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
NoneExample
Program Text
*     TC01OD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2010 NICONET e.V.
*
*     .. 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 -1.0Program 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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