1 *> \brief \b ZGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.
3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
9 *> Download ZGETC2 + dependencies
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21 * SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDA, N
26 * .. Array Arguments ..
27 * INTEGER IPIV( * ), JPIV( * )
28 * COMPLEX*16 A( LDA, * )
37 *> ZGETC2 computes an LU factorization, using complete pivoting, of the
38 *> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
39 *> where P and Q are permutation matrices, L is lower triangular with
40 *> unit diagonal elements and U is upper triangular.
42 *> This is a level 1 BLAS version of the algorithm.
51 *> The order of the matrix A. N >= 0.
56 *> A is COMPLEX*16 array, dimension (LDA, N)
57 *> On entry, the n-by-n matrix to be factored.
58 *> On exit, the factors L and U from the factorization
59 *> A = P*L*U*Q; the unit diagonal elements of L are not stored.
60 *> If U(k, k) appears to be less than SMIN, U(k, k) is given the
61 *> value of SMIN, giving a nonsingular perturbed system.
67 *> The leading dimension of the array A. LDA >= max(1, N).
72 *> IPIV is INTEGER array, dimension (N).
73 *> The pivot indices; for 1 <= i <= N, row i of the
74 *> matrix has been interchanged with row IPIV(i).
79 *> JPIV is INTEGER array, dimension (N).
80 *> The pivot indices; for 1 <= j <= N, column j of the
81 *> matrix has been interchanged with column JPIV(j).
87 *> = 0: successful exit
88 *> > 0: if INFO = k, U(k, k) is likely to produce overflow if
89 *> one tries to solve for x in Ax = b. So U is perturbed
90 *> to avoid the overflow.
96 *> \author Univ. of Tennessee
97 *> \author Univ. of California Berkeley
98 *> \author Univ. of Colorado Denver
103 *> \ingroup complex16GEauxiliary
105 *> \par Contributors:
108 *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
109 *> Umea University, S-901 87 Umea, Sweden.
111 * =====================================================================
112 SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
114 * -- LAPACK auxiliary routine (version 3.6.1) --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 * .. Scalar Arguments ..
122 * .. Array Arguments ..
123 INTEGER IPIV( * ), JPIV( * )
124 COMPLEX*16 A( LDA, * )
127 * =====================================================================
130 DOUBLE PRECISION ZERO, ONE
131 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
133 * .. Local Scalars ..
134 INTEGER I, IP, IPV, J, JP, JPV
135 DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
137 * .. External Subroutines ..
138 EXTERNAL ZGERU, ZSWAP
140 * .. External Functions ..
141 DOUBLE PRECISION DLAMCH
144 * .. Intrinsic Functions ..
145 INTRINSIC ABS, DCMPLX, MAX
147 * .. Executable Statements ..
151 * Quick return if possible
156 * Set constants to control overflow
159 SMLNUM = DLAMCH( 'S' ) / EPS
160 BIGNUM = ONE / SMLNUM
161 CALL DLABAD( SMLNUM, BIGNUM )
163 * Handle the case N=1 by itself
168 IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
170 A( 1, 1 ) = DCMPLX( SMLNUM, ZERO )
175 * Factorize A using complete pivoting.
176 * Set pivots less than SMIN to SMIN
180 * Find max element in matrix A
185 IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
186 XMAX = ABS( A( IP, JP ) )
193 $ SMIN = MAX( EPS*XMAX, SMLNUM )
198 $ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
204 $ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
207 * Check for singularity
209 IF( ABS( A( I, I ) ).LT.SMIN ) THEN
211 A( I, I ) = DCMPLX( SMIN, ZERO )
214 A( J, I ) = A( J, I ) / A( I, I )
216 CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
217 $ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
220 IF( ABS( A( N, N ) ).LT.SMIN ) THEN
222 A( N, N ) = DCMPLX( SMIN, ZERO )
225 * Set last pivots to N