LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ chetrs_aa_2stage()

 subroutine chetrs_aa_2stage ( character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info )

CHETRS_AA_2STAGE

Purpose:
``` CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real
hermitian matrix A using the factorization A = U**T*T*U or
A = L*T*L**T computed by CHETRF_AA_2STAGE.```
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 COMPLEX array, dimension (LDA,N) Details of factors computed by CHETRF_AA_2STAGE.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] TB ``` TB is COMPLEX array, dimension (LTB) Details of factors computed by CHETRF_AA_2STAGE.``` [in] LTB ``` LTB is INTEGER The size of the array TB. LTB >= 4*N.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges as computed by CHETRF_AA_2STAGE.``` [in] IPIV2 ``` IPIV2 is INTEGER array, dimension (N) Details of the interchanges as computed by CHETRF_AA_2STAGE.``` [in,out] B ``` B is COMPLEX 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] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 139 of file chetrs_aa_2stage.f.

141*
142* -- LAPACK computational routine --
143* -- LAPACK is a software package provided by Univ. of Tennessee, --
144* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*
146 IMPLICIT NONE
147*
148* .. Scalar Arguments ..
149 CHARACTER UPLO
150 INTEGER N, NRHS, LDA, LTB, LDB, INFO
151* ..
152* .. Array Arguments ..
153 INTEGER IPIV( * ), IPIV2( * )
154 COMPLEX A( LDA, * ), TB( * ), B( LDB, * )
155* ..
156*
157* =====================================================================
158*
159 COMPLEX ONE
160 parameter( one = ( 1.0e+0, 0.0e+0 ) )
161* ..
162* .. Local Scalars ..
163 INTEGER LDTB, NB
164 LOGICAL UPPER
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 EXTERNAL lsame
169* ..
170* .. External Subroutines ..
171 EXTERNAL cgbtrs, claswp, ctrsm, xerbla
172* ..
173* .. Intrinsic Functions ..
174 INTRINSIC max
175* ..
176* .. Executable Statements ..
177*
178 info = 0
179 upper = lsame( uplo, 'U' )
180 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
181 info = -1
182 ELSE IF( n.LT.0 ) THEN
183 info = -2
184 ELSE IF( nrhs.LT.0 ) THEN
185 info = -3
186 ELSE IF( lda.LT.max( 1, n ) ) THEN
187 info = -5
188 ELSE IF( ltb.LT.( 4*n ) ) THEN
189 info = -7
190 ELSE IF( ldb.LT.max( 1, n ) ) THEN
191 info = -11
192 END IF
193 IF( info.NE.0 ) THEN
194 CALL xerbla( 'CHETRS_AA_2STAGE', -info )
195 RETURN
196 END IF
197*
198* Quick return if possible
199*
200 IF( n.EQ.0 .OR. nrhs.EQ.0 )
201 \$ RETURN
202*
203* Read NB and compute LDTB
204*
205 nb = int( tb( 1 ) )
206 ldtb = ltb/n
207*
208 IF( upper ) THEN
209*
210* Solve A*X = B, where A = U**T*T*U.
211*
212 IF( n.GT.nb ) THEN
213*
214* Pivot, P**T * B -> B
215*
216 CALL claswp( nrhs, b, ldb, nb+1, n, ipiv, 1 )
217*
218* Compute (U**T \ B) -> B [ (U**T \P**T * B) ]
219*
220 CALL ctrsm( 'L', 'U', 'C', 'U', n-nb, nrhs, one, a(1, nb+1),
221 \$ lda, b(nb+1, 1), ldb)
222*
223 END IF
224*
225* Compute T \ B -> B [ T \ (U**T \P**T * B) ]
226*
227 CALL cgbtrs( 'N', n, nb, nb, nrhs, tb, ldtb, ipiv2, b, ldb,
228 \$ info)
229 IF( n.GT.nb ) THEN
230*
231* Compute (U \ B) -> B [ U \ (T \ (U**T \P**T * B) ) ]
232*
233 CALL ctrsm( 'L', 'U', 'N', 'U', n-nb, nrhs, one, a(1, nb+1),
234 \$ lda, b(nb+1, 1), ldb)
235*
236* Pivot, P * B [ P * (U \ (T \ (U**T \P**T * B) )) ]
237*
238 CALL claswp( nrhs, b, ldb, nb+1, n, ipiv, -1 )
239*
240 END IF
241*
242 ELSE
243*
244* Solve A*X = B, where A = L*T*L**T.
245*
246 IF( n.GT.nb ) THEN
247*
248* Pivot, P**T * B
249*
250 CALL claswp( nrhs, b, ldb, nb+1, n, ipiv, 1 )
251*
252* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
253*
254 CALL ctrsm( 'L', 'L', 'N', 'U', n-nb, nrhs, one, a(nb+1, 1),
255 \$ lda, b(nb+1, 1), ldb)
256*
257 END IF
258*
259* Compute T \ B -> B [ T \ (L \P**T * B) ]
260*
261 CALL cgbtrs( 'N', n, nb, nb, nrhs, tb, ldtb, ipiv2, b, ldb,
262 \$ info)
263 IF( n.GT.nb ) THEN
264*
265* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
266*
267 CALL ctrsm( 'L', 'L', 'C', 'U', n-nb, nrhs, one, a(nb+1, 1),
268 \$ lda, b(nb+1, 1), ldb)
269*
270* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
271*
272 CALL claswp( nrhs, b, ldb, nb+1, n, ipiv, -1 )
273*
274 END IF
275 END IF
276*
277 RETURN
278*
279* End of CHETRS_AA_2STAGE
280*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine cgbtrs(trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
CGBTRS
Definition cgbtrs.f:138
subroutine claswp(n, a, lda, k1, k2, ipiv, incx)
CLASWP performs a series of row interchanges on a general rectangular matrix.
Definition claswp.f:115
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ctrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRSM
Definition ctrsm.f:180
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