# ?laqsb

Scales a symmetric band matrix, using scaling factors computed by ?pbequ.

## Syntax

call slaqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )

call dlaqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )

call claqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )

call zlaqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )

• mkl.fi

## Description

The routine equilibrates a symmetric band matrix A using the scaling factors in the vector s.

## Input Parameters

uplo

CHARACTER*1.

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.

If uplo = 'U': upper triangular.

If uplo = 'L': lower triangular.

n

INTEGER. The order of the matrix A.

n 0.

kd

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

REAL for slaqsb

DOUBLE PRECISION for dlaqsb

COMPLEX for claqsb

DOUBLE COMPLEX for zlaqsb

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) ≤ ij;

if uplo = 'L', ab(1+i-j,j) = A(i,j) for ji ≤ min(n,j+kd).

ldab

INTEGER. The leading dimension of the array ab.

ldabkd+1.

s

REAL for slaqsb/claqsb

DOUBLE PRECISION for dlaqsb/zlaqsb

Array, DIMENSION (n). The scale factors for A.

scond

REAL for slaqsb/claqsb

DOUBLE PRECISION for dlaqsb/zlaqsb

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

amax

REAL for slaqsb/claqsb

DOUBLE PRECISION for dlaqsb/zlaqsb

Absolute value of largest matrix entry.

## Output Parameters

ab

On exit, if info = 0, the triangular factor U or L from the Cholesky factorization of the band matrix A that can be A = UT*U or A = L*LT for real flavors and A = UH*U or A = L*LH for complex flavors, in the same storage format as A.

equed

CHARACTER*1.

Specifies whether or not equilibration was done.

If equed = 'N': No equilibration.

If equed = 'Y': Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s).

## Application Notes

The routine uses internal parameters thresh, large, and small, which have the following meaning. thresh is a threshold value used to decide if scaling should be 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.

For more complete information about compiler optimizations, see our Optimization Notice.