claqhb(3)

NAME

CLAQHB - equilibrate a symmetric band matrix A using the

scaling factors in the vector S

SYNOPSIS

SUBROUTINE  CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX,
EQUED )
    CHARACTER      EQUED, UPLO
    INTEGER        KD, LDAB, N
    REAL           AMAX, SCOND
    REAL           S( * )
    COMPLEX        AB( LDAB, * )

PURPOSE

CLAQHB 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 triangu

lar
= '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 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

scaling should be done based on the absolute size of the largest

matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is

done.

LAPACK version 3.0 15 June 2000

CLAQHB(3)