TESTING/MATGEN/zlahilb.f(3)

NAME
TESTING/MATGEN/zlahilb.f

SYNOPSIS

  Functions/Subroutines
subroutine zlahilb (n, nrhs, a, lda, x, ldx, b, ldb, work, info, path)
ZLAHILB

Function/Subroutine Documentation

  subroutine zlahilb (integer n, integer nrhs, complex*16, dimension(lda,n) a, integer lda, complex*16, dimension(ldx, nrhs) x, integer ldx, complex*16, dimension(ldb, nrhs) b, integer ldb, double precision, dimension(n) work, integer info, character*3 path)

ZLAHILB

Purpose:

    !>
    !> ZLAHILB generates an N by N scaled Hilbert matrix in A along with
    !> NRHS right-hand sides in B and solutions in X such that A*X=B.
    !>
    !> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all
    !> entries are integers.  The right-hand sides are the first NRHS
    !> columns of M * the identity matrix, and the solutions are the
    !> first NRHS columns of the inverse Hilbert matrix.
    !>
    !> The condition number of the Hilbert matrix grows exponentially with
    !> its size, roughly as O(e ** (3.5*N)).  Additionally, the inverse
    !> Hilbert matrices beyond a relatively small dimension cannot be
    !> generated exactly without extra precision.  Precision is exhausted
    !> when the largest entry in the inverse Hilbert matrix is greater than
    !> 2 to the power of the number of bits in the fraction of the data type
    !> used plus one, which is 24 for single precision.
    !>
    !> In single, the generated solution is exact for N <= 6 and has
    !> small componentwise error for 7 <= N <= 11.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The dimension of the matrix A.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The requested number of right-hand sides.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA, N)
    !>          The generated scaled Hilbert matrix.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= N.
    !>

    X

    !>          X is COMPLEX array, dimension (LDX, NRHS)
    !>          The generated exact solutions.  Currently, the first NRHS
    !>          columns of the inverse Hilbert matrix.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= N.
    !>

    B

    !>          B is REAL array, dimension (LDB, NRHS)
    !>          The generated right-hand sides.  Currently, the first NRHS
    !>          columns of LCM(1, 2, ..., 2*N-1) * the identity matrix.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= N.
    !>

    WORK

    !>          WORK is REAL array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          = 1: N is too large; the data is still generated but may not
    !>               be not exact.
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

    PATH

    !>          PATH is CHARACTER*3
    !>          The LAPACK path name.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 132 of file zlahilb.f.

Author

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