 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zhesv_rook()

 subroutine zhesv_rook ( character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZHESV_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:
``` ZHESV_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.

ZHETRF_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 ZHETRS_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*16 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 ZHETRF_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*16 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*16 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 ZHETRF_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 zhesv_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*16 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 ..
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, 'ZHETRF_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( 'ZHESV_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 zhetrf_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 zhetrs_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 ZHESV_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 zhetrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using fac...
Definition: zhetrs_rook.f:136
subroutine zhetrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: zhetrf_rook.f:212
Here is the call graph for this function:
Here is the caller graph for this function: