Contents

function DEMO_RI_GE_T_N(istest)
% Computes the solution of the Hinf Riccati equation for a random generated
% generalized system. The computations are done with the RADI method for
% the control and filter Hinf Riccati equations. Afterwards, the real
% residual norms are shown and compared to the set tolerance.
%
% Input:
% istest  decides whether the function runs as an interactive demo or a
%         continuous integration test. (optional; defaults to 0, i.e.
%         interactive demo)
%

%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, see <http://www.gnu.org/licenses/>.
%
% Copyright (C) Jens Saak, Martin Koehler, Peter Benner and others
%               2009-2020
%
if nargin<1, istest=0; end

Construction of system data.

if exist('OCTAVE_VERSION', 'builtin')
    rand('seed', 1.0); %#ok<RAND>
    eqn.A_ = rand(500) - 250 * eye(500);
    rand('seed', 2.0); %#ok<RAND>
    eqn.E_ = rand(500);
    eqn.E_ = eqn.E_' * eqn.E_;

    rand('seed', 3.0); %#ok<RAND>
    eqn.B2 = rand(500, 2);
    rand('seed', 4.0); %#ok<RAND>
    B1 = rand(500, 2);

    rand('seed', 5.0); %#ok<RAND>
    eqn.C2 = rand(3, 500);
    rand('seed', 6.0); %#ok<RAND>
    C1 = rand(3, 500);
else
    rng(1.0);
    eqn.A_ = rand(500) - 250 * eye(500);
    rng(2.0);
    eqn.E_ = rand(500);
    eqn.E_ = eqn.E_' * eqn.E_;

    rng(3.0);
    eqn.B2 = rand(500, 2);
    rng(4.0);
    B1 = rand(500, 2);

    rng(5.0);
    eqn.C2 = rand(3, 500);
    rng(6.0);
    C1 = rand(3, 500);
end

eqn.haveE = 1;

gam = 5; % Scaling term for disturbances.

Set operator.

oper = operatormanager('default');

Construction of options struct.

RADI settings.

opts.radi.maxiter      = 100;
opts.radi.res_tol      = 1.0e-12;
opts.radi.rel_diff_tol = 1.0e-16;
opts.radi.info         = 1;
opts.radi.trunc_tol    = eps;

% Shift options.
opts.shifts.num_desired     = 5;
opts.shifts.method = 'projection';

% RI settings.
opts.ri.riccati_solver = 'radi';
opts.ri.maxiter        = 10;
opts.ri.res_tol        = 1.0e-09;
opts.ri.rel_diff_tol   = 1.0e-16;
opts.ri.compres_tol    = 1.0e-16;
opts.ri.info           = 1;
opts.ri.trunc_tol      = eps;

% global options
opts.norm           = 2;

Solve the control equation.

tic;
eqn.type = 'T';
eqn.B1   = 1/gam * B1;
eqn.C1   = C1;
[outControl, eqn, opts, oper] = mess_lrri(eqn, opts, oper);
toc;
RADI step:    1 pc: -6.595647e+00 + 0.000000e+00i normalized residual: 9.236423e-01 relative change in Z: 1.000000e+00
RADI step:    2 pc: -5.503746e+00 + 0.000000e+00i normalized residual: 9.138310e-01 relative change in Z: 5.497570e-01
RADI step:    3 pc: -4.751833e-04 + 0.000000e+00i normalized residual: 8.805950e-01 relative change in Z: 1.497923e-01
RADI step:    4 pc: -2.103132e+00 + 0.000000e+00i normalized residual: 8.752092e-01 relative change in Z: 2.918227e-01
RADI step:    5 pc: -9.586933e-04 + 0.000000e+00i normalized residual: 6.573983e-01 relative change in Z: 5.055678e-02
RADI step:    6 pc: -8.245415e+01 + 0.000000e+00i normalized residual: 6.513484e-01 relative change in Z: 7.981100e-01
RADI step:    7 pc: -8.192174e+00 + 0.000000e+00i normalized residual: 6.469973e-01 relative change in Z: 2.040896e-01
RADI step:    8 pc: -5.428094e+01 + 0.000000e+00i normalized residual: 6.479712e-01 relative change in Z: 4.332318e-01
RADI step:    9 pc: -1.948282e+00 + 0.000000e+00i normalized residual: 6.420417e-01 relative change in Z: 7.723426e-02
RADI step:   10 pc: -2.641502e-03 + 0.000000e+00i normalized residual: 1.004718e-01 relative change in Z: 1.427654e-02
RADI step:   11 pc: -1.399131e+03 + 0.000000e+00i normalized residual: 9.760732e-02 relative change in Z: 8.108794e-01
RADI step:   12 pc: -3.081852e+01 + 0.000000e+00i normalized residual: 9.786744e-02 relative change in Z: 1.039725e-01
RADI step:   13 pc: -1.266450e+02 + 0.000000e+00i normalized residual: 9.722493e-02 relative change in Z: 1.954600e-01
RADI step:   14 pc: -5.328434e+00 + 0.000000e+00i normalized residual: 9.721685e-02 relative change in Z: 3.879684e-02
RADI step:   15 pc: -1.643385e+04 + 0.000000e+00i normalized residual: 9.593976e-02 relative change in Z: 8.343566e-01
RADI step:   16 pc: -4.700072e-03 + 0.000000e+00i normalized residual: 1.014750e-03 relative change in Z: 1.347891e-03
RADI step:   17 pc: -2.847214e+02 + 0.000000e+00i normalized residual: 9.363992e-04 relative change in Z: 9.714434e-02
RADI step:   18 pc: -3.895369e+01 + 0.000000e+00i normalized residual: 9.299439e-04 relative change in Z: 3.494885e-02
RADI step:   19 pc: -1.770581e+01 + 0.000000e+00i normalized residual: 9.297762e-04 relative change in Z: 2.349740e-02
RADI step:   20 pc: -2.062053e+05 + 0.000000e+00i normalized residual: 3.897790e-04 relative change in Z: 8.204956e-01
RADI step:   21 pc: -4.973095e-03 + 0.000000e+00i normalized residual: 3.615338e-04 relative change in Z: 1.321272e-04
RADI step:   22 pc: -3.571063e+03 + 0.000000e+00i normalized residual: 2.990567e-04 relative change in Z: 9.651357e-02
RADI step:   23 pc: -1.855638e+00 + 0.000000e+00i normalized residual: 2.990224e-04 relative change in Z: 2.076200e-03
RADI step:   24 pc: -1.509223e+02 + 0.000000e+00i normalized residual: 2.972224e-04 relative change in Z: 1.865532e-02
RADI step:   25 pc: -4.972659e-03 + 0.000000e+00i normalized residual: 2.972223e-04 relative change in Z: 1.067691e-04
RADI step:   26 pc: -3.896030e+06 + 0.000000e+00i normalized residual: 6.819848e-05 relative change in Z: 8.524739e-01
RADI step:   27 pc: -2.032899e+04 + 0.000000e+00i normalized residual: 4.213357e-05 relative change in Z: 5.229367e-02
RADI step:   28 pc: -1.616135e+00 + 0.000000e+00i normalized residual: 4.212646e-05 relative change in Z: 4.208969e-04
RADI step:   29 pc: -3.038675e+03 + 0.000000e+00i normalized residual: 4.035805e-05 relative change in Z: 1.765306e-02
RADI step:   30 pc: -7.297810e+06 + 0.000000e+00i normalized residual: 1.676264e-05 relative change in Z: 2.615684e-01
RADI step:   31 pc: -1.643177e+00 + 0.000000e+00i normalized residual: 1.675956e-05 relative change in Z: 2.820280e-04
RADI step:   32 pc: -1.233952e+05 + 0.000000e+00i normalized residual: 4.932777e-06 relative change in Z: 4.867860e-02
RADI step:   33 pc: -3.777727e+02 + 0.000000e+00i normalized residual: 4.667946e-06 relative change in Z: 1.795552e-03
RADI step:   34 pc: -4.633499e+03 + 0.000000e+00i normalized residual: 4.347147e-06 relative change in Z: 5.958112e-03
RADI step:   35 pc: -1.997167e+00 + 0.000000e+00i normalized residual: 4.346960e-06 relative change in Z: 1.215088e-04
RADI step:   36 pc: -7.300033e+06 + 0.000000e+00i normalized residual: 3.389639e-06 relative change in Z: 1.342975e-02
RADI step:   37 pc: -1.521493e+05 + 0.000000e+00i normalized residual: 8.825532e-07 relative change in Z: 2.170168e-02
RADI step:   38 pc: -4.604190e+02 + 0.000000e+00i normalized residual: 8.696676e-07 relative change in Z: 8.243518e-04
RADI step:   39 pc: -2.623980e+04 + 0.000000e+00i normalized residual: 6.717361e-07 relative change in Z: 5.725098e-03
RADI step:   40 pc: -7.490774e+01 + 0.000000e+00i normalized residual: 6.711509e-07 relative change in Z: 2.869241e-04
RADI step:   41 pc: -4.416647e+06 + 0.000000e+00i normalized residual: 4.416699e-07 relative change in Z: 6.568612e-03
RADI step:   42 pc: -9.701281e+02 + 0.000000e+00i normalized residual: 4.372665e-07 relative change in Z: 8.351355e-04
RADI step:   43 pc: -4.619811e+05 + 0.000000e+00i normalized residual: 1.242999e-09 relative change in Z: 9.055298e-03
RADI step:   44 pc: -7.538829e+03 + 0.000000e+00i normalized residual: 2.861339e-10 relative change in Z: 1.106760e-04
RADI step:   45 pc: -1.133603e+02 + 0.000000e+00i normalized residual: 2.820544e-10 relative change in Z: 9.592387e-06
RADI step:   46 pc: -4.619818e+05 + 0.000000e+00i normalized residual: 1.559031e-10 relative change in Z: 8.668421e-05
RADI step:   47 pc: -9.717231e+02 + 0.000000e+00i normalized residual: 1.376846e-10 relative change in Z: 2.028000e-05
RADI step:   48 pc: -3.939646e+04 + 0.000000e+00i normalized residual: 2.236631e-11 relative change in Z: 7.505787e-05
RADI step:   49 pc: -5.173477e+03 + 0.000000e+00i normalized residual: 1.756751e-11 relative change in Z: 1.302220e-05
RADI step:   50 pc: -5.228703e+01 + 0.000000e+00i normalized residual: 1.706862e-11 relative change in Z: 1.212845e-06
RADI step:   51 pc: -4.619818e+05 + 0.000000e+00i normalized residual: 7.175113e-12 relative change in Z: 2.026676e-05
RADI step:   52 pc: -3.939162e+04 + 0.000000e+00i normalized residual: 1.627665e-12 relative change in Z: 1.511270e-05
RADI step:   53 pc: -8.050653e+02 + 0.000000e+00i normalized residual: 1.534716e-12 relative change in Z: 1.367708e-06
RADI step:   54 pc: -1.705819e+03 + 0.000000e+00i normalized residual: 1.430741e-12 relative change in Z: 1.906266e-06
RADI step:   55 pc: -1.450528e+01 + 0.000000e+00i normalized residual: 1.223702e-12 relative change in Z: 1.809568e-07
RADI step:   56 pc: -1.530546e+05 + 0.000000e+00i normalized residual: 6.500373e-14 relative change in Z: 6.937972e-06
RI step:    1  normalized residual: 3.560137e-02 relative change in Z: 1.000000e+00
               number of RADI steps:   56

RADI step:    1 pc: -3.403506e+00 + 0.000000e+00i normalized residual: 9.943999e-01 relative change in Z: 1.000000e+00
RADI step:    2 pc: -4.771368e-03 + 0.000000e+00i normalized residual: 1.193780e-04 relative change in Z: 9.949786e-01
RADI step:    3 pc: -1.196700e+01 + 0.000000e+00i normalized residual: 1.190079e-04 relative change in Z: 5.992934e-02
RADI step:    4 pc: -6.831295e+00 + 0.000000e+00i normalized residual: 1.185588e-04 relative change in Z: 3.302110e-02
RADI step:    5 pc: -2.168815e+00 + 0.000000e+00i normalized residual: 1.175102e-04 relative change in Z: 1.730776e-02
RADI step:    6 pc: -4.875837e-03 + 0.000000e+00i normalized residual: 9.386139e-08 relative change in Z: 1.069987e-02
RADI step:    7 pc: -1.711991e+00 + 0.000000e+00i normalized residual: 8.971046e-08 relative change in Z: 1.480520e-02
RADI step:    8 pc: -4.875801e-03 + 0.000000e+00i normalized residual: 8.969924e-08 relative change in Z: 7.813892e-04
RADI step:    9 pc: -2.710502e+02 + 0.000000e+00i normalized residual: 2.177494e-08 relative change in Z: 1.092012e-01
RADI step:   10 pc: -2.307914e+01 + 0.000000e+00i normalized residual: 1.366111e-08 relative change in Z: 2.464808e-02
RADI step:   11 pc: -5.814548e+00 + 0.000000e+00i normalized residual: 1.295964e-08 relative change in Z: 1.119859e-02
RADI step:   12 pc: -2.298447e+00 + 0.000000e+00i normalized residual: 1.272513e-08 relative change in Z: 6.939127e-03
RADI step:   13 pc: -2.040699e+03 + 0.000000e+00i normalized residual: 2.907191e-09 relative change in Z: 1.160054e-01
RADI step:   14 pc: -4.875801e-03 + 0.000000e+00i normalized residual: 2.906884e-09 relative change in Z: 1.643910e-04
RADI step:   15 pc: -5.423219e+01 + 0.000000e+00i normalized residual: 1.870928e-09 relative change in Z: 1.551389e-02
RADI step:   16 pc: -2.334785e+02 + 0.000000e+00i normalized residual: 1.687032e-09 relative change in Z: 2.762474e-02
RADI step:   17 pc: -6.750872e+00 + 0.000000e+00i normalized residual: 1.683103e-09 relative change in Z: 4.465060e-03
RADI step:   18 pc: -1.511730e+04 + 0.000000e+00i normalized residual: 4.694473e-10 relative change in Z: 1.344507e-01
RADI step:   19 pc: -4.875776e-03 + 0.000000e+00i normalized residual: 4.694457e-10 relative change in Z: 6.789777e-05
RADI step:   20 pc: -3.686070e+02 + 0.000000e+00i normalized residual: 4.313667e-10 relative change in Z: 1.761330e-02
RADI step:   21 pc: -5.319727e+01 + 0.000000e+00i normalized residual: 4.281389e-10 relative change in Z: 6.414951e-03
RADI step:   22 pc: -5.816955e+02 + 0.000000e+00i normalized residual: 4.077584e-10 relative change in Z: 2.063975e-02
RADI step:   23 pc: -2.564565e+00 + 0.000000e+00i normalized residual: 4.076828e-10 relative change in Z: 1.344832e-03
RADI step:   24 pc: -9.235864e+04 + 0.000000e+00i normalized residual: 1.603660e-10 relative change in Z: 1.673551e-01
RADI step:   25 pc: -3.601629e+01 + 0.000000e+00i normalized residual: 1.597409e-10 relative change in Z: 2.747174e-03
RADI step:   26 pc: -9.122426e+03 + 0.000000e+00i normalized residual: 1.273375e-10 relative change in Z: 3.868424e-02
RADI step:   27 pc: -9.625942e+02 + 0.000000e+00i normalized residual: 1.252362e-10 relative change in Z: 1.200583e-02
RADI step:   28 pc: -6.202076e+05 + 0.000000e+00i normalized residual: 4.061536e-11 relative change in Z: 1.915115e-01
RADI step:   29 pc: -1.580679e+00 + 0.000000e+00i normalized residual: 4.061416e-11 relative change in Z: 2.693313e-04
RADI step:   30 pc: -2.649398e+04 + 0.000000e+00i normalized residual: 3.689326e-11 relative change in Z: 3.316074e-02
RADI step:   31 pc: -3.219120e+01 + 0.000000e+00i normalized residual: 3.688569e-11 relative change in Z: 1.136712e-03
RADI step:   32 pc: -4.038845e+03 + 0.000000e+00i normalized residual: 3.659692e-11 relative change in Z: 1.264380e-02
RADI step:   33 pc: -1.576024e+00 + 0.000000e+00i normalized residual: 3.659682e-11 relative change in Z: 2.490798e-04
RADI step:   34 pc: -7.161214e+06 + 0.000000e+00i normalized residual: 1.147303e-12 relative change in Z: 2.509567e-01
RADI step:   35 pc: -7.706049e+01 + 0.000000e+00i normalized residual: 1.144103e-12 relative change in Z: 3.920670e-04
RADI step:   36 pc: -1.503327e+05 + 0.000000e+00i normalized residual: 2.551178e-13 relative change in Z: 1.090171e-02
RI step:    2  normalized residual: 1.522697e-05 relative change in Z: 5.864875e-08
               number of RADI steps:   36

RADI step:    1 pc: -2.634325e+00 + 0.000000e+00i normalized residual: 9.926300e-01 relative change in Z: 1.000000e+00
RADI step:    2 pc: -4.869153e-03 + 0.000000e+00i normalized residual: 6.879508e-08 relative change in Z: 9.963082e-01
RADI step:    3 pc: -4.398232e+00 + 0.000000e+00i normalized residual: 6.848595e-08 relative change in Z: 2.928788e-05
RADI step:    4 pc: -2.525668e+00 + 0.000000e+00i normalized residual: 6.795855e-08 relative change in Z: 2.435724e-05
RADI step:    5 pc: -4.871718e-03 + 0.000000e+00i normalized residual: 1.194578e-14 relative change in Z: 2.606869e-04
RI step:    3  normalized residual: 2.731859e-12 relative change in Z: 2.050871e-11
               number of RADI steps:    5

Elapsed time is 0.406764 seconds.

Solve the filter equation.

tic;
eqn.type = 'N';
eqn.B1   = B1;
eqn.C1   = 1/gam * C1;
[outFilter, eqn, opts, ~] = mess_lrri(eqn, opts, oper);
toc;
RADI step:    1 pc: -6.733023e+00 + 0.000000e+00i normalized residual: 9.045840e-01 relative change in Z: 1.000000e+00
RADI step:    2 pc: -6.101093e-04 + 0.000000e+00i normalized residual: 8.537235e-01 relative change in Z: 1.610629e-01
RADI step:    3 pc: -3.305161e+01 + 0.000000e+00i normalized residual: 8.370617e-01 relative change in Z: 7.791775e-01
RADI step:    4 pc: -1.388380e+01 + 0.000000e+00i normalized residual: 8.325987e-01 relative change in Z: 3.781421e-01
RADI step:    5 pc: -3.178887e+00 + 0.000000e+00i normalized residual: 8.289544e-01 relative change in Z: 1.730686e-01
RADI step:    6 pc: -1.228092e-03 + 0.000000e+00i normalized residual: 5.357085e-01 relative change in Z: 3.301825e-02
RADI step:    7 pc: -1.746772e+00 + 0.000000e+00i normalized residual: 5.318790e-01 relative change in Z: 1.235617e-01
RADI step:    8 pc: -3.186932e-03 + 0.000000e+00i normalized residual: 4.938200e-02 relative change in Z: 1.686849e-02
RADI step:    9 pc: -5.233184e+02 + 0.000000e+00i normalized residual: 4.311709e-02 relative change in Z: 8.291444e-01
RADI step:   10 pc: -3.773325e+01 + 0.000000e+00i normalized residual: 4.368398e-02 relative change in Z: 1.806956e-01
RADI step:   11 pc: -1.073615e+01 + 0.000000e+00i normalized residual: 4.267700e-02 relative change in Z: 9.272202e-02
RADI step:   12 pc: -4.624748e+00 + 0.000000e+00i normalized residual: 4.334177e-02 relative change in Z: 6.031714e-02
RADI step:   13 pc: -4.955884e-03 + 0.000000e+00i normalized residual: 4.224669e-03 relative change in Z: 2.766628e-03
RADI step:   14 pc: -4.148474e+03 + 0.000000e+00i normalized residual: 1.893079e-03 relative change in Z: 8.057708e-01
RADI step:   15 pc: -9.544956e+01 + 0.000000e+00i normalized residual: 1.709084e-03 relative change in Z: 1.124349e-01
RADI step:   16 pc: -3.929615e+02 + 0.000000e+00i normalized residual: 1.580603e-03 relative change in Z: 2.147091e-01
RADI step:   17 pc: -4.402123e+01 + 0.000000e+00i normalized residual: 1.573369e-03 relative change in Z: 7.063560e-02
RADI step:   18 pc: -5.072252e-03 + 0.000000e+00i normalized residual: 1.572828e-03 relative change in Z: 7.575539e-04
RADI step:   19 pc: -1.244760e+05 + 0.000000e+00i normalized residual: 1.288151e-03 relative change in Z: 9.476746e-01
RADI step:   20 pc: -2.550884e+03 + 0.000000e+00i normalized residual: 1.178627e-03 relative change in Z: 1.236269e-01
RADI step:   21 pc: -1.989884e+00 + 0.000000e+00i normalized residual: 1.178542e-03 relative change in Z: 3.393657e-03
RADI step:   22 pc: -1.365710e+02 + 0.000000e+00i normalized residual: 1.175046e-03 relative change in Z: 2.807692e-02
RADI step:   23 pc: -3.694524e+06 + 0.000000e+00i normalized residual: 2.311225e-04 relative change in Z: 9.353425e-01
RADI step:   24 pc: -5.072256e-03 + 0.000000e+00i normalized residual: 2.311224e-04 relative change in Z: 3.093179e-05
RADI step:   25 pc: -1.667683e+04 + 0.000000e+00i normalized residual: 1.581918e-04 relative change in Z: 5.001227e-02
RADI step:   26 pc: -1.732932e+00 + 0.000000e+00i normalized residual: 1.581834e-04 relative change in Z: 4.829152e-04
RADI step:   27 pc: -1.837717e+02 + 0.000000e+00i normalized residual: 1.574734e-04 relative change in Z: 4.966972e-03
RADI step:   28 pc: -7.299948e+06 + 0.000000e+00i normalized residual: 1.229622e-04 relative change in Z: 3.086847e-01
RADI step:   29 pc: -5.071265e-03 + 0.000000e+00i normalized residual: 1.229622e-04 relative change in Z: 1.669139e-05
RADI step:   30 pc: -3.231355e+04 + 0.000000e+00i normalized residual: 9.054101e-05 relative change in Z: 3.849275e-02
RADI step:   31 pc: -1.785471e+00 + 0.000000e+00i normalized residual: 9.053733e-05 relative change in Z: 2.663204e-04
RADI step:   32 pc: -1.532271e+03 + 0.000000e+00i normalized residual: 8.888265e-05 relative change in Z: 7.742921e-03
RADI step:   33 pc: -7.300040e+06 + 0.000000e+00i normalized residual: 6.910066e-05 relative change in Z: 3.145313e-02
RADI step:   34 pc: -1.732368e+00 + 0.000000e+00i normalized residual: 6.909949e-05 relative change in Z: 2.284201e-04
RADI step:   35 pc: -9.937569e+04 + 0.000000e+00i normalized residual: 2.863381e-05 relative change in Z: 4.476690e-02
RADI step:   36 pc: -2.093670e+02 + 0.000000e+00i normalized residual: 2.857127e-05 relative change in Z: 1.613631e-03
RADI step:   37 pc: -3.746753e+03 + 0.000000e+00i normalized residual: 2.760527e-05 relative change in Z: 6.754993e-03
RADI step:   38 pc: -7.300040e+06 + 0.000000e+00i normalized residual: 2.142996e-05 relative change in Z: 1.756580e-02
RADI step:   39 pc: -3.537397e+00 + 0.000000e+00i normalized residual: 2.142926e-05 relative change in Z: 1.812080e-04
RADI step:   40 pc: -1.532049e+05 + 0.000000e+00i normalized residual: 5.401100e-06 relative change in Z: 2.827968e-02
RADI step:   41 pc: -1.219379e+02 + 0.000000e+00i normalized residual: 5.394626e-06 relative change in Z: 5.339952e-04
RADI step:   42 pc: -6.378062e+03 + 0.000000e+00i normalized residual: 5.097276e-06 relative change in Z: 3.803607e-03
RADI step:   43 pc: -7.299957e+06 + 0.000000e+00i normalized residual: 3.956172e-06 relative change in Z: 7.548001e-03
RADI step:   44 pc: -6.374550e+00 + 0.000000e+00i normalized residual: 3.955944e-06 relative change in Z: 1.044255e-04
RADI step:   45 pc: -1.532062e+05 + 0.000000e+00i normalized residual: 9.968280e-07 relative change in Z: 1.215313e-02
RADI step:   46 pc: -3.109064e+02 + 0.000000e+00i normalized residual: 9.939287e-07 relative change in Z: 3.658711e-04
RADI step:   47 pc: -1.041230e+03 + 0.000000e+00i normalized residual: 9.848668e-07 relative change in Z: 6.674492e-04
RADI step:   48 pc: -4.619818e+05 + 0.000000e+00i normalized residual: 3.953227e-10 relative change in Z: 7.011239e-03
RADI step:   49 pc: -1.055804e+01 + 0.000000e+00i normalized residual: 3.936006e-10 relative change in Z: 1.439463e-06
RADI step:   50 pc: -2.766858e+04 + 0.000000e+00i normalized residual: 5.106404e-11 relative change in Z: 2.857172e-05
RADI step:   51 pc: -6.481520e+03 + 0.000000e+00i normalized residual: 4.055702e-12 relative change in Z: 7.839431e-06
RADI step:   52 pc: -4.569015e+03 + 0.000000e+00i normalized residual: 1.087772e-12 relative change in Z: 2.239776e-06
RADI step:   53 pc: -1.704325e+01 + 0.000000e+00i normalized residual: 9.973310e-13 relative change in Z: 1.088866e-07
RI step:    1  normalized residual: 3.356225e-02 relative change in Z: 1.000000e+00
               number of RADI steps:   53

RADI step:    1 pc: -7.574421e+00 + 0.000000e+00i normalized residual: 9.974283e-01 relative change in Z: 1.000000e+00
RADI step:    2 pc: -3.220744e+00 + 0.000000e+00i normalized residual: 9.913783e-01 relative change in Z: 6.216922e-01
RADI step:    3 pc: -4.872673e-03 + 0.000000e+00i normalized residual: 1.123939e-04 relative change in Z: 9.903921e-01
RADI step:    4 pc: -1.975461e+00 + 0.000000e+00i normalized residual: 1.113818e-04 relative change in Z: 2.264970e-02
RADI step:    5 pc: -4.976483e-03 + 0.000000e+00i normalized residual: 1.610903e-07 relative change in Z: 1.044024e-02
RADI step:    6 pc: -8.610186e+01 + 0.000000e+00i normalized residual: 4.827575e-08 relative change in Z: 9.088001e-02
RADI step:    7 pc: -1.324074e+01 + 0.000000e+00i normalized residual: 3.435078e-08 relative change in Z: 2.870125e-02
RADI step:    8 pc: -4.713681e+00 + 0.000000e+00i normalized residual: 3.290065e-08 relative change in Z: 1.586653e-02
RADI step:    9 pc: -2.928940e+00 + 0.000000e+00i normalized residual: 3.218537e-08 relative change in Z: 1.231829e-02
RADI step:   10 pc: -1.835637e+03 + 0.000000e+00i normalized residual: 6.682075e-09 relative change in Z: 1.410303e-01
RADI step:   11 pc: -4.976497e-03 + 0.000000e+00i normalized residual: 6.681496e-09 relative change in Z: 2.314884e-04
RADI step:   12 pc: -8.100726e+01 + 0.000000e+00i normalized residual: 3.752070e-09 relative change in Z: 2.522864e-02
RADI step:   13 pc: -1.336725e+01 + 0.000000e+00i normalized residual: 3.498875e-09 relative change in Z: 8.943889e-03
RADI step:   14 pc: -1.147560e+02 + 0.000000e+00i normalized residual: 2.562013e-09 relative change in Z: 2.354616e-02
RADI step:   15 pc: -1.307415e-01 + 0.000000e+00i normalized residual: 2.561363e-09 relative change in Z: 7.328728e-04
RADI step:   16 pc: -7.606035e+04 + 0.000000e+00i normalized residual: 1.715988e-09 relative change in Z: 2.041503e-01
RADI step:   17 pc: -4.250217e+00 + 0.000000e+00i normalized residual: 1.696638e-09 relative change in Z: 3.355057e-03
RADI step:   18 pc: -2.952055e+03 + 0.000000e+00i normalized residual: 7.117715e-10 relative change in Z: 5.563952e-02
RADI step:   19 pc: -1.241621e+03 + 0.000000e+00i normalized residual: 4.657994e-10 relative change in Z: 2.812855e-02
RADI step:   20 pc: -1.574560e+00 + 0.000000e+00i normalized residual: 4.650671e-10 relative change in Z: 9.768986e-04
RADI step:   21 pc: -6.189853e+05 + 0.000000e+00i normalized residual: 3.106909e-10 relative change in Z: 3.557937e-01
RADI step:   22 pc: -3.827685e+01 + 0.000000e+00i normalized residual: 3.008423e-10 relative change in Z: 3.625177e-03
RADI step:   23 pc: -1.972188e+04 + 0.000000e+00i normalized residual: 1.865601e-10 relative change in Z: 6.043149e-02
RADI step:   24 pc: -3.560786e+03 + 0.000000e+00i normalized residual: 1.717880e-10 relative change in Z: 2.435425e-02
RADI step:   25 pc: -7.299434e+06 + 0.000000e+00i normalized residual: 1.968733e-11 relative change in Z: 4.690284e-01
RADI step:   26 pc: -2.019994e+00 + 0.000000e+00i normalized residual: 1.937088e-11 relative change in Z: 2.002452e-04
RADI step:   27 pc: -1.502418e+05 + 0.000000e+00i normalized residual: 1.588877e-11 relative change in Z: 1.270582e-02
RADI step:   28 pc: -3.802545e+01 + 0.000000e+00i normalized residual: 1.122050e-11 relative change in Z: 7.196274e-04
RADI step:   29 pc: -1.391610e+04 + 0.000000e+00i normalized residual: 9.011598e-12 relative change in Z: 2.704261e-03
RADI step:   30 pc: -2.129749e+01 + 0.000000e+00i normalized residual: 7.351011e-12 relative change in Z: 4.155734e-04
RADI step:   31 pc: -7.300039e+06 + 0.000000e+00i normalized residual: 7.294351e-12 relative change in Z: 2.346285e-03
RADI step:   32 pc: -5.155106e+02 + 0.000000e+00i normalized residual: 5.103894e-13 relative change in Z: 9.417065e-04
RI step:    2  normalized residual: 1.335744e-05 relative change in Z: 1.918792e-08
               number of RADI steps:   32

RADI step:    1 pc: -2.822581e+00 + 0.000000e+00i normalized residual: 9.929778e-01 relative change in Z: 1.000000e+00
RADI step:    2 pc: -4.969368e-03 + 0.000000e+00i normalized residual: 1.059603e-07 relative change in Z: 9.964828e-01
RADI step:    3 pc: -1.823048e+01 + 0.000000e+00i normalized residual: 1.058433e-07 relative change in Z: 2.068993e-05
RADI step:    4 pc: -4.995930e+00 + 0.000000e+00i normalized residual: 1.054208e-07 relative change in Z: 2.260497e-05
RADI step:    5 pc: -2.908119e+00 + 0.000000e+00i normalized residual: 1.047001e-07 relative change in Z: 2.699886e-05
RADI step:    6 pc: -2.051177e+00 + 0.000000e+00i normalized residual: 1.036890e-07 relative change in Z: 3.180196e-05
RADI step:    7 pc: -4.972615e-03 + 0.000000e+00i normalized residual: 1.444437e-16 relative change in Z: 3.220063e-04
RI step:    3  normalized residual: 2.076327e-12 relative change in Z: 4.678203e-12
               number of RADI steps:    7

Elapsed time is 0.335395 seconds.

Compute real residuals.

absControl = norm(eqn.A_' * (outControl.Z * outControl.Z') * eqn.E_ ...
    + eqn.E_' * (outControl.Z * outControl.Z') * eqn.A_ ...
    + eqn.E_' * (outControl.Z * outControl.Z') * (1/gam^2 * (B1 * B1') ...
    - eqn.B2 * eqn.B2') * (outControl.Z * outControl.Z') * eqn.E_ ...
    + C1' * C1, 2);
relControl = absControl / norm(C1 * C1', 2);
fprintf(1, '\nControl -> set tolerance vs. real residual: %e | %e\n', ...
    opts.ri.res_tol, relControl);

absFilter = norm(eqn.A_ * (outFilter.Z * outFilter.Z') * eqn.E_' ...
    + eqn.E_ * (outFilter.Z * outFilter.Z') * eqn.A_' ...
    + eqn.E_ * (outFilter.Z * outFilter.Z') * (1/gam^2 * (C1' * C1) ...
    - eqn.C2' * eqn.C2) * (outFilter.Z * outFilter.Z') * eqn.E_' ...
    + B1 * B1', 2);
relFilter = absFilter / norm(B1' * B1, 2);
fprintf(1, 'Filter  -> set tolerance vs. real residual: %e | %e\n', ...
    opts.ri.res_tol, relFilter);

if istest
    assert(relControl < opts.ri.res_tol, ...
        'MESS:TEST:accuracy','unexpectedly inaccurate result');
    assert(relFilter < opts.ri.res_tol, ...
        'MESS:TEST:accuracy','unexpectedly inaccurate result');
end
Control -> set tolerance vs. real residual: 1.000000e-09 | 2.407758e-11
Filter  -> set tolerance vs. real residual: 1.000000e-09 | 3.833806e-11