Cholesky decomposition in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Cholesky decomposition function from scipy.linalg.

SciPy

from scipy.linalg import [1]

# Now you can use the function for decomposition

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Aeig

Binv

Ccholesky

Dsvd

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the wrong function like 'inv' or 'eig'.

Using 'svd' which is for singular value decomposition, not Cholesky.

The cholesky function from scipy.linalg computes the Cholesky decomposition of a matrix.

2fill in blank

medium

Complete the code to perform Cholesky decomposition on matrix 'A'.

SciPy

import numpy as np
from scipy.linalg import cholesky

A = np.array([[4, 2], [2, 3]])
L = cholesky([1], lower=True)
print(L)

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AA

BL

Cnp

Dcholesky

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the function name instead of the matrix.

Passing the result variable 'L' before it is assigned.

The matrix A is passed to the cholesky function to compute its Cholesky decomposition.

3fill in blank

hard

Fix the error in the code to correctly compute the Cholesky decomposition.

SciPy

import numpy as np
from scipy.linalg import cholesky

B = np.array([[1, 2], [2, 1]])
L = cholesky([1], lower=True)
print(L)

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Anp

BB

Ccholesky

DL

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the function name or other variables instead of the matrix.

Using a matrix that is not positive definite (this matrix is not positive definite, so decomposition will fail).

The matrix B is passed to the cholesky function. The matrix must be positive definite for Cholesky decomposition to work.

4fill in blank

hard

Fill both blanks to create a dictionary of Cholesky decompositions for matrices with keys 'X' and 'Y'.

SciPy

matrices = {'X': np.array([[9, 3], [3, 5]]), 'Y': np.array([[16, 4], [4, 10]])}
decompositions = {key: [1](mat, lower=True) for key, mat in matrices.items() if mat.shape[0] == [2]
print(decompositions)

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Acholesky

B2

C1

Dnp.linalg.cholesky

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong function name like 'np.linalg.cholesky' when importing from scipy.linalg.

Checking for wrong matrix size.

The cholesky function is used to decompose each matrix. The condition checks if the matrix is 2x2 by verifying mat.shape[0] == 2.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that stores the upper triangular Cholesky decomposition for each matrix in 'data'.

SciPy

data = {'A': np.array([[25, 15], [15, 18]]), 'B': np.array([[36, 12], [12, 20]])}
results = { [1]: cholesky(mat, lower=[2]) for [3], mat in data.items() }
print(results)

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A'A'

BFalse

Ckey

DTrue

Attempts:

3 left

💡 Hint

Common Mistakes

Using a string literal instead of the variable for keys.

Setting lower=True instead of False.

Not unpacking the dictionary items correctly.

The dictionary comprehension uses key as the dictionary key. Setting lower=False computes the upper triangular matrix. The loop unpacks key, mat from data.items().