def test_lag1st_to_trig(self):
# scalar case
dest_weight = core.change_projection_base(self.src_weights, self.src_test_funcs, self.trig_test_funcs[0])
dest_approx_handle_s = core.back_project_from_base(dest_weight, self.trig_test_funcs[0])
# standard case
dest_weights = core.change_projection_base(self.src_weights, self.src_test_funcs, self.trig_test_funcs)
dest_approx_handle = core.back_project_from_base(dest_weights, self.trig_test_funcs)
error = np.sum(np.power(
np.subtract(self.real_func_handle(self.z_values), dest_approx_handle(self.z_values)),
2))
if show_plots:
pw = pg.plot(title="change projection base")
i1 = pw.plot(x=self.z_values, y=self.real_func_handle(self.z_values), pen="r")
i2 = pw.plot(x=self.z_values, y=self.src_approx_handle(self.z_values),
pen=pg.mkPen("g", style=pg.QtCore.Qt.DashLine))
i3 = pw.plot(x=self.z_values, y=dest_approx_handle_s(self.z_values), pen="b")
i4 = pw.plot(x=self.z_values, y=dest_approx_handle(self.z_values), pen="c")
legend = pw.addLegend()
legend.addItem(i1, "f(x) = x")
legend.addItem(i2, "2x Lagrange1st")
legend.addItem(i3, "sin(x)")
legend.addItem(i4, "sin(wx) with w in [1, {0}]".format(dest_weights.shape[0]))
app.exec_()
# should fit pretty nice
self.assertLess(error, 1e-2)
def test_back_projection_from_lagrange_1st(self):
vec_real_func = np.vectorize(self.funcs[1])
real_weights = vec_real_func(self.nodes)
approx_func = core.back_project_from_base(real_weights, self.initial_functions)
approx_func_dz = core.back_project_from_base(real_weights, get_base("ini_funcs", 1))
self.assertTrue(np.allclose(approx_func(self.z_values), vec_real_func(self.z_values)))
if show_plots:
# lines should match exactly
pw = pg.plot(title="back projected linear function")
pw.plot(x=self.z_values, y=vec_real_func(self.z_values), pen="r")
pw.plot(x=self.z_values, y=approx_func(self.z_values), pen="g")
pw.plot(x=self.z_values, y=approx_func_dz(self.z_values), pen="b")
app.exec_()
def setUp(self):
# real function
self.z_values = np.linspace(0, 1, 1000)
self.real_func = core.Function(lambda x: x)
self.real_func_handle = np.vectorize(self.real_func)
# approximation by lag1st
self.nodes, self.src_test_funcs = shapefunctions.cure_interval(shapefunctions.LagrangeFirstOrder, (0, 1),
node_count=2)
register_base("test_funcs", self.src_test_funcs, overwrite=True)
self.src_weights = core.project_on_base(self.real_func, self.src_test_funcs)
self.assertTrue(np.allclose(self.src_weights, [0, 1])) # just to be sure
self.src_approx_handle = core.back_project_from_base(self.src_weights, self.src_test_funcs)
# approximation by sin(w*x)
def trig_factory(freq):
def func(x):
return np.sin(freq*x)
return func
self.trig_test_funcs = np.array([core.Function(trig_factory(w), domain=(0, 1)) for w in range(1, 3)])
