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']))
# The determination of employment.
# We now have 11 equations and 11 unknowns. **Each of the eleven unknowns has been set on the left-hand side of an equation** (This implies that we can use the Gauss-Seidel algorithm to iterate to a solution, convergence is not guaranteed but we can try.)
# ###### Solve
# We have set the default for all of the variables to 0, and that will be used as an initial solution.
# In[15]:
model.solve(iterations=100, threshold=1e-4)
# In[16]:
prev = round_solution(model.solutions[-2], decimals=1)
solution = round_solution(model.solutions[-1], decimals=1)
print("Y : " + str(solution['Y']))
print("T : " + str(solution['Ts']))
print("YD : " + str(solution['YD']))
print("C : " + str(solution['Cs']))
print("Hs-Hs(-1) : " + str(solution['Hs'] - prev['Hs']))
print("Hh-Hh(-1) : " + str(solution['Hh'] - prev['Hh']))
print("H : " + str(solution['Hh']))
# ### The code for the full model
# To make the model easier to manipulate, I will encapsulate model creation into a single function.
# In[17]:
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
start = time.clock()
sim = create_model()
for _ in xrange(100):
sim.solve(iterations=100, threshold=1e-5)
prev_soln = sim.solutions[-2]
soln = sim.solutions[-1]
if is_close(prev_soln, soln, atol=1e-3):
break
end = time.clock()
print "elapsed time = " + str(end - start)
print round_solution(sim.solutions[-1], decimals=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']))
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
steady_state = create_simex_model()
steady_state.set_parameters({'alpha1': 0.6,
'alpha2': 0.4,
'theta': 0.2})
steady_state.set_parameters({'Gd': 20,
'W': 1})
steady_state.variables['YD'].value = steady_state.evaluate('Gd*(1-theta)')
for _ in range(100):
steady_state.solve(iterations=100, threshold=1e-5)
if is_close(steady_state.solutions[-2],
steady_state.solutions[-1],
atol=1e-4):
break
print(round_solution(steady_state.solutions[-1], decimals=1))
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');
model.solve(iterations=100, threshold=1e-4);
prev = round_solution(model.solutions[-2], decimals=1)
solution = round_solution(model.solutions[-1], decimals=1)
print ("Y : " + str(solution['Y']))
print ("T : " + str(solution['Ts']))
print ("YD : " + str(solution['YD']))
print ("C : " + str(solution['Cs']))
print ("Hs-Hs(-1) : " + str(solution['Hs'] - prev['Hs']))
print ("Hh-Hh(-1) : " + str(solution['Hh'] - prev['Hh']))
print ("H : " + str(solution['Hh']))
'Rb': 0.03,
'Pbl': 20})
sim.set_parameters({'alpha1': 0.8,
'alpha2': 0.2,
'chi': 0.1,
'lambda20': 0.44196,
'lambda22': 1.1,
'lambda23': 1,
'lambda24': 0.03,
'lambda30': 0.3997,
'lambda32': 1,
'lambda33': 1.1,
'lambda34': 0.03,
'theta': 0.1938})
sim.set_parameters({'G': 20,
'Rbar': 0.03,
'Pblbar': 20})
for _ in xrange(100):
sim.solve(iterations=100, threshold=1e-5)
prev_soln = sim.solutions[-2]
soln = sim.solutions[-1]
if is_close(prev_soln, soln, atol=1e-3):
break
end = time.clock()
print "elapsed time = " + str(end-start)
print round_solution(sim.solutions[-1], decimals=1)
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
steady_state = create_simex_model()
steady_state.set_parameters({'alpha1': 0.6,
'alpha2': 0.4,
'theta': 0.2})
steady_state.set_parameters({'Gd': 20,
'W': 1})
steady_state.variables['YD'].value = steady_state.evaluate('Gd*(1-theta)')
for _ in xrange(100):
steady_state.solve(iterations=100, threshold=1e-5)
if is_close(steady_state.solutions[-2],
steady_state.solutions[-1],
atol=1e-4):
break
print round_solution(steady_state.solutions[-1], decimals=1)