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

UPLO, N, AP, S, SCOND, AMAX, INFO )

CHARACTER
UPLO

INTEGER
INFO, N

REAL
AMAX, SCOND

REAL
AP( * ), S( * )
PURPOSE
SPPEQU computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A in packed storage 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
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
 N (input) INTEGER

The order of the matrix A. N >= 0.
 AP (input) REAL array, dimension (N*(N+1)/2)

The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The jth column of A is stored
in the array AP as follows:
if UPLO = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = aqLaq, AP(i + (j1)*(2nj)/2) = A(i,j) for j<=i<=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 sppequ
 sppequ (3)
 sppcon (l)  estimates the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
 spprfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
 sppsv (l)  computes the solution to a real system of linear equations A * X = B,
 sppsvx (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,
 spptrf (l)  computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
 spptri (l)  computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
 spptrs (l)  solves a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF