LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dsysv_aa()

subroutine dsysv_aa ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Download DSYSV_AA + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DSYSV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
 matrices.

 Aasen's algorithm is used to factor A as
    A = U * T * U**T,  if UPLO = 'U', or
    A = L * T * L**T,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and T is symmetric tridiagonal. The factored
 form of A is then used to solve the system of equations A * X = B.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
[in]N
          N is INTEGER
          The number of linear equations, i.e., 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,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          N-by-N upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading N-by-N lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if INFO = 0, the tridiagonal matrix T and the
          multipliers used to obtain the factor U or L from the
          factorization A = U*T*U**T or A = L*T*L**T as computed by
          DSYTRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
          the best performance, LWORK >= MAX(1,N*NB), where NB is
          the optimal blocksize for DSYTRF_AA.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
               has been completed, but the block diagonal matrix D is
               exactly singular, so the solution could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2017

Definition at line 164 of file dsysv_aa.f.

164 *
165 * -- LAPACK driver routine (version 3.8.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * November 2017
169 *
170 * .. Scalar Arguments ..
171  CHARACTER uplo
172  INTEGER info, lda, ldb, lwork, n, nrhs
173 * ..
174 * .. Array Arguments ..
175  INTEGER ipiv( * )
176  DOUBLE PRECISION a( lda, * ), b( ldb, * ), work( * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. Local Scalars ..
182  LOGICAL lquery
183  INTEGER lwkopt, lwkopt_sytrf, lwkopt_sytrs
184 * ..
185 * .. External Functions ..
186  LOGICAL lsame
187  INTEGER ilaenv
188  EXTERNAL ilaenv, lsame
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL xerbla, dsytrf_aa, dsytrs_aa
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC max
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input parameters.
199 *
200  info = 0
201  lquery = ( lwork.EQ.-1 )
202  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
203  info = -1
204  ELSE IF( n.LT.0 ) THEN
205  info = -2
206  ELSE IF( nrhs.LT.0 ) THEN
207  info = -3
208  ELSE IF( lda.LT.max( 1, n ) ) THEN
209  info = -5
210  ELSE IF( ldb.LT.max( 1, n ) ) THEN
211  info = -8
212  ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
213  info = -10
214  END IF
215 *
216  IF( info.EQ.0 ) THEN
217  CALL dsytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
218  lwkopt_sytrf = int( work(1) )
219  CALL dsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
220  $ -1, info )
221  lwkopt_sytrs = int( work(1) )
222  lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
223  work( 1 ) = lwkopt
224  IF( lwork.LT.lwkopt .AND. .NOT.lquery ) THEN
225  info = -10
226  END IF
227  END IF
228 *
229  IF( info.NE.0 ) THEN
230  CALL xerbla( 'DSYSV_AA ', -info )
231  RETURN
232  ELSE IF( lquery ) THEN
233  RETURN
234  END IF
235 *
236 * Compute the factorization A = U*T*U**T or A = L*T*L**T.
237 *
238  CALL dsytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
239  IF( info.EQ.0 ) THEN
240 *
241 * Solve the system A*X = B, overwriting B with X.
242 *
243  CALL dsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
244  $ lwork, info )
245 *
246  END IF
247 *
248  work( 1 ) = lwkopt
249 *
250  RETURN
251 *
252 * End of DSYSV_AA
253 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dsytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF_AA
Definition: dsytrf_aa.f:134
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dsytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
DSYTRS_AA
Definition: dsytrs_aa.f:131
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