Moved some stuff to examples and added some missing pages

book/examples/example_gumbel.py

@@ -0,0 +1,61 @@
+from grading import check
+from math import isclose
+
+tolerance = 0.001
+
+# Using rel_tol is more reliable in the face of aliasing, but to fit the instructions give we use abs_total
+check_float = lambda a, b: isclose(a, b, rel_tol=0, abs_tol=tolerance)
+
+# We have to pass in the globals object since we need to have access to changes as well
+@check
+def check_example(glob):
+	mu, beta = glob["mu"], glob["beta"]
+	if (check_float(mu, -1.7461520011511888) and check_float(beta, 2.553428469837263)):
+		print(f"Part 1: you got the parameters right, well done! (checked with tolerance {tolerance})")
+	else:
+		print(f"Part 1: your parameters are incorrect. (checked with tolerance {tolerance})")
+		print(f"          Other parts won't be graded until these are fixed. ")
+		return 
+
+	function = glob["find_x_with_probability_p"]
+	
+	test_inputs = [(1 - 0.001, 15.891029744351862), (1 - 0.2, 2.0838374640878863), (1 - 0.9, -3.875794191615308)]
+	failed = []
+
+	for x, out in test_inputs:
+		result = function(x)
+		if not check_float(result, out):
+			failed.append((x, out, result))
+
+	if len(failed) == 0:
+		print(f"Part 2: Well done, your inverse function is correct! (checked with tolerance {tolerance})")	
+	else:
+		print(f"Part 2: Your function failed some tests. Keep in mind the tolerance is {tolerance}")
+		print("    --> Failed inputs:")
+		for case in failed:
+			print(f"{case[0]} gave {case[2]}, expected {case[1]}")
+		print(f"      Other parts won't be graded until these are fixed.")
+
+	x = glob["x"]
+	if check_float(x, 15.891029744351862):
+		print(f"Part 3: you got the value of x right, well done! (checked with tolerance {tolerance})")
+	else:
+		print(f"Part 3: your value of x is incorrect. (checked with tolerance {tolerance})")
+		return 
+"""
+Task 0:
+x_1 = 4
+p_1 = 1 - .1
+x_2 = 10
+p_2 = 1 - .01
+
+Task 1:
+	beta = -(x_2 - x_1) / log(log(p_2) / log(p_1))
+    mu = x_1 + beta * log(-log(p_1))
+
+Task 2:
+x = mu - beta * log(-log(p))
+
+Task 3:
+x = find_x_with_probability_p(1 - 0.001)
+"""