 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ chesv_rook()

 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

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.```
```  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 203 of file chesv_rook.f.

205 *
206 * -- LAPACK driver routine --
207 * -- LAPACK is a software package provided by Univ. of Tennessee, --
208 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
209 *
210 * .. Scalar Arguments ..
211  CHARACTER UPLO
212  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
213 * ..
214 * .. Array Arguments ..
215  INTEGER IPIV( * )
216  COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
217 * ..
218 *
219 * =====================================================================
220 *
221 * .. Local Scalars ..
222  LOGICAL LQUERY
223  INTEGER LWKOPT, NB
224 * ..
225 * .. External Functions ..
226  LOGICAL LSAME
227  INTEGER ILAENV
228  EXTERNAL lsame, ilaenv
229 * ..
230 * .. External Subroutines ..
231  EXTERNAL xerbla, chetrf_rook, chetrs_rook
232 * ..
233 * .. Intrinsic Functions ..
234  INTRINSIC max
235 * ..
236 * .. Executable Statements ..
237 *
238 * Test the input parameters.
239 *
240  info = 0
241  lquery = ( lwork.EQ.-1 )
242  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
243  info = -1
244  ELSE IF( n.LT.0 ) THEN
245  info = -2
246  ELSE IF( nrhs.LT.0 ) THEN
247  info = -3
248  ELSE IF( lda.LT.max( 1, n ) ) THEN
249  info = -5
250  ELSE IF( ldb.LT.max( 1, n ) ) THEN
251  info = -8
252  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
253  info = -10
254  END IF
255 *
256  IF( info.EQ.0 ) THEN
257  IF( n.EQ.0 ) THEN
258  lwkopt = 1
259  ELSE
260  nb = ilaenv( 1, 'CHETRF_ROOK', uplo, n, -1, -1, -1 )
261  lwkopt = n*nb
262  END IF
263  work( 1 ) = lwkopt
264  END IF
265 *
266  IF( info.NE.0 ) THEN
267  CALL xerbla( 'CHESV_ROOK ', -info )
268  RETURN
269  ELSE IF( lquery ) THEN
270  RETURN
271  END IF
272 *
273 * Compute the factorization A = U*D*U**H or A = L*D*L**H.
274 *
275  CALL chetrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
276  IF( info.EQ.0 ) THEN
277 *
278 * Solve the system A*X = B, overwriting B with X.
279 *
280 * Solve with TRS ( Use Level BLAS 2)
281 *
282  CALL chetrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
283 *
284  END IF
285 *
286  work( 1 ) = lwkopt
287 *
288  RETURN
289 *
290 * End of CHESV_ROOK
291 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:136
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:212
Here is the call graph for this function:
Here is the caller graph for this function: