Singular Value Decomposition (svd) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the SVD function from scipy.

SciPy

from scipy.linalg import [1]

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

Asvd

Beig

Cinv

Ddet

Attempts:

3 left

💡 Hint

Common Mistakes

Importing eigenvalue functions like eig instead of svd.

Trying to import from the wrong module.

The svd function is used to perform Singular Value Decomposition in scipy.

2fill in blank

medium

Complete the code to perform SVD on matrix A.

SciPy

U, s, VT = [1](A)

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

Aeig

Binv

Csvd

Ddot

Attempts:

3 left

💡 Hint

Common Mistakes

Using eigenvalue decomposition function eig instead of svd.

Trying to invert the matrix instead of decomposing.

The svd function decomposes matrix A into U, s, and VT.

3fill in blank

hard

Fix the error in the code to reconstruct matrix A from SVD components.

SciPy

A_reconstructed = U @ [1] @ VT

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

Anp.diag(s)

Bs

Cnp.dot(s)

Dnp.sum(s)

Attempts:

3 left

💡 Hint

Common Mistakes

Using s directly without converting to diagonal matrix.

Using np.dot(s) which is incorrect syntax.

Summing singular values instead of creating a diagonal matrix.

The singular values s must be converted to a diagonal matrix using np.diag(s) before multiplication.

4fill in blank

hard

Fill both blanks to create a reduced SVD keeping only the top 2 singular values.

SciPy

U_reduced = U[:, :[1]]
s_reduced = np.diag(s[:[2]])

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

A2

B3

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong slice indices like 3 or 1.

Not converting singular values to diagonal matrix.

To keep the top 2 singular values, slice the first 2 columns of U and first 2 singular values from s.

5fill in blank

hard

Fill all three blanks to reconstruct matrix A using reduced SVD components.

SciPy

A_approx = U_reduced @ [1] @ [2][:[3], :]

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

As_reduced

BVT

C2

DU

Attempts:

3 left

💡 Hint

Common Mistakes

Using full VT instead of sliced.

Using wrong slicing index.

Using U instead of VT in multiplication.

Multiply U_reduced by the diagonal matrix s_reduced and the first 2 rows of VT to reconstruct the approximation.

Practice

1.

What does the svd function in scipy.linalg return when applied to a matrix?

easy

A. The determinant of the matrix

B. Only the singular values as a matrix

C. The inverse of the matrix

D. Three matrices: U, singular values as a vector, and VT

Solution

1. Step 1: Understand the output of SVD

   The Singular Value Decomposition splits a matrix into three parts: U, singular values, and VT.

2. Step 2: Recall scipy.linalg.svd output

   Scipy's svd returns U (left singular vectors), a vector of singular values, and VT (right singular vectors transposed).

3. Final Answer:

   Three matrices: U, singular values as a vector, and VT -> Option D

4. Quick Check:

   SVD output = U, s, VT [OK]

Hint: Remember SVD splits matrix into U, s, VT [OK]

Common Mistakes:

• Thinking svd returns only singular values
• Confusing VT with V
• Expecting a single matrix output

2.

Which of the following is the correct way to import and use svd from scipy.linalg?

???

easy

A. import svd from scipy.linalg
U, s, VT = svd(matrix)

B. import scipy.linalg.svd
U, s, VT = scipy.linalg.svd(matrix)

C. from scipy.linalg import svd
U, s, VT = svd(matrix)

D. from scipy import svd
U, s, VT = svd(matrix)

Solution

1. Step 1: Check correct import syntax

   Correct import for svd is from scipy.linalg import svd.

2. Step 2: Confirm usage

   Then call svd(matrix) to get U, s, VT.

3. Final Answer:

   from scipy.linalg import svd\nU, s, VT = svd(matrix) -> Option C

4. Quick Check:

   Correct import and call = from scipy.linalg import svd U, s, VT = svd(matrix) [OK]

Hint: Use 'from scipy.linalg import svd' to import [OK]

Common Mistakes:

• Using incorrect import syntax
• Trying to import svd directly from scipy
• Using 'import svd from' which is invalid

3.

Given the code below, what is the shape of U, s, and VT?

import numpy as np
from scipy.linalg import svd

matrix = np.array([[1, 2], [3, 4], [5, 6]])
U, s, VT = svd(matrix)

medium

A. U: (3, 3), s: (2,), VT: (2, 2)

B. U: (3, 2), s: (2,), VT: (2, 2)

C. U: (2, 2), s: (2,), VT: (3, 3)

D. U: (3, 3), s: (3,), VT: (2, 2)

Solution

1. Step 1: Identify matrix shape

   The matrix is 3 rows by 2 columns (3x2).

2. Step 2: Recall full SVD shapes

   Full SVD returns U as (m, m), s as (min(m,n),), VT as (n, n). Here m=3, n=2, so U=(3,3), s=(2,), VT=(2,2).

3. Final Answer:

   U: (3, 3), s: (2,), VT: (2, 2) -> Option A

4. Quick Check:

   Full SVD shapes = U(m,m), s(min(m,n)), VT(n,n) [OK]

Hint: Full SVD U shape = (m,m), VT = (n,n), s length = min(m,n) [OK]

Common Mistakes:

• Assuming U shape is (m,n) instead of (m,m)
• Confusing s shape with VT shape
• Mixing up rows and columns in shapes

4.

What is wrong with the following code snippet that tries to compute the SVD of a matrix?

from scipy.linalg import svd

matrix = [[1, 0], [0, 1]]
U, s, VT = svd(matrix)
print(U, s, VT)

medium

A. svd function does not return three values

B. The matrix should be a NumPy array, not a list of lists

C. The import statement is incorrect

D. The print statement syntax is wrong

Solution

1. Step 1: Check input type for svd

   svd expects a NumPy array or similar numeric array, not a plain Python list.

2. Step 2: Identify error cause

   Passing a list of lists can cause unexpected behavior or errors; converting to np.array fixes this.

3. Final Answer:

   The matrix should be a NumPy array, not a list of lists -> Option B

4. Quick Check:

   Input must be np.array for svd [OK]

Hint: Always convert input to np.array before svd [OK]

Common Mistakes:

• Passing Python lists directly to svd
• Assuming svd returns a single matrix
• Incorrect import or print syntax

5.

You have a large dataset matrix X of shape (1000, 50). You want to reduce its dimensionality to 10 while keeping most information. Which step using scipy.linalg.svd helps achieve this?

hard

A. Compute full SVD, then keep only the first 10 singular values and corresponding vectors

B. Compute SVD and discard the singular values

C. Use svd to get U and VT, then multiply all components without truncation

D. Apply svd only on a 10x10 submatrix of X

Solution

1. Step 1: Understand dimensionality reduction with SVD

   Reducing dimensions means keeping top singular values and vectors that capture most variance.

2. Step 2: Apply truncation after full SVD

   Compute full SVD, then keep first 10 singular values and corresponding columns of U and rows of VT to reduce size.

3. Final Answer:

   Compute full SVD, then keep only the first 10 singular values and corresponding vectors -> Option A

4. Quick Check:

   Truncate SVD components to reduce dimensions [OK]

Hint: Keep top singular values and vectors for reduction [OK]

Common Mistakes:

• Discarding singular values loses information
• Using only a submatrix loses global structure
• Not truncating leads to no reduction