Annotation of rpl/lapack/lapack/zgetrf.f, revision 1.18
1.8 bertrand 1: *> \brief \b ZGETRF
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download ZGETRF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgetrf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgetrf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetrf.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, M, N
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * )
28: * COMPLEX*16 A( LDA, * )
29: * ..
1.15 bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZGETRF computes an LU factorization of a general M-by-N matrix A
38: *> using partial pivoting with row interchanges.
39: *>
40: *> The factorization has the form
41: *> A = P * L * U
42: *> where P is a permutation matrix, L is lower triangular with unit
43: *> diagonal elements (lower trapezoidal if m > n), and U is upper
44: *> triangular (upper trapezoidal if m < n).
45: *>
46: *> This is the right-looking Level 3 BLAS version of the algorithm.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] M
53: *> \verbatim
54: *> M is INTEGER
55: *> The number of rows of the matrix A. M >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The number of columns of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in,out] A
65: *> \verbatim
66: *> A is COMPLEX*16 array, dimension (LDA,N)
67: *> On entry, the M-by-N matrix to be factored.
68: *> On exit, the factors L and U from the factorization
69: *> A = P*L*U; the unit diagonal elements of L are not stored.
70: *> \endverbatim
71: *>
72: *> \param[in] LDA
73: *> \verbatim
74: *> LDA is INTEGER
75: *> The leading dimension of the array A. LDA >= max(1,M).
76: *> \endverbatim
77: *>
78: *> \param[out] IPIV
79: *> \verbatim
80: *> IPIV is INTEGER array, dimension (min(M,N))
81: *> The pivot indices; for 1 <= i <= min(M,N), row i of the
82: *> matrix was interchanged with row IPIV(i).
83: *> \endverbatim
84: *>
85: *> \param[out] INFO
86: *> \verbatim
87: *> INFO is INTEGER
88: *> = 0: successful exit
89: *> < 0: if INFO = -i, the i-th argument had an illegal value
90: *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
91: *> has been completed, but the factor U is exactly
92: *> singular, and division by zero will occur if it is used
93: *> to solve a system of equations.
94: *> \endverbatim
95: *
96: * Authors:
97: * ========
98: *
1.15 bertrand 99: *> \author Univ. of Tennessee
100: *> \author Univ. of California Berkeley
101: *> \author Univ. of Colorado Denver
102: *> \author NAG Ltd.
1.8 bertrand 103: *
104: *> \ingroup complex16GEcomputational
105: *
106: * =====================================================================
1.1 bertrand 107: SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
108: *
1.18 ! bertrand 109: * -- LAPACK computational routine --
1.1 bertrand 110: * -- LAPACK is a software package provided by Univ. of Tennessee, --
111: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112: *
113: * .. Scalar Arguments ..
114: INTEGER INFO, LDA, M, N
115: * ..
116: * .. Array Arguments ..
117: INTEGER IPIV( * )
118: COMPLEX*16 A( LDA, * )
119: * ..
120: *
121: * =====================================================================
122: *
123: * .. Parameters ..
124: COMPLEX*16 ONE
125: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
126: * ..
127: * .. Local Scalars ..
128: INTEGER I, IINFO, J, JB, NB
129: * ..
130: * .. External Subroutines ..
1.13 bertrand 131: EXTERNAL XERBLA, ZGEMM, ZGETRF2, ZLASWP, ZTRSM
1.1 bertrand 132: * ..
133: * .. External Functions ..
134: INTEGER ILAENV
135: EXTERNAL ILAENV
136: * ..
137: * .. Intrinsic Functions ..
138: INTRINSIC MAX, MIN
139: * ..
140: * .. Executable Statements ..
141: *
142: * Test the input parameters.
143: *
144: INFO = 0
145: IF( M.LT.0 ) THEN
146: INFO = -1
147: ELSE IF( N.LT.0 ) THEN
148: INFO = -2
149: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
150: INFO = -4
151: END IF
152: IF( INFO.NE.0 ) THEN
153: CALL XERBLA( 'ZGETRF', -INFO )
154: RETURN
155: END IF
156: *
157: * Quick return if possible
158: *
159: IF( M.EQ.0 .OR. N.EQ.0 )
160: $ RETURN
161: *
162: * Determine the block size for this environment.
163: *
164: NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 )
165: IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
166: *
167: * Use unblocked code.
168: *
1.13 bertrand 169: CALL ZGETRF2( M, N, A, LDA, IPIV, INFO )
1.1 bertrand 170: ELSE
171: *
172: * Use blocked code.
173: *
174: DO 20 J = 1, MIN( M, N ), NB
175: JB = MIN( MIN( M, N )-J+1, NB )
176: *
177: * Factor diagonal and subdiagonal blocks and test for exact
178: * singularity.
179: *
1.13 bertrand 180: CALL ZGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
1.1 bertrand 181: *
182: * Adjust INFO and the pivot indices.
183: *
184: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
185: $ INFO = IINFO + J - 1
186: DO 10 I = J, MIN( M, J+JB-1 )
187: IPIV( I ) = J - 1 + IPIV( I )
188: 10 CONTINUE
189: *
190: * Apply interchanges to columns 1:J-1.
191: *
192: CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
193: *
194: IF( J+JB.LE.N ) THEN
195: *
196: * Apply interchanges to columns J+JB:N.
197: *
198: CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
199: $ IPIV, 1 )
200: *
201: * Compute block row of U.
202: *
203: CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
204: $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
205: $ LDA )
206: IF( J+JB.LE.M ) THEN
207: *
208: * Update trailing submatrix.
209: *
210: CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1,
211: $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
212: $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
213: $ LDA )
214: END IF
215: END IF
216: 20 CONTINUE
217: END IF
218: RETURN
219: *
220: * End of ZGETRF
221: *
222: END
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