Python/linear_algebra/README.md

Linear algebra library for Python

This module contains classes and functions for doing linear algebra.

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Overview

class Vector

• • This class represents a vector of arbitrary size and related operations.

  Overview of the methods:

  • constructor(components) : init the vector
  • set(components) : changes the vector components.
  • __str__() : toString method
  • component(i): gets the i-th component (0-indexed)
  • __len__() : gets the size / length of the vector (number of components)
  • euclidean_length() : returns the eulidean length of the vector
  • operator + : vector addition
  • operator - : vector subtraction
  • operator * : scalar multiplication and dot product
  • copy() : copies this vector and returns it
  • change_component(pos,value) : changes the specified component

• function zero_vector(dimension)

  • returns a zero vector of 'dimension'

• function unit_basis_vector(dimension, pos)

  • returns a unit basis vector with a one at index 'pos' (0-indexed)

• function axpy(scalar, vector1, vector2)

  • computes the axpy operation

• function random_vector(N, a, b)

  • returns a random vector of size N, with random integer components between 'a' and 'b' inclusive

class Matrix

• • This class represents a matrix of arbitrary size and operations on it.

  Overview of the methods:

  • __str__() : returns a string representation
  • operator * : implements the matrix vector multiplication implements the matrix-scalar multiplication.
  • change_component(x, y, value) : changes the specified component.
  • component(x, y) : returns the specified component.
  • width() : returns the width of the matrix
  • height() : returns the height of the matrix
  • determinant() : returns the determinant of the matrix if it is square
  • operator + : implements the matrix-addition.
  • operator - : implements the matrix-subtraction

• function square_zero_matrix(N)

  • returns a square zero-matrix of dimension NxN

• function random_matrix(W, H, a, b)

  • returns a random matrix WxH with integer components between 'a' and 'b' inclusive

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Documentation

This module uses docstrings to enable the use of Python's in-built help(...) function. For instance, try help(Vector), help(unit_basis_vector), and help(CLASSNAME.METHODNAME).

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Usage

Import the module lib.py from the src directory into your project. Alternatively, you can directly use the Python bytecode file lib.pyc.

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Tests

src/tests.py contains Python unit tests which can be run with python3 -m unittest -v.