tablepress / libraries / vendor / Matrix / Functions.php

Functions.php in TablePress – Tables in WordPress made easy 2.0.4, at libraries/vendor/Matrix/Functions.php

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1	<?php
2
3	namespace TablePress\Matrix;
4
5	class Functions
6	{
7	/**
8	* Validates an array of matrix, converting an array to a matrix if required.
9	*
10	* @param TablePress\Matrix\|array $matrix TablePress\Matrix or an array to treat as a matrix.
11	* @return TablePress\Matrix The new matrix
12	* @throws Exception If argument isn't a valid matrix or array.
13	*/
14	private static function validateMatrix($matrix)
15	{
16	if (is_array($matrix)) {
17	$matrix = new Matrix($matrix);
18	}
19	if (!$matrix instanceof Matrix) {
20	throw new Exception('Must be TablePress\Matrix or array');
21	}
22
23	return $matrix;
24	}
25
26	/**
27	* Calculate the adjoint of the matrix
28	*
29	* @param TablePress\Matrix $matrix The matrix whose adjoint we wish to calculate
30	* @return TablePress\Matrix
31	*
32	* @throws Exception
33	*/
34	private static function getAdjoint(TablePress\Matrix $matrix)
35	{
36	return self::transpose(
37	self::getCofactors($matrix)
38	);
39	}
40
41	/**
42	* Return the adjoint of this matrix
43	* The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.
44	* The adjugate has sometimes been called the "adjoint", but today the "adjoint" of a matrix normally refers
45	* to its corresponding adjoint operator, which is its conjugate transpose.
46	*
47	* @param TablePress\Matrix\|array $matrix The matrix whose adjoint we wish to calculate
48	* @return TablePress\Matrix
49	* @throws Exception
50	**/
51	public static function adjoint($matrix)
52	{
53	$matrix = self::validateMatrix($matrix);
54
55	if (!$matrix->isSquare()) {
56	throw new Exception('Adjoint can only be calculated for a square matrix');
57	}
58
59	return self::getAdjoint($matrix);
60	}
61
62	/**
63	* Calculate the cofactors of the matrix
64	*
65	* @param TablePress\Matrix $matrix The matrix whose cofactors we wish to calculate
66	* @return TablePress\Matrix
67	*
68	* @throws Exception
69	*/
70	private static function getCofactors(TablePress\Matrix $matrix)
71	{
72	$cofactors = self::getMinors($matrix);
73	$dimensions = $matrix->rows;
74
75	$cof = 1;
76	for ($i = 0; $i < $dimensions; ++$i) {
77	$cofs = $cof;
78	for ($j = 0; $j < $dimensions; ++$j) {
79	$cofactors[$i][$j] *= $cofs;
80	$cofs = -$cofs;
81	}
82	$cof = -$cof;
83	}
84
85	return new Matrix($cofactors);
86	}
87
88	/**
89	* Return the cofactors of this matrix
90	*
91	* @param TablePress\Matrix\|array $matrix The matrix whose cofactors we wish to calculate
92	* @return TablePress\Matrix
93	*
94	* @throws Exception
95	*/
96	public static function cofactors($matrix)
97	{
98	$matrix = self::validateMatrix($matrix);
99
100	if (!$matrix->isSquare()) {
101	throw new Exception('Cofactors can only be calculated for a square matrix');
102	}
103
104	return self::getCofactors($matrix);
105	}
106
107	/**
108	* @param TablePress\Matrix $matrix
109	* @param int $row
110	* @param int $column
111	* @return float
112	* @throws Exception
113	*/
114	private static function getDeterminantSegment(TablePress\Matrix $matrix, $row, $column)
115	{
116	$tmpMatrix = $matrix->toArray();
117	unset($tmpMatrix[$row]);
118	array_walk(
119	$tmpMatrix,
120	function (&$row) use ($column) {
121	unset($row[$column]);
122	}
123	);
124
125	return self::getDeterminant(new Matrix($tmpMatrix));
126	}
127
128	/**
129	* Calculate the determinant of the matrix
130	*
131	* @param TablePress\Matrix $matrix The matrix whose determinant we wish to calculate
132	* @return float
133	*
134	* @throws Exception
135	*/
136	private static function getDeterminant(TablePress\Matrix $matrix)
137	{
138	$dimensions = $matrix->rows;
139	$determinant = 0;
140
141	switch ($dimensions) {
142	case 1:
143	$determinant = $matrix->getValue(1, 1);
144	break;
145	case 2:
146	$determinant = $matrix->getValue(1, 1) * $matrix->getValue(2, 2) -
147	$matrix->getValue(1, 2) * $matrix->getValue(2, 1);
148	break;
149	default:
150	for ($i = 1; $i <= $dimensions; ++$i) {
151	$det = $matrix->getValue(1, $i) * self::getDeterminantSegment($matrix, 0, $i - 1);
152	if (($i % 2) == 0) {
153	$determinant -= $det;
154	} else {
155	$determinant += $det;
156	}
157	}
158	break;
159	}
160
161	return $determinant;
162	}
163
164	/**
165	* Return the determinant of this matrix
166	*
167	* @param TablePress\Matrix\|array $matrix The matrix whose determinant we wish to calculate
168	* @return float
169	* @throws Exception
170	**/
171	public static function determinant($matrix)
172	{
173	$matrix = self::validateMatrix($matrix);
174
175	if (!$matrix->isSquare()) {
176	throw new Exception('Determinant can only be calculated for a square matrix');
177	}
178
179	return self::getDeterminant($matrix);
180	}
181
182	/**
183	* Return the diagonal of this matrix
184	*
185	* @param TablePress\Matrix\|array $matrix The matrix whose diagonal we wish to calculate
186	* @return TablePress\Matrix
187	* @throws Exception
188	**/
189	public static function diagonal($matrix)
190	{
191	$matrix = self::validateMatrix($matrix);
192
193	if (!$matrix->isSquare()) {
194	throw new Exception('Diagonal can only be extracted from a square matrix');
195	}
196
197	$dimensions = $matrix->rows;
198	$grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
199	->toArray();
200
201	for ($i = 0; $i < $dimensions; ++$i) {
202	$grid[$i][$i] = $matrix->getValue($i + 1, $i + 1);
203	}
204
205	return new Matrix($grid);
206	}
207
208	/**
209	* Return the antidiagonal of this matrix
210	*
211	* @param TablePress\Matrix\|array $matrix The matrix whose antidiagonal we wish to calculate
212	* @return TablePress\Matrix
213	* @throws Exception
214	**/
215	public static function antidiagonal($matrix)
216	{
217	$matrix = self::validateMatrix($matrix);
218
219	if (!$matrix->isSquare()) {
220	throw new Exception('Anti-Diagonal can only be extracted from a square matrix');
221	}
222
223	$dimensions = $matrix->rows;
224	$grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
225	->toArray();
226
227	for ($i = 0; $i < $dimensions; ++$i) {
228	$grid[$i][$dimensions - $i - 1] = $matrix->getValue($i + 1, $dimensions - $i);
229	}
230
231	return new Matrix($grid);
232	}
233
234	/**
235	* Return the identity matrix
236	* The identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix
237	* with ones on the main diagonal and zeros elsewhere
238	*
239	* @param TablePress\Matrix\|array $matrix The matrix whose identity we wish to calculate
240	* @return TablePress\Matrix
241	* @throws Exception
242	**/
243	public static function identity($matrix)
244	{
245	$matrix = self::validateMatrix($matrix);
246
247	if (!$matrix->isSquare()) {
248	throw new Exception('Identity can only be created for a square matrix');
249	}
250
251	$dimensions = $matrix->rows;
252
253	return Builder::createIdentityMatrix($dimensions);
254	}
255
256	/**
257	* Return the inverse of this matrix
258	*
259	* @param TablePress\Matrix\|array $matrix The matrix whose inverse we wish to calculate
260	* @return TablePress\Matrix
261	* @throws Exception
262	**/
263	public static function inverse($matrix, string $type = 'inverse')
264	{
265	$matrix = self::validateMatrix($matrix);
266
267	if (!$matrix->isSquare()) {
268	throw new Exception(ucfirst($type) . ' can only be calculated for a square matrix');
269	}
270
271	$determinant = self::getDeterminant($matrix);
272	if ($determinant == 0.0) {
273	throw new Div0Exception(ucfirst($type) . ' can only be calculated for a matrix with a non-zero determinant');
274	}
275
276	if ($matrix->rows == 1) {
277	return new Matrix([[1 / $matrix->getValue(1, 1)]]);
278	}
279
280	return self::getAdjoint($matrix)
281	->multiply(1 / $determinant);
282	}
283
284	/**
285	* Calculate the minors of the matrix
286	*
287	* @param TablePress\Matrix $matrix The matrix whose minors we wish to calculate
288	* @return array[]
289	*
290	* @throws Exception
291	*/
292	protected static function getMinors(TablePress\Matrix $matrix)
293	{
294	$minors = $matrix->toArray();
295	$dimensions = $matrix->rows;
296	if ($dimensions == 1) {
297	return $minors;
298	}
299
300	for ($i = 0; $i < $dimensions; ++$i) {
301	for ($j = 0; $j < $dimensions; ++$j) {
302	$minors[$i][$j] = self::getDeterminantSegment($matrix, $i, $j);
303	}
304	}
305
306	return $minors;
307	}
308
309	/**
310	* Return the minors of the matrix
311	* The minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or
312	* more of its rows or columns.
313	* Minors obtained by removing just one row and one column from square matrices (first minors) are required for
314	* calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of
315	* square matrices.
316	*
317	* @param TablePress\Matrix\|array $matrix The matrix whose minors we wish to calculate
318	* @return TablePress\Matrix
319	* @throws Exception
320	**/
321	public static function minors($matrix)
322	{
323	$matrix = self::validateMatrix($matrix);
324
325	if (!$matrix->isSquare()) {
326	throw new Exception('Minors can only be calculated for a square matrix');
327	}
328
329	return new Matrix(self::getMinors($matrix));
330	}
331
332	/**
333	* Return the trace of this matrix
334	* The trace is defined as the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right)
335	* of the matrix
336	*
337	* @param TablePress\Matrix\|array $matrix The matrix whose trace we wish to calculate
338	* @return float
339	* @throws Exception
340	**/
341	public static function trace($matrix)
342	{
343	$matrix = self::validateMatrix($matrix);
344
345	if (!$matrix->isSquare()) {
346	throw new Exception('Trace can only be extracted from a square matrix');
347	}
348
349	$dimensions = $matrix->rows;
350	$result = 0;
351	for ($i = 1; $i <= $dimensions; ++$i) {
352	$result += $matrix->getValue($i, $i);
353	}
354
355	return $result;
356	}
357
358	/**
359	* Return the transpose of this matrix
360	*
361	* @param TablePress\Matrix\|\a $matrix The matrix whose transpose we wish to calculate
362	* @return TablePress\Matrix
363	**/
364	public static function transpose($matrix)
365	{
366	$matrix = self::validateMatrix($matrix);
367
368	$array = array_values(array_merge([null], $matrix->toArray()));
369	$grid = call_user_func_array(
370	'array_map',
371	$array
372	);
373
374	return new Matrix($grid);
375	}
376	}
377