LAPACK  3.9.0
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 * T * U,  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
          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 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
          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 190 of file dsysv_aa_2stage.f.

190 *
191 * -- LAPACK computational routine (version 3.8.0) --
192 * -- LAPACK is a software package provided by Univ. of Tennessee, --
193 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
194 * November 2017
195 *
196  IMPLICIT NONE
197 *
198 * .. Scalar Arguments ..
199  CHARACTER UPLO
200  INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
201 * ..
202 * .. Array Arguments ..
203  INTEGER IPIV( * ), IPIV2( * )
204  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
205 * ..
206 *
207 * =====================================================================
208 *
209 * .. Local Scalars ..
210  LOGICAL UPPER, TQUERY, WQUERY
211  INTEGER LWKOPT
212 * ..
213 * .. External Functions ..
214  LOGICAL LSAME
215  EXTERNAL lsame
216 * ..
217 * .. External Subroutines ..
218  EXTERNAL dsytrf_aa_2stage, dsytrs_aa_2stage,
219  $ xerbla
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 dsytrf_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( 'DSYSV_AA_2STAGE', -info )
256  RETURN
257  ELSE IF( wquery .OR. tquery ) THEN
258  RETURN
259  END IF
260 *
261 *
262 * Compute the factorization A = U**T*T*U or A = L*T*L**T.
263 *
264  CALL dsytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
265  $ work, lwork, info )
266  IF( info.EQ.0 ) THEN
267 *
268 * Solve the system A*X = B, overwriting B with X.
269 *
270  CALL dsytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
271  $ ipiv2, b, ldb, info )
272 *
273  END IF
274 *
275  work( 1 ) = lwkopt
276 *
277  RETURN
278 *
279 * End of DSYSV_AA_2STAGE
280 *
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dsytrf_aa_2stage
subroutine dsytrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
DSYTRF_AA_2STAGE
Definition: dsytrf_aa_2stage.f:162
dsytrs_aa_2stage
subroutine dsytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
DSYTRS_AA_2STAGE
Definition: dsytrs_aa_2stage.f:141
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55