LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cgetrf.f
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1 *> \brief \b CGETRF
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetrf.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CGETRF( M, N, A, LDA, IPIV, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDA, M, N
25 * ..
26 * .. Array Arguments ..
27 * INTEGER IPIV( * )
28 * COMPLEX A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CGETRF 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 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 *
104 *> \ingroup complexGEcomputational
105 *
106 * =====================================================================
107  SUBROUTINE cgetrf( M, N, A, LDA, IPIV, INFO )
108 *
109 * -- LAPACK computational routine --
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 A( LDA, * )
119 * ..
120 *
121 * =====================================================================
122 *
123 * .. Parameters ..
124  COMPLEX ONE
125  parameter( one = ( 1.0e+0, 0.0e+0 ) )
126 * ..
127 * .. Local Scalars ..
128  INTEGER I, IINFO, J, JB, NB
129 * ..
130 * .. External Subroutines ..
131  EXTERNAL cgemm, cgetrf2, claswp, ctrsm, xerbla
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( 'CGETRF', -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, 'CGETRF', ' ', m, n, -1, -1 )
165  IF( nb.LE.1 .OR. nb.GE.min( m, n ) ) THEN
166 *
167 * Use unblocked code.
168 *
169  CALL cgetrf2( m, n, a, lda, ipiv, info )
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 *
180  CALL cgetrf2( m-j+1, jb, a( j, j ), lda, ipiv( j ), iinfo )
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 claswp( 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 claswp( 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 ctrsm( '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 cgemm( '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 CGETRF
221 *
222  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
recursive subroutine cgetrf2(M, N, A, LDA, IPIV, INFO)
CGETRF2
Definition: cgetrf2.f:113
subroutine cgetrf(M, N, A, LDA, IPIV, INFO)
CGETRF
Definition: cgetrf.f:108
subroutine claswp(N, A, LDA, K1, K2, IPIV, INCX)
CLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: claswp.f:115