NAME

       zheequb.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
           ZHEEQUB

Function/Subroutine Documentation

   subroutine zheequb (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA,
       double precision, dimension( * )S, double precisionSCOND, double precisionAMAX,
       complex*16, dimension( * )WORK, integerINFO)
       ZHEEQUB

       Purpose:

            ZHEEQUB computes row and column scalings intended to equilibrate a
            Hermitian matrix A and reduce its condition number
            (with respect to the two-norm).  S contains the scale factors,
            S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
            elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
            choice of S puts the condition number of B within a factor N of the
            smallest possible condition number over all possible diagonal
            scalings.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangles of A and B are stored;
                     = 'L':  Lower triangles of A and B are stored.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     The N-by-N Hermitian matrix whose scaling
                     factors are to be computed.  Only the diagonal elements of A
                     are referenced.

           LDA

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

           S

                     S is DOUBLE PRECISION array, dimension (N)
                     If INFO = 0, S contains the scale factors for A.

           SCOND

                     SCOND is DOUBLE PRECISION
                     If INFO = 0, S contains the ratio of the smallest S(i) to
                     the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
                     large nor too small, it is not worth scaling by S.

           AMAX

                     AMAX is DOUBLE PRECISION
                     Absolute value of largest matrix element.  If AMAX is very
                     close to overflow or very close to underflow, the matrix
                     should be scaled.

           WORK

                     WORK is COMPLEX*16 array, dimension (3*N)

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           April 2012

       Definition at line 127 of file zheequb.f.

Author

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