sppcon(3S)

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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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