Correlation with np.correlate() in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the correlation of two arrays using numpy.

NumPy

import numpy as np

x = np.array([1, 2, 3])
y = np.array([0, 1, 0])
result = np.correlate(x, y, [1])
print(result)

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

A"full"

B"valid"

C"same"

D"none"

Attempts:

3 left

💡 Hint

Common Mistakes

Using an invalid mode string causes an error.

Using "valid" or "same" changes the output size.

The mode "full" returns the full discrete linear correlation, which is the default and most complete result.

2fill in blank

medium

Complete the code to compute the correlation of two arrays with mode 'valid'.

NumPy

import numpy as np

a = np.array([1, 2, 3, 4])
b = np.array([0, 1, 0])
correlation = np.correlate(a, b, mode=[1])
print(correlation)

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

A"same"

B"partial"

C"valid"

D"full"

Attempts:

3 left

💡 Hint

Common Mistakes

Using an unsupported mode string causes an error.

Confusing "valid" with "full" changes the output length.

The mode "valid" returns only those parts of the correlation that are computed without zero-padded edges.

3fill in blank

hard

Fix the error in the code to correctly compute correlation with np.correlate.

NumPy

import numpy as np

x = np.array([1, 2, 3])
y = np.array([0, 1, 0])
result = np.correlate(x, y, [1])
print(result)

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

A"valid"

Bfull

Cvalid

D"full"

Attempts:

3 left

💡 Hint

Common Mistakes

Passing mode without quotes causes a TypeError.

Using an invalid mode string causes a ValueError.

The mode argument must be a string, so it needs quotes around it.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each number to its correlation with a fixed array.

NumPy

import numpy as np

fixed = np.array([1, 0, -1])
numbers = [1, 2, 3]
correlations = {num: np.correlate(np.array([num, num, num]), fixed, mode=[1])[[2]] for num in numbers}
print(correlations)

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

A"valid"

B"full"

C0

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using an invalid mode string.

Using an index out of range.

Using mode "full" gives the full correlation array, and index 0 accesses the first correlation value.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each word to the correlation of its length with a fixed array.

NumPy

import numpy as np

fixed = np.array([1, 2, 3])
words = ["cat", "dog", "bird"]
correlation_dict = {word: np.correlate(np.array([len(word)] * 3), fixed, mode=[1])[[2]] for word in words if len(word) [3] 3}
print(correlation_dict)

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

A"valid"

B0

C>

D"full"

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect mode strings.

Using wrong index values.

Using wrong comparison operators.

Use mode "full" for full correlation, index 0 for the first value, and filter words with length greater than 3.

Practice

1.

What does the np.correlate() function compute between two arrays?

easy

A. The similarity by sliding one array over another and summing products

B. The sum of all elements in both arrays

C. The difference between the maximum values of the arrays

D. The element-wise multiplication without any sliding

Solution

1. Step 1: Understand correlation concept

   Correlation measures how similar two sequences are by sliding one over the other and summing the products of overlapping elements.

2. Step 2: Relate to np.correlate()

   The np.correlate() function implements this sliding and summing operation to compute similarity.

3. Final Answer:

   The similarity by sliding one array over another and summing products -> Option A

4. Quick Check:

   Correlation = similarity by sliding and summing [OK]

Hint: Correlation slides and sums products to measure similarity [OK]

Common Mistakes:

• Confusing correlation with element-wise multiplication only
• Thinking it sums all elements instead of sliding sums
• Mixing correlation with difference or subtraction

2.

Which of the following is the correct syntax to compute the full correlation of two arrays a and b using NumPy?

import numpy as np
a = np.array([1, 2, 3])
b = np.array([0, 1, 0])
# What is the correct call?

easy

A. np.correlate(a, b)

B. np.correlate(a, b, method='slide')

C. np.corrcoef(a, b)

D. np.correlate(a, b, mode='full')

Solution

1. Step 1: Recall np.correlate syntax

   The function np.correlate() takes two arrays and an optional mode parameter to control output size.

2. Step 2: Identify correct usage

   Using mode='full' returns the complete correlation result. The default mode is 'valid'. np.correlate(a, b, mode='full') uses correct syntax and mode.

3. Final Answer:

   np.correlate(a, b, mode='full') -> Option D

4. Quick Check:

   np.correlate with mode='full' is correct syntax [OK]

Hint: Use mode='full' for complete correlation output [OK]

Common Mistakes:

• Using np.corrcoef instead of np.correlate
• Passing invalid parameter 'method'
• Omitting mode when full output is needed

3.

What is the output of the following code?

import numpy as np
x = np.array([1, 2, 3])
y = np.array([0, 1, 0])
result = np.correlate(x, y, mode='full')
print(result)

medium

A. [3 2 1 0 0]

B. [0 1 2]

C. [0 1 2 3 0]

D. [0 1 2 0 0]

Solution

1. Step 1: Understand mode='full' output length

   For arrays of length 3 and 3, full mode output length is 3+3-1=5.

2. Step 2: Calculate correlation values

   Sliding y over x:
   Positions and sums:
   Index 0: x[0]*y[2]=1*0=0
   Index 1: x[0]*y[1]+x[1]*y[2]=1*1+2*0=1
   Index 2: x[0]*y[0]+x[1]*y[1]+x[2]*y[2]=1*0+2*1+3*0=2
   Index 3: x[1]*y[0]+x[2]*y[1]=2*0+3*1=3
   Index 4: x[2]*y[0]=3*0=0
   So result is [0 1 2 3 0]

3. Final Answer:

   [0 1 2 3 0] -> Option C

4. Quick Check:

   np.correlate full mode length = 5, values match [OK]

Hint: Remember full mode length = len(a)+len(b)-1 [OK]

Common Mistakes:

• Not flipping second array in correlation
• Confusing correlation with convolution
• Wrong output length for full mode

4.

Identify the error in the following code snippet:

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5])
result = np.correlate(x, y, mode='middle')
print(result)

medium

A. 'middle' is not a valid mode for np.correlate()

B. Arrays x and y must be the same length

C. np.correlate requires 3 arrays as input

D. The function np.correlate does not exist in numpy

Solution

1. Step 1: Check valid modes for np.correlate()

   Valid modes are 'valid', 'same', and 'full'. 'middle' is not a valid mode.

2. Step 2: Confirm function usage

   Arrays can be different lengths; np.correlate supports that. The function exists and takes two arrays.

3. Final Answer:

   'middle' is not a valid mode for np.correlate() -> Option A

4. Quick Check:

   Valid modes = 'valid', 'same', 'full' only [OK]

Hint: Use only 'valid', 'same', or 'full' for mode [OK]

Common Mistakes:

• Using unsupported mode strings
• Assuming arrays must be same length
• Thinking np.correlate needs more than two arrays

5.

You have two time series arrays representing daily sales: sales_a = np.array([10, 20, 30, 40]) and sales_b = np.array([0, 1, 0]). You want to find the day offset where sales_b best matches sales_a. Which np.correlate() call and mode should you use to find this offset?

hard

A. np.correlate(sales_a, sales_b, mode='valid')

B. np.correlate(sales_a, sales_b, mode='full')

C. np.correlate(sales_b, sales_a, mode='same')

D. np.correlate(sales_a, sales_b, mode='same')

Solution

1. Step 1: Understand the goal

   To find the best matching offset, we need the full correlation result to see similarity at all shifts.

2. Step 2: Choose correct mode and order

   Using mode='full' gives all possible overlaps. The order np.correlate(sales_a, sales_b) is correct to slide sales_b over sales_a.

3. Final Answer:

   np.correlate(sales_a, sales_b, mode='full') -> Option B

4. Quick Check:

   Full mode shows all offsets for best match [OK]

Hint: Use mode='full' to find best offset in correlation [OK]

Common Mistakes:

• Using 'valid' mode which limits output length
• Swapping array order incorrectly
• Using 'same' mode which centers output, hiding edges