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<HTML>
<HEAD><TITLE>AB07MD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="AB07MD">AB07MD</A></H2>
<H3>
Dual of a given state-space representation
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To find the dual of a given state-space representation.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE AB07MD( JOBD, N, M, P, A, LDA, B, LDB, C, LDC, D, LDD,
$ INFO )
C .. Scalar Arguments ..
CHARACTER JOBD
INTEGER INFO, LDA, LDB, LDC, LDD, M, N, P
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
JOBD CHARACTER*1
Specifies whether or not a non-zero matrix D appears in
the given state space model:
= 'D': D is present;
= 'Z': D is assumed a zero matrix.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the state-space representation. N >= 0.
M (input) INTEGER
The number of system inputs. M >= 0.
P (input) INTEGER
The number of system outputs. P >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the original state dynamics matrix A.
On exit, the leading N-by-N part of this array contains
the dual state dynamics matrix A'.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,N).
B (input/output) DOUBLE PRECISION array, dimension
(LDB,MAX(M,P))
On entry, the leading N-by-M part of this array must
contain the original input/state matrix B.
On exit, the leading N-by-P part of this array contains
the dual input/state matrix C'.
LDB INTEGER
The leading dimension of array B. LDB >= MAX(1,N).
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the leading P-by-N part of this array must
contain the original state/output matrix C.
On exit, the leading M-by-N part of this array contains
the dual state/output matrix B'.
LDC INTEGER
The leading dimension of array C.
LDC >= MAX(1,M,P) if N > 0.
LDC >= 1 if N = 0.
D (input/output) DOUBLE PRECISION array, dimension
(LDD,MAX(M,P))
On entry, if JOBD = 'D', the leading P-by-M part of this
array must contain the original direct transmission
matrix D.
On exit, if JOBD = 'D', the leading M-by-P part of this
array contains the dual direct transmission matrix D'.
The array D is not referenced if JOBD = 'Z'.
LDD INTEGER
The leading dimension of array D.
LDD >= MAX(1,M,P) if JOBD = 'D'.
LDD >= 1 if JOBD = 'Z'.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
If the given state-space representation is the M-input/P-output
(A,B,C,D), its dual is simply the P-input/M-output (A',C',B',D').
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
None
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
None
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
* AB07MD EXAMPLE PROGRAM TEXT
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER NMAX, MMAX, PMAX
PARAMETER ( NMAX = 20, MMAX = 20, PMAX = 20 )
INTEGER MAXMP
PARAMETER ( MAXMP = MAX( MMAX, PMAX ) )
INTEGER LDA, LDB, LDC, LDD
PARAMETER ( LDA = NMAX, LDB = NMAX, LDC = MAXMP,
$ LDD = MAXMP )
* .. Local Scalars ..
CHARACTER*1 JOBD
INTEGER I, INFO, J, M, N, P
* .. Local Arrays ..
DOUBLE PRECISION A(LDA,NMAX), B(LDB,MAXMP), C(LDC,NMAX),
$ D(LDD,MAXMP)
* .. External functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL AB07MD
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read in the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) N, M, P, JOBD
IF ( N.LE.0 .OR. N.GT.NMAX ) THEN
WRITE ( NOUT, FMT = 99992 ) N
ELSE
READ ( NIN, FMT = * ) ( ( A(I,J), J = 1,N ), I = 1,N )
IF ( M.LE.0 .OR. M.GT.MMAX ) THEN
WRITE ( NOUT, FMT = 99991 ) M
ELSE
READ ( NIN, FMT = * ) ( ( B(I,J), J = 1,M ), I = 1,N )
IF ( P.LE.0 .OR. P.GT.PMAX ) THEN
WRITE ( NOUT, FMT = 99990 ) P
ELSE
READ ( NIN, FMT = * ) ( ( C(I,J), J = 1,N ), I = 1,P )
READ ( NIN, FMT = * ) ( ( D(I,J), J = 1,M ), I = 1,P )
* Find the dual of the ssr (A,B,C,D).
CALL AB07MD( JOBD, N, M, P, A, LDA, B, LDB, C, LDC, D,
$ LDD, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
DO 20 I = 1, N
WRITE ( NOUT, FMT = 99996 ) ( A(I,J), J = 1,N )
20 CONTINUE
WRITE ( NOUT, FMT = 99995 )
DO 40 I = 1, N
WRITE ( NOUT, FMT = 99996 ) ( B(I,J), J = 1,P )
40 CONTINUE
WRITE ( NOUT, FMT = 99994 )
DO 60 I = 1, M
WRITE ( NOUT, FMT = 99996 ) ( C(I,J), J = 1,N )
60 CONTINUE
IF ( LSAME( JOBD, 'D' ) ) THEN
WRITE ( NOUT, FMT = 99993 )
DO 80 I = 1, M
WRITE ( NOUT, FMT = 99996 ) ( D(I,J), J = 1,P )
80 CONTINUE
END IF
END IF
END IF
END IF
END IF
STOP
*
99999 FORMAT (' AB07MD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from AB07MD = ',I2)
99997 FORMAT (' The dual state dynamics matrix is ')
99996 FORMAT (20(1X,F8.4))
99995 FORMAT (/' The dual input/state matrix is ')
99994 FORMAT (/' The dual state/output matrix is ')
99993 FORMAT (/' The dual direct transmission matrix is ')
99992 FORMAT (/' N is out of range.',/' N = ',I5)
99991 FORMAT (/' M is out of range.',/' M = ',I5)
99990 FORMAT (/' P is out of range.',/' P = ',I5)
END
</PRE>
<B>Program Data</B>
<PRE>
AB07MD EXAMPLE PROGRAM DATA
3 1 2 D
1.0 2.0 0.0
4.0 -1.0 0.0
0.0 0.0 1.0
1.0 0.0 1.0
0.0 1.0 -1.0
0.0 0.0 1.0
0.0 1.0
</PRE>
<B>Program Results</B>
<PRE>
AB07MD EXAMPLE PROGRAM RESULTS
The dual state dynamics matrix is
1.0000 4.0000 0.0000
2.0000 -1.0000 0.0000
0.0000 0.0000 1.0000
The dual input/state matrix is
0.0000 0.0000
1.0000 0.0000
-1.0000 1.0000
The dual state/output matrix is
1.0000 0.0000 1.0000
The dual direct transmission matrix is
0.0000 1.0000
</PRE>
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