LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 recursive subroutine cgetrf2 ( integer M, integer N, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO )

CGETRF2

Purpose:
``` CGETRF2 computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.

The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).

This is the recursive version of the algorithm. It divides
the matrix into four submatrices:

[  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = min(m,n)/2
[  A21 | A22  ]       n2 = n-n1

[ A11 ]
The subroutine calls itself to factor [ --- ],
[ A12 ]
[ A12 ]
do the swaps on [ --- ], solve A12, update A22,
[ A22 ]

then calls itself to factor A22 and do the swaps on A21.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [out] IPIV ``` IPIV is INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.```
Date
June 2016

Definition at line 115 of file cgetrf2.f.

115 *
116 * -- LAPACK computational routine (version 3.6.1) --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 * June 2016
120 *
121 * .. Scalar Arguments ..
122  INTEGER info, lda, m, n
123 * ..
124 * .. Array Arguments ..
125  INTEGER ipiv( * )
126  COMPLEX a( lda, * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  COMPLEX one, zero
133  parameter ( one = ( 1.0e+0, 0.0e+0 ),
134  \$ zero = ( 0.0e+0, 0.0e+0 ) )
135 * ..
136 * .. Local Scalars ..
137  REAL sfmin
138  COMPLEX temp
139  INTEGER i, iinfo, n1, n2
140 * ..
141 * .. External Functions ..
142  REAL slamch
143  INTEGER icamax
144  EXTERNAL slamch, icamax
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL cgemm, cscal, claswp, ctrsm, xerbla
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC max, min
151 * ..
152 * .. Executable Statements ..
153 *
154 * Test the input parameters
155 *
156  info = 0
157  IF( m.LT.0 ) THEN
158  info = -1
159  ELSE IF( n.LT.0 ) THEN
160  info = -2
161  ELSE IF( lda.LT.max( 1, m ) ) THEN
162  info = -4
163  END IF
164  IF( info.NE.0 ) THEN
165  CALL xerbla( 'CGETRF2', -info )
166  RETURN
167  END IF
168 *
169 * Quick return if possible
170 *
171  IF( m.EQ.0 .OR. n.EQ.0 )
172  \$ RETURN
173
174  IF ( m.EQ.1 ) THEN
175 *
176 * Use unblocked code for one row case
177 * Just need to handle IPIV and INFO
178 *
179  ipiv( 1 ) = 1
180  IF ( a(1,1).EQ.zero )
181  \$ info = 1
182 *
183  ELSE IF( n.EQ.1 ) THEN
184 *
185 * Use unblocked code for one column case
186 *
187 *
188 * Compute machine safe minimum
189 *
190  sfmin = slamch('S')
191 *
192 * Find pivot and test for singularity
193 *
194  i = icamax( m, a( 1, 1 ), 1 )
195  ipiv( 1 ) = i
196  IF( a( i, 1 ).NE.zero ) THEN
197 *
198 * Apply the interchange
199 *
200  IF( i.NE.1 ) THEN
201  temp = a( 1, 1 )
202  a( 1, 1 ) = a( i, 1 )
203  a( i, 1 ) = temp
204  END IF
205 *
206 * Compute elements 2:M of the column
207 *
208  IF( abs(a( 1, 1 )) .GE. sfmin ) THEN
209  CALL cscal( m-1, one / a( 1, 1 ), a( 2, 1 ), 1 )
210  ELSE
211  DO 10 i = 1, m-1
212  a( 1+i, 1 ) = a( 1+i, 1 ) / a( 1, 1 )
213  10 CONTINUE
214  END IF
215 *
216  ELSE
217  info = 1
218  END IF
219 *
220  ELSE
221 *
222 * Use recursive code
223 *
224  n1 = min( m, n ) / 2
225  n2 = n-n1
226 *
227 * [ A11 ]
228 * Factor [ --- ]
229 * [ A21 ]
230 *
231  CALL cgetrf2( m, n1, a, lda, ipiv, iinfo )
232
233  IF ( info.EQ.0 .AND. iinfo.GT.0 )
234  \$ info = iinfo
235 *
236 * [ A12 ]
237 * Apply interchanges to [ --- ]
238 * [ A22 ]
239 *
240  CALL claswp( n2, a( 1, n1+1 ), lda, 1, n1, ipiv, 1 )
241 *
242 * Solve A12
243 *
244  CALL ctrsm( 'L', 'L', 'N', 'U', n1, n2, one, a, lda,
245  \$ a( 1, n1+1 ), lda )
246 *
247 * Update A22
248 *
249  CALL cgemm( 'N', 'N', m-n1, n2, n1, -one, a( n1+1, 1 ), lda,
250  \$ a( 1, n1+1 ), lda, one, a( n1+1, n1+1 ), lda )
251 *
252 * Factor A22
253 *
254  CALL cgetrf2( m-n1, n2, a( n1+1, n1+1 ), lda, ipiv( n1+1 ),
255  \$ iinfo )
256 *
257 * Adjust INFO and the pivot indices
258 *
259  IF ( info.EQ.0 .AND. iinfo.GT.0 )
260  \$ info = iinfo + n1
261  DO 20 i = n1+1, min( m, n )
262  ipiv( i ) = ipiv( i ) + n1
263  20 CONTINUE
264 *
265 * Apply interchanges to A21
266 *
267  CALL claswp( n1, a( 1, 1 ), lda, n1+1, min( m, n), ipiv, 1 )
268 *
269  END IF
270  RETURN
271 *
272 * End of CGETRF2
273 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:54
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:182
recursive subroutine cgetrf2(M, N, A, LDA, IPIV, INFO)
CGETRF2
Definition: cgetrf2.f:115
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
subroutine claswp(N, A, LDA, K1, K2, IPIV, INCX)
CLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: claswp.f:116

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