 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zsysv_aa()

 subroutine zsysv_aa ( character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

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

Purpose:
``` ZSYSV 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 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 tridiagonal. The factored
form of A is then used to solve the system of equations A * X = B.```
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 number of linear equations, i.e., 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, if INFO = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by ZSYTRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [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).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` LWORK is INTEGER The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for the best performance, LWORK >= MAX(1,N*NB), where NB is the optimal blocksize for ZSYTRF_AA. 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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.```

Definition at line 160 of file zsysv_aa.f.

162*
163* -- LAPACK driver routine --
164* -- LAPACK is a software package provided by Univ. of Tennessee, --
165* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167* .. Scalar Arguments ..
168 CHARACTER UPLO
169 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
170* ..
171* .. Array Arguments ..
172 INTEGER IPIV( * )
173 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
174* ..
175*
176* =====================================================================
177*
178* .. Local Scalars ..
179 LOGICAL LQUERY
180 INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
181* ..
182* .. External Functions ..
183 LOGICAL LSAME
184 INTEGER ILAENV
185 EXTERNAL ilaenv, lsame
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla, zsytrf_aa, zsytrs_aa
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max
192* ..
193* .. Executable Statements ..
194*
195* Test the input parameters.
196*
197 info = 0
198 lquery = ( lwork.EQ.-1 )
199 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
200 info = -1
201 ELSE IF( n.LT.0 ) THEN
202 info = -2
203 ELSE IF( nrhs.LT.0 ) THEN
204 info = -3
205 ELSE IF( lda.LT.max( 1, n ) ) THEN
206 info = -5
207 ELSE IF( ldb.LT.max( 1, n ) ) THEN
208 info = -8
209 ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
210 info = -10
211 END IF
212*
213 IF( info.EQ.0 ) THEN
214 CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
215 lwkopt_sytrf = int( work(1) )
216 CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
217 \$ -1, info )
218 lwkopt_sytrs = int( work(1) )
219 lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
220 work( 1 ) = lwkopt
221 END IF
222*
223 IF( info.NE.0 ) THEN
224 CALL xerbla( 'ZSYSV_AA ', -info )
225 RETURN
226 ELSE IF( lquery ) THEN
227 RETURN
228 END IF
229*
230* Compute the factorization A = U**T*T*U or A = L*T*L**T.
231*
232 CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
233 IF( info.EQ.0 ) THEN
234*
235* Solve the system A*X = B, overwriting B with X.
236*
237 CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
238 \$ lwork, info )
239*
240 END IF
241*
242 work( 1 ) = lwkopt
243*
244 RETURN
245*
246* End of ZSYSV_AA
247*
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zsytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYTRS_AA
Definition: zsytrs_aa.f:131
subroutine zsytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF_AA
Definition: zsytrf_aa.f:132
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