## TC01OD

### Dual of a left/right polynomial matrix representation

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

      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.

Specification

          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,*)

Arguments

Mode Parameters

      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.

Input/Output Parameters

      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).

Error Indicator

      INFO    INTEGER
              = 0:  successful exit;
              < 0:  if INFO = -i, the i-th argument had an illegal
                    value.

Method

      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).

References

      None.

Numerical Aspects

      None.

Further Comments

      None

Example

Program Text

    *     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

Program Data

     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

Program Results

     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

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