-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathbenchmodred.html
249 lines (236 loc) · 10.5 KB
/
benchmodred.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
<h3>Benchmark Examples for Model Reduction</h3><P>
<hr noshade color="#666666">
<h4>Benchmark Examples for Model Reduction
of Linear Time Invariant Dynamical Systems</h4>
<p>
This benchmark collection contains several "real world" examples, reflecting current problems in applications,
which can be used to test the numerical methods for model reduction.<br>
<p>
The examples are stored as compressed MATLAB MAT files.
<p>Each MAT data file contains part or all of the matrices
<b> <i>A</i>, <i>B</i>, <i>C</i>, <i>D</i> </b> and <b> <i>E</i></b>
for descriptor systems:
<br><br><i>
<b>
Edx(t)/dt = Ax(t) + Bu(t),<br>
y(t) = Cx(t) + Du(t)</b></i><br><br>
If <b><i>D</i>, <i>C</i> </b> or
<b><i>E</i></b> are missing, it means that
<b><i>D=0</i>, <i>C=B<sup>T</sup></i></b> or <b><i>E=I</i></b>, respectively.
<p>
Some files contain a vector of the Hankel singular values, <i><b>hsv</b></i>, a frequency
vector, <i><b>w</b></i>, and the corresponding frequency response, <i><b>mag</b></i>.
When the controllability and the observability Gramians are positive definite,
the data files contain two matrices, <i><b>S</b></i> and <b><i>R</i></b>, which
are the Cholesky factors of the Gramians, rather than the Gramians themselves
(for more details see the <a href="../SLICOT-Reports/SLWN2002-2.pdf">report</a>).
If there are several gramians for SISO subsystems, they are denoted with subscripts.
<div align="Left">
There are three kinds of models: dense models, sparse models and second
order models (see the <a href="../SLICOT-Reports/SLWN2002-2.pdf">report</a>
for a detailed description of each one).<br>
<p>
The following table gives the data files with a short description.<br>
<br><br>
<table cellpadding="2" cellspacing="1" border="2" width="740" align="Center">
<tbody>
<tr>
<td valign="Middle" align="Center" width="162"><b>data</b></td>
<td valign="Middle" align="Center" width="105"><b>name of file</b></td>
<td valign="Middle" align="Center" width="205"><b> description</b></td>
<td valign="Middle" align="Center" width="69"><b> order N</b></td>
<td valign="Middle" align="Center" width="70"><b>inputs m</b></td>
<td valign="Middle" align="Center" width="75"><b>outputs p</b></td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Eady example</ahref></td>
<td valign="Middle" align="Center" width="105"><a
href="eady.mat">
eady.mat</a></td>
<td valign="Middle" align="Center" width="205">model of an atmospheric storm track</td>
<td valign="Middle" align="Center" width="69">598</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Transmission line model</td>
<td valign="Middle" align="Center" width="105"><a
href="tline.mat">
tline.mat</ahref></a></td>
<td valign="Middle" align="Center" width="205">example of a transmission line model</td>
<td valign="Middle" align="Center" width="69"> 256</td>
<td valign="Middle" align="Center" width="70">2</td>
<td valign="Middle" align="Center" width="75">2</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">CD player</td>
<td valign="Middle" align="Center" width="105"><a
href="CDplayer.mat">
CDplayer.mat</a></td>
<td valign="Middle" align="Center" width="205">classical CD player model</td>
<td valign="Middle" align="Center" width="69">120</td>
<td valign="Middle" align="Center" width="70">2</td>
<td valign="Middle" align="Center" width="75">2</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">PEEC model</td>
<td valign="Middle" align="Center" width="105"><a
href="peec.mat">
peec.mat</a></td>
<td valign="Middle" align="Center" width="205">partial element equivalent circuit model</td>
<td valign="Middle" align="Center" width="69">480</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">FOM model</td>
<td valign="Middle" align="Center" width="105"><a
href="fom.mat">
fom.mat</a></td>
<td valign="Middle" align="Center" width="205">block-diagonal model</td>
<td valign="Middle" align="Center" width="69">1006</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Random example</td>
<td valign="Middle" align="Center" width="105"><a
href="random.mat">
random.mat</a></td>
<td valign="Middle" align="Center" width="205">random model</td>
<td valign="Middle" align="Center" width="69">200</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">PDE example</td>
<td valign="Middle" align="Center" width="105"><a
href="pde.mat">
pde.mat</a></td>
<td valign="Middle" align="Center" width="205">partial differential equation</td>
<td valign="Middle" align="Center" width="69">84</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Heat equation (continuous case)</td>
<td valign="Middle" align="Center" width="105"><a
href="heat-cont.mat">
heat-cont.mat</a></td>
<td valign="Middle" align="Center" width="205">heat equation in a thin rod</td>
<td valign="Middle" align="Center" width="69">200</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Heat equation (discrete case)</td>
<td valign="Middle" align="Center" width="105"><a
href="heat-disc.mat">
heat-disc.mat</a></td>
<td valign="Middle" align="Center" width="205">discretization of the
previous equation</td>
<td valign="Middle" align="Center" width="69">200</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Orr-Somerfeld example</td>
<td valign="Middle" align="Center" width="105"><a
href="Orr-Som.mat">
Orr-Som.mat</a></td>
<td valign="Middle" align="Center" width="205">Orr-Sommerfeld operator <br>
for Couette flow</td>
<td valign="Middle" align="Center" width="69">200</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">MNA example - 1</td>
<td valign="Middle" align="Center" width="105"><a
href="MNA_1.mat">
MNA_1.mat</a></td>
<td valign="Middle" align="Center" width="205">Modified Nodal Analysis model</td>
<td valign="Middle" align="Center" width="69">578</td>
<td valign="Middle" align="Center" width="70">9</td>
<td valign="Middle" align="Center" width="75">9</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">MNA example - 2</td>
<td valign="Middle" align="Center" width="105"><a
href="MNA_2.mat">
MNA_2.mat</a></td>
<td valign="Middle" align="Center" width="205">"</td>
<td valign="Middle" align="Center" width="69">9223</td>
<td valign="Middle" align="Center" width="70">18</td>
<td valign="Middle" align="Center" width="75">18</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">MNA example - 3</td>
<td valign="Middle" align="Center" width="105"><a
href="MNA_3.mat">
MNA_3.mat</a></td>
<td valign="Middle" align="Center" width="205">"</td>
<td valign="Middle" align="Center" width="69">4863</td>
<td valign="Middle" align="Center" width="70">22</td>
<td valign="Middle" align="Center" width="75">22</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">MNA example - 4</td>
<td valign="Middle" align="Center" width="105"><a
href="MNA_4.mat">
MNA_4.mat</a></td>
<td valign="Middle" align="Center" width="205">"</td>
<td valign="Middle" align="Center" width="69">980</td>
<td valign="Middle" align="Center" width="70">4</td>
<td valign="Middle" align="Center" width="75">4</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">MNA example - 5</td>
<td valign="Middle" align="Center" width="105"><a
href="MNA_5.mat">
MNA_5.mat</a></td>
<td valign="Middle" align="Center" width="205">"</td>
<td valign="Middle" align="Center" width="69">10913</td>
<td valign="Middle" align="Center" width="70">9</td>
<td valign="Middle" align="Center" width="75">9</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">International space station</td>
<td valign="Middle" align="Center" width="105"><a
href="iss.mat">
iss.mat</a></td>
<td valign="Middle" align="Center" width="205">component 1r of the
International Space Station</td>
<td valign="Middle" align="Center" width="69">270</td>
<td valign="Middle" align="Center" width="70">3</td>
<td valign="Middle" align="Center" width="75">3</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Building model</td>
<td valign="Middle" align="Center" width="105"><a
href="build.mat">
build.mat</a></td>
<td valign="Middle" align="Center" width="205">motion problem in a building</td>
<td valign="Middle" align="Center" width="69">48</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
<tr>
<td valign="Middle" align="Center" width="162">Clamped beam model</td>
<td valign="Middle" align="Center" width="105"><a
href="beam.mat">
beam.mat</a></td>
<td valign="Middle" align="Center" width="205">Clamped beam model</td>
<td valign="Middle" align="Center" width="69">348</td>
<td valign="Middle" align="Center" width="70">1</td>
<td valign="Middle" align="Center" width="75">1</td>
</tr>
</table>
<br><br>
<hr noshade color="#666666">
<h4>Available Reports</h4>
1. <i>Younès Chahlaoui and Paul Van Dooren: </i><a href="../SLICOT-Reports/SLWN2002-2.pdf">A
collection of benchmark examples for model reduction of linear time invariant
dynamical systems</a>; SLICOT Working Note 2002-2: February 2002.
<br><br>
<hr noshade color="#666666">