Linear Algebra Python Module

Single-file python module linear_algebra.py implements basic Vector and Matrix classes.

Features

• Vector * number, Vector / number

• Vector + Vector, Vector - Vector

• Vector * Vector <==> Vector.dot(Vector)

• Vector.cross(Vector)

• Vector.normalize()

• Matrix * number, Matrix / number

• Matrix + Matrix, Matrix - Matrix

• Matrix * Matrix, Matrix * Vector, Vector * Matrix

• Matrix.transpose()

• Matrix.trace()

• Matrix.det()

• Matrix.eigenvalues()

Usage

• Copy file linear_algebra.py to your project
• Use from linear_algebra import *
• Use Vector and Matrix classes

Examples

Working with Vector

from linear_algebra import *

v1 = Vector(5) # zero vector with 5 components
v2 = Vector.Zero(5) # zero vector with 5 components
v1 == v2 # True
print v1 # 0.0, 0.0, 0.0, 0.0, 0.0
print repr(v1) # Vector([0.0, 0.0, 0.0, 0.0, 0.0])
v1.size == 5 # True
v1.magnitude == 0 # True
v1.values == [0, 0, 0, 0, 0] # True
v1.isZero() # True
v1 == 0 # True

v3 = Vector([2, 5, -6, 4]) # vector form list
v4 = Vector.FromList([2, 5, -6, 4]) # vector form list
v3 == v4 # True
print v3 # 2.0, 5.0, -6.0, 4.0
print repr(v3) # Vector([2.0, 5.0, -6.0, 4.0])
v3.size == 4 # True
v3.magnitude == 9 # True

v3 - v4 == 0 # True
v3 + v4 == 2 * v3 # True
-v3 == Vector([-2, -5, 6, -4]) # True
v3 / 2 == Vector([1, 2.5, -3, 2]) # True
v3 * v4 == 81 # True
v3.dot(v4) == 81 # True

v5 = v3.normalize()
print v5 # 0.222222222222, 0.555555555556, -0.666666666667, 0.444444444444
v5 == v3 / v3.magnitude # True
v5.magnitude == 1 # True
v5.isNormalized() # True

v6 = Vector([2, 5, 7])
v7 = Vector([3, 1, 2])
v6.cross(v7) == Vector([3, 17, -13]) # True

Working with Matrix

from linear_algebra import *

m1 = Matrix(2, 3) # zero matrix with 2 rows and 3 columns
m2 = Matrix.Zero(2, 3) # zero matrix with 2 rows and 3 columns
m1 == m2 # True
print m1 # [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
print repr(m1) # Matrix([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])
m1.size == (2, 3) # True
m1.m == 2 # True
m1.n == 3 # True
m1.isZero() # True
m1 == 0 # True

m3 = Matrix([[1,0,0], [0,1,0], [0,0,1]]) # matrix from list of rows 3x3
m4 = Matrix.Identity(3) # identity matrix 3x3
m3 == m4 # True
m3.size == (3, 3) # True
m3.isSquare() # True
m3.isDiagonal() # True
m3.isIdentity() # True
m3 == 1 # True

m5 = Matrix([[1,2,4], [4,5,6]]) # matrix from list of rows
m6 = Matrix.FromListOfRows([[1,2,4], [4,5,6]]) # matrix from list of rows
m7 = Matrix.FromListOfCols([[1,4], [2,5], [4,6]]) # matrix from list of columns
m5 == m6 # True
m5 == m7 # True
print m5 # [[1.0, 2.0, 4.0], [4.0, 5.0, 6.0]]
print repr(m5) # Matrix([[1.0, 2.0, 4.0], [4.0, 5.0, 6.0]])
m5.rows == [Vector([1,2,4]), Vector([4,5,6])] # True
m5.cols == [Vector([1,4]), Vector([2,5]), Vector([4,6])] # True
m5.getDiagonal() == Vector([1,5]) # True

m8 = Matrix.RowFromVector([1,2,3])
m9 = Matrix.ColFromVector([1,2,3])
print m8 # [[1.0, 2.0, 3.0]]
print m9 # [[1.0], [2.0], [3.0]]
m8.transpose() == m9 # True
m8.isVector() # True
m9.isVector() # True
m8.asVector() == Vector([1,2,3]) # True
m9.asVector() == Vector([1,2,3]) # True

m10 = Matrix.Diagonal([1,2,3])
print m10 # [[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 3.0]]
m10.isSquare() # True
m10.isDiagonal() # True
m10.getDiagonal() == Vector([1,2,3]) # True

m11 = Matrix([[1,2,3], [2,4,5], [3,5,6]])
print m11 # [[1.0, 2.0, 3.0], [2.0, 4.0, 5.0], [3.0, 5.0, 6.0]]
m11.isSquare() # True
m11.isSymmetric() # True
m11.transpose() == m11 # True
m11.trace() == 11 # True
m11.det() == -1 # True

m5 - m6 == 0 # True
m5 + m1 == m5 # True
m5 + m6 == 2 * m5 # True
m5 / 2 == Matrix([[0.5,1,2], [2,2.5,3]]) # True
m5 * m3 == m5 # True
m8 * m11 == Matrix([[14, 25, 31]]) # True
m5 * m9 == Matrix([[17], [32]]) # True
Vector([1,2,3]) * m11 == Matrix([[14, 25, 31]]) # True
m5 * Vector([1,2,3]) == Matrix([[17], [32]]) # True

List of all attributes

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Vector Static Methods

• Vector.Zero(int) -> Vector
• Vector.FromList(iterable) -> Vector

Vector Properties

• Vector.size -> int
• Vector.values -> list
• Vector.magnitude -> float

Vector Methods

• Vector.isZero() -> bool
• Vector.isNormalized() -> bool
• Vector.asList() -> list
• Vector.dot(other) -> float
• Vector.cross(other) -> Vector
• Vector.round(ndigits=0) -> Vector
• Vector.floor() -> Vector
• Vector.ceil() -> Vector
• Vector.trunc() -> Vector
• Vector.normalize() -> Vector
• Vector.__str__() -> str
• Vector.__repr__() -> str
• Vector.__len__() -> int
• Vector.__iter__() -> iter
• Vector.__getitem__(key) -> float or Vector
• Vector.__setitem__(key, value)
• Vector.__eq__(other) -> bool
• Vector.__ne__(other) -> bool
• Vector.__pos__() -> Vector
• Vector.__neg__() -> Vector
• Vector.__add__(other) -> Vector
• Vector.__radd__(other) -> Vector
• Vector.__sub__(other) -> Vector
• Vector.__mul__(other) -> Vector or float
• Vector.__rmul__(other) -> Vector
• Vector.__div__(other) -> Vector

Matrix Static Methods

• Matrix.Zero(int, int) -> Matrix
• Matrix.Identity(int) -> Matrix
• Matrix.FromListOfRows(iterable) -> Matrix
• Matrix.FromListOfCols(iterable) -> Matrix
• Matrix.RowFromVector(iterable) -> Matrix
• Matrix.ColFromVector(iterable) -> Matrix
• Matrix.Diagonal(iterable) -> Matrix

Matrix Properties

• Matrix.size -> tuple
• Matrix.m -> int
• Matrix.n -> int
• Matrix.rows -> list
• Matrix.cols -> list

Matrix Methods

• Matrix.isZero() -> bool
• Matrix.isIdentity() -> bool
• Matrix.isScalar() -> bool
• Matrix.isVector() -> bool
• Matrix.isSquare() -> bool
• Matrix.isDiagonal() -> bool
• Matrix.isSymmetric() -> bool
• Matrix.asList() -> list
• Matrix.getRow(n) -> Vector
• Matrix.getCol(n) -> Vector
• Matrix.getDiagonal() -> Vector
• Matrix.asScalar() -> float
• Matrix.asVector() -> Vector
• Matrix.transpose() -> Matrix
• Matrix.round(n=0) -> Matrix
• Matrix.floor() -> Matrix
• Matrix.ceil() -> Matrix
• Matrix.trunc() -> Matrix
• Matrix.trace() -> float
• Matrix.det() -> float
• Matrix.eigenvalues() -> list
• Matrix.__str__() -> str
• Matrix.__repr__() -> str
• Matrix.__getitem__(key) -> float
• Matrix.__setitem__(key, value)
• Matrix.__eq__(other) -> bool
• Matrix.__ne__(other) -> bool
• Matrix.__pos__() -> Matrix
• Matrix.__neg__() -> Matrix
• Matrix.__add__(other) -> Matrix
• Matrix.__radd__(other) -> Matrix
• Matrix.__sub__(other) -> Matrix
• Matrix.__mul__(other) -> Matrix
• Matrix.__rmul__(other) -> Matrix
• Matrix.__div__(other) -> Matrix

Changelog

0.2.0 [2017-05-22]

• Add Matrix class
• Add comparison of matrices
• Add all operations with matrices (+, -, *, /)
• Add matrix*vector and vector*matrix
• Add other matrix methods
• Add matrix_tests.py
• Add support of sum function
• Fix some comments
• Fix vector_tests.py
• Known Limitation: Eigenvalues implemented for matrices: diagonal, 2x2, symmetric 3x3

0.1.0 [2017-05-14]

• Add Vector class
• Add comparison of vectors
• Add all operations with vectors (+, -, *, /, .dot, .cross)
• Add other vector methods

Readme last update 2017-05-22