lammps/lib/linalg/dpotf2.f

*> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPOTF2 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 unblocked version of the algorithm, calling Level 2 BLAS.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          symmetric matrix A is stored.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \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 = -k, the k-th argument had an illegal value
*>          > 0: if INFO = k, the leading minor of order k is not
*>               positive definite, 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.
*
*> \date December 2016
*
*> \ingroup doublePOcomputational
*
*  =====================================================================
      SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, DISNAN
      DOUBLE PRECISION   DDOT
      EXTERNAL           LSAME, DDOT, DISNAN
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMV, DSCAL, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SQRT
*     ..
*     .. 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( 'DPOTF2', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
      IF( UPPER ) THEN
*
*        Compute the Cholesky factorization A = U**T *U.
*
         DO 10 J = 1, N
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
            AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
            IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
               A( J, J ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            A( J, J ) = AJJ
*
*           Compute elements J+1:N of row J.
*
            IF( J.LT.N ) THEN
               CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
     $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
               CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
            END IF
   10    CONTINUE
      ELSE
*
*        Compute the Cholesky factorization A = L*L**T.
*
         DO 20 J = 1, N
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
            AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
     $            LDA )
            IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
               A( J, J ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            A( J, J ) = AJJ
*
*           Compute elements J+1:N of column J.
*
            IF( J.LT.N ) THEN
               CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
     $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
               CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
            END IF
   20    CONTINUE
      END IF
      GO TO 40
*
   30 CONTINUE
      INFO = J
*
   40 CONTINUE
      RETURN
*
*     End of DPOTF2
*
      END