LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine chesv_rook ( character  UPLO,
integer  N,
integer  NRHS,
complex, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method

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Purpose:
 CHESV_ROOK computes the solution to a complex system of linear equations
    A * X = B,
 where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
 matrices.

 The bounded Bunch-Kaufman ("rook") 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 Hermitian and block diagonal with
 1-by-1 and 2-by-2 diagonal blocks.

 CHETRF_ROOK is called to compute the factorization of a complex
 Hermition 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 CHETRS_ROOK (uses BLAS 2).
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 COMPLEX array, dimension (LDA,N)
          On entry, the Hermitian 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**H or A = L*D*L**H as computed by
          CHETRF_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.

          If UPLO = 'U':
             Only the last KB elements of IPIV are set.

             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':
             Only the first KB elements of IPIV are set.

             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 COMPLEX 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 COMPLEX 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
          CHETRF_ROOK.
          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.
Date
November 2013
  November 2013,  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 207 of file chesv_rook.f.

207 *
208 * -- LAPACK driver routine (version 3.5.0) --
209 * -- LAPACK is a software package provided by Univ. of Tennessee, --
210 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
211 * November 2013
212 *
213 * .. Scalar Arguments ..
214  CHARACTER uplo
215  INTEGER info, lda, ldb, lwork, n, nrhs
216 * ..
217 * .. Array Arguments ..
218  INTEGER ipiv( * )
219  COMPLEX a( lda, * ), b( ldb, * ), work( * )
220 * ..
221 *
222 * =====================================================================
223 *
224 * .. Local Scalars ..
225  LOGICAL lquery
226  INTEGER lwkopt, nb
227 * ..
228 * .. External Functions ..
229  LOGICAL lsame
230  INTEGER ilaenv
231  EXTERNAL lsame, ilaenv
232 * ..
233 * .. External Subroutines ..
234  EXTERNAL xerbla, chetrf_rook, chetrs_rook
235 * ..
236 * .. Intrinsic Functions ..
237  INTRINSIC max
238 * ..
239 * .. Executable Statements ..
240 *
241 * Test the input parameters.
242 *
243  info = 0
244  lquery = ( lwork.EQ.-1 )
245  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
246  info = -1
247  ELSE IF( n.LT.0 ) THEN
248  info = -2
249  ELSE IF( nrhs.LT.0 ) THEN
250  info = -3
251  ELSE IF( lda.LT.max( 1, n ) ) THEN
252  info = -5
253  ELSE IF( ldb.LT.max( 1, n ) ) THEN
254  info = -8
255  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
256  info = -10
257  END IF
258 *
259  IF( info.EQ.0 ) THEN
260  IF( n.EQ.0 ) THEN
261  lwkopt = 1
262  ELSE
263  nb = ilaenv( 1, 'CHETRF_ROOK', uplo, n, -1, -1, -1 )
264  lwkopt = n*nb
265  END IF
266  work( 1 ) = lwkopt
267  END IF
268 *
269  IF( info.NE.0 ) THEN
270  CALL xerbla( 'CHESV_ROOK ', -info )
271  RETURN
272  ELSE IF( lquery ) THEN
273  RETURN
274  END IF
275 *
276 * Compute the factorization A = U*D*U**H or A = L*D*L**H.
277 *
278  CALL chetrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
279  IF( info.EQ.0 ) THEN
280 *
281 * Solve the system A*X = B, overwriting B with X.
282 *
283 * Solve with TRS ( Use Level BLAS 2)
284 *
285  CALL chetrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
286 *
287  END IF
288 *
289  work( 1 ) = lwkopt
290 *
291  RETURN
292 *
293 * End of CHESV_ROOK
294 *
subroutine chetrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using fac...
Definition: chetrs_rook.f:138
subroutine chetrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: chetrf_rook.f:214
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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