 LAPACK  3.10.0 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

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```

Definition at line 185 of file dsysv_aa_2stage.f.

188 *
189 * -- LAPACK computational routine --
190 * -- LAPACK is a software package provided by Univ. of Tennessee, --
191 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192 *
193  IMPLICIT NONE
194 *
195 * .. Scalar Arguments ..
196  CHARACTER UPLO
197  INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
198 * ..
199 * .. Array Arguments ..
200  INTEGER IPIV( * ), IPIV2( * )
201  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
202 * ..
203 *
204 * =====================================================================
205 *
206 * .. Local Scalars ..
207  LOGICAL UPPER, TQUERY, WQUERY
208  INTEGER LWKOPT
209 * ..
210 * .. External Functions ..
211  LOGICAL LSAME
212  EXTERNAL lsame
213 * ..
214 * .. External Subroutines ..
216  \$ xerbla
217 * ..
218 * .. Intrinsic Functions ..
219  INTRINSIC max
220 * ..
221 * .. Executable Statements ..
222 *
223 * Test the input parameters.
224 *
225  info = 0
226  upper = lsame( uplo, 'U' )
227  wquery = ( lwork.EQ.-1 )
228  tquery = ( ltb.EQ.-1 )
229  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
230  info = -1
231  ELSE IF( n.LT.0 ) THEN
232  info = -2
233  ELSE IF( nrhs.LT.0 ) THEN
234  info = -3
235  ELSE IF( lda.LT.max( 1, n ) ) THEN
236  info = -5
237  ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
238  info = -7
239  ELSE IF( ldb.LT.max( 1, n ) ) THEN
240  info = -11
241  ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
242  info = -13
243  END IF
244 *
245  IF( info.EQ.0 ) THEN
246  CALL dsytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
247  \$ ipiv2, work, -1, info )
248  lwkopt = int( work(1) )
249  END IF
250 *
251  IF( info.NE.0 ) THEN
252  CALL xerbla( 'DSYSV_AA_2STAGE', -info )
253  RETURN
254  ELSE IF( wquery .OR. tquery ) THEN
255  RETURN
256  END IF
257 *
258 *
259 * Compute the factorization A = U**T*T*U or A = L*T*L**T.
260 *
261  CALL dsytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
262  \$ work, lwork, info )
263  IF( info.EQ.0 ) THEN
264 *
265 * Solve the system A*X = B, overwriting B with X.
266 *
267  CALL dsytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
268  \$ ipiv2, b, ldb, info )
269 *
270  END IF
271 *
272  work( 1 ) = lwkopt
273 *
274  RETURN
275 *
276 * End of DSYSV_AA_2STAGE
277 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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