 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zhesv_aa_2stage()

 subroutine zhesv_aa_2stage ( character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( * ) IPIV, integer, dimension( * ) IPIV2, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:
``` ZHESV_AA_2STAGE 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 2-stage 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 band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS.```
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 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, L is stored below (or above) the subdiaonal blocks, when UPLO is 'L' (or 'U').``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] TB ``` TB is COMPLEX*16 array, dimension (LTB) On exit, details of the LU factorization of the band matrix.``` [in] LTB ``` LTB is INTEGER The size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA.``` [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).``` [out] IPIV2 ``` IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the 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 workspace of size LWORK` [in] LWORK ``` LWORK is INTEGER The size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB. 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, band LU factorization failed on i-th column```

Definition at line 184 of file zhesv_aa_2stage.f.

187*
188* -- LAPACK driver routine --
189* -- LAPACK is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192 IMPLICIT NONE
193*
194* .. Scalar Arguments ..
195 CHARACTER UPLO
196 INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
197* ..
198* .. Array Arguments ..
199 INTEGER IPIV( * ), IPIV2( * )
200 COMPLEX*16 A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
201* ..
202*
203* =====================================================================
204* .. Parameters ..
205 COMPLEX*16 ZERO, ONE
206 parameter( zero = ( 0.0d+0, 0.0d+0 ),
207 \$ one = ( 1.0d+0, 0.0d+0 ) )
208*
209* .. Local Scalars ..
210 LOGICAL UPPER, TQUERY, WQUERY
211 INTEGER LWKOPT
212* ..
213* .. External Functions ..
214 LOGICAL LSAME
215 INTEGER ILAENV
216 EXTERNAL lsame, ilaenv
217* ..
218* .. External Subroutines ..
220* ..
221* .. Intrinsic Functions ..
222 INTRINSIC max
223* ..
224* .. Executable Statements ..
225*
226* Test the input parameters.
227*
228 info = 0
229 upper = lsame( uplo, 'U' )
230 wquery = ( lwork.EQ.-1 )
231 tquery = ( ltb.EQ.-1 )
232 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
233 info = -1
234 ELSE IF( n.LT.0 ) THEN
235 info = -2
236 ELSE IF( nrhs.LT.0 ) THEN
237 info = -3
238 ELSE IF( lda.LT.max( 1, n ) ) THEN
239 info = -5
240 ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
241 info = -7
242 ELSE IF( ldb.LT.max( 1, n ) ) THEN
243 info = -11
244 ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
245 info = -13
246 END IF
247*
248 IF( info.EQ.0 ) THEN
249 CALL zhetrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
250 \$ ipiv2, work, -1, info )
251 lwkopt = int( work(1) )
252 END IF
253*
254 IF( info.NE.0 ) THEN
255 CALL xerbla( 'ZHESV_AA_2STAGE', -info )
256 RETURN
257 ELSE IF( wquery .OR. tquery ) THEN
258 RETURN
259 END IF
260*
261* Compute the factorization A = U**H*T*U or A = L*T*L**H.
262*
263 CALL zhetrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
264 \$ work, lwork, info )
265 IF( info.EQ.0 ) THEN
266*
267* Solve the system A*X = B, overwriting B with X.
268*
269 CALL zhetrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
270 \$ ipiv2, b, ldb, info )
271*
272 END IF
273*
274 work( 1 ) = lwkopt
275*
276 RETURN
277*
278* End of ZHESV_AA_2STAGE
279*
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_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
ZHETRS_AA_2STAGE
subroutine zhetrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
ZHETRF_AA_2STAGE
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