Academic Year 2022 Sample
Python example test – session 2
General note: The following code is executed as the first cell of the notebook in which all other problems’ codes are run.
import numpy as np from scipy.integrate
import solve_ivp
import scipy.stats as st from scipy
import signal
import matplotlib.pyplot as plt 1. What is the output of this code?
A = np.array([ [1, 2], [3, 4] ])
b = np.array([5, 6])
c = np.array([0, 1])
print(np.dot(A.T + c, b))| A | B | C | D | E | F |
|---------|---------|---------|---------|---------|---------|
| [23 45] | [17 50] | [34 34] | [28 39] | [29 40] | [22 44] |2. What is the output of this code?
A = np.arange(9).reshape(3, -1)
B = np.eye(3)
print(np.trace(A - 2 * B))| A | B | C | D | E | F | G |
|----|----|----|---|---|---|----|
| 10 | -6 | -1 | 0 | 1 | 6 | 10 |3. What is the output of this code?
I = np.array([
[1, 1, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1]
])
S_x = np.outer( np.array([1, 2, 1]).T, np.array([-1, 0, 1]) )
print(signal.convolve2d(I, S_x, boundary='symm'))A.
[[0 0 0 0 2 2 0 0 0 0]
[ 0 0 0 0 2 2 0 0 0 0]
[ 0 0 0 0 2 2 0 0 0 0]
[ 0 0 0 0 2 2 0 0 0 0]
[ 0 0 0 0 1 1 0 0 0 0]
[ 0 0 0 0 -1 -1 0 0 0 0]
[ 0 0 0 0 -2 -2 0 0 0 0]
[ 0 0 0 0 -2 -2 0 0 0 0]
[ 0 0 0 0 -2 -2 0 0 0 0]
[ 0 0 0 0 -2 -2 0 0 0 0]]B.
[[0 0 0 0 4 4 0 0 0 0]
[ 0 0 0 0 4 4 0 0 0 0]
[ 0 0 0 0 4 4 0 0 0 0]
[ 0 0 0 0 4 4 0 0 0 0]
[ 0 0 0 0 2 2 0 0 0 0]
[ 0 0 0 0 -2 -2 0 0 0 0]
[ 0 0 0 0 -4 -4 0 0 0 0]
[ 0 0 0 0 -4 -4 0 0 0 0]
[ 0 0 0 0 -4 -4 0 0 0 0]
[ 0 0 0 0 -4 -4 0 0 0 0]]C.
[[0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 2 2 2 2 1 -1 -2 -2 -2 -2]
[ 2 2 2 2 1 -1 -2 -2 -2 -2]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]]D.
[[0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 4 4 4 4 2 -2 -4 -4 -4 -4]
[ 4 4 4 4 2 -2 -4 -4 -4 -4]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0]]4. What is the output of this code?
from sympy import Symbol, Limit, sin
x = Symbol('x')
ans = Limit(np.power((1 + (1 / x)), x), x, np.inf).doit()
print(round(ans, 2))| A | B | C | D | E | F | G | H | I |
|-------|-------|-------|------|---|-----|------|------|------|
| -7.39 | -3.14 | -2.72 | -1.0 | 0 | 1.0 | 2.72 | 3.14 | 7.39 |5. What is the output of this code?
def is_prime(num):
for n in range(2, int(num ** 1/2) + 1):
if num % n == 0:
return False
return True
def sum_digits(num):
return (num % 10) + (num // 10)
a, b = [2**i for i in range(4, 6)]
c, d = [10*i for i in range(2, 4)]
a1 = np.arange(a, b)
a2 = np.arange(c, d)
s1 = set(filter(is_prime, a1))
s2 = set([i for i in a2 if sum_digits(i) < 2**3])
print(len(s1.union(s2)))| A | B | C | D | E | F | G | H |
|---|---|---|----|----|----|----|----|
| 0 | 7 | 9 | 10 | 11 | 12 | 13 | 42 |6. What is the output of this code?
import pandas as pd
from sklearn.neighbors import KernelDensity
from scipy.integrate import quad
def pdf2cdf(X):
'''
Calculates cumulative distribution function (CDF) using
integration
'''
kde = KernelDensity(kernel='gaussian', bandwidth=0.75) .fit(X[:, np.newaxis])
gmm_pdf = lambda x: np.exp(kde.score(np.array([x]).reshape(-1, 1)))
x_cdf = np.arange(-5, 20, 0.1)
y_cdf = np.array([tup[0]
for tup in [quad(gmm_pdf, a, b)
for a, b in [(a, b)
for a, b in zip(x_cdf, x_cdf[1:len(x_cdf)])]]] + [0] ).cumsum()
return x_cdf, y_cdf
N = 10000
# a guassian-mixture PDF
X = np.concatenate((
np.random.normal(10, 2, 10*N),
np.random.normal(0, 1, 2 *N)
))
s = pd.Series(X)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 6))
s.plot(kind='kde', bw_method='scott', ax=ax1)
ax1.set_title('Mixed gaussian PDF')
x, y_cdf = pdf2cdf(X)
ax2.plot(x, y_cdf, color='b')
ax2.set_title('CDF from integration over gaussian-mixture PDF')A.
B.
C.
D.
E.
F.
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