*> \brief \b CGETRF2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * RECURSIVE SUBROUTINE CGETRF2( M, N, A, LDA, IPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CGETRF2 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 recursive version of the algorithm. It divides *> the matrix into four submatrices: *> *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 *> A = [ -----|----- ] with n1 = min(m,n)/2 *> [ A21 | A22 ] n2 = n-n1 *> *> [ A11 ] *> The subroutine calls itself to factor [ --- ], *> [ A12 ] *> [ A12 ] *> do the swaps on [ --- ], solve A12, update A22, *> [ A22 ] *> *> then calls itself to factor A22 and do the swaps on A21. *> *> \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 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 June 2016 * *> \ingroup complexGEcomputational * * ===================================================================== RECURSIVE SUBROUTINE CGETRF2( 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..-- * June 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), \$ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. REAL SFMIN COMPLEX TEMP INTEGER I, IINFO, N1, N2 * .. * .. External Functions .. REAL SLAMCH INTEGER ICAMAX EXTERNAL SLAMCH, ICAMAX * .. * .. External Subroutines .. EXTERNAL CGEMM, CSCAL, CLASWP, CTRSM, XERBLA * .. * .. 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( 'CGETRF2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) \$ RETURN IF ( M.EQ.1 ) THEN * * Use unblocked code for one row case * Just need to handle IPIV and INFO * IPIV( 1 ) = 1 IF ( A(1,1).EQ.ZERO ) \$ INFO = 1 * ELSE IF( N.EQ.1 ) THEN * * Use unblocked code for one column case * * * Compute machine safe minimum * SFMIN = SLAMCH('S') * * Find pivot and test for singularity * I = ICAMAX( M, A( 1, 1 ), 1 ) IPIV( 1 ) = I IF( A( I, 1 ).NE.ZERO ) THEN * * Apply the interchange * IF( I.NE.1 ) THEN TEMP = A( 1, 1 ) A( 1, 1 ) = A( I, 1 ) A( I, 1 ) = TEMP END IF * * Compute elements 2:M of the column * IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN CALL CSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 ) ELSE DO 10 I = 1, M-1 A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 ) 10 CONTINUE END IF * ELSE INFO = 1 END IF * ELSE * * Use recursive code * N1 = MIN( M, N ) / 2 N2 = N-N1 * * [ A11 ] * Factor [ --- ] * [ A21 ] * CALL CGETRF2( M, N1, A, LDA, IPIV, IINFO ) IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) \$ INFO = IINFO * * [ A12 ] * Apply interchanges to [ --- ] * [ A22 ] * CALL CLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 ) * * Solve A12 * CALL CTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA, \$ A( 1, N1+1 ), LDA ) * * Update A22 * CALL CGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA, \$ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA ) * * Factor A22 * CALL CGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ), \$ IINFO ) * * Adjust INFO and the pivot indices * IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) \$ INFO = IINFO + N1 DO 20 I = N1+1, MIN( M, N ) IPIV( I ) = IPIV( I ) + N1 20 CONTINUE * * Apply interchanges to A21 * CALL CLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 ) * END IF RETURN * * End of CGETRF2 * END