00001 SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO ) 00002 * 00003 * -- LAPACK auxiliary routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, LDA, N 00010 * .. 00011 * .. Array Arguments .. 00012 INTEGER IPIV( * ), JPIV( * ) 00013 COMPLEX*16 A( LDA, * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * ZGETC2 computes an LU factorization, using complete pivoting, of the 00020 * n-by-n matrix A. The factorization has the form A = P * L * U * Q, 00021 * where P and Q are permutation matrices, L is lower triangular with 00022 * unit diagonal elements and U is upper triangular. 00023 * 00024 * This is a level 1 BLAS version of the algorithm. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * N (input) INTEGER 00030 * The order of the matrix A. N >= 0. 00031 * 00032 * A (input/output) COMPLEX*16 array, dimension (LDA, N) 00033 * On entry, the n-by-n matrix to be factored. 00034 * On exit, the factors L and U from the factorization 00035 * A = P*L*U*Q; the unit diagonal elements of L are not stored. 00036 * If U(k, k) appears to be less than SMIN, U(k, k) is given the 00037 * value of SMIN, giving a nonsingular perturbed system. 00038 * 00039 * LDA (input) INTEGER 00040 * The leading dimension of the array A. LDA >= max(1, N). 00041 * 00042 * IPIV (output) INTEGER array, dimension (N). 00043 * The pivot indices; for 1 <= i <= N, row i of the 00044 * matrix has been interchanged with row IPIV(i). 00045 * 00046 * JPIV (output) INTEGER array, dimension (N). 00047 * The pivot indices; for 1 <= j <= N, column j of the 00048 * matrix has been interchanged with column JPIV(j). 00049 * 00050 * INFO (output) INTEGER 00051 * = 0: successful exit 00052 * > 0: if INFO = k, U(k, k) is likely to produce overflow if 00053 * one tries to solve for x in Ax = b. So U is perturbed 00054 * to avoid the overflow. 00055 * 00056 * Further Details 00057 * =============== 00058 * 00059 * Based on contributions by 00060 * Bo Kagstrom and Peter Poromaa, Department of Computing Science, 00061 * Umea University, S-901 87 Umea, Sweden. 00062 * 00063 * ===================================================================== 00064 * 00065 * .. Parameters .. 00066 DOUBLE PRECISION ZERO, ONE 00067 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00068 * .. 00069 * .. Local Scalars .. 00070 INTEGER I, IP, IPV, J, JP, JPV 00071 DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX 00072 * .. 00073 * .. External Subroutines .. 00074 EXTERNAL ZGERU, ZSWAP 00075 * .. 00076 * .. External Functions .. 00077 DOUBLE PRECISION DLAMCH 00078 EXTERNAL DLAMCH 00079 * .. 00080 * .. Intrinsic Functions .. 00081 INTRINSIC ABS, DCMPLX, MAX 00082 * .. 00083 * .. Executable Statements .. 00084 * 00085 * Set constants to control overflow 00086 * 00087 INFO = 0 00088 EPS = DLAMCH( 'P' ) 00089 SMLNUM = DLAMCH( 'S' ) / EPS 00090 BIGNUM = ONE / SMLNUM 00091 CALL DLABAD( SMLNUM, BIGNUM ) 00092 * 00093 * Factorize A using complete pivoting. 00094 * Set pivots less than SMIN to SMIN 00095 * 00096 DO 40 I = 1, N - 1 00097 * 00098 * Find max element in matrix A 00099 * 00100 XMAX = ZERO 00101 DO 20 IP = I, N 00102 DO 10 JP = I, N 00103 IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN 00104 XMAX = ABS( A( IP, JP ) ) 00105 IPV = IP 00106 JPV = JP 00107 END IF 00108 10 CONTINUE 00109 20 CONTINUE 00110 IF( I.EQ.1 ) 00111 $ SMIN = MAX( EPS*XMAX, SMLNUM ) 00112 * 00113 * Swap rows 00114 * 00115 IF( IPV.NE.I ) 00116 $ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA ) 00117 IPIV( I ) = IPV 00118 * 00119 * Swap columns 00120 * 00121 IF( JPV.NE.I ) 00122 $ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 ) 00123 JPIV( I ) = JPV 00124 * 00125 * Check for singularity 00126 * 00127 IF( ABS( A( I, I ) ).LT.SMIN ) THEN 00128 INFO = I 00129 A( I, I ) = DCMPLX( SMIN, ZERO ) 00130 END IF 00131 DO 30 J = I + 1, N 00132 A( J, I ) = A( J, I ) / A( I, I ) 00133 30 CONTINUE 00134 CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1, 00135 $ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA ) 00136 40 CONTINUE 00137 * 00138 IF( ABS( A( N, N ) ).LT.SMIN ) THEN 00139 INFO = N 00140 A( N, N ) = DCMPLX( SMIN, ZERO ) 00141 END IF 00142 RETURN 00143 * 00144 * End of ZGETC2 00145 * 00146 END
1.7.2