1*> \brief \b CGETRF2
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       RECURSIVE SUBROUTINE CGETRF2( M, N, A, LDA, IPIV, INFO )
12*
13*       .. Scalar Arguments ..
14*       INTEGER            INFO, LDA, M, N
15*       ..
16*       .. Array Arguments ..
17*       INTEGER            IPIV( * )
18*       COMPLEX            A( LDA, * )
19*       ..
20*
21*
22*> \par Purpose:
23*  =============
24*>
25*> \verbatim
26*>
27*> CGETRF2 computes an LU factorization of a general M-by-N matrix A
28*> using partial pivoting with row interchanges.
29*>
30*> The factorization has the form
31*>    A = P * L * U
32*> where P is a permutation matrix, L is lower triangular with unit
33*> diagonal elements (lower trapezoidal if m > n), and U is upper
34*> triangular (upper trapezoidal if m < n).
35*>
36*> This is the recursive version of the algorithm. It divides
37*> the matrix into four submatrices:
38*>
39*>        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
40*>    A = [ -----|----- ]  with n1 = min(m,n)/2
41*>        [  A21 | A22  ]       n2 = n-n1
42*>
43*>                                       [ A11 ]
44*> The subroutine calls itself to factor [ --- ],
45*>                                       [ A12 ]
46*>                 [ A12 ]
47*> do the swaps on [ --- ], solve A12, update A22,
48*>                 [ A22 ]
49*>
50*> then calls itself to factor A22 and do the swaps on A21.
51*>
52*> \endverbatim
53*
54*  Arguments:
55*  ==========
56*
57*> \param[in] M
58*> \verbatim
59*>          M is INTEGER
60*>          The number of rows of the matrix A.  M >= 0.
61*> \endverbatim
62*>
63*> \param[in] N
64*> \verbatim
65*>          N is INTEGER
66*>          The number of columns of the matrix A.  N >= 0.
67*> \endverbatim
68*>
69*> \param[in,out] A
70*> \verbatim
71*>          A is COMPLEX array, dimension (LDA,N)
72*>          On entry, the M-by-N matrix to be factored.
73*>          On exit, the factors L and U from the factorization
74*>          A = P*L*U; the unit diagonal elements of L are not stored.
75*> \endverbatim
76*>
77*> \param[in] LDA
78*> \verbatim
79*>          LDA is INTEGER
80*>          The leading dimension of the array A.  LDA >= max(1,M).
81*> \endverbatim
82*>
83*> \param[out] IPIV
84*> \verbatim
85*>          IPIV is INTEGER array, dimension (min(M,N))
86*>          The pivot indices; for 1 <= i <= min(M,N), row i of the
87*>          matrix was interchanged with row IPIV(i).
88*> \endverbatim
89*>
90*> \param[out] INFO
91*> \verbatim
92*>          INFO is INTEGER
93*>          = 0:  successful exit
94*>          < 0:  if INFO = -i, the i-th argument had an illegal value
95*>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
96*>                has been completed, but the factor U is exactly
97*>                singular, and division by zero will occur if it is used
98*>                to solve a system of equations.
99*> \endverbatim
100*
101*  Authors:
102*  ========
103*
104*> \author Univ. of Tennessee
105*> \author Univ. of California Berkeley
106*> \author Univ. of Colorado Denver
107*> \author NAG Ltd.
108*
109*> \ingroup complexGEcomputational
110*
111*  =====================================================================
112      RECURSIVE SUBROUTINE CGETRF2( M, N, A, LDA, IPIV, INFO )
113*
114*  -- LAPACK computational routine --
115*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
116*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118*     .. Scalar Arguments ..
119      INTEGER            INFO, LDA, M, N
120*     ..
121*     .. Array Arguments ..
122      INTEGER            IPIV( * )
123      COMPLEX            A( LDA, * )
124*     ..
125*
126*  =====================================================================
127*
128*     .. Parameters ..
129      COMPLEX            ONE, ZERO
130      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
131     $                     ZERO = ( 0.0E+0, 0.0E+0 ) )
132*     ..
133*     .. Local Scalars ..
134      REAL               SFMIN
135      COMPLEX            TEMP
136      INTEGER            I, IINFO, N1, N2
137*     ..
138*     .. External Functions ..
139      REAL               SLAMCH
140      INTEGER            ICAMAX
141      EXTERNAL           SLAMCH, ICAMAX
142*     ..
143*     .. External Subroutines ..
144      EXTERNAL           CGEMM, CSCAL, CLASWP, CTRSM, XERBLA
145*     ..
146*     .. Intrinsic Functions ..
147      INTRINSIC          MAX, MIN
148*     ..
149*     .. Executable Statements ..
150*
151*     Test the input parameters
152*
153      INFO = 0
154      IF( M.LT.0 ) THEN
155         INFO = -1
156      ELSE IF( N.LT.0 ) THEN
157         INFO = -2
158      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
159         INFO = -4
160      END IF
161      IF( INFO.NE.0 ) THEN
162         CALL XERBLA( 'CGETRF2', -INFO )
163         RETURN
164      END IF
165*
166*     Quick return if possible
167*
168      IF( M.EQ.0 .OR. N.EQ.0 )
169     $   RETURN
170
171      IF ( M.EQ.1 ) THEN
172*
173*        Use unblocked code for one row case
174*        Just need to handle IPIV and INFO
175*
176         IPIV( 1 ) = 1
177         IF ( A(1,1).EQ.ZERO )
178     $      INFO = 1
179*
180      ELSE IF( N.EQ.1 ) THEN
181*
182*        Use unblocked code for one column case
183*
184*
185*        Compute machine safe minimum
186*
187         SFMIN = SLAMCH('S')
188*
189*        Find pivot and test for singularity
190*
191         I = ICAMAX( M, A( 1, 1 ), 1 )
192         IPIV( 1 ) = I
193         IF( A( I, 1 ).NE.ZERO ) THEN
194*
195*           Apply the interchange
196*
197            IF( I.NE.1 ) THEN
198               TEMP = A( 1, 1 )
199               A( 1, 1 ) = A( I, 1 )
200               A( I, 1 ) = TEMP
201            END IF
202*
203*           Compute elements 2:M of the column
204*
205            IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN
206               CALL CSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 )
207            ELSE
208               DO 10 I = 1, M-1
209                  A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 )
210   10          CONTINUE
211            END IF
212*
213         ELSE
214            INFO = 1
215         END IF
216*
217      ELSE
218*
219*        Use recursive code
220*
221         N1 = MIN( M, N ) / 2
222         N2 = N-N1
223*
224*               [ A11 ]
225*        Factor [ --- ]
226*               [ A21 ]
227*
228         CALL CGETRF2( M, N1, A, LDA, IPIV, IINFO )
229
230         IF ( INFO.EQ.0 .AND. IINFO.GT.0 )
231     $      INFO = IINFO
232*
233*                              [ A12 ]
234*        Apply interchanges to [ --- ]
235*                              [ A22 ]
236*
237         CALL CLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 )
238*
239*        Solve A12
240*
241         CALL CTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA,
242     $               A( 1, N1+1 ), LDA )
243*
244*        Update A22
245*
246         CALL CGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA,
247     $               A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA )
248*
249*        Factor A22
250*
251         CALL CGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ),
252     $                 IINFO )
253*
254*        Adjust INFO and the pivot indices
255*
256         IF ( INFO.EQ.0 .AND. IINFO.GT.0 )
257     $      INFO = IINFO + N1
258         DO 20 I = N1+1, MIN( M, N )
259            IPIV( I ) = IPIV( I ) + N1
260   20    CONTINUE
261*
262*        Apply interchanges to A21
263*
264         CALL CLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 )
265*
266      END IF
267      RETURN
268*
269*     End of CGETRF2
270*
271      END
272