visualizer / vendor / markbaker / matrix / README.md

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1	PHPMatrix
2	==========
3
4	---
5
6	PHP Class for handling Matrices
7
8	Master: [](http://travis-ci.org/MarkBaker/PHPMatrix![Build Status](https://travis-ci.org/MarkBaker/PHPMatrix.png?branch=master)](http://travis-ci.org/MarkBaker/PHPMatrix](http://travis-ci.org/MarkBaker/PHPMatrix)
9
10	Develop: [](http://travis-ci.org/MarkBaker/PHPMatrix![Build Status](https://travis-ci.org/MarkBaker/PHPMatrix.png?branch=develop)](http://travis-ci.org/MarkBaker/PHPMatrix](http://travis-ci.org/MarkBaker/PHPMatrix)
11
12	[](https://xkcd.com/184/![Matrix Transform](https://imgs.xkcd.com/comics/matrix_transform.png)](https://xkcd.com/184/](https://xkcd.com/184/)
13
14	Matrix Transform
15
16	---
17
18	This library currently provides the following operations:
19
20	- addition
21	- direct sum
22	- subtraction
23	- multiplication
24	- division (using [A].[B]<sup>-1</sup>)
25	- division by
26	- division into
27
28	together with functions for
29
30	- adjoint
31	- antidiagonal
32	- cofactors
33	- determinant
34	- diagonal
35	- identity
36	- inverse
37	- minors
38	- trace
39	- transpose
40
41
42	## TO DO
43
44	- power()
45	- EigenValues
46	- EigenVectors
47	- Decomposition
48
49	---
50
51	# Usage
52
53	To create a new Matrix object, provide an array as the constructor argument
54
55	```
56	$grid = [
57	[16, 3, 2, 13],
58	[ 5, 10, 11, 8],
59	[ 9, 6, 7, 12],
60	[ 4, 15, 14, 1],
61	];
62
63	$matrix = new Matrix\Matrix($grid);
64	```
65	The `Builder` class provides helper methods for creating specific matrices, specifically an identity matrix of a specified size; or a matrix of a specified dimensions, with every cell containing a set value.
66	```
67	$matrix = new Matrix\Builder::createFilledMatrix(1, 5, 3);
68	```
69	Will create a matrix of 5 rows and 3 columns, filled with a `1` in every cell; while
70	```
71	$matrix = new Matrix\Builder::createIdentityMatrix(3);
72	```
73	will create a 3x3 identity matrix.
74
75
76	Matrix objects are immutable: whenever you call a method or pass a grid to a function that returns a matrix value, a new Matrix object will be returned, and the original will remain unchanged. This also allows you to chain multiple methods as you would for a fluent interface (as long as they are methods that will return a Matrix result).
77
78	## Performing Mathematical Operations
79
80	To perform mathematical operations with Matrices, you can call the appropriate method against a matrix value, passing other values as arguments
81
82	```
83	$matrix1 = new Matrix([
84	[2, 7, 6],
85	[9, 5, 1],
86	[4, 3, 8],
87	]);
88	$matrix2 = new Matrix([
89	[1, 2, 3],
90	[4, 5, 6],
91	[7, 8, 9],
92	]);
93
94	echo $matrix1->multiply($matrix2);
95	```
96	or pass all values to the appropriate function
97	```
98	$matrix1 = new Matrix([
99	[2, 7, 6],
100	[9, 5, 1],
101	[4, 3, 8],
102	]);
103	$matrix2 = new Matrix([
104	[1, 2, 3],
105	[4, 5, 6],
106	[7, 8, 9],
107	]);
108
109	echo Matrix\multiply($matrix1, $matrix2);
110	```
111	You can pass in the arguments as Matrix objects, or as arrays.
112
113	If you want to perform the same operation against multiple values (e.g. to add three or more matrices), then you can pass multiple arguments to any of the operations.
114
115	## Using functions
116
117	When calling any of the available functions for a matrix value, you can either call the relevant method for the Matrix object
118	```
119	$grid = [
120	[16, 3, 2, 13],
121	[ 5, 10, 11, 8],
122	[ 9, 6, 7, 12],
123	[ 4, 15, 14, 1],
124	];
125
126	$matrix = new Matrix\Matrix($grid);
127
128	echo $matrix->trace();
129	```
130	or you can call the function as you would in procedural code, passing the Matrix object as an argument
131	```
132	$grid = [
133	[16, 3, 2, 13],
134	[ 5, 10, 11, 8],
135	[ 9, 6, 7, 12],
136	[ 4, 15, 14, 1],
137	];
138
139	$matrix = new Matrix\Matrix($grid);
140	echo Matrix\trace($matrix);
141	```
142	When called procedurally using the function, you can pass in the argument as a Matrix object, or as an array.
143	```
144	$grid = [
145	[16, 3, 2, 13],
146	[ 5, 10, 11, 8],
147	[ 9, 6, 7, 12],
148	[ 4, 15, 14, 1],
149	];
150
151	echo Matrix\trace($grid);
152	```
153	As an alternative, it is also possible to call the method directly from the `Functions` class.
154	```
155	$grid = [
156	[16, 3, 2, 13],
157	[ 5, 10, 11, 8],
158	[ 9, 6, 7, 12],
159	[ 4, 15, 14, 1],
160	];
161
162	$matrix = new Matrix\Matrix($grid);
163	echo Matrix\Functions::trace($matrix);
164	```
165	Used this way, methods must be called statically, and the argument must be the Matrix object, and cannot be an array.
166