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