MB03QV

Compute eigenvalues of an upper quasi-triangular matrix pencil

Purpose

  To compute the eigenvalues of an upper quasi-triangular matrix
  pencil.

      SUBROUTINE MB03QV( N, S, LDS, T, LDT, ALPHAR, ALPHAI, BETA, INFO )
C     .. Scalar Arguments ..
      INTEGER          INFO, LDS, LDT, N
C     .. Array Arguments ..
      DOUBLE PRECISION ALPHAI(*), ALPHAR(*), BETA(*), S(LDS,*), T(LDT,*)

Input/Output Parameters

  N       (input) INTEGER
          The order of the matrices S and T.  N >= 0.

  S       (input) DOUBLE PRECISION array, dimension(LDS,N)
          The upper quasi-triangular matrix S.

  LDS     INTEGER
          The leading dimension of the array S.  LDS >= max(1,N).

  T       (input) DOUBLE PRECISION array, dimension(LDT,N)
          The upper triangular matrix T.

  LDT     INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
  BETA    (output) DOUBLE PRECISION array, dimension (N)
          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N,
          are the generalized eigenvalues.
          ALPHAR(j) + ALPHAI(j)*i, and  BETA(j),j=1,...,N, are the
          diagonals of the complex Schur form (S,T) that would
          result if the 2-by-2 diagonal blocks of the real Schur
          form of (A,B) were further reduced to triangular form
          using 2-by-2 complex unitary transformations.
          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
          positive, then the j-th and (j+1)-st eigenvalues are a
          complex conjugate pair, with ALPHAI(j+1) negative.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

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Program Text

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