NAME

sppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF

SYNOPSIS

SUBROUTINE SPPCON(
UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )

CHARACTER UPLO

INTEGER INFO, N

REAL ANORM, RCOND

INTEGER IWORK( ∗ )

REAL AP( ∗ ), WORK( ∗ )

PURPOSE

SPPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF. 
 
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM ∗ norm(inv(A))).
 

ARGUMENTS

UPLO    (input) CHARACTER∗1
= ’U’:  Upper triangle of A is stored;
= ’L’:  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 triangular factor U or L from the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T, packed columnwise in a linear array.  The j-th column of U or L is stored in the array AP as follows: if UPLO = ’U’, AP(i + (j-1)∗j/2) = U(i,j) for 1<=i<=j; if UPLO = ’L’, AP(i + (j-1)∗(2n-j)/2) = L(i,j) for j<=i<=n.

ANORM   (input) REAL
The 1-norm (or infinity-norm) of the symmetric matrix A.

RCOND   (output) REAL
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM ∗ AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

WORK    (workspace) REAL array, dimension (3∗N)

IWORK   (workspace) INTEGER array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunSoft, Inc.  —  Last change: 27 Jun 1995