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SUBROUTINE MC01WD( DP, P, U1, U2, Q, 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 a given real polynomial P(x) and a quadratic
C polynomial B(x), the quotient polynomial Q(x) and the linear
C remainder polynomial R(x) such that
C
C P(x) = B(x) * Q(x) + R(x),
C
C 2
C where B(x) = u1 + u2 * x + x , R(x) = q(1) + q(2) * (u2 + x)
C and u1, u2, q(1) and q(2) are real scalars.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C DP (input) INTEGER
C The degree of the polynomial P(x). DP >= 0.
C
C P (input) DOUBLE PRECISION array, dimension (DP+1)
C This array must contain the coefficients of P(x) in
C increasing powers of x.
C
C U1 (input) DOUBLE PRECISION
C The value of the constant term of the quadratic
C polynomial B(x).
C
C U2 (input) DOUBLE PRECISION
C The value of the coefficient of x of the quadratic
C polynomial B(x).
C
C Q (output) DOUBLE PRECISION array, dimension (DP+1)
C If DP >= 1 on entry, then elements Q(1) and Q(2) contain
C the coefficients q(1) and q(2), respectively, of the
C remainder polynomial R(x), and the next (DP-1) elements
C of this array contain the coefficients of the quotient
C polynomial Q(x) in increasing powers of x.
C If DP = 0 on entry, then element Q(1) contains the
C coefficient q(1) of the remainder polynomial R(x) = q(1);
C Q(x) is the zero polynomial.
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
C METHOD
C
C Given the real polynomials
C
C DP i 2
C P(x) = SUM p(i+1) * x and B(x) = u1 + u2 * x + x
C i=0
C
C the routine uses the recurrence relationships
C
C q(DP+1) = p(DP+1),
C
C q(DP) = p(DP) - u2 * q(DP+1) and
C
C q(i) = p(i) - u2 * q(i+1) - u1 * q(i+2) for i = DP-1, ..., 1
C
C to determine the coefficients of the quotient polynomial
C
C DP-2 i
C Q(x) = SUM q(i+3) * x
C i=0
C
C and the remainder polynomial
C
C R(x) = q(1) + q(2) * (u2 + x).
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 MC01KD by A.J. Geurts.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Elementary polynomial operations, polynomial operations,
C quadratic polynomial.
C
C ******************************************************************
C
C .. Scalar Arguments ..
INTEGER DP, INFO
DOUBLE PRECISION U1, U2
C .. Array Arguments ..
DOUBLE PRECISION P(*), Q(*)
C .. Local Scalars ..
INTEGER I, N
DOUBLE PRECISION A, B, C
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Executable Statements ..
C
C Test the input scalar arguments.
C
IF ( DP.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'MC01WD', -INFO )
RETURN
END IF
C
INFO = 0
N = DP + 1
Q(N) = P(N)
IF ( N.GT.1 ) THEN
B = Q(N)
Q(N-1) = P(N-1) - U2*B
IF ( N.GT.2 ) THEN
A = Q(N-1)
C
DO 20 I = N - 2, 1, -1
C = P(I) - U2*A - U1*B
Q(I) = C
B = A
A = C
20 CONTINUE
C
END IF
END IF
C
RETURN
C *** Last line of MC01WD ***
END
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