LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ chesv_aa_2stage()

 subroutine chesv_aa_2stage ( character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info )

CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:
``` CHESV_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 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 subdiagonal 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 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 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 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 183 of file chesv_aa_2stage.f.

186*
187* -- LAPACK computational routine --
188* -- LAPACK is a software package provided by Univ. of Tennessee, --
189* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190*
191 IMPLICIT NONE
192*
193* .. Scalar Arguments ..
194 CHARACTER UPLO
195 INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
196* ..
197* .. Array Arguments ..
198 INTEGER IPIV( * ), IPIV2( * )
199 COMPLEX A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
200* ..
201*
202* =====================================================================
203*
204* .. Local Scalars ..
205 LOGICAL UPPER, TQUERY, WQUERY
206 INTEGER LWKOPT
207* ..
208* .. External Functions ..
209 LOGICAL LSAME
210 REAL SROUNDUP_LWORK
211 EXTERNAL lsame, sroundup_lwork
212* ..
213* .. External Subroutines ..
215 \$ xerbla
216* ..
217* .. Intrinsic Functions ..
218 INTRINSIC max
219* ..
220* .. Executable Statements ..
221*
222* Test the input parameters.
223*
224 info = 0
225 upper = lsame( uplo, 'U' )
226 wquery = ( lwork.EQ.-1 )
227 tquery = ( ltb.EQ.-1 )
228 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
229 info = -1
230 ELSE IF( n.LT.0 ) THEN
231 info = -2
232 ELSE IF( nrhs.LT.0 ) THEN
233 info = -3
234 ELSE IF( lda.LT.max( 1, n ) ) THEN
235 info = -5
236 ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
237 info = -7
238 ELSE IF( ldb.LT.max( 1, n ) ) THEN
239 info = -11
240 ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
241 info = -13
242 END IF
243*
244 IF( info.EQ.0 ) THEN
245 CALL chetrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
246 \$ ipiv2, work, -1, info )
247 lwkopt = int( work(1) )
248 END IF
249*
250 IF( info.NE.0 ) THEN
251 CALL xerbla( 'CHESV_AA_2STAGE', -info )
252 RETURN
253 ELSE IF( wquery .OR. tquery ) THEN
254 RETURN
255 END IF
256*
257*
258* Compute the factorization A = U**H*T*U or A = L*T*L**H.
259*
260 CALL chetrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
261 \$ work, lwork, info )
262 IF( info.EQ.0 ) THEN
263*
264* Solve the system A*X = B, overwriting B with X.
265*
266 CALL chetrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
267 \$ ipiv2, b, ldb, info )
268*
269 END IF
270*
271 work( 1 ) = sroundup_lwork(lwkopt)
272*
273 RETURN
274*
275* End of CHESV_AA_2STAGE
276*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chetrf_aa_2stage(uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
CHETRF_AA_2STAGE
subroutine chetrs_aa_2stage(uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
CHETRS_AA_2STAGE
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
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