LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zsysv_aa_2stage()

 subroutine zsysv_aa_2stage ( character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info )

ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:
``` ZSYSV_AA_2STAGE computes the solution to a complex 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 183 of file zsysv_aa_2stage.f.

186*
187* -- LAPACK computational routine --
188* -- LAPACK is a software package provided by Univ. of Tennessee, --
189* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190*
191 IMPLICIT NONE
192*
193* .. Scalar Arguments ..
194 CHARACTER UPLO
195 INTEGER N, NRHS, LDA, LDB, LTB, LWORK, INFO
196* ..
197* .. Array Arguments ..
198 INTEGER IPIV( * ), IPIV2( * )
199 COMPLEX*16 A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
200* ..
201*
202* =====================================================================
203*
204* .. Local Scalars ..
205 LOGICAL UPPER, TQUERY, WQUERY
206 INTEGER LWKOPT
207* ..
208* .. External Functions ..
209 LOGICAL LSAME
210 EXTERNAL lsame
211* ..
212* .. External Subroutines ..
213 EXTERNAL xerbla, zsytrf_aa_2stage,
215* ..
216* .. Intrinsic Functions ..
217 INTRINSIC max
218* ..
219* .. Executable Statements ..
220*
221* Test the input parameters.
222*
223 info = 0
224 upper = lsame( uplo, 'U' )
225 wquery = ( lwork.EQ.-1 )
226 tquery = ( ltb.EQ.-1 )
227 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
228 info = -1
229 ELSE IF( n.LT.0 ) THEN
230 info = -2
231 ELSE IF( nrhs.LT.0 ) THEN
232 info = -3
233 ELSE IF( lda.LT.max( 1, n ) ) THEN
234 info = -5
235 ELSE IF( ltb.LT.( 4*n ) .AND. .NOT.tquery ) THEN
236 info = -7
237 ELSE IF( ldb.LT.max( 1, n ) ) THEN
238 info = -11
239 ELSE IF( lwork.LT.n .AND. .NOT.wquery ) THEN
240 info = -13
241 END IF
242*
243 IF( info.EQ.0 ) THEN
244 CALL zsytrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
245 \$ ipiv2, work, -1, info )
246 lwkopt = int( work(1) )
247 END IF
248*
249 IF( info.NE.0 ) THEN
250 CALL xerbla( 'ZSYSV_AA_2STAGE', -info )
251 RETURN
252 ELSE IF( wquery .OR. tquery ) THEN
253 RETURN
254 END IF
255*
256*
257* Compute the factorization A = U**T*T*U or A = L*T*L**T.
258*
259 CALL zsytrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
260 \$ work, lwork, info )
261 IF( info.EQ.0 ) THEN
262*
263* Solve the system A*X = B, overwriting B with X.
264*
265 CALL zsytrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
266 \$ ipiv2, b, ldb, info )
267*
268 END IF
269*
270 work( 1 ) = lwkopt
271*
272* End of ZSYSV_AA_2STAGE
273*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zsytrf_aa_2stage(uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
ZSYTRF_AA_2STAGE
subroutine zsytrs_aa_2stage(uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
ZSYTRS_AA_2STAGE
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
Here is the call graph for this function:
Here is the caller graph for this function: