cleanup
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4067766478
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@ -447,15 +447,10 @@ def eigsolve(num_modes: int,
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continue
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break
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def rtrace_AtB(A, B):
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return real(numpy.sum(A.conj() * B))
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def symmetrize(A):
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return (A + A.conj().T) * 0.5
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max_iters = 10000
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for iter in range(max_iters):
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U = numpy.linalg.inv(Z.conj().T @ Z)
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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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AZU = AZ @ U
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ZtAZU = Z.conj().T @ AZU
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@ -469,47 +464,44 @@ def eigsolve(num_modes: int,
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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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gamma_numerator = traceGtKG
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traceGtKG = _rtrace_AtB(G, KG)
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reset_iters = 100
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reset_iters = 100 # TODO
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if prev_traceGtKG == 0 or iter % reset_iters == 0:
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print('RESET!')
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logger.inf('CG reset')
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gamma = 0
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else:
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gamma = gamma_numerator / prev_traceGtKG
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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_scale = numpy.sqrt(_rtrace_AtB(D, D)) / num_modes
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D /= d_scale
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ZtAZ = Z.conj().T @ AZ
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AD = scipy_op @ D
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DtD = D.conj().T @ D
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DtAD = D.conj().T @ AD
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ZtD = Z.conj().T @ D
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ZtAD = Z.conj().T @ AD
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symZtD = symmetrize(ZtD)
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symZtAD = symmetrize(ZtAD)
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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) - rtrace_AtB(ZtAZU, U_sZtD))
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dE = 2.0 * (_rtrace_AtB(U, symZtAD) -
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_rtrace_AtB(ZtAZU, U_sZtD))
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S2 = DtD - 4 * symZtD @ U_sZtD
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d2E = 2 * (rtrace_AtB(U, DtAD) -
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rtrace_AtB(ZtAZU, U @ S2) -
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4 * rtrace_AtB(U, symZtAD @ 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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# ZtAZU * ZtZ = ZtAZ for use in line search
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ZtZ = Z.conj().T @ Z
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ZtAZ = ZtAZU @ ZtZ.conj().T
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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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@ -525,10 +517,10 @@ def eigsolve(num_modes: int,
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# if c or s small, taylor expand
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if c < 1e-4 * s and c != 0:
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Qi = numpy.linalg.inv(DtD)
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Qi = Qi / (s*s) - 2*c/(s*s*s) * (Qi @ symZtD.conj().T @ Qi.conj().T)
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Qi = Qi / (s*s) - 2*c/(s*s*s) * (Qi @ (Qi @ symZtD).conj().T)
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elif s < 1e-4 * c and s != 0:
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Qi = numpy.linalg.inv(ZtZ)
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Qi = Qi / (c*c) - 2*s/(c*c*c) * (Qi @ symZtD.conj().T @ Qi.conj().T)
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Qi = Qi / (c*c) - 2*s/(c*c*c) * (Qi @ (Qi @ symZtD).conj().T)
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else:
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raise Exception('Inexplicable singularity in trace_func')
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memo[0] = theta
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@ -540,22 +532,24 @@ def eigsolve(num_modes: int,
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s = numpy.sin(theta)
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Qi = Qi_func(theta)
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R = c*c * ZtAZ + s*s * DtAD + 2*s*c * symZtAD
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trace = rtrace_AtB(R, Qi)
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trace = _rtrace_AtB(R, Qi)
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return numpy.abs(trace)
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#def trace_deriv(theta):
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# Qi = Qi_func(theta)
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# c2 = numpy.cos(2 * theta)
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# s2 = numpy.sin(2 * theta)
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# F = -0.5*s2 * (ZtAZ - DtAD) + c2 * symZtAD
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# trace_deriv = rtrace_AtB(Qi, F)
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'''
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def trace_deriv(theta):
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Qi = Qi_func(theta)
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c2 = numpy.cos(2 * theta)
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s2 = numpy.sin(2 * theta)
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F = -0.5*s2 * (ZtAZ - DtAD) + c2 * symZtAD
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trace_deriv = _rtrace_AtB(Qi, F)
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# G = Qi @ F.conj().T @ Qi.conj().T
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# H = -0.5*s2 * (ZtZ - DtD) + c2 * symZtD
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# trace_deriv -= rtrace_AtB(G, H)
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G = Qi @ F.conj().T @ Qi.conj().T
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H = -0.5*s2 * (ZtZ - DtD) + c2 * symZtD
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trace_deriv -= _rtrace_AtB(G, H)
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# trace_deriv *= 2
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# return trace_deriv * sgn
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trace_deriv *= 2
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return trace_deriv * sgn
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'''
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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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@ -597,29 +591,36 @@ 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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#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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# 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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# return x, fx, dfx
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def _rtrace_AtB(A, B):
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return real(numpy.sum(A.conj() * B))
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def _symmetrize(A):
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return (A + A.conj().T) * 0.5
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