MB05OY

Restoring a matrix after balancing transformations (permutations and scalings)

Purpose

  To restore a matrix after it has been transformed by applying
  balancing transformations (permutations and scalings), as
  determined by LAPACK Library routine DGEBAL.

      SUBROUTINE MB05OY( JOB, N, LOW, IGH, A, LDA, SCALE, INFO )
C     .. Scalar Arguments ..
      CHARACTER         JOB
      INTEGER           IGH, INFO, LDA, LOW, N
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA,*), SCALE(*)

Mode Parameters

  JOB     CHARACTER*1
          Specifies the type of backward transformation required,
          as follows:
          = 'N', do nothing, return immediately;
          = 'P', do backward transformation for permutation only;
          = 'S', do backward transformation for scaling only;
          = 'B', do backward transformations for both permutation
                 and scaling.
          JOB must be the same as the argument JOB supplied
          to DGEBAL.

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

  LOW     (input) INTEGER
  IGH     (input) INTEGER
          The integers LOW and IGH determined by DGEBAL.
          1 <= LOW <= IGH <= N, if N > 0; LOW=1 and IGH=0, if N=0.

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the leading N-by-N part of this array must
          contain the matrix to be back-transformed.
          On exit, the leading N-by-N part of this array contains
          the transformed matrix.

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

  SCALE   (input) DOUBLE PRECISION array, dimension (N)
          Details of the permutation and scaling factors, as
          returned by DGEBAL.

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

  Let P be a permutation matrix, and D a diagonal matrix of scaling
  factors, both of order N. The routine computes
                  -1
     A <-- P D A D  P'.

  where the permutation and scaling factors are encoded in the
  array SCALE.

  None.

                            2
  The algorithm requires O(N ) operations.

  None

Program Text

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