Purpose
To compute the coefficients of a real polynomial P(x) from its zeros.Specification
SUBROUTINE MC01PD( K, REZ, IMZ, P, DWORK, INFO )
C .. Scalar Arguments ..
INTEGER INFO, K
C .. Array Arguments ..
DOUBLE PRECISION DWORK(*), IMZ(*), P(*), REZ(*)
Arguments
Input/Output Parameters
K (input) INTEGER
The number of zeros (and hence the degree) of P(x).
K >= 0.
REZ (input) DOUBLE PRECISION array, dimension (K)
IMZ (input) DOUBLE PRECISION array, dimension (K)
The real and imaginary parts of the i-th zero of P(x)
must be stored in REZ(i) and IMZ(i), respectively, where
i = 1, 2, ..., K. The zeros may be supplied in any order,
except that complex conjugate zeros must appear
consecutively.
P (output) DOUBLE PRECISION array, dimension (K+1)
This array contains the coefficients of P(x) in increasing
powers of x. If K = 0, then P(1) is set to one.
Workspace
DWORK DOUBLE PRECISION array, dimension (K+1)
If K = 0, this array is not referenced.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value;
> 0: if INFO = i, (REZ(i),IMZ(i)) is a complex zero but
(REZ(i-1),IMZ(i-1)) is not its conjugate.
Method
The routine computes the coefficients of the real K-th degree
polynomial P(x) as
P(x) = (x - r(1)) * (x - r(2)) * ... * (x - r(K))
where r(i) = (REZ(i),IMZ(i)).
Note that REZ(i) = REZ(j) and IMZ(i) = -IMZ(j) if r(i) and r(j)
form a complex conjugate pair (where i <> j), and that IMZ(i) = 0
if r(i) is real.
Numerical Aspects
None.Further Comments
NoneExample
Program Text
* MC01PD EXAMPLE PROGRAM TEXT
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER KMAX
PARAMETER ( KMAX = 10 )
* .. Local Scalars ..
INTEGER I, INFO, K
* .. Local Arrays ..
DOUBLE PRECISION DWORK(KMAX+1), IMZ(KMAX), P(KMAX+1), REZ(KMAX)
* .. External Subroutines ..
EXTERNAL MC01PD
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) K
IF ( K.LT.0 .OR. K.GT.KMAX ) THEN
WRITE ( NOUT, FMT = 99995 ) K
ELSE
READ ( NIN, FMT = * ) ( REZ(I), IMZ(I), I = 1,K )
* Compute the coefficients of P(x) from the given zeros.
CALL MC01PD( K, REZ, IMZ, P, DWORK, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
WRITE ( NOUT, FMT = 99996 ) ( I, P(I+1), I = 0,K )
END IF
END IF
STOP
*
99999 FORMAT (' MC01PD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from MC01PD = ',I2)
99997 FORMAT (' The coefficients of the polynomial P(x) are ',//' powe',
$ 'r of x coefficient ')
99996 FORMAT (2X,I5,9X,F9.4)
99995 FORMAT (' K is out of range.',/' K = ',I5)
END
Program Data
MC01PD EXAMPLE PROGRAM DATA 5 0.0 1.0 0.0 -1.0 2.0 0.0 1.0 3.0 1.0 -3.0Program Results
MC01PD EXAMPLE PROGRAM RESULTS
The coefficients of the polynomial P(x) are
power of x coefficient
0 -20.0000
1 14.0000
2 -24.0000
3 15.0000
4 -4.0000
5 1.0000