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 zlaqsb.f(3) LAPACK zlaqsb.f(3)

zlaqsb.f -

# SYNOPSIS

## Functions/Subroutines

subroutine zlaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

# Function/Subroutine Documentation

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

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
Purpose:
``` ZLAQSB equilibrates a symmetric 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= 'Y':  Equilibration was done, i.e., A has been replaced by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
NAG Ltd.
Date:
September 2012
Definition at line 142 of file zlaqsb.f.

# Author

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