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sppcon(3P)		    Sun Performance Library		    sppcon(3P)

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, A, ANORM, RCOND, WORK, WORK2, INFO)

       CHARACTER * 1 UPLO
       INTEGER N, INFO
       INTEGER WORK2(*)
       REAL ANORM, RCOND
       REAL A(*), WORK(*)

       SUBROUTINE SPPCON_64(UPLO, N, A, ANORM, RCOND, WORK, WORK2, INFO)

       CHARACTER * 1 UPLO
       INTEGER*8 N, INFO
       INTEGER*8 WORK2(*)
       REAL ANORM, RCOND
       REAL A(*), WORK(*)

   F95 INTERFACE
       SUBROUTINE PPCON(UPLO, [N], A, ANORM, RCOND, [WORK], [WORK2], [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, INFO
       INTEGER, DIMENSION(:) :: WORK2
       REAL :: ANORM, RCOND
       REAL, DIMENSION(:) :: A, WORK

       SUBROUTINE PPCON_64(UPLO, [N], A, ANORM, RCOND, [WORK], [WORK2], [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, INFO
       INTEGER(8), DIMENSION(:) :: WORK2
       REAL :: ANORM, RCOND
       REAL, DIMENSION(:) :: A, WORK

   C INTERFACE
       #include <sunperf.h>

       void  sppcon(char uplo, int n, float *a, float anorm, float *rcond, int
		 *info);

       void sppcon_64(char uplo, long n, float *a, float anorm, float  *rcond,
		 long *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)
		 = 'U':	 Upper triangle of A is stored;
		 = 'L':	 Lower triangle of A is stored.

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

       A (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 A as
		 follows:  if  UPLO  =	'U',  A(i  +  (j-1)*j/2)  = U(i,j) for
		 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2)	=  L(i,j)  for
		 j<=i<=n.

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

       RCOND (output)
		 The  reciprocal of the condition number of the matrix A, com‐
		 puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
		 mate of the 1-norm of inv(A) computed in this routine.

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

       WORK2 (workspace)
		 INTEGER array, dimension(N)

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

				  6 Mar 2009			    sppcon(3P)

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