@@ -3,8 +3,10 @@ jupytext:
33 text_representation :
44 extension : .md
55 format_name : myst
6+ format_version : 0.13
7+ jupytext_version : 1.16.7
68kernelspec :
7- display_name : Python 3
9+ display_name : Python 3 (ipykernel)
810 language : python
911 name : python3
1012---
@@ -29,10 +31,9 @@ kernelspec:
2931
3032In addition to what's in Anaconda, this lecture will need the following libraries:
3133
32- ``` {code-cell} ipython
33- ---
34- tags: [hide-output]
35- ---
34+ ``` {code-cell} ipython3
35+ :tags: [hide-output]
36+
3637!pip install quantecon
3738```
3839
@@ -54,9 +55,8 @@ Required knowledge: Familiarity with matrix manipulations, multivariate normal d
5455
5556We'll need the following imports:
5657
57- ``` {code-cell} ipython
58+ ``` {code-cell} ipython3
5859import matplotlib.pyplot as plt
59- plt.rcParams["figure.figsize"] = (11, 5) #set default figure size
6060from scipy import linalg
6161import numpy as np
6262import matplotlib.cm as cm
@@ -122,10 +122,9 @@ $2 \times 2$ covariance matrix. In our simulations, we will suppose that
122122
123123This density $p(x)$ is shown below as a contour map, with the center of the red ellipse being equal to $\hat x$.
124124
125- ``` {code-cell} python3
126- ---
127- tags: [output_scroll]
128- ---
125+ ``` {code-cell} ipython3
126+ :tags: [output_scroll]
127+
129128# Set up the Gaussian prior density p
130129Σ = [[0.4, 0.3], [0.3, 0.45]]
131130Σ = np.matrix(Σ)
@@ -186,7 +185,7 @@ def bivariate_normal(x, y, σ_x=1.0, σ_y=1.0, μ_x=0.0, μ_y=0.0, σ_xy=0.0):
186185
187186def gen_gaussian_plot_vals(μ, C):
188187 "Z values for plotting the bivariate Gaussian N(μ, C)"
189- m_x, m_y = float(μ[0]), float(μ[1])
188+ m_x, m_y = float(μ[0,0 ]), float(μ[1,0 ])
190189 s_x, s_y = np.sqrt(C[0, 0]), np.sqrt(C[1, 1])
191190 s_xy = C[0, 1]
192191 return bivariate_normal(X, Y, s_x, s_y, m_x, m_y, s_xy)
@@ -213,15 +212,15 @@ The good news is that the missile has been located by our sensors, which report
213212The next figure shows the original prior $p(x)$ and the new reported
214213location $y$
215214
216- ``` {code-cell} python3
215+ ``` {code-cell} ipython3
217216fig, ax = plt.subplots(figsize=(10, 8))
218217ax.grid()
219218
220219Z = gen_gaussian_plot_vals(x_hat, Σ)
221220ax.contourf(X, Y, Z, 6, alpha=0.6, cmap=cm.jet)
222221cs = ax.contour(X, Y, Z, 6, colors="black")
223222ax.clabel(cs, inline=1, fontsize=10)
224- ax.text(float(y[0]) , float(y[1]), "$y$", fontsize=20, color="black")
223+ ax.text(float(y[0].item()) , float(y[1].item() ), "$y$", fontsize=20, color="black")
225224
226225plt.show()
227226```
@@ -284,7 +283,7 @@ This new density $p(x \,|\, y) = N(\hat x^F, \Sigma^F)$ is shown in the next fig
284283
285284The original density is left in as contour lines for comparison
286285
287- ``` {code-cell} python3
286+ ``` {code-cell} ipython3
288287fig, ax = plt.subplots(figsize=(10, 8))
289288ax.grid()
290289
@@ -298,7 +297,7 @@ new_Z = gen_gaussian_plot_vals(x_hat_F, Σ_F)
298297cs2 = ax.contour(X, Y, new_Z, 6, colors="black")
299298ax.clabel(cs2, inline=1, fontsize=10)
300299ax.contourf(X, Y, new_Z, 6, alpha=0.6, cmap=cm.jet)
301- ax.text(float(y[0]) , float(y[1]), "$y$", fontsize=20, color="black")
300+ ax.text(float(y[0].item()) , float(y[1].item() ), "$y$", fontsize=20, color="black")
302301
303302plt.show()
304303```
391390Q = 0.3 * \Sigma
392391$$
393392
394- ``` {code-cell} python3
393+ ``` {code-cell} ipython3
395394fig, ax = plt.subplots(figsize=(10, 8))
396395ax.grid()
397396
@@ -415,7 +414,7 @@ new_Z = gen_gaussian_plot_vals(new_x_hat, new_Σ)
415414cs3 = ax.contour(X, Y, new_Z, 6, colors="black")
416415ax.clabel(cs3, inline=1, fontsize=10)
417416ax.contourf(X, Y, new_Z, 6, alpha=0.6, cmap=cm.jet)
418- ax.text(float(y[0]) , float(y[1]), "$y$", fontsize=20, color="black")
417+ ax.text(float(y[0].item()) , float(y[1].item() ), "$y$", fontsize=20, color="black")
419418
420419plt.show()
421420```
@@ -577,7 +576,7 @@ Your figure should -- modulo randomness -- look something like this
577576:class: dropdown
578577```
579578
580- ``` {code-cell} python3
579+ ``` {code-cell} ipython3
581580# Parameters
582581θ = 10 # Constant value of state x_t
583582A, C, G, H = 1, 0, 1, 1
@@ -598,7 +597,7 @@ xgrid = np.linspace(θ - 5, θ + 2, 200)
598597
599598for i in range(N):
600599 # Record the current predicted mean and variance
601- m, v = [float(z) for z in (kalman.x_hat, kalman.Sigma)]
600+ m, v = [float(z) for z in (kalman.x_hat.item() , kalman.Sigma.item() )]
602601 # Plot, update filter
603602 ax.plot(xgrid, norm.pdf(xgrid, loc=m, scale=np.sqrt(v)), label=f'$t={i}$')
604603 kalman.update(y[i])
@@ -641,7 +640,7 @@ Your figure should show error erratically declining something like this
641640:class: dropdown
642641```
643642
644- ``` {code-cell} python3
643+ ``` {code-cell} ipython3
645644ϵ = 0.1
646645θ = 10 # Constant value of state x_t
647646A, C, G, H = 1, 0, 1, 1
@@ -657,7 +656,7 @@ y = y.flatten()
657656
658657for t in range(T):
659658 # Record the current predicted mean and variance and plot their densities
660- m, v = [float(temp) for temp in (kalman.x_hat, kalman.Sigma)]
659+ m, v = [float(temp) for temp in (kalman.x_hat.item() , kalman.Sigma.item() )]
661660
662661 f = lambda x: norm.pdf(x, loc=m, scale=np.sqrt(v))
663662 integral, error = quad(f, θ - ϵ, θ + ϵ)
@@ -745,7 +744,7 @@ Observe how, after an initial learning period, the Kalman filter performs quite
745744:class: dropdown
746745```
747746
748- ``` {code-cell} python3
747+ ``` {code-cell} ipython3
749748# Define A, C, G, H
750749G = np.identity(2)
751750H = np.sqrt(0.5) * np.identity(2)
0 commit comments