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SUBROUTINE TB04BV( ORDER, P, M, MD, IGN, LDIGN, IGD, LDIGD, GN,
$ GD, D, LDD, TOL, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To separate the strictly proper part G0 from the constant part D
C of an P-by-M proper transfer function matrix G.
C
C ARGUMENTS
C
C Mode Parameters
C
C ORDER CHARACTER*1
C Specifies the order in which the polynomial coefficients
C of the transfer function matrix are stored, as follows:
C = 'I': Increasing order of powers of the indeterminate;
C = 'D': Decreasing order of powers of the indeterminate.
C
C Input/Output Parameters
C
C P (input) INTEGER
C The number of the system outputs. P >= 0.
C
C M (input) INTEGER
C The number of the system inputs. M >= 0.
C
C MD (input) INTEGER
C The maximum degree of the polynomials in G, plus 1, i.e.,
C MD = MAX(IGD(I,J)) + 1.
C I,J
C
C IGN (input/output) INTEGER array, dimension (LDIGN,M)
C On entry, the leading P-by-M part of this array must
C contain the degrees of the numerator polynomials in G:
C the (i,j) element of IGN must contain the degree of the
C numerator polynomial of the polynomial ratio G(i,j).
C On exit, the leading P-by-M part of this array contains
C the degrees of the numerator polynomials in G0.
C
C LDIGN INTEGER
C The leading dimension of array IGN. LDIGN >= max(1,P).
C
C IGD (input) INTEGER array, dimension (LDIGD,M)
C The leading P-by-M part of this array must contain the
C degrees of the denominator polynomials in G (and G0):
C the (i,j) element of IGD contains the degree of the
C denominator polynomial of the polynomial ratio G(i,j).
C
C LDIGD INTEGER
C The leading dimension of array IGD. LDIGD >= max(1,P).
C
C GN (input/output) DOUBLE PRECISION array, dimension (P*M*MD)
C On entry, this array must contain the coefficients of the
C numerator polynomials, Num(i,j), of the transfer function
C matrix G. The polynomials are stored in a column-wise
C order, i.e., Num(1,1), Num(2,1), ..., Num(P,1), Num(1,2),
C Num(2,2), ..., Num(P,2), ..., Num(1,M), Num(2,M), ...,
C Num(P,M); MD memory locations are reserved for each
C polynomial, hence, the (i,j) polynomial is stored starting
C from the location ((j-1)*P+i-1)*MD+1. The coefficients
C appear in increasing or decreasing order of the powers
C of the indeterminate, according to ORDER.
C On exit, this array contains the coefficients of the
C numerator polynomials of the strictly proper part G0 of
C the transfer function matrix G, stored similarly.
C
C GD (input) DOUBLE PRECISION array, dimension (P*M*MD)
C This array must contain the coefficients of the
C denominator polynomials, Den(i,j), of the transfer
C function matrix G. The polynomials are stored as for the
C numerator polynomials.
C
C D (output) DOUBLE PRECISION array, dimension (LDD,M)
C The leading P-by-M part of this array contains the
C matrix D.
C
C LDD INTEGER
C The leading dimension of array D. LDD >= max(1,P).
C
C Tolerances
C
C TOL DOUBLE PRECISION
C The tolerance to be used in determining the degrees of
C the numerators Num0(i,j) of the strictly proper part of
C the transfer function matrix G. If the user sets TOL > 0,
C then the given value of TOL is used as an absolute
C tolerance; the leading coefficients with absolute value
C less than TOL are considered neglijible. If the user sets
C TOL <= 0, then an implicitly computed, default tolerance,
C defined by TOLDEF = IGN(i,j)*EPS*NORM( Num(i,j) ) is used
C instead, where EPS is the machine precision (see LAPACK
C Library routine DLAMCH), and NORM denotes the infinity
C norm (the maximum coefficient in absolute value).
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value;
C = 1: if the transfer function matrix is not proper;
C = 2: if a denominator polynomial is null.
C
C METHOD
C
C The (i,j) entry of the real matrix D is zero, if the degree of
C Num(i,j), IGN(i,j), is less than the degree of Den(i,j), IGD(i,j),
C and it is given by the ratio of the leading coefficients of
C Num(i,j) and Den(i,j), if IGN(i,j) is equal to IGD(i,j),
C for i = 1 : P, and for j = 1 : M.
C
C FURTHER COMMENTS
C
C For maximum efficiency of index calculations, GN and GD are
C implemented as one-dimensional arrays.
C
C CONTRIBUTORS
C
C V. Sima, Research Institute for Informatics, Bucharest, May 2002.
C Based on the BIMASC Library routine TMPRP by A. Varga.
C
C REVISIONS
C
C V. Sima, Research Institute for Informatics, Bucharest, Feb. 2004.
C
C KEYWORDS
C
C State-space representation, transfer function.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C .. Scalar Arguments ..
CHARACTER ORDER
DOUBLE PRECISION TOL
INTEGER INFO, LDD, LDIGD, LDIGN, M, MD, P
C .. Array Arguments ..
DOUBLE PRECISION D(LDD,*), GD(*), GN(*)
INTEGER IGD(LDIGD,*), IGN(LDIGN,*)
C .. Local Scalars ..
LOGICAL ASCEND
INTEGER I, II, J, K, KK, KM, ND, NN
DOUBLE PRECISION DIJ, EPS, TOLDEF
C .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH, IDAMAX, LSAME
C .. External Subroutines ..
EXTERNAL DAXPY, XERBLA
C .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN
C ..
C .. Executable Statements ..
C
C Test the input scalar parameters.
C
INFO = 0
ASCEND = LSAME( ORDER, 'I' )
IF( .NOT.ASCEND .AND. .NOT.LSAME( ORDER, 'D' ) ) THEN
INFO = -1
ELSE IF( P.LT.0 ) THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( MD.LT.1 ) THEN
INFO = -4
ELSE IF( LDIGN.LT.MAX( 1, P ) ) THEN
INFO = -6
ELSE IF( LDIGD.LT.MAX( 1, P ) ) THEN
INFO = -8
ELSE IF( LDD.LT.MAX( 1, P ) ) THEN
INFO = -12
END IF
C
IF ( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'TB04BV', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( MIN( P, M ).EQ.0 )
$ RETURN
C
C Prepare the computation of the default tolerance.
C
TOLDEF = TOL
IF( TOLDEF.LE.ZERO )
$ EPS = DLAMCH( 'Epsilon' )
C
K = 1
C
IF ( ASCEND ) THEN
C
C Polynomial coefficients are stored in increasing order.
C
DO 40 J = 1, M
C
DO 30 I = 1, P
NN = IGN(I,J)
ND = IGD(I,J)
IF ( NN.GT.ND ) THEN
C
C Error return: the transfer function matrix is
C not proper.
C
INFO = 1
RETURN
ELSE IF ( NN.LT.ND .OR. ( ND.EQ.0 .AND. GN(K).EQ.ZERO ) )
$ THEN
D(I,J) = ZERO
ELSE
C
C Here NN = ND.
C
KK = K + NN
C
IF ( GD(KK).EQ.ZERO ) THEN
C
C Error return: the denominator is null.
C
INFO = 2
RETURN
ENDIF
C
DIJ = GN(KK) / GD(KK)
D(I,J) = DIJ
GN(KK) = ZERO
IF ( NN.GT.0 ) THEN
CALL DAXPY( NN, -DIJ, GD(K), 1, GN(K), 1 )
IF ( TOL.LE.ZERO )
$ TOLDEF = DBLE( NN )*EPS*
$ ABS( GN(IDAMAX( NN, GN(K), 1 ) ) )
KM = NN
DO 10 II = 1, KM
KK = KK - 1
NN = NN - 1
IF ( ABS( GN(KK) ).GT.TOLDEF )
$ GO TO 20
10 CONTINUE
C
20 CONTINUE
C
IGN(I,J) = NN
ENDIF
ENDIF
K = K + MD
30 CONTINUE
C
40 CONTINUE
C
ELSE
C
C Polynomial coefficients are stored in decreasing order.
C
DO 90 J = 1, M
C
DO 80 I = 1, P
NN = IGN(I,J)
ND = IGD(I,J)
IF ( NN.GT.ND ) THEN
C
C Error return: the transfer function matrix is
C not proper.
C
INFO = 1
RETURN
ELSE IF ( NN.LT.ND .OR. ( ND.EQ.0 .AND. GN(K).EQ.ZERO ) )
$ THEN
D(I,J) = ZERO
ELSE
C
C Here NN = ND.
C
KK = K
C
IF ( GD(KK).EQ.ZERO ) THEN
C
C Error return: the denominator is null.
C
INFO = 2
RETURN
ENDIF
C
DIJ = GN(KK) / GD(KK)
D(I,J) = DIJ
GN(KK) = ZERO
IF ( NN.GT.0 ) THEN
CALL DAXPY( NN, -DIJ, GD(K+1), 1, GN(K+1), 1 )
IF ( TOL.LE.ZERO )
$ TOLDEF = DBLE( NN )*EPS*
$ ABS( GN(IDAMAX( NN, GN(K+1), 1 ) ) )
KM = NN
DO 50 II = 1, KM
KK = KK + 1
NN = NN - 1
IF ( ABS( GN(KK) ).GT.TOLDEF )
$ GO TO 60
50 CONTINUE
C
60 CONTINUE
C
IGN(I,J) = NN
DO 70 II = 0, NN
GN(K+II) = GN(KK+II)
70 CONTINUE
C
ENDIF
ENDIF
K = K + MD
80 CONTINUE
C
90 CONTINUE
C
ENDIF
C
RETURN
C *** Last line of TB04BV ***
END
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