SPPCON (3lapack)

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