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NAME SLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S SYNOPSIS SUBROUTINE SLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) CHARACTER EQUED, UPLO INTEGER KD, LDAB, N REAL AMAX, SCOND REAL AB( LDAB, * ), S( * ) PURPOSE SLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S. ARGUMENTS UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0. AB (input/output) REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the sym- metric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U'*U or A = L*L' of the band matrix A, in the same storage format as A. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. S (output) REAL array, dimension (N) The scale factors for A. SCOND (input) REAL Ratio of the smallest S(i) to the largest S(i). AMAX (input) REAL Absolute value of largest matrix entry. EQUED (output) CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). PARAMETERS THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done. LARGE and SMALL are threshold values used to decide if scal- ing should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done.