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SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* June 30, 1999
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), JPIV( * )
COMPLEX*16 A( LDA, * )
* ..
*
* Purpose
* =======
*
* 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.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) 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.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1, N).
*
* IPIV (output) INTEGER array, dimension (N).
* The pivot indices; for 1 <= i <= N, row i of the
* matrix has been interchanged with row IPIV(i).
*
* JPIV (output) INTEGER array, dimension (N).
* The pivot indices; for 1 <= j <= N, column j of the
* matrix has been interchanged with column JPIV(j).
*
* INFO (output) 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.
*
* Further Details
* ===============
*
* Based on contributions by
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
* Umea University, S-901 87 Umea, Sweden.
*
* =====================================================================
*
* .. 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
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCMPLX, MAX
* ..
* .. Executable Statements ..
*
* Set constants to control overflow
*
INFO = 0
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* 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
RETURN
*
* End of ZGETC2
*
END
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