LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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cgetrs.f
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1*> \brief \b CGETRS
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CGETRS + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetrs.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetrs.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetrs.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER TRANS
25* INTEGER INFO, LDA, LDB, N, NRHS
26* ..
27* .. Array Arguments ..
28* INTEGER IPIV( * )
29* COMPLEX A( LDA, * ), B( LDB, * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> CGETRS solves a system of linear equations
39*> A * X = B, A**T * X = B, or A**H * X = B
40*> with a general N-by-N matrix A using the LU factorization computed
41*> by CGETRF.
42*> \endverbatim
43*
44* Arguments:
45* ==========
46*
47*> \param[in] TRANS
48*> \verbatim
49*> TRANS is CHARACTER*1
50*> Specifies the form of the system of equations:
51*> = 'N': A * X = B (No transpose)
52*> = 'T': A**T * X = B (Transpose)
53*> = 'C': A**H * X = B (Conjugate transpose)
54*> \endverbatim
55*>
56*> \param[in] N
57*> \verbatim
58*> N is INTEGER
59*> The order of the matrix A. N >= 0.
60*> \endverbatim
61*>
62*> \param[in] NRHS
63*> \verbatim
64*> NRHS is INTEGER
65*> The number of right hand sides, i.e., the number of columns
66*> of the matrix B. NRHS >= 0.
67*> \endverbatim
68*>
69*> \param[in] A
70*> \verbatim
71*> A is COMPLEX array, dimension (LDA,N)
72*> The factors L and U from the factorization A = P*L*U
73*> as computed by CGETRF.
74*> \endverbatim
75*>
76*> \param[in] LDA
77*> \verbatim
78*> LDA is INTEGER
79*> The leading dimension of the array A. LDA >= max(1,N).
80*> \endverbatim
81*>
82*> \param[in] IPIV
83*> \verbatim
84*> IPIV is INTEGER array, dimension (N)
85*> The pivot indices from CGETRF; for 1<=i<=N, row i of the
86*> matrix was interchanged with row IPIV(i).
87*> \endverbatim
88*>
89*> \param[in,out] B
90*> \verbatim
91*> B is COMPLEX array, dimension (LDB,NRHS)
92*> On entry, the right hand side matrix B.
93*> On exit, the solution matrix X.
94*> \endverbatim
95*>
96*> \param[in] LDB
97*> \verbatim
98*> LDB is INTEGER
99*> The leading dimension of the array B. LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] INFO
103*> \verbatim
104*> INFO is INTEGER
105*> = 0: successful exit
106*> < 0: if INFO = -i, the i-th argument had an illegal value
107*> \endverbatim
108*
109* Authors:
110* ========
111*
112*> \author Univ. of Tennessee
113*> \author Univ. of California Berkeley
114*> \author Univ. of Colorado Denver
115*> \author NAG Ltd.
116*
117*> \ingroup complexGEcomputational
118*
119* =====================================================================
120 SUBROUTINE cgetrs( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER TRANS
128 INTEGER INFO, LDA, LDB, N, NRHS
129* ..
130* .. Array Arguments ..
131 INTEGER IPIV( * )
132 COMPLEX A( LDA, * ), B( LDB, * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 COMPLEX ONE
139 parameter( one = ( 1.0e+0, 0.0e+0 ) )
140* ..
141* .. Local Scalars ..
142 LOGICAL NOTRAN
143* ..
144* .. External Functions ..
145 LOGICAL LSAME
146 EXTERNAL lsame
147* ..
148* .. External Subroutines ..
149 EXTERNAL claswp, ctrsm, xerbla
150* ..
151* .. Intrinsic Functions ..
152 INTRINSIC max
153* ..
154* .. Executable Statements ..
155*
156* Test the input parameters.
157*
158 info = 0
159 notran = lsame( trans, 'N' )
160 IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
161 $ lsame( trans, 'C' ) ) THEN
162 info = -1
163 ELSE IF( n.LT.0 ) THEN
164 info = -2
165 ELSE IF( nrhs.LT.0 ) THEN
166 info = -3
167 ELSE IF( lda.LT.max( 1, n ) ) THEN
168 info = -5
169 ELSE IF( ldb.LT.max( 1, n ) ) THEN
170 info = -8
171 END IF
172 IF( info.NE.0 ) THEN
173 CALL xerbla( 'CGETRS', -info )
174 RETURN
175 END IF
176*
177* Quick return if possible
178*
179 IF( n.EQ.0 .OR. nrhs.EQ.0 )
180 $ RETURN
181*
182 IF( notran ) THEN
183*
184* Solve A * X = B.
185*
186* Apply row interchanges to the right hand sides.
187*
188 CALL claswp( nrhs, b, ldb, 1, n, ipiv, 1 )
189*
190* Solve L*X = B, overwriting B with X.
191*
192 CALL ctrsm( 'Left', 'Lower', 'No transpose', 'Unit', n, nrhs,
193 $ one, a, lda, b, ldb )
194*
195* Solve U*X = B, overwriting B with X.
196*
197 CALL ctrsm( 'Left', 'Upper', 'No transpose', 'Non-unit', n,
198 $ nrhs, one, a, lda, b, ldb )
199 ELSE
200*
201* Solve A**T * X = B or A**H * X = B.
202*
203* Solve U**T *X = B or U**H *X = B, overwriting B with X.
204*
205 CALL ctrsm( 'Left', 'Upper', trans, 'Non-unit', n, nrhs, one,
206 $ a, lda, b, ldb )
207*
208* Solve L**T *X = B, or L**H *X = B overwriting B with X.
209*
210 CALL ctrsm( 'Left', 'Lower', trans, 'Unit', n, nrhs, one, a,
211 $ lda, b, ldb )
212*
213* Apply row interchanges to the solution vectors.
214*
215 CALL claswp( nrhs, b, ldb, 1, n, ipiv, -1 )
216 END IF
217*
218 RETURN
219*
220* End of CGETRS
221*
222 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine cgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CGETRS
Definition: cgetrs.f:121
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