SRC/chetri_3.f(3)

NAME
SRC/chetri_3.f

SYNOPSIS

  Functions/Subroutines
subroutine chetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
CHETRI_3

Function/Subroutine Documentation

  subroutine chetri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CHETRI_3

Purpose:

    !> CHETRI_3 computes the inverse of a complex Hermitian indefinite
    !> matrix A using the factorization computed by CHETRF_RK or CHETRF_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.
    !>
    !> CHETRI_3 sets the leading dimension of the workspace  before calling
    !> CHETRI_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 array, dimension (LDA,N)
    !>          On entry, diagonal of the block diagonal matrix D and
    !>          factors U or L as computed by CHETRF_RK and CHETRF_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 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 CHETRF_RK or CHETRF_BK.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (MAX(1,LWORK)).
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK.
    !>          If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).
    !>
    !>          If LWORK = -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 169 of file chetri_3.f.

Author

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