zpoequb (l)  Linux Man Pages
zpoequb: computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the twonorm)
Command to display zpoequb
manual in Linux: $ man l zpoequb
NAME
ZPOEQUB  computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the twonorm)
SYNOPSIS
 SUBROUTINE ZPOEQUB(

N, A, LDA, S, SCOND, AMAX, INFO )

IMPLICIT
NONE

INTEGER
INFO, LDA, N

DOUBLE
PRECISION AMAX, SCOND

COMPLEX*16
A( LDA, * )

DOUBLE
PRECISION S( * )
PURPOSE
ZPOEQUB computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A and reduce its condition number
(with respect to the twonorm). 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.
ARGUMENTS
 N (input) INTEGER

The order of the matrix A. N >= 0.
 A (input) COMPLEX*16 array, dimension (LDA,N)

The NbyN symmetric positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
 LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).
 S (output) DOUBLE PRECISION array, dimension (N)

If INFO = 0, S contains the scale factors for A.
 SCOND (output) 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 (output) 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 (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the ith diagonal element is nonpositive.
Pages related to zpoequb
 zpoequb (3)
 zpoequ (l)  computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the twonorm)
 zpocon (l)  estimates the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF
 zporfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
 zporfsx (l)  ZPORFSX improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution
 zposv (l)  computes the solution to a complex system of linear equations A * X = B,
 zposvx (l)  uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
 zposvxx (l)  ZPOSVXX use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a complex*16 system of linear equations A * X = B, where A is an NbyN symmetric positive definite matrix and X and B are NbyNRHS matrices