MaxPoon / Pylinear

A lightweight python package for solving linear algebra problems

Pylinear

A lightweight python package for solving linear algebra problems

Installation

pip install:

sudo pip install Pylinear

Usage

Vector

Create and print vectors:

Example:

from Pylinear import Vector
>>> v1 = Vector([1,2,3])
>>> v2 = Vector([6,5,4])
>>> print(v1, v2)
Vector: (1, 2, 3) Vector: (6, 5, 4)

Addition and subtraction: + and -

Example:

>>> v = v1 + v2
>>> print(v)
Vector: (7, 7, 7)

>>> v = v1 + 3
>>> print(v)
Vector: (4, 5, 6)

>>> v = v1 - v2
>>> print(v)
Vector: (-5, -3, -1)

Multiplication: *

Example:

>>> v = v1 * 3
>>> print(v)
Vector: (3, 6, 9)

Division: /

Example:

>>> v = v1 / 3
>>> print(v)
Vector: (0.3333333333333333, 0.6666666666666666, 1.0)

Dot product: *

Example:

>>> v = v1 * v2
>>> print(v)
28

Cross product: **

Example:

>>> v = v1 ** v2
>>> print(v)
Vector: (-7, 14, -7)

Get magnitude: Vector.mag()

Example:

>>> v1.mag()
3.7416573867739413

Get cosine similarity: Vector.sim()

Example:

>>> v1.sim(v2)
0.8528028654224418

Get angle: Vector.angle()

Example:

>>> v1.angle(v2)
0.5494672447576273
>>> v1.angle(v2, degree = True)
62.96430821058771

Checking for parallelism and orthogonality: Vector.parallel() and Vector.orthogonal()

Example:

>>> v1.parallel(v2)
False

>>> v1.orthogonal(v2)
False

Vector projection: Vector.projectTo()

Example:

>>> v = v1.projectTo(v2)
>>> print(v)
Vector: (2.1818181818181817, 1.8181818181818181, 1.4545454545454544)

Linear Equation:

Initialization: Lineq(normal_vector, constant_term=0)

Example:

>>> from Pylinear import Lineq
>>> l1 = Lineq([1,1],1)
>>> l2 = Lineq([2,3],7)
>>> l3 = Lineq([0,0],5)
>>> print(l1)
x_1 + x_2 = 1

Addition, subtraction, multiplication and division: +, -, *, /

Example:

>>> print(l1 + l2)
3x_1 + 4x_2 = 8
>>> print(l1-l2)
-x_1 - 2x_2 = -6
>>> print(3*l1)
3x_1 + 3x_2 = 3
>>> print(l1/3)
0.333x_1 + 0.333x_2 = 0.333

Checking for validation: Lineq.valid()

Example:

>> l1.valid()
True
>>> l3.valid()
False

LinearSystem

Initialization: LinearSystem(equations)

Example:

>>> from Pylinear import LinearSystem
>>> s = LinearSystem([l1, l2])
>>> print(s)
Linear System:
Equation 1: x_1 + x_2 = 1
Equation 2: 2x_1 + 3x_2 = 7

Get the triangular form: LinearSystem.triangularForm()

Example:

>>> print(s.triangularForm())
Linear System:
Equation 1: x_1 + x_2 = 1
Equation 2: x_2 = 5

Solve the system: LinearSystem.solve()

Example:

>>> result = s.solve()
>>> print(result)
[-4.0, 5.0]

Line

Initialization: Line(normal vector, constant term)

Example:

>>> from Pylinear import Line
>>> l1 = Line([1,2],3)
>>> l2 = Line([1,2],4)
>>> l3 = Line([2,4],6)

>>> print(l1)
x_1 + 2x_2 = 3

Checking for parallelism: Line.parallel(Line)

Example:

>>> l1.parallel(l3)
True

Checking for equality: ==

Example:

>>> l1 == l2
False
>>> l1 == l3
True

Plane

Initialization: Plane(normal vector, constant term)

Example:

from Pylinear import Plane
>>> p1 = Plane([1,2,3],4)
>>> p2 = Plane([2,4,6],8)

Checking for parallelism: Plane.parallel(Plane)

Example:

>>> p1.parallel(p2)
True

Checking for equality: ==

Example:

>>> p1 == p2
True

Todo:

• Add Matrix class and its methods.
• Add Optimization class and the methods to solve linear programming problem.