LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssysv_rook()

 subroutine ssysv_rook ( character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info )

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

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

Purpose:
SSYSV_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.

SSYTRF_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 SSYTRS_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 REAL 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 SSYTRF_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 SSYTRF_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 REAL 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 REAL 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 SSYTRF_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.
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 202 of file ssysv_rook.f.

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