unit2

AM205 Unit 2: Numerical Linear Algebra

norm_inf.py

Shows that the p-norm converges to the infinity norm as p increases.

norm_monte_carlo.py

Computes the matrix norm induced by a "black box" vector norm using the Monte-Carlo method.

cholesky.py

Implements the Cholesky factorization algorithm, applies it to a tridiagonal matrix and compares with the results of numpy.linalg.cholesky.

cholesky_time.py

Compares the execution time of Cholesky decomposition implemented in Python using for-loops and numpy.linalg.cholesky.

cholesky_time.cpp

Measures the execution time of a C++ implementation of Cholesky decomposition.

sparse.py

Demonstrates basic features of scipy.sparse. Creates a sparse matrix in various formats (COO, CSR, CSC) and solves a linear system with that matrix.

sparse_pattern.py

Visualizes the changes in the sparsity pattern during the LU and Cholesky factorization algorithms.

pca.py

Performs the principal component analysis (PCA) on a two-dimensional data set.