LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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ssytrs_aa.f
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1*> \brief \b SSYTRS_AA
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrs_aa.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
22* WORK, 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*> SSYTRS_AA solves a system of linear equations A*X = B with a real
40*> symmetric matrix A using the factorization A = U**T*T*U or
41*> A = L*T*L**T computed by SSYTRF_AA.
42*> \endverbatim
43*
44* Arguments:
45* ==========
46*
47*> \param[in] UPLO
48*> \verbatim
49*> UPLO is CHARACTER*1
50*> Specifies whether the details of the factorization are stored
51*> as an upper or lower triangular matrix.
52*> = 'U': Upper triangular, form is A = U**T*T*U;
53*> = 'L': Lower triangular, form is A = L*T*L**T.
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 REAL array, dimension (LDA,N)
72*> Details of factors computed by SSYTRF_AA.
73*> \endverbatim
74*>
75*> \param[in] LDA
76*> \verbatim
77*> LDA is INTEGER
78*> The leading dimension of the array A. LDA >= max(1,N).
79*> \endverbatim
80*>
81*> \param[in] IPIV
82*> \verbatim
83*> IPIV is INTEGER array, dimension (N)
84*> Details of the interchanges as computed by SSYTRF_AA.
85*> \endverbatim
86*>
87*> \param[in,out] B
88*> \verbatim
89*> B is REAL array, dimension (LDB,NRHS)
90*> On entry, the right hand side matrix B.
91*> On exit, the solution matrix X.
92*> \endverbatim
93*>
94*> \param[in] LDB
95*> \verbatim
96*> LDB is INTEGER
97*> The leading dimension of the array B. LDB >= max(1,N).
98*> \endverbatim
99*>
100*> \param[out] WORK
101*> \verbatim
102*> WORK is REAL array, dimension (MAX(1,LWORK))
103*> \endverbatim
104*>
105*> \param[in] LWORK
106*> \verbatim
107*> LWORK is INTEGER
108*> The dimension of the array WORK. LWORK >= max(1,3*N-2).
109*> \endverbatim
110*>
111*> \param[out] INFO
112*> \verbatim
113*> INFO is INTEGER
114*> = 0: successful exit
115*> < 0: if INFO = -i, the i-th argument had an illegal value
116*> \endverbatim
117*
118* Authors:
119* ========
120*
121*> \author Univ. of Tennessee
122*> \author Univ. of California Berkeley
123*> \author Univ. of Colorado Denver
124*> \author NAG Ltd.
125*
126*> \ingroup realSYcomputational
127*
128* =====================================================================
129 SUBROUTINE ssytrs_aa( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
130 \$ WORK, LWORK, INFO )
131*
132* -- LAPACK computational routine --
133* -- LAPACK is a software package provided by Univ. of Tennessee, --
134* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135*
136 IMPLICIT NONE
137*
138* .. Scalar Arguments ..
139 CHARACTER UPLO
140 INTEGER N, NRHS, LDA, LDB, LWORK, INFO
141* ..
142* .. Array Arguments ..
143 INTEGER IPIV( * )
144 REAL A( LDA, * ), B( LDB, * ), WORK( * )
145* ..
146*
147* =====================================================================
148*
149 REAL ONE
150 parameter( one = 1.0e+0 )
151* ..
152* .. Local Scalars ..
153 LOGICAL LQUERY, UPPER
154 INTEGER K, KP, LWKOPT
155* ..
156* .. External Functions ..
157 LOGICAL LSAME
158 EXTERNAL lsame
159* ..
160* .. External Subroutines ..
161 EXTERNAL sgtsv, sswap, slacpy, strsm, xerbla
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC max
165* ..
166* .. Executable Statements ..
167*
168 info = 0
169 upper = lsame( uplo, 'U' )
170 lquery = ( lwork.EQ.-1 )
171 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
172 info = -1
173 ELSE IF( n.LT.0 ) THEN
174 info = -2
175 ELSE IF( nrhs.LT.0 ) THEN
176 info = -3
177 ELSE IF( lda.LT.max( 1, n ) ) THEN
178 info = -5
179 ELSE IF( ldb.LT.max( 1, n ) ) THEN
180 info = -8
181 ELSE IF( lwork.LT.max( 1, 3*n-2 ) .AND. .NOT.lquery ) THEN
182 info = -10
183 END IF
184 IF( info.NE.0 ) THEN
185 CALL xerbla( 'SSYTRS_AA', -info )
186 RETURN
187 ELSE IF( lquery ) THEN
188 lwkopt = (3*n-2)
189 work( 1 ) = lwkopt
190 RETURN
191 END IF
192*
193* Quick return if possible
194*
195 IF( n.EQ.0 .OR. nrhs.EQ.0 )
196 \$ RETURN
197*
198 IF( upper ) THEN
199*
200* Solve A*X = B, where A = U**T*T*U.
201*
202* 1) Forward substitution with U**T
203*
204 IF( n.GT.1 ) THEN
205*
206* Pivot, P**T * B -> B
207*
208 k = 1
209 DO WHILE ( k.LE.n )
210 kp = ipiv( k )
211 IF( kp.NE.k )
212 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
213 k = k + 1
214 END DO
215*
216* Compute U**T \ B -> B [ (U**T \P**T * B) ]
217*
218 CALL strsm( 'L', 'U', 'T', 'U', n-1, nrhs, one, a( 1, 2 ),
219 \$ lda, b( 2, 1 ), ldb)
220 END IF
221*
222* 2) Solve with triangular matrix T
223*
224* Compute T \ B -> B [ T \ (U**T \P**T * B) ]
225*
226 CALL slacpy( 'F', 1, n, a(1, 1), lda+1, work(n), 1)
227 IF( n.GT.1 ) THEN
228 CALL slacpy( 'F', 1, n-1, a(1, 2), lda+1, work(1), 1)
229 CALL slacpy( 'F', 1, n-1, a(1, 2), lda+1, work(2*n), 1)
230 END IF
231 CALL sgtsv(n, nrhs, work(1), work(n), work(2*n), b, ldb,
232 \$ info)
233*
234* 3) Backward substitution with U
235*
236 IF( n.GT.1 ) THEN
237*
238*
239* Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ]
240*
241 CALL strsm( 'L', 'U', 'N', 'U', n-1, nrhs, one, a( 1, 2 ),
242 \$ lda, b(2, 1), ldb)
243*
244* Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
245*
246 k = n
247 DO WHILE ( k.GE.1 )
248 kp = ipiv( k )
249 IF( kp.NE.k )
250 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
251 k = k - 1
252 END DO
253 END IF
254*
255 ELSE
256*
257* Solve A*X = B, where A = L*T*L**T.
258*
259* 1) Forward substitution with L
260*
261 IF( n.GT.1 ) THEN
262*
263* Pivot, P**T * B -> B
264*
265 k = 1
266 DO WHILE ( k.LE.n )
267 kp = ipiv( k )
268 IF( kp.NE.k )
269 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
270 k = k + 1
271 END DO
272*
273* Compute L \ B -> B [ (L \P**T * B) ]
274*
275 CALL strsm( 'L', 'L', 'N', 'U', n-1, nrhs, one, a( 2, 1),
276 \$ lda, b(2, 1), ldb)
277 END IF
278*
279* 2) Solve with triangular matrix T
280*
281* Compute T \ B -> B [ T \ (L \P**T * B) ]
282*
283 CALL slacpy( 'F', 1, n, a(1, 1), lda+1, work(n), 1)
284 IF( n.GT.1 ) THEN
285 CALL slacpy( 'F', 1, n-1, a(2, 1), lda+1, work(1), 1)
286 CALL slacpy( 'F', 1, n-1, a(2, 1), lda+1, work(2*n), 1)
287 END IF
288 CALL sgtsv(n, nrhs, work(1), work(n), work(2*n), b, ldb,
289 \$ info)
290*
291* 3) Backward substitution with L**T
292*
293 IF( n.GT.1 ) THEN
294*
295* Compute L**T \ B -> B [ L**T \ (T \ (L \P**T * B) ) ]
296*
297 CALL strsm( 'L', 'L', 'T', 'U', n-1, nrhs, one, a( 2, 1 ),
298 \$ lda, b( 2, 1 ), ldb)
299*
300* Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
301*
302 k = n
303 DO WHILE ( k.GE.1 )
304 kp = ipiv( k )
305 IF( kp.NE.k )
306 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
307 k = k - 1
308 END DO
309 END IF
310*
311 END IF
312*
313 RETURN
314*
315* End of SSYTRS_AA
316*
317 END
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgtsv(N, NRHS, DL, D, DU, B, LDB, INFO)
SGTSV computes the solution to system of linear equations A * X = B for GT matrices
Definition: sgtsv.f:127
subroutine ssytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYTRS_AA
Definition: ssytrs_aa.f:131
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181