Matrix creation and operations in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of matrix multiplication with SciPy

What is the output of the following code that multiplies two sparse matrices?

SciPy

import numpy as np
from scipy.sparse import csr_matrix

A = csr_matrix(np.array([[1, 0, 2], [0, 3, 0]]))
B = csr_matrix(np.array([[0, 3], [1, 0], [4, 5]]))
C = A.dot(B)
print(C.toarray())

A

[[8 13]
 [0 0]]

B

[[8 10]
 [3 0]]

C

[[8 13]
 [3 0]]

D

[[8 13]
 [0 3]]

💡 Hint

Remember that matrix multiplication sums the products of row elements of A with column elements of B.

Matrix multiplication of A and B results in a 2x2 matrix. For example, element (0,0) is 1*0 + 0*1 + 2*4 = 8, and element (0,1) is 1*3 + 0*0 + 2*5 = 13.

❓ data_output

intermediate

Shape and type of a sparse matrix

After running this code, what are the shape and type of the matrix M?

SciPy

from scipy.sparse import lil_matrix

M = lil_matrix((3, 4))
M[1, 2] = 5
M[2, 3] = 10
print(M.shape, type(M))

A (3, 4) <class 'numpy.ndarray'>

B (4, 3) <class 'numpy.ndarray'>

C (4, 3) <class 'scipy.sparse.lil_matrix'>

D (3, 4) <class 'scipy.sparse.lil_matrix'>

💡 Hint

The shape is set when creating the matrix. The type depends on the sparse format used.

The matrix M is created with shape (3,4) using lil_matrix, so its type is scipy.sparse.lil_matrix and shape is (3,4).

🔧 Debug

advanced

Identify the error in matrix addition

What error will this code raise when adding two sparse matrices of different shapes?

SciPy

from scipy.sparse import csr_matrix

A = csr_matrix([[1, 2], [3, 4]])
B = csr_matrix([[5, 6, 7], [8, 9, 10]])
C = A + B

A ValueError: matrix dimension mismatch

B ValueError: matrices are not aligned

C TypeError: unsupported operand type(s) for +

D No error, addition succeeds

💡 Hint

Check if the shapes of the matrices are compatible for addition.

Adding sparse matrices requires them to have the same shape. Here, A is 2x2 and B is 2x3, so a ValueError about dimension mismatch is raised.

❓ visualization

advanced

Visualizing a sparse matrix

Which option correctly creates a visualization of the nonzero elements of a sparse matrix using matplotlib?

SciPy

import matplotlib.pyplot as plt
from scipy.sparse import coo_matrix

row = [0, 1, 2, 0]
col = [0, 2, 2, 1]
data = [4, 5, 7, 9]
M = coo_matrix((data, (row, col)), shape=(3, 3))

plt.figure()
# Fill in the missing code here
plt.show()

A plt.spy(M)

B plt.imshow(M.toarray())

C plt.scatter(M.row, M.col, s=100, c='red')

D plt.plot(M.data)

💡 Hint

Use a function designed to show sparsity patterns.

plt.spy() is designed to visualize the sparsity pattern of a matrix, showing nonzero elements clearly.

🧠 Conceptual

expert

Memory efficiency of sparse matrix formats

Which sparse matrix format is generally most memory efficient for fast arithmetic operations on large, sparse matrices?

A LIL (List of Lists)

B CSR (Compressed Sparse Row)

C COO (Coordinate format)

D DOK (Dictionary of Keys)

💡 Hint

Consider which format is optimized for arithmetic and slicing.

CSR format stores data efficiently and supports fast arithmetic and matrix-vector operations, making it best for large sparse matrices.