LAPACK 3.11.0 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 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 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 EXTERNAL lsame
212* ..
213* .. External Subroutines ..
215 \$ xerbla
216* ..
217* .. Intrinsic Functions ..
218 INTRINSIC max
219* ..
220* .. Executable Statements ..
221*
222* Test the input parameters.
223*
224 info = 0
225 upper = lsame( uplo, 'U' )
226 wquery = ( lwork.EQ.-1 )
227 tquery = ( ltb.EQ.-1 )
228 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
229 info = -1
230 ELSE IF( n.LT.0 ) THEN
231 info = -2
232 ELSE IF( nrhs.LT.0 ) THEN
233 info = -3
234 ELSE IF( lda.LT.max( 1, n ) ) THEN
235 info = -5
236 ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
237 info = -7
238 ELSE IF( ldb.LT.max( 1, n ) ) THEN
239 info = -11
240 ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
241 info = -13
242 END IF
243*
244 IF( info.EQ.0 ) THEN
245 CALL ssytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
246 \$ ipiv2, work, -1, info )
247 lwkopt = int( work(1) )
248 END IF
249*
250 IF( info.NE.0 ) THEN
251 CALL xerbla( 'SSYSV_AA_2STAGE', -info )
252 RETURN
253 ELSE IF( wquery .OR. tquery ) THEN
254 RETURN
255 END IF
256*
257*
258* Compute the factorization A = U**T*T*U or A = L*T*L**T.
259*
260 CALL ssytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
261 \$ work, lwork, info )
262 IF( info.EQ.0 ) THEN
263*
264* Solve the system A*X = B, overwriting B with X.
265*
266 CALL ssytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
267 \$ ipiv2, b, ldb, info )
268*
269 END IF
270*
271 work( 1 ) = lwkopt
272*
273 RETURN
274*
275* End of SSYSV_AA_2STAGE
276*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
SSYTRS_AA_2STAGE
subroutine ssytrf_aa_2stage(UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
SSYTRF_AA_2STAGE
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