LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhesv_aa()

 subroutine zhesv_aa ( 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_AA computes the solution to system of linear equations A * X = B for HE matrices

Purpose:
``` ZHESV_AA 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.

Aasen's algorithm is used to factor A as
A = U**H * T * U,  if UPLO = 'U', or
A = L * T * L**H,  if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is Hermitian and tridiagonal. The factored form
of A is then used to solve the system of equations A * X = B.```
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 tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**H*T*U or A = L*T*L**H as computed by ZHETRF_AA.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] IPIV ``` IPIV is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).``` [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 >= MAX(1,2*N,3*N-2), and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF. 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.```

Definition at line 160 of file zhesv_aa.f.

162 *
163 * -- LAPACK driver routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  CHARACTER UPLO
169  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
170 * ..
171 * .. Array Arguments ..
172  INTEGER IPIV( * )
173  COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Local Scalars ..
179  LOGICAL LQUERY
180  INTEGER LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS
181 * ..
182 * .. External Functions ..
183  LOGICAL LSAME
184  INTEGER ILAENV
185  EXTERNAL lsame, ilaenv
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL xerbla, zhetrf_aa, zhetrs_aa
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max
192 * ..
193 * .. Executable Statements ..
194 *
195 * Test the input parameters.
196 *
197  info = 0
198  lquery = ( lwork.EQ.-1 )
199  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
200  info = -1
201  ELSE IF( n.LT.0 ) THEN
202  info = -2
203  ELSE IF( nrhs.LT.0 ) THEN
204  info = -3
205  ELSE IF( lda.LT.max( 1, n ) ) THEN
206  info = -5
207  ELSE IF( ldb.LT.max( 1, n ) ) THEN
208  info = -8
209  ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
210  info = -10
211  END IF
212 *
213  IF( info.EQ.0 ) THEN
214  CALL zhetrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
215  lwkopt_hetrf = int( work(1) )
216  CALL zhetrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
217  \$ -1, info )
218  lwkopt_hetrs = int( work(1) )
219  lwkopt = max( lwkopt_hetrf, lwkopt_hetrs )
220  work( 1 ) = lwkopt
221  END IF
222 *
223  IF( info.NE.0 ) THEN
224  CALL xerbla( 'ZHESV_AA ', -info )
225  RETURN
226  ELSE IF( lquery ) THEN
227  RETURN
228  END IF
229 *
230 * Compute the factorization A = U**H*T*U or A = L*T*L**H.
231 *
232  CALL zhetrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
233  IF( info.EQ.0 ) THEN
234 *
235 * Solve the system A*X = B, overwriting B with X.
236 *
237  CALL zhetrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
238  \$ lwork, info )
239 *
240  END IF
241 *
242  work( 1 ) = lwkopt
243 *
244  RETURN
245 *
246 * End of ZHESV_AA
247 *
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 zhetrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_AA
Definition: zhetrf_aa.f:132
subroutine zhetrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHETRS_AA
Definition: zhetrs_aa.f:132
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