numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/VARIANTS/lu/LL/sgetrf.f | 6647B | -rw-r--r-- |
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C> \brief \b SGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * REAL A( LDA, * ) * .. * * Purpose * ======= * C>\details \b Purpose: C>\verbatim C> C> SGETRF computes an LU factorization of a general M-by-N matrix A C> using partial pivoting with row interchanges. C> C> The factorization has the form C> A = P * L * U C> where P is a permutation matrix, L is lower triangular with unit C> diagonal elements (lower trapezoidal if m > n), and U is upper C> triangular (upper trapezoidal if m < n). C> C> This is the left-looking Level 3 BLAS version of the algorithm. C> C>\endverbatim * * Arguments: * ========== * C> \param[in] M C> \verbatim C> M is INTEGER C> The number of rows of the matrix A. M >= 0. C> \endverbatim C> C> \param[in] N C> \verbatim C> N is INTEGER C> The number of columns of the matrix A. N >= 0. C> \endverbatim C> C> \param[in,out] A C> \verbatim C> A is REAL array, dimension (LDA,N) C> On entry, the M-by-N matrix to be factored. C> On exit, the factors L and U from the factorization C> A = P*L*U; the unit diagonal elements of L are not stored. C> \endverbatim C> C> \param[in] LDA C> \verbatim C> LDA is INTEGER C> The leading dimension of the array A. LDA >= max(1,M). C> \endverbatim C> C> \param[out] IPIV C> \verbatim C> IPIV is INTEGER array, dimension (min(M,N)) C> The pivot indices; for 1 <= i <= min(M,N), row i of the C> matrix was interchanged with row IPIV(i). C> \endverbatim C> C> \param[out] INFO C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value C> > 0: if INFO = i, U(i,i) is exactly zero. The factorization C> has been completed, but the factor U is exactly C> singular, and division by zero will occur if it is used C> to solve a system of equations. C> \endverbatim C> * * Authors: * ======== * C> \author Univ. of Tennessee C> \author Univ. of California Berkeley C> \author Univ. of Colorado Denver C> \author NAG Ltd. * C> \date December 2016 * C> \ingroup variantsGEcomputational * * ===================================================================== SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER IPIV( * ) REAL A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IINFO, J, JB, K, NB * .. * .. External Subroutines .. EXTERNAL SGEMM, SGETF2, SLASWP, STRSM, 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( 'SGETRF', -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, 'SGETRF', ' ', M, N, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN * * Use unblocked code. * CALL SGETF2( 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 SLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 ) * * Compute block row of U. * CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', $ NB, JB, ONE, A( K, K ), LDA, $ A( K, J ), LDA ) * * Update trailing submatrix. * CALL SGEMM( '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 SGETF2( 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 SLASWP( 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 SLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 ) DO 50 K = 1, M, NB JB = MIN( M-K+1, NB ) * CALL STRSM( '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 SGEMM( '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 SGETRF * END