 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zsytri_3()

 subroutine zsytri_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 )

ZSYTRI_3

Purpose:
``` ZSYTRI_3 computes the inverse of a complex symmetric indefinite
matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

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

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

ZSYTRI_3 sets the leading dimension of the workspace  before calling
ZSYTRI_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 ZSYTRF_RK and ZSYTRF_BK: a) ONLY diagonal elements of the symmetric 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 symmetric 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 symmetric 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 ZSYTRF_RK or ZSYTRF_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 zsytri_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 zsytri_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, 'ZSYTRI_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( 'ZSYTRI_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 zsytri_3x( uplo, n, a, lda, e, ipiv, work, nb, info )
238*
239 work( 1 ) = lwkopt
240*
241 RETURN
242*
243* End of ZSYTRI_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 zsytri_3x(UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)
ZSYTRI_3X
Definition: zsytri_3x.f:159
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