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
|
SUBROUTINE TC01OD( LERI, M, P, INDLIM, PCOEFF, LDPCO1, LDPCO2,
$ QCOEFF, LDQCO1, LDQCO2, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To find the dual right (left) polynomial matrix representation of
C a given left (right) polynomial matrix representation, where the
C right and left polynomial matrix representations are of the form
C Q(s)*inv(P(s)) and inv(P(s))*Q(s) respectively.
C
C ARGUMENTS
C
C Mode Parameters
C
C LERI CHARACTER*1
C Indicates whether a left or right matrix fraction is input
C as follows:
C = 'L': A left matrix fraction is input;
C = 'R': A right matrix fraction is input.
C
C Input/Output Parameters
C
C M (input) INTEGER
C The number of system inputs. M >= 0.
C
C P (input) INTEGER
C The number of system outputs. P >= 0.
C
C INDLIM (input) INTEGER
C The highest value of K for which PCOEFF(.,.,K) and
C QCOEFF(.,.,K) are to be transposed.
C K = kpcoef + 1, where kpcoef is the maximum degree of the
C polynomials in P(s). INDLIM >= 1.
C
C PCOEFF (input/output) DOUBLE PRECISION array, dimension
C (LDPCO1,LDPCO2,INDLIM)
C If LERI = 'L' then porm = P, otherwise porm = M.
C On entry, the leading porm-by-porm-by-INDLIM part of this
C array must contain the coefficients of the denominator
C matrix P(s).
C PCOEFF(I,J,K) is the coefficient in s**(INDLIM-K) of
C polynomial (I,J) of P(s), where K = 1,2,...,INDLIM.
C On exit, the leading porm-by-porm-by-INDLIM part of this
C array contains the coefficients of the denominator matrix
C P'(s) of the dual system.
C
C LDPCO1 INTEGER
C The leading dimension of array PCOEFF.
C LDPCO1 >= MAX(1,P) if LERI = 'L',
C LDPCO1 >= MAX(1,M) if LERI = 'R'.
C
C LDPCO2 INTEGER
C The second dimension of array PCOEFF.
C LDPCO2 >= MAX(1,P) if LERI = 'L',
C LDPCO2 >= MAX(1,M) if LERI = 'R'.
C
C QCOEFF (input/output) DOUBLE PRECISION array, dimension
C (LDQCO1,LDQCO2,INDLIM)
C On entry, the leading P-by-M-by-INDLIM part of this array
C must contain the coefficients of the numerator matrix
C Q(s).
C QCOEFF(I,J,K) is the coefficient in s**(INDLIM-K) of
C polynomial (I,J) of Q(s), where K = 1,2,...,INDLIM.
C On exit, the leading M-by-P-by-INDLIM part of the array
C contains the coefficients of the numerator matrix Q'(s)
C of the dual system.
C
C LDQCO1 INTEGER
C The leading dimension of array QCOEFF.
C LDQCO1 >= MAX(1,M,P).
C
C LDQCO2 INTEGER
C The second dimension of array QCOEFF.
C LDQCO2 >= MAX(1,M,P).
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C If the given M-input/P-output left (right) polynomial matrix
C representation has numerator matrix Q(s) and denominator matrix
C P(s), its dual P-input/M-output right (left) polynomial matrix
C representation simply has numerator matrix Q'(s) and denominator
C matrix P'(s).
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996.
C Supersedes Release 2.0 routine TC01CD by T.W.C.Williams, Kingston
C Polytechnic, United Kingdom, March 1982.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Coprime matrix fraction, elementary polynomial operations,
C polynomial matrix, state-space representation, transfer matrix.
C
C ******************************************************************
C
C .. Scalar Arguments ..
CHARACTER LERI
INTEGER INFO, INDLIM, LDPCO1, LDPCO2, LDQCO1, LDQCO2, M,
$ P
C .. Array Arguments ..
DOUBLE PRECISION PCOEFF(LDPCO1,LDPCO2,*), QCOEFF(LDQCO1,LDQCO2,*)
C .. Local Scalars ..
LOGICAL LLERI
INTEGER J, K, MINMP, MPLIM, PORM
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DCOPY, DSWAP, XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C .. Executable Statements ..
C
INFO = 0
LLERI = LSAME( LERI, 'L' )
MPLIM = MAX( M, P )
MINMP = MIN( M, P )
C
C Test the input scalar arguments.
C
IF( .NOT.LLERI .AND. .NOT.LSAME( LERI, 'R' ) ) THEN
INFO = -1
ELSE IF( M.LT.0 ) THEN
INFO = -2
ELSE IF( P.LT.0 ) THEN
INFO = -3
ELSE IF( INDLIM.LT.1 ) THEN
INFO = -4
ELSE IF( ( LLERI .AND. LDPCO1.LT.MAX( 1, P ) ) .OR.
$ ( .NOT.LLERI .AND. LDPCO1.LT.MAX( 1, M ) ) ) THEN
INFO = -6
ELSE IF( ( LLERI .AND. LDPCO2.LT.MAX( 1, P ) ) .OR.
$ ( .NOT.LLERI .AND. LDPCO2.LT.MAX( 1, M ) ) ) THEN
INFO = -7
ELSE IF( LDQCO1.LT.MAX( 1, MPLIM ) ) THEN
INFO = -9
ELSE IF( LDQCO2.LT.MAX( 1, MPLIM ) ) THEN
INFO = -10
END IF
C
IF ( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'TC01OD', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF ( M.EQ.0 .OR. P.EQ.0 )
$ RETURN
C
IF ( MPLIM.NE.1 ) THEN
C
C Non-scalar system: transpose numerator matrix Q(s).
C
DO 20 K = 1, INDLIM
C
DO 10 J = 1, MPLIM
IF ( J.LT.MINMP ) THEN
CALL DSWAP( MINMP-J, QCOEFF(J+1,J,K), 1,
$ QCOEFF(J,J+1,K), LDQCO1 )
ELSE IF ( J.GT.P ) THEN
CALL DCOPY( P, QCOEFF(1,J,K), 1, QCOEFF(J,1,K),
$ LDQCO1 )
ELSE IF ( J.GT.M ) THEN
CALL DCOPY( M, QCOEFF(J,1,K), LDQCO1, QCOEFF(1,J,K),
$ 1 )
END IF
10 CONTINUE
C
20 CONTINUE
C
C Find dimension of denominator matrix P(s): M (P) for
C right (left) polynomial matrix representation.
C
PORM = M
IF ( LLERI ) PORM = P
IF ( PORM.NE.1 ) THEN
C
C Non-scalar P(s): transpose it.
C
DO 40 K = 1, INDLIM
C
DO 30 J = 1, PORM - 1
CALL DSWAP( PORM-J, PCOEFF(J+1,J,K), 1,
$ PCOEFF(J,J+1,K), LDPCO1 )
30 CONTINUE
C
40 CONTINUE
C
END IF
END IF
C
RETURN
C *** Last line of TC01OD ***
END
|
