1
|
|
|
<?php |
2
|
|
|
|
3
|
|
|
declare(strict_types=1); |
4
|
|
|
|
5
|
|
|
namespace Phpml\Math; |
6
|
|
|
|
7
|
|
|
use Phpml\Exception\InvalidArgumentException; |
8
|
|
|
use Phpml\Exception\MatrixException; |
9
|
|
|
|
10
|
|
|
class Matrix |
11
|
|
|
{ |
12
|
|
|
/** |
13
|
|
|
* @var array |
14
|
|
|
*/ |
15
|
|
|
private $matrix; |
16
|
|
|
|
17
|
|
|
/** |
18
|
|
|
* @var int |
19
|
|
|
*/ |
20
|
|
|
private $rows; |
21
|
|
|
|
22
|
|
|
/** |
23
|
|
|
* @var int |
24
|
|
|
*/ |
25
|
|
|
private $columns; |
26
|
|
|
|
27
|
|
|
/** |
28
|
|
|
* @var float |
29
|
|
|
*/ |
30
|
|
|
private $determinant; |
31
|
|
|
|
32
|
|
|
/** |
33
|
|
|
* @param array $matrix |
34
|
|
|
* @param bool $validate |
35
|
|
|
* |
36
|
|
|
* @throws InvalidArgumentException |
37
|
|
|
*/ |
38
|
|
|
public function __construct(array $matrix, bool $validate = true) |
39
|
|
|
{ |
40
|
|
|
// When a row vector is given |
41
|
|
|
if (!is_array($matrix[0])) { |
42
|
|
|
$this->rows = 1; |
43
|
|
|
$this->columns = count($matrix); |
44
|
|
|
$matrix = [$matrix]; |
45
|
|
|
} else { |
46
|
|
|
$this->rows = count($matrix); |
47
|
|
|
$this->columns = count($matrix[0]); |
48
|
|
|
} |
49
|
|
|
|
50
|
|
|
if ($validate) { |
51
|
|
|
for ($i = 0; $i < $this->rows; ++$i) { |
52
|
|
|
if (count($matrix[$i]) !== $this->columns) { |
53
|
|
|
throw InvalidArgumentException::matrixDimensionsDidNotMatch(); |
54
|
|
|
} |
55
|
|
|
} |
56
|
|
|
} |
57
|
|
|
|
58
|
|
|
$this->matrix = $matrix; |
59
|
|
|
} |
60
|
|
|
|
61
|
|
|
/** |
62
|
|
|
* @param array $array |
63
|
|
|
* |
64
|
|
|
* @return Matrix |
65
|
|
|
*/ |
66
|
|
|
public static function fromFlatArray(array $array) |
67
|
|
|
{ |
68
|
|
|
$matrix = []; |
69
|
|
|
foreach ($array as $value) { |
70
|
|
|
$matrix[] = [$value]; |
71
|
|
|
} |
72
|
|
|
|
73
|
|
|
return new self($matrix); |
74
|
|
|
} |
75
|
|
|
|
76
|
|
|
/** |
77
|
|
|
* @return array |
78
|
|
|
*/ |
79
|
|
|
public function toArray() |
80
|
|
|
{ |
81
|
|
|
return $this->matrix; |
82
|
|
|
} |
83
|
|
|
|
84
|
|
|
/** |
85
|
|
|
* @return float |
86
|
|
|
*/ |
87
|
|
|
public function toScalar() |
88
|
|
|
{ |
89
|
|
|
return $this->matrix[0][0]; |
90
|
|
|
} |
91
|
|
|
|
92
|
|
|
/** |
93
|
|
|
* @return int |
94
|
|
|
*/ |
95
|
|
|
public function getRows() |
96
|
|
|
{ |
97
|
|
|
return $this->rows; |
98
|
|
|
} |
99
|
|
|
|
100
|
|
|
/** |
101
|
|
|
* @return int |
102
|
|
|
*/ |
103
|
|
|
public function getColumns() |
104
|
|
|
{ |
105
|
|
|
return $this->columns; |
106
|
|
|
} |
107
|
|
|
|
108
|
|
|
/** |
109
|
|
|
* @param $column |
110
|
|
|
* |
111
|
|
|
* @return array |
112
|
|
|
* |
113
|
|
|
* @throws MatrixException |
114
|
|
|
*/ |
115
|
|
|
public function getColumnValues($column) |
116
|
|
|
{ |
117
|
|
|
if ($column >= $this->columns) { |
118
|
|
|
throw MatrixException::columnOutOfRange(); |
119
|
|
|
} |
120
|
|
|
|
121
|
|
|
return array_column($this->matrix, $column); |
122
|
|
|
} |
123
|
|
|
|
124
|
|
|
|
125
|
|
|
/** |
126
|
|
|
* @return float|int |
127
|
|
|
* |
128
|
|
|
* @throws MatrixException |
129
|
|
|
*/ |
130
|
|
|
public function getDeterminant() |
131
|
|
|
{ |
132
|
|
|
if ($this->determinant) { |
133
|
|
|
return $this->determinant; |
134
|
|
|
} |
135
|
|
|
|
136
|
|
|
if (!$this->isSquare()) { |
137
|
|
|
throw MatrixException::notSquareMatrix(); |
138
|
|
|
} |
139
|
|
|
|
140
|
|
|
return $this->determinant = $this->calculateDeterminant(); |
|
|
|
|
141
|
|
|
} |
142
|
|
|
|
143
|
|
|
/** |
144
|
|
|
* @return float|int |
145
|
|
|
* |
146
|
|
|
* @throws MatrixException |
147
|
|
|
*/ |
148
|
|
|
private function calculateDeterminant() |
149
|
|
|
{ |
150
|
|
|
$determinant = 0; |
151
|
|
|
if ($this->rows == 1 && $this->columns == 1) { |
152
|
|
|
$determinant = $this->matrix[0][0]; |
153
|
|
|
} elseif ($this->rows == 2 && $this->columns == 2) { |
154
|
|
|
$determinant = |
155
|
|
|
$this->matrix[0][0] * $this->matrix[1][1] - |
156
|
|
|
$this->matrix[0][1] * $this->matrix[1][0]; |
157
|
|
|
} else { |
158
|
|
|
for ($j = 0; $j < $this->columns; ++$j) { |
159
|
|
|
$subMatrix = $this->crossOut(0, $j); |
160
|
|
|
$minor = $this->matrix[0][$j] * $subMatrix->getDeterminant(); |
161
|
|
|
$determinant += fmod((float) $j, 2.0) == 0 ? $minor : -$minor; |
162
|
|
|
} |
163
|
|
|
} |
164
|
|
|
|
165
|
|
|
return $determinant; |
166
|
|
|
} |
167
|
|
|
|
168
|
|
|
/** |
169
|
|
|
* @return bool |
170
|
|
|
*/ |
171
|
|
|
public function isSquare() |
172
|
|
|
{ |
173
|
|
|
return $this->columns === $this->rows; |
174
|
|
|
} |
175
|
|
|
|
176
|
|
|
/** |
177
|
|
|
* @return Matrix |
178
|
|
|
*/ |
179
|
|
|
public function transpose() |
180
|
|
|
{ |
181
|
|
|
if ($this->rows == 1) { |
182
|
|
|
$matrix = array_map(function ($el) { |
183
|
|
|
return [$el]; |
184
|
|
|
}, $this->matrix[0]); |
185
|
|
|
} else { |
186
|
|
|
$matrix = array_map(null, ...$this->matrix); |
187
|
|
|
} |
188
|
|
|
|
189
|
|
|
return new self($matrix, false); |
190
|
|
|
} |
191
|
|
|
|
192
|
|
|
/** |
193
|
|
|
* @param Matrix $matrix |
194
|
|
|
* |
195
|
|
|
* @return Matrix |
196
|
|
|
* |
197
|
|
|
* @throws InvalidArgumentException |
198
|
|
|
*/ |
199
|
|
|
public function multiply(Matrix $matrix) |
200
|
|
|
{ |
201
|
|
|
if ($this->columns != $matrix->getRows()) { |
202
|
|
|
throw InvalidArgumentException::inconsistentMatrixSupplied(); |
203
|
|
|
} |
204
|
|
|
|
205
|
|
|
$product = []; |
206
|
|
|
$multiplier = $matrix->toArray(); |
207
|
|
|
for ($i = 0; $i < $this->rows; ++$i) { |
208
|
|
|
$columns = $matrix->getColumns(); |
209
|
|
|
for ($j = 0; $j < $columns; ++$j) { |
210
|
|
|
$product[$i][$j] = 0; |
211
|
|
|
for ($k = 0; $k < $this->columns; ++$k) { |
212
|
|
|
$product[$i][$j] += $this->matrix[$i][$k] * $multiplier[$k][$j]; |
213
|
|
|
} |
214
|
|
|
} |
215
|
|
|
} |
216
|
|
|
|
217
|
|
|
return new self($product, false); |
218
|
|
|
} |
219
|
|
|
|
220
|
|
|
/** |
221
|
|
|
* @param $value |
222
|
|
|
* |
223
|
|
|
* @return Matrix |
224
|
|
|
*/ |
225
|
|
|
public function divideByScalar($value) |
|
|
|
|
226
|
|
|
{ |
227
|
|
|
$newMatrix = []; |
228
|
|
|
for ($i = 0; $i < $this->rows; ++$i) { |
229
|
|
|
for ($j = 0; $j < $this->columns; ++$j) { |
230
|
|
|
$newMatrix[$i][$j] = $this->matrix[$i][$j] / $value; |
231
|
|
|
} |
232
|
|
|
} |
233
|
|
|
|
234
|
|
|
return new self($newMatrix, false); |
235
|
|
|
} |
236
|
|
|
|
237
|
|
|
/** |
238
|
|
|
* @param $value |
239
|
|
|
* |
240
|
|
|
* @return Matrix |
241
|
|
|
*/ |
242
|
|
|
public function multiplyByScalar($value) |
|
|
|
|
243
|
|
|
{ |
244
|
|
|
$newMatrix = []; |
245
|
|
|
for ($i = 0; $i < $this->rows; ++$i) { |
246
|
|
|
for ($j = 0; $j < $this->columns; ++$j) { |
247
|
|
|
$newMatrix[$i][$j] = $this->matrix[$i][$j] * $value; |
248
|
|
|
} |
249
|
|
|
} |
250
|
|
|
|
251
|
|
|
return new self($newMatrix, false); |
252
|
|
|
} |
253
|
|
|
|
254
|
|
|
/** |
255
|
|
|
* Element-wise addition of the matrix with another one |
256
|
|
|
* |
257
|
|
|
* @param Matrix $other |
258
|
|
|
*/ |
259
|
|
|
public function add(Matrix $other) |
260
|
|
|
{ |
261
|
|
|
return $this->_add($other); |
262
|
|
|
} |
263
|
|
|
|
264
|
|
|
/** |
265
|
|
|
* Element-wise subtracting of another matrix from this one |
266
|
|
|
* |
267
|
|
|
* @param Matrix $other |
268
|
|
|
*/ |
269
|
|
|
public function subtract(Matrix $other) |
270
|
|
|
{ |
271
|
|
|
return $this->_add($other, -1); |
272
|
|
|
} |
273
|
|
|
|
274
|
|
|
/** |
275
|
|
|
* Element-wise addition or substraction depending on the given sign parameter |
276
|
|
|
* |
277
|
|
|
* @param Matrix $other |
278
|
|
|
* @param type $sign |
279
|
|
|
*/ |
280
|
|
|
protected function _add(Matrix $other, $sign = 1) |
281
|
|
|
{ |
282
|
|
|
$a1 = $this->toArray(); |
283
|
|
|
$a2 = $other->toArray(); |
284
|
|
|
|
285
|
|
|
$newMatrix = []; |
286
|
|
|
for ($i=0; $i < $this->rows; $i++) { |
287
|
|
|
for ($k=0; $k < $this->columns; $k++) { |
288
|
|
|
$newMatrix[$i][$k] = $a1[$i][$k] + $sign * $a2[$i][$k]; |
289
|
|
|
} |
290
|
|
|
} |
291
|
|
|
|
292
|
|
|
return new Matrix($newMatrix, false); |
293
|
|
|
} |
294
|
|
|
|
295
|
|
|
/** |
296
|
|
|
* @return Matrix |
297
|
|
|
* |
298
|
|
|
* @throws MatrixException |
299
|
|
|
*/ |
300
|
|
|
public function inverse() |
301
|
|
|
{ |
302
|
|
|
if (!$this->isSquare()) { |
303
|
|
|
throw MatrixException::notSquareMatrix(); |
304
|
|
|
} |
305
|
|
|
|
306
|
|
|
if ($this->isSingular()) { |
307
|
|
|
throw MatrixException::singularMatrix(); |
308
|
|
|
} |
309
|
|
|
|
310
|
|
|
$newMatrix = []; |
311
|
|
|
for ($i = 0; $i < $this->rows; ++$i) { |
312
|
|
|
for ($j = 0; $j < $this->columns; ++$j) { |
313
|
|
|
$minor = $this->crossOut($i, $j)->getDeterminant(); |
314
|
|
|
$newMatrix[$i][$j] = fmod((float) ($i + $j), 2.0) == 0 ? $minor : -$minor; |
315
|
|
|
} |
316
|
|
|
} |
317
|
|
|
|
318
|
|
|
$cofactorMatrix = new self($newMatrix, false); |
319
|
|
|
|
320
|
|
|
return $cofactorMatrix->transpose()->divideByScalar($this->getDeterminant()); |
321
|
|
|
} |
322
|
|
|
|
323
|
|
|
/** |
324
|
|
|
* @param int $row |
325
|
|
|
* @param int $column |
326
|
|
|
* |
327
|
|
|
* @return Matrix |
328
|
|
|
*/ |
329
|
|
|
public function crossOut(int $row, int $column) |
330
|
|
|
{ |
331
|
|
|
$newMatrix = []; |
332
|
|
|
$r = 0; |
333
|
|
|
for ($i = 0; $i < $this->rows; ++$i) { |
334
|
|
|
$c = 0; |
335
|
|
|
if ($row != $i) { |
336
|
|
|
for ($j = 0; $j < $this->columns; ++$j) { |
337
|
|
|
if ($column != $j) { |
338
|
|
|
$newMatrix[$r][$c] = $this->matrix[$i][$j]; |
339
|
|
|
++$c; |
340
|
|
|
} |
341
|
|
|
} |
342
|
|
|
++$r; |
343
|
|
|
} |
344
|
|
|
} |
345
|
|
|
|
346
|
|
|
return new self($newMatrix, false); |
347
|
|
|
} |
348
|
|
|
|
349
|
|
|
/** |
350
|
|
|
* @return bool |
351
|
|
|
*/ |
352
|
|
|
public function isSingular() : bool |
353
|
|
|
{ |
354
|
|
|
return 0 == $this->getDeterminant(); |
355
|
|
|
} |
356
|
|
|
|
357
|
|
|
/** |
358
|
|
|
* Returns the transpose of given array |
359
|
|
|
* |
360
|
|
|
* @param array $array |
361
|
|
|
* |
362
|
|
|
* @return array |
363
|
|
|
*/ |
364
|
|
|
public static function transposeArray(array $array) |
365
|
|
|
{ |
366
|
|
|
return (new Matrix($array, false))->transpose()->toArray(); |
367
|
|
|
} |
368
|
|
|
|
369
|
|
|
/** |
370
|
|
|
* Returns the dot product of two arrays<br> |
371
|
|
|
* Matrix::dot(x, y) ==> x.y' |
372
|
|
|
* |
373
|
|
|
* @param array $array1 |
374
|
|
|
* @param array $array2 |
375
|
|
|
* |
376
|
|
|
* @return array |
377
|
|
|
*/ |
378
|
|
|
public static function dot(array $array1, array $array2) |
379
|
|
|
{ |
380
|
|
|
$m1 = new Matrix($array1, false); |
381
|
|
|
$m2 = new Matrix($array2, false); |
382
|
|
|
|
383
|
|
|
return $m1->multiply($m2->transpose())->toArray()[0]; |
384
|
|
|
} |
385
|
|
|
} |
386
|
|
|
|
Our type inference engine has found a suspicous assignment of a value to a property. This check raises an issue when a value that can be of a mixed type is assigned to a property that is type hinted more strictly.
For example, imagine you have a variable
$accountId
that can either hold an Id object or false (if there is no account id yet). Your code now assigns that value to theid
property of an instance of theAccount
class. This class holds a proper account, so the id value must no longer be false.Either this assignment is in error or a type check should be added for that assignment.