SPPCON(3)      LAPACK routine of NEC Numeric Library Collection      SPPCON(3)



NAME
       SPPCON

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



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)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

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

           RCOND     (output)
                     RCOND is 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      (output)
                     WORK is REAL array, dimension (3*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (N)

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



LAPACK routine                  31 October 2017                      SPPCON(3)