LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ zhesv()

subroutine zhesv ( 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 
)

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

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

Purpose:
 ZHESV 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*16 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
          ZHETRF.
[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 ZHETRF.  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
          ZHETRF.
          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 zhesv.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*16 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  EXTERNAL lsame, ilaenv
195 * ..
196 * .. External Subroutines ..
197  EXTERNAL xerbla, zhetrf, zhetrs, zhetrs2
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC max
201 * ..
202 * .. Executable Statements ..
203 *
204 * Test the input parameters.
205 *
206  info = 0
207  lquery = ( lwork.EQ.-1 )
208  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
209  info = -1
210  ELSE IF( n.LT.0 ) THEN
211  info = -2
212  ELSE IF( nrhs.LT.0 ) THEN
213  info = -3
214  ELSE IF( lda.LT.max( 1, n ) ) THEN
215  info = -5
216  ELSE IF( ldb.LT.max( 1, n ) ) THEN
217  info = -8
218  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
219  info = -10
220  END IF
221 *
222  IF( info.EQ.0 ) THEN
223  IF( n.EQ.0 ) THEN
224  lwkopt = 1
225  ELSE
226  nb = ilaenv( 1, 'ZHETRF', uplo, n, -1, -1, -1 )
227  lwkopt = n*nb
228  END IF
229  work( 1 ) = lwkopt
230  END IF
231 *
232  IF( info.NE.0 ) THEN
233  CALL xerbla( 'ZHESV ', -info )
234  RETURN
235  ELSE IF( lquery ) THEN
236  RETURN
237  END IF
238 *
239 * Compute the factorization A = U*D*U**H or A = L*D*L**H.
240 *
241  CALL zhetrf( uplo, n, a, lda, ipiv, work, lwork, info )
242  IF( info.EQ.0 ) THEN
243 *
244 * Solve the system A*X = B, overwriting B with X.
245 *
246  IF ( lwork.LT.n ) THEN
247 *
248 * Solve with TRS ( Use Level BLAS 2)
249 *
250  CALL zhetrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
251 *
252  ELSE
253 *
254 * Solve with TRS2 ( Use Level BLAS 3)
255 *
256  CALL zhetrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
257 *
258  END IF
259 *
260  END IF
261 *
262  work( 1 ) = lwkopt
263 *
264  RETURN
265 *
266 * End of ZHESV
267 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zhetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS
Definition: zhetrs.f:120
subroutine zhetrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF
Definition: zhetrf.f:177
subroutine zhetrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
ZHETRS2
Definition: zhetrs2.f:127
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