SPOTF2 - compute the Cholesky factorization of a real sym­
       metric positive definite matrix A


SYNOPSIS

       SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, N

           REAL           A( LDA, * )


PURPOSE

       SPOTF2 computes the Cholesky factorization of a real  sym­
       metric  positive definite matrix A.  The factorization has
       the form
          A = U' * U ,  if UPLO = 'U', or
          A = L  * L',  if UPLO = 'L',
       where U is an upper triangular matrix and L is lower  tri­
       angular.

       This  is  the  unblocked version of the algorithm, calling
       Level 2 BLAS.


ARGUMENTS

       UPLO    (input) CHARACTER*1
               Specifies whether the upper  or  lower  triangular
               part  of the symmetric matrix A is stored.  = 'U':
               Upper triangular
               = 'L':  Lower triangular

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

       A       (input/output) REAL array, dimension (LDA,N)
               On entry, the symmetric matrix A.  If UPLO =  'U',
               the leading n by n upper triangular part of A con­
               tains the upper triangular part of the  matrix  A,
               and the strictly lower triangular part of A is not
               referenced.  If UPLO = 'L', the  leading  n  by  n
               lower triangular part of A contains the lower tri­
               angular part of the matrix  A,  and  the  strictly
               upper triangular part of A is not referenced.

               On  exit,  if INFO = 0, the factor U or L from the
               Cholesky factorization A = U'*U  or A = L*L'.

       LDA     (input) INTEGER
               The leading dimension of  the  array  A.   LDA  >=
               max(1,N).

               = 0: successful exit
               <  0: if INFO = -k, the k-th argument had an ille­
               gal value
               > 0: if INFO = k, the leading minor of order k  is
               not positive definite, and the factorization could
               not be completed.


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