def test_broyden(self): """ Test solving with Broyden's method, instead of the default Gauss-Seidel """ # pylint: disable=too-many-statements model = Model() model.set_var_default(0) model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs', 'Cd', 'Ns', 'Nd') model.set_param_default(0) Gd = model.param('Gd') W = model.param('W') alpha1 = model.param('alpha1') alpha2 = model.param('alpha2') theta = model.param('theta') model.add('Cs = Cd') model.add('Gs = Gd') model.add('Ts = Td') model.add('Ns = Nd') model.add('YD = (W*Ns) - Ts') model.add('Td = theta * W * Ns') model.add('Cd = alpha1*YD + alpha2*Hh(-1)') model.add('Hs - Hs(-1) = Gd - Td') model.add('Hh - Hh(-1) = YD - Cd') model.add('Y = Cs + Gs') model.add('Nd = Y/W') # setup default parameter values Gd.value = 20. W.value = 1.0 alpha1.value = 0.6 alpha2.value = 0.4 theta.value = 0.2 debuglist = [] model.solve(iterations=100, threshold=1e-4, debuglist=debuglist, method='broyden') soln = round_solution(model.solutions[-1], decimals=1) print(soln) self.assertTrue(numpy.isclose(38.5, soln['Y'])) self.assertTrue(numpy.isclose(7.7, soln['Ts'])) self.assertTrue(numpy.isclose(30.8, soln['YD'])) self.assertTrue(numpy.isclose(18.5, soln['Cs'])) self.assertTrue(numpy.isclose(12.3, soln['Hs'])) self.assertTrue(numpy.isclose(12.3, soln['Hh'])) self.assertTrue(numpy.isclose(0, soln['_Hs__1'])) self.assertTrue(numpy.isclose(0, soln['_Hh__1']))
def test_full_model(self): """ Test by implementing a model This model is taken from the book Monetary Economics 2ed, Godley and Lavoie, 2012 Chapter 3, The Simplest Model wtih Government Money Model SIM """ # pylint: disable=too-many-statements model = Model() model.set_var_default(0) model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs', 'Cd', 'Ns', 'Nd') model.set_param_default(0) Gd = model.param('Gd') W = model.param('W') alpha1 = model.param('alpha1') alpha2 = model.param('alpha2') theta = model.param('theta') model.add('Cs = Cd') model.add('Gs = Gd') model.add('Ts = Td') model.add('Ns = Nd') model.add('YD = (W*Ns) - Ts') model.add('Td = theta * W * Ns') model.add('Cd = alpha1*YD + alpha2*Hh(-1)') model.add('Hs - Hs(-1) = Gd - Td') model.add('Hh - Hh(-1) = YD - Cd') model.add('Y = Cs + Gs') model.add('Nd = Y/W') # setup default parameter values Gd.value = 20. W.value = 1.0 alpha1.value = 0.6 alpha2.value = 0.4 theta.value = 0.2 model.solve(iterations=200, threshold=1e-3) soln = round_solution(model.solutions[-1], decimals=1) self.assertTrue(numpy.isclose(38.5, soln['Y'])) self.assertTrue(numpy.isclose(7.7, soln['Ts'])) self.assertTrue(numpy.isclose(30.8, soln['YD'])) self.assertTrue(numpy.isclose(18.5, soln['Cs'])) self.assertTrue(numpy.isclose(12.3, soln['Hs'])) self.assertTrue(numpy.isclose(12.3, soln['Hh'])) self.assertTrue(numpy.isclose(0, soln['_Hs__1'])) self.assertTrue(numpy.isclose(0, soln['_Hh__1'])) model.solve(iterations=200, threshold=1e-3) soln = round_solution(model.solutions[-1], decimals=1) self.assertTrue(numpy.isclose(47.9, soln['Y'])) self.assertTrue(numpy.isclose(9.6, soln['Ts'])) self.assertTrue(numpy.isclose(38.3, soln['YD'])) self.assertTrue(numpy.isclose(27.9, soln['Cs'])) self.assertTrue(numpy.isclose(22.7, soln['Hs'])) self.assertTrue(numpy.isclose(22.7, soln['Hh'])) self.assertTrue(numpy.isclose(12.3, soln['_Hs__1'])) self.assertTrue(numpy.isclose(12.3, soln['_Hh__1'])) # Now run until the solutions themselves converge prev_soln = model.solutions[-1] converges = False for _ in range(100): model.solve(iterations=100, threshold=1e-3) # run until we converge soln = model.solutions[-1] if is_close(prev_soln, soln, atol=1e-3): converges = True break prev_soln = soln self.assertTrue(converges) prev = round_solution(model.solutions[-2], decimals=1) soln = round_solution(model.solutions[-1], decimals=1) self.assertTrue(numpy.isclose(100, soln['Y'])) self.assertTrue(numpy.isclose(20, soln['Ts'])) self.assertTrue(numpy.isclose(80, soln['YD'])) self.assertTrue(numpy.isclose(80, soln['Cs'])) self.assertTrue(numpy.isclose(0, soln['Hs'] - prev['Hs'])) self.assertTrue(numpy.isclose(0, soln['Hh'] - prev['Hh']))
def test_full_model(self): """ Test by implementing a model This model is taken from the book Monetary Economics 2ed, Godley and Lavoie, 2012 Chapter 3, The Simplest Model wtih Government Money Model SIM """ # pylint: disable=too-many-statements model = Model() model.set_var_default(0) model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs', 'Cd', 'Ns', 'Nd') model.set_param_default(0) Gd = model.param('Gd') W = model.param('W') alpha1 = model.param('alpha1') alpha2 = model.param('alpha2') theta = model.param('theta') model.add('Cs = Cd') model.add('Gs = Gd') model.add('Ts = Td') model.add('Ns = Nd') model.add('YD = (W*Ns) - Ts') model.add('Td = theta * W * Ns') model.add('Cd = alpha1*YD + alpha2*Hh(-1)') model.add('Hs - Hs(-1) = Gd - Td') model.add('Hh - Hh(-1) = YD - Cd') model.add('Y = Cs + Gs') model.add('Nd = Y/W') # setup default parameter values Gd.value = 20. W.value = 1.0 alpha1.value = 0.6 alpha2.value = 0.4 theta.value = 0.2 model.solve(iterations=200, threshold=1e-3) soln = round_solution(model.solutions[-1], decimals=1) self.assertTrue(numpy.isclose(38.5, soln['Y'])) self.assertTrue(numpy.isclose(7.7, soln['Ts'])) self.assertTrue(numpy.isclose(30.8, soln['YD'])) self.assertTrue(numpy.isclose(18.5, soln['Cs'])) self.assertTrue(numpy.isclose(12.3, soln['Hs'])) self.assertTrue(numpy.isclose(12.3, soln['Hh'])) model.solve(iterations=200, threshold=1e-3) soln = round_solution(model.solutions[-1], decimals=1) self.assertTrue(numpy.isclose(47.9, soln['Y'])) self.assertTrue(numpy.isclose(9.6, soln['Ts'])) self.assertTrue(numpy.isclose(38.3, soln['YD'])) self.assertTrue(numpy.isclose(27.9, soln['Cs'])) self.assertTrue(numpy.isclose(22.7, soln['Hs'])) self.assertTrue(numpy.isclose(22.7, soln['Hh'])) # Now run until the solutions themselves converge prev_soln = model.solutions[-1] converges = False for _ in xrange(100): model.solve(iterations=100, threshold=1e-3) # run until we converge soln = model.solutions[-1] if is_close(prev_soln, soln, atol=1e-3): converges = True break prev_soln = soln self.assertTrue(converges) prev = round_solution(model.solutions[-2], decimals=1) soln = round_solution(model.solutions[-1], decimals=1) self.assertTrue(numpy.isclose(100, soln['Y'])) self.assertTrue(numpy.isclose(20, soln['Ts'])) self.assertTrue(numpy.isclose(80, soln['YD'])) self.assertTrue(numpy.isclose(80, soln['Cs'])) self.assertTrue(numpy.isclose(0, soln['Hs'] - prev['Hs'])) self.assertTrue(numpy.isclose(0, soln['Hh'] - prev['Hh']))