Annotation of rpl/lapack/lapack/dgetrf.f, revision 1.14
1.8 bertrand 1: *> \brief \b DGETRF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGETRF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, M, N
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * )
28: * DOUBLE PRECISION A( LDA, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DGETRF 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 DOUBLE PRECISION 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: *
99: *> \author Univ. of Tennessee
100: *> \author Univ. of California Berkeley
101: *> \author Univ. of Colorado Denver
102: *> \author NAG Ltd.
103: *
1.13 bertrand 104: *> \date November 2015
1.8 bertrand 105: *
106: *> \ingroup doubleGEcomputational
107: *
108: * =====================================================================
1.1 bertrand 109: SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
110: *
1.13 bertrand 111: * -- LAPACK computational routine (version 3.6.0) --
1.1 bertrand 112: * -- LAPACK is a software package provided by Univ. of Tennessee, --
113: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.13 bertrand 114: * November 2015
1.1 bertrand 115: *
116: * .. Scalar Arguments ..
117: INTEGER INFO, LDA, M, N
118: * ..
119: * .. Array Arguments ..
120: INTEGER IPIV( * )
121: DOUBLE PRECISION A( LDA, * )
122: * ..
123: *
124: * =====================================================================
125: *
126: * .. Parameters ..
127: DOUBLE PRECISION ONE
128: PARAMETER ( ONE = 1.0D+0 )
129: * ..
130: * .. Local Scalars ..
131: INTEGER I, IINFO, J, JB, NB
132: * ..
133: * .. External Subroutines ..
1.13 bertrand 134: EXTERNAL DGEMM, DGETRF2, DLASWP, DTRSM, XERBLA
1.1 bertrand 135: * ..
136: * .. External Functions ..
137: INTEGER ILAENV
138: EXTERNAL ILAENV
139: * ..
140: * .. Intrinsic Functions ..
141: INTRINSIC MAX, MIN
142: * ..
143: * .. Executable Statements ..
144: *
145: * Test the input parameters.
146: *
147: INFO = 0
148: IF( M.LT.0 ) THEN
149: INFO = -1
150: ELSE IF( N.LT.0 ) THEN
151: INFO = -2
152: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
153: INFO = -4
154: END IF
155: IF( INFO.NE.0 ) THEN
156: CALL XERBLA( 'DGETRF', -INFO )
157: RETURN
158: END IF
159: *
160: * Quick return if possible
161: *
162: IF( M.EQ.0 .OR. N.EQ.0 )
163: $ RETURN
164: *
165: * Determine the block size for this environment.
166: *
167: NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )
168: IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
169: *
170: * Use unblocked code.
171: *
1.13 bertrand 172: CALL DGETRF2( M, N, A, LDA, IPIV, INFO )
1.1 bertrand 173: ELSE
174: *
175: * Use blocked code.
176: *
177: DO 20 J = 1, MIN( M, N ), NB
178: JB = MIN( MIN( M, N )-J+1, NB )
179: *
180: * Factor diagonal and subdiagonal blocks and test for exact
181: * singularity.
182: *
1.13 bertrand 183: CALL DGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
1.1 bertrand 184: *
185: * Adjust INFO and the pivot indices.
186: *
187: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
188: $ INFO = IINFO + J - 1
189: DO 10 I = J, MIN( M, J+JB-1 )
190: IPIV( I ) = J - 1 + IPIV( I )
191: 10 CONTINUE
192: *
193: * Apply interchanges to columns 1:J-1.
194: *
195: CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
196: *
197: IF( J+JB.LE.N ) THEN
198: *
199: * Apply interchanges to columns J+JB:N.
200: *
201: CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
202: $ IPIV, 1 )
203: *
204: * Compute block row of U.
205: *
206: CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
207: $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
208: $ LDA )
209: IF( J+JB.LE.M ) THEN
210: *
211: * Update trailing submatrix.
212: *
213: CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1,
214: $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
215: $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
216: $ LDA )
217: END IF
218: END IF
219: 20 CONTINUE
220: END IF
221: RETURN
222: *
223: * End of DGETRF
224: *
225: END
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