2329
|
1 SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) |
|
2 * |
3333
|
3 * -- LAPACK routine (version 3.0) -- |
2329
|
4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
|
5 * Courant Institute, Argonne National Lab, and Rice University |
|
6 * September 30, 1994 |
|
7 * |
|
8 * .. Scalar Arguments .. |
|
9 INTEGER INFO, LDA, M, N |
|
10 * .. |
|
11 * .. Array Arguments .. |
|
12 INTEGER IPIV( * ) |
|
13 COMPLEX*16 A( LDA, * ) |
|
14 * .. |
|
15 * |
|
16 * Purpose |
|
17 * ======= |
|
18 * |
|
19 * ZGETRF computes an LU factorization of a general M-by-N matrix A |
|
20 * using partial pivoting with row interchanges. |
|
21 * |
|
22 * The factorization has the form |
|
23 * A = P * L * U |
|
24 * where P is a permutation matrix, L is lower triangular with unit |
|
25 * diagonal elements (lower trapezoidal if m > n), and U is upper |
|
26 * triangular (upper trapezoidal if m < n). |
|
27 * |
|
28 * This is the right-looking Level 3 BLAS version of the algorithm. |
|
29 * |
|
30 * Arguments |
|
31 * ========= |
|
32 * |
|
33 * M (input) INTEGER |
|
34 * The number of rows of the matrix A. M >= 0. |
|
35 * |
|
36 * N (input) INTEGER |
|
37 * The number of columns of the matrix A. N >= 0. |
|
38 * |
|
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
|
40 * On entry, the M-by-N matrix to be factored. |
|
41 * On exit, the factors L and U from the factorization |
|
42 * A = P*L*U; the unit diagonal elements of L are not stored. |
|
43 * |
|
44 * LDA (input) INTEGER |
|
45 * The leading dimension of the array A. LDA >= max(1,M). |
|
46 * |
|
47 * IPIV (output) INTEGER array, dimension (min(M,N)) |
|
48 * The pivot indices; for 1 <= i <= min(M,N), row i of the |
|
49 * matrix was interchanged with row IPIV(i). |
|
50 * |
|
51 * INFO (output) INTEGER |
|
52 * = 0: successful exit |
|
53 * < 0: if INFO = -i, the i-th argument had an illegal value |
|
54 * > 0: if INFO = i, U(i,i) is exactly zero. The factorization |
|
55 * has been completed, but the factor U is exactly |
|
56 * singular, and division by zero will occur if it is used |
|
57 * to solve a system of equations. |
|
58 * |
|
59 * ===================================================================== |
|
60 * |
|
61 * .. Parameters .. |
|
62 COMPLEX*16 ONE |
|
63 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) |
|
64 * .. |
|
65 * .. Local Scalars .. |
|
66 INTEGER I, IINFO, J, JB, NB |
|
67 * .. |
|
68 * .. External Subroutines .. |
|
69 EXTERNAL XERBLA, ZGEMM, ZGETF2, ZLASWP, ZTRSM |
|
70 * .. |
|
71 * .. External Functions .. |
|
72 INTEGER ILAENV |
|
73 EXTERNAL ILAENV |
|
74 * .. |
|
75 * .. Intrinsic Functions .. |
|
76 INTRINSIC MAX, MIN |
|
77 * .. |
|
78 * .. Executable Statements .. |
|
79 * |
|
80 * Test the input parameters. |
|
81 * |
|
82 INFO = 0 |
|
83 IF( M.LT.0 ) THEN |
|
84 INFO = -1 |
|
85 ELSE IF( N.LT.0 ) THEN |
|
86 INFO = -2 |
|
87 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
|
88 INFO = -4 |
|
89 END IF |
|
90 IF( INFO.NE.0 ) THEN |
|
91 CALL XERBLA( 'ZGETRF', -INFO ) |
|
92 RETURN |
|
93 END IF |
|
94 * |
|
95 * Quick return if possible |
|
96 * |
|
97 IF( M.EQ.0 .OR. N.EQ.0 ) |
|
98 $ RETURN |
|
99 * |
|
100 * Determine the block size for this environment. |
|
101 * |
|
102 NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 ) |
|
103 IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN |
|
104 * |
|
105 * Use unblocked code. |
|
106 * |
|
107 CALL ZGETF2( M, N, A, LDA, IPIV, INFO ) |
|
108 ELSE |
|
109 * |
|
110 * Use blocked code. |
|
111 * |
|
112 DO 20 J = 1, MIN( M, N ), NB |
|
113 JB = MIN( MIN( M, N )-J+1, NB ) |
|
114 * |
|
115 * Factor diagonal and subdiagonal blocks and test for exact |
|
116 * singularity. |
|
117 * |
|
118 CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) |
|
119 * |
|
120 * Adjust INFO and the pivot indices. |
|
121 * |
|
122 IF( INFO.EQ.0 .AND. IINFO.GT.0 ) |
|
123 $ INFO = IINFO + J - 1 |
|
124 DO 10 I = J, MIN( M, J+JB-1 ) |
|
125 IPIV( I ) = J - 1 + IPIV( I ) |
|
126 10 CONTINUE |
|
127 * |
|
128 * Apply interchanges to columns 1:J-1. |
|
129 * |
|
130 CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) |
|
131 * |
|
132 IF( J+JB.LE.N ) THEN |
|
133 * |
|
134 * Apply interchanges to columns J+JB:N. |
|
135 * |
|
136 CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, |
|
137 $ IPIV, 1 ) |
|
138 * |
|
139 * Compute block row of U. |
|
140 * |
|
141 CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, |
|
142 $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), |
|
143 $ LDA ) |
|
144 IF( J+JB.LE.M ) THEN |
|
145 * |
|
146 * Update trailing submatrix. |
|
147 * |
|
148 CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1, |
|
149 $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, |
|
150 $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), |
|
151 $ LDA ) |
|
152 END IF |
|
153 END IF |
|
154 20 CONTINUE |
|
155 END IF |
|
156 RETURN |
|
157 * |
|
158 * End of ZGETRF |
|
159 * |
|
160 END |