ulloaluis / linear-algebra

implemented vector and matrix classes with reST-formatted docstrings in Python 3+

linear-algebra-ulloa

Implemented vector and matrix classes with reST-formatted docstrings in Python 3+

General Layout

The Vector class imitates the m x 1 vector from linear algebra and contains many useful functions for dealing and interacting with Vectors.

Getting values directly from the vector should be done using the get(index) function or [] operator since the comp vector location in memory may change with functions like mag() or zero() (those which change current vector comp).

class Vector

__init__(comp)          - takes in a list of components or a valid mx1 Matrix

resize(length)          - while preserving current elements or filling with 0's, changes current vector length

set(comp, index=-1)     - sets entire list at once or one specific index/value

get(index)              - returns item at specified index of vector

zero()                  - turns the current vector into a zero vector and returns it

mag()                   - returns the magnitude of current vector

normalize(change=False) - returns normalized current vector, if change=True, internal vector is updated

same_normalized(other)  - returns True/False depending on equality of the two vectors once normalized

dot(other)              - returns the dot product of th two vectors

cross(other)            - returns the cross product of u x v (u is current vector, v is other)

perp(other)             - returns True/False if current and other are/aren't perpendicular

parallel(other)         - returns True/False if current and other are/aren't parallel

indep(other)          - returns True/False if curr vector and other vector(s) are linearly independent

operator +              - returns sum of two vectors, component wise addition

operator -              - returns difference of two vectors, component wise subtraction

operator *              - alternate for dot product, or can use for vector scaling

operator **             - returns original vector with its components raised to power

operator ==             - checks to see if lists are equal

to string method        - format: "<elem1, elem2, ...>"

len() method            - can use len() to get vector length

get and set []          - user can get and set values in vector with index based operations []


comp = vector composition, list of components

length = number of components in vector

rows = same as length, used with cols for backwards compatibility with Matrix

cols = 1 (num of columns)

The Matrix class imitates the matrix concept from linear algebra and allows for different ways of dealing and interacting with matrices and vectors.

Getting values directly from the vector should be done using the get(row, col) function or [], [][] operator since the matrix comp location in memory may change with functions that change the underlying data type.

class Matrix

__init__(comp)          - takes in a list of components or a valid Vector

resize(rows, cols)      - while preserving current elements or filling with 0's, changes current vector length

set(comp, index=None)   - sets entire list at once or one specific index/value (tuple or array as (row, col))

get(row=None,col=None)  - can get a specific row, column, or entire matrix composition (no args for matrix)

zero()                  - replaces values in current matrix with all zeroes and returns it

det()                   - takes the determinant of the current NxN matrix

transpose()             - transposes the current mxn matrix to an nxm matrix (1st row becomes 1st col, etc.)

row_echelon()           - returns the current matrix in row echelon form

row_reduce()            - returns the current matrix to reduced row echelon form

identity(n)             - static method that returns the nxn identity matrix

combine(first, second)  - static method that combines two matrices by concatenation

inverse()               - returns the inverse of current nxn matrix, or None if singular

operator +              - returns sum of two matrices, component wise addition

operator -              - returns difference of two matrices, component wise subtraction

operator *              - matrix multiplication, matrix-vector product, scalar multiplication

operator **             - returns original matrix with its components raised to power

operator ==             - checks to see if internal lists are equal

to string method        - format: "[row1\n row2\n row3\n ...]" and floats are shown as fractions

len() method            - returns tuple formatted as (row, col)

get and set [][]        - can get rows and specific values with [] or [][], and set specific values with [][]


comp = matrix composition, list of lists where each list is a row

rows = number of rows in matrix

cols = number of columns in matrix

Tests

There is a file for writing tests. At the moment, it is only a series of assertions. In the future, I will update the testing file to use a more standardized version/library for testing.

Docstrings/Documentation

There is thorough documentation throughout the library. Python library contains a help() function that could be used to view the docstrings for a specific class/method.

Class: help(classname)

Method: help(classname.methodname)

For example, help(Vector.resize) shows you ...

resize(self, length)

    Re-sizes the vector to the specified length. If length is greater than

    current size, the new components are initialized with 0, otherwise if length

    is less than current size, the last few components are lost.

    :param length: new length of vector

    :type length: int

    :return: current vector, now resized

    :rtype: Vector

and vice versa. help(Vector) and help(Matrix) return major class overviews.

Using library

pip:

pip install linear-algebra-ulloa

or

pip3 install linear-algebra-ulloa

Use

from linear_lib.linear import *

to be able to create and utilize vector and matrix classes without the linear.Vector or linear.Matrix prefix.

Potential additions to library in future

Vector Class

• Method for checking if current vector and other vector are orthogonal

• Support for plotting/graphing a certain amount of 2D maybe 3D vectors using matplotlib or a similar library

• Cross products

Matrix Class

• Determinant

• Row Reducing Matrices

• Finding inverse of Matrices

• Transposing matrices

• Standalone function for fitting a straight line with least squares approximation

• General least squares method as part of matrices class

Additional

• index access with [] [][] operator

• identify whether a set of vectors are linearly independent

• identify whether two vectors are parallel

• static method for generating arbitrarily sized identity matrix

• static method for concatenating two matrices

• floats are shown as proper fractions when printed

• equality tests account for floating point error