def test_temporal_derive(self):
b_desired = 0.4
k = 5 # = k1 + k2
k1, k2, b = ut.split_domain(k, b_desired, self.l, mode='coprime')[0:3]
# q
E = tr.coefficient_recursion(self.y, self.beta*self.y, self.param)
q = tr.temporal_derived_power_series(self.l-b, E, int(self.n_y/2)-1, self.n_y)
# u
B = tr.coefficient_recursion(self.y, self.alpha*self.y, self.param)
xq = tr.temporal_derived_power_series(self.l, B, int(self.n_y/2)-1, self.n_y, spatial_der_order=0)
d_xq = tr.temporal_derived_power_series(self.l, B, int(self.n_y/2)-1, self.n_y, spatial_der_order=1)
u = d_xq + self.beta*xq
# x(0,t)
C = tr.coefficient_recursion(q, self.beta*q, self.param)
D = tr.coefficient_recursion(np.zeros(u.shape), u, self.param)
x_0t = tr.power_series(0, self.t, C)
if show_plots:
pw = pg.plot(title="control_input")
pw.plot(self.t, x_0t)
app.exec_()
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