def test_calling_sympy_functions(self): """ Test the calling of sympy functions """ model = Model() model.var('x') model.param('a') model.set_values({'x': 12, 'a': 5}) self.assertEquals(1.1, model.evaluate('Max(1, 1.1)'))
def test_param_default(self): """ Test the set_param_default """ model = Model() param = model.param('test') self.assertEquals(None, param.default) model.set_param_default(122) param = model.param('test2') self.assertEquals(122, param.default)
def test_set_parameters_equation(self): """ Test set_values of parameters using equations """ model = Model() model.param('a', default=-1) model.var('x', default=0) model.set_values({'a': 'x+12'}) self.assertEquals(12, model.parameters['a'].value)
def test_set_variables_equation(self): """ Test set_values of variables using equations """ model = Model() model.param('a', default=-1) model.var('x', default=0) model.set_values({'x': 'a+12'}) self.assertEquals(11, model.variables['x'].value)
def test_evaluate(self): """ Test arbitrary function evaluation """ model = Model() model.var('x', default=1) model.var('y', default=10) model.param('a', default=.5) self.assertEquals(11, model.evaluate('x+y'))
def test_evaluate_series_access(self): """ Test evaluation with series accessor """ model = Model() model.var('x', default=1) model.var('y', default=10) model.param('a', default=.5) model.solutions = [{'x': 2, 'y': 11, 'a': 60}] self.assertEquals(11, model.evaluate('y(-1)')) self.assertEquals(73, model.evaluate('x(-1) + y(-1) + a(-1)'))
def test_delta(self): """ test the d() function """ model = Model() model.var('x', default=-1) model.var('y', default=10) model.param('a', default=.5) model.solutions = [{'x': 2, 'y': 11, 'a': 60}] model.variables['x'].value = 5 self.assertEquals(3, model.evaluate('d(x)'))
def test_delta_error(self): model = Model() model.var('x', default=-1) model.var('y', default=10) model.param('a', default=.5) model.solutions = [{'x': 2, 'y': 11, 'a': 60}] model.variables['x'].value = 5 with self.assertRaises(EquationError) as context: model.evaluate('d(-1)') self.assertEquals('d-arg-not-a-variable', context.exception.errorid)
def test_setting_multiple_variables(self): """ Test set_values() with multiple variables """ model = Model() model.param('a', default=3) model.param('b', default=4) model.var('x', default=-1) model.var('y', default=-2) model.set_values({'a': 'a+11', 'b': '4*b'}) self.assertEquals(14, model.parameters['a'].value) self.assertEquals(16, model.parameters['b'].value)
def test_param(self): """ Test parameter creation """ model = Model() param_x = model.param('x') self.assertIsNotNone(param_x) with self.assertRaises(DuplicateNameError): model.var('x') with self.assertRaises(DuplicateNameError): model.param('x') self.assertTrue('x' not in model.variables) self.assertTrue('x' in model.parameters)
def create_sim_model(): model = Model() model.set_var_default(0) model.var('Cd', desc='Consumption goods demand by households') model.var('Cs', desc='Consumption goods supply') model.var('Gs', desc='Government goods, supply') model.var('Hh', desc='Cash money held by households') model.var('Hs', desc='Cash money supplied by the government') model.var('Nd', desc='Demand for labor') model.var('Ns', desc='Supply of labor') model.var('Td', desc='Taxes, demand') model.var('Ts', desc='Taxes, supply') model.var('Y', desc='Income = GDP') model.var('YD', desc='Disposable income of households') model.param('Gd', desc='Government goods, demand') model.param('W', desc='Wage rate') model.param('alpha1', desc='Propensity to consume out of income') model.param('alpha2', desc='Propensity to consume out of wealth') model.param('theta', desc='Tax rate') model.add('Cs = Cd') # 3.1 model.add('Gs = Gd') # 3.2 model.add('Ts = Td') # 3.3 model.add('Ns = Nd') # 3.4 model.add('YD = (W*Ns) - Ts') # 3.5 model.add('Td = theta * W * Ns') # 3.6, theta < 1.0 model.add('Cd = alpha1*YD + alpha2*Hh(-1)') # 3.7, 0 < alpha2 < alpha1 < 1 model.add('Hs - Hs(-1) = Gd - Td') # 3.8 model.add('Hh - Hh(-1) = YD - Cd') # 3.9 model.add('Y = Cs + Gs') # 3.10 model.add('Nd = Y/W') # 3.11 return model
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 create_model(): """ Creates model SIM """ model = Model() model.set_var_default(0) model.var('Cd', desc='Consumption goods demand by households') model.var('Cs', desc='Consumption goods supply') model.var('Gs', desc='Government goods, supply') model.var('Hh', desc='Cash money held by households') model.var('Hs', desc='Cash money supplied by the government') model.var('Nd', desc='Demand for labor') model.var('Ns', desc='Supply of labor') model.var('Td', desc='Taxes, demand') model.var('Ts', desc='Taxes, supply') model.var('Y', desc='Income = GDP') model.var('YD', desc='Disposable income of households') # This is a shorter way to declare multiple variables # model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs', # 'Cd', 'Ns', 'Nd') model.param('Gd', desc='Government goods, demand', default=20) model.param('W', desc='Wage rate', default=1) model.param('alpha1', desc='Propensity to consume out of income', default=0.6) model.param('alpha2', desc='Propensity to consume o of wealth', default=0.4) model.param('theta', desc='Tax rate', default=0.2) 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') return model
def test_set_parameters(self): """ Test set_values of parameters """ model = Model() param_a = model.param('a', default=-1) self.assertEquals(-1, param_a.value) model.set_values({'a': 22}) self.assertEquals(22, param_a.value) with self.assertRaises(ValueError): model.set_values({'zz': -1})
def create_simex_model(): """ Create the SIMEX model """ model = Model() model.set_var_default(0) model.var('Cd', desc='Consumption goods demand by households') model.var('Cs', desc='Consumption goods supply') model.var('Gs', desc='Government goods, supply') model.var('Hd', desc='Cash money demanded by households') model.var('Hh', desc='Cash money held by households') model.var('Hs', desc='Cash money supplied by the government') model.var('Nd', desc='Demand for labor') model.var('Ns', desc='Supply of labor') model.var('Td', desc='Taxes, demand') model.var('Ts', desc='Taxes, supply') model.var('Y', desc='Income = GDP') model.var('YD', desc='Disposable income of households') model.var('YDe', desc='Expected disposable income') model.set_param_default(0) model.param('Gd', desc='Government goods, demand') model.param('W', desc='Wage rate') model.param('alpha1', desc='Propensity to consume out of income') model.param('alpha2', desc='Propensity to consume o of wealth') model.param('theta', desc='Tax rate') model.add('Cs = Cd') # 3.1 model.add('Gs = Gd') # 3.2 model.add('Ts = Td') # 3.3 model.add('Ns = Nd') # 3.4 model.add('YD = (W*Ns) - Ts') # 3.5 model.add('Td = theta * W * Ns') # 3.6, theta < 1.0 model.add('Cd = alpha1*YDe + alpha2*Hh(-1)') # 3.7E model.add('Hs - Hs(-1) = Gd - Td') # 3.8 model.add('Hh - Hh(-1) = YD - Cd') # 3.9 model.add('Hd - Hs(-1) = YDe - Cd') # 3.18 model.add('Y = Cs + Gs') # 3.10 model.add('Nd = Y/W') # 3.11 model.add('YDe = YD(-1)') # 3.20 return model
# # In addition the parameter values could be changed like this: # ```python # Gd = model.param('Gd', initial=10) # # ... # # at some later time # Gd.value = 20 # # or this would work also # model.parameters['Gd'].value = 20 # ``` # Some of the parameters (alpha1, alpha2 and theta) have not been explained yet, but will be explained when we add the equations that use them. # In[6]: model.param('Gd', desc='Government goods, demand', default=20.) model.param('W', desc='Wage rate', default=1.) model.param('alpha1', desc='Propensity to consume out of income', default=0.6) model.param('alpha2', desc='Propensity to consume o of wealth', default=0.4) model.param('theta', desc='Tax rate', default=0.2) # ###### Define the equations # Adding an equation is just adding the textual form of the equation. There are some restrictions. Linear systems only. # In[7]: model.add('Cs = Cd') model.add('Gs = Gd') model.add('Ts = Td') model.add('Ns = Nd')
def create_lp_model(): """ Creates model LP """ # pylint: disable=too-many-statements model = Model() model.set_var_default(0) model.var('Bcb', desc='Government bills held by the Central Bank') model.var('Bd', desc='Demand for government bills') model.var('Bh', desc='Government bills held by households') model.var('Bs', desc='Government bills supplied by government') model.var('BLd', desc='Demand for government bonds') model.var('BLh', desc='Government bonds held by households') model.var('BLs', desc='Supply of government bonds') model.var('CG', desc='Capital gains on bonds') model.var('CGe', desc='Expected capital gains on bonds') model.var('C', desc='Consumption') model.var('ERrbl', desc='Expected rate of return on bonds') model.var('Hd', desc='Demand for cash') model.var('Hh', desc='Cash held by households') model.var('Hs', desc='Cash supplied by the central bank') model.var('Pbl', desc='Price of bonds') model.var('Pble', desc='Expected price of bonds') model.var('Rb', desc='Interest rate on government bills') model.var('Rbl', desc='Interest rate on government bonds') model.var('T', desc='Taxes') model.var('V', desc='Household wealth') model.var('Ve', desc='Expected household wealth') model.var('Y', desc='Income = GDP') model.var('YDr', desc='Regular disposable income of households') model.var('YDre', desc='Expected regular disposable income of households') model.set_param_default(0) model.param('alpha1', desc='Propensity to consume out of income') model.param('alpha2', desc='Propensit to consume out of wealth') model.param('chi', desc='Weight of conviction in expected bond price') model.param('lambda10', desc='Parameter in asset demand function') model.param('lambda12', desc='Parameter in asset demand function') model.param('lambda13', desc='Parameter in asset demand function') model.param('lambda14', desc='Parameter in asset demand function') model.param('lambda20', desc='Parameter in asset demand function') model.param('lambda22', desc='Parameter in asset demand function') model.param('lambda23', desc='Parameter in asset demand function') model.param('lambda24', desc='Parameter in asset demand function') model.param('lambda30', desc='Parameter in asset demand function') model.param('lambda32', desc='Parameter in asset demand function') model.param('lambda33', desc='Parameter in asset demand function') model.param('lambda34', desc='Parameter in asset demand function') model.param('theta', desc='Tax rate') model.param('G', desc='Government goods') model.param('Rbar', desc='Exogenously set interest rate on govt bills') model.param('Pblbar', desc='Exogenously set price of bonds') model.add('Y = C + G') # 5.1 model.add('YDr = Y - T + Rb(-1)*Bh(-1) + BLh(-1)') # 5.2 model.add('T = theta *(Y + Rb(-1)*Bh(-1) + BLh(-1))') # 5.3 model.add('V - V(-1) = (YDr - C) + CG') # 5.4 model.add('CG = (Pbl - Pbl(-1))*BLh(-1)') model.add('C = alpha1*YDre + alpha2*V(-1)') model.add('Ve = V(-1) + (YDre - C) + CG') model.add('Hh = V - Bh - Pbl*BLh') model.add('Hd = Ve - Bd - Pbl*BLd') model.add('Bd = Ve*lambda20 + Ve*lambda22*Rb - ' + 'Ve*lambda23*ERrbl - lambda24*YDre') model.add('BLd = (Ve*lambda30 - Ve*lambda32*Rb ' + ' + Ve*lambda33*ERrbl - lambda34*YDre)/Pbl') model.add('Bh = Bd') model.add('BLh = BLd') model.add('Bs - Bs(-1) = (G + Rb(-1)*Bs(-1) + ' + 'BLs(-1)) - (T + Rb(-1)*Bcb(-1)) - (BLs - BLs(-1))*Pbl') model.add('Hs - Hs(-1) = Bcb - Bcb(-1)') model.add('Bcb = Bs - Bh') model.add('BLs = BLh') model.add('ERrbl = Rbl + chi * (Pble - Pbl) / Pbl') model.add('Rbl = 1./Pbl') model.add('Pble = Pbl') model.add('CGe = chi * (Pble - Pbl)*BLh') model.add('YDre = YDr(-1)') model.add('Rb = Rbar') model.add('Pbl = Pblbar') # if_true(x) returns 1 if x is true, else 0 is returned model.add('z1 = if_true(tp > top)') model.add('z2 = if_true(tp < bot)') return model
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']))
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']))