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SUBROUTINE MC01PY( K, REZ, IMZ, P, DWORK, 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 the coefficients of a real polynomial P(x) from its
C zeros. The coefficients are stored in decreasing order of the
C powers of x.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C K (input) INTEGER
C The number of zeros (and hence the degree) of P(x).
C K >= 0.
C
C REZ (input) DOUBLE PRECISION array, dimension (K)
C IMZ (input) DOUBLE PRECISION array, dimension (K)
C The real and imaginary parts of the i-th zero of P(x)
C must be stored in REZ(i) and IMZ(i), respectively, where
C i = 1, 2, ..., K. The zeros may be supplied in any order,
C except that complex conjugate zeros must appear
C consecutively.
C
C P (output) DOUBLE PRECISION array, dimension (K+1)
C This array contains the coefficients of P(x) in decreasing
C powers of x.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (K)
C If K = 0, this array is not referenced.
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 > 0: if INFO = i, (REZ(i),IMZ(i)) is a complex zero but
C (REZ(i-1),IMZ(i-1)) is not its conjugate.
C
C METHOD
C
C The routine computes the coefficients of the real K-th degree
C polynomial P(x) as
C
C P(x) = (x - r(1)) * (x - r(2)) * ... * (x - r(K))
C
C where r(i) = (REZ(i),IMZ(i)).
C
C Note that REZ(i) = REZ(j) and IMZ(i) = -IMZ(j) if r(i) and r(j)
C form a complex conjugate pair (where i <> j), and that IMZ(i) = 0
C if r(i) is real.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C V. Sima, Research Institute for Informatics, Bucharest, May 2002.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Elementary polynomial operations, polynomial operations.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
INTEGER INFO, K
C .. Array Arguments ..
DOUBLE PRECISION DWORK(*), IMZ(*), P(*), REZ(*)
C .. Local Scalars ..
INTEGER I
DOUBLE PRECISION U, V
C .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, XERBLA
C .. Executable Statements ..
C
C Test the input scalar arguments.
C
IF( K.LT.0 ) THEN
INFO = -1
C
C Error return.
C
CALL XERBLA( 'MC01PY', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
INFO = 0
P(1) = ONE
IF ( K.EQ.0 )
$ RETURN
C
I = 1
C WHILE ( I <= K ) DO
20 IF ( I.LE.K ) THEN
U = REZ(I)
V = IMZ(I)
DWORK(I) = ZERO
C
IF ( V.EQ.ZERO ) THEN
CALL DAXPY( I, -U, P, 1, DWORK, 1 )
C
ELSE
IF ( I.EQ.K ) THEN
INFO = K
RETURN
ELSE IF ( ( U.NE.REZ(I+1) ) .OR. ( V.NE.-IMZ(I+1) ) ) THEN
INFO = I + 1
RETURN
END IF
C
DWORK(I+1) = ZERO
CALL DAXPY( I, -(U + U), P, 1, DWORK, 1 )
CALL DAXPY( I, U**2+V**2, P, 1, DWORK(2), 1 )
I = I + 1
END IF
C
CALL DCOPY( I, DWORK, 1, P(2), 1 )
I = I + 1
GO TO 20
END IF
C END WHILE 20
C
RETURN
C *** Last line of MC01PY ***
END
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