Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  - equilibrates a Hermitian band matrix A using the scaling factors in the vector
S

```

#### SYNOPSIS

```       SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

CHARACTER      EQUED, UPLO

INTEGER        KD, LDAB, N

DOUBLE         PRECISION AMAX, SCOND

DOUBLE         PRECISION S( * )

COMPLEX*16     AB( LDAB, * )

```

#### PURPOSE

```       ZLAQHB equilibrates a Hermitian band matrix A using the scaling factors in the vector S.

```

#### ARGUMENTS

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

N       (input) INTEGER
The order of the matrix A.  N >= 0.

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.

AB      (input/output) 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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

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

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

AMAX    (input) DOUBLE PRECISION
Absolute value of largest matrix entry.

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= 'Y':  Equilibration was done, i.e., A has been replaced by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

```

#### 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.

LAPACK auxiliary routine (version 3.3.1)   April 2011                            ZLAQHB(3lapack)
```