Purpose
To compute the coefficients of a complex polynomial P(x) from its zeros.Specification
SUBROUTINE MC01OD( K, REZ, IMZ, REP, IMP, DWORK, INFO ) C .. Scalar Arguments .. INTEGER INFO, K C .. Array Arguments .. DOUBLE PRECISION DWORK(*), IMP(*), IMZ(*), REP(*), 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. REP (output) DOUBLE PRECISION array, dimension (K+1) IMP (output) DOUBLE PRECISION array, dimension (K+1) These arrays contain the real and imaginary parts, respectively, of the coefficients of P(x) in increasing powers of x. If K = 0, then REP(1) is set to one and IMP(1) is set to zero.Workspace
DWORK DOUBLE PRECISION array, dimension (2*K+2) 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.Method
The routine computes the coefficients of the complex 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)), using real arithmetic.Numerical Aspects
None.Further Comments
NoneExample
Program Text
* MC01OD EXAMPLE PROGRAM TEXT * Copyright (c) 2002-2017 NICONET e.V. * * .. 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(2*KMAX+2), IMP(KMAX+1), IMZ(KMAX), $ REP(KMAX+1), REZ(KMAX) * .. External Subroutines .. EXTERNAL MC01OD * .. 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 MC01OD( K, REZ, IMZ, REP, IMP, DWORK, INFO ) * IF ( INFO.NE.0 ) THEN WRITE ( NOUT, FMT = 99998 ) INFO ELSE WRITE ( NOUT, FMT = 99997 ) WRITE ( NOUT, FMT = 99996 ) $ ( I, REP(I+1), IMP(I+1), I = 0,K ) END IF END IF STOP * 99999 FORMAT (' MC01OD EXAMPLE PROGRAM RESULTS',/1X) 99998 FORMAT (' INFO on exit from MC01OD = ',I2) 99997 FORMAT (' The coefficients of the polynomial P(x) are ',//' powe', $ 'r of x real part imag part ') 99996 FORMAT (2X,I5,8X,F9.4,5X,F9.4) 99995 FORMAT (/' K is out of range.',/' K = ',I5) ENDProgram Data
MC01OD EXAMPLE PROGRAM DATA 5 1.1 0.9 0.6 -0.7 -2.0 0.3 -0.8 2.5 -0.3 -0.4Program Results
MC01OD EXAMPLE PROGRAM RESULTS The coefficients of the polynomial P(x) are power of x real part imag part 0 2.7494 -2.1300 1 -1.7590 -5.4205 2 0.0290 2.8290 3 -1.6500 -1.7300 4 1.4000 -2.6000 5 1.0000 0.0000