LAPACK  3.8.0
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

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Purpose:
 ZSYTRS_AA solves a system of linear equations A*X = B with a complex
 symmetric matrix A using the factorization A = U*T*U**T 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*U**T;
          = '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).
[in]WORK
          WORK is DOUBLE array, dimension (MAX(1,LWORK))
[in]LWORK
          LWORK is INTEGER, LWORK >= MAX(1,3*N-2).

 \param[out] INFO
 \verbatim
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2017

Definition at line 131 of file zsytrs_aa.f.

131 *
132 * -- LAPACK computational routine (version 3.8.0) --
133 * -- LAPACK is a software package provided by Univ. of Tennessee, --
134 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135 * November 2017
136 *
137  IMPLICIT NONE
138 *
139 * .. Scalar Arguments ..
140  CHARACTER uplo
141  INTEGER n, nrhs, lda, ldb, lwork, info
142 * ..
143 * .. Array Arguments ..
144  INTEGER ipiv( * )
145  COMPLEX*16 a( lda, * ), b( ldb, * ), work( * )
146 * ..
147 *
148 * =====================================================================
149 *
150  COMPLEX*16 one
151  parameter( one = 1.0d+0 )
152 * ..
153 * .. Local Scalars ..
154  LOGICAL lquery, upper
155  INTEGER k, kp, lwkopt
156 * ..
157 * .. External Functions ..
158  LOGICAL lsame
159  EXTERNAL lsame
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zgtsv, zswap, zlacpy, ztrsm, 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( 'ZSYTRS_AA', -info )
187  RETURN
188  ELSE IF( lquery ) THEN
189  lwkopt = (3*n-2)
190  work( 1 ) = 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*U**T.
202 *
203 * Pivot, P**T * B
204 *
205  DO k = 1, n
206  kp = ipiv( k )
207  IF( kp.NE.k )
208  $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
209  END DO
210 *
211 * Compute (U \P**T * B) -> B [ (U \P**T * B) ]
212 *
213  CALL ztrsm('L', 'U', 'T', 'U', n-1, nrhs, one, a( 1, 2 ), lda,
214  $ b( 2, 1 ), ldb)
215 *
216 * Compute T \ B -> B [ T \ (U \P**T * B) ]
217 *
218  CALL zlacpy( 'F', 1, n, a( 1, 1 ), lda+1, work( n ), 1)
219  IF( n.GT.1 ) THEN
220  CALL zlacpy( 'F', 1, n-1, a( 1, 2 ), lda+1, work( 1 ), 1 )
221  CALL zlacpy( 'F', 1, n-1, a( 1, 2 ), lda+1, work( 2*n ), 1 )
222  END IF
223  CALL zgtsv( n, nrhs, work( 1 ), work( n ), work( 2*n ), b, ldb,
224  $ info )
225 *
226 * Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
227 *
228  CALL ztrsm( 'L', 'U', 'N', 'U', n-1, nrhs, one, a( 1, 2 ), lda,
229  $ b( 2, 1 ), ldb)
230 *
231 * Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
232 *
233  DO k = n, 1, -1
234  kp = ipiv( k )
235  IF( kp.NE.k )
236  $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
237  END DO
238 *
239  ELSE
240 *
241 * Solve A*X = B, where A = L*T*L**T.
242 *
243 * Pivot, P**T * B
244 *
245  DO k = 1, n
246  kp = ipiv( k )
247  IF( kp.NE.k )
248  $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
249  END DO
250 *
251 * Compute (L \P**T * B) -> B [ (L \P**T * B) ]
252 *
253  CALL ztrsm( 'L', 'L', 'N', 'U', n-1, nrhs, one, a( 2, 1 ), lda,
254  $ b( 2, 1 ), ldb)
255 *
256 * Compute T \ B -> B [ T \ (L \P**T * B) ]
257 *
258  CALL zlacpy( 'F', 1, n, a(1, 1), lda+1, work(n), 1)
259  IF( n.GT.1 ) THEN
260  CALL zlacpy( 'F', 1, n-1, a( 2, 1 ), lda+1, work( 1 ), 1 )
261  CALL zlacpy( 'F', 1, n-1, a( 2, 1 ), lda+1, work( 2*n ), 1 )
262  END IF
263  CALL zgtsv( n, nrhs, work( 1 ), work(n), work( 2*n ), b, ldb,
264  $ info)
265 *
266 * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
267 *
268  CALL ztrsm( 'L', 'L', 'T', 'U', n-1, nrhs, one, a( 2, 1 ), lda,
269  $ b( 2, 1 ), ldb)
270 *
271 * Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
272 *
273  DO k = n, 1, -1
274  kp = ipiv( k )
275  IF( kp.NE.k )
276  $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
277  END DO
278 *
279  END IF
280 *
281  RETURN
282 *
283 * End of ZSYTRS_AA
284 *
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:83
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:182
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:126
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