*> \brief \b ZGETC2 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 ZGETC2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * INTEGER IPIV( * ), JPIV( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGETC2 computes an LU factorization, using 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 a level 1 BLAS version of the 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 COMPLEX*16 array, dimension (LDA, N) *> On entry, the n-by-n matrix 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, 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 overflow if *> one tries 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. * *> \ingroup complex16GEauxiliary * *> \par Contributors: * ================== *> *> Bo Kagstrom and Peter Poromaa, Department of Computing Science, *> Umea University, S-901 87 Umea, Sweden. * * ===================================================================== SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO ) * * -- LAPACK auxiliary 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, N * .. * .. Array Arguments .. INTEGER IPIV( * ), JPIV( * ) COMPLEX*16 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 ZGERU, ZSWAP, DLABAD * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, DCMPLX, 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 ) = DCMPLX( SMLNUM, ZERO ) 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 ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA ) IPIV( I ) = IPV * * Swap columns * IF( JPV.NE.I ) \$ CALL ZSWAP( 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 ) = DCMPLX( SMIN, ZERO ) END IF DO 30 J = I + 1, N A( J, I ) = A( J, I ) / A( I, I ) 30 CONTINUE CALL ZGERU( N-I, N-I, -DCMPLX( 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 ) = DCMPLX( SMIN, ZERO ) END IF * * Set last pivots to N * IPIV( N ) = N JPIV( N ) = N * RETURN * * End of ZGETC2 * END