LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ 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

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

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

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 = int( 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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