First SciPy computation - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of SciPy integration

What is the output of this code that uses SciPy to integrate a simple function?

SciPy

from scipy.integrate import quad

def f(x):
    return x**2

result, error = quad(f, 0, 1)
print(round(result, 3))

A 0.500

B 1.000

C 0.333

D 0.250

💡 Hint

Think about the integral of x squared from 0 to 1.

The integral of x^2 from 0 to 1 is 1/3, which is approximately 0.333.

❓ data_output

intermediate

Result of SciPy root finding

What is the value of root found by SciPy's root_scalar for the function f(x) = x^3 - 1 near x=1?

SciPy

from scipy.optimize import root_scalar

def f(x):
    return x**3 - 1

sol = root_scalar(f, bracket=[0, 2])
print(round(sol.root, 3))

A 0.000

B 1.000

C -1.000

D 2.000

💡 Hint

The cube root of 1 is?

The root of x^3 - 1 = 0 is x = 1, so the root_scalar finds 1.000.

❓ visualization

advanced

Plotting a Gaussian PDF with SciPy

Which option produces the correct plot of a Gaussian probability density function (PDF) using SciPy?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

x = np.linspace(-3, 3, 100)

# Plot code here
plt.plot(x, norm.pdf(x))
plt.title('Gaussian PDF')
plt.show()

A Plots a flat horizontal line

B Plots a straight line increasing from left to right

C Plots a curve with two peaks

D Plots a bell-shaped curve centered at 0

💡 Hint

The normal distribution has one peak at the mean.

The norm.pdf function returns the Gaussian PDF values, which form a bell-shaped curve centered at 0.

🧠 Conceptual

advanced

Understanding SciPy's optimize.minimize output

After running SciPy's optimize.minimize on a function, what does the 'success' attribute in the result indicate?

A 'success' is True if the optimizer found a solution meeting the criteria

B 'success' is the minimum value found by the optimizer

C 'success' is the number of iterations performed

D 'success' is the initial guess provided to the optimizer

💡 Hint

Think about what success means in optimization.

The 'success' attribute is a boolean that tells if the optimizer successfully found a solution.

🔧 Debug

expert

Identify the error in this SciPy interpolation code

What error will this code raise when run?

SciPy

import numpy as np
from scipy.interpolate import interp1d

x = np.array([0, 1, 2])
y = np.array([0, 1])

f = interp1d(x, y)
print(f(1.5))

A ValueError: x and y must have same length

B TypeError: unsupported operand type(s)

C IndexError: index out of range

D No error, prints 1.5

💡 Hint

Check the lengths of x and y arrays.

interp1d requires x and y arrays to have the same length. Here y has length 2 but x has length 3.