SYNOPSIS

SUBROUTINE ZLAQHB(

UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

    

CHARACTER EQUED, UPLO

    

INTEGER KD, LDAB, N

    

DOUBLE PRECISION AMAX, SCOND

    

DOUBLE PRECISION S( * )

    

COMPLEX*16 AB( LDAB, * )

PURPOSE

ZLAQHB 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) 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 = '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) DOUBLE PRECISION array, dimension (N)

The scale factors for A.

SCOND (input) DOUBLE PRECISION

Ratio of the smallest S(i) to the largest S(i).

AMAX (input) DOUBLE PRECISION

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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done.