*> \brief \b DGETRF2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, M, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGETRF2 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 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.
*> \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.
*
*> \ingroup doubleGEcomputational
*
* =====================================================================
RECURSIVE SUBROUTINE DGETRF2( 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( * )
DOUBLE PRECISION A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION SFMIN, TEMP
INTEGER I, IINFO, N1, N2
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
INTEGER IDAMAX
EXTERNAL DLAMCH, IDAMAX
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DSCAL, DLASWP, DTRSM, 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( 'DGETRF2', -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 = DLAMCH('S')
*
* Find pivot and test for singularity
*
I = IDAMAX( 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 DSCAL( 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 DGETRF2( M, N1, A, LDA, IPIV, IINFO )
IF ( INFO.EQ.0 .AND. IINFO.GT.0 )
$ INFO = IINFO
*
* [ A12 ]
* Apply interchanges to [ --- ]
* [ A22 ]
*
CALL DLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 )
*
* Solve A12
*
CALL DTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA,
$ A( 1, N1+1 ), LDA )
*
* Update A22
*
CALL DGEMM( '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 DGETRF2( 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 DLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 )
*
END IF
RETURN
*
* End of DGETRF2
*
END