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zlaqhb.f(3) LAPACK zlaqhb.f(3)

NAME

zlaqhb.f -

SYNOPSIS

Functions/Subroutines


subroutine zlaqhb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
ZLAQHB scales 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= 'Y': Equilibration was done, i.e., A has been replaced by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

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Tue Sep 25 2012 Version 3.4.2