#include "ESMF_LapackBlas.inc" !> \brief \b DGETRF ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DGETRF + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrf.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrf.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, LDA, M, N ! .. ! .. Array Arguments .. ! INTEGER IPIV( * ) ! DOUBLE PRECISION 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 < 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 DOUBLE PRECISION 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 <= i <= 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 !> < 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 doubleGEcomputational ! ! ===================================================================== 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 ! ! .. Scalar Arguments .. INTEGER INFO, LDA, M, N ! .. ! .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+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 ) & RETURN ! ! 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 IF 20 CONTINUE END IF RETURN ! ! End of DGETRF ! END