TESTING/MATGEN/slahilb.f(3)

NAME
TESTING/MATGEN/slahilb.f

SYNOPSIS

  Functions/Subroutines
subroutine slahilb (n, nrhs, a, lda, x, ldx, b, ldb, work, info)
SLAHILB

Function/Subroutine Documentation

  subroutine slahilb (integer n, integer nrhs, real, dimension(lda, n) a, integer lda, real, dimension(ldx, nrhs) x, integer ldx, real, dimension(ldb, nrhs) b, integer ldb, real, dimension(n) work, integer info)

SLAHILB

Purpose:

    !>
    !> SLAHILB 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 REAL 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 REAL 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 123 of file slahilb.f.

Author

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