 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zsytrs_aa()

 subroutine zsytrs_aa ( character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZSYTRS_AA

Purpose:
``` ZSYTRS_AA solves a system of linear equations A*X = B with a complex
symmetric matrix A using the factorization A = U**T*T*U or
A = L*T*L**T computed by ZSYTRF_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 COMPLEX*16 array, dimension (LDA,N) Details of factors computed by ZSYTRF_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 ZSYTRF_AA.``` [in,out] B ``` B is COMPLEX*16 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 COMPLEX*16 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 zsytrs_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  COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
145 * ..
146 *
147 * =====================================================================
148 *
149  COMPLEX*16 ONE
150  parameter( one = 1.0d+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 zgtsv, zswap, zlacpy, ztrsm, 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( 'ZSYTRS_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  DO k = 1, n
209  kp = ipiv( k )
210  IF( kp.NE.k )
211  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
212  END DO
213 *
214 * Compute U**T \ B -> B [ (U**T \P**T * B) ]
215 *
216  CALL ztrsm( 'L', 'U', 'T', 'U', n-1, nrhs, one, a( 1, 2 ),
217  \$ lda, b( 2, 1 ), ldb)
218  END IF
219 *
220 * 2) Solve with triangular matrix T
221 *
222 * Compute T \ B -> B [ T \ (U**T \P**T * B) ]
223 *
224  CALL zlacpy( 'F', 1, n, a( 1, 1 ), lda+1, work( n ), 1)
225  IF( n.GT.1 ) THEN
226  CALL zlacpy( 'F', 1, n-1, a( 1, 2 ), lda+1, work( 1 ), 1 )
227  CALL zlacpy( 'F', 1, n-1, a( 1, 2 ), lda+1, work( 2*n ), 1 )
228  END IF
229  CALL zgtsv( n, nrhs, work( 1 ), work( n ), work( 2*n ), b, ldb,
230  \$ info )
231 *
232 * 3) Backward substitution with U
233 *
234  IF( n.GT.1 ) THEN
235 *
236 * Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ]
237 *
238  CALL ztrsm( 'L', 'U', 'N', 'U', n-1, nrhs, one, a( 1, 2 ),
239  \$ lda, b( 2, 1 ), ldb)
240 *
241 * Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
242 *
243  DO k = n, 1, -1
244  kp = ipiv( k )
245  IF( kp.NE.k )
246  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
247  END DO
248  END IF
249 *
250  ELSE
251 *
252 * Solve A*X = B, where A = L*T*L**T.
253 *
254 * 1) Forward substitution with L
255 *
256  IF( n.GT.1 ) THEN
257 *
258 * Pivot, P**T * B -> B
259 *
260  DO k = 1, n
261  kp = ipiv( k )
262  IF( kp.NE.k )
263  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
264  END DO
265 *
266 * Compute L \ B -> B [ (L \P**T * B) ]
267 *
268  CALL ztrsm( 'L', 'L', 'N', 'U', n-1, nrhs, one, a( 2, 1 ),
269  \$ lda, b( 2, 1 ), ldb)
270  END IF
271 *
272 * 2) Solve with triangular matrix T
273 *
274 * Compute T \ B -> B [ T \ (L \P**T * B) ]
275 *
276  CALL zlacpy( 'F', 1, n, a(1, 1), lda+1, work(n), 1)
277  IF( n.GT.1 ) THEN
278  CALL zlacpy( 'F', 1, n-1, a( 2, 1 ), lda+1, work( 1 ), 1 )
279  CALL zlacpy( 'F', 1, n-1, a( 2, 1 ), lda+1, work( 2*n ), 1 )
280  END IF
281  CALL zgtsv( n, nrhs, work( 1 ), work(n), work( 2*n ), b, ldb,
282  \$ info)
283 *
284 * 3) Backward substitution with L**T
285 *
286  IF( n.GT.1 ) THEN
287 *
288 * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
289 *
290  CALL ztrsm( 'L', 'L', 'T', 'U', n-1, nrhs, one, a( 2, 1 ),
291  \$ lda, b( 2, 1 ), ldb)
292 *
293 * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
294 *
295  DO k = n, 1, -1
296  kp = ipiv( k )
297  IF( kp.NE.k )
298  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
299  END DO
300  END IF
301 *
302  END IF
303 *
304  RETURN
305 *
306 * End of ZSYTRS_AA
307 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine zgtsv(N, NRHS, DL, D, DU, B, LDB, INFO)
ZGTSV computes the solution to system of linear equations A * X = B for GT matrices
Definition: zgtsv.f:124
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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