Contents
function BT_TripleChain(version, istest)
% % Computes a reduced order model (ROM) for the triple chain example of % Truhar and Veselic [1] via Balanced truncation, e.g. [2]. % % Usage: BT_TripleChain(version, istest) % % Input: % % version Decides the Balanced Truncation version to use. % Possible values: % 'FO' for reduction of the first order form to first order form % 'VV' velocity-velocity balancing of the second order form to % second order form. % 'PP' position-position balancing of the second order form to % second order form. % 'PV' position-velocity balancing of the second order form to % second order form. % 'VP' velocity-position balancing of the second order form to % second order form. % % istest flag to determine whether this demo runs as a CI test or % interactive demo % (optional, defaults to 0, i.e. interactive demo) % % References: % % [1] N. Truhar and K. Veselic, An efficient method for estimating the % optimal dampers’ viscosity for linear vibrating systems using % Lyapunov equation, SIAM J. Matrix Anal. Appl., 31 (2009), pp. 18–39. % % [2] A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, Vol. % 6 of Adv. Des. Control, SIAM Publications, Philadelphia, PA, 2005. % https://doi.org/10.1137/1.9780898718713. %
% % 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 % narginchk(0,2) if nargin==0, version = 'FO'; end if nargin<2, istest=0; end format long e;
set operation
oper = operatormanager('so_1');
Initialize problem data
n1=500; alpha=.002; beta=alpha; v=5; [eqn.M_,eqn.E_,eqn.K_]=triplechain_MSD(n1,alpha,beta,v); s = size(eqn.K_,1); O = zeros(s,1); Cv = O'; Cp = ones(1,size(eqn.K_,1)); B = ones(size(eqn.K_,1),1); eqn.B = [O; B]; eqn.C = [Cp, Cv]; eqn.haveE=1;
ADI tolerances and maximum iteration number
opts.adi.maxiter = 300; opts.adi.res_tol = 1e-10; opts.adi.rel_diff_tol = 0; opts.norm = 'fro'; opts.adi.info = 1; opts.adi.accumulateK = 0; opts.adi.accumulateDeltaK = 0; opts.adi.compute_sol_fac = 1; opts.norm = 'fro';
%Heuristic shift parameters via projection opts.shifts.num_desired=5; opts.shifts.info=0; opts.shifts.method = 'projection';
Compute controlability Gramian factor
eqn.type = 'N'; tic; outB = mess_lradi(eqn, opts, oper); toc; if istest if min(outB.res)>=1e-1 error('MESS:TEST:accuracy','unexpectedly inaccurate result'); end else figure(1); semilogy(outB.res); title('0= AXM^T + MXA^T -BB^T'); xlabel('number of iterations'); ylabel('normalized residual norm'); pause(1); end disp('size outB.Z:'); disp(size(outB.Z));
ADI step: 1 normalized residual: 5.073506e-01 ADI step: 2 normalized residual: 5.560323e-01 ADI step: 4 normalized residual: 2.325197e-01 ADI step: 6 normalized residual: 2.106015e-01 ADI step: 7 normalized residual: 2.270676e-01 ADI step: 8 normalized residual: 8.370974e-02 ADI step: 9 normalized residual: 1.592188e-01 ADI step: 10 normalized residual: 1.514040e-01 ADI step: 12 normalized residual: 1.113157e-01 ADI step: 14 normalized residual: 9.340643e-02 ADI step: 15 normalized residual: 7.596297e-02 ADI step: 17 normalized residual: 7.107314e-02 ADI step: 19 normalized residual: 5.571037e-02 ADI step: 20 normalized residual: 5.792667e-02 ADI step: 21 normalized residual: 4.856437e-02 ADI step: 22 normalized residual: 5.849958e-02 ADI step: 24 normalized residual: 5.367959e-02 ADI step: 26 normalized residual: 5.289025e-02 ADI step: 28 normalized residual: 5.246617e-02 ADI step: 29 normalized residual: 3.877912e-02 ADI step: 31 normalized residual: 4.018146e-02 ADI step: 33 normalized residual: 3.840383e-02 ADI step: 34 normalized residual: 4.766065e-02 ADI step: 36 normalized residual: 4.931627e-02 ADI step: 37 normalized residual: 5.143612e-02 ADI step: 39 normalized residual: 3.584359e-02 ADI step: 41 normalized residual: 3.616331e-02 ADI step: 42 normalized residual: 4.160551e-02 ADI step: 44 normalized residual: 3.229327e-02 ADI step: 46 normalized residual: 3.099704e-02 ADI step: 47 normalized residual: 3.571161e-02 ADI step: 49 normalized residual: 2.642895e-02 ADI step: 51 normalized residual: 2.652633e-02 ADI step: 52 normalized residual: 4.057050e-02 ADI step: 54 normalized residual: 3.577600e-02 ADI step: 56 normalized residual: 3.570631e-02 ADI step: 58 normalized residual: 3.416888e-02 ADI step: 59 normalized residual: 3.416453e-02 ADI step: 61 normalized residual: 3.721183e-02 ADI step: 63 normalized residual: 3.735574e-02 ADI step: 64 normalized residual: 2.840138e-02 ADI step: 66 normalized residual: 2.859885e-02 ADI step: 68 normalized residual: 3.284944e-02 ADI step: 69 normalized residual: 3.733041e-02 ADI step: 71 normalized residual: 3.606839e-02 ADI step: 72 normalized residual: 3.698424e-02 ADI step: 74 normalized residual: 3.376612e-02 ADI step: 75 normalized residual: 3.409764e-02 ADI step: 77 normalized residual: 3.618049e-02 ADI step: 79 normalized residual: 3.452871e-02 ADI step: 81 normalized residual: 3.517617e-02 ADI step: 83 normalized residual: 3.397545e-02 ADI step: 84 normalized residual: 3.128982e-02 ADI step: 85 normalized residual: 3.250133e-02 ADI step: 86 normalized residual: 3.669776e-02 ADI step: 88 normalized residual: 3.582128e-02 ADI step: 89 normalized residual: 3.059702e-02 ADI step: 90 normalized residual: 3.661604e-02 ADI step: 92 normalized residual: 3.277411e-02 ADI step: 94 normalized residual: 3.169164e-02 ADI step: 95 normalized residual: 3.138957e-02 ADI step: 97 normalized residual: 2.562323e-02 ADI step: 99 normalized residual: 2.869309e-02 ADI step: 100 normalized residual: 2.804258e-02 ADI step: 102 normalized residual: 2.780144e-02 ADI step: 104 normalized residual: 2.672203e-02 ADI step: 105 normalized residual: 2.745734e-02 ADI step: 107 normalized residual: 2.742431e-02 ADI step: 109 normalized residual: 2.552217e-02 ADI step: 110 normalized residual: 2.514516e-02 ADI step: 112 normalized residual: 2.349271e-02 ADI step: 114 normalized residual: 2.342001e-02 ADI step: 116 normalized residual: 2.345776e-02 ADI step: 118 normalized residual: 2.582442e-02 ADI step: 119 normalized residual: 2.265546e-02 ADI step: 120 normalized residual: 2.203365e-02 ADI step: 122 normalized residual: 2.168591e-02 ADI step: 124 normalized residual: 2.221375e-02 ADI step: 125 normalized residual: 1.851511e-02 ADI step: 127 normalized residual: 1.817853e-02 ADI step: 129 normalized residual: 1.969048e-02 ADI step: 130 normalized residual: 1.861911e-02 ADI step: 132 normalized residual: 1.852719e-02 ADI step: 134 normalized residual: 1.886756e-02 ADI step: 135 normalized residual: 1.785993e-02 ADI step: 137 normalized residual: 1.784447e-02 ADI step: 139 normalized residual: 1.727064e-02 ADI step: 140 normalized residual: 1.682476e-02 ADI step: 142 normalized residual: 1.839691e-02 ADI step: 144 normalized residual: 1.830817e-02 ADI step: 145 normalized residual: 1.768449e-02 ADI step: 147 normalized residual: 1.759622e-02 ADI step: 149 normalized residual: 1.603948e-02 ADI step: 150 normalized residual: 1.602936e-02 ADI step: 152 normalized residual: 1.591953e-02 ADI step: 154 normalized residual: 1.572462e-02 ADI step: 155 normalized residual: 1.574657e-02 ADI step: 157 normalized residual: 1.579002e-02 ADI step: 159 normalized residual: 1.560752e-02 ADI step: 160 normalized residual: 1.574328e-02 ADI step: 162 normalized residual: 1.586069e-02 ADI step: 164 normalized residual: 1.586593e-02 ADI step: 165 normalized residual: 1.619715e-02 ADI step: 167 normalized residual: 1.630662e-02 ADI step: 169 normalized residual: 1.585621e-02 ADI step: 170 normalized residual: 1.563056e-02 ADI step: 172 normalized residual: 1.557036e-02 ADI step: 174 normalized residual: 1.530038e-02 ADI step: 176 normalized residual: 1.525292e-02 ADI step: 178 normalized residual: 1.519329e-02 ADI step: 179 normalized residual: 1.443154e-02 ADI step: 181 normalized residual: 1.432359e-02 ADI step: 183 normalized residual: 1.416207e-02 ADI step: 184 normalized residual: 1.501705e-02 ADI step: 186 normalized residual: 1.492314e-02 ADI step: 188 normalized residual: 1.465939e-02 ADI step: 189 normalized residual: 1.419830e-02 ADI step: 191 normalized residual: 1.407954e-02 ADI step: 193 normalized residual: 1.383250e-02 ADI step: 194 normalized residual: 1.379505e-02 ADI step: 195 normalized residual: 1.386819e-02 ADI step: 197 normalized residual: 1.387153e-02 ADI step: 199 normalized residual: 1.335800e-02 ADI step: 200 normalized residual: 1.350071e-02 ADI step: 202 normalized residual: 1.328525e-02 ADI step: 204 normalized residual: 1.312048e-02 ADI step: 205 normalized residual: 1.341718e-02 ADI step: 207 normalized residual: 1.295163e-02 ADI step: 209 normalized residual: 1.296555e-02 ADI step: 211 normalized residual: 1.289083e-02 ADI step: 212 normalized residual: 1.307441e-02 ADI step: 214 normalized residual: 1.286655e-02 ADI step: 216 normalized residual: 1.284829e-02 ADI step: 218 normalized residual: 1.278199e-02 ADI step: 219 normalized residual: 1.181346e-02 ADI step: 220 normalized residual: 1.196528e-02 ADI step: 222 normalized residual: 1.192453e-02 ADI step: 224 normalized residual: 1.173848e-02 ADI step: 226 normalized residual: 1.182620e-02 ADI step: 227 normalized residual: 1.168293e-02 ADI step: 229 normalized residual: 1.164928e-02 ADI step: 230 normalized residual: 1.174547e-02 ADI step: 232 normalized residual: 1.171024e-02 ADI step: 234 normalized residual: 1.159652e-02 ADI step: 235 normalized residual: 1.129590e-02 ADI step: 237 normalized residual: 1.129445e-02 ADI step: 239 normalized residual: 1.087763e-02 ADI step: 241 normalized residual: 1.081713e-02 ADI step: 242 normalized residual: 1.107433e-02 ADI step: 244 normalized residual: 1.091260e-02 ADI step: 245 normalized residual: 1.105498e-02 ADI step: 247 normalized residual: 1.105117e-02 ADI step: 249 normalized residual: 1.102331e-02 ADI step: 250 normalized residual: 1.109212e-02 ADI step: 252 normalized residual: 1.095684e-02 ADI step: 254 normalized residual: 1.103310e-02 ADI step: 255 normalized residual: 1.117404e-02 ADI step: 257 normalized residual: 1.117405e-02 ADI step: 259 normalized residual: 1.117017e-02 ADI step: 260 normalized residual: 1.095007e-02 ADI step: 262 normalized residual: 1.089079e-02 ADI step: 264 normalized residual: 1.085239e-02 ADI step: 265 normalized residual: 1.096006e-02 ADI step: 267 normalized residual: 1.082644e-02 ADI step: 269 normalized residual: 1.072482e-02 ADI step: 270 normalized residual: 1.063044e-02 ADI step: 272 normalized residual: 1.058604e-02 ADI step: 274 normalized residual: 1.054422e-02 ADI step: 275 normalized residual: 1.042107e-02 ADI step: 277 normalized residual: 1.043413e-02 ADI step: 279 normalized residual: 1.042914e-02 ADI step: 280 normalized residual: 1.043981e-02 ADI step: 282 normalized residual: 1.035215e-02 ADI step: 284 normalized residual: 1.032968e-02 ADI step: 285 normalized residual: 1.029359e-02 ADI step: 287 normalized residual: 1.019644e-02 ADI step: 289 normalized residual: 1.005929e-02 ADI step: 290 normalized residual: 1.014151e-02 ADI step: 292 normalized residual: 1.013369e-02 ADI step: 294 normalized residual: 1.009579e-02 ADI step: 295 normalized residual: 9.819899e-03 ADI step: 297 normalized residual: 9.823660e-03 ADI step: 299 normalized residual: 9.824014e-03 ADI step: 301 normalized residual: 9.825429e-03 Elapsed time is 0.531542 seconds. size outB.Z: 3002 301

Compute observability Gramian factor
eqn.type = 'T'; tic; outC = mess_lradi(eqn, opts, oper); toc; if istest if min(outC.res)>=1e-1 error('MESS:TEST:accuracy','unexpectedly inaccurate result'); end else figure(2); semilogy(outC.res); title('0= A^TXM + M^TXA -C^TC'); xlabel('number of iterations'); ylabel('normalized residual norm'); pause(1); end disp('size outC.Z:'); disp(size(outC.Z)); switch upper(version) case 'FO'
Compute first order ROM
opts.srm.max_ord = 150; opts.srm.tol = eps; opts.srm.info = 1; [TL,TR] = mess_square_root_method(eqn,opts,oper,outB.Z,outC.Z); ROM.E = eye(size(TL,2)); ROM.A = TL'*oper.mul_A(eqn, opts, 'N', TR, 'N'); ROM.B = TL'*eqn.B; ROM.C = eqn.C*TR; ROM.D = [];
reduced system order: 150 (max possible/allowed: 301/150)
case 'VV' U = outB.Z(1:s,:); V = outC.Z(1:s,:); case 'PP' U = outB.Z(s+1:end,:); V = outC.Z(s+1:end,:); case 'PV' U = outB.Z(s+1:end,:); V = outC.Z(1:s,:); case 'VP' U = outB.Z(1:s,:); V = outC.Z(s+1:end,:); end if not(strcmp(version,'FO')) max_ord = 75; tol = eps; info = 1; [TL,TR] = square_root_method_SO(eqn.M_, max_ord, tol, info, U, V); ROM.M = eye(size(TL,2)); ROM.E = TL'*(eqn.E_*TR); ROM.K = TL'*(eqn.K_*TR); ROM.B = TL'*B; ROM.Cv = Cv*TR; ROM.Cp = Cp*TR; end
Warning: Could not compute initial projection shifts. Going to retry with random right hand side. ADI step: 1 normalized residual: 8.993042e+01 ADI step: 2 normalized residual: 1.871791e+03 ADI step: 4 normalized residual: 4.038661e+02 ADI step: 6 normalized residual: 2.893253e+02 ADI step: 8 normalized residual: 1.999807e+02 ADI step: 10 normalized residual: 2.156404e+02 ADI step: 12 normalized residual: 1.080239e+02 ADI step: 14 normalized residual: 1.077604e+01 ADI step: 16 normalized residual: 8.584757e+00 ADI step: 18 normalized residual: 7.864729e+00 ADI step: 20 normalized residual: 8.055562e+00 ADI step: 22 normalized residual: 1.600772e+01 ADI step: 24 normalized residual: 1.598200e+01 ADI step: 26 normalized residual: 1.623130e+01 ADI step: 28 normalized residual: 1.620898e+01 ADI step: 30 normalized residual: 3.165546e+00 ADI step: 32 normalized residual: 2.968809e+00 ADI step: 34 normalized residual: 6.467635e+00 ADI step: 36 normalized residual: 3.651244e+00 ADI step: 38 normalized residual: 3.522482e+00 ADI step: 40 normalized residual: 3.618827e+00 ADI step: 42 normalized residual: 3.749865e+00 ADI step: 44 normalized residual: 3.506128e+00 ADI step: 46 normalized residual: 3.083317e+00 ADI step: 48 normalized residual: 2.234514e+00 ADI step: 50 normalized residual: 2.257119e+00 ADI step: 52 normalized residual: 2.086722e+00 ADI step: 54 normalized residual: 1.824802e+00 ADI step: 56 normalized residual: 1.584989e+00 ADI step: 58 normalized residual: 8.749579e-01 ADI step: 60 normalized residual: 9.494202e-01 ADI step: 62 normalized residual: 1.076366e+00 ADI step: 64 normalized residual: 1.064889e+00 ADI step: 66 normalized residual: 9.097189e-01 ADI step: 68 normalized residual: 9.085496e-01 ADI step: 70 normalized residual: 8.466477e-01 ADI step: 72 normalized residual: 8.464474e-01 ADI step: 74 normalized residual: 8.087247e-01 ADI step: 76 normalized residual: 6.766887e-01 ADI step: 78 normalized residual: 6.681048e-01 ADI step: 80 normalized residual: 6.636005e-01 ADI step: 82 normalized residual: 5.429122e-01 ADI step: 84 normalized residual: 4.098463e-01 ADI step: 86 normalized residual: 4.124024e-01 ADI step: 88 normalized residual: 4.232941e-01 ADI step: 90 normalized residual: 3.710197e-01 ADI step: 92 normalized residual: 3.721455e-01 ADI step: 94 normalized residual: 3.744466e-01 ADI step: 96 normalized residual: 3.749530e-01 ADI step: 98 normalized residual: 3.417626e-01 ADI step: 100 normalized residual: 2.148271e-01 ADI step: 102 normalized residual: 2.114754e-01 ADI step: 104 normalized residual: 2.155816e-01 ADI step: 106 normalized residual: 2.009715e-01 ADI step: 108 normalized residual: 2.677825e-01 ADI step: 110 normalized residual: 2.613580e-01 ADI step: 112 normalized residual: 2.648517e-01 ADI step: 114 normalized residual: 1.849123e-01 ADI step: 116 normalized residual: 1.801405e-01 ADI step: 118 normalized residual: 1.245365e-01 ADI step: 120 normalized residual: 1.196336e-01 ADI step: 122 normalized residual: 1.179762e-01 ADI step: 123 normalized residual: 1.882856e-01 ADI step: 125 normalized residual: 1.889197e-01 ADI step: 127 normalized residual: 1.666612e-01 ADI step: 129 normalized residual: 1.648121e-01 ADI step: 131 normalized residual: 1.460991e-01 ADI step: 132 normalized residual: 1.634997e-01 ADI step: 134 normalized residual: 1.574838e-01 ADI step: 136 normalized residual: 9.052325e-02 ADI step: 137 normalized residual: 1.516192e-01 ADI step: 139 normalized residual: 1.510527e-01 ADI step: 141 normalized residual: 1.110716e-01 ADI step: 142 normalized residual: 1.166668e-01 ADI step: 144 normalized residual: 1.138791e-01 ADI step: 145 normalized residual: 7.582910e-02 ADI step: 147 normalized residual: 7.554166e-02 ADI step: 149 normalized residual: 7.475937e-02 ADI step: 151 normalized residual: 9.078688e-02 ADI step: 152 normalized residual: 7.896775e-02 ADI step: 153 normalized residual: 7.231434e-02 ADI step: 155 normalized residual: 7.278308e-02 ADI step: 157 normalized residual: 9.559090e-02 ADI step: 159 normalized residual: 9.718121e-02 ADI step: 161 normalized residual: 7.308056e-02 ADI step: 162 normalized residual: 5.589240e-02 ADI step: 164 normalized residual: 5.903661e-02 ADI step: 166 normalized residual: 5.902791e-02 ADI step: 167 normalized residual: 5.773111e-02 ADI step: 168 normalized residual: 5.703586e-02 ADI step: 170 normalized residual: 5.872204e-02 ADI step: 172 normalized residual: 6.339445e-02 ADI step: 173 normalized residual: 6.778912e-02 ADI step: 175 normalized residual: 6.531972e-02 ADI step: 177 normalized residual: 6.009730e-02 ADI step: 178 normalized residual: 4.952164e-02 ADI step: 180 normalized residual: 4.762458e-02 ADI step: 182 normalized residual: 4.095207e-02 ADI step: 183 normalized residual: 4.426863e-02 ADI step: 185 normalized residual: 4.292039e-02 ADI step: 187 normalized residual: 4.340993e-02 ADI step: 189 normalized residual: 4.175578e-02 ADI step: 191 normalized residual: 4.335983e-02 ADI step: 192 normalized residual: 4.045103e-02 ADI step: 193 normalized residual: 3.525875e-02 ADI step: 195 normalized residual: 3.659094e-02 ADI step: 197 normalized residual: 3.693414e-02 ADI step: 199 normalized residual: 3.828920e-02 ADI step: 201 normalized residual: 3.481999e-02 ADI step: 202 normalized residual: 3.304130e-02 ADI step: 204 normalized residual: 2.998493e-02 ADI step: 206 normalized residual: 3.015276e-02 ADI step: 207 normalized residual: 3.316541e-02 ADI step: 208 normalized residual: 2.958614e-02 ADI step: 210 normalized residual: 2.956777e-02 ADI step: 212 normalized residual: 2.828313e-02 ADI step: 213 normalized residual: 2.970362e-02 ADI step: 215 normalized residual: 2.944692e-02 ADI step: 217 normalized residual: 3.243872e-02 ADI step: 218 normalized residual: 3.292494e-02 ADI step: 220 normalized residual: 3.288985e-02 ADI step: 222 normalized residual: 2.673468e-02 ADI step: 223 normalized residual: 2.741752e-02 ADI step: 225 normalized residual: 2.711779e-02 ADI step: 227 normalized residual: 2.638249e-02 ADI step: 228 normalized residual: 2.604764e-02 ADI step: 230 normalized residual: 2.506144e-02 ADI step: 232 normalized residual: 2.418405e-02 ADI step: 233 normalized residual: 2.383077e-02 ADI step: 235 normalized residual: 2.336131e-02 ADI step: 237 normalized residual: 2.179747e-02 ADI step: 238 normalized residual: 2.052418e-02 ADI step: 240 normalized residual: 2.178833e-02 ADI step: 242 normalized residual: 2.105169e-02 ADI step: 244 normalized residual: 2.093933e-02 ADI step: 245 normalized residual: 2.055711e-02 ADI step: 247 normalized residual: 1.974146e-02 ADI step: 249 normalized residual: 1.728568e-02 ADI step: 251 normalized residual: 1.710271e-02 ADI step: 252 normalized residual: 1.734985e-02 ADI step: 253 normalized residual: 1.687294e-02 ADI step: 255 normalized residual: 1.885352e-02 ADI step: 257 normalized residual: 2.059584e-02 ADI step: 258 normalized residual: 2.024229e-02 ADI step: 260 normalized residual: 2.001355e-02 ADI step: 262 normalized residual: 1.775256e-02 ADI step: 263 normalized residual: 1.694120e-02 ADI step: 265 normalized residual: 1.693334e-02 ADI step: 267 normalized residual: 1.645783e-02 ADI step: 269 normalized residual: 1.652104e-02 ADI step: 270 normalized residual: 1.602112e-02 ADI step: 272 normalized residual: 1.589620e-02 ADI step: 273 normalized residual: 1.416399e-02 ADI step: 275 normalized residual: 1.465861e-02 ADI step: 277 normalized residual: 1.538592e-02 ADI step: 278 normalized residual: 1.498473e-02 ADI step: 280 normalized residual: 1.509517e-02 ADI step: 282 normalized residual: 1.305592e-02 ADI step: 283 normalized residual: 1.390804e-02 ADI step: 285 normalized residual: 1.420802e-02 ADI step: 287 normalized residual: 1.403487e-02 ADI step: 288 normalized residual: 1.257510e-02 ADI step: 290 normalized residual: 1.252698e-02 ADI step: 292 normalized residual: 1.294582e-02 ADI step: 294 normalized residual: 1.278812e-02 ADI step: 296 normalized residual: 1.203515e-02 ADI step: 297 normalized residual: 1.204933e-02 ADI step: 299 normalized residual: 1.206596e-02 ADI step: 301 normalized residual: 1.172421e-02 Elapsed time is 0.516285 seconds. size outC.Z: 3002 301
plot results
opts.sigma.fmin = 1e-4; opts.sigma.fmax = 1e0; opts.sigma.nsample = 200; if istest opts.sigma.info = 1; else opts.sigma.info = 2; end out = mess_sigma_plot(eqn, opts, oper, ROM); err = out.err; if istest if max(err) > 1000 error('MESS:TEST:accuracy','unexpectedly inaccurate result %g',max(err)); end end
Computing TFMs of original and reduced order systems and MOR errors Step 20 / 200 Step 40 / 200 Step 60 / 200 Step 80 / 200 Step 100 / 200 Step 120 / 200 Step 140 / 200 Step 160 / 200 Step 180 / 200 Step 200 / 200

