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dgebal (3)
  • >> dgebal (3) ( Solaris man: Библиотечные вызовы )
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    NAME
         dgebal - balance a general real matrix A
    
    SYNOPSIS
         SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
    
         CHARACTER JOB
    
         INTEGER IHI, ILO, INFO, LDA, N
    
         DOUBLE PRECISION A( LDA, * ), SCALE( * )
    
    
    
         #include <sunperf.h>
    
         void dgebal(char job, int n, double *da, int lda, int  *ilo,
                   int *ihi, double *dscale, int *info) ;
    
    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 ele-
         ments on the diagonal; and second, applying a diagonal simi-
         larity 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 eigenvec-
         tors.
    
    
    ARGUMENTS
         JOB       (input) 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         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         A         (input/output) DOUBLE PRECISION  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
                   (input) INTEGER The leading dimension of the array
                   A.  LDA >= max(1,N).
    
         ILO       (output) INTEGER
                   IHI     (output) 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     (output) DOUBLE PRECISION 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      (output) INTEGER
                   = 0:  successful exit.
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    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  eigen-
         values  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.
    
    
    
    


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