LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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

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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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