## MB03QV

### Compute eigenvalues of an upper quasi-triangular matrix pencil

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

Purpose

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

Specification

          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,*)

Arguments

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.

Error Indicator

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

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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