dpotrf.f

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*> \brief \b DPOTRF
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPOTRF computes the Cholesky factorization of a real symmetric
*> 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 triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is 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 contains 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
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*>          > 0:  if INFO = i, the leading principal minor of order i
*>                is not positive, and the factorization could not be
*>                completed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup potrf
*
*  =====================================================================
      SUBROUTINE dpotrf( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J, JB, NB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dpotrf2, dsyrk, dtrsm,
     $                   xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -4
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DPOTRF', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Determine the block size for this environment.
*
      nb = ilaenv( 1, 'DPOTRF', uplo, n, -1, -1, -1 )
      IF( nb.LE.1 .OR. nb.GE.n ) THEN
*
*        Use unblocked code.
*
         CALL dpotrf2( uplo, n, a, lda, info )
      ELSE
*
*        Use blocked code.
*
         IF( upper ) THEN
*
*           Compute the Cholesky factorization A = U**T*U.
*
            DO 10 j = 1, n, nb
*
*              Update and factorize the current diagonal block and test
*              for non-positive-definiteness.
*
               jb = min( nb, n-j+1 )
               CALL dsyrk( 'Upper', 'Transpose', jb, j-1, -one,
     $                     a( 1, j ), lda, one, a( j, j ), lda )
               CALL dpotrf2( 'Upper', jb, a( j, j ), lda, info )
               IF( info.NE.0 )
     $            GO TO 30
               IF( j+jb.LE.n ) THEN
*
*                 Compute the current block row.
*
                  CALL dgemm( 'Transpose', 'No transpose', jb,
     $                        n-j-jb+1,
     $                        j-1, -one, a( 1, j ), lda, a( 1, j+jb ),
     $                        lda, one, a( j, j+jb ), lda )
                  CALL dtrsm( 'Left', 'Upper', 'Transpose',
     $                        'Non-unit',
     $                        jb, n-j-jb+1, one, a( j, j ), lda,
     $                        a( j, j+jb ), lda )
               END IF
   10       CONTINUE
*
         ELSE
*
*           Compute the Cholesky factorization A = L*L**T.
*
            DO 20 j = 1, n, nb
*
*              Update and factorize the current diagonal block and test
*              for non-positive-definiteness.
*
               jb = min( nb, n-j+1 )
               CALL dsyrk( 'Lower', 'No transpose', jb, j-1, -one,
     $                     a( j, 1 ), lda, one, a( j, j ), lda )
               CALL dpotrf2( 'Lower', jb, a( j, j ), lda, info )
               IF( info.NE.0 )
     $            GO TO 30
               IF( j+jb.LE.n ) THEN
*
*                 Compute the current block column.
*
                  CALL dgemm( 'No transpose', 'Transpose', n-j-jb+1,
     $                        jb,
     $                        j-1, -one, a( j+jb, 1 ), lda, a( j, 1 ),
     $                        lda, one, a( j+jb, j ), lda )
                  CALL dtrsm( 'Right', 'Lower', 'Transpose',
     $                        'Non-unit',
     $                        n-j-jb+1, jb, one, a( j, j ), lda,
     $                        a( j+jb, j ), lda )
               END IF
   20       CONTINUE
         END IF
      END IF
      GO TO 40
*
   30 CONTINUE
      info = info + j - 1
*
   40 CONTINUE
      RETURN
*
*     End of DPOTRF
*
      SUBROUTINE dpotrf( UPLO, N, A, LDA, INFO ) …
      END