 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhetri_3()

 subroutine zhetri_3 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZHETRI_3

Purpose:
``` ZHETRI_3 computes the inverse of a complex Hermitian indefinite
matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

ZHETRI_3 sets the leading dimension of the workspace  before calling
ZHETRI_3X that actually computes the inverse.  This is the blocked
version of the algorithm, calling Level 3 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. On exit, if INFO = 0, the Hermitian inverse of the original matrix. If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] E ``` E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.``` [out] WORK ``` WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` LWORK is INTEGER The length of WORK. LWORK >= (N+NB+1)*(NB+3). If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of 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) = 0; the matrix is singular and its inverse could not be computed.```
Contributors:
```  November 2017,  Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 168 of file zhetri_3.f.

170 *
171 * -- LAPACK computational routine --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 *
175 * .. Scalar Arguments ..
176  CHARACTER UPLO
177  INTEGER INFO, LDA, LWORK, N
178 * ..
179 * .. Array Arguments ..
180  INTEGER IPIV( * )
181  COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
182 * ..
183 *
184 * =====================================================================
185 *
186 * .. Local Scalars ..
187  LOGICAL UPPER, LQUERY
188  INTEGER LWKOPT, NB
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  INTEGER ILAENV
193  EXTERNAL lsame, ilaenv
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL zhetri_3x, xerbla
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input parameters.
204 *
205  info = 0
206  upper = lsame( uplo, 'U' )
207  lquery = ( lwork.EQ.-1 )
208 *
209 * Determine the block size
210 *
211  nb = max( 1, ilaenv( 1, 'ZHETRI_3', uplo, n, -1, -1, -1 ) )
212  lwkopt = ( n+nb+1 ) * ( nb+3 )
213 *
214  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
215  info = -1
216  ELSE IF( n.LT.0 ) THEN
217  info = -2
218  ELSE IF( lda.LT.max( 1, n ) ) THEN
219  info = -4
220  ELSE IF ( lwork .LT. lwkopt .AND. .NOT.lquery ) THEN
221  info = -8
222  END IF
223 *
224  IF( info.NE.0 ) THEN
225  CALL xerbla( 'ZHETRI_3', -info )
226  RETURN
227  ELSE IF( lquery ) THEN
228  work( 1 ) = lwkopt
229  RETURN
230  END IF
231 *
232 * Quick return if possible
233 *
234  IF( n.EQ.0 )
235  \$ RETURN
236 *
237  CALL zhetri_3x( uplo, n, a, lda, e, ipiv, work, nb, info )
238 *
239  work( 1 ) = lwkopt
240 *
241  RETURN
242 *
243 * End of ZHETRI_3
244 *
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 zhetri_3x(UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)
ZHETRI_3X
Definition: zhetri_3x.f:159
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