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SUBROUTINE MC01QD( DA, DB, A, B, RQ, IWARN, 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 compute, for two given real polynomials A(x) and B(x), the
C quotient polynomial Q(x) and the remainder polynomial R(x) of
C A(x) divided by B(x).
C
C The polynomials Q(x) and R(x) satisfy the relationship
C
C A(x) = B(x) * Q(x) + R(x),
C
C where the degree of R(x) is less than the degree of B(x).
C
C ARGUMENTS
C
C Input/Output Parameters
C
C DA (input) INTEGER
C The degree of the numerator polynomial A(x). DA >= -1.
C
C DB (input/output) INTEGER
C On entry, the degree of the denominator polynomial B(x).
C DB >= 0.
C On exit, if B(DB+1) = 0.0 on entry, then DB contains the
C index of the highest power of x for which B(DB+1) <> 0.0.
C
C A (input) DOUBLE PRECISION array, dimension (DA+1)
C This array must contain the coefficients of the
C numerator polynomial A(x) in increasing powers of x
C unless DA = -1 on entry, in which case A(x) is taken
C to be the zero polynomial.
C
C B (input) DOUBLE PRECISION array, dimension (DB+1)
C This array must contain the coefficients of the
C denominator polynomial B(x) in increasing powers of x.
C
C RQ (output) DOUBLE PRECISION array, dimension (DA+1)
C If DA < DB on exit, then this array contains the
C coefficients of the remainder polynomial R(x) in
C increasing powers of x; Q(x) is the zero polynomial.
C Otherwise, the leading DB elements of this array contain
C the coefficients of R(x) in increasing powers of x, and
C the next (DA-DB+1) elements contain the coefficients of
C Q(x) in increasing powers of x.
C
C Warning Indicator
C
C IWARN INTEGER
C = 0: no warning;
C = k: if the degree of the denominator polynomial B(x) has
C been reduced to (DB - k) because B(DB+1-j) = 0.0 on
C entry for j = 0, 1, ..., k-1 and B(DB+1-k) <> 0.0.
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 on entry, DB >= 0 and B(i) = 0.0, where
C i = 1, 2, ..., DB+1.
C
C METHOD
C
C Given real polynomials
C DA
C A(x) = a(1) + a(2) * x + ... + a(DA+1) * x
C
C and
C DB
C B(x) = b(1) + b(2) * x + ... + b(DB+1) * x
C
C where b(DB+1) is non-zero, the routine computes the coeffcients of
C the quotient polynomial
C DA-DB
C Q(x) = q(1) + q(2) * x + ... + q(DA-DB+1) * x
C
C and the remainder polynomial
C DB-1
C R(x) = r(1) + r(2) * x + ... + r(DB) * x
C
C such that A(x) = B(x) * Q(x) + R(x).
C
C The algorithm used is synthetic division of polynomials (see [1]),
C which involves the following steps:
C
C (a) compute q(k+1) = a(DB+k+1) / b(DB+1)
C
C and
C
C (b) set a(j) = a(j) - q(k+1) * b(j-k) for j = k+1, ..., DB+k.
C
C Steps (a) and (b) are performed for k = DA-DB, DA-DB-1, ..., 0 and
C the algorithm terminates with r(i) = a(i) for i = 1, 2, ..., DB.
C
C REFERENCES
C
C [1] Knuth, D.E.
C The Art of Computer Programming, (Vol. 2, Seminumerical
C Algorithms).
C Addison-Wesley, Reading, Massachusetts (2nd Edition), 1981.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Mar. 1997.
C Supersedes Release 2.0 routine MC01ED by A.J. Geurts.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Elementary polynomial operations, polynomial operations.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C .. Scalar Arguments ..
INTEGER DA, DB, INFO, IWARN
C .. Array Arguments ..
DOUBLE PRECISION A(*), B(*), RQ(*)
C .. Local Scalars ..
INTEGER N
DOUBLE PRECISION Q
C .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, XERBLA
C .. Executable Statements ..
C
C Test the input scalar arguments.
C
IWARN = 0
INFO = 0
IF( DA.LT.-1 ) THEN
INFO = -1
ELSE IF( DB.LT.0 ) THEN
INFO = -2
END IF
C
IF ( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'MC01QD', -INFO )
RETURN
END IF
C
C WHILE ( DB >= 0 and B(DB+1) = 0 ) DO
20 IF ( DB.GE.0 ) THEN
IF ( B(DB+1).EQ.ZERO ) THEN
DB = DB - 1
IWARN = IWARN + 1
GO TO 20
END IF
END IF
C END WHILE 20
IF ( DB.EQ.-1 ) THEN
INFO = 1
RETURN
END IF
C
C B(x) is non-zero.
C
IF ( DA.GE.0 ) THEN
N = DA
CALL DCOPY( N+1, A, 1, RQ, 1 )
C WHILE ( N >= DB ) DO
40 IF ( N.GE.DB ) THEN
IF ( RQ(N+1).NE.ZERO ) THEN
Q = RQ(N+1)/B(DB+1)
CALL DAXPY( DB, -Q, B, 1, RQ(N-DB+1), 1 )
RQ(N+1) = Q
END IF
N = N - 1
GO TO 40
END IF
C END WHILE 40
END IF
C
RETURN
C *** Last line of MC01QD ***
END
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