LAPACK  3.9.0 LAPACK: Linear Algebra PACKage

## ◆ csysv_aa()

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

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

Purpose:
``` CSYSV 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 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 CSYTRF.``` [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 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 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(2*N, 3*N-2), and for the best performance, LWORK >= max(1,N*NB), where NB is the optimal blocksize for CSYTRF_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.```
Date
November 2017

Definition at line 164 of file csysv_aa.f.

164 *
165 * -- LAPACK driver routine (version 3.8.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * November 2017
169 *
170 * .. Scalar Arguments ..
171  CHARACTER UPLO
172  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
173 * ..
174 * .. Array Arguments ..
175  INTEGER IPIV( * )
176  COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. Local Scalars ..
182  LOGICAL LQUERY
183  INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
184 * ..
185 * .. External Functions ..
186  LOGICAL LSAME
187  INTEGER ILAENV
188  EXTERNAL ilaenv, lsame
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL xerbla, csytrf_aa, csytrs_aa
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC max
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input parameters.
199 *
200  info = 0
201  lquery = ( lwork.EQ.-1 )
202  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
203  info = -1
204  ELSE IF( n.LT.0 ) THEN
205  info = -2
206  ELSE IF( nrhs.LT.0 ) THEN
207  info = -3
208  ELSE IF( lda.LT.max( 1, n ) ) THEN
209  info = -5
210  ELSE IF( ldb.LT.max( 1, n ) ) THEN
211  info = -8
212  ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
213  info = -10
214  END IF
215 *
216  IF( info.EQ.0 ) THEN
217  CALL csytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
218  lwkopt_sytrf = int( work(1) )
219  CALL csytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
220  \$ -1, info )
221  lwkopt_sytrs = int( work(1) )
222  lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
223  work( 1 ) = lwkopt
224  END IF
225 *
226  IF( info.NE.0 ) THEN
227  CALL xerbla( 'CSYSV_AA ', -info )
228  RETURN
229  ELSE IF( lquery ) THEN
230  RETURN
231  END IF
232 *
233 * Compute the factorization A = U**T*T*U or A = L*T*L**T.
234 *
235  CALL csytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
236  IF( info.EQ.0 ) THEN
237 *
238 * Solve the system A*X = B, overwriting B with X.
239 *
240  CALL csytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
241  \$ lwork, info )
242 *
243  END IF
244 *
245  work( 1 ) = lwkopt
246 *
247  RETURN
248 *
249 * End of CSYSV_AA
250 *
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csytrf_aa
subroutine csytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CSYTRF_AA
Definition: csytrf_aa.f:134
csytrs_aa
subroutine csytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
CSYTRS_AA
Definition: csytrs_aa.f:133
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
ilaenv
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83