spoequb (l)  Linux Man Pages
spoequb: 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 spoequb
manual in Linux: $ man l spoequb
NAME
SPOEQUB  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 SPOEQUB(

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

IMPLICIT
NONE

INTEGER
INFO, LDA, N

REAL
AMAX, SCOND

REAL
A( LDA, * ), S( * )
PURPOSE
SPOEQU 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) REAL 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) REAL array, dimension (N)

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

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) REAL

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 spoequb
 spoequb (3)
 spoequ (l)  computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the twonorm)
 spocon (l)  estimates the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
 sporfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
 sporfsx (l)  SPORFSX 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
 sposv (l)  computes the solution to a real system of linear equations A * X = B,
 sposvx (l)  uses the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
 sposvxx (l)  SPOSVXX use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, where A is an NbyN symmetric positive definite matrix and X and B are NbyNRHS matrices