test_grudge.py

    r = sym.cse(sym.sqrt(nodes[0]**2 + nodes[1]**2))

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

    z = bind(discr, sym.norm(2, bessel_zero))(actx)

    assert z < 1e-15

# }}}


# {{{ function symbol

def test_external_call(actx_factory):
    actx = actx_factory()

    def double(queue, x):
        return 2 * x

    dims = 2

    mesh = mgen.generate_regular_rect_mesh(
            a=(0,) * dims, b=(1,) * dims, nelements_per_axis=(4,) * dims)
    discr = DiscretizationCollection(actx, mesh, order=1)

    ones = sym.Ones(dof_desc.DD_VOLUME)
    op = (
            ones * 3
            + sym.FunctionSymbol("double")(ones))

    from grudge.function_registry import (
            base_function_registry, register_external_function)

    freg = register_external_function(
            base_function_registry,
            "double",
            implementation=double,
            dd=dof_desc.DD_VOLUME)

    bound_op = bind(discr, op, function_registry=freg)

    result = bound_op(actx, double=double)
    assert actx.to_numpy(flatten(result) == 5).all()


@pytest.mark.parametrize("array_type", ["scalar", "vector"])
def test_function_symbol_array(actx_factory, array_type):
    """Test if `FunctionSymbol` distributed properly over 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=4)
    discr = DiscretizationCollection(actx, mesh, order=4)
    volume_discr = discr.discr_from_dd(dof_desc.DD_VOLUME)

    if array_type == "scalar":
        sym_x = sym.var("x")
        x = thaw(actx, actx.np.cos(volume_discr.nodes()[0]))
    elif array_type == "vector":
        sym_x = sym.make_sym_array("x", dim)
        x = thaw(actx, volume_discr.nodes())
    else:
        raise ValueError("unknown array type")

    norm = bind(discr, sym.norm(2, sym_x))(x=x)
    assert isinstance(norm, float)

# }}}


@pytest.mark.parametrize("p", [2, np.inf])
def test_norm_obj_array(actx_factory, p):
    """Test :func:`grudge.symbolic.operators.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)
    discr = DiscretizationCollection(actx, mesh, order=4)

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

    # {{ scalar

    sym_w = sym.var("w")
    norm = bind(discr, sym.norm(p, sym_w))(actx, w=w[0])

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

    # }}}

    # {{{ vector

    sym_w = sym.make_sym_array("w", dim)
    norm = bind(discr, sym.norm(p, sym_w))(actx, w=w)

    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_map_if(actx_factory):
    """Test :meth:`grudge.symbolic.execution.ExecutionMapper.map_if` handling
    of scalar conditions.
    """

    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)
    discr = DiscretizationCollection(actx, mesh, order=4)

    sym_if = sym.If(sym.Comparison(2.0, "<", 1.0e-14), 1.0, 2.0)
    bind(discr, sym_if)(actx)


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)
    discr = DiscretizationCollection(actx, mesh, order=4)
    normal = bind(discr,
            sym.normal(BTAG_NONE, dim, dim=dim - 1))(actx)
    from meshmode.dof_array import DOFArray
    for component in normal:
        assert isinstance(component, DOFArray)
        assert len(component) == len(discr.discr_from_dd(BTAG_NONE).groups)


def test_operator_compiler_overwrite(actx_factory):
    """Tests that the same expression in ``eval_code`` and ``discr_code``
    does not confuse the OperatorCompiler in grudge/symbolic/compiler.py.
    """

    actx = actx_factory()

    ambient_dim = 2
    target_order = 4

    from meshmode.mesh.generation import generate_regular_rect_mesh
    mesh = generate_regular_rect_mesh(
            a=(-0.5,)*ambient_dim, b=(0.5,)*ambient_dim,
            n=(8,)*ambient_dim, order=1)
    discr = DiscretizationCollection(actx, mesh, order=target_order)

    # {{{ test

    sym_u = sym.nodes(ambient_dim)
    sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))

    div_u = bind(discr, sym_div_u)(actx)
    error = bind(discr, sym.norm(2, sym.var("x")))(actx, x=div_u - discr.dim)
    logger.info("error: %.5e", error)

    # }}}


@pytest.mark.parametrize("ambient_dim", [
    2,
    # FIXME, cf. https://github.com/inducer/grudge/pull/78/
    pytest.param(3, marks=pytest.mark.xfail)
    ])
def test_incorrect_assignment_aggregation(actx_factory, ambient_dim):
    """Tests that the greedy assignemnt aggregation code works on a non-trivial
    expression (on which it didn't work at the time of writing).
    """

    actx = actx_factory()

    target_order = 4

    from meshmode.mesh.generation import generate_regular_rect_mesh
    mesh = generate_regular_rect_mesh(
            a=(-0.5,)*ambient_dim, b=(0.5,)*ambient_dim,
            n=(8,)*ambient_dim, order=1)
    discr = DiscretizationCollection(actx, mesh, order=target_order)

    # {{{ test with a relative norm

    from grudge.dof_desc import DD_VOLUME
    dd = DD_VOLUME
    sym_x = sym.make_sym_array("y", ambient_dim, dd=dd)
    sym_y = sym.make_sym_array("y", ambient_dim, dd=dd)

    sym_norm_y = sym.norm(2, sym_y, dd=dd)
    sym_norm_d = sym.norm(2, sym_x - sym_y, dd=dd)
    sym_op = sym_norm_d / sym_norm_y
    logger.info("%s", sym.pretty(sym_op))

    # FIXME: this shouldn't raise a RuntimeError
    with pytest.raises(RuntimeError):
        bind(discr, sym_op)(actx, x=1.0, y=discr.discr_from_dd(dd).nodes())

    # }}}

    # {{{ test with repeated mass inverses

    sym_minv_y = sym.cse(sym.InverseMassOperator()(sym_y), "minv_y")

    sym_u = make_obj_array([0.5 * sym.Ones(dd), 0.0, 0.0])[:ambient_dim]
    sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))

    sym_op = sym.MassOperator(dd)(sym_u) \
            + sym.MassOperator(dd)(sym_minv_y * sym_div_u)
    logger.info("%s", sym.pretty(sym_op))

    # FIXME: this shouldn't raise a RuntimeError either
    bind(discr, sym_op)(actx, y=discr.discr_from_dd(dd).nodes())

    # }}}


# 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