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