SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. INTEGER IPIV( * ), JPIV( * ) COMPLEX A( LDA, * ) * .. * * Purpose * ======= * * CGETC2 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 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 .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IP, IPV, J, JP, JPV REAL BIGNUM, EPS, SMIN, SMLNUM, XMAX * .. * .. External Subroutines .. EXTERNAL CGERU, CSWAP, SLABAD * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, CMPLX, MAX * .. * .. Executable Statements .. * * Set constants to control overflow * INFO = 0 EPS = SLAMCH( 'P' ) SMLNUM = SLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM CALL SLABAD( 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 CSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA ) IPIV( I ) = IPV * * Swap columns * IF( JPV.NE.I ) \$ CALL CSWAP( 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 ) = CMPLX( SMIN, ZERO ) END IF DO 30 J = I + 1, N A( J, I ) = A( J, I ) / A( I, I ) 30 CONTINUE CALL CGERU( N-I, N-I, -CMPLX( 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 ) = CMPLX( SMIN, ZERO ) END IF RETURN * * End of CGETC2 * END