SB01BX

Choosing the closest real (complex conjugate) eigenvalue(s) to a given real (complex) value

Purpose

  To choose a real eigenvalue or a pair of complex conjugate
  eigenvalues at "minimal" distance to a given real or complex
  value.

      SUBROUTINE SB01BX( REIG, N, XR, XI, WR, WI, S, P )
C     .. Scalar Arguments ..
      LOGICAL          REIG
      INTEGER          N
      DOUBLE PRECISION P, S, XI ,XR
C     .. Array Arguments ..
      DOUBLE PRECISION WI(*), WR(*)

Mode Parameters

  REIG    LOGICAL
          Specifies the type of eigenvalues as follows:
          = .TRUE.,  a real eigenvalue is to be selected;
          = .FALSE., a pair of complex eigenvalues is to be
                     selected.

  N       (input) INTEGER
          The number of eigenvalues contained in the arrays WR
          and WI.  N >= 1.

  XR,XI   (input) DOUBLE PRECISION
          If REIG = .TRUE., XR must contain the real value and XI
          is assumed zero and therefore not referenced.
          If REIG = .FALSE., XR must contain the real part and XI
          the imaginary part, respectively, of the complex value.

  WR,WI   (input/output) DOUBLE PRECISION array, dimension (N)
          On entry, if REIG = .TRUE., WR must contain the real
          eigenvalues from which an eigenvalue at minimal distance
          to XR is to be selected. In this case, WI is considered
          zero and therefore not referenced.
          On entry, if REIG = .FALSE., WR and WI must contain the
          real and imaginary parts, respectively, of the eigenvalues
          from which a pair of complex conjugate eigenvalues at
          minimal "distance" to XR + jXI is to be selected.
          The eigenvalues of each pair of complex conjugate
          eigenvalues must appear consecutively.
          On exit, the elements of these arrays are reordered such
          that the selected eigenvalue(s) is (are) found in the
          last element(s) of these arrays.

  S,P     (output) DOUBLE PRECISION
          If REIG = .TRUE., S (and also P) contains the value of
          the selected real eigenvalue.
          If REIG = .FALSE., S and P contain the sum and product,
          respectively, of the selected complex conjugate pair of
          eigenvalues.

  For efficiency reasons, |x| + |y| is used for a complex number
  x + jy, instead of its modulus.

Program Text

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