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spotrf

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

 SYNOPSIS
      SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO )

          CHARACTER      UPLO

          INTEGER        INFO, LDA, N

          REAL           A( LDA, * )

 PURPOSE
      SPOTRF 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) 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 triangular
              part of the matrix A, and the strictly upper tri-
              angular 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
              < 0:  if INFO = -i, the i-th argument had an illegal
              value
              > 0:  if INFO = i, the leading minor of order i is
              not positive definite, and the factorization could
              not be completed.