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dgetrf
C DGETRF    SOURCE    FANDEUR   22/05/02    21:15:05     11359          *> \brief \b DGETRF**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**> \htmlonly*> Download SGETRF + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrf.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrf.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )**       .. Scalar Arguments ..*       INTEGER            INFO, LDA, M, N*       ..*       .. Array Arguments ..*       INTEGER            IPIV( * )*       REAL               A( LDA, * )*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> DGETRF computes an LU factorization of a general M-by-N matrix A*> using partial pivoting with row interchanges.*>*> The factorization has the form*>    A = P * L * U*> where P is a permutation matrix, L is lower triangular with unit*> diagonal elements (lower trapezoidal if m > n), and U is upper*> triangular (upper trapezoidal if m &lt; n).*>*> This is the right-looking Level 3 BLAS version of the algorithm.*> \endverbatim**  Arguments:*  ==========**> \param[in] M*> \verbatim*>          M is INTEGER*>          The number of rows of the matrix A.  M >= 0.*> \endverbatim*>*> \param[in] N*> \verbatim*>          N is INTEGER*>          The number of columns of the matrix A.  N >= 0.*> \endverbatim*>*> \param[in,out] A*> \verbatim*>          A is REAL array, dimension (LDA,N)*>          On entry, the M-by-N matrix to be factored.*>          On exit, the factors L and U from the factorization*>          A = P*L*U; the unit diagonal elements of L are not stored.*> \endverbatim*>*> \param[in] LDA*> \verbatim*>          LDA is INTEGER*>          The leading dimension of the array A.  LDA >= max(1,M).*> \endverbatim*>*> \param[out] IPIV*> \verbatim*>          IPIV is INTEGER array, dimension (min(M,N))*>          The pivot indices; for 1 &lt;= i &lt;= min(M,N), row i of the*>          matrix was interchanged with row IPIV(i).*> \endverbatim*>*> \param[out] INFO*> \verbatim*>          INFO is INTEGER*>          = 0:  successful exit*>          &lt; 0:  if INFO = -i, the i-th argument had an illegal value*>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization*>                has been completed, but the factor U is exactly*>                singular, and division by zero will occur if it is used*>                to solve a system of equations.*> \endverbatim**  Authors:*  ========**> \author Univ. of Tennessee*> \author Univ. of California Berkeley*> \author Univ. of Colorado Denver*> \author NAG Ltd.**> \date December 2016**> \ingroup realGEcomputational**  =====================================================================      SUBROUTINE DGETRF( M, N, A, LDA, IPIV, 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       IMPLICIT INTEGER(I-N)      IMPLICIT REAL*8(A-H,O-Z)**     .. Scalar Arguments ..      INTEGER            INFO, LDA, M, N*     ..*     .. Array Arguments ..      INTEGER            IPIV( * )      REAL*8             A( LDA, * )*     ..*  =====================================================================*     ..*     .. Parameters ..      REAL*8   ONE, ZERO      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 ) *     .. Local Scalars ..      INTEGER            I, IINFO, J, JB, NB*     ..*     .. External Subroutines ..      EXTERNAL           DGEMM, DGETRF2, DLASWP, DTRSM,     &                   XERBLA*     ..*     .. External Functions ..      INTEGER            ILAENV      EXTERNAL           ILAENV*     ..*     .. Intrinsic Functions ..*      INTRINSIC          MAX, MIN*     ..*     .. Executable Statements ..**     Test the input parameters.*      INFO = 0      IF ( M.LT.0 ) THEN         INFO = -1      ELSE IF( N.LT.0 ) THEN         INFO = -2      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN         INFO = -4      END IF      IF ( INFO.NE.0 ) THEN         CALL XERBLA( 'DGETRF', -INFO )         RETURN      END IF    **     Quick return if possible*      IF (M.EQ.0 .OR. N.EQ.0) THEN        RETURN      ENDIF **     Determine the block size for this environment.*      NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )       IF (NB.LE.1 .OR. NB.GE.MIN(M,N)) THEN**        Use unblocked code.*         CALL DGETRF2( M, N, A, LDA, IPIV, INFO )       ELSE**        Use blocked code.*         DO 20 J = 1, MIN( M, N ), NB            JB = MIN( MIN( M, N )-J+1, NB )**           Factor diagonal and subdiagonal blocks and test for exact*           singularity.*            CALL DGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )**           Adjust INFO and the pivot indices.*            IF( INFO.EQ.0 .AND. IINFO.GT.0 )     &         INFO = IINFO + J - 1            DO 10 I = J, MIN( M, J+JB-1 )               IPIV( I ) = J - 1 + IPIV( I )10          CONTINUE**           Apply interchanges to columns 1:J-1.*            CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )*            IF( J+JB.LE.N ) THEN**              Apply interchanges to columns J+JB:N.*               CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,     &                      IPIV, 1 )**              Compute block row of U.*               CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,     &                     N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),     &                     LDA )               IF( J+JB.LE.M ) THEN**                 Update trailing submatrix.*                  CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1,     &                        N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,     &                        A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),     &                        LDA )               END IF            END IF20       CONTINUE      END IF      RETURN**     End of DGETRF*      END     

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