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.

**FURTHER** **DETAILS**

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)