LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dsysv_rook()

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

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Purpose:
 DSYSV_ROOK 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.

 DSYTRF_ROOK is called to compute the factorization of a real
 symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
 pivoting method.

 The factored form of A is then used to solve the system
 of equations A * X = B by calling DSYTRS_ROOK.
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_ROOK.
[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_ROOK.

          If UPLO = 'U':
               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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k-1 and -IPIV(k-1) were inerchaged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

          If UPLO = 'L':
               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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k+1 and -IPIV(k+1) were inerchaged,
               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_ROOK.

          TRS will be done with Level 2 BLAS

          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
April 2012
Contributors:
   April 2012, Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 206 of file dsysv_rook.f.

206 *
207 * -- LAPACK driver routine (version 3.7.0) --
208 * -- LAPACK is a software package provided by Univ. of Tennessee, --
209 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
210 * April 2012
211 *
212 * .. Scalar Arguments ..
213  CHARACTER uplo
214  INTEGER info, lda, ldb, lwork, n, nrhs
215 * ..
216 * .. Array Arguments ..
217  INTEGER ipiv( * )
218  DOUBLE PRECISION a( lda, * ), b( ldb, * ), work( * )
219 * ..
220 *
221 * =====================================================================
222 *
223 * .. Local Scalars ..
224  LOGICAL lquery
225  INTEGER lwkopt
226 * ..
227 * .. External Functions ..
228  LOGICAL lsame
229  EXTERNAL lsame
230 * ..
231 * .. External Subroutines ..
232  EXTERNAL xerbla, dsytrf_rook, dsytrs_rook
233 * ..
234 * .. Intrinsic Functions ..
235  INTRINSIC max
236 * ..
237 * .. Executable Statements ..
238 *
239 * Test the input parameters.
240 *
241  info = 0
242  lquery = ( lwork.EQ.-1 )
243  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
244  info = -1
245  ELSE IF( n.LT.0 ) THEN
246  info = -2
247  ELSE IF( nrhs.LT.0 ) THEN
248  info = -3
249  ELSE IF( lda.LT.max( 1, n ) ) THEN
250  info = -5
251  ELSE IF( ldb.LT.max( 1, n ) ) THEN
252  info = -8
253  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
254  info = -10
255  END IF
256 *
257  IF( info.EQ.0 ) THEN
258  IF( n.EQ.0 ) THEN
259  lwkopt = 1
260  ELSE
261  CALL dsytrf_rook( uplo, n, a, lda, ipiv, work, -1, info )
262  lwkopt = work(1)
263  END IF
264  work( 1 ) = lwkopt
265  END IF
266 *
267  IF( info.NE.0 ) THEN
268  CALL xerbla( 'DSYSV_ROOK ', -info )
269  RETURN
270  ELSE IF( lquery ) THEN
271  RETURN
272  END IF
273 *
274 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
275 *
276  CALL dsytrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
277  IF( info.EQ.0 ) THEN
278 *
279 * Solve the system A*X = B, overwriting B with X.
280 *
281 * Solve with TRS_ROOK ( Use Level 2 BLAS)
282 *
283  CALL dsytrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
284 *
285  END IF
286 *
287  work( 1 ) = lwkopt
288 *
289  RETURN
290 *
291 * End of DSYSV_ROOK
292 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dsytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS_ROOK
Definition: dsytrs_rook.f:138
subroutine dsytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF_ROOK
Definition: dsytrf_rook.f:210
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