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In [13]:

    
import matplotlib.pyplot as plt
import pandas as pd



In [14]:

    
%run src/lg_model.py



In [15]:

    
lg = LinearGaussian()



In [16]:

    
a = lrm_analytic(lg)



In [17]:

    
a









    Out[17]:





1.000046629250375

A figure showing approximation of stability exponent at different levels of discretization.



In [18]:

    
D_vals = np.arange(5, 250, step=5)
discrete_exponent_vals = np.empty_like(D_vals, dtype=np.float64)



In [19]:

    
for d, D in enumerate(D_vals):
    discrete_exponent_vals[d] = lrm_discretized(lg, D=D)



In [20]:

    
fig, ax = plt.subplots()
ax.ticklabel_format(useOffset=False) 
#ax.set_ylim((a - 1.5 * 1e-8, a + 2 * 1e-9))
ax.plot(D_vals, np.ones_like(D_vals) * a, label="true value")
ax.plot(D_vals, discrete_exponent_vals, label="discrete approximation")
ax.legend()









    Out[20]:





<matplotlib.legend.Legend at 0x7f0650c847b8>



In [ ]:

A table that compares discretized val vs actual value for different values of the parameters



In [21]:

    
lg.γ









    Out[21]:





10.0

Preference params from SSY



In [22]:

    
β = 0.998
ψ = 1.5



In [23]:

    
D_vals = [5, 50, 100, 200]
gamma_vals = [7.5, 10, 12.5]

MC_table = np.empty((len(gamma_vals), len(D_vals) + 1))
Lambda_table = np.empty_like(MC_table)



In [24]:

    
for i, γ in enumerate(gamma_vals):
    lg = LinearGaussian(γ=γ)
    MC_table[i, 0] = lrm_analytic(lg)
    Lambda_table[i, 0] = lg.β * MC_table[i, 0]**(1 - 1/lg.ψ)
    for j, d in enumerate(D_vals):
        MC_table[i, j+1] = round(lrm_discretized(lg, D=d), 7)
        Lambda_table[i, j+1] = β * MC_table[i, j+1]**(1 - 1/ψ)



In [25]:

    
MC_table









    Out[25]:





array([[1.00045044, 1.0004998 , 1.0004549 , 1.0004527 , 1.0004516 ],
       [1.00004663, 1.0001658 , 1.0000584 , 1.0000525 , 1.0000496 ],
       [0.99964298, 0.9998662 , 0.9996673 , 0.9996552 , 0.9996491 ]])



In [26]:

    
def make_table(table):
    pd_table = pd.DataFrame(table)
    print(pd_table.to_latex(float_format=lambda x: '%1.7f' % x))



In [27]:

    
make_table(MC_table)









    



\begin{tabular}{lrrrrr}
\toprule
{} &         0 &         1 &         2 &         3 &         4 \\
\midrule
0 & 1.0004504 & 1.0004998 & 1.0004549 & 1.0004527 & 1.0004516 \\
1 & 1.0000466 & 1.0001658 & 1.0000584 & 1.0000525 & 1.0000496 \\
2 & 0.9996430 & 0.9998662 & 0.9996673 & 0.9996552 & 0.9996491 \\
\bottomrule
\end{tabular}



In [28]:

    
make_table(Lambda_table)









    



\begin{tabular}{lrrrrr}
\toprule
{} &         0 &         1 &         2 &         3 &         4 \\
\midrule
0 & 0.9981498 & 0.9981662 & 0.9981513 & 0.9981506 & 0.9981502 \\
1 & 0.9980155 & 0.9980552 & 0.9980194 & 0.9980175 & 0.9980165 \\
2 & 0.9978812 & 0.9979555 & 0.9978893 & 0.9978853 & 0.9978833 \\
\bottomrule
\end{tabular}



In [29]:

    
gamma_vals









    Out[29]:





[7.5, 10, 12.5]



In [32]:

    
lg = LinearGaussian(γ=1)



In [33]:

    
lrm_analytic(lg)









    Out[33]:





1.000046629250375



In [ ]: