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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 Crout 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, NB * .. * .. External Subroutines .. EXTERNAL DGEMM, DGETF2, DLASWP, DTRSM, XERBLA * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD * .. * .. 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 current block. * CALL DGEMM( 'No transpose', 'No transpose', $ M-J+1, JB, J-1, -ONE, $ A( J, 1 ), LDA, A( 1, J ), LDA, ONE, $ A( J, J ), LDA ) * * 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 * * Apply interchanges to column 1:J-1 * CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) * IF ( J+JB.LE.N ) THEN * * Apply interchanges to column J+JB:N * CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, $ IPIV, 1 ) * CALL DGEMM( 'No transpose', 'No transpose', $ JB, N-J-JB+1, J-1, -ONE, $ A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE, $ A( J, J+JB ), LDA ) * * 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 ) END IF 20 CONTINUE END IF RETURN * * End of DGETRF * END |