LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ chesv()

 subroutine chesv ( 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 )

CHESV computes the solution to system of linear equations A * X = B for HE matrices

Purpose:
``` CHESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**H,  if UPLO = 'U', or
A = L * D * L**H,  if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian 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 Hermitian 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**H or A = L*D*L**H as computed by CHETRF.``` [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 CHETRF. 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 CHETRF. 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 chesv.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, NB
190* ..
191* .. External Functions ..
192 LOGICAL LSAME
193 INTEGER ILAENV
194 REAL SROUNDUP_LWORK
195 EXTERNAL lsame, ilaenv, sroundup_lwork
196* ..
197* .. External Subroutines ..
198 EXTERNAL xerbla, chetrf, chetrs, chetrs2
199* ..
200* .. Intrinsic Functions ..
201 INTRINSIC max
202* ..
203* .. Executable Statements ..
204*
205* Test the input parameters.
206*
207 info = 0
208 lquery = ( lwork.EQ.-1 )
209 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
210 info = -1
211 ELSE IF( n.LT.0 ) THEN
212 info = -2
213 ELSE IF( nrhs.LT.0 ) THEN
214 info = -3
215 ELSE IF( lda.LT.max( 1, n ) ) THEN
216 info = -5
217 ELSE IF( ldb.LT.max( 1, n ) ) THEN
218 info = -8
219 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
220 info = -10
221 END IF
222*
223 IF( info.EQ.0 ) THEN
224 IF( n.EQ.0 ) THEN
225 lwkopt = 1
226 ELSE
227 nb = ilaenv( 1, 'CHETRF', uplo, n, -1, -1, -1 )
228 lwkopt = n*nb
229 END IF
230 work( 1 ) = sroundup_lwork(lwkopt)
231 END IF
232*
233 IF( info.NE.0 ) THEN
234 CALL xerbla( 'CHESV ', -info )
235 RETURN
236 ELSE IF( lquery ) THEN
237 RETURN
238 END IF
239*
240* Compute the factorization A = U*D*U**H or A = L*D*L**H.
241*
242 CALL chetrf( uplo, n, a, lda, ipiv, work, lwork, info )
243 IF( info.EQ.0 ) THEN
244*
245* Solve the system A*X = B, overwriting B with X.
246*
247 IF ( lwork.LT.n ) THEN
248*
249* Solve with TRS ( Use Level BLAS 2)
250*
251 CALL chetrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
252*
253 ELSE
254*
255* Solve with TRS2 ( Use Level BLAS 3)
256*
257 CALL chetrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
258*
259 END IF
260*
261 END IF
262*
263 work( 1 ) = sroundup_lwork(lwkopt)
264*
265 RETURN
266*
267* End of CHESV
268*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chetrf(uplo, n, a, lda, ipiv, work, lwork, info)
CHETRF
Definition chetrf.f:177
subroutine chetrs2(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)
CHETRS2
Definition chetrs2.f:127
subroutine chetrs(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
CHETRS
Definition chetrs.f:120
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
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