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.TH CLAQHB l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
CLAQHB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
.SH SYNOPSIS
.TP 19
SUBROUTINE CLAQHB(
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
REAL
AMAX, SCOND
.TP 19
.ti +4
REAL
S( * )
.TP 19
.ti +4
COMPLEX
AB( LDAB, * )
.SH PURPOSE
CLAQHB 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.
= 'U': Upper triangular
.br
= 'L': 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 = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
.TP 8
AB (input/output) COMPLEX 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.
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
.TP 8
S (output) REAL array, dimension (N)
The scale factors for A.
.TP 8
SCOND (input) REAL
Ratio of the smallest S(i) to the largest S(i).
.TP 8
AMAX (input) REAL
Absolute value of largest matrix entry.
.TP 8
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
.br
= 'Y': Equilibration was done, i.e., A has been replaced by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.
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