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SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* March 2008
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION A( LDA, * )
* ..
*
* Purpose
* =======
*
* 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 left-looking Level 3 BLAS version of the algorithm.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* A (input/output) 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.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* IPIV (output) 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).
*
* INFO (output) 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.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IINFO, J, JB, K, NB
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DGETF2, 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 DGETF2( 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 )
*
* Update before factoring the current panel
*
DO 30 K = 1, J-NB, NB
*
* Apply interchanges to rows K:K+NB-1.
*
CALL DLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
*
* Compute block row of U.
*
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
$ NB, JB, ONE, A( K, K ), LDA,
$ A( K, J ), LDA )
*
* Update trailing submatrix.
*
CALL DGEMM( 'No transpose', 'No transpose',
$ M-K-NB+1, JB, NB, -ONE,
$ A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
$ A( K+NB, J ), LDA )
30 CONTINUE
*
* Factor diagonal and subdiagonal blocks and test for exact
* singularity.
*
CALL DGETF2( 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
*
20 CONTINUE
*
* Apply interchanges to the left-overs
*
DO 40 K = 1, MIN( M, N ), NB
CALL DLASWP( K-1, A( 1, 1 ), LDA, K,
$ MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
40 CONTINUE
*
* Apply update to the M+1:N columns when N > M
*
IF ( N.GT.M ) THEN
CALL DLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )
DO 50 K = 1, M, NB
JB = MIN( M-K+1, NB )
*
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
$ JB, N-M, ONE, A( K, K ), LDA,
$ A( K, M+1 ), LDA )
*
IF ( K+NB.LE.M ) THEN
CALL DGEMM( 'No transpose', 'No transpose',
$ M-K-NB+1, N-M, NB, -ONE,
$ A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
$ A( K+NB, M+1 ), LDA )
END IF
50 CONTINUE
END IF
*
END IF
RETURN
*
* End of DGETRF
*
END
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