dgebal.f(3)

NAME
dgebal.f -

SYNOPSIS

  Functions/Subroutines

subroutine dgebal (JOB, N, A, LDA, ILO, IHI, SCALE, INFO)
DGEBAL

Function/Subroutine Documentation

  subroutine dgebal (characterJOB, integerN, double precision, dimension( lda, * )A, integerLDA, integerILO, integerIHI, double precision, dimension( * )SCALE, integerINFO)

DGEBAL

Purpose:

     DGEBAL balances a general real matrix A.  This involves, first,
     permuting A by a similarity transformation to isolate eigenvalues
     in the first 1 to ILO-1 and last IHI+1 to N elements on the
     diagonal; and second, applying a diagonal similarity transformation
     to rows and columns ILO to IHI to make the rows and columns as
     close in norm as possible.  Both steps are optional.

     Balancing may reduce the 1-norm of the matrix, and improve the
     accuracy of the computed eigenvalues and/or eigenvectors.

Parameters:
    JOB

              JOB is CHARACTER*1
              Specifies the operations to be performed on A:
              = 'N':  none:  simply set ILO = 1, IHI = N, SCALE(I) = 1.0
                      for i = 1,...,N;
              = 'P':  permute only;
              = 'S':  scale only;
              = 'B':  both permute and scale.

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    A

              A is DOUBLE array, dimension (LDA,N)
              On entry, the input matrix A.
              On exit,  A is overwritten by the balanced matrix.
              If JOB = 'N', A is not referenced.
              See Further Details.

    LDA

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

    ILO

              ILO is INTEGER

    IHI

              IHI is INTEGER
              ILO and IHI are set to integers such that on exit
              A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
              If JOB = 'N' or 'S', ILO = 1 and IHI = N.

    SCALE

              SCALE is DOUBLE array, dimension (N)
              Details of the permutations and scaling factors applied to
              A.  If P(j) is the index of the row and column interchanged
              with row and column j and D(j) is the scaling factor
              applied to row and column j, then
              SCALE(j) = P(j)    for j = 1,...,ILO-1
                       = D(j)    for j = ILO,...,IHI
                       = P(j)    for j = IHI+1,...,N.
              The order in which the interchanges are made is N to IHI+1,
              then 1 to ILO-1.

    INFO

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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2013

Further Details:

      The permutations consist of row and column interchanges which put
      the matrix in the form

                 ( T1   X   Y  )
         P A P = (  0   B   Z  )
                 (  0   0   T2 )

      where T1 and T2 are upper triangular matrices whose eigenvalues lie
      along the diagonal.  The column indices ILO and IHI mark the starting
      and ending columns of the submatrix B. Balancing consists of applying
      a diagonal similarity transformation inv(D) * B * D to make the
      1-norms of each row of B and its corresponding column nearly equal.
      The output matrix is

         ( T1     X*D          Y    )
         (  0  inv(D)*B*D  inv(D)*Z ).
         (  0      0           T2   )

      Information about the permutations P and the diagonal matrix D is
      returned in the vector SCALE.

      This subroutine is based on the EISPACK routine BALANC.

      Modified by Tzu-Yi Chen, Computer Science Division, University of
        California at Berkeley, USA

Definition at line 161 of file dgebal.f.

Author

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