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<HTML>
<HEAD><TITLE>TC01OD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="TC01OD">TC01OD</A></H2>
<H3>
Dual of a left/right polynomial matrix 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 right (left) polynomial matrix representation of
a given left (right) polynomial matrix representation, where the
right and left polynomial matrix representations are of the form
Q(s)*inv(P(s)) and inv(P(s))*Q(s) respectively.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE TC01OD( LERI, M, P, INDLIM, PCOEFF, LDPCO1, LDPCO2,
$ QCOEFF, LDQCO1, LDQCO2, INFO )
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,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
LERI CHARACTER*1
Indicates whether a left or right matrix fraction is input
as follows:
= 'L': A left matrix fraction is input;
= 'R': A right matrix fraction is input.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
M (input) INTEGER
The number of system inputs. M >= 0.
P (input) INTEGER
The number of system outputs. P >= 0.
INDLIM (input) INTEGER
The highest value of K for which PCOEFF(.,.,K) and
QCOEFF(.,.,K) are to be transposed.
K = kpcoef + 1, where kpcoef is the maximum degree of the
polynomials in P(s). INDLIM >= 1.
PCOEFF (input/output) DOUBLE PRECISION array, dimension
(LDPCO1,LDPCO2,INDLIM)
If LERI = 'L' then porm = P, otherwise porm = M.
On entry, the leading porm-by-porm-by-INDLIM part of this
array must contain the coefficients of the denominator
matrix P(s).
PCOEFF(I,J,K) is the coefficient in s**(INDLIM-K) of
polynomial (I,J) of P(s), where K = 1,2,...,INDLIM.
On exit, the leading porm-by-porm-by-INDLIM part of this
array contains the coefficients of the denominator matrix
P'(s) of the dual system.
LDPCO1 INTEGER
The leading dimension of array PCOEFF.
LDPCO1 >= MAX(1,P) if LERI = 'L',
LDPCO1 >= MAX(1,M) if LERI = 'R'.
LDPCO2 INTEGER
The second dimension of array PCOEFF.
LDPCO2 >= MAX(1,P) if LERI = 'L',
LDPCO2 >= MAX(1,M) if LERI = 'R'.
QCOEFF (input/output) DOUBLE PRECISION array, dimension
(LDQCO1,LDQCO2,INDLIM)
On entry, the leading P-by-M-by-INDLIM part of this array
must contain the coefficients of the numerator matrix
Q(s).
QCOEFF(I,J,K) is the coefficient in s**(INDLIM-K) of
polynomial (I,J) of Q(s), where K = 1,2,...,INDLIM.
On exit, the leading M-by-P-by-INDLIM part of the array
contains the coefficients of the numerator matrix Q'(s)
of the dual system.
LDQCO1 INTEGER
The leading dimension of array QCOEFF.
LDQCO1 >= MAX(1,M,P).
LDQCO2 INTEGER
The second dimension of array QCOEFF.
LDQCO2 >= MAX(1,M,P).
</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 M-input/P-output left (right) polynomial matrix
representation has numerator matrix Q(s) and denominator matrix
P(s), its dual P-input/M-output right (left) polynomial matrix
representation simply has numerator matrix Q'(s) and denominator
matrix P'(s).
</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>
* TC01OD EXAMPLE PROGRAM TEXT
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER MMAX, PMAX, INDMAX
PARAMETER ( MMAX = 20, PMAX = 20, INDMAX = 20 )
INTEGER MAXMP
PARAMETER ( MAXMP = MAX( MMAX, PMAX ) )
INTEGER LDPCO1, LDPCO2, LDQCO1, LDQCO2
PARAMETER ( LDPCO1 = MAXMP, LDPCO2 = MAXMP,
$ LDQCO1 = MAXMP, LDQCO2 = MAXMP )
* .. Local Scalars ..
INTEGER I, INDLIM, INFO, J, K, M, P, PORM
CHARACTER*1 LERI
LOGICAL LLERI
* .. Local Arrays ..
DOUBLE PRECISION PCOEFF(LDPCO1,LDPCO2,INDMAX),
$ QCOEFF(LDQCO1,LDQCO2,INDMAX)
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL TC01OD
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) M, P, INDLIM, LERI
LLERI = LSAME( LERI, 'L' )
IF ( M.LE.0 .OR. M.GT.MMAX ) THEN
WRITE ( NOUT, FMT = 99994 ) M
ELSE IF ( P.LE.0 .OR. P.GT.PMAX ) THEN
WRITE ( NOUT, FMT = 99993 ) P
ELSE IF ( INDLIM.LE.0 .OR. INDLIM.GT.INDMAX ) THEN
WRITE ( NOUT, FMT = 99992 ) INDLIM
ELSE
PORM = P
IF ( .NOT.LLERI ) PORM = M
READ ( NIN, FMT = * )
$ ( ( ( PCOEFF(I,J,K), K = 1,INDLIM ), J = 1,PORM ),
$ I = 1,PORM )
READ ( NIN, FMT = * )
$ ( ( ( QCOEFF(I,J,K), K = 1,INDLIM ), J = 1,M ), I = 1,P )
* Find the dual right pmr of the given left pmr.
CALL TC01OD( LERI, M, P, INDLIM, PCOEFF, LDPCO1, LDPCO2,
$ QCOEFF, LDQCO1, LDQCO2, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
DO 40 I = 1, PORM
DO 20 J = 1, PORM
WRITE ( NOUT, FMT = 99996 ) I, J,
$ ( PCOEFF(I,J,K), K = 1,INDLIM )
20 CONTINUE
40 CONTINUE
WRITE ( NOUT, FMT = 99995 )
DO 80 I = 1, M
DO 60 J = 1, P
WRITE ( NOUT, FMT = 99996 ) I, J,
$ ( QCOEFF(I,J,K), K = 1,INDLIM )
60 CONTINUE
80 CONTINUE
END IF
END IF
STOP
*
99999 FORMAT (' TC01OD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from TC01OD = ',I2)
99997 FORMAT (' The coefficients of the denominator matrix of the dual',
$ ' system are ')
99996 FORMAT (/' element (',I2,',',I2,') is ',20(1X,F6.2))
99995 FORMAT (//' The coefficients of the numerator matrix of the dual',
$ ' system are ')
99994 FORMAT (/' M is out of range.',/' M = ',I5)
99993 FORMAT (/' P is out of range.',/' P = ',I5)
99992 FORMAT (/' INDLIM is out of range.',/' INDLIM = ',I5)
END
</PRE>
<B>Program Data</B>
<PRE>
TC01OD EXAMPLE PROGRAM DATA
2 2 3 L
2.0 3.0 1.0
4.0 -1.0 -1.0
5.0 7.0 -6.0
3.0 2.0 2.0
6.0 -1.0 5.0
1.0 7.0 5.0
1.0 1.0 1.0
4.0 1.0 -1.0
</PRE>
<B>Program Results</B>
<PRE>
TC01OD EXAMPLE PROGRAM RESULTS
The coefficients of the denominator matrix of the dual system are
element ( 1, 1) is 2.00 3.00 1.00
element ( 1, 2) is 5.00 7.00 -6.00
element ( 2, 1) is 4.00 -1.00 -1.00
element ( 2, 2) is 3.00 2.00 2.00
The coefficients of the numerator matrix of the dual system are
element ( 1, 1) is 6.00 -1.00 5.00
element ( 1, 2) is 1.00 1.00 1.00
element ( 2, 1) is 1.00 7.00 5.00
element ( 2, 2) is 4.00 1.00 -1.00
</PRE>
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