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1	PHPMatrix
2	==========
3
4	---
5
6	PHP Class for handling Matrices
7
8	[](http://travis-ci.org/MarkBaker/PHPMatrix![Build Status](https://travis-ci.org/MarkBaker/PHPMatrix.png?branch=1.2)](http://travis-ci.org/MarkBaker/PHPMatrix](http://travis-ci.org/MarkBaker/PHPMatrix)
9
10	[](https://xkcd.com/184/![Matrix Transform](https://imgs.xkcd.com/comics/matrix_transform.png)](https://xkcd.com/184/](https://xkcd.com/184/)
11
12	Matrix Transform
13
14	---
15
16	This library currently provides the following operations:
17
18	- addition
19	- direct sum
20	- subtraction
21	- multiplication
22	- division (using [A].[B]<sup>-1</sup>)
23	- division by
24	- division into
25
26	together with functions for
27
28	- adjoint
29	- antidiagonal
30	- cofactors
31	- determinant
32	- diagonal
33	- identity
34	- inverse
35	- minors
36	- trace
37	- transpose
38	- solve
39
40	Given Matrices A and B, calculate X for A.X = B
41
42	and classes for
43
44	- Decomposition
45	- LU Decomposition with partial row pivoting,
46
47	such that [P].[A] = [L].[U] and [A] = [P]<sup>\|</sup>.[L].[U]
48	- QR Decomposition
49
50	such that [A] = [Q].[R]
51
52	## TO DO
53
54	- power() function
55	- Decomposition
56	- Cholesky Decomposition
57	- EigenValue Decomposition
58	- EigenValues
59	- EigenVectors
60
61	---
62
63	# Usage
64
65	To create a new Matrix object, provide an array as the constructor argument
66
67	```php
68	$grid = [
69	[16, 3, 2, 13],
70	[ 5, 10, 11, 8],
71	[ 9, 6, 7, 12],
72	[ 4, 15, 14, 1],
73	];
74
75	$matrix = new Matrix\Matrix($grid);
76	```
77	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.
78	```php
79	$matrix = Matrix\Builder::createFilledMatrix(1, 5, 3);
80	```
81	Will create a matrix of 5 rows and 3 columns, filled with a `1` in every cell; while
82	```php
83	$matrix = Matrix\Builder::createIdentityMatrix(3);
84	```
85	will create a 3x3 identity matrix.
86
87
88	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).
89
90	## Performing Mathematical Operations
91
92	To perform mathematical operations with Matrices, you can call the appropriate method against a matrix value, passing other values as arguments
93
94	```php
95	$matrix1 = new Matrix\Matrix([
96	[2, 7, 6],
97	[9, 5, 1],
98	[4, 3, 8],
99	]);
100	$matrix2 = new Matrix\Matrix([
101	[1, 2, 3],
102	[4, 5, 6],
103	[7, 8, 9],
104	]);
105
106	var_dump($matrix1->multiply($matrix2)->toArray());
107	```
108	or pass all values to the appropriate function
109	```php
110	$matrix1 = new Matrix\Matrix([
111	[2, 7, 6],
112	[9, 5, 1],
113	[4, 3, 8],
114	]);
115	$matrix2 = new Matrix\Matrix([
116	[1, 2, 3],
117	[4, 5, 6],
118	[7, 8, 9],
119	]);
120
121	var_dump(Matrix\multiply($matrix1, $matrix2)->toArray());
122	```
123	You can pass in the arguments as Matrix objects, or as arrays.
124
125	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.
126
127	## Using functions
128
129	When calling any of the available functions for a matrix value, you can either call the relevant method for the Matrix object
130	```php
131	$grid = [
132	[16, 3, 2, 13],
133	[ 5, 10, 11, 8],
134	[ 9, 6, 7, 12],
135	[ 4, 15, 14, 1],
136	];
137
138	$matrix = new Matrix\Matrix($grid);
139
140	echo $matrix->trace();
141	```
142	or you can call the function as you would in procedural code, passing the Matrix object as an argument
143	```php
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	$matrix = new Matrix\Matrix($grid);
152	echo Matrix\trace($matrix);
153	```
154	When called procedurally using the function, you can pass in the argument as a Matrix object, or as an array.
155	```php
156	$grid = [
157	[16, 3, 2, 13],
158	[ 5, 10, 11, 8],
159	[ 9, 6, 7, 12],
160	[ 4, 15, 14, 1],
161	];
162
163	echo Matrix\trace($grid);
164	```
165	As an alternative, it is also possible to call the method directly from the `Functions` class.
166	```php
167	$grid = [
168	[16, 3, 2, 13],
169	[ 5, 10, 11, 8],
170	[ 9, 6, 7, 12],
171	[ 4, 15, 14, 1],
172	];
173
174	$matrix = new Matrix\Matrix($grid);
175	echo Matrix\Functions::trace($matrix);
176	```
177	Used this way, methods must be called statically, and the argument must be the Matrix object, and cannot be an array.
178
179	## Decomposition
180
181	The library also provides classes for matrix decomposition. You can access these using
182	```php
183	$grid = [
184	[1, 2],
185	[3, 4],
186	];
187
188	$matrix = new Matrix\Matrix($grid);
189
190	$decomposition = new Matrix\Decomposition\QR($matrix);
191	$Q = $decomposition->getQ();
192	$R = $decomposition->getR();
193	```
194
195	or alternatively us the `Decomposition` factory, identifying which form of decomposition you want to use
196	```php
197	$grid = [
198	[1, 2],
199	[3, 4],
200	];
201
202	$matrix = new Matrix\Matrix($grid);
203
204	$decomposition = Matrix\Decomposition\Decomposition::decomposition(Matrix\Decomposition\Decomposition::QR, $matrix);
205	$Q = $decomposition->getQ();
206	$R = $decomposition->getR();
207	```
208