LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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

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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.
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 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  EXTERNAL lsame
227 * ..
228 * .. External Subroutines ..
229  EXTERNAL xerbla, ssytrf_rook, ssytrs_rook
230 * ..
231 * .. Intrinsic Functions ..
232  INTRINSIC max
233 * ..
234 * .. Executable Statements ..
235 *
236 * Test the input parameters.
237 *
238  info = 0
239  lquery = ( lwork.EQ.-1 )
240  IF( .NOT.lsame( uplo, 'U' ) .AND. .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 ssytrf_rook( uplo, n, a, lda, ipiv, work, -1, info )
259  lwkopt = work(1)
260  END IF
261  work( 1 ) = lwkopt
262  END IF
263 *
264  IF( info.NE.0 ) THEN
265  CALL xerbla( 'SSYSV_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 ssytrf_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 ssytrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
281 *
282  END IF
283 *
284  work( 1 ) = lwkopt
285 *
286  RETURN
287 *
288 * End of SSYSV_ROOK
289 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_ROOK
Definition: ssytrf_rook.f:208
subroutine ssytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS_ROOK
Definition: ssytrs_rook.f:136
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