SB04NX

Solving a system of equations in Hessenberg form with two consecutive offdiagonals and two right-hand sides

Purpose

  To solve a system of equations in Hessenberg form with two
  consecutive offdiagonals and two right-hand sides.

      SUBROUTINE SB04NX( RC, UL, M, A, LDA, LAMBD1, LAMBD2, LAMBD3,
     $                   LAMBD4, D, TOL, IWORK, DWORK, LDDWOR, INFO )
C     .. Scalar Arguments ..
      CHARACTER         RC, UL
      INTEGER           INFO, LDA, LDDWOR, M
      DOUBLE PRECISION  LAMBD1, LAMBD2, LAMBD3, LAMBD4, TOL
C     .. Array Arguments ..
      INTEGER           IWORK(*)
      DOUBLE PRECISION  A(LDA,*), D(*), DWORK(LDDWOR,*)

Mode Parameters

  RC      CHARACTER*1
          Indicates processing by columns or rows, as follows:
          = 'R':  Row transformations are applied;
          = 'C':  Column transformations are applied.

  UL      CHARACTER*1
          Indicates whether AB is upper or lower Hessenberg matrix,
          as follows:
          = 'U':  AB is upper Hessenberg;
          = 'L':  AB is lower Hessenberg.

  M       (input) INTEGER
          The order of the matrix A.  M >= 0.

  A       (input) DOUBLE PRECISION array, dimension (LDA,M)
          The leading M-by-M part of this array must contain a
          matrix A in Hessenberg form.

  LDA     INTEGER
          The leading dimension of array A.  LDA >= MAX(1,M).

  LAMBD1, (input) DOUBLE PRECISION
  LAMBD2, These variables must contain the 2-by-2 block to be added
  LAMBD3, to the diagonal blocks of A.
  LAMBD4

  D       (input/output) DOUBLE PRECISION array, dimension (2*M)
          On entry, this array must contain the two right-hand
          side vectors of the Hessenberg system, stored row-wise.
          On exit, if INFO = 0, this array contains the two solution
          vectors of the Hessenberg system, stored row-wise.

  TOL     DOUBLE PRECISION
          The tolerance to be used to test for near singularity of
          the triangular factor R of the Hessenberg matrix. A matrix
          whose estimated condition number is less than 1/TOL is
          considered to be nonsingular.

  IWORK   INTEGER array, dimension (2*M)

  DWORK   DOUBLE PRECISION array, dimension (LDDWOR,2*M+3)
          The leading 2*M-by-2*M part of this array is used for
          computing the triangular factor of the QR decomposition
          of the Hessenberg matrix. The remaining 6*M elements are
          used as workspace for the computation of the reciprocal
          condition estimate.

  LDDWOR  INTEGER
          The leading dimension of array DWORK.
          LDDWOR >= MAX(1,2*M).

  INFO    INTEGER
          = 0:  successful exit;
          = 1:  if the Hessenberg matrix is (numerically) singular.
                That is, its estimated reciprocal condition number
                is less than or equal to TOL.

  None.

  None

Program Text

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