# claqhb.f man page

claqhb.f

## Synopsis

### Functions/Subroutines

subroutine claqhb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

## Function/Subroutine Documentation

### subroutine claqhb (character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) S, real SCOND, real AMAX, character EQUED)

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

Purpose:

``` CLAQHB equilibrates an 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 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 REAL array, dimension (N)
The scale factors for A.```

SCOND

```          SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).```

AMAX

```          AMAX is REAL
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= 'Y':  Equilibration was done, i.e., A has been replaced by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

NAG Ltd.

Date:

December 2016

Definition at line 143 of file claqhb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page claqhb(3) is an alias of claqhb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK