Purpose
To evaluate the transfer matrix T(s) of a left polynomial matrix representation [T(s) = inv(P(s))*Q(s)] or a right polynomial matrix representation [T(s) = Q(s)*inv(P(s))] at any specified complex frequency s = SVAL. This routine will calculate the standard frequency response matrix at frequency omega if SVAL is supplied as (0.0,omega).Specification
      SUBROUTINE TC05AD( LERI, M, P, SVAL, INDEX, PCOEFF, LDPCO1,
     $                   LDPCO2, QCOEFF, LDQCO1, LDQCO2, RCOND, CFREQR,
     $                   LDCFRE, IWORK, DWORK, ZWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         LERI
      INTEGER           INFO, LDCFRE, LDPCO1, LDPCO2, LDQCO1, LDQCO2, M,
     $                  P
      DOUBLE PRECISION  RCOND
      COMPLEX*16        SVAL
C     .. Array Arguments ..
      INTEGER           INDEX(*), IWORK(*)
      DOUBLE PRECISION  DWORK(*), PCOEFF(LDPCO1,LDPCO2,*),
     $                  QCOEFF(LDQCO1,LDQCO2,*)
      COMPLEX*16        CFREQR(LDCFRE,*), ZWORK(*)
Arguments
Mode Parameters
  LERI    CHARACTER*1
          Indicates whether a left polynomial matrix representation
          or a right polynomial matrix representation is to be used
          to evaluate the transfer matrix 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.
  SVAL    (input) COMPLEX*16
          The frequency at which the transfer matrix or the
          frequency respose matrix is to be evaluated.
          For a standard frequency response set the real part
          of SVAL to zero.
  INDEX   (input) INTEGER array, dimension (MAX(M,P))
          If LERI = 'L', INDEX(I), I = 1,2,...,P, must contain the
          maximum degree of the polynomials in the I-th row of the
          denominator matrix P(s) of the given left polynomial
          matrix representation.
          If LERI = 'R', INDEX(I), I = 1,2,...,M, must contain the
          maximum degree of the polynomials in the I-th column of
          the denominator matrix P(s) of the given right polynomial
          matrix representation.
  PCOEFF  (input) DOUBLE PRECISION array, dimension
          (LDPCO1,LDPCO2,kpcoef), where kpcoef = MAX(INDEX(I)) + 1.
          If LERI = 'L' then porm = P, otherwise porm = M.
          The leading porm-by-porm-by-kpcoef part of this array must
          contain the coefficients of the denominator matrix P(s).
          PCOEFF(I,J,K) is the coefficient in s**(INDEX(iorj)-K+1)
          of polynomial (I,J) of P(s), where K = 1,2,...,kpcoef; if
          LERI = 'L' then iorj = I, otherwise iorj = J.
          Thus for LERI = 'L', P(s) =
          diag(s**INDEX(I))*(PCOEFF(.,.,1)+PCOEFF(.,.,2)/s+...).
          If LERI = 'R', PCOEFF is modified by the routine but
          restored on exit.
  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) DOUBLE PRECISION array, dimension
          (LDQCO1,LDQCO2,kpcoef)
          If LERI = 'L' then porp = M, otherwise porp = P.
          The leading porm-by-porp-by-kpcoef part of this array must
          contain the coefficients of the numerator matrix Q(s).
          QCOEFF(I,J,K) is defined as for PCOEFF(I,J,K).
          If LERI = 'R', QCOEFF is modified by the routine but
          restored on exit.
  LDQCO1  INTEGER
          The leading dimension of array QCOEFF.
          LDQCO1 >= MAX(1,P)   if LERI = 'L',
          LDQCO1 >= MAX(1,M,P) if LERI = 'R'.
  LDQCO2  INTEGER
          The second dimension of array QCOEFF.
          LDQCO2 >= MAX(1,M)   if LERI = 'L',
          LDQCO2 >= MAX(1,M,P) if LERI = 'R'.
  RCOND   (output) DOUBLE PRECISION
          The estimated reciprocal of the condition number of the
          denominator matrix P(SVAL).
          If RCOND is nearly zero, SVAL is approximately a system
          pole.
  CFREQR  (output) COMPLEX*16 array, dimension (LDCFRE,MAX(M,P))
          The leading porm-by-porp part of this array contains the
          frequency response matrix T(SVAL).
  LDCFRE  INTEGER
          The leading dimension of array CFREQR.
          LDCFRE >= MAX(1,P)   if LERI = 'L',
          LDCFRE >= MAX(1,M,P) if LERI = 'R'.
Workspace
  IWORK   INTEGER array, dimension (liwork)
          where liwork = P, if LERI = 'L',
                liwork = M, if LERI = 'R'.
  DWORK   DOUBLE PRECISION array, dimension (ldwork)
          where ldwork = 2*P, if LERI = 'L',
                ldwork = 2*M, if LERI = 'R'.
  ZWORK   COMPLEX*16 array, dimension (lzwork),
          where lzwork = P*(P+2), if LERI = 'L',
                lzwork = M*(M+2), if LERI = 'R'.
Error Indicator
  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value;
          = 1:  if P(SVAL) is exactly or nearly singular;
                no frequency response is calculated.
Method
The method for a left matrix fraction will be described here; right matrix fractions are dealt with by obtaining the dual left fraction and calculating its frequency response (see SLICOT Library routine TC01OD). The first step is to calculate the complex value P(SVAL) of the denominator matrix P(s) at the desired frequency SVAL. If P(SVAL) is approximately singular, SVAL is approximately a pole of this system and so the frequency response matrix T(SVAL) is not calculated; in this case, the routine returns with the Error Indicator (INFO) set to 1. Otherwise, the complex value Q(SVAL) of the numerator matrix Q(s) at frequency SVAL is calculated in a similar way to P(SVAL), and the desired response matrix T(SVAL) = inv(P(SVAL))*Q(SVAL) is found by solving the corresponding system of complex linear equations.References
NoneNumerical Aspects
3 The algorithm requires 0(N ) operations.Further Comments
NoneExample
Program Text
*     TC05AD EXAMPLE PROGRAM TEXT.
*     Copyright (c) 2002-2010 NICONET e.V.
*
*     .. Parameters ..
      INTEGER          NIN, NOUT
      PARAMETER        ( NIN = 5, NOUT = 6 )
      INTEGER          MMAX, PMAX, KPCMAX
      PARAMETER        ( MMAX = 20, PMAX = 20, KPCMAX = 20 )
      INTEGER          MAXMP
      PARAMETER        ( MAXMP = MAX( MMAX, PMAX ) )
      INTEGER          LDCFRE, LDPCO1, LDPCO2, LDQCO1, LDQCO2
      PARAMETER        ( LDCFRE = MAXMP, LDPCO1 = MAXMP,
     $                   LDPCO2 = MAXMP, LDQCO1 = MAXMP,
     $                   LDQCO2 = MAXMP )
      INTEGER          LDWORK
      PARAMETER        ( LDWORK = 2*MAXMP )
      INTEGER          LZWORK
      PARAMETER        ( LZWORK = ( MAXMP )*( MAXMP+2 ) )
*     .. Local Scalars ..
      COMPLEX*16       SVAL
      DOUBLE PRECISION RCOND
      INTEGER          I, INFO, J, K, KPCOEF, M, P, PORM, PORP
      CHARACTER*1      LERI
      LOGICAL          LLERI
*     .. Local Arrays ..
      COMPLEX*16       CFREQR(LDCFRE,MAXMP), ZWORK(LZWORK)
      DOUBLE PRECISION DWORK(LDWORK), PCOEFF(LDPCO1,LDPCO2,KPCMAX),
     $                 QCOEFF(LDQCO1,LDQCO2,KPCMAX)
      INTEGER          INDEX(MAXMP), IWORK(MAXMP)
*     .. External Functions ..
      LOGICAL          LSAME
      EXTERNAL         LSAME
*     .. External Subroutines ..
      EXTERNAL         TC05AD
*     .. 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, SVAL, LERI
      LLERI = LSAME( LERI, 'L' )
      IF ( M.LE.0 .OR. M.GT.MMAX ) THEN
         WRITE ( NOUT, FMT = 99995 ) M
      ELSE IF ( P.LE.0 .OR. P.GT.PMAX ) THEN
         WRITE ( NOUT, FMT = 99994 ) P
      ELSE
         PORM = P
         IF ( .NOT.LLERI ) PORM = M
         READ ( NIN, FMT = * ) ( INDEX(I), I = 1,PORM )
         PORP = M
         IF ( .NOT.LLERI ) PORP = P
         KPCOEF = 0
         DO 20 I = 1, PORM
            KPCOEF = MAX( KPCOEF, INDEX(I) )
   20    CONTINUE
         KPCOEF = KPCOEF + 1
         IF ( KPCOEF.LE.0 .OR. KPCOEF.GT.KPCMAX ) THEN
            WRITE ( NOUT, FMT = 99993 ) KPCOEF
         ELSE
            READ ( NIN, FMT = * )
     $         ( ( ( PCOEFF(I,J,K), K = 1,KPCOEF ), J = 1,PORM ),
     $                              I = 1,PORM )
            READ ( NIN, FMT = * )
     $         ( ( ( QCOEFF(I,J,K), K = 1,KPCOEF ), J = 1,PORP ),
     $                              I = 1,PORM )
*           Find the standard frequency response matrix of left pmr
*           at 0.5*j.
            CALL TC05AD( LERI, M, P, SVAL, INDEX, PCOEFF, LDPCO1,
     $                   LDPCO2, QCOEFF, LDQCO1, LDQCO2, RCOND, CFREQR,
     $                   LDCFRE, IWORK, DWORK, ZWORK, INFO )
*
            IF ( INFO.NE.0 ) THEN
               WRITE ( NOUT, FMT = 99998 ) INFO
            ELSE
               WRITE ( NOUT, FMT = 99997 ) RCOND
               DO 40 I = 1, PORM
                  WRITE ( NOUT, FMT = 99996 )
     $                  ( CFREQR(I,J), J = 1,PORP )
   40          CONTINUE
            END IF
         END IF
      END IF
      STOP
*
99999 FORMAT (' TC05AD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from TC05AD = ',I2)
99997 FORMAT (' RCOND = ',F4.2,//' The frequency response matrix T(SVA',
     $       'L) is ')
99996 FORMAT (20(' (',F5.2,',',F5.2,') ',:))
99995 FORMAT (/' M is out of range.',/' M = ',I5)
99994 FORMAT (/' P is out of range.',/' P = ',I5)
99993 FORMAT (/' KPCOEF is out of range.',/' KPCOEF = ',I5)
      END
Program Data
TC05AD EXAMPLE PROGRAM DATA 2 2 (0.0,0.5) L 2 2 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
TC05AD EXAMPLE PROGRAM RESULTS RCOND = 0.19 The frequency response matrix T(SVAL) is (-0.25,-0.33) ( 0.26,-0.45) (-1.48, 0.35) (-2.25,-1.11)
Click here to get a compressed (gzip) tar file containing the source code of the routine, the example program, data, documentation, and related files.
Return to index