# ?laqhb

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

## Syntax

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

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

## Include Files

• Fortran: mkl.fi
• C: mkl.h

## Description

The routine equilibrates a Hermetian 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 band 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

COMPLEX for claqhb

DOUBLE COMPLEX for zlaqhb

Array, DIMENSION (ldab,n). On entry, the upper or lower triangle of the 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)`.

ldab

INTEGER. The leading dimension of the array ab.

`ldab ≥ kd+1`.

scond

REAL for claqsb

DOUBLE PRECISION for zlaqsb

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

amax

REAL for claqsb

DOUBLE PRECISION for 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 `A = UH*U` or `A = L*LH` of the band matrix A, in the same storage format as A.

s

REAL for claqsb

DOUBLE PRECISION for zlaqsb

Array, DIMENSION (n). The scale factors for 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If equed = 'Y': Equilibration was done, that is, A has been replaced by `diag(s)*A*diag(s)`.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.

The values 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.