from math import fsum

import numpy as np


def is_near_equal(a, b, tol):
    return np.allclose(a, b, rtol=0.0, atol=tol)


def run(mesh, volume, convol_norms, ce_ratio_norms, cellvol_norms, tol=1.0e-12):
    # Check cell volumes.
    total_cellvolume = fsum(mesh.cell_volumes)
    assert abs(volume - total_cellvolume) < tol * volume, total_cellvolume
    norm2 = np.linalg.norm(mesh.cell_volumes, ord=2)
    norm_inf = np.linalg.norm(mesh.cell_volumes, ord=np.inf)
    assert is_near_equal(cellvol_norms, [norm2, norm_inf], tol), [norm2, norm_inf]

    # If everything is Delaunay and the boundary elements aren't flat, the volume of the
    # domain is given by
    #   1/n * edge_lengths * ce_ratios.
    # Unfortunately, this isn't always the case.
    # ```
    # total_ce_ratio = \
    #     fsum(mesh.edge_lengths**2 * mesh.get_ce_ratios_per_edge() / dim)
    # self.assertAlmostEqual(volume, total_ce_ratio, delta=tol * volume)
    # ```
    # Check ce_ratio norms.
    alpha2 = fsum((mesh.ce_ratios**2).flat)
    alpha_inf = max(abs(mesh.ce_ratios).flat)
    assert is_near_equal(ce_ratio_norms, [alpha2, alpha_inf], tol), [alpha2, alpha_inf]

    # Check the volume by summing over the absolute value of the control volumes.
    vol = fsum(mesh.control_volumes)
    assert abs(volume - vol) < tol * volume, vol
    # Check control volume norms.
    norm2 = np.linalg.norm(mesh.control_volumes, ord=2)
    norm_inf = np.linalg.norm(mesh.control_volumes, ord=np.inf)
    assert is_near_equal(convol_norms, [norm2, norm_inf], tol), [norm2, norm_inf]


def assert_norms(x, ref, tol):
    ref = np.asarray(ref)
    val = np.array(
        [
            np.linalg.norm(x.flat, 1),
            np.linalg.norm(x.flat, 2),
            np.linalg.norm(x.flat, np.inf),
        ]
    )
    assert np.all(np.abs(val - ref) < tol * np.abs(ref)), (
        "Norms don't coincide.\n"
        f"Expected: [{ref[0]:.16e}, {ref[1]:.16e}, {ref[2]:.16e}]\n"
        f"Computed: [{val[0]:.16e}, {val[1]:.16e}, {val[2]:.16e}]\n"
    )