![[The AI Show Episode 142]: ChatGPT’s New Image Generator, Studio Ghibli Craze and Backlash, Gemini 2.5, OpenAI Academy, 4o Updates, Vibe Marketing & xAI Acquires X](https://www.marketingaiinstitute.com/hubfs/ep%20142%20cover.png)
![[FREE EBOOKS] The Kubernetes Bible, The Ultimate Linux Shell Scripting Guide & Four More Best Selling Titles](https://www.javacodegeeks.com/wp-content/uploads/2012/12/jcg-logo.jpg){kind=logo}
![From drop-out to software architect with Jason Lengstorf [Podcast #167]](https://cdn.hashnode.com/res/hashnode/image/upload/v1743796461357/f3d19cd7-e6f5-4d7c-8bfc-eb974bc8da68.png?#)
.png?#)
.jpg?#)
_Christophe_Coat_Alamy.jpg?#)
![Rapidus in Talks With Apple as It Accelerates Toward 2nm Chip Production [Report]](https://www.iclarified.com/images/news/96937/96937/96937-640.jpg)
Solved: PV2 Laplacian Eigenvalue Problem in Python
python # Author: Alberto # PV2 - Laplacian Eigenvalue Approximation on a 2D Square Domain import numpy as np from scipy.sparse import diags from scipy.sparse.linalg import eigsh def solve_pv2_laplacian(n): N = n * n main_diag = 4 * np.ones(N) side_diag = -1 * np.ones(N - 1) side_diag[np.arange(1, N) % n == 0] = 0 up_down_diag = -1 * np.ones(N - n) diagonals = [main_diag, side_diag, side_diag, up_down_diag, up_down_diag] offsets = [0, -1, 1, -n, n] A = diags(diagonals, offsets, format='csr') eigenvalues, _ = eigsh(A, k=1, which='SM') # Smallest magnitude eigenvalue return eigenvalues[0] # Example usage n = 30 # Grid resolution (can be increased for higher precision) result = solve_pv2_laplacian(n) print("Approximated smallest eigenvalue for PV2:", result)
python
# Author: Alberto
# PV2 - Laplacian Eigenvalue Approximation on a 2D Square Domain
import numpy as np
from scipy.sparse import diags
from scipy.sparse.linalg import eigsh
def solve_pv2_laplacian(n):
N = n * n
main_diag = 4 * np.ones(N)
side_diag = -1 * np.ones(N - 1)
side_diag[np.arange(1, N) % n == 0] = 0
up_down_diag = -1 * np.ones(N - n)
diagonals = [main_diag, side_diag, side_diag, up_down_diag, up_down_diag]
offsets = [0, -1, 1, -n, n]
A = diags(diagonals, offsets, format='csr')
eigenvalues, _ = eigsh(A, k=1, which='SM') # Smallest magnitude eigenvalue
return eigenvalues[0]
# Example usage
n = 30 # Grid resolution (can be increased for higher precision)
result = solve_pv2_laplacian(n)
print("Approximated smallest eigenvalue for PV2:", result)
