Contents
function [Er,Ar,Br,Cr] = IRKA_rail(k,r,istest)
Load matrix data
if nargin<1
k=2;
end
eqn = mess_get_linear_rail(k);
register corresponding usfs
oper = operatormanager('default');
collect IRKA parameters
if nargin<2
opts.irka.r = 20;
else
opts.irka.r = r;
end
if nargin < 3
istest = 0;
end
opts.irka.maxiter =100;
opts.irka.shift_tol = 1e-3;
opts.irka.h2_tol = 1e-6;
if istest
opts.irka.info = 1;
else
opts.irka.info = 3;
end
opts.irka.init = 'logspace';
Run IRKA
[Er,Ar,Br,Cr] = mess_tangential_irka(eqn, opts, oper);
if istest
[~, ID] = lastwarn;
lastwarn('');
if strcmp(ID,'MESS:IRKA:convergence')
error('IRKA converged unexpectedly slow');
end
end
if exist('sparss','class')
sys = sparss(eqn.A_, eqn.B, eqn.C, [], eqn.E_);
[Er,Ar,Br,Cr] = mess_tangential_irka(sys,opts);
if istest
[~, ID] = lastwarn;
lastwarn('');
if strcmp(ID,'MESS:IRKA:convergence')
error('IRKA converged unexpectedly slow');
end
end
end
Warning: IRKA step 1 : 1 non-stable reduced eigenvalues detected.
IRKA step 1, rel. chg. shifts = 1.466613e+02 , rel. H2-norm chg. ROM = 1.000000e+00
Warning: IRKA step 2 : 2 non-stable reduced eigenvalues detected.
IRKA step 2, rel. chg. shifts = 1.822055e+03 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 3 : 1 non-stable reduced eigenvalues detected.
IRKA step 3, rel. chg. shifts = 6.280324e+01 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 4 : 1 non-stable reduced eigenvalues detected.
IRKA step 4, rel. chg. shifts = 5.642539e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 5, rel. chg. shifts = 9.017783e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 6, rel. chg. shifts = 6.886421e+00 , rel. H2-norm chg. ROM = 1.726136e-01
IRKA step 7, rel. chg. shifts = 5.602410e+01 , rel. H2-norm chg. ROM = 2.890137e-01
IRKA step 8, rel. chg. shifts = 4.752392e+00 , rel. H2-norm chg. ROM = 6.865068e-02
Warning: IRKA step 9 : 1 non-stable reduced eigenvalues detected.
IRKA step 9, rel. chg. shifts = 4.937011e+01 , rel. H2-norm chg. ROM = Inf
IRKA step 10, rel. chg. shifts = 2.900032e+02 , rel. H2-norm chg. ROM = 6.323034e-02
IRKA step 11, rel. chg. shifts = 1.390184e+00 , rel. H2-norm chg. ROM = 3.265683e-02
IRKA step 12, rel. chg. shifts = 1.529164e+01 , rel. H2-norm chg. ROM = 2.877978e-02
IRKA step 13, rel. chg. shifts = 8.828485e+00 , rel. H2-norm chg. ROM = 2.233436e-02
IRKA step 14, rel. chg. shifts = 6.394496e+01 , rel. H2-norm chg. ROM = 2.069950e-02
Warning: IRKA step 15 : 1 non-stable reduced eigenvalues detected.
IRKA step 15, rel. chg. shifts = 5.778572e+01 , rel. H2-norm chg. ROM = Inf
IRKA step 16, rel. chg. shifts = 1.519369e+01 , rel. H2-norm chg. ROM = 5.844751e-02
Warning: IRKA step 17 : 1 non-stable reduced eigenvalues detected.
IRKA step 17, rel. chg. shifts = 4.711225e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 18, rel. chg. shifts = 3.897068e+02 , rel. H2-norm chg. ROM = 4.204387e-02
Warning: IRKA step 19 : 1 non-stable reduced eigenvalues detected.
IRKA step 19, rel. chg. shifts = 6.249422e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 20, rel. chg. shifts = 1.233692e+01 , rel. H2-norm chg. ROM = 2.322628e-02
Warning: IRKA step 21 : 1 non-stable reduced eigenvalues detected.
IRKA step 21, rel. chg. shifts = 3.312523e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 22, rel. chg. shifts = 1.072041e+00 , rel. H2-norm chg. ROM = 2.203301e-02
Warning: IRKA step 23 : 1 non-stable reduced eigenvalues detected.
IRKA step 23, rel. chg. shifts = 1.787796e+01 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 24 : 1 non-stable reduced eigenvalues detected.
IRKA step 24, rel. chg. shifts = 3.121030e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 25, rel. chg. shifts = 3.502610e+01 , rel. H2-norm chg. ROM = 2.006740e-02
Warning: IRKA step 26 : 1 non-stable reduced eigenvalues detected.
IRKA step 26, rel. chg. shifts = 3.323900e+00 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 27 : 1 non-stable reduced eigenvalues detected.
IRKA step 27, rel. chg. shifts = 4.197663e+02 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 28 : 1 non-stable reduced eigenvalues detected.
IRKA step 28, rel. chg. shifts = 1.444383e+01 , rel. H2-norm chg. ROM = Inf
IRKA step 29, rel. chg. shifts = 3.763672e+00 , rel. H2-norm chg. ROM = 1.011194e-01
IRKA step 30, rel. chg. shifts = 3.736885e+00 , rel. H2-norm chg. ROM = 7.804086e-02
IRKA step 31, rel. chg. shifts = 9.157203e+00 , rel. H2-norm chg. ROM = 4.195266e-02
IRKA step 32, rel. chg. shifts = 3.568281e+00 , rel. H2-norm chg. ROM = 2.956314e-02
IRKA step 33, rel. chg. shifts = 1.086653e-01 , rel. H2-norm chg. ROM = 2.434783e-02
IRKA step 34, rel. chg. shifts = 1.962402e-01 , rel. H2-norm chg. ROM = 1.350349e-02
IRKA step 35, rel. chg. shifts = 1.210196e-01 , rel. H2-norm chg. ROM = 7.828472e-03
IRKA step 36, rel. chg. shifts = 9.670155e+01 , rel. H2-norm chg. ROM = 6.040303e-03
IRKA step 37, rel. chg. shifts = 1.785820e-01 , rel. H2-norm chg. ROM = 6.441283e-03
IRKA step 38, rel. chg. shifts = 2.692214e-01 , rel. H2-norm chg. ROM = 5.358345e-03
IRKA step 39, rel. chg. shifts = 1.117715e+01 , rel. H2-norm chg. ROM = 5.246648e-03
IRKA step 40, rel. chg. shifts = 1.851457e-01 , rel. H2-norm chg. ROM = 5.190250e-03
IRKA step 41, rel. chg. shifts = 8.957171e-02 , rel. H2-norm chg. ROM = 5.139455e-03
IRKA step 42, rel. chg. shifts = 1.014407e-01 , rel. H2-norm chg. ROM = 5.154813e-03
IRKA step 43, rel. chg. shifts = 6.534359e-02 , rel. H2-norm chg. ROM = 5.132784e-03
IRKA step 44, rel. chg. shifts = 4.742445e-02 , rel. H2-norm chg. ROM = 4.847910e-03
IRKA step 45, rel. chg. shifts = 3.341427e-02 , rel. H2-norm chg. ROM = 4.415675e-03
IRKA step 46, rel. chg. shifts = 2.597584e-02 , rel. H2-norm chg. ROM = 3.824924e-03
IRKA step 47, rel. chg. shifts = 1.485318e-02 , rel. H2-norm chg. ROM = 3.208998e-03
IRKA step 48, rel. chg. shifts = 1.893867e-02 , rel. H2-norm chg. ROM = 2.610692e-03
IRKA step 49, rel. chg. shifts = 8.889384e-03 , rel. H2-norm chg. ROM = 2.086134e-03
IRKA step 50, rel. chg. shifts = 1.127285e-02 , rel. H2-norm chg. ROM = 1.644853e-03
IRKA step 51, rel. chg. shifts = 5.238606e-03 , rel. H2-norm chg. ROM = 1.285527e-03
IRKA step 52, rel. chg. shifts = 5.608026e-03 , rel. H2-norm chg. ROM = 1.000867e-03
IRKA step 53, rel. chg. shifts = 3.093888e-03 , rel. H2-norm chg. ROM = 7.753566e-04
IRKA step 54, rel. chg. shifts = 2.960968e-03 , rel. H2-norm chg. ROM = 6.009653e-04
IRKA step 55, rel. chg. shifts = 1.835191e-03 , rel. H2-norm chg. ROM = 4.640285e-04
IRKA step 56, rel. chg. shifts = 1.627322e-03 , rel. H2-norm chg. ROM = 3.591596e-04
IRKA step 57, rel. chg. shifts = 1.092269e-03 , rel. H2-norm chg. ROM = 2.769905e-04
IRKA step 58, rel. chg. shifts = 9.167929e-04 , rel. H2-norm chg. ROM = 2.143245e-04
IRKA terminated due to relative change of shifts criterion.
Computing TFMs of original and reduced order systems and MOR errors
Step 10 / 100 Step 20 / 100 Step 30 / 100 Step 40 / 100 Step 50 / 100 Step 60 / 100 Step 70 / 100 Step 80 / 100 Step 90 / 100 Step 100 / 100
Warning: IRKA step 1 : 1 non-stable reduced eigenvalues detected.
IRKA step 1, rel. chg. shifts = 1.466613e+02 , rel. H2-norm chg. ROM = 1.000000e+00
Warning: IRKA step 2 : 2 non-stable reduced eigenvalues detected.
IRKA step 2, rel. chg. shifts = 1.822055e+03 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 3 : 1 non-stable reduced eigenvalues detected.
IRKA step 3, rel. chg. shifts = 6.280324e+01 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 4 : 1 non-stable reduced eigenvalues detected.
IRKA step 4, rel. chg. shifts = 5.642539e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 5, rel. chg. shifts = 9.017783e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 6, rel. chg. shifts = 6.886421e+00 , rel. H2-norm chg. ROM = 1.726136e-01
IRKA step 7, rel. chg. shifts = 5.602410e+01 , rel. H2-norm chg. ROM = 2.890137e-01
IRKA step 8, rel. chg. shifts = 4.752392e+00 , rel. H2-norm chg. ROM = 6.865068e-02
Warning: IRKA step 9 : 1 non-stable reduced eigenvalues detected.
IRKA step 9, rel. chg. shifts = 4.937011e+01 , rel. H2-norm chg. ROM = Inf
IRKA step 10, rel. chg. shifts = 2.900032e+02 , rel. H2-norm chg. ROM = 6.323034e-02
IRKA step 11, rel. chg. shifts = 1.390184e+00 , rel. H2-norm chg. ROM = 3.265683e-02
IRKA step 12, rel. chg. shifts = 1.529164e+01 , rel. H2-norm chg. ROM = 2.877978e-02
IRKA step 13, rel. chg. shifts = 8.828485e+00 , rel. H2-norm chg. ROM = 2.233436e-02
IRKA step 14, rel. chg. shifts = 6.394496e+01 , rel. H2-norm chg. ROM = 2.069950e-02
Warning: IRKA step 15 : 1 non-stable reduced eigenvalues detected.
IRKA step 15, rel. chg. shifts = 5.778572e+01 , rel. H2-norm chg. ROM = Inf
IRKA step 16, rel. chg. shifts = 1.519369e+01 , rel. H2-norm chg. ROM = 5.844751e-02
Warning: IRKA step 17 : 1 non-stable reduced eigenvalues detected.
IRKA step 17, rel. chg. shifts = 4.711225e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 18, rel. chg. shifts = 3.897068e+02 , rel. H2-norm chg. ROM = 4.204387e-02
Warning: IRKA step 19 : 1 non-stable reduced eigenvalues detected.
IRKA step 19, rel. chg. shifts = 6.249422e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 20, rel. chg. shifts = 1.233692e+01 , rel. H2-norm chg. ROM = 2.322628e-02
Warning: IRKA step 21 : 1 non-stable reduced eigenvalues detected.
IRKA step 21, rel. chg. shifts = 3.312523e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 22, rel. chg. shifts = 1.072041e+00 , rel. H2-norm chg. ROM = 2.203301e-02
Warning: IRKA step 23 : 1 non-stable reduced eigenvalues detected.
IRKA step 23, rel. chg. shifts = 1.787796e+01 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 24 : 1 non-stable reduced eigenvalues detected.
IRKA step 24, rel. chg. shifts = 3.121030e+00 , rel. H2-norm chg. ROM = Inf
IRKA step 25, rel. chg. shifts = 3.502610e+01 , rel. H2-norm chg. ROM = 2.006740e-02
Warning: IRKA step 26 : 1 non-stable reduced eigenvalues detected.
IRKA step 26, rel. chg. shifts = 3.323900e+00 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 27 : 1 non-stable reduced eigenvalues detected.
IRKA step 27, rel. chg. shifts = 4.197663e+02 , rel. H2-norm chg. ROM = Inf
Warning: IRKA step 28 : 1 non-stable reduced eigenvalues detected.
IRKA step 28, rel. chg. shifts = 1.444383e+01 , rel. H2-norm chg. ROM = Inf
IRKA step 29, rel. chg. shifts = 3.763672e+00 , rel. H2-norm chg. ROM = 1.011194e-01
IRKA step 30, rel. chg. shifts = 3.736885e+00 , rel. H2-norm chg. ROM = 7.804086e-02
IRKA step 31, rel. chg. shifts = 9.157203e+00 , rel. H2-norm chg. ROM = 4.195266e-02
IRKA step 32, rel. chg. shifts = 3.568281e+00 , rel. H2-norm chg. ROM = 2.956314e-02
IRKA step 33, rel. chg. shifts = 1.086653e-01 , rel. H2-norm chg. ROM = 2.434783e-02
IRKA step 34, rel. chg. shifts = 1.962402e-01 , rel. H2-norm chg. ROM = 1.350349e-02
IRKA step 35, rel. chg. shifts = 1.210196e-01 , rel. H2-norm chg. ROM = 7.828472e-03
IRKA step 36, rel. chg. shifts = 9.670155e+01 , rel. H2-norm chg. ROM = 6.040303e-03
IRKA step 37, rel. chg. shifts = 1.785820e-01 , rel. H2-norm chg. ROM = 6.441283e-03
IRKA step 38, rel. chg. shifts = 2.692214e-01 , rel. H2-norm chg. ROM = 5.358345e-03
IRKA step 39, rel. chg. shifts = 1.117715e+01 , rel. H2-norm chg. ROM = 5.246648e-03
IRKA step 40, rel. chg. shifts = 1.851457e-01 , rel. H2-norm chg. ROM = 5.190250e-03
IRKA step 41, rel. chg. shifts = 8.957171e-02 , rel. H2-norm chg. ROM = 5.139455e-03
IRKA step 42, rel. chg. shifts = 1.014407e-01 , rel. H2-norm chg. ROM = 5.154813e-03
IRKA step 43, rel. chg. shifts = 6.534359e-02 , rel. H2-norm chg. ROM = 5.132784e-03
IRKA step 44, rel. chg. shifts = 4.742445e-02 , rel. H2-norm chg. ROM = 4.847910e-03
IRKA step 45, rel. chg. shifts = 3.341427e-02 , rel. H2-norm chg. ROM = 4.415675e-03
IRKA step 46, rel. chg. shifts = 2.597584e-02 , rel. H2-norm chg. ROM = 3.824924e-03
IRKA step 47, rel. chg. shifts = 1.485318e-02 , rel. H2-norm chg. ROM = 3.208998e-03
IRKA step 48, rel. chg. shifts = 1.893867e-02 , rel. H2-norm chg. ROM = 2.610692e-03
IRKA step 49, rel. chg. shifts = 8.889384e-03 , rel. H2-norm chg. ROM = 2.086134e-03
IRKA step 50, rel. chg. shifts = 1.127285e-02 , rel. H2-norm chg. ROM = 1.644853e-03
IRKA step 51, rel. chg. shifts = 5.238606e-03 , rel. H2-norm chg. ROM = 1.285527e-03
IRKA step 52, rel. chg. shifts = 5.608026e-03 , rel. H2-norm chg. ROM = 1.000867e-03
IRKA step 53, rel. chg. shifts = 3.093888e-03 , rel. H2-norm chg. ROM = 7.753566e-04
IRKA step 54, rel. chg. shifts = 2.960968e-03 , rel. H2-norm chg. ROM = 6.009653e-04
IRKA step 55, rel. chg. shifts = 1.835191e-03 , rel. H2-norm chg. ROM = 4.640285e-04
IRKA step 56, rel. chg. shifts = 1.627322e-03 , rel. H2-norm chg. ROM = 3.591596e-04
IRKA step 57, rel. chg. shifts = 1.092269e-03 , rel. H2-norm chg. ROM = 2.769905e-04
IRKA step 58, rel. chg. shifts = 9.167929e-04 , rel. H2-norm chg. ROM = 2.143245e-04
IRKA terminated due to relative change of shifts criterion.
Computing TFMs of original and reduced order systems and MOR errors
Step 10 / 100 Step 20 / 100 Step 30 / 100 Step 40 / 100 Step 50 / 100 Step 60 / 100 Step 70 / 100 Step 80 / 100 Step 90 / 100 Step 100 / 100
ans =
Columns 1 through 13
1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
Columns 14 through 20
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1