LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dgetc2()

 subroutine dgetc2 ( integer N, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer, dimension( * ) JPIV, integer INFO )

DGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.

Download DGETC2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` DGETC2 computes an LU factorization with complete pivoting of the
n-by-n matrix A. The factorization has the form A = P * L * U * Q,
where P and Q are permutation matrices, L is lower triangular with
unit diagonal elements and U is upper triangular.

This is the Level 2 BLAS algorithm.```
Parameters
 [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is DOUBLE PRECISION array, dimension (LDA, N) On entry, the n-by-n matrix A to be factored. On exit, the factors L and U from the factorization A = P*L*U*Q; the unit diagonal elements of L are not stored. If U(k, k) appears to be less than SMIN, U(k, k) is given the value of SMIN, i.e., giving a nonsingular perturbed system.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] IPIV ``` IPIV is INTEGER array, dimension(N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).``` [out] JPIV ``` JPIV is INTEGER array, dimension(N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).``` [out] INFO ``` INFO is INTEGER = 0: successful exit > 0: if INFO = k, U(k, k) is likely to produce overflow if we try to solve for x in Ax = b. So U is perturbed to avoid the overflow.```
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 110 of file dgetc2.f.

111*
112* -- LAPACK auxiliary routine --
113* -- LAPACK is a software package provided by Univ. of Tennessee, --
114* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115*
116* .. Scalar Arguments ..
117 INTEGER INFO, LDA, N
118* ..
119* .. Array Arguments ..
120 INTEGER IPIV( * ), JPIV( * )
121 DOUBLE PRECISION A( LDA, * )
122* ..
123*
124* =====================================================================
125*
126* .. Parameters ..
127 DOUBLE PRECISION ZERO, ONE
128 parameter( zero = 0.0d+0, one = 1.0d+0 )
129* ..
130* .. Local Scalars ..
131 INTEGER I, IP, IPV, J, JP, JPV
132 DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
133* ..
134* .. External Subroutines ..
135 EXTERNAL dger, dswap, dlabad
136* ..
137* .. External Functions ..
138 DOUBLE PRECISION DLAMCH
139 EXTERNAL dlamch
140* ..
141* .. Intrinsic Functions ..
142 INTRINSIC abs, max
143* ..
144* .. Executable Statements ..
145*
146 info = 0
147*
148* Quick return if possible
149*
150 IF( n.EQ.0 )
151 \$ RETURN
152*
153* Set constants to control overflow
154*
155 eps = dlamch( 'P' )
156 smlnum = dlamch( 'S' ) / eps
157 bignum = one / smlnum
158 CALL dlabad( smlnum, bignum )
159*
160* Handle the case N=1 by itself
161*
162 IF( n.EQ.1 ) THEN
163 ipiv( 1 ) = 1
164 jpiv( 1 ) = 1
165 IF( abs( a( 1, 1 ) ).LT.smlnum ) THEN
166 info = 1
167 a( 1, 1 ) = smlnum
168 END IF
169 RETURN
170 END IF
171*
172* Factorize A using complete pivoting.
173* Set pivots less than SMIN to SMIN.
174*
175 DO 40 i = 1, n - 1
176*
177* Find max element in matrix A
178*
179 xmax = zero
180 DO 20 ip = i, n
181 DO 10 jp = i, n
182 IF( abs( a( ip, jp ) ).GE.xmax ) THEN
183 xmax = abs( a( ip, jp ) )
184 ipv = ip
185 jpv = jp
186 END IF
187 10 CONTINUE
188 20 CONTINUE
189 IF( i.EQ.1 )
190 \$ smin = max( eps*xmax, smlnum )
191*
192* Swap rows
193*
194 IF( ipv.NE.i )
195 \$ CALL dswap( n, a( ipv, 1 ), lda, a( i, 1 ), lda )
196 ipiv( i ) = ipv
197*
198* Swap columns
199*
200 IF( jpv.NE.i )
201 \$ CALL dswap( n, a( 1, jpv ), 1, a( 1, i ), 1 )
202 jpiv( i ) = jpv
203*
204* Check for singularity
205*
206 IF( abs( a( i, i ) ).LT.smin ) THEN
207 info = i
208 a( i, i ) = smin
209 END IF
210 DO 30 j = i + 1, n
211 a( j, i ) = a( j, i ) / a( i, i )
212 30 CONTINUE
213 CALL dger( n-i, n-i, -one, a( i+1, i ), 1, a( i, i+1 ), lda,
214 \$ a( i+1, i+1 ), lda )
215 40 CONTINUE
216*
217 IF( abs( a( n, n ) ).LT.smin ) THEN
218 info = n
219 a( n, n ) = smin
220 END IF
221*
222* Set last pivots to N
223*
224 ipiv( n ) = n
225 jpiv( n ) = n
226*
227 RETURN
228*
229* End of DGETC2
230*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69