LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dsysv_aa_2stage.f
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1*> \brief <b> DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices</b>
2*
3* @generated from SRC/chesv_aa_2stage.f, fortran c -> d, Tue Oct 31 11:22:31 2017
4*
5* =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8* http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download DSYSV_AA_2STAGE + dependencies
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16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsysv_aa_2stage.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20* Definition:
21* ===========
22*
23* SUBROUTINE DSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
24* IPIV, IPIV2, B, LDB, WORK, LWORK,
25* INFO )
26*
27* .. Scalar Arguments ..
28* CHARACTER UPLO
29* INTEGER N, NRHS, LDA, LTB, LDB, LWORK, INFO
30* ..
31* .. Array Arguments ..
32* INTEGER IPIV( * ), IPIV2( * )
33* DOUBLE PRECISION A( LDA, * ), TB( * ), B( LDB, *), WORK( * )
34* ..
35*
36*> \par Purpose:
37* =============
38*>
39*> \verbatim
40*>
41*> DSYSV_AA_2STAGE computes the solution to a real system of
42*> linear equations
43*> A * X = B,
44*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
45*> matrices.
46*>
47*> Aasen's 2-stage algorithm is used to factor A as
48*> A = U**T * T * U, if UPLO = 'U', or
49*> A = L * T * L**T, if UPLO = 'L',
50*> where U (or L) is a product of permutation and unit upper (lower)
51*> triangular matrices, and T is symmetric and band. The matrix T is
52*> then LU-factored with partial pivoting. The factored form of A
53*> is then used to solve the system of equations A * X = B.
54*>
55*> This is the blocked version of the algorithm, calling Level 3 BLAS.
56*> \endverbatim
57*
58* Arguments:
59* ==========
60*
61*> \param[in] UPLO
62*> \verbatim
63*> UPLO is CHARACTER*1
64*> = 'U': Upper triangle of A is stored;
65*> = 'L': Lower triangle of A is stored.
66*> \endverbatim
67*>
68*> \param[in] N
69*> \verbatim
70*> N is INTEGER
71*> The order of the matrix A. N >= 0.
72*> \endverbatim
73*>
74*> \param[in] NRHS
75*> \verbatim
76*> NRHS is INTEGER
77*> The number of right hand sides, i.e., the number of columns
78*> of the matrix B. NRHS >= 0.
79*> \endverbatim
80*>
81*> \param[in,out] A
82*> \verbatim
83*> A is DOUBLE PRECISION array, dimension (LDA,N)
84*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
85*> N-by-N upper triangular part of A contains the upper
86*> triangular part of the matrix A, and the strictly lower
87*> triangular part of A is not referenced. If UPLO = 'L', the
88*> leading N-by-N lower triangular part of A contains the lower
89*> triangular part of the matrix A, and the strictly upper
90*> triangular part of A is not referenced.
91*>
92*> On exit, L is stored below (or above) the subdiaonal blocks,
93*> when UPLO is 'L' (or 'U').
94*> \endverbatim
95*>
96*> \param[in] LDA
97*> \verbatim
98*> LDA is INTEGER
99*> The leading dimension of the array A. LDA >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] TB
103*> \verbatim
104*> TB is DOUBLE PRECISION array, dimension (LTB)
105*> On exit, details of the LU factorization of the band matrix.
106*> \endverbatim
107*>
108*> \param[in] LTB
109*> \verbatim
110*> LTB is INTEGER
111*> The size of the array TB. LTB >= 4*N, internally
112*> used to select NB such that LTB >= (3*NB+1)*N.
113*>
114*> If LTB = -1, then a workspace query is assumed; the
115*> routine only calculates the optimal size of LTB,
116*> returns this value as the first entry of TB, and
117*> no error message related to LTB is issued by XERBLA.
118*> \endverbatim
119*>
120*> \param[out] IPIV
121*> \verbatim
122*> IPIV is INTEGER array, dimension (N)
123*> On exit, it contains the details of the interchanges, i.e.,
124*> the row and column k of A were interchanged with the
125*> row and column IPIV(k).
126*> \endverbatim
127*>
128*> \param[out] IPIV2
129*> \verbatim
130*> IPIV2 is INTEGER array, dimension (N)
131*> On exit, it contains the details of the interchanges, i.e.,
132*> the row and column k of T were interchanged with the
133*> row and column IPIV(k).
134*> \endverbatim
135*>
136*> \param[in,out] B
137*> \verbatim
138*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
139*> On entry, the right hand side matrix B.
140*> On exit, the solution matrix X.
141*> \endverbatim
142*>
143*> \param[in] LDB
144*> \verbatim
145*> LDB is INTEGER
146*> The leading dimension of the array B. LDB >= max(1,N).
147*> \endverbatim
148*>
149*> \param[out] WORK
150*> \verbatim
151*> WORK is DOUBLE PRECISION workspace of size LWORK
152*> \endverbatim
153*>
154*> \param[in] LWORK
155*> \verbatim
156*> LWORK is INTEGER
157*> The size of WORK. LWORK >= N, internally used to select NB
158*> such that LWORK >= N*NB.
159*>
160*> If LWORK = -1, then a workspace query is assumed; the
161*> routine only calculates the optimal size of the WORK array,
162*> returns this value as the first entry of the WORK array, and
163*> no error message related to LWORK is issued by XERBLA.
164*> \endverbatim
165*>
166*> \param[out] INFO
167*> \verbatim
168*> INFO is INTEGER
169*> = 0: successful exit
170*> < 0: if INFO = -i, the i-th argument had an illegal value.
171*> > 0: if INFO = i, band LU factorization failed on i-th column
172*> \endverbatim
173*
174* Authors:
175* ========
176*
177*> \author Univ. of Tennessee
178*> \author Univ. of California Berkeley
179*> \author Univ. of Colorado Denver
180*> \author NAG Ltd.
181*
182*> \ingroup doubleSYsolve
183*
184* =====================================================================
185 SUBROUTINE dsysv_aa_2stage( UPLO, N, NRHS, A, LDA, TB, LTB,
186 $ IPIV, IPIV2, B, LDB, WORK, LWORK,
187 $ INFO )
188*
189* -- LAPACK computational routine --
190* -- LAPACK is a software package provided by Univ. of Tennessee, --
191* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192*
193 IMPLICIT NONE
194*
195* .. Scalar Arguments ..
196 CHARACTER UPLO
197 INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
198* ..
199* .. Array Arguments ..
200 INTEGER IPIV( * ), IPIV2( * )
201 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
202* ..
203*
204* =====================================================================
205*
206* .. Local Scalars ..
207 LOGICAL UPPER, TQUERY, WQUERY
208 INTEGER LWKOPT
209* ..
210* .. External Functions ..
211 LOGICAL LSAME
212 EXTERNAL LSAME
213* ..
214* .. External Subroutines ..
216 $ xerbla
217* ..
218* .. Intrinsic Functions ..
219 INTRINSIC max
220* ..
221* .. Executable Statements ..
222*
223* Test the input parameters.
224*
225 info = 0
226 upper = lsame( uplo, 'U' )
227 wquery = ( lwork.EQ.-1 )
228 tquery = ( ltb.EQ.-1 )
229 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
230 info = -1
231 ELSE IF( n.LT.0 ) THEN
232 info = -2
233 ELSE IF( nrhs.LT.0 ) THEN
234 info = -3
235 ELSE IF( lda.LT.max( 1, n ) ) THEN
236 info = -5
237 ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
238 info = -7
239 ELSE IF( ldb.LT.max( 1, n ) ) THEN
240 info = -11
241 ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
242 info = -13
243 END IF
244*
245 IF( info.EQ.0 ) THEN
246 CALL dsytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
247 $ ipiv2, work, -1, info )
248 lwkopt = int( work(1) )
249 END IF
250*
251 IF( info.NE.0 ) THEN
252 CALL xerbla( 'DSYSV_AA_2STAGE', -info )
253 RETURN
254 ELSE IF( wquery .OR. tquery ) THEN
255 RETURN
256 END IF
257*
258*
259* Compute the factorization A = U**T*T*U or A = L*T*L**T.
260*
261 CALL dsytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
262 $ work, lwork, info )
263 IF( info.EQ.0 ) THEN
264*
265* Solve the system A*X = B, overwriting B with X.
266*
267 CALL dsytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
268 $ ipiv2, b, ldb, info )
269*
270 END IF
271*
272 work( 1 ) = lwkopt
273*
274 RETURN
275*
276* End of DSYSV_AA_2STAGE
277*
278 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dsytrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
DSYTRF_AA_2STAGE
subroutine dsytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
DSYTRS_AA_2STAGE
subroutine dsysv_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, WORK, LWORK, INFO)
DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices