*> \brief \b ZGETRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGETRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGETRF 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 COMPLEX*16 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 complex16GEcomputational * * ===================================================================== SUBROUTINE ZGETRF( 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( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, IINFO, J, JB, NB * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMM, ZGETRF2, ZLASWP, ZTRSM * .. * .. 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( 'ZGETRF', -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, 'ZGETRF', ' ', M, N, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN * * Use unblocked code. * CALL ZGETRF2( 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 ZGETRF2( 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 ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) * IF( J+JB.LE.N ) THEN * * Apply interchanges to columns J+JB:N. * CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, \$ IPIV, 1 ) * * Compute block row of U. * CALL ZTRSM( '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 ZGEMM( '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 ZGETRF * END