test_grudge.py

    r = actx.np.sqrt(nodes[0]**2 + nodes[1]**2)

    # FIXME: Bessel functions need to brought out of the symbolic
    # layer. Related issue: https://github.com/inducer/grudge/issues/93
    def bessel_j(actx, n, r):
        from grudge import sym, bind
        return bind(dcoll, sym.bessel_j(n, sym.var("r")))(actx, r=r)

    # https://dlmf.nist.gov/10.6.1
    n = 3
    bessel_zero = (bessel_j(actx, n+1, r)
                   + bessel_j(actx, n-1, r)
                   - 2*n/r * bessel_j(actx, n, r))

    z = op.norm(dcoll, bessel_zero, 2)

    assert z < 1e-15

# }}}


@pytest.mark.parametrize("p", [2, np.inf])
def test_norm_complex(actx_factory, p):
    actx = actx_factory()

    dim = 2
    mesh = mgen.generate_regular_rect_mesh(
            a=(0,)*dim, b=(1,)*dim,
            nelements_per_axis=(8,)*dim, order=1)
    dcoll = DiscretizationCollection(actx, mesh, order=4)

    nodes = thaw(dcoll.nodes(), actx)
    f = nodes[0] + 1j * nodes[0]

    norm = op.norm(dcoll, f, p)
    if p == 2:
        ref_norm = ((1/3)*dim)**0.5
    elif p == np.inf:
        ref_norm = 2**0.5

    assert abs(norm-ref_norm) / abs(ref_norm) < 1e-13


@pytest.mark.parametrize("p", [2, np.inf])
def test_norm_obj_array(actx_factory, p):
    """Test :func:`grudge.op.norm` for object arrays."""

    actx = actx_factory()

    dim = 2
    mesh = mgen.generate_regular_rect_mesh(
            a=(-0.5,)*dim, b=(0.5,)*dim,
            nelements_per_axis=(8,)*dim, order=1)
    dcoll = DiscretizationCollection(actx, mesh, order=4)

    w = make_obj_array([1.0, 2.0, 3.0])[:dim]

    # {{ scalar

    norm = op.norm(dcoll, w[0], p)

    norm_exact = w[0]
    logger.info("norm: %.5e %.5e", norm, norm_exact)
    assert abs(norm - norm_exact) < 1.0e-14

    # }}}

    # {{{ vector

    norm = op.norm(dcoll, w, p)

    norm_exact = np.sqrt(np.sum(w**2)) if p == 2 else np.max(w)
    logger.info("norm: %.5e %.5e", norm, norm_exact)
    assert abs(norm - norm_exact) < 1.0e-14

    # }}}


def test_empty_boundary(actx_factory):
    # https://github.com/inducer/grudge/issues/54

    from meshmode.mesh import BTAG_NONE

    actx = actx_factory()

    dim = 2
    mesh = mgen.generate_regular_rect_mesh(
            a=(-0.5,)*dim, b=(0.5,)*dim,
            nelements_per_axis=(8,)*dim, order=4)
    dcoll = DiscretizationCollection(actx, mesh, order=4)
    normal = dcoll.normal(BTAG_NONE)
    from meshmode.dof_array import DOFArray
    for component in normal:
        assert isinstance(component, DOFArray)
        assert len(component) == len(dcoll.discr_from_dd(BTAG_NONE).groups)


# You can test individual routines by typing
# $ python test_grudge.py 'test_routine()'

if __name__ == "__main__":
    import sys
    if len(sys.argv) > 1:
        exec(sys.argv[1])
    else:
        pytest.main([__file__])

# vim: fdm=marker