Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  computes row and column scalings intended to equilibrate a symmetric matrix A
and reduce its condition number (with respect to the two-norm)

SYNOPSIS

SUBROUTINE SSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )

IMPLICIT        NONE

INTEGER         INFO, LDA, N

REAL            AMAX, SCOND

CHARACTER       UPLO

REAL            A( LDA, * ), S( * ), WORK( * )

PURPOSE

SSYEQUB computes row and column scalings intended to equilibrate a symmetric 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.

ARGUMENTS

UPLO    (input) CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**T;
= 'L':  Lower triangular, form is A = L*D*L**T.

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

A       (input) REAL array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling
factors are to be computed.  Only the diagonal elements of A
are referenced.

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

S       (output) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND   (output) REAL
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    (output) REAL
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.

WORK    (workspace) REAL array, dimension (3*N)

INFO    (output) 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.

FURTHERDETAILS

Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf

LAPACK routine (version 3.2.2)          April 2011                           SSYEQUB(3lapack)