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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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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 logging
import numpy import numpy
from numpy import pi, real, trace from numpy import pi, real, trace
@ -83,7 +83,6 @@ import scipy.optimize
from scipy.linalg import norm from scipy.linalg import norm
import scipy.sparse.linalg as spalg import scipy.sparse.linalg as spalg
from .eigensolvers import rayleigh_quotient_iteration
from . import field_t from . import field_t
logger = logging.getLogger(__name__) logger = logging.getLogger(__name__)
@ -256,7 +255,7 @@ def hmn_2_hxyz(k0: numpy.ndarray,
:return: Function for converting h_mn into H_xyz :return: Function for converting h_mn into H_xyz
""" """
shape = epsilon[0].shape + (1,) 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): def operator(h: numpy.ndarray):
hin_m, hin_n = [hi.reshape(shape) for hi in numpy.split(h, 2)] 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 return res.x * direction, res.fun + frequency
def eigsolve(num_modes: int, def eigsolve(num_modes: int,
k0: numpy.ndarray, k0: numpy.ndarray,
G_matrix: numpy.ndarray, G_matrix: numpy.ndarray,
@ -432,10 +430,8 @@ def eigsolve(num_modes: int,
Z = y0 Z = y0
while True: while True:
Z *= num_modes / norm(Z)
ZtZ = Z.conj().T @ Z ZtZ = Z.conj().T @ Z
Z_norm = numpy.sqrt(real(trace(ZtZ))) / num_modes
Z /= Z_norm
ZtZ /= Z_norm * Z_norm
try: try:
U = numpy.linalg.inv(ZtZ) U = numpy.linalg.inv(ZtZ)
except numpy.linalg.LinAlgError: except numpy.linalg.LinAlgError:
@ -449,7 +445,7 @@ def eigsolve(num_modes: int,
continue continue
break break
for iter in range(max_iters): for i in range(max_iters):
ZtZ = Z.conj().T @ Z ZtZ = Z.conj().T @ Z
U = numpy.linalg.inv(ZtZ) U = numpy.linalg.inv(ZtZ)
AZ = scipy_op @ Z AZ = scipy_op @ Z
@ -460,22 +456,22 @@ def eigsolve(num_modes: int,
E = numpy.abs(E_signed) E = numpy.abs(E_signed)
G = (AZU - Z @ U @ ZtAZU) * sgn 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)) logging.info('Optimization succeded: {} - 5e-8 < {} * {} / 2'.format(abs(E - prev_E), tolerance, E + prev_E))
break break
KG = scipy_iop @ G KG = scipy_iop @ G
traceGtKG = _rtrace_AtB(G, KG) 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') logger.info('CG reset')
gamma = 0 gamma = 0
else: else:
gamma = traceGtKG / prev_traceGtKG gamma = traceGtKG / prev_traceGtKG
D = gamma * d_scale * D + KG D = gamma / d_scale * D + KG
d_scale = numpy.sqrt(_rtrace_AtB(D, D)) / num_modes d_scale = num_modes / norm(D)
D /= d_scale D *= d_scale
ZtAZ = Z.conj().T @ AZ ZtAZ = Z.conj().T @ AZ
@ -486,22 +482,6 @@ def eigsolve(num_modes: int,
symZtD = _symmetrize(Z.conj().T @ D) symZtD = _symmetrize(Z.conj().T @ D)
symZtAD = _symmetrize(Z.conj().T @ AD) 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]): def Qi_func(theta, memo=[None, None]):
if memo[0] == theta: if memo[0] == theta:
@ -549,12 +529,25 @@ def eigsolve(num_modes: int,
trace_deriv *= 2 trace_deriv *= 2
return trace_deriv * sgn 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) result = scipy.optimize.minimize_scalar(trace_func, bounds=(0, pi), tol=tolerance)
new_E = result.fun new_E = result.fun
theta = result.x theta = result.x
@ -591,32 +584,33 @@ def eigsolve(num_modes: int,
order = numpy.argsort(numpy.abs(eigvals)) order = numpy.argsort(numpy.abs(eigvals))
return eigvals[order], eigvecs.T[order] 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: 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):
# 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)) if df0 > 0:
# return -x0, f0, -df0 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))
# elif df0 == 0: return -x0, f0, -df0
# return 0, f0, df0 elif df0 == 0:
# else: return 0, f0, df0
# x = x_guess else:
# fx = f0 x = x_guess
# dfx = df0 fx = f0
dfx = df0
# isave = numpy.zeros((2,), numpy.intc) isave = numpy.zeros((2,), numpy.intc)
# dsave = numpy.zeros((13,), float) dsave = numpy.zeros((13,), float)
# x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task, x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task,
# x_min, x_max, isave, dsave) x_min, x_max, isave, dsave)
# for i in range(int(1e6)): for i in range(int(1e6)):
# if task != 'F': if task != 'F':
# logging.info('search converged in {} iterations'.format(i)) logging.info('search converged in {} iterations'.format(i))
# break break
# fx = f(x, dfx) fx = f(x, dfx)
# x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task, x, fx, dfx, task = minpack2.dsrch(x, fx, dfx, f_tol, df_tol, x_tol, task,
# x_min, x_max, isave, dsave) x_min, x_max, isave, dsave)
# return x, fx, dfx
return x, fx, dfx
'''
def _rtrace_AtB(A, B): def _rtrace_AtB(A, B):
return real(numpy.sum(A.conj() * B)) return real(numpy.sum(A.conj() * B))

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