LAPACK  3.10.0
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.

Definition at line 169 of file dsysv.f.

171 *
172 * -- LAPACK driver routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  CHARACTER UPLO
178  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
179 * ..
180 * .. Array Arguments ..
181  INTEGER IPIV( * )
182  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Local Scalars ..
188  LOGICAL LQUERY
189  INTEGER LWKOPT
190 * ..
191 * .. External Functions ..
192  LOGICAL LSAME
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL xerbla, dsytrf, dsytrs, dsytrs2
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input parameters.
204 *
205  info = 0
206  lquery = ( lwork.EQ.-1 )
207  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
208  info = -1
209  ELSE IF( n.LT.0 ) THEN
210  info = -2
211  ELSE IF( nrhs.LT.0 ) THEN
212  info = -3
213  ELSE IF( lda.LT.max( 1, n ) ) THEN
214  info = -5
215  ELSE IF( ldb.LT.max( 1, n ) ) THEN
216  info = -8
217  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
218  info = -10
219  END IF
220 *
221  IF( info.EQ.0 ) THEN
222  IF( n.EQ.0 ) THEN
223  lwkopt = 1
224  ELSE
225  CALL dsytrf( uplo, n, a, lda, ipiv, work, -1, info )
226  lwkopt = work(1)
227  END IF
228  work( 1 ) = lwkopt
229  END IF
230 *
231  IF( info.NE.0 ) THEN
232  CALL xerbla( 'DSYSV ', -info )
233  RETURN
234  ELSE IF( lquery ) THEN
235  RETURN
236  END IF
237 *
238 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
239 *
240  CALL dsytrf( uplo, n, a, lda, ipiv, work, lwork, info )
241  IF( info.EQ.0 ) THEN
242 *
243 * Solve the system A*X = B, overwriting B with X.
244 *
245  IF ( lwork.LT.n ) THEN
246 *
247 * Solve with TRS ( Use Level BLAS 2)
248 *
249  CALL dsytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
250 *
251  ELSE
252 *
253 * Solve with TRS2 ( Use Level BLAS 3)
254 *
255  CALL dsytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
256 *
257  END IF
258 *
259  END IF
260 *
261  work( 1 ) = lwkopt
262 *
263  RETURN
264 *
265 * End of DSYSV
266 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS
Definition: dsytrs.f:120
subroutine dsytrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
DSYTRS2
Definition: dsytrs2.f:132
subroutine dsytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF
Definition: dsytrf.f:182
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