_dim
if regularized:
reg_row = (1. / G) * sp.mat(phi) / (PHI_STD_REG**2) # 1 x G
mu_reg_row = reg_row * kernel_mat # 1 x kernel_dim
grad_row += mu_reg_row # 1 x kernel_dim
# Make sure grad_array is valid
grad_array = sp.array(grad_row).ravel()
if not all(np.isreal(grad_array)):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ grad_array is not real: grad_array = %s'
% grad_array)
if not all(np.isfinite(grad_array)):
raise ControlledError(
'/gradient_per_datum_from_coeffs/ grad_array is not finite: grad_array = %s'
% grad_array)
return sp.array(grad_row).ravel() # Returns an array