LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dsysv()

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

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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.

 The diagonal pivoting method is used to factor A as
    A = U * D * U**T,  if UPLO = 'U', or
    A = L * D * L**T,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and D is symmetric and block diagonal with
 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
          multipliers used to obtain the factor U or L from the
          factorization A = U*D*U**T or A = L*D*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)
          Details of the interchanges and the block structure of D, as
          determined by DSYTRF.  If IPIV(k) > 0, then rows and columns
          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
          then rows and columns k-1 and -IPIV(k) were interchanged and
          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
          diagonal block.
[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 >= 1, and for best performance
          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
          DSYTRF.
          for LWORK < N, TRS will be done with Level BLAS 2
          for LWORK >= N, TRS will be done with Level BLAS 3

          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
December 2016

Definition at line 173 of file dsysv.f.

173 *
174 * -- LAPACK driver routine (version 3.7.0) --
175 * -- LAPACK is a software package provided by Univ. of Tennessee, --
176 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177 * December 2016
178 *
179 * .. Scalar Arguments ..
180  CHARACTER uplo
181  INTEGER info, lda, ldb, lwork, n, nrhs
182 * ..
183 * .. Array Arguments ..
184  INTEGER ipiv( * )
185  DOUBLE PRECISION a( lda, * ), b( ldb, * ), work( * )
186 * ..
187 *
188 * =====================================================================
189 *
190 * .. Local Scalars ..
191  LOGICAL lquery
192  INTEGER lwkopt
193 * ..
194 * .. External Functions ..
195  LOGICAL lsame
196  EXTERNAL lsame
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL xerbla, dsytrf, dsytrs, dsytrs2
200 * ..
201 * .. Intrinsic Functions ..
202  INTRINSIC max
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input parameters.
207 *
208  info = 0
209  lquery = ( lwork.EQ.-1 )
210  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
211  info = -1
212  ELSE IF( n.LT.0 ) THEN
213  info = -2
214  ELSE IF( nrhs.LT.0 ) THEN
215  info = -3
216  ELSE IF( lda.LT.max( 1, n ) ) THEN
217  info = -5
218  ELSE IF( ldb.LT.max( 1, n ) ) THEN
219  info = -8
220  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
221  info = -10
222  END IF
223 *
224  IF( info.EQ.0 ) THEN
225  IF( n.EQ.0 ) THEN
226  lwkopt = 1
227  ELSE
228  CALL dsytrf( uplo, n, a, lda, ipiv, work, -1, info )
229  lwkopt = work(1)
230  END IF
231  work( 1 ) = lwkopt
232  END IF
233 *
234  IF( info.NE.0 ) THEN
235  CALL xerbla( 'DSYSV ', -info )
236  RETURN
237  ELSE IF( lquery ) THEN
238  RETURN
239  END IF
240 *
241 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
242 *
243  CALL dsytrf( uplo, n, a, lda, ipiv, work, lwork, info )
244  IF( info.EQ.0 ) THEN
245 *
246 * Solve the system A*X = B, overwriting B with X.
247 *
248  IF ( lwork.LT.n ) THEN
249 *
250 * Solve with TRS ( Use Level BLAS 2)
251 *
252  CALL dsytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
253 *
254  ELSE
255 *
256 * Solve with TRS2 ( Use Level BLAS 3)
257 *
258  CALL dsytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
259 *
260  END IF
261 *
262  END IF
263 *
264  work( 1 ) = lwkopt
265 *
266  RETURN
267 *
268 * End of DSYSV
269 *
subroutine dsytrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
DSYTRS2
Definition: dsytrs2.f:134
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS
Definition: dsytrs.f:122
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dsytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF
Definition: dsytrf.f:184
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