LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dsysv_aa_2stage()

subroutine dsysv_aa_2stage ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TB,
integer  LTB,
integer, dimension( * )  IPIV,
integer, dimension( * )  IPIV2,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Download DSYSV_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DSYSV_AA_2STAGE computes the solution to a real system of
 linear equations
    A * X = B,
 where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
 matrices.

 Aasen's 2-stage algorithm is used to factor A as
    A = U * T * U**T,  if UPLO = 'U', or
    A = L * T * L**T,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and T is symmetric 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 DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the symmetric 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 DOUBLE PRECISION array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.
[in]LTB
          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
          IPIV 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 DOUBLE PRECISION 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 DOUBLE PRECISION workspace of size LWORK
[in]LWORK
          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 188 of file dsysv_aa_2stage.f.

188 *
189 * -- LAPACK computational routine (version 3.8.0) --
190 * -- LAPACK is a software package provided by Univ. of Tennessee, --
191 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192 * November 2017
193 *
194  IMPLICIT NONE
195 *
196 * .. Scalar Arguments ..
197  CHARACTER uplo
198  INTEGER n, nrhs, lda, ldb, ltb, lwork, info
199 * ..
200 * .. Array Arguments ..
201  INTEGER ipiv( * ), ipiv2( * )
202  DOUBLE PRECISION a( lda, * ), b( ldb, * ), tb( * ), work( * )
203 * ..
204 *
205 * =====================================================================
206 *
207 * .. Local Scalars ..
208  LOGICAL upper, tquery, wquery
209  INTEGER lwkopt
210 * ..
211 * .. External Functions ..
212  LOGICAL lsame
213  EXTERNAL lsame
214 * ..
215 * .. External Subroutines ..
217  $ xerbla
218 * ..
219 * .. Intrinsic Functions ..
220  INTRINSIC max
221 * ..
222 * .. Executable Statements ..
223 *
224 * Test the input parameters.
225 *
226  info = 0
227  upper = lsame( uplo, 'U' )
228  wquery = ( lwork.EQ.-1 )
229  tquery = ( ltb.EQ.-1 )
230  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
231  info = -1
232  ELSE IF( n.LT.0 ) THEN
233  info = -2
234  ELSE IF( nrhs.LT.0 ) THEN
235  info = -3
236  ELSE IF( lda.LT.max( 1, n ) ) THEN
237  info = -5
238  ELSE IF( ldb.LT.max( 1, n ) ) THEN
239  info = -11
240  END IF
241 *
242  IF( info.EQ.0 ) THEN
243  CALL dsytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
244  $ ipiv2, work, -1, info )
245  lwkopt = int( work(1) )
246  IF( ltb.LT.int( tb(1) ) .AND. .NOT.tquery ) THEN
247  info = -7
248  ELSE IF( lwork.LT.lwkopt .AND. .NOT.wquery ) THEN
249  info = -13
250  END IF
251  END IF
252 *
253  IF( info.NE.0 ) THEN
254  CALL xerbla( 'DSYSV_AA_2STAGE', -info )
255  RETURN
256  ELSE IF( wquery .OR. tquery ) THEN
257  RETURN
258  END IF
259 *
260 *
261 * Compute the factorization A = U*T*U**T or A = L*T*L**T.
262 *
263  CALL dsytrf_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 dsytrs_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 DSYSV_AA_2STAGE
279 *
subroutine dsytrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
DSYTRF_AA_2STAGE
subroutine dsytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
DSYTRS_AA_2STAGE
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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