Remove inline magic

Author: Smit-create

lectures/lp_intro.md

@@ -51,7 +51,6 @@ from ortools.linear_solver import pywraplp
 from scipy.optimize import linprog
 import matplotlib.pyplot as plt
 from matplotlib.patches import Polygon
-%matplotlib inline
 ```
 
 Let's start with some examples of linear programming problem.

lectures/scalar_dynam.md

@@ -37,7 +37,6 @@ and understand key concepts.
 Let's start with some standard imports:
 
 ```{code-cell} ipython
-%matplotlib inline
 import matplotlib.pyplot as plt
 import numpy as np
 ```
@@ -50,27 +49,27 @@ This section sets out the objects of interest and the kinds of properties we stu
 
 For this lecture you should know the following.
 
-If 
+If
 
 * $g$ is a function from $A$ to $B$ and
-* $f$ is a function from $B$ to $C$, 
+* $f$ is a function from $B$ to $C$,
 
 then the **composition** $f \circ g$ of $f$ and $g$ is defined by
 
-$$ 
+$$
     (f \circ g)(x) = f(g(x))
 $$
 
-For example, if 
+For example, if
 
-* $A=B=C=\mathbb R$, the set of real numbers, 
+* $A=B=C=\mathbb R$, the set of real numbers,
 * $g(x)=x^2$ and $f(x)=\sqrt{x}$, then $(f \circ g)(x) = \sqrt{x^2} = |x|$.
 
 If $f$ is a function from $A$ to itself, then $f^2$ is the composition of $f$
 with itself.
 
 For example, if $A = (0, \infty)$, the set of positive numbers, and $f(x) =
-\sqrt{x}$, then 
+\sqrt{x}$, then
 
 $$
     f^2(x) = \sqrt{\sqrt{x}} = x^{1/4}
@@ -113,7 +112,7 @@ a sequence $\{x_t\}$ of points in $S$ by setting
 ```{math}
 :label: sdsod
     x_{t+1} = g(x_t)
-    \quad \text{ with } 
+    \quad \text{ with }
     x_0 \text{ given}.
 ```
 
@@ -131,8 +130,8 @@ This sequence $\{x_t\}$ is called the **trajectory** of $x_0$ under $g$.
 In this setting, $S$ is called the **state space** and $x_t$ is called the
 **state variable**.
 
-Recalling that $g^n$ is the $n$ compositions of $g$ with itself, 
-we can write the trajectory more simply as 
+Recalling that $g^n$ is the $n$ compositions of $g$ with itself,
+we can write the trajectory more simply as
 
 $$
     x_t = g^t(x_0) \quad \text{ for } t \geq 0.
@@ -155,13 +154,13 @@ b$, where $a, b$ are fixed constants.
 This leads to the **linear difference equation**
 
 $$
-    x_{t+1} = a x_t + b 
-    \quad \text{ with } 
+    x_{t+1} = a x_t + b
+    \quad \text{ with }
     x_0 \text{ given}.
 $$
 
 
-The trajectory of $x_0$ is 
+The trajectory of $x_0$ is
 
 ```{math}
 :label: sdslinmodpath

lectures/schelling.md

@@ -70,7 +70,6 @@ awarded the 2005 Nobel Prize in Economic Sciences (joint with Robert Aumann).
 Let's start with some imports:
 
 ```{code-cell} ipython3
-%matplotlib inline
 import matplotlib.pyplot as plt
 from random import uniform, seed
 from math import sqrt

lectures/time_series_with_matrices.md

@@ -50,7 +50,6 @@ We will use the following imports:
 
 ```{code-cell} ipython
 import numpy as np
-%matplotlib inline
 import matplotlib.pyplot as plt
 from matplotlib import cm
 plt.rcParams["figure.figsize"] = (11, 5)  #set default figure size
@@ -180,15 +179,15 @@ Now let’s solve for the path of $y$.
 If $y_t$ is GNP at time $t$, then we have a version of
 Samuelson’s model of the dynamics for GNP.
 
-To solve $y = A^{-1} b$ we can either invert $A$ directly, as in 
+To solve $y = A^{-1} b$ we can either invert $A$ directly, as in
 
 ```{code-cell} python3
 A_inv = np.linalg.inv(A)
 
 y = A_inv @ b
 ```
 
-or we can use `np.linalg.solve`: 
+or we can use `np.linalg.solve`:
 
 
 ```{code-cell} python3
@@ -204,7 +203,7 @@ np.allclose(y, y_second_method)
 
 ```{note}
 In general, `np.linalg.solve` is more numerically stable than using
-`np.linalg.inv` directly. 
+`np.linalg.inv` directly.
 However, stability is not an issue for this small example. Moreover, we will
 repeatedly use `A_inv` in what follows, so there is added value in computing
 it directly.
@@ -366,9 +365,9 @@ $$
 
 You can read about multivariate normal distributions in this lecture [Multivariate Normal Distribution](https://python.quantecon.org/multivariate_normal.html).
 
-Let's write our  model as 
+Let's write our  model as
 
-$$ 
+$$
 y = \tilde A (b + u)
 $$
 
@@ -382,11 +381,11 @@ $$
 
 where
 
-$$ 
+$$
 \mu_y = \tilde A b
 $$
 
-and 
+and
 
 $$
 \Sigma_y = \tilde A (\sigma_u^2 I_{T \times T} ) \tilde A^T
@@ -425,7 +424,7 @@ class population_moments:
         A_inv = np.linalg.inv(A)
 
         self.A, self.b, self.A_inv, self.sigma_u, self.T = A, b, A_inv, sigma_u, T
-    
+
     def sample_y(self, n):
         """
         Give a sample of size n of y.
@@ -451,14 +450,14 @@ class population_moments:
 
 my_process = population_moments(
     alpha0=10.0, alpha1=1.53, alpha2=-.9, T=80, y_1=28., y0=24., sigma_u=1)
-    
+
 mu_y, Sigma_y = my_process.get_moments()
 A_inv = my_process.A_inv
 ```
 
 It is enlightening  to study the $\mu_y, \Sigma_y$'s implied by  various parameter values.
 
-Among other things, we can use the class to exhibit how  **statistical stationarity** of $y$ prevails only for very special initial conditions. 
+Among other things, we can use the class to exhibit how  **statistical stationarity** of $y$ prevails only for very special initial conditions.
 
 Let's begin by generating $N$ time realizations of $y$ plotting them together with  population  mean $\mu_y$ .
 
@@ -496,15 +495,15 @@ Let's print out the covariance matrix $\Sigma_y$ for a  time series $y$
 
 ```{code-cell} ipython3
 my_process = population_moments(alpha0=0, alpha1=.8, alpha2=0, T=6, y_1=0., y0=0., sigma_u=1)
-    
+
 mu_y, Sigma_y = my_process.get_moments()
 print("mu_y = ",mu_y)
 print("Sigma_y = ", Sigma_y)
 ```
 
 Notice that  the covariance between $y_t$ and $y_{t-1}$ -- the elements on the superdiagonal -- are **not** identical.
 
-This is is an indication that the time series respresented by our $y$ vector is not **stationary**.  
+This is is an indication that the time series respresented by our $y$ vector is not **stationary**.
 
 To make it stationary, we'd have to alter our system so that our **initial conditions** $(y_1, y_0)$ are not fixed numbers but instead a jointly normally distributed random vector with a particular mean and  covariance matrix.
 
@@ -530,7 +529,7 @@ There is a lot to be learned about the process by staring at the off diagonal el
 
 ## Moving Average Representation
 
-Let's print out  $A^{-1}$ and stare at  its structure 
+Let's print out  $A^{-1}$ and stare at  its structure
 
   *  is it triangular or almost triangular or $\ldots$ ?
 
@@ -546,7 +545,7 @@ with np.printoptions(precision=3, suppress=True):
 
 
 
-Evidently, $A^{-1}$ is a lower triangular matrix. 
+Evidently, $A^{-1}$ is a lower triangular matrix.
 
 
 Let's print out the lower right hand corner of $A^{-1}$ and stare at it.
@@ -561,13 +560,13 @@ Notice how  every row ends with the previous row's pre-diagonal entries.
 
 
 
- 
 
-Since $A^{-1}$ is lower triangular,  each  row represents  $ y_t$ for a particular $t$ as the sum of 
-- a time-dependent function $A^{-1} b$ of the initial conditions incorporated in $b$, and 
+
+Since $A^{-1}$ is lower triangular,  each  row represents  $ y_t$ for a particular $t$ as the sum of
+- a time-dependent function $A^{-1} b$ of the initial conditions incorporated in $b$, and
 - a weighted sum of  current and past values of the IID shocks $\{u_t\}$
 
-Thus,  let $\tilde{A}=A^{-1}$. 
+Thus,  let $\tilde{A}=A^{-1}$.
 
 Evidently,  for $t\geq0$,
 
@@ -577,7 +576,7 @@ $$
 
 This is  a **moving average** representation with time-varying coefficients.
 
-Just as system {eq}`eq:eqma` constitutes  a 
+Just as system {eq}`eq:eqma` constitutes  a
 **moving average** representation for $y$, system  {eq}`eq:eqar` constitutes  an **autoregressive** representation for $y$.
 
 
@@ -692,4 +691,3 @@ plt.legend()
 
 plt.show()
 ```
-