LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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csysv.f
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1*> \brief <b> CSYSV computes the solution to system of linear equations A * X = B for SY matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
22* LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, LDA, LDB, LWORK, N, NRHS
27* ..
28* .. Array Arguments ..
29* INTEGER IPIV( * )
30* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CSYSV computes the solution to a complex system of linear equations
40*> A * X = B,
41*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
42*> matrices.
43*>
44*> The diagonal pivoting method is used to factor A as
45*> A = U * D * U**T, if UPLO = 'U', or
46*> A = L * D * L**T, if UPLO = 'L',
47*> where U (or L) is a product of permutation and unit upper (lower)
48*> triangular matrices, and D is symmetric and block diagonal with
49*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
50*> used to solve the system of equations A * X = B.
51*> \endverbatim
52*
53* Arguments:
54* ==========
55*
56*> \param[in] UPLO
57*> \verbatim
58*> UPLO is CHARACTER*1
59*> = 'U': Upper triangle of A is stored;
60*> = 'L': Lower triangle of A is stored.
61*> \endverbatim
62*>
63*> \param[in] N
64*> \verbatim
65*> N is INTEGER
66*> The number of linear equations, i.e., the order of the
67*> matrix A. N >= 0.
68*> \endverbatim
69*>
70*> \param[in] NRHS
71*> \verbatim
72*> NRHS is INTEGER
73*> The number of right hand sides, i.e., the number of columns
74*> of the matrix B. NRHS >= 0.
75*> \endverbatim
76*>
77*> \param[in,out] A
78*> \verbatim
79*> A is COMPLEX array, dimension (LDA,N)
80*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
81*> N-by-N upper triangular part of A contains the upper
82*> triangular part of the matrix A, and the strictly lower
83*> triangular part of A is not referenced. If UPLO = 'L', the
84*> leading N-by-N lower triangular part of A contains the lower
85*> triangular part of the matrix A, and the strictly upper
86*> triangular part of A is not referenced.
87*>
88*> On exit, if INFO = 0, the block diagonal matrix D and the
89*> multipliers used to obtain the factor U or L from the
90*> factorization A = U*D*U**T or A = L*D*L**T as computed by
91*> CSYTRF.
92*> \endverbatim
93*>
94*> \param[in] LDA
95*> \verbatim
96*> LDA is INTEGER
97*> The leading dimension of the array A. LDA >= max(1,N).
98*> \endverbatim
99*>
100*> \param[out] IPIV
101*> \verbatim
102*> IPIV is INTEGER array, dimension (N)
103*> Details of the interchanges and the block structure of D, as
104*> determined by CSYTRF. If IPIV(k) > 0, then rows and columns
105*> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
106*> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
107*> then rows and columns k-1 and -IPIV(k) were interchanged and
108*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
109*> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
110*> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
111*> diagonal block.
112*> \endverbatim
113*>
114*> \param[in,out] B
115*> \verbatim
116*> B is COMPLEX array, dimension (LDB,NRHS)
117*> On entry, the N-by-NRHS right hand side matrix B.
118*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
119*> \endverbatim
120*>
121*> \param[in] LDB
122*> \verbatim
123*> LDB is INTEGER
124*> The leading dimension of the array B. LDB >= max(1,N).
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
130*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
131*> \endverbatim
132*>
133*> \param[in] LWORK
134*> \verbatim
135*> LWORK is INTEGER
136*> The length of WORK. LWORK >= 1, and for best performance
137*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
138*> CSYTRF.
139*> for LWORK < N, TRS will be done with Level BLAS 2
140*> for LWORK >= N, TRS will be done with Level BLAS 3
141*>
142*> If LWORK = -1, then a workspace query is assumed; the routine
143*> only calculates the optimal size of the WORK array, returns
144*> this value as the first entry of the WORK array, and no error
145*> message related to LWORK is issued by XERBLA.
146*> \endverbatim
147*>
148*> \param[out] INFO
149*> \verbatim
150*> INFO is INTEGER
151*> = 0: successful exit
152*> < 0: if INFO = -i, the i-th argument had an illegal value
153*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
154*> has been completed, but the block diagonal matrix D is
155*> exactly singular, so the solution could not be computed.
156*> \endverbatim
157*
158* Authors:
159* ========
160*
161*> \author Univ. of Tennessee
162*> \author Univ. of California Berkeley
163*> \author Univ. of Colorado Denver
164*> \author NAG Ltd.
165*
166*> \ingroup complexSYsolve
167*
168* =====================================================================
169 SUBROUTINE csysv( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
170 \$ LWORK, INFO )
171*
172* -- LAPACK driver routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 CHARACTER UPLO
178 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
179* ..
180* .. Array Arguments ..
181 INTEGER IPIV( * )
182 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
183* ..
184*
185* =====================================================================
186*
187* .. Local Scalars ..
188 LOGICAL LQUERY
189 INTEGER LWKOPT
190* ..
191* .. External Functions ..
192 LOGICAL LSAME
193 EXTERNAL lsame
194* ..
195* .. External Subroutines ..
196 EXTERNAL xerbla, csytrf, csytrs, csytrs2
197* ..
198* .. Intrinsic Functions ..
199 INTRINSIC max
200* ..
201* .. Executable Statements ..
202*
203* Test the input parameters.
204*
205 info = 0
206 lquery = ( lwork.EQ.-1 )
207 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
208 info = -1
209 ELSE IF( n.LT.0 ) THEN
210 info = -2
211 ELSE IF( nrhs.LT.0 ) THEN
212 info = -3
213 ELSE IF( lda.LT.max( 1, n ) ) THEN
214 info = -5
215 ELSE IF( ldb.LT.max( 1, n ) ) THEN
216 info = -8
217 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
218 info = -10
219 END IF
220*
221 IF( info.EQ.0 ) THEN
222 IF( n.EQ.0 ) THEN
223 lwkopt = 1
224 ELSE
225 CALL csytrf( uplo, n, a, lda, ipiv, work, -1, info )
226 lwkopt = int( work( 1 ) )
227 END IF
228 work( 1 ) = lwkopt
229 END IF
230*
231 IF( info.NE.0 ) THEN
232 CALL xerbla( 'CSYSV ', -info )
233 RETURN
234 ELSE IF( lquery ) THEN
235 RETURN
236 END IF
237*
238* Compute the factorization A = U*D*U**T or A = L*D*L**T.
239*
240 CALL csytrf( uplo, n, a, lda, ipiv, work, lwork, info )
241 IF( info.EQ.0 ) THEN
242*
243* Solve the system A*X = B, overwriting B with X.
244*
245 IF ( lwork.LT.n ) THEN
246*
247* Solve with TRS ( Use Level BLAS 2)
248*
249 CALL csytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
250*
251 ELSE
252*
253* Solve with TRS2 ( Use Level BLAS 3)
254*
255 CALL csytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
256*
257 END IF
258*
259 END IF
260*
261 work( 1 ) = lwkopt
262*
263 RETURN
264*
265* End of CSYSV
266*
267 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine csytrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
CSYTRS2
Definition: csytrs2.f:132
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:120
subroutine csytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CSYTRF
Definition: csytrf.f:182
subroutine csysv(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
CSYSV computes the solution to system of linear equations A * X = B for SY matrices
Definition: csysv.f:171