## MC01OD

### Coefficients of a complex polynomial, given its zeros

[Specification] [Arguments] [Method] [References] [Comments] [Example]

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

      None

Example

Program Text

    *     MC01OD 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(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)
          END

Program Data

     MC01OD EXAMPLE PROGRAM DATA
       5
       1.1   0.9
       0.6  -0.7
      -2.0   0.3
      -0.8   2.5
      -0.3  -0.4

Program 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

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