ZHETRI_3X 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.


 This is the blocked version of the algorithm, calling Level 3 BLAS.

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.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

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.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

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.

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.

WORK

          WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3).

NB

          NB is INTEGER


          Block size.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2017