LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssytrs_aa()

 subroutine ssytrs_aa ( character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info )

SSYTRS_AA

Purpose:
``` SSYTRS_AA solves a system of linear equations A*X = B with a real
symmetric matrix A using the factorization A = U**T*T*U or
A = L*T*L**T computed by SSYTRF_AA.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U**T*T*U; = 'L': Lower triangular, form is A = L*T*L**T.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) Details of factors computed by SSYTRF_AA.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges as computed by SSYTRF_AA.``` [in,out] B ``` B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] WORK ` WORK is REAL array, dimension (MAX(1,LWORK))` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,3*N-2).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 129 of file ssytrs_aa.f.

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 REAL SROUNDUP_LWORK
159 EXTERNAL lsame, sroundup_lwork
160* ..
161* .. External Subroutines ..
162 EXTERNAL sgtsv, sswap, slacpy, strsm, xerbla
163* ..
164* .. Intrinsic Functions ..
165 INTRINSIC max
166* ..
167* .. Executable Statements ..
168*
169 info = 0
170 upper = lsame( uplo, 'U' )
171 lquery = ( lwork.EQ.-1 )
172 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
173 info = -1
174 ELSE IF( n.LT.0 ) THEN
175 info = -2
176 ELSE IF( nrhs.LT.0 ) THEN
177 info = -3
178 ELSE IF( lda.LT.max( 1, n ) ) THEN
179 info = -5
180 ELSE IF( ldb.LT.max( 1, n ) ) THEN
181 info = -8
182 ELSE IF( lwork.LT.max( 1, 3*n-2 ) .AND. .NOT.lquery ) THEN
183 info = -10
184 END IF
185 IF( info.NE.0 ) THEN
186 CALL xerbla( 'SSYTRS_AA', -info )
187 RETURN
188 ELSE IF( lquery ) THEN
189 lwkopt = (3*n-2)
190 work( 1 ) = sroundup_lwork(lwkopt)
191 RETURN
192 END IF
193*
194* Quick return if possible
195*
196 IF( n.EQ.0 .OR. nrhs.EQ.0 )
197 \$ RETURN
198*
199 IF( upper ) THEN
200*
201* Solve A*X = B, where A = U**T*T*U.
202*
203* 1) Forward substitution with U**T
204*
205 IF( n.GT.1 ) THEN
206*
207* Pivot, P**T * B -> B
208*
209 k = 1
210 DO WHILE ( k.LE.n )
211 kp = ipiv( k )
212 IF( kp.NE.k )
213 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
214 k = k + 1
215 END DO
216*
217* Compute U**T \ B -> B [ (U**T \P**T * B) ]
218*
219 CALL strsm( 'L', 'U', 'T', 'U', n-1, nrhs, one, a( 1, 2 ),
220 \$ lda, b( 2, 1 ), ldb)
221 END IF
222*
223* 2) Solve with triangular matrix T
224*
225* Compute T \ B -> B [ T \ (U**T \P**T * B) ]
226*
227 CALL slacpy( 'F', 1, n, a(1, 1), lda+1, work(n), 1)
228 IF( n.GT.1 ) THEN
229 CALL slacpy( 'F', 1, n-1, a(1, 2), lda+1, work(1), 1)
230 CALL slacpy( 'F', 1, n-1, a(1, 2), lda+1, work(2*n), 1)
231 END IF
232 CALL sgtsv(n, nrhs, work(1), work(n), work(2*n), b, ldb,
233 \$ info)
234*
235* 3) Backward substitution with U
236*
237 IF( n.GT.1 ) THEN
238*
239*
240* Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ]
241*
242 CALL strsm( 'L', 'U', 'N', 'U', n-1, nrhs, one, a( 1, 2 ),
243 \$ lda, b(2, 1), ldb)
244*
245* Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
246*
247 k = n
248 DO WHILE ( k.GE.1 )
249 kp = ipiv( k )
250 IF( kp.NE.k )
251 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
252 k = k - 1
253 END DO
254 END IF
255*
256 ELSE
257*
258* Solve A*X = B, where A = L*T*L**T.
259*
260* 1) Forward substitution with L
261*
262 IF( n.GT.1 ) THEN
263*
264* Pivot, P**T * B -> B
265*
266 k = 1
267 DO WHILE ( k.LE.n )
268 kp = ipiv( k )
269 IF( kp.NE.k )
270 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
271 k = k + 1
272 END DO
273*
274* Compute L \ B -> B [ (L \P**T * B) ]
275*
276 CALL strsm( 'L', 'L', 'N', 'U', n-1, nrhs, one, a( 2, 1),
277 \$ lda, b(2, 1), ldb)
278 END IF
279*
280* 2) Solve with triangular matrix T
281*
282* Compute T \ B -> B [ T \ (L \P**T * B) ]
283*
284 CALL slacpy( 'F', 1, n, a(1, 1), lda+1, work(n), 1)
285 IF( n.GT.1 ) THEN
286 CALL slacpy( 'F', 1, n-1, a(2, 1), lda+1, work(1), 1)
287 CALL slacpy( 'F', 1, n-1, a(2, 1), lda+1, work(2*n), 1)
288 END IF
289 CALL sgtsv(n, nrhs, work(1), work(n), work(2*n), b, ldb,
290 \$ info)
291*
292* 3) Backward substitution with L**T
293*
294 IF( n.GT.1 ) THEN
295*
296* Compute L**T \ B -> B [ L**T \ (T \ (L \P**T * B) ) ]
297*
298 CALL strsm( 'L', 'L', 'T', 'U', n-1, nrhs, one, a( 2, 1 ),
299 \$ lda, b( 2, 1 ), ldb)
300*
301* Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
302*
303 k = n
304 DO WHILE ( k.GE.1 )
305 kp = ipiv( k )
306 IF( kp.NE.k )
307 \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
308 k = k - 1
309 END DO
310 END IF
311*
312 END IF
313*
314 RETURN
315*
316* End of SSYTRS_AA
317*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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 slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
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
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