NAME¶

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

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