## MC01PD

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

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

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

      None

Example

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  -3.0

Program 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

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