SRC/zhetri_3.f(3)          Library Functions Manual          SRC/zhetri_3.f(3)

NAME
       SRC/zhetri_3.f

SYNOPSIS
   Functions/Subroutines
       subroutine zhetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           ZHETRI_3

Function/Subroutine Documentation
   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
           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).
           !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
           !>

           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.
           !>

           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.
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Contributors:


           !>
           !>  November 2017,  Igor Kozachenko,
           !>                  Computer Science Division,
           !>                  University of California, Berkeley
           !>
           !>

       Definition at line 168 of file zhetri_3.f.

Author
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LAPACK                          Version 3.12.0               SRC/zhetri_3.f(3)