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

Download SSYSV_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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