.TH ZLAQHB 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME ZLAQHB - a symmetric band matrix A using the scaling factors in the vector S .SH SYNOPSIS .TP 19 SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) .TP 19 .ti +4 CHARACTER EQUED, UPLO .TP 19 .ti +4 INTEGER KD, LDAB, N .TP 19 .ti +4 DOUBLE PRECISION AMAX, SCOND .TP 19 .ti +4 DOUBLE PRECISION S( * ) .TP 19 .ti +4 COMPLEX*16 AB( LDAB, * ) .SH PURPOSE ZLAQHB equilibrates a symmetric band matrix A using the scaling factors in the vector S. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = \(aqU\(aq: Upper triangular .br = \(aqL\(aq: Lower triangular .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = \(aqU\(aq, or the number of sub-diagonals if UPLO = \(aqL\(aq. KD >= 0. .TP 8 AB (input/output) COMPLEX*16 array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric 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 = \(aqU\(aq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = \(aqL\(aq, 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\(aq*U or A = L*L\(aq of the band matrix A, in the same storage format as A. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. .TP 8 S (output) DOUBLE PRECISION array, dimension (N) The scale factors for A. .TP 8 SCOND (input) DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i). .TP 8 AMAX (input) DOUBLE PRECISION Absolute value of largest matrix entry. .TP 8 EQUED (output) CHARACTER*1 Specifies whether or not equilibration was done. = \(aqN\(aq: No equilibration. .br = \(aqY\(aq: Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). .SH 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 scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done.