LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zsysv()

 subroutine zsysv ( 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 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.

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*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 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 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) Details of the interchanges and the block structure of D, as determined by ZSYTRF. 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*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 >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZSYTRF. 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.
Date
December 2016

Definition at line 173 of file zsysv.f.

173 *
174 * -- LAPACK driver routine (version 3.7.0) --
175 * -- LAPACK is a software package provided by Univ. of Tennessee, --
176 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177 * December 2016
178 *
179 * .. Scalar Arguments ..
180  CHARACTER uplo
181  INTEGER info, lda, ldb, lwork, n, nrhs
182 * ..
183 * .. Array Arguments ..
184  INTEGER ipiv( * )
185  COMPLEX*16 a( lda, * ), b( ldb, * ), work( * )
186 * ..
187 *
188 * =====================================================================
189 *
190 * .. Local Scalars ..
191  LOGICAL lquery
192  INTEGER lwkopt
193 * ..
194 * .. External Functions ..
195  LOGICAL lsame
196  EXTERNAL lsame
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL xerbla, zsytrf, zsytrs, zsytrs2
200 * ..
201 * .. Intrinsic Functions ..
202  INTRINSIC max
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input parameters.
207 *
208  info = 0
209  lquery = ( lwork.EQ.-1 )
210  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
211  info = -1
212  ELSE IF( n.LT.0 ) THEN
213  info = -2
214  ELSE IF( nrhs.LT.0 ) THEN
215  info = -3
216  ELSE IF( lda.LT.max( 1, n ) ) THEN
217  info = -5
218  ELSE IF( ldb.LT.max( 1, n ) ) THEN
219  info = -8
220  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
221  info = -10
222  END IF
223 *
224  IF( info.EQ.0 ) THEN
225  IF( n.EQ.0 ) THEN
226  lwkopt = 1
227  ELSE
228  CALL zsytrf( uplo, n, a, lda, ipiv, work, -1, info )
229  lwkopt = work(1)
230  END IF
231  work( 1 ) = lwkopt
232  END IF
233 *
234  IF( info.NE.0 ) THEN
235  CALL xerbla( 'ZSYSV ', -info )
236  RETURN
237  ELSE IF( lquery ) THEN
238  RETURN
239  END IF
240 *
241 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
242 *
243  CALL zsytrf( uplo, n, a, lda, ipiv, work, lwork, info )
244  IF( info.EQ.0 ) THEN
245 *
246 * Solve the system A*X = B, overwriting B with X.
247 *
248  IF ( lwork.LT.n ) THEN
249 *
250 * Solve with TRS ( Use Level BLAS 2)
251 *
252  CALL zsytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
253 *
254  ELSE
255 *
256 * Solve with TRS2 ( Use Level BLAS 3)
257 *
258  CALL zsytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
259 *
260  END IF
261 *
262  END IF
263 *
264  work( 1 ) = lwkopt
265 *
266  RETURN
267 *
268 * End of ZSYSV
269 *
subroutine zsytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF
Definition: zsytrf.f:184
subroutine zsytrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
ZSYTRS2
Definition: zsytrs2.f:134
subroutine zsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZSYTRS
Definition: zsytrs.f:122
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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