LAPACK  3.9.0
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

Download ZHESV_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

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.
Date
November 2017

Definition at line 189 of file zhesv_aa_2stage.f.

189 *
190 * -- LAPACK driver routine (version 3.8.0) --
191 * -- LAPACK is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 * November 2017
194 *
195  IMPLICIT NONE
196 *
197 * .. Scalar Arguments ..
198  CHARACTER UPLO
199  INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
200 * ..
201 * .. Array Arguments ..
202  INTEGER IPIV( * ), IPIV2( * )
203  COMPLEX*16 A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
204 * ..
205 *
206 * =====================================================================
207 * .. Parameters ..
208  COMPLEX*16 ZERO, ONE
209  parameter( zero = ( 0.0d+0, 0.0d+0 ),
210  $ one = ( 1.0d+0, 0.0d+0 ) )
211 *
212 * .. Local Scalars ..
213  LOGICAL UPPER, TQUERY, WQUERY
214  INTEGER LWKOPT
215 * ..
216 * .. External Functions ..
217  LOGICAL LSAME
218  INTEGER ILAENV
219  EXTERNAL lsame, ilaenv
220 * ..
221 * .. External Subroutines ..
222  EXTERNAL xerbla, zhetrf_aa_2stage, zhetrs_aa_2stage
223 * ..
224 * .. Intrinsic Functions ..
225  INTRINSIC max
226 * ..
227 * .. Executable Statements ..
228 *
229 * Test the input parameters.
230 *
231  info = 0
232  upper = lsame( uplo, 'U' )
233  wquery = ( lwork.EQ.-1 )
234  tquery = ( ltb.EQ.-1 )
235  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
236  info = -1
237  ELSE IF( n.LT.0 ) THEN
238  info = -2
239  ELSE IF( nrhs.LT.0 ) THEN
240  info = -3
241  ELSE IF( lda.LT.max( 1, n ) ) THEN
242  info = -5
243  ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
244  info = -7
245  ELSE IF( ldb.LT.max( 1, n ) ) THEN
246  info = -11
247  ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
248  info = -13
249  END IF
250 *
251  IF( info.EQ.0 ) THEN
252  CALL zhetrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
253  $ ipiv2, work, -1, info )
254  lwkopt = int( work(1) )
255  END IF
256 *
257  IF( info.NE.0 ) THEN
258  CALL xerbla( 'ZHESV_AA_2STAGE', -info )
259  RETURN
260  ELSE IF( wquery .OR. tquery ) THEN
261  RETURN
262  END IF
263 *
264 * Compute the factorization A = U**H*T*U or A = L*T*L**H.
265 *
266  CALL zhetrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
267  $ work, lwork, info )
268  IF( info.EQ.0 ) THEN
269 *
270 * Solve the system A*X = B, overwriting B with X.
271 *
272  CALL zhetrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
273  $ ipiv2, b, ldb, info )
274 *
275  END IF
276 *
277  work( 1 ) = lwkopt
278 *
279  RETURN
280 *
281 * End of ZHESV_AA_2STAGE
282 *
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zhetrs_aa_2stage
subroutine zhetrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
ZHETRS_AA_2STAGE
Definition: zhetrs_aa_2stage.f:143
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
ilaenv
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
zhetrf_aa_2stage
subroutine zhetrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
ZHETRF_AA_2STAGE
Definition: zhetrf_aa_2stage.f:162