polymers 0.3.7

"""Module to test the local module.

"""
import unittest
import numpy as np
from polymers import physics
from ..test import Parameters

parameters = Parameters()
WLC = physics.single_chain.wlc.thermodynamics.isotensional.WLC


class Base(unittest.TestCase):
    """Class for basic tests.

    """
    def test_init(self):
        """Function to test instantiation.

        """
        for _ in range(parameters.number_of_loops):
            _ = WLC(
                parameters.number_of_links_minimum,
                parameters.link_length_reference,
                parameters.hinge_mass_reference,
                parameters.persistance_length_reference
            )

    def test_number_of_links(self):
        """Function to test the number of links during instantiation.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            self.assertEqual(
                number_of_links,
                WLC(
                    number_of_links,
                    parameters.link_length_reference,
                    parameters.hinge_mass_reference,
                    parameters.persistance_length_reference
                ).number_of_links
            )

    def test_link_length(self):
        """Function to test the link length during instantiation.

        """
        for _ in range(parameters.number_of_loops):
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            self.assertEqual(
                link_length,
                WLC(
                    parameters.number_of_links_minimum,
                    link_length,
                    parameters.hinge_mass_reference,
                    parameters.persistance_length_reference
                ).link_length
            )

    def test_hinge_mass(self):
        """Function to test the hinge mass during instantiation.

        """
        for _ in range(parameters.number_of_loops):
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            self.assertEqual(
                hinge_mass,
                WLC(
                    parameters.number_of_links_minimum,
                    parameters.link_length_reference,
                    hinge_mass,
                    parameters.persistance_length_reference
                ).hinge_mass
            )

    def test_persistance_length(self):
        """Function to test the persistance length during instantiation.

        """
        for _ in range(parameters.number_of_loops):
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            self.assertEqual(
                persistance_length,
                WLC(
                    parameters.number_of_links_minimum,
                    parameters.link_length_reference,
                    parameters.hinge_mass_reference,
                    persistance_length
                ).persistance_length
            )

    def test_all_parameters(self):
        """Function to test all parameters during instantiation.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            self.assertEqual(
                number_of_links,
                model.number_of_links
            )
            self.assertEqual(
                link_length,
                model.link_length
            )
            self.assertEqual(
                hinge_mass,
                model.hinge_mass,
                persistance_length
            )
            self.assertEqual(
                persistance_length,
                model.persistance_length
            )


class Nondimensional(unittest.TestCase):
    """Class for nondimensionalization tests.

    """
    def test_end_to_end_length(self):
        """Function to test the nondimensionalization
        of the end-to-end length.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length = \

                model.nondimensional_end_to_end_length(
                    np.array(nondimensional_force)
                )
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length = \

                model.end_to_end_length(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                end_to_end_length \

                / link_length \

                - nondimensional_end_to_end_length
            residual_rel = \

                residual_abs / \

                nondimensional_end_to_end_length
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_end_to_end_length_per_link(self):
        """Function to test the nondimensionalization
        of the end-to-end length per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length_per_link = \

                model.nondimensional_end_to_end_length_per_link(
                    np.array(nondimensional_force)
                )
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length_per_link = \

                model.end_to_end_length_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                end_to_end_length_per_link \

                / link_length \

                - nondimensional_end_to_end_length_per_link
            residual_rel = \

                residual_abs / \

                nondimensional_end_to_end_length_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_gibbs_free_energy(self):
        """Function to test the nondimensionalization
        of the Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy = \

                model.nondimensional_gibbs_free_energy(
                    np.array(nondimensional_force),
                    temperature
                )
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy = \

                model.gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy / \

                parameters.boltzmann_constant/temperature \

                - nondimensional_gibbs_free_energy
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_gibbs_free_energy_per_link(self):
        """Function to test the nondimensionalization
        of the Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy = \

                model.nondimensional_gibbs_free_energy_per_link(
                    np.array(nondimensional_force),
                    temperature
                )
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy = \

                model.gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy / \

                parameters.boltzmann_constant/temperature \

                - nondimensional_gibbs_free_energy
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_relative_gibbs_free_energy(self):
        """Function to test the nondimensionalization
        of the relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy = \

                model.nondimensional_relative_gibbs_free_energy(
                    np.array(nondimensional_force)
                )
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy = \

                model.relative_gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy / \

                parameters.boltzmann_constant/temperature \

                - nondimensional_gibbs_free_energy
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_relative_gibbs_free_energy_per_link(self):
        """Function to test the nondimensionalization
        of the relative Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy = \

                model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(nondimensional_force)
                )
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy = \

                model.relative_gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy / \

                parameters.boltzmann_constant/temperature \

                - nondimensional_gibbs_free_energy
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )


class PerLink(unittest.TestCase):
    """Class for per-linkness tests.

    """
    def test_end_to_end_length(self):
        """Function to test the per-linkness
        of the end-to-end length.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length = \

                model.end_to_end_length(
                    np.array(force),
                    temperature
                )
            end_to_end_length_per_link = \

                model.end_to_end_length_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                end_to_end_length / \

                number_of_links \

                - end_to_end_length_per_link
            residual_rel = \

                residual_abs / \

                end_to_end_length_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_end_to_end_length(self):
        """Function to test the per-linkness
        of the nondimensional end-to-end length.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length = \

                model.nondimensional_end_to_end_length(
                    np.array(nondimensional_force)
                )
            nondimensional_end_to_end_length_per_link = \

                model.nondimensional_end_to_end_length_per_link(
                    np.array(nondimensional_force)
                )
            residual_abs = \

                nondimensional_end_to_end_length / \

                number_of_links \

                - nondimensional_end_to_end_length_per_link
            residual_rel = \

                residual_abs / \

                nondimensional_end_to_end_length_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_gibbs_free_energy(self):
        """Function to test the per-linkness
        of the Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy = \

                model.gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy_per_link = \

                model.gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy / \

                number_of_links \

                - gibbs_free_energy_per_link
            residual_rel = \

                residual_abs / \

                gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_relative_gibbs_free_energy(self):
        """Function to test the per-linkness
        of the relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            relative_gibbs_free_energy = \

                model.relative_gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            relative_gibbs_free_energy_per_link = \

                model.relative_gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                relative_gibbs_free_energy / \

                number_of_links \

                - relative_gibbs_free_energy_per_link
            residual_rel = \

                residual_abs / \

                relative_gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_gibbs_free_energy(self):
        """Function to test the per-linkness
        of the nondimensional Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy = \

                model.nondimensional_gibbs_free_energy(
                    np.array(nondimensional_force),
                    temperature
                )
            nondimensional_gibbs_free_energy_per_link = \

                model.nondimensional_gibbs_free_energy_per_link(
                    np.array(nondimensional_force),
                    temperature
                )
            residual_abs = \

                nondimensional_gibbs_free_energy / \

                number_of_links \

                - nondimensional_gibbs_free_energy_per_link
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_relative_gibbs_free_energy(self):
        """Function to test the per-linkness
        of the nondimensional relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            nondimensional_relative_gibbs_free_energy = \

                model.nondimensional_relative_gibbs_free_energy(
                    np.array(nondimensional_force)
                )
            nondimensional_relative_gibbs_free_energy_per_link = \

                model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(nondimensional_force)
                )
            residual_abs = \

                nondimensional_relative_gibbs_free_energy / \

                number_of_links \

                - nondimensional_relative_gibbs_free_energy_per_link
            residual_rel = \

                residual_abs / \

                nondimensional_relative_gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )


class Relative(unittest.TestCase):
    """Class for relativeness tests.

    """
    def test_gibbs_free_energy(self):
        """Function to test the relativeness
        of the Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy = \

                model.gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy_0 = \

                model.gibbs_free_energy(
                    np.array(
                        parameters.zero *
                        parameters.boltzmann_constant*temperature/link_length
                    ),
                    temperature
                )
            relative_gibbs_free_energy = \

                model.relative_gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy \

                - gibbs_free_energy_0 \

                - relative_gibbs_free_energy
            residual_rel = \

                residual_abs / \

                gibbs_free_energy_0
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol *
                parameters.boltzmann_constant*temperature/link_length
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_gibbs_free_energy_per_link(self):
        """Function to test the relativeness
        of the Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            gibbs_free_energy_per_link = \

                model.gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy_per_link_0 = \

                model.gibbs_free_energy_per_link(
                    np.array(
                        parameters.zero *
                        parameters.boltzmann_constant*temperature/link_length
                    ),
                    temperature
                )
            relative_gibbs_free_energy_per_link = \

                model.relative_gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            residual_abs = \

                gibbs_free_energy_per_link \

                - gibbs_free_energy_per_link_0 \

                - relative_gibbs_free_energy_per_link
            residual_rel = \

                residual_abs / \

                gibbs_free_energy_per_link_0
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol *
                parameters.boltzmann_constant*temperature/link_length
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_gibbs_free_energy(self):
        """Function to test the relativeness
        of the nondimensional Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy = \

                model.nondimensional_gibbs_free_energy(
                    np.array(nondimensional_force),
                    temperature
                )
            nondimensional_gibbs_free_energy_0 = \

                model.nondimensional_gibbs_free_energy(
                    np.array(parameters.zero),
                    temperature
                )
            nondimensional_relative_gibbs_free_energy = \

                model.nondimensional_relative_gibbs_free_energy(
                    np.array(nondimensional_force)
                )
            residual_abs = \

                nondimensional_gibbs_free_energy \

                - nondimensional_gibbs_free_energy_0 \

                - nondimensional_relative_gibbs_free_energy
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy_0
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_gibbs_free_energy_per_link(self):
        """Function to test the relativeness
        of the nondimensional Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_gibbs_free_energy_per_link = \

                model.nondimensional_gibbs_free_energy_per_link(
                    np.array(nondimensional_force),
                    temperature
                )
            nondimensional_gibbs_free_energy_per_link_0 = \

                model.nondimensional_gibbs_free_energy_per_link(
                    np.array(parameters.zero),
                    temperature
                )
            nondimensional_relative_gibbs_free_energy_per_link = \

                model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(nondimensional_force)
                )
            residual_abs = \

                nondimensional_gibbs_free_energy_per_link \

                - nondimensional_gibbs_free_energy_per_link_0 \

                - nondimensional_relative_gibbs_free_energy_per_link
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy_per_link_0
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )


class Zero(unittest.TestCase):
    """Class for zero tests.

    """
    def test_relative_gibbs_free_energy(self):
        """Function to test the zero
        of the relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            relative_gibbs_free_energy_0 = \

                model.relative_gibbs_free_energy(
                    np.array(
                        parameters.zero *
                        parameters.boltzmann_constant*temperature/link_length
                    ),
                    temperature
                )
            self.assertLessEqual(
                relative_gibbs_free_energy_0,
                parameters.abs_tol *
                parameters.boltzmann_constant*temperature
            )

    def test_relative_gibbs_free_energy_per_link(self):
        """Function to test the zero
        of the relative Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            relative_gibbs_free_energy_per_link_0 = \

                model.relative_gibbs_free_energy_per_link(
                    np.array(
                        parameters.zero *
                        parameters.boltzmann_constant*temperature/link_length
                    ),
                    temperature
                )
            self.assertLessEqual(
                relative_gibbs_free_energy_per_link_0,
                parameters.abs_tol *
                parameters.boltzmann_constant*temperature
            )

    def test_nondimensional_relative_gibbs_free_energy(self):
        """Function to test the zero
        of the relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_relative_gibbs_free_energy_0 = \

                model.nondimensional_relative_gibbs_free_energy(
                    np.array(parameters.zero)
                )
            self.assertLessEqual(
                nondimensional_relative_gibbs_free_energy_0,
                parameters.abs_tol
            )

    def test_nondimensional_relative_gibbs_free_energy_per_link(self):
        """Function to test the zero
        of the nondimensional relative Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_relative_gibbs_free_energy_per_link_0 = \

                model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(parameters.zero)
                )
            self.assertLessEqual(
                nondimensional_relative_gibbs_free_energy_per_link_0,
                parameters.abs_tol
            )


class Connection(unittest.TestCase):
    """Class for connection tests.

    """
    def test_end_to_end_length(self):
        """Function to test the connection
        of the end-to-end length.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length = \

                model.end_to_end_length(
                    np.array(force),
                    temperature
                )
            h_step = parameters.rel_tol * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length_from_derivative = -(
                model.relative_gibbs_free_energy(
                    np.array(force + 0.5*h_step),
                    temperature
                )
                - model.relative_gibbs_free_energy(
                    np.array(force - 0.5*h_step),
                    temperature
                ))/h_step
            residual_abs = \

                end_to_end_length \

                - end_to_end_length_from_derivative
            self.assertLessEqual(
                np.abs(residual_abs), h_step
            )

    def test_end_to_end_length_per_link(self):
        """Function to test the connection
        of the end-to-end length per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length_per_link = \

                model.end_to_end_length_per_link(
                    np.array(force),
                    temperature
                )
            h_step = parameters.rel_tol * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length_per_link_from_derivative = -(
                model.relative_gibbs_free_energy_per_link(
                    np.array(force + 0.5*h_step),
                    temperature
                )
                - model.relative_gibbs_free_energy_per_link(
                    np.array(force - 0.5*h_step),
                    temperature
                ))/h_step
            residual_abs = \

                end_to_end_length_per_link \

                - end_to_end_length_per_link_from_derivative
            self.assertLessEqual(
                np.abs(residual_abs), h_step
            )

    def test_nondimensional_end_to_end_length(self):
        """Function to test the connection
        of the nondimensional end-to-end length.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length = \

                model.nondimensional_end_to_end_length(
                    np.array(nondimensional_force)
                )
            h_step = parameters.rel_tol
            nondimensional_end_to_end_length_from_derivative = -(
                model.nondimensional_relative_gibbs_free_energy(
                    np.array(nondimensional_force + 0.5*h_step)
                )
                - model.nondimensional_relative_gibbs_free_energy(
                    np.array(nondimensional_force - 0.5*h_step)
                ))/h_step
            residual_abs = \

                nondimensional_end_to_end_length \

                - nondimensional_end_to_end_length_from_derivative
            self.assertLessEqual(
                np.abs(residual_abs), h_step
            )

    def test_nondimensional_end_to_end_length_per_link(self):
        """Function to test the connection
        of the nondimensional end-to-end length per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters.nondimensional_force_reference + \

                parameters.nondimensional_force_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length_per_link = \

                model.nondimensional_end_to_end_length_per_link(
                    np.array(nondimensional_force)
                )
            h_step = parameters.rel_tol
            nondimensional_end_to_end_length_per_link_from_derivative = -(
                model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(nondimensional_force + 0.5*h_step)
                )
                - model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(nondimensional_force - 0.5*h_step)
                ))/h_step
            residual_abs = \

                nondimensional_end_to_end_length_per_link \

                - nondimensional_end_to_end_length_per_link_from_derivative
            self.assertLessEqual(
                np.abs(residual_abs), h_step
            )


class Legendre(unittest.TestCase):
    """Class for Legendre tests.

    """
    def test_gibbs_free_energy(self):
        """Function to test the Legendre transformation
        of the Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length = \

                model.end_to_end_length(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy = \

                model.gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy_legendre = \

                model.legendre.helmholtz_free_energy(
                    np.array(force),
                    temperature
                ) - force*end_to_end_length
            residual_abs = \

                gibbs_free_energy \

                - gibbs_free_energy_legendre
            residual_rel = \

                residual_abs / \

                gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_gibbs_free_energy_per_link(self):
        """Function to test the Legendre transformation
        of the Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length_per_link = \

                model.end_to_end_length_per_link(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy_per_link = \

                model.gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            gibbs_free_energy_per_link_legendre = \

                model.legendre.helmholtz_free_energy_per_link(
                    np.array(force),
                    temperature
                ) - force*end_to_end_length_per_link
            residual_abs = \

                gibbs_free_energy_per_link \

                - gibbs_free_energy_per_link_legendre
            residual_rel = \

                residual_abs / \

                gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_relative_gibbs_free_energy(self):
        """Function to test the Legendre transformation
        of the relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length = \

                model.end_to_end_length(
                    np.array(force),
                    temperature
                )
            end_to_end_length_0 = \

                model.end_to_end_length(
                    np.array(
                        parameters.boltzmann_constant*temperature/link_length
                        * parameters.zero
                    ),
                    temperature
                )
            relative_gibbs_free_energy = \

                model.relative_gibbs_free_energy(
                    np.array(force),
                    temperature
                )
            relative_gibbs_free_energy_legendre = \

                model.legendre.relative_helmholtz_free_energy(
                    np.array(force),
                    temperature
                ) - force*end_to_end_length \

                + end_to_end_length_0 \

                * parameters.boltzmann_constant*temperature/link_length \

                * parameters.zero
            residual_abs = \

                relative_gibbs_free_energy \

                - relative_gibbs_free_energy_legendre
            residual_rel = \

                residual_abs / \

                relative_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_relative_gibbs_free_energy_per_link(self):
        """Function to test the Legendre transformation
        of the relative Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            end_to_end_length_per_link = \

                model.end_to_end_length_per_link(
                    np.array(force),
                    temperature
                )
            end_to_end_length_per_link_0 = \

                model.end_to_end_length_per_link(
                    np.array(
                        parameters.boltzmann_constant*temperature/link_length
                        * parameters.zero
                    ),
                    temperature
                )
            relative_gibbs_free_energy_per_link = \

                model.relative_gibbs_free_energy_per_link(
                    np.array(force),
                    temperature
                )
            relative_gibbs_free_energy_per_link_legendre = \

                model.legendre.relative_helmholtz_free_energy_per_link(
                    np.array(force),
                    temperature
                ) - force*end_to_end_length_per_link \

                + end_to_end_length_per_link_0 \

                * parameters.boltzmann_constant*temperature/link_length \

                * parameters.zero
            residual_abs = \

                relative_gibbs_free_energy_per_link \

                - relative_gibbs_free_energy_per_link_legendre
            residual_rel = \

                residual_abs / \

                relative_gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_gibbs_free_energy(self):
        """Function to test the Legendre transformation
        of the nondimensional Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length = \

                model.nondimensional_end_to_end_length(
                    np.array(nondimensional_force)
                )
            nondimensional_gibbs_free_energy = \

                model.nondimensional_gibbs_free_energy(
                    np.array(nondimensional_force),
                    temperature
                )
            nondimensional_gibbs_free_energy_legendre = \

                model.legendre.nondimensional_helmholtz_free_energy(
                    np.array(nondimensional_force),
                    temperature
                ) - nondimensional_force*nondimensional_end_to_end_length
            residual_abs = \

                nondimensional_gibbs_free_energy \

                - nondimensional_gibbs_free_energy_legendre
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_gibbs_free_energy_per_link(self):
        """Function to test the Legendre transformation
        of the nondimensional Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            nondimensional_end_to_end_length_per_link = \

                model.nondimensional_end_to_end_length_per_link(
                    np.array(nondimensional_force)
                )
            nondimensional_gibbs_free_energy_per_link = \

                model.nondimensional_gibbs_free_energy_per_link(
                    np.array(nondimensional_force),
                    temperature
                )
            nondimensional_gibbs_free_energy_per_link_legendre = \

                model.legendre.nondimensional_helmholtz_free_energy_per_link(
                    np.array(nondimensional_force),
                    temperature
                ) - nondimensional_force * \

                nondimensional_end_to_end_length_per_link
            residual_abs = \

                nondimensional_gibbs_free_energy_per_link \

                - nondimensional_gibbs_free_energy_per_link_legendre
            residual_rel = \

                residual_abs / \

                nondimensional_gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_relative_gibbs_free_energy(self):
        """Function to test the Legendre transformation
        of the nondimensional relative Gibbs free energy.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            nondimensional_end_to_end_length = \

                model.nondimensional_end_to_end_length(
                    np.array(nondimensional_force)
                )
            nondimensional_end_to_end_length_0 = \

                model.nondimensional_end_to_end_length(
                    np.array(parameters.zero)
                )
            nondimensional_relative_gibbs_free_energy = \

                model.nondimensional_relative_gibbs_free_energy(
                    np.array(nondimensional_force)
                )
            nondimensional_relative_gibbs_free_energy_legendre = \

                model.legendre.nondimensional_relative_helmholtz_free_energy(
                    np.array(nondimensional_force)
                ) - nondimensional_force*nondimensional_end_to_end_length \

                + parameters.zero*nondimensional_end_to_end_length_0
            residual_abs = \

                nondimensional_relative_gibbs_free_energy \

                - nondimensional_relative_gibbs_free_energy_legendre
            residual_rel = \

                residual_abs / \

                nondimensional_relative_gibbs_free_energy
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )

    def test_nondimensional_relative_gibbs_free_energy_per_link(self):
        """Function to test the Legendre transformation
        of the nondimensional relative Gibbs free energy per link.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            nondimensional_end_to_end_length_per_link = \

                model.nondimensional_end_to_end_length_per_link(
                    np.array(nondimensional_force)
                )
            nondimensional_end_to_end_length_per_link_0 = \

                model.nondimensional_end_to_end_length_per_link(
                    np.array(parameters.zero)
                )
            nondimensional_relative_gibbs_free_energy_per_link = \

                model.nondimensional_relative_gibbs_free_energy_per_link(
                    np.array(nondimensional_force)
                )
            nondimensional_relative_gibbs_free_energy_per_link_legendre = \

                model.legendre.\

                nondimensional_relative_helmholtz_free_energy_per_link(
                    np.array(nondimensional_force)
                ) - nondimensional_force * \

                nondimensional_end_to_end_length_per_link \

                + parameters.zero*nondimensional_end_to_end_length_per_link_0
            residual_abs = \

                nondimensional_relative_gibbs_free_energy_per_link \

                - nondimensional_relative_gibbs_free_energy_per_link_legendre
            residual_rel = \

                residual_abs / \

                nondimensional_relative_gibbs_free_energy_per_link
            self.assertLessEqual(
                np.abs(residual_abs),
                parameters.abs_tol
            )
            self.assertLessEqual(
                np.abs(residual_rel),
                parameters.rel_tol
            )


class LegendreConnection(unittest.TestCase):
    """Class for Legendre connection tests.

    """
    def test_force(self):
        """Function to test the Legendre transformation connection
        of the force.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            temperature = \

                parameters.temperature_reference + \

                parameters.temperature_scale*(0.5 - np.random.rand())
            force = nondimensional_force * \

                parameters.boltzmann_constant*temperature/link_length
            h_step = parameters.rel_tol * \

                parameters.boltzmann_constant*temperature/link_length
            force_from_derivative = (
                model.legendre.relative_helmholtz_free_energy(
                    np.array(
                        force + 0.5*h_step
                    ), temperature
                )
                - model.legendre.relative_helmholtz_free_energy(
                    np.array(
                        force - 0.5*h_step
                    ), temperature
                ))/(
                model.end_to_end_length(
                    np.array(
                        force + 0.5*h_step
                    ), temperature
                )
                - model.end_to_end_length(
                    np.array(
                        force - 0.5*h_step
                    ), temperature
                ))
            residual_abs = \

                force \

                - force_from_derivative
            residual_rel = residual_abs/force
            self.assertLessEqual(
                np.abs(residual_rel), h_step
            )

    def test_nondimensional_force(self):
        """Function to test the Legendre transformation connection
        of the nondimensional force.

        """
        for _ in range(parameters.number_of_loops):
            number_of_links = \

                np.random.randint(
                    parameters.number_of_links_minimum,
                    high=parameters.number_of_links_maximum
                )
            link_length = \

                parameters.link_length_reference + \

                parameters.link_length_scale*(0.5 - np.random.rand())
            hinge_mass = \

                parameters.hinge_mass_reference + \

                parameters.hinge_mass_scale*(0.5 - np.random.rand())
            persistance_length = \

                parameters.persistance_length_reference + \

                parameters.persistance_length_scale*(0.5 - np.random.rand())
            model = WLC(
                number_of_links,
                link_length,
                hinge_mass,
                persistance_length
            )
            nondimensional_force = \

                parameters. \

                nondimensional_force_reference + \

                parameters. \

                nondimensional_force_scale * \

                (0.5 - np.random.rand())
            h_step = parameters.rel_tol
            nondimensional_force_from_derivative = (
                model.legendre.
                nondimensional_relative_helmholtz_free_energy_per_link(
                    np.array(
                        nondimensional_force + 0.5*h_step
                    )
                )
                - model.legendre.
                nondimensional_relative_helmholtz_free_energy_per_link(
                    np.array(
                        nondimensional_force - 0.5*h_step
                    )
                ))/(
                model.nondimensional_end_to_end_length_per_link(
                    np.array(
                        nondimensional_force + 0.5*h_step
                    )
                )
                - model.nondimensional_end_to_end_length_per_link(
                    np.array(
                        nondimensional_force - 0.5*h_step
                    )
                ))
            residual_abs = \

                nondimensional_force \

                - nondimensional_force_from_derivative
            residual_rel = residual_abs/nondimensional_force
            self.assertLessEqual(
                np.abs(residual_rel), h_step
            )