Merge pull request #256 from Smit-create/i-176

Few bug fixes on convergence conditions

Author: jstac

lectures/_static/lecture_specific/coleman_policy_iter/solve_time_iter.py

@@ -17,10 +17,9 @@ def solve_model_time_iter(model,    # Class with model information
             print(f"Error at iteration {i} is {error}.")
         σ = σ_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return σ_new

lectures/_static/lecture_specific/optgrowth/solve_model.py

@@ -21,10 +21,9 @@ def solve_model(og,
             print(f"Error at iteration {i} is {error}.")
         v = v_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return v_greedy, v_new

lectures/cake_eating_numerical.md

@@ -88,11 +88,11 @@ The basic idea is:
 
 1. Take an arbitary intial guess of $v$.
 1. Obtain an update $w$ defined by
-   
+
    $$
    w(x) = \max_{0\leq c \leq x} \{u(c) + \beta v(x-c)\}
    $$
-   
+
 1. Stop if $w$ is approximately equal to $v$, otherwise set
    $v=w$ and go back to step 2.
 
@@ -299,10 +299,9 @@ def compute_value_function(ce,
 
         v = v_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return v_new
@@ -657,10 +656,9 @@ def iterate_euler_equation(ce,
 
         σ = σ_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return σ
@@ -685,4 +683,4 @@ plt.show()
 ```
 
 ```{solution-end}
-```
+```

lectures/career.md

@@ -300,12 +300,11 @@ def solve_model(cw,
             print(f"Error at iteration {i} is {error}.")
         v = v_new
 
-    if i == max_iter and error > tol:
+    if error > tol:
         print("Failed to converge!")
 
-    else:
-        if verbose:
-            print(f"\nConverged in {i} iterations.")
+    elif verbose:
+        print(f"\nConverged in {i} iterations.")
 
     return v_new
 ```
@@ -545,4 +544,4 @@ has become more concentrated around the mean, making high-paying jobs
 less realistic.
 
 ```{solution-end}
-```
+```

lectures/ifp_advanced.md

@@ -494,10 +494,9 @@ def solve_model_time_iter(model,        # Class with model information
             print(f"Error at iteration {i} is {error}.")
         a_vec, σ_vec = np.copy(a_new), np.copy(σ_new)
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return a_new, σ_new

lectures/jv.md

@@ -362,10 +362,9 @@ def solve_model(jv,
             print(f"Error at iteration {i} is {error}.")
         v = v_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return v_new
@@ -569,4 +568,4 @@ This seems reasonable and helps us confirm that our dynamic programming
 solutions are probably correct.
 
 ```{solution-end}
-```
+```

lectures/mccall_correlated.md

@@ -281,10 +281,9 @@ def compute_fixed_point(js,
             print(f"Error at iteration {i} is {error}.")
         f_in[:] = f_out
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return f_out
@@ -453,4 +452,4 @@ plt.show()
 The figure shows that more patient individuals tend to wait longer before accepting an offer.
 
 ```{solution-end}
-```
+```

lectures/mccall_model.md

@@ -91,7 +91,7 @@ economists to inject randomness into their models.)
 
 In this lecture, we adopt the following simple environment:
 
-* $\{s_t\}$ is IID, with $q(s)$ being the probability of observing state $s$ in $\mathbb{S}$ at each point in time, 
+* $\{s_t\}$ is IID, with $q(s)$ being the probability of observing state $s$ in $\mathbb{S}$ at each point in time,
 * the agent observes $s_t$ at the start of $t$ and hence knows
   $w_t = w(s_t)$,
 * the set $\mathbb S$ is finite.
@@ -120,7 +120,7 @@ The variable  $y_t$ is income, equal to
 * unemployment compensation $c$ when unemployed
 
 The worker knows  that $\{s_t\}$ is IID with common
-distribution $q$ and uses knowledge when he or she computes mathematical expectations of various random variables that are functions of 
+distribution $q$ and uses knowledge when he or she computes mathematical expectations of various random variables that are functions of
 $s_t$.
 
 ### A Trade-Off
@@ -134,7 +134,7 @@ To decide optimally in the face of this trade-off, we use dynamic programming.
 
 Dynamic programming can be thought of as a two-step procedure that
 
-1. first assigns values to "states" 
+1. first assigns values to "states"
 1. then deduces optimal actions given those values
 
 We'll go through these steps in turn.
@@ -160,16 +160,16 @@ Let $v^*(s)$ be the optimal value of the problem when $s \in \mathbb{S}$  for a
 
 
 
-Thus, the function $v^*(s)$ is the maximum value of  objective 
+Thus, the function $v^*(s)$ is the maximum value of  objective
 {eq}`objective` for a previously unemployed worker who has offer $w(s)$ in  hand and has yet to choose whether to accept it.
 
 Notice that $v^*(s)$ is part of the **solution** of the problem, so it isn't obvious that it is a good idea  to start working on the problem by focusing on  $v^*(s)$.
 
 There is a chicken and egg problem: we don't know how to compute  $v^*(s)$  because we don't yet know
 what decisions are optimal and what aren't!
 
-But it turns out to be a really good idea by asking what properties the optimal value function $v^*(s)$ must have in order it 
-to qualify as an optimal value function. 
+But it turns out to be a really good idea by asking what properties the optimal value function $v^*(s)$ must have in order it
+to qualify as an optimal value function.
 
 Think of $v^*$ as a function that assigns to each possible state
 $s$ the maximal expected discounted income stream  that can be obtained with that offer in
@@ -192,7 +192,7 @@ for every possible $s$  in $\mathbb S$.
 Notice how the function $v^*(s)$ appears on both the right and left sides of  equation {eq}`odu_pv` -- that is why it is called
 a **functional equation**, i.e., an equation that restricts a **function**.
 
-This important equation is a version of a **Bellman equation**, an equation that is 
+This important equation is a version of a **Bellman equation**, an equation that is
 ubiquitous in economic dynamics and other fields involving planning over time.
 
 The intuition behind it is as follows:
@@ -218,7 +218,7 @@ Once we have this function in hand we can figure out how  behave optimally (i.e.
 
 All we have to do is select the maximal choice on the r.h.s. of {eq}`odu_pv`.
 
-The optimal action in state $s$ can be  thought of as a part of a **policy** that  maps a 
+The optimal action in state $s$ can be  thought of as a part of a **policy** that  maps a
 state into an  action.
 
 Given *any* $s$, we can read off the corresponding best choice (accept or
@@ -351,7 +351,7 @@ Moreover, it's immediate from the definition of $T$ that this fixed
 point is $v^*$.
 
 A second implication of the  Banach contraction mapping theorem is that
-$\{ T^k v \}$ converges to the fixed point $v^*$ regardless of the initial 
+$\{ T^k v \}$ converges to the fixed point $v^*$ regardless of the initial
 $v \in \mathbb R^n$.
 
 ### Implementation
@@ -386,7 +386,7 @@ We are going to use Numba to accelerate our code.
 
 * See, in particular, the discussion of `@jitclass` in [our lecture on Numba](https://python-programming.quantecon.org/numba.html).
 
-The following helps Numba by providing some information about types 
+The following helps Numba by providing some information about types
 
 ```{code-cell} python3
 mccall_data = [
@@ -490,15 +490,15 @@ def compute_reservation_wage(mcm,
     n = len(w)
     v = w / (1 - β)          # initial guess
     v_next = np.empty_like(v)
-    i = 0
+    j = 0
     error = tol + 1
-    while i < max_iter and error > tol:
+    while j < max_iter and error > tol:
 
         for i in range(n):
             v_next[i] = np.max(mcm.state_action_values(i, v))
 
         error = np.max(np.abs(v_next - v))
-        i += 1
+        j += 1
 
         v[:] = v_next  # copy contents into v
 

lectures/navy_captain.md

@@ -538,7 +538,7 @@ def solve_model(wf, tol=1e-4, max_iter=1000):
         i += 1
         h = h_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
 
     return h_new
@@ -621,25 +621,25 @@ conditioning on knowing for sure that nature has selected $f_{0}$,
 in the first case, or $f_{1}$, in the second case.
 
 1. under $f_{0}$,
-   
+
    $$
    V^{0}\left(\pi\right)=\begin{cases}
    0 & \text{if }\alpha\leq\pi,\\
    c+EV^{0}\left(\pi^{\prime}\right) & \text{if }\beta\leq\pi<\alpha,\\
    \bar L_{1} & \text{if }\pi<\beta.
    \end{cases}
    $$
-   
+
 1. under $f_{1}$
-   
+
    $$
    V^{1}\left(\pi\right)=\begin{cases}
    \bar L_{0} & \text{if }\alpha\leq\pi,\\
    c+EV^{1}\left(\pi^{\prime}\right) & \text{if }\beta\leq\pi<\alpha,\\
    0 & \text{if }\pi<\beta.
    \end{cases}
    $$
-   
+
 
 where
 $\pi^{\prime}=\frac{\pi f_{0}\left(z^{\prime}\right)}{\pi f_{0}\left(z^{\prime}\right)+\left(1-\pi\right)f_{1}\left(z^{\prime}\right)}$.
@@ -1118,4 +1118,3 @@ plt.title('Uncond. distribution of log likelihood ratio at frequentist  t')
 
 plt.show()
 ```
-

lectures/odu.md

@@ -149,10 +149,10 @@ $$
 
 
 
-The  worker's time $t$ subjective belief about the  the distribution of $W_t$  is 
+The  worker's time $t$ subjective belief about the  the distribution of $W_t$  is
 
 $$
-\pi_t f + (1 - \pi_t) g, 
+\pi_t f + (1 - \pi_t) g,
 $$
 
 where $\pi_t$ updates via
@@ -427,10 +427,9 @@ def solve_model(sp,
             print(f"Error at iteration {i} is {error}.")
         v = v_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
 
@@ -731,10 +730,9 @@ def solve_wbar(sp,
             print(f"Error at iteration {i} is {error}.")
         w = w_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
-
-    if verbose and i < max_iter:
+    elif verbose:
         print(f"\nConverged in {i} iterations.")
 
     return w_new
@@ -1178,4 +1176,3 @@ after having acquired less information about the wage distribution.
 ```{code-cell} python3
 job_search_example(1, 1, 3, 1.2, c=0.1)
 ```
-

lectures/wald_friedman.md

@@ -526,7 +526,7 @@ def solve_model(wf, tol=1e-4, max_iter=1000):
         i += 1
         h = h_new
 
-    if i == max_iter:
+    if error > tol:
         print("Failed to converge!")
 
     return h_new
@@ -902,11 +902,11 @@ Wald summarizes Neyman and Pearson's setup as follows:
 
 > Neyman and Pearson show that a region consisting of all samples
 > $(z_1, z_2, \ldots, z_n)$ which satisfy the inequality
-> 
+>
 > $$
   \frac{ f_1(z_1) \cdots f_1(z_n)}{f_0(z_1) \cdots f_0(z_n)} \geq k
   $$
-> 
+>
 > is a most powerful critical region for testing the hypothesis
 > $H_0$ against the alternative hypothesis $H_1$. The term
 > $k$ on the right side is a constant chosen so that the region