Numerical Methods for Variational Problems - Canonical Ordering Nodes

example.py

def lagrange_points(cell, degree):
    """Construct the locations of the equispaced Lagrange nodes on cell.

    :param cell: the :class:`~.reference_elements.ReferenceCell`
    :param degree: the degree of polynomials for which to construct nodes.

    :returns: a rank 2 :class:`~numpy.array` whose rows are the
        coordinates of the nodes.

    The implementation of this function is left as an :ref:`exercise
    <ex-lagrange-points>`.

    """
    if cell is ReferenceInterval:
        points = [[i / degree] for i in range(degree + 1)]
        points_mapped = []

        for dim in range(0, cell.dim + 1):
            for entity in range(0, cell.entity_counts[dim]):
                for point in points:
                    if cell.point_in_entity(point, (dim, entity)) and point not in points_mapped:
                        points_mapped.append(point)

        return np.array(points_mapped, dtype=np.float64)
    elif cell is ReferenceTriangle:
        points = [[i / degree, j / degree]
                   for j in range(degree + 1)
                   for i in range(degree + 1 - j)]
        points_mapped = []

        for dim in range(0, cell.dim + 1):
            for entity in range(0, cell.entity_counts[dim]):
                for point in points:
                    if cell.point_in_entity(point, (dim, entity)) and point not in points_mapped:
                        points_mapped.append(point)

        return np.array(points_mapped, dtype=np.float64)
    else:
        return NotImplementedError