 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ csysv()

 subroutine csysv ( 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 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.

The diagonal pivoting method is used to factor A as
A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*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) Details of the interchanges and the block structure of D, as determined by CSYTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.``` [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 >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for CSYTRF. for LWORK < N, TRS will be done with Level BLAS 2 for LWORK >= N, TRS will be done with Level BLAS 3 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 169 of file csysv.f.

171 *
172 * -- LAPACK driver routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  CHARACTER UPLO
178  INTEGER INFO, LDA, LDB, LWORK, N, NRHS
179 * ..
180 * .. Array Arguments ..
181  INTEGER IPIV( * )
182  COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Local Scalars ..
188  LOGICAL LQUERY
189  INTEGER LWKOPT
190 * ..
191 * .. External Functions ..
192  LOGICAL LSAME
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL xerbla, csytrf, csytrs, csytrs2
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input parameters.
204 *
205  info = 0
206  lquery = ( lwork.EQ.-1 )
207  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
208  info = -1
209  ELSE IF( n.LT.0 ) THEN
210  info = -2
211  ELSE IF( nrhs.LT.0 ) THEN
212  info = -3
213  ELSE IF( lda.LT.max( 1, n ) ) THEN
214  info = -5
215  ELSE IF( ldb.LT.max( 1, n ) ) THEN
216  info = -8
217  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
218  info = -10
219  END IF
220 *
221  IF( info.EQ.0 ) THEN
222  IF( n.EQ.0 ) THEN
223  lwkopt = 1
224  ELSE
225  CALL csytrf( uplo, n, a, lda, ipiv, work, -1, info )
226  lwkopt = real( work(1) )
227  END IF
228  work( 1 ) = lwkopt
229  END IF
230 *
231  IF( info.NE.0 ) THEN
232  CALL xerbla( 'CSYSV ', -info )
233  RETURN
234  ELSE IF( lquery ) THEN
235  RETURN
236  END IF
237 *
238 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
239 *
240  CALL csytrf( uplo, n, a, lda, ipiv, work, lwork, info )
241  IF( info.EQ.0 ) THEN
242 *
243 * Solve the system A*X = B, overwriting B with X.
244 *
245  IF ( lwork.LT.n ) THEN
246 *
247 * Solve with TRS ( Use Level BLAS 2)
248 *
249  CALL csytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
250 *
251  ELSE
252 *
253 * Solve with TRS2 ( Use Level BLAS 3)
254 *
255  CALL csytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
256 *
257  END IF
258 *
259  END IF
260 *
261  work( 1 ) = lwkopt
262 *
263  RETURN
264 *
265 * End of CSYSV
266 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine csytrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
CSYTRS2
Definition: csytrs2.f:132
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:120
subroutine csytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CSYTRF
Definition: csytrf.f:182
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