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own_cg
jan 6 years ago
parent 0e47fdd5fb
commit e8f836c908
1 changed files with 50 additions and 56 deletions
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106
fdfd_tools/bloch.py
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@ -73,7 +73,7 @@ This module contains functions for generating and solving the
'''
from typing import List, Tuple, Callable, Dict
from typing import Tuple, Callable
import logging
import numpy
from numpy import pi, real, trace
@ -83,7 +83,6 @@ import scipy.optimize
from scipy.linalg import norm
import scipy.sparse.linalg as spalg
from .eigensolvers import rayleigh_quotient_iteration
from . import field_t
logger = logging.getLogger(__name__)
@ -256,7 +255,7 @@ def hmn_2_hxyz(k0: numpy.ndarray,
:return: Function for converting h_mn into H_xyz
"""
shape = epsilon[0].shape + (1,)
k_mag, m, n = generate_kmn(k0, G_matrix, shape)
_k_mag, m, n = generate_kmn(k0, G_matrix, shape)
def operator(h: numpy.ndarray):
hin_m, hin_n = [hi.reshape(shape) for hi in numpy.split(h, 2)]
@ -379,7 +378,6 @@ def find_k(frequency: float,
return res.x * direction, res.fun + frequency
def eigsolve(num_modes: int,
k0: numpy.ndarray,
G_matrix: numpy.ndarray,
@ -432,10 +430,8 @@ def eigsolve(num_modes: int,
Z = y0
while True:
Z *= num_modes / norm(Z)
ZtZ = Z.conj().T @ Z
Z_norm = numpy.sqrt(real(trace(ZtZ))) / num_modes
Z /= Z_norm
ZtZ /= Z_norm * Z_norm
try:
U = numpy.linalg.inv(ZtZ)
except numpy.linalg.LinAlgError:
@ -449,7 +445,7 @@ def eigsolve(num_modes: int,
continue
break
for iter in range(max_iters):
for i in range(max_iters):
ZtZ = Z.conj().T @ Z
U = numpy.linalg.inv(ZtZ)
AZ = scipy_op @ Z
@ -460,22 +456,22 @@ def eigsolve(num_modes: int,
E = numpy.abs(E_signed)
G = (AZU - Z @ U @ ZtAZU) * sgn
if iter > 0 and abs(E - prev_E) < tolerance * 0.5 * (E + prev_E + 1e-7):
if i > 0 and abs(E - prev_E) < tolerance * 0.5 * (E + prev_E + 1e-7):
logging.info('Optimization succeded: {} - 5e-8 < {} * {} / 2'.format(abs(E - prev_E), tolerance, E + prev_E))
break
KG = scipy_iop @ G
traceGtKG = _rtrace_AtB(G, KG)
if prev_traceGtKG == 0 or iter % reset_iters == 0:
if prev_traceGtKG == 0 or i % reset_iters == 0:
logger.info('CG reset')
gamma = 0
else:
gamma = traceGtKG / prev_traceGtKG
D = gamma * d_scale * D + KG
d_scale = numpy.sqrt(_rtrace_AtB(D, D)) / num_modes
D /= d_scale
D = gamma / d_scale * D + KG
d_scale = num_modes / norm(D)
D *= d_scale
ZtAZ = Z.conj().T @ AZ
@ -486,22 +482,6 @@ def eigsolve(num_modes: int,
symZtD = _symmetrize(Z.conj().T @ D)
symZtAD = _symmetrize(Z.conj().T @ AD)
'''
U_sZtD = U @ symZtD
dE = 2.0 * (_rtrace_AtB(U, symZtAD) -
_rtrace_AtB(ZtAZU, U_sZtD))
d2E = 2 * (_rtrace_AtB(U, DtAD) -
_rtrace_AtB(ZtAZU, U @ (DtD - 4 * symZtD @ U_sZtD)) -
4 * _rtrace_AtB(U, symZtAD @ U_sZtD))
# Newton-Raphson to find a root of the first derivative:
theta = -dE/d2E
if d2E < 0 or abs(theta) >= pi:
theta = -abs(prev_theta) * numpy.sign(dE)
'''
def Qi_func(theta, memo=[None, None]):
if memo[0] == theta:
@ -549,12 +529,25 @@ def eigsolve(num_modes: int,
trace_deriv *= 2
return trace_deriv * sgn
'''
U_sZtD = U @ symZtD
dE = 2.0 * (_rtrace_AtB(U, symZtAD) -
_rtrace_AtB(ZtAZU, U_sZtD))
d2E = 2 * (_rtrace_AtB(U, DtAD) -
_rtrace_AtB(ZtAZU, U @ (DtD - 4 * symZtD @ U_sZtD)) -
4 * _rtrace_AtB(U, symZtAD @ U_sZtD))
# Newton-Raphson to find a root of the first derivative:
theta = -dE/d2E
if d2E < 0 or abs(theta) >= pi:
theta = -abs(prev_theta) * numpy.sign(dE)
# theta, new_E, new_dE = linmin(theta, E, dE, 0.1, min(tolerance, 1e-6), 1e-14, 0, -numpy.sign(dE) * K_PI, trace_func)
theta, n, _, new_E, _, _new_dE = scipy.optimize.line_search(trace_func, trace_deriv, xk=theta, pk=numpy.ones((1,1)), gfk=dE, old_fval=E, c1=min(tolerance, 1e-6), c2=0.1, amax=pi)
'''
theta, new_E, new_dE = linmin(theta, E, dE, 0.1, min(tolerance, 1e-6), 1e-14, 0, -numpy.sign(dE) * K_PI, trace_func)
'''
#theta, n, _, new_E, _, _new_dE = scipy.optimize.line_search(trace_func, trace_deriv, xk=theta, pk=numpy.ones((1,1)), gfk=dE, old_fval=E, c1=min(tolerance, 1e-6), c2=0.1, amax=pi)
result = scipy.optimize.minimize_scalar(trace_func, bounds=(0, pi), tol=tolerance)
new_E = result.fun
theta = result.x
@ -591,32 +584,33 @@ def eigsolve(num_modes: int,
order = numpy.argsort(numpy.abs(eigvals))
return eigvals[order], eigvecs.T[order]
#def linmin(x_guess, f0, df0, x_max, f_tol=0.1, df_tol=min(tolerance, 1e-6), x_tol=1e-14, x_min=0, linmin_func):
# if df0 > 0:
# x0, f0, df0 = linmin(-x_guess, f0, -df0, -x_max, f_tol, df_tol, x_tol, -x_min, lambda q, dq: -linmin_func(q, dq))
# return -x0, f0, -df0
# elif df0 == 0:
# return 0, f0, df0
# else:
# x = x_guess
# fx = f0
# dfx = df0
'''
def linmin(x_guess, f0, df0, x_max, f_tol=0.1, df_tol=min(tolerance, 1e-6), x_tol=1e-14, x_min=0, linmin_func):
if df0 > 0:
x0, f0, df0 = linmin(-x_guess, f0, -df0, -x_max, f_tol, df_tol, x_tol, -x_min, lambda q, dq: -linmin_func(q, dq))
return -x0, f0, -df0
elif df0 == 0:
return 0, f0, df0
else:
x = x_guess
fx = f0
dfx = df0
# isave = numpy.zeros((2,), numpy.intc)
# dsave = numpy.zeros((13,), float)
isave = numpy.zeros((2,), numpy.intc)
dsave = numpy.zeros((13,), float)
# x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task,
# x_min, x_max, isave, dsave)
# for i in range(int(1e6)):
# if task != 'F':
# logging.info('search converged in {} iterations'.format(i))
# break
# fx = f(x, dfx)
# x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task,
# x_min, x_max, isave, dsave)
# return x, fx, dfx
x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task,
x_min, x_max, isave, dsave)
for i in range(int(1e6)):
if task != 'F':
logging.info('search converged in {} iterations'.format(i))
break
fx = f(x, dfx)
x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task,
x_min, x_max, isave, dsave)
return x, fx, dfx
'''
def _rtrace_AtB(A, B):
return real(numpy.sum(A.conj() * B))

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