# Source code for sfepy.tests.test_linearization

    import os
    import numpy as nm

    import sfepy.base.testing as tst

    def test_linearization(output_dir):
        from sfepy.base.base import Struct
        from sfepy.discrete.fem import Mesh, FEDomain, Field
        from sfepy import data_dir

        geometries = ['2_3', '2_4', '3_4', '3_8']
        approx_orders = [1, 2]
        funs = [nm.cos, nm.sin, lambda x: x]

        ok = True
        for geometry in geometries:
            name = os.path.join(data_dir,
                                'meshes/elements/%s_1.mesh' % geometry)
            mesh = Mesh.from_file(name)

            domain = FEDomain('', mesh)
            domain = domain.refine()

            domain.mesh.write(os.path.join(output_dir,
                                           'linearizer-%s-0.mesh' % geometry))

            omega = domain.create_region('Omega', 'all')

            for approx_order in approx_orders:
                for dpn in [1, mesh.dim]:
                    tst.report('geometry: %s, approx. order: %d, dpn: %d' %
                               (geometry, approx_order, dpn))

                    field = Field.from_args('fu', nm.float64, dpn, omega,
                                            approx_order=approx_order)

                    cc = field.get_coor()
                    dofs = nm.zeros((field.n_nod, dpn), dtype=nm.float64)

                    for ic in range(dpn):
                        dofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))

                    vmesh, vdofs, level = field.linearize(dofs,
                                                          min_level=0,
                                                          max_level=3,
                                                          eps=1e-2)

                    if approx_order == 1:
                        _ok = level == 0

                    else:
                        _ok = level > 0
                    tst.report('max. refinement level: %d: %s' % (level, _ok))

                    ok = ok and _ok

                    rdofs = nm.zeros((vmesh.n_nod, dpn), dtype=nm.float64)
                    cc = vmesh.coors
                    for ic in range(dpn):
                        rdofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))

                    _ok = nm.allclose(rdofs, vdofs, rtol=0.0, atol=0.03)
                    tst.report('interpolation: %s' % _ok)
                    ok = ok and _ok

                    out = {
                        'u' : Struct(name='output_data',
                                     mode='vertex', data=vdofs,
                                     var_name='u', dofs=None)
                    }

                    name = os.path.join(output_dir,
                                        'linearizer-%s-%d-%d'
                                        % (geometry, approx_order, dpn))

                    vmesh.write(name + '.mesh')
                    vmesh.write(name + '.vtk', out=out)

        assert ok