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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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