Eigenvalue problems (eigs, eigsh) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function for computing eigenvalues of a sparse matrix.

SciPy

from scipy.sparse.linalg import [1]

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Asvd

Beigs

Ceig

Deigsh

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing eigs with eigsh which is for symmetric matrices.

Trying to import eig from scipy.linalg instead of scipy.sparse.linalg.

The eigs function computes eigenvalues and eigenvectors of a square matrix, suitable for sparse matrices.

2fill in blank

medium

Complete the code to compute the 3 largest magnitude eigenvalues of a sparse matrix A using eigs.

SciPy

vals, vecs = eigs(A, k=[1])

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A10

B5

C1

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using a value of k larger than the matrix size.

Confusing k with the index of eigenvalues.

The parameter k specifies how many eigenvalues to compute. Here, we want 3.

3fill in blank

hard

Fix the error in the code to compute the 2 smallest eigenvalues of a symmetric matrix using eigsh.

SciPy

vals, vecs = eigsh(A, k=[1], which='SM')

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A2

B1

C3

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Setting k larger than matrix size.

Confusing eigsh with eigs.

The parameter k should be 2 to compute 2 eigenvalues. Use which='SM' for the smallest magnitude eigenvalues.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each word to its length only if the length is greater than 3.

SciPy

{word: [1] for word in words if [2]

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Alen(word)

Bword

Clen(word) > 3

Dword > 3

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself as the value instead of its length.

Checking if the word is greater than 3 instead of its length.

The dictionary maps each word to its length, so the value is len(word). The condition filters words with length greater than 3, so the condition is len(word) > 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase keys to values only if the value is positive.

SciPy

result = { [1]: [2] for [3], v in data.items() if v > 0 }

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Ak.upper()

Bv

Ck

Dv.upper()

Attempts:

3 left

💡 Hint

Common Mistakes

Using the value instead of the key for uppercase conversion.

Using v as the key variable in the loop.

The key is converted to uppercase with k.upper(). The value is v. The loop variable for keys is k.