MC01PY

Coefficients of a real polynomial, stored in decreasing order, given its zeros

Purpose

  To compute the coefficients of a real polynomial P(x) from its
  zeros. The coefficients are stored in decreasing order of the
  powers of x.

      SUBROUTINE MC01PY( K, REZ, IMZ, P, DWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, K
C     .. Array Arguments ..
      DOUBLE PRECISION  DWORK(*), IMZ(*), P(*), REZ(*)

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 decreasing
          powers of x.

  DWORK   DOUBLE PRECISION array, dimension (K)
          If K = 0, this array is not referenced.

  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.

  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.

  None.

  None

Program Text

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