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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zlaqhb.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zlaqhb.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/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 (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

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.

Definition at line 140 of file zlaqhb.f.

Author

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Version 3.12.0 LAPACK