LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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

Download CHESV_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

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

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  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
214  $ xerbla
215 * ..
216 * .. Intrinsic Functions ..
217  INTRINSIC max
218 * ..
219 * .. Executable Statements ..
220 *
221 * Test the input parameters.
222 *
223  info = 0
224  upper = lsame( uplo, 'U' )
225  wquery = ( lwork.EQ.-1 )
226  tquery = ( ltb.EQ.-1 )
227  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
228  info = -1
229  ELSE IF( n.LT.0 ) THEN
230  info = -2
231  ELSE IF( nrhs.LT.0 ) THEN
232  info = -3
233  ELSE IF( lda.LT.max( 1, n ) ) THEN
234  info = -5
235  ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
236  info = -7
237  ELSE IF( ldb.LT.max( 1, n ) ) THEN
238  info = -11
239  ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
240  info = -13
241  END IF
242 *
243  IF( info.EQ.0 ) THEN
244  CALL chetrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
245  $ ipiv2, work, -1, info )
246  lwkopt = int( work(1) )
247  END IF
248 *
249  IF( info.NE.0 ) THEN
250  CALL xerbla( 'CHESV_AA_2STAGE', -info )
251  RETURN
252  ELSE IF( wquery .OR. tquery ) THEN
253  RETURN
254  END IF
255 *
256 *
257 * Compute the factorization A = U**H*T*U or A = L*T*L**H.
258 *
259  CALL chetrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
260  $ work, lwork, info )
261  IF( info.EQ.0 ) THEN
262 *
263 * Solve the system A*X = B, overwriting B with X.
264 *
265  CALL chetrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
266  $ ipiv2, b, ldb, info )
267 *
268  END IF
269 *
270  work( 1 ) = lwkopt
271 *
272  RETURN
273 *
274 * End of CHESV_AA_2STAGE
275 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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