QR decomposition in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the QR decomposition function from scipy.

SciPy

from scipy.linalg import [1]

# Now you can use qr() to decompose matrices

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Aqr

Bsvd

Ceig

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the wrong function like svd or eig.

Trying to import from numpy.linalg instead of scipy.linalg.

The qr function from scipy.linalg performs QR decomposition.

2fill in blank

medium

Complete the code to perform QR decomposition on matrix A.

SciPy

Q, R = qr([1])

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Aqr

BQ

CA

DR

Attempts:

3 left

💡 Hint

Common Mistakes

Passing Q or R instead of A to the qr function.

Passing the function name qr instead of the matrix.

You pass the matrix A to the qr function to get matrices Q and R.

3fill in blank

hard

Fix the error in the code to correctly compute the QR decomposition and print Q.

SciPy

from scipy.linalg import qr

A = [[1, 2], [3, 4]]
Q, R = qr([1])
print(Q)

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AA

B[1, 2], [3, 4]

Cqr

DQ

Attempts:

3 left

💡 Hint

Common Mistakes

Passing multiple lists instead of a single matrix variable.

Passing the function name or Q instead of the matrix.

The variable A must be passed as a single argument to qr. Passing the list of lists directly without brackets causes an error.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each column index to the norm of that column in Q.

SciPy

col_norms = {i: [1] for i in range(Q.shape[[2]])}

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Anp.linalg.norm(Q[:, i])

B0

C1

DQ.shape[0]

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong axis index for shape.

Calculating norm on rows instead of columns.

The dictionary comprehension calculates the norm of each column i in Q. The number of columns is Q.shape[1].

5fill in blank

hard

Complete the code to create a dictionary comprehension that maps each row index to the sum of absolute values in that row of R, but only for rows where the sum is greater than 1.

SciPy

row_sums = {i: sum(abs(R[i, :]) ) for i in range(R.shape[[1]]) if sum(abs(R[i, :])) > 1}

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A:]

B0

C:

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect slice notation like ':]' or '1'.

Using the wrong axis index for shape.

The code sums the absolute values of all columns in each row i of R. The row count is R.shape[0]. The slice : selects all columns.