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*> \brief \b DGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DGETC2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetc2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetc2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetc2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * ), JPIV( * )
* DOUBLE PRECISION A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGETC2 computes an LU factorization with complete pivoting of the
*> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
*> where P and Q are permutation matrices, L is lower triangular with
*> unit diagonal elements and U is upper triangular.
*>
*> This is the Level 2 BLAS algorithm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA, N)
*> On entry, the n-by-n matrix A to be factored.
*> On exit, the factors L and U from the factorization
*> A = P*L*U*Q; the unit diagonal elements of L are not stored.
*> If U(k, k) appears to be less than SMIN, U(k, k) is given the
*> value of SMIN, i.e., giving a nonsingular perturbed system.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension(N).
*> The pivot indices; for 1 <= i <= N, row i of the
*> matrix has been interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[out] JPIV
*> \verbatim
*> JPIV is INTEGER array, dimension(N).
*> The pivot indices; for 1 <= j <= N, column j of the
*> matrix has been interchanged with column JPIV(j).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> > 0: if INFO = k, U(k, k) is likely to produce owerflow if
*> we try to solve for x in Ax = b. So U is perturbed to
*> avoid the overflow.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2013
*
*> \ingroup doubleGEauxiliary
*
*> \par Contributors:
* ==================
*>
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
*
* =====================================================================
SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* -- LAPACK auxiliary routine (version 3.5.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2013
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), JPIV( * )
DOUBLE PRECISION A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IP, IPV, J, JP, JPV
DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
* ..
* .. External Subroutines ..
EXTERNAL DGER, DSWAP
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Executable Statements ..
*
INFO = 0
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Set constants to control overflow
*
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* Handle the case N=1 by itself
*
IF( N.EQ.1 ) THEN
IPIV( 1 ) = 1
JPIV( 1 ) = 1
IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
INFO = 1
A( 1, 1 ) = SMLNUM
END IF
RETURN
END IF
*
* Factorize A using complete pivoting.
* Set pivots less than SMIN to SMIN.
*
DO 40 I = 1, N - 1
*
* Find max element in matrix A
*
XMAX = ZERO
DO 20 IP = I, N
DO 10 JP = I, N
IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
XMAX = ABS( A( IP, JP ) )
IPV = IP
JPV = JP
END IF
10 CONTINUE
20 CONTINUE
IF( I.EQ.1 )
$ SMIN = MAX( EPS*XMAX, SMLNUM )
*
* Swap rows
*
IF( IPV.NE.I )
$ CALL DSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
IPIV( I ) = IPV
*
* Swap columns
*
IF( JPV.NE.I )
$ CALL DSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
JPIV( I ) = JPV
*
* Check for singularity
*
IF( ABS( A( I, I ) ).LT.SMIN ) THEN
INFO = I
A( I, I ) = SMIN
END IF
DO 30 J = I + 1, N
A( J, I ) = A( J, I ) / A( I, I )
30 CONTINUE
CALL DGER( N-I, N-I, -ONE, A( I+1, I ), 1, A( I, I+1 ), LDA,
$ A( I+1, I+1 ), LDA )
40 CONTINUE
*
IF( ABS( A( N, N ) ).LT.SMIN ) THEN
INFO = N
A( N, N ) = SMIN
END IF
*
* Set last pivots to N
*
IPIV( N ) = N
JPIV( N ) = N
*
RETURN
*
* End of DGETC2
*
END
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