# zlaqhb.f man page

zlaqhb.f —

## Synopsis

### Functions/Subroutines

subroutinezlaqhb(UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)ZLAQHBscales a Hermitian band matrix, using scaling factors computed by cpbequ.

## Function/Subroutine Documentation

### subroutine zlaqhb (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED)

**ZLAQHB** scales a Hermitian band matrix, using scaling factors computed by cpbequ.

**Purpose:**

```
ZLAQHB equilibrates a Hermitian 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 COMPLEX*16 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**H *U or A = L*L**H 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= 'Y': Equilibration was done, i.e., A has been replaced by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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 142 of file zlaqhb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlaqhb(3) is an alias of zlaqhb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK