Use L-BFGS instead of CG, and remove rayleigh iteration refinement
scipy CG doesn't seem to converge as well as L-BFGS... worth looking into later
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@ -359,6 +359,8 @@ def eigsolve(num_modes: int,
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"""
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h_size = 2 * epsilon[0].size
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kmag = norm(G_matrix @ k0)
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'''
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Generate the operators
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'''
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@ -409,16 +411,26 @@ def eigsolve(num_modes: int,
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result = scipy.optimize.minimize(rayleigh_quotient,
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numpy.random.rand(*y_shape),
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jac=True,
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method='CG',
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tol=1e-5,
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options={'maxiter': 30, 'disp':True})
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method='L-BFGS-B',
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tol=1e-20,
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options={'maxiter': 2000, 'gtol':0, 'ftol':1e-20 , 'disp':True})#, 'maxls':80, 'm':30})
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result = scipy.optimize.minimize(lambda y: rayleigh_quotient(y, False),
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result.x,
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jac=True,
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method='CG',
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tol=1e-13,
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options={'maxiter': 100, 'disp':True})
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method='L-BFGS-B',
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tol=1e-20,
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options={'maxiter': 2000, 'ptol':1e-18, 'disp':True})
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for i in range(20):
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result = scipy.optimize.minimize(lambda y: rayleigh_quotient(y, False),
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result.x,
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jac=True,
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method='L-BFGS-B',
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tol=1e-20,
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options={'maxiter': 70, 'gtol':1e-18, 'disp':True})
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z = result.x.reshape(y_shape)
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@ -436,25 +448,13 @@ def eigsolve(num_modes: int,
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v = eigvecs[:, i]
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n = eigvals[i]
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v /= norm(v)
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logger.info('eigness {}: {}'.format(i, norm(scipy_op @ v - (v.conj() @ (scipy_op @ v)) * v )))
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eigness = norm(scipy_op @ v - (v.conj() @ (scipy_op @ v)) * v )
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f = numpy.sqrt(-numpy.real(n))
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df = numpy.sqrt(-numpy.real(n + eigness))
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neff_err = kmag * (1/df - 1/f)
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logger.info('eigness {}: {}\n neff_err: {}'.format(i, eigness, neff_err))
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ev2 = eigvecs.copy()
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for i in range(len(eigvals)):
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logger.info('Refining eigenvector {}'.format(i))
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eigvals[i], ev2[:, i] = rayleigh_quotient_iteration(scipy_op,
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guess_vector=eigvecs[:, i],
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iterations=40,
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tolerance=tolerance * numpy.real(numpy.sqrt(eigvals[i])) * 2,
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solver = lambda A, b: spalg.bicgstab(A, b, maxiter=200)[0])
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eigvecs = ev2
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order = numpy.argsort(numpy.abs(eigvals))
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for i in range(len(eigvals)):
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v = eigvecs[:, i]
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n = eigvals[i]
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v /= norm(v)
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logger.info('eigness {}: {}'.format(i, norm(scipy_op @ v - (v.conj() @ (scipy_op @ v)) * v )))
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return eigvals[order], eigvecs.T[order]
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