flake8 fixes
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@ -684,11 +684,11 @@ def eigsolve(
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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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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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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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@ -696,12 +696,12 @@ def eigsolve(
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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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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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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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@ -253,7 +253,8 @@ def operator_e(
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mu_yx = sparse.diags(numpy.hstack((mu_parts[1], mu_parts[0])))
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mu_z_inv = sparse.diags(1 / mu_parts[2])
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op = (omega * omega * mu_yx @ eps_xy
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op = (
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omega * omega * mu_yx @ eps_xy
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+ mu_yx @ sparse.vstack((-Dby, Dbx)) @ mu_z_inv @ sparse.hstack((-Dfy, Dfx))
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+ sparse.vstack((Dfx, Dfy)) @ eps_z_inv @ sparse.hstack((Dbx, Dby)) @ eps_xy
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)
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@ -321,7 +322,8 @@ def operator_h(
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mu_xy = sparse.diags(numpy.hstack((mu_parts[0], mu_parts[1])))
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mu_z_inv = sparse.diags(1 / mu_parts[2])
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op = (omega * omega * eps_yx @ mu_xy
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op = (
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omega * omega * eps_yx @ mu_xy
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+ eps_yx @ sparse.vstack((-Dfy, Dfx)) @ eps_z_inv @ sparse.hstack((-Dby, Dbx))
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+ sparse.vstack((Dbx, Dby)) @ mu_z_inv @ sparse.hstack((Dfx, Dfy)) @ mu_xy
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)
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@ -799,14 +801,12 @@ def sensitivity(
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Dfx, Dfy = deriv_forward(dxes[0])
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Dbx, Dby = deriv_back(dxes[1])
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eps_x, eps_y, eps_z = numpy.split(epsilon, 3)
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eps_xy = sparse.diags(numpy.hstack((eps_x, eps_y)))
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eps_z_inv = sparse.diags(1 / eps_z)
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mu_x, mu_y, mu_z = numpy.split(mu, 3)
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mu_x, mu_y, _mu_z = numpy.split(mu, 3)
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mu_yx = sparse.diags(numpy.hstack((mu_y, mu_x)))
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mu_z_inv = sparse.diags(1 / mu_z)
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da_exxhyy = vec(dxes[1][0][:, None] * dxes[0][1][None, :])
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da_eyyhxx = vec(dxes[1][1][None, :] * dxes[0][0][:, None])
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@ -816,7 +816,7 @@ def sensitivity(
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sens_xy1 = (hv_yx_conj @ (omega * omega * mu_yx)) * ev_xy
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sens_xy2 = (hv_yx_conj @ sparse.vstack((Dfx, Dfy)) @ eps_z_inv @ sparse.hstack((Dbx, Dby))) * ev_xy
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sens_z = (hv_yx_conj @ sparse.vstack((Dfx, Dfy)) @ (-eps_z_inv * eps_z_inv)) * (sparse.hstack((Dbx, Dby)) @ eps_xy @ ev_xy)
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sens_z = (hv_yx_conj @ sparse.vstack((Dfx, Dfy)) @ (-eps_z_inv * eps_z_inv)) * (sparse.hstack((Dbx, Dby)) @ eps_xy @ ev_xy)
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norm = hv_yx_conj @ ev_xy
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sens_tot = numpy.concatenate([sens_xy1 + sens_xy2, sens_z]) / (2 * wavenumber * norm)
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@ -19,9 +19,13 @@ def conducting_boundary(
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dirs.remove(direction)
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u, v = dirs
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boundary_slice: list[Any]
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shifted1_slice: list[Any]
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shifted2_slice: list[Any]
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if polarity < 0:
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boundary_slice = [slice(None)] * 3 # type: list[Any]
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shifted1_slice = [slice(None)] * 3 # type: list[Any]
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boundary_slice = [slice(None)] * 3
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shifted1_slice = [slice(None)] * 3
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boundary_slice[direction] = 0
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shifted1_slice[direction] = 1
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@ -42,7 +46,7 @@ def conducting_boundary(
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if polarity > 0:
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boundary_slice = [slice(None)] * 3
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shifted1_slice = [slice(None)] * 3
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shifted2_slice = [slice(None)] * 3 # type: list[Any]
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shifted2_slice = [slice(None)] * 3
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boundary_slice[direction] = -1
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shifted1_slice[direction] = -2
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shifted2_slice[direction] = -3
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