SciPy — Sparse Matrices

What are sparse matrices?

Matrices where most elements are zero, stored efficiently.

Create sparse matrix

from scipy.sparse import csr_matrix
import numpy as np

dense = np.array([[1, 0, 0], [0, 0, 3], [0, 4, 0]])
sparse = csr_matrix(dense)
print(f"Dense: {dense.nbytes} bytes")
print(f"Sparse: {sparse.data.nbytes} bytes")

COO format

from scipy.sparse import coo_matrix

row = np.array([0, 1, 2])
col = np.array([0, 2, 1])
data = np.array([1, 3, 4])

sparse = coo_matrix((data, (row, col)), shape=(3, 3))
print(sparse.toarray())

Operations

from scipy.sparse import csr_matrix
import numpy as np

A = csr_matrix(np.array([[1, 2], [3, 4]]))
B = csr_matrix(np.array([[5, 6], [7, 8]]))

# Matrix multiplication
C = A @ B
print(f"A * B:\n{C.toarray()}")

# Transpose
AT = A.T
print(f"A^T:\n{AT.toarray()}")

Solving sparse systems

from scipy.sparse.linalg import spsolve
import numpy as np
from scipy.sparse import csr_matrix

A = csr_matrix(np.array([[4, 1], [1, 3]]))
b = np.array([1, 2])

x = spsolve(A, b)
print(f"Solution: {x}")

Sparse eigenvalues

from scipy.sparse.linalg import eigsh
import numpy as np
from scipy.sparse import random

A = random(100, 100, density=0.1, format='csr')
eigenvalues, eigenvectors = eigsh(A, k=5)
print(f"Top 5 eigenvalues: {eigenvalues}")

Conversion

# To dense
dense = sparse.toarray()

# From dense
sparse = csr_matrix(dense)

# Change format
csc = sparse.tocsc()
lil = sparse.tolil()

Mini Practice

1. Create sparse matrices
2. Perform matrix operations
3. Solve sparse systems
4. Find eigenvalues

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Continue with Special Functions - Mathematical functions.