@@ -864,7 +864,8 @@ a

864864Mutability leads to the following behavior (which can be shocking to MATLAB programmers...)865865866866```{code-cell} python3867-a = np.random.randn(3)867+rng = np.random.default_rng()868+a = rng.standard_normal(3)868869a869870```870871

@@ -894,7 +895,7 @@ It is of course possible to make `b` an independent copy of `a` when required.

894895This can be done using `np.copy`895896896897```{code-cell} python3897-a = np.random.randn(3)898+a = rng.standard_normal(3)898899a899900```900901

@@ -972,7 +973,7 @@ def f(x):

972973The NumPy function `np.where` provides a vectorized alternative:973974974975```{code-cell} python3975-x = np.random.randn(4)976+x = rng.standard_normal(4)976977x977978```978979

@@ -1049,11 +1050,12 @@ z[z > 3]

10491050NumPy provides some additional functionality related to scientific programming10501051through its sub-packages.105110521052-We've already seen how we can generate random variables using np.random1053+We've already seen how we can generate random variables using NumPy's 1054+[random `Generator`](https://numpy.org/doc/stable/reference/random/generator.html#random-generator).1053105510541056```{code-cell} python31055-z = np.random.randn(10000) # Generate standard normals1056-y = np.random.binomial(10, 0.5, size=1000) # 1,000 draws from Bin(10, 0.5)1057+z = rng.standard_normal(10000) # Generate standard normals1058+y = rng.binomial(10, 0.5, size=1000) # 1,000 draws from Bin(10, 0.5)10571059y.mean()10581060```10591061

@@ -1099,7 +1101,7 @@ It takes a few seconds to run.

10991101n = 2011001102m = 100011011103for i in range(n):1102- X = np.random.randn(m, m)1104+ X = rng.standard_normal((m, m))11031105 λ = np.linalg.eigvals(X)11041106```11051107

@@ -1240,28 +1242,28 @@ Here's our first pass at a solution:

1240124212411243```{code-cell} python312421244from numpy import cumsum1243-from numpy.random import uniform1244124512451246class DiscreteRV:12461247 """12471248 Generates an array of draws from a discrete random variable with vector of12481249 probabilities given by q.12491250 """125012511251- def __init__(self, q):1252+ def __init__(self, q, seed=None):12521253 """12531254 The argument q is a NumPy array, or array like, nonnegative and sums12541255 to 112551256 """12561257 self.q = q12571258 self.Q = cumsum(q)1259+ self.rng = np.random.default_rng(seed)1258126012591261 def draw(self, k=1):12601262 """12611263 Returns k draws from q. For each such draw, the value i is returned12621264 with probability q[i].12631265 """1264- return self.Q.searchsorted(uniform(0, 1, size=k))1266+ return self.Q.searchsorted(self.rng.uniform(0, 1, size=k))12651267```1266126812671269The logic is not obvious, but if you take your time and read it slowly,

@@ -1390,7 +1392,8 @@ Here's an example of usage

1390139213911393```{code-cell} python313921394fig, ax = plt.subplots()1393-X = np.random.randn(1000)1395+rng = np.random.default_rng()1396+X = rng.standard_normal(1000)13941397F = ECDF(X)13951398F.plot(ax)13961399```

@@ -1411,9 +1414,9 @@ In this exercise, try to use `for` loops to replicate the result of the followin

1411141414121415```{code-cell} python3141314161414-np.random.seed(123)1415-x = np.random.randn(4, 4)1416-y = np.random.randn(4)1417+rng = np.random.default_rng(123)1418+x = rng.standard_normal((4, 4))1419+y = rng.standard_normal(4)14171420A = x / y14181421```14191422

@@ -1441,9 +1444,9 @@ Now we can import the quantecon package.

1441144414421445```{code-cell} python3144314461444-np.random.seed(123)1445-x = np.random.randn(1000, 100, 100)1446-y = np.random.randn(100)1447+rng = np.random.default_rng(123)1448+x = rng.standard_normal((1000, 100, 100))1449+y = rng.standard_normal(100)1447145014481451with qe.Timer("Broadcasting operation"):14491452 B = x / y

@@ -1469,9 +1472,9 @@ print(B)

14691472**Part 1 Solution**1470147314711474```{code-cell} python31472-np.random.seed(123)1473-x = np.random.randn(4, 4)1474-y = np.random.randn(4)1475+rng = np.random.default_rng(123)1476+x = rng.standard_normal((4, 4))1477+y = rng.standard_normal(4)1475147814761479C = np.empty_like(x)14771480n = len(x)

@@ -1500,9 +1503,9 @@ print(np.array_equal(A, C))

1500150315011504```{code-cell} python3150215051503-np.random.seed(123)1504-x = np.random.randn(1000, 100, 100)1505-y = np.random.randn(100)1506+rng = np.random.default_rng(123)1507+x = rng.standard_normal((1000, 100, 100))1508+y = rng.standard_normal(100)1506150915071510with qe.Timer("For loop operation"):15081511 D = np.empty_like(x)