LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ 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

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

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 () 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.
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 200 of file dsysv_rook.f.

203*
204* -- LAPACK driver routine --
205* -- LAPACK is a software package provided by Univ. of Tennessee, --
206* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
207*
208* .. Scalar Arguments ..
209 CHARACTER UPLO
210 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
211* ..
212* .. Array Arguments ..
213 INTEGER IPIV( * )
214 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
215* ..
216*
217* =====================================================================
218*
219* .. Local Scalars ..
220 LOGICAL LQUERY
221 INTEGER LWKOPT
222* ..
223* .. External Functions ..
224 LOGICAL LSAME
225 EXTERNAL lsame
226* ..
227* .. External Subroutines ..
228 EXTERNAL xerbla, dsytrf_rook, dsytrs_rook
229* ..
230* .. Intrinsic Functions ..
231 INTRINSIC max
232* ..
233* .. Executable Statements ..
234*
235* Test the input parameters.
236*
237 info = 0
238 lquery = ( lwork.EQ.-1 )
239 IF( .NOT.lsame( uplo, 'U' ) .AND.
240 $ .NOT.lsame( uplo, 'L' ) ) THEN
241 info = -1
242 ELSE IF( n.LT.0 ) THEN
243 info = -2
244 ELSE IF( nrhs.LT.0 ) THEN
245 info = -3
246 ELSE IF( lda.LT.max( 1, n ) ) THEN
247 info = -5
248 ELSE IF( ldb.LT.max( 1, n ) ) THEN
249 info = -8
250 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
251 info = -10
252 END IF
253*
254 IF( info.EQ.0 ) THEN
255 IF( n.EQ.0 ) THEN
256 lwkopt = 1
257 ELSE
258 CALL dsytrf_rook( uplo, n, a, lda, ipiv, work, -1, info )
259 lwkopt = int( work( 1 ) )
260 END IF
261 work( 1 ) = lwkopt
262 END IF
263*
264 IF( info.NE.0 ) THEN
265 CALL xerbla( 'DSYSV_ROOK ', -info )
266 RETURN
267 ELSE IF( lquery ) THEN
268 RETURN
269 END IF
270*
271* Compute the factorization A = U*D*U**T or A = L*D*L**T.
272*
273 CALL dsytrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
274 IF( info.EQ.0 ) THEN
275*
276* Solve the system A*X = B, overwriting B with X.
277*
278* Solve with TRS_ROOK ( Use Level 2 BLAS)
279*
280 CALL dsytrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb,
281 $ info )
282*
283 END IF
284*
285 work( 1 ) = lwkopt
286*
287 RETURN
288*
289* End of DSYSV_ROOK
290*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dsytrf_rook
subroutine dsytrf_rook(uplo, n, a, lda, ipiv, work, lwork, info)
DSYTRF_ROOK
Definition dsytrf_rook.f:207
dsytrs_rook
subroutine dsytrs_rook(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
DSYTRS_ROOK
Definition dsytrs_rook.f:134
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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