LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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ssysv_aa.f
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1*> \brief <b> SSYSV_AA 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 SSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
22* LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
27* ..
28* .. Array Arguments ..
29* INTEGER IPIV( * )
30* REAL A( LDA, * ), B( LDB, * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SSYSV computes the solution to a real 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*> Aasen's algorithm is used to factor A as
45*> A = U**T * T * U, if UPLO = 'U', or
46*> A = L * T * L**T, if UPLO = 'L',
47*> where U (or L) is a product of permutation and unit upper (lower)
48*> triangular matrices, and T is symmetric tridiagonal. The factored
49*> form of A is then used to solve the system of equations A * X = B.
50*> \endverbatim
51*
52* Arguments:
53* ==========
54*
55*> \param[in] UPLO
56*> \verbatim
57*> UPLO is CHARACTER*1
58*> = 'U': Upper triangle of A is stored;
59*> = 'L': Lower triangle of A is stored.
60*> \endverbatim
61*>
62*> \param[in] N
63*> \verbatim
64*> N is INTEGER
65*> The number of linear equations, i.e., the order of the
66*> matrix A. N >= 0.
67*> \endverbatim
68*>
69*> \param[in] NRHS
70*> \verbatim
71*> NRHS is INTEGER
72*> The number of right hand sides, i.e., the number of columns
73*> of the matrix B. NRHS >= 0.
74*> \endverbatim
75*>
76*> \param[in,out] A
77*> \verbatim
78*> A is REAL array, dimension (LDA,N)
79*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
80*> N-by-N upper triangular part of A contains the upper
81*> triangular part of the matrix A, and the strictly lower
82*> triangular part of A is not referenced. If UPLO = 'L', the
83*> leading N-by-N lower triangular part of A contains the lower
84*> triangular part of the matrix A, and the strictly upper
85*> triangular part of A is not referenced.
86*>
87*> On exit, if INFO = 0, the tridiagonal matrix T and the
88*> multipliers used to obtain the factor U or L from the
89*> factorization A = U**T*T*U or A = L*T*L**T as computed by
90*> SSYTRF.
91*> \endverbatim
92*>
93*> \param[in] LDA
94*> \verbatim
95*> LDA is INTEGER
96*> The leading dimension of the array A. LDA >= max(1,N).
97*> \endverbatim
98*>
99*> \param[out] IPIV
100*> \verbatim
101*> IPIV is INTEGER array, dimension (N)
102*> On exit, it contains the details of the interchanges, i.e.,
103*> the row and column k of A were interchanged with the
104*> row and column IPIV(k).
105*> \endverbatim
106*>
107*> \param[in,out] B
108*> \verbatim
109*> B is REAL array, dimension (LDB,NRHS)
110*> On entry, the N-by-NRHS right hand side matrix B.
111*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
112*> \endverbatim
113*>
114*> \param[in] LDB
115*> \verbatim
116*> LDB is INTEGER
117*> The leading dimension of the array B. LDB >= max(1,N).
118*> \endverbatim
119*>
120*> \param[out] WORK
121*> \verbatim
122*> WORK is REAL array, dimension (MAX(1,LWORK))
123*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
124*> \endverbatim
125*>
126*> \param[in] LWORK
127*> \verbatim
128*> LWORK is INTEGER
129*> The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for
130*> the best performance, LWORK >= MAX(1,N*NB), where NB is
131*> the optimal blocksize for SSYTRF_AA.
132*>
133*> If LWORK = -1, then a workspace query is assumed; the routine
134*> only calculates the optimal size of the WORK array, returns
135*> this value as the first entry of the WORK array, and no error
136*> message related to LWORK is issued by XERBLA.
137*> \endverbatim
138*>
139*> \param[out] INFO
140*> \verbatim
141*> INFO is INTEGER
142*> = 0: successful exit
143*> < 0: if INFO = -i, the i-th argument had an illegal value
144*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
145*> has been completed, but the block diagonal matrix D is
146*> exactly singular, so the solution could not be computed.
147*> \endverbatim
148*
149* Authors:
150* ========
151*
152*> \author Univ. of Tennessee
153*> \author Univ. of California Berkeley
154*> \author Univ. of Colorado Denver
155*> \author NAG Ltd.
156*
157*> \ingroup hesv_aa
158*
159* =====================================================================
160 SUBROUTINE ssysv_aa( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
161 \$ LWORK, INFO )
162*
163* -- LAPACK driver routine --
164* -- LAPACK is a software package provided by Univ. of Tennessee, --
165* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167* .. Scalar Arguments ..
168 CHARACTER UPLO
169 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
170* ..
171* .. Array Arguments ..
172 INTEGER IPIV( * )
173 REAL A( LDA, * ), B( LDB, * ), WORK( * )
174* ..
175*
176* =====================================================================
177*
178* .. Local Scalars ..
179 LOGICAL LQUERY
180 INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
181* ..
182* .. External Functions ..
183 LOGICAL LSAME
184 REAL SROUNDUP_LWORK
185 EXTERNAL lsame, sroundup_lwork
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla, ssytrs_aa, ssytrf_aa
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max
192* ..
193* .. Executable Statements ..
194*
195* Test the input parameters.
196*
197 info = 0
198 lquery = ( lwork.EQ.-1 )
199 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
200 info = -1
201 ELSE IF( n.LT.0 ) THEN
202 info = -2
203 ELSE IF( nrhs.LT.0 ) THEN
204 info = -3
205 ELSE IF( lda.LT.max( 1, n ) ) THEN
206 info = -5
207 ELSE IF( ldb.LT.max( 1, n ) ) THEN
208 info = -8
209 ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
210 info = -10
211 END IF
212*
213 IF( info.EQ.0 ) THEN
214 CALL ssytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
215 lwkopt_sytrf = int( work(1) )
216 CALL ssytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
217 \$ -1, info )
218 lwkopt_sytrs = int( work(1) )
219 lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
220 work( 1 ) = sroundup_lwork(lwkopt)
221 END IF
222*
223 IF( info.NE.0 ) THEN
224 CALL xerbla( 'SSYSV_AA', -info )
225 RETURN
226 ELSE IF( lquery ) THEN
227 RETURN
228 END IF
229*
230* Compute the factorization A = U**T*T*U or A = L*T*L**T.
231*
232 CALL ssytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
233 IF( info.EQ.0 ) THEN
234*
235* Solve the system A*X = B, overwriting B with X.
236*
237 CALL ssytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
238 \$ lwork, info )
239*
240 END IF
241*
242 work( 1 ) = sroundup_lwork(lwkopt)
243*
244 RETURN
245*
246* End of SSYSV_AA
247*
248 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssysv_aa(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
Definition ssysv_aa.f:162
subroutine ssytrf_aa(uplo, n, a, lda, ipiv, work, lwork, info)
SSYTRF_AA
Definition ssytrf_aa.f:132
subroutine ssytrs_aa(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYTRS_AA
Definition ssytrs_aa.f:131