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

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zppequ.f

SYNOPSIS

Functions/Subroutines


subroutine ZPPEQU (uplo, n, ap, s, scond, amax, info)
ZPPEQU

Function/Subroutine Documentation

subroutine ZPPEQU (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

ZPPEQU

Purpose:

!>
!> ZPPEQU computes row and column scalings intended to equilibrate a
!> Hermitian positive definite matrix A in packed storage and reduce
!> its condition number (with respect to the two-norm).  S contains the
!> scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
!> B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
!> This choice of S puts the condition number of B within a factor N of
!> the smallest possible condition number over all possible diagonal
!> scalings.
!> 

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!> 

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

AP

!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The upper or lower triangle of the Hermitian matrix A, packed
!>          columnwise in a linear array.  The j-th column of A is stored
!>          in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
!> 

S

!>          S is DOUBLE PRECISION array, dimension (N)
!>          If INFO = 0, S contains the scale factors for A.
!> 

SCOND

!>          SCOND is DOUBLE PRECISION
!>          If INFO = 0, S contains the ratio of the smallest S(i) to
!>          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
!>          large nor too small, it is not worth scaling by S.
!> 

AMAX

!>          AMAX is DOUBLE PRECISION
!>          Absolute value of largest matrix element.  If AMAX is very
!>          close to overflow or very close to underflow, the matrix
!>          should be scaled.
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 116 of file zppequ.f.

Author

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Version 3.12.0 LAPACK