pylinlin 0.0.4

A nice linear algebra library

pylinlin

Nice linear algebra library in python

Examples

from pylinlin.matrix import Matrix
from pylinlin.lu_factorization import compute_lu_factorization
from pylinlin.qr_factorization import compute_qr_factorization

# Create matrix
matrix = Matrix.from_cols([[1, 2, 3], [4, 5, 6], [7, 8, 10]])  # preferred way to initialize a matrix
matrix2 = Matrix.from_rows([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

column_as_list = [1, 2, 3, 4, 5]
column_vector = Matrix.from_cols([column_as_list])  # column vectors can be represented as matrices
magnitude_sq = column_vector.transpose().multiply(column_vector).get(0, 0)  # 55

print(matrix.size())      # Get dimensions of matrix (rows, columns)
print(matrix.get_col(0))  # Get first column from matrix
print(matrix.get_row(1))  # Get second row from matrix

print(matrix.all_cols())  # List of matrix columns

matL, matU = compute_lu_factorization(matrix)
matQ, matR = compute_qr_factorization(matrix)
print(matQ.all_cols())
print(matQ.transpose().multiply(matQ).all_cols())  # approximately an identity matrix

product = matrix.multiply(matrix)  # matrix multiplication

Goals

• Test-driven development
• Profiling of performance
• Profiling of numerical stability
• Lightweight, easy to port over to other languages

TODOs

Algorithms

• LU factorization
• LU factorization with partial pivoting
• QR factorization with householder matrices
• QR factorization with pivoting
• Gram Schmidt and Modified Gram Schmidt (help wanted!)
• Spectral decomposition
• SVD
• Conjugate gradients
• Condition number of a matrix
• Jacobi SVD
• Power iteration
• Matrix Pseudoinverse

Profiling

• Profile time taken varying size of matrices
• Profile time taken to solve linear system comparing different algorithms
• Graph error distribution on random matrices

Others

• Make curve fitting demonstration
• Make IK demonstration