Minimizing scalar functions (minimize_scalar) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function for minimizing scalar functions.

SciPy

from scipy.optimize import [1]

Drag options to blanks, or click blank then click option'

Aminimize_scalar

Bminimize_vector

Cminimize_matrix

Dminimize_function

Attempts:

3 left

💡 Hint

Common Mistakes

Trying to import a non-existent function like minimize_vector.

Confusing minimize_scalar with minimize_function.

The minimize_scalar function from scipy.optimize is used to find the minimum of a scalar function.

2fill in blank

medium

Complete the code to define a simple quadratic function to minimize.

SciPy

def f(x):
    return (x - [1]) ** 2

Drag options to blanks, or click blank then click option'

A3

B0

C5

D-2

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing 0 or negative numbers which change the minimum location.

Using a number not matching the intended minimum.

This function returns the square of (x - 3). The minimum is at x = 3.

3fill in blank

hard

Fix the error in the code to minimize the function f using minimize_scalar.

SciPy

result = [1](f)
print(result.x)

Drag options to blanks, or click blank then click option'

Aminimize_vector

Bminimize_matrix

Cminimize_scalar

Dminimize_function

Attempts:

3 left

💡 Hint

Common Mistakes

Using a non-existent function like minimize_vector.

Misspelling the function name.

The correct function to minimize a scalar function is minimize_scalar.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps numbers to their squares for numbers greater than 2.

SciPy

squares = {x: x[1]2 for x in range(1, 6) if x [2] 2}

Drag options to blanks, or click blank then click option'

A**

B>

C<

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of exponentiation for squaring.

Using the wrong comparison operator like '<' instead of '>'.

The operator ** is used for exponentiation (power). The condition x > 2 filters numbers greater than 2.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths for words longer than 3 characters.

SciPy

result = {{ { [1] } : [2] for word in words if len(word) [3] 3}}

Drag options to blanks, or click blank then click option'

Aword.upper()

Blen(word)

C>

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself as the key instead of uppercase.

Using '<' instead of '>' in the condition.

The key is the uppercase word using word.upper(). The value is the length of the word using len(word). The condition len(word) > 3 filters words longer than 3 characters.

Practice

1. What does the minimize_scalar function in scipy do?

easy

A. Integrates a function over a range

B. Finds the maximum value of a function with multiple variables

C. Calculates the derivative of a function

D. Finds the minimum value of a function with one variable

Solution

1. Step 1: Understand the purpose of minimize_scalar

   The function is designed to find the lowest point (minimum) of a scalar function with one variable.

2. Step 2: Compare options to the function's purpose

   Only Finds the minimum value of a function with one variable correctly describes this purpose; others describe different tasks.

3. Final Answer:

   Finds the minimum value of a function with one variable -> Option D

4. Quick Check:

   minimize_scalar finds minimum [OK]

Hint: Remember: minimize_scalar finds lowest point of one-variable function [OK]

Common Mistakes:

• Confusing minimize_scalar with maximization functions
• Thinking it works for multi-variable functions
• Mixing it up with derivative or integration functions

2. Which of the following is the correct way to import minimize_scalar from scipy.optimize?

easy

A. from scipy.optimize import minimize_scalar

B. import minimize_scalar from scipy.optimize

C. from scipy import minimize_scalar

D. import scipy.optimize.minimize_scalar

Solution

1. Step 1: Recall Python import syntax

   To import a specific function, use 'from module import function'.

2. Step 2: Match syntax to options

   from scipy.optimize import minimize_scalar matches correct syntax: 'from scipy.optimize import minimize_scalar'. Others are invalid Python syntax.

3. Final Answer:

   from scipy.optimize import minimize_scalar -> Option A

4. Quick Check:

   Correct import syntax = from scipy.optimize import minimize_scalar [OK]

Hint: Use 'from module import function' to import specific functions [OK]

Common Mistakes:

• Using 'import function from module' which is invalid
• Trying to import directly from 'scipy' without submodule
• Using dot notation in import statement incorrectly

3. What is the output of this code?

from scipy.optimize import minimize_scalar

result = minimize_scalar(lambda x: (x - 3)**2)
print(round(result.x, 2))

medium

A. 3.00

B. 0.00

C. -3.00

D. None

Solution

1. Step 1: Understand the function minimized

   The function is (x - 3)^2, which has its minimum at x = 3.

2. Step 2: Check the minimize_scalar result

   The optimizer finds x close to 3; rounding to 2 decimals gives 3.00.

3. Final Answer:

   3.00 -> Option A

4. Quick Check:

   Minimum of (x-3)^2 is at 3 [OK]

Hint: Minimum of (x - a)^2 is at x = a [OK]

Common Mistakes:

• Confusing minimum location with function value
• Not rounding result.x before printing
• Assuming minimum at zero without checking function

4. Identify the error in this code snippet:

from scipy.optimize import minimize_scalar

def f(x):
    return x**2

result = minimize_scalar(f, bounds=(1, 2))
print(result.x)

medium

A. minimize_scalar does not accept bounds argument

B. Function f should return negative values

C. Missing method='bounded' for bounded minimization

D. Bounds should be a list, not a tuple

Solution

1. Step 1: Check usage of bounds in minimize_scalar

   When using bounds, method='bounded' must be specified explicitly.

2. Step 2: Identify missing method argument

   The code misses method='bounded', so it will ignore bounds or error.

3. Final Answer:

   Missing method='bounded' for bounded minimization -> Option C

4. Quick Check:

   Bounds require method='bounded' [OK]

Hint: Use method='bounded' when specifying bounds [OK]

Common Mistakes:

• Forgetting method='bounded' with bounds
• Assuming bounds work without method argument
• Incorrect bounds format (tuple is correct though)

5. You want to find the minimum of f(x) = (x-1)^2 + 2 but only for x between 0 and 2. Which code correctly finds this minimum using minimize_scalar?

hard

A. minimize_scalar(lambda x: (x-1)**2 + 2, bounds=(0, 2))

B. minimize_scalar(lambda x: (x-1)**2 + 2, bounds=(0, 2), method='bounded')

C. minimize_scalar(lambda x: (x-1)**2 + 2, method='bounded')

D. minimize_scalar(lambda x: (x-1)**2 + 2, method='brent')

Solution

1. Step 1: Understand bounded minimization requirements

   To limit search to [0, 2], bounds must be set and method='bounded' used.

2. Step 2: Evaluate options for correct usage

   Only minimize_scalar(lambda x: (x-1)**2 + 2, bounds=(0, 2), method='bounded') uses both bounds and method='bounded' correctly.

3. Final Answer:

   minimize_scalar(lambda x: (x-1)**2 + 2, bounds=(0, 2), method='bounded') -> Option B

4. Quick Check:

   Bounds + method='bounded' needed for limited range [OK]

Hint: Use bounds with method='bounded' to limit search range [OK]

Common Mistakes:

• Omitting method='bounded' when using bounds
• Using method='brent' which ignores bounds
• Not specifying bounds when needed