LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssysv_aa_2stage()

 subroutine ssysv_aa_2stage ( character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info )

SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:
``` SSYSV_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 REAL 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 subdiagonal 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 REAL 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 REAL 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 REAL 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 184 of file ssysv_aa_2stage.f.

187*
188* -- LAPACK driver routine --
189* -- LAPACK is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192 IMPLICIT NONE
193*
194* .. Scalar Arguments ..
195 CHARACTER UPLO
196 INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
197* ..
198* .. Array Arguments ..
199 INTEGER IPIV( * ), IPIV2( * )
200 REAL A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
201* ..
202*
203* =====================================================================
204* ..
205* .. Local Scalars ..
206 LOGICAL UPPER, TQUERY, WQUERY
207 INTEGER LWKOPT
208* ..
209* .. External Functions ..
210 LOGICAL LSAME
211 REAL SROUNDUP_LWORK
212 EXTERNAL lsame, sroundup_lwork
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 ssytrf_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( 'SSYSV_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 ssytrf_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 ssytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
268 \$ ipiv2, b, ldb, info )
269*
270 END IF
271*
272 work( 1 ) = sroundup_lwork(lwkopt)
273*
274 RETURN
275*
276* End of SSYSV_AA_2STAGE
277*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssytrf_aa_2stage(uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
SSYTRF_AA_2STAGE
subroutine ssytrs_aa_2stage(uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
SSYTRS_AA_2STAGE
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
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