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claqhb.f(3) LAPACK claqhb.f(3)

NAME

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= 'Y': Equilibration was done, i.e., A has been replaced by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

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 143 of file claqhb.f.

Author

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Tue Nov 14 2017 Version 3.8.0