# dlaqsb (3) - Linux Manuals

dlaqsb.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dlaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

## Function/Subroutine Documentation

### subroutine dlaqsb (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

DLAQSB equilibrates a symmetric band matrix A using the scaling
factors in the vector S.

Parameters:

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U':  Upper triangular
= 'L':  Lower triangular

N

N is INTEGER
The order of the matrix A.  N >= 0.

KD

KD is 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

AB is DOUBLE PRECISION 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**T*U or A = L*L**T of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

S

S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.

EQUED

EQUED is 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= 'Y':  Equilibration was done, i.e., A has been replaced by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).

Internal 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley