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]

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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)

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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

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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]])

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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], :]

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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.