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


SYNOPSIS

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

           CHARACTER      UPLO

           INTEGER        INFO, LDA, N

           DOUBLE         PRECISION A( LDA, * )


PURPOSE

       DPOTRF computes the Cholesky factorization of a real  sym­
       metric  positive definite matrix A.  The factorization has
       the form
          A = U**T * U,  if UPLO = 'U', or
          A = L  * L**T,  if UPLO = 'L',
       where U is an upper triangular matrix and L is lower  tri­
       angular.

       This  is the block version of the algorithm, calling Level
       3 BLAS.


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.

       A       (input/output) DOUBLE PRECISION 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**T*U or A = L*L**T.

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

       INFO    (output) INTEGER
               = 0:  successful exit

               gal value
               > 0:  if INFO = i, the leading minor of order i is
               not positive definite, and the factorization could
               not be completed.


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