ILIAS  release_5-4 Revision v5.4.26-12-gabc799a52e6
Static Public Member Functions | Static Protected Member Functions | Static Private Member Functions
Matrix\Functions Class Reference
+ Collaboration diagram for Matrix\Functions:

Static Public Member Functions

static adjoint (Matrix $matrix)
 Return the adjoint of this matrix The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix. More...
 
static cofactors (Matrix $matrix)
 Return the cofactors of this matrix. More...
 
static determinant (Matrix $matrix)
 Return the determinant of this matrix. More...
 
static diagonal (Matrix $matrix)
 Return the diagonal of this matrix. More...
 
static antidiagonal (Matrix $matrix)
 Return the antidiagonal of this matrix. More...
 
static identity (Matrix $matrix)
 Return the identity matrix The identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. More...
 
static inverse (Matrix $matrix, string $type='inverse')
 Return the inverse of this matrix. More...
 
static minors (Matrix $matrix)
 Return the minors of the matrix The minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows or columns. More...
 
static trace (Matrix $matrix)
 Return the trace of this matrix The trace is defined as the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of the matrix. More...
 
static transpose (Matrix $matrix)
 Return the transpose of this matrix. More...
 

Static Protected Member Functions

static getMinors (Matrix $matrix)
 Calculate the minors of the matrix. More...
 

Static Private Member Functions

static getAdjoint (Matrix $matrix)
 Calculate the adjoint of the matrix. More...
 
static getCofactors (Matrix $matrix)
 Calculate the cofactors of the matrix. More...
 
static getDeterminantSegment (Matrix $matrix, $row, $column)
 
static getDeterminant (Matrix $matrix)
 Calculate the determinant of the matrix. More...
 

Detailed Description

Definition at line 5 of file Functions.php.

Member Function Documentation

◆ adjoint()

static Matrix\Functions::adjoint ( Matrix  $matrix)
static

Return the adjoint of this matrix The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.

The adjugate has sometimes been called the "adjoint", but today the "adjoint" of a matrix normally refers to its corresponding adjoint operator, which is its conjugate transpose.

Parameters
Matrix$matrixThe matrix whose adjoint we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 32 of file Functions.php.

33 {
34 if (!$matrix->isSquare()) {
35 throw new Exception('Adjoint can only be calculated for a square matrix');
36 }
37
38 return self::getAdjoint($matrix);
39 }
Matrix\Functions\getAdjoint
static getAdjoint(Matrix $matrix)
Calculate the adjoint of the matrix.
Definition: Functions.php:15
$matrix
$matrix
Definition: test.php:18

References $matrix.

◆ antidiagonal()

static Matrix\Functions::antidiagonal ( Matrix  $matrix)
static

Return the antidiagonal of this matrix.

Parameters
Matrix$matrixThe matrix whose antidiagonal we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 188 of file Functions.php.

189 {
190 if (!$matrix->isSquare()) {
191 throw new Exception('Anti-Diagonal can only be extracted from a square matrix');
192 }
193
194 $dimensions = $matrix->rows;
195 $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
196 ->toArray();
197
198 for ($i = 0; $i < $dimensions; ++$i) {
199 $grid[$i][$dimensions - $i - 1] = $matrix->getValue($i + 1, $dimensions - $i);
200 }
201
202 return new Matrix($grid);
203 }
Matrix\Builder\createFilledMatrix
static createFilledMatrix($fillValue, $rows, $columns=null)
Create a new matrix of specified dimensions, and filled with a specified value If the column argument...
Definition: Builder.php:30
$i
$i
Definition: disco.tpl.php:19
$grid
$grid
Definition: test.php:8
Matrix
Class for the creating "special" Matrices.
Definition: Builder.php:11

References $grid, $i, and $matrix.

◆ cofactors()

static Matrix\Functions::cofactors ( Matrix  $matrix)
static

Return the cofactors of this matrix.

Parameters
Matrix$matrixThe matrix whose cofactors we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 75 of file Functions.php.

76 {
77 if (!$matrix->isSquare()) {
78 throw new Exception('Cofactors can only be calculated for a square matrix');
79 }
80
81 return self::getCofactors($matrix);
82 }
Matrix\Functions\getCofactors
static getCofactors(Matrix $matrix)
Calculate the cofactors of the matrix.
Definition: Functions.php:49

References $matrix.

◆ determinant()

static Matrix\Functions::determinant ( Matrix  $matrix)
static

Return the determinant of this matrix.

Parameters
Matrix$matrixThe matrix whose determinant we wish to calculate
Returns
float
Exceptions
Exception

Definition at line 148 of file Functions.php.

149 {
150 if (!$matrix->isSquare()) {
151 throw new Exception('Determinant can only be calculated for a square matrix');
152 }
153
154 return self::getDeterminant($matrix);
155 }
Matrix\Functions\getDeterminant
static getDeterminant(Matrix $matrix)
Calculate the determinant of the matrix.
Definition: Functions.php:113

References $matrix.

◆ diagonal()

static Matrix\Functions::diagonal ( Matrix  $matrix)
static

Return the diagonal of this matrix.

Parameters
Matrix$matrixThe matrix whose diagonal we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 164 of file Functions.php.

165 {
166 if (!$matrix->isSquare()) {
167 throw new Exception('Diagonal can only be extracted from a square matrix');
168 }
169
170 $dimensions = $matrix->rows;
171 $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
172 ->toArray();
173
174 for ($i = 0; $i < $dimensions; ++$i) {
175 $grid[$i][$i] = $matrix->getValue($i + 1, $i + 1);
176 }
177
178 return new Matrix($grid);
179 }

References $grid, $i, and $matrix.

◆ getAdjoint()

static Matrix\Functions::getAdjoint ( Matrix  $matrix)
staticprivate

Calculate the adjoint of the matrix.

Parameters
Matrix$matrixThe matrix whose adjoint we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 15 of file Functions.php.

16 {
17 return self::transpose(
18 self::getCofactors($matrix)
19 );
20 }
Matrix\Functions\transpose
static transpose(Matrix $matrix)
Return the transpose of this matrix.
Definition: Functions.php:327

References $matrix.

◆ getCofactors()

static Matrix\Functions::getCofactors ( Matrix  $matrix)
staticprivate

Calculate the cofactors of the matrix.

Parameters
Matrix$matrixThe matrix whose cofactors we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 49 of file Functions.php.

50 {
51 $cofactors = self::getMinors($matrix);
52 $dimensions = $matrix->rows;
53
54 $cof = 1;
55 for ($i = 0; $i < $dimensions; ++$i) {
56 $cofs = $cof;
57 for ($j = 0; $j < $dimensions; ++$j) {
58 $cofactors[$i][$j] *= $cofs;
59 $cofs = -$cofs;
60 }
61 $cof = -$cof;
62 }
63
64 return new Matrix($cofactors);
65 }
Matrix\Functions\getMinors
static getMinors(Matrix $matrix)
Calculate the minors of the matrix.
Definition: Functions.php:259

References $i, and $matrix.

◆ getDeterminant()

static Matrix\Functions::getDeterminant ( Matrix  $matrix)
staticprivate

Calculate the determinant of the matrix.

Parameters
Matrix$matrixThe matrix whose determinant we wish to calculate
Returns
float
Exceptions
Exception

Definition at line 113 of file Functions.php.

114 {
115 $dimensions = $matrix->rows;
116 $determinant = 0;
117
118 switch ($dimensions) {
119 case 1:
120 $determinant = $matrix->getValue(1, 1);
121 break;
122 case 2:
123 $determinant = $matrix->getValue(1, 1) * $matrix->getValue(2, 2) -
124 $matrix->getValue(1, 2) * $matrix->getValue(2, 1);
125 break;
126 default:
127 for ($i = 1; $i <= $dimensions; ++$i) {
128 $det = $matrix->getValue(1, $i) * self::getDeterminantSegment($matrix, 0, $i - 1);
129 if (($i % 2) == 0) {
130 $determinant -= $det;
131 } else {
132 $determinant += $det;
133 }
134 }
135 break;
136 }
137
138 return $determinant;
139 }
Matrix\Functions\getDeterminantSegment
static getDeterminantSegment(Matrix $matrix, $row, $column)
Definition: Functions.php:91

References $i, and $matrix.

◆ getDeterminantSegment()

static Matrix\Functions::getDeterminantSegment ( Matrix  $matrix,
  $row,
  $column 
)
staticprivate
Parameters
Matrix$matrix
int$row
int$column
Returns
float
Exceptions
Exception

Definition at line 91 of file Functions.php.

92 {
93 $tmpMatrix = $matrix->toArray();
94 unset($tmpMatrix[$row]);
95 array_walk(
96 $tmpMatrix,
97 function (&$row) use ($column) {
98 unset($row[$column]);
99 }
100 );
101
102 return self::getDeterminant(new Matrix($tmpMatrix));
103 }
$row
$row
Definition: migrateto20.php:360

References $matrix, and $row.

◆ getMinors()

static Matrix\Functions::getMinors ( Matrix  $matrix)
staticprotected

Calculate the minors of the matrix.

Parameters
Matrix$matrixThe matrix whose minors we wish to calculate
Returns
array[]
Exceptions
Exception

Definition at line 259 of file Functions.php.

260 {
261 $minors = $matrix->toArray();
262 $dimensions = $matrix->rows;
263 if ($dimensions == 1) {
264 return $minors;
265 }
266
267 for ($i = 0; $i < $dimensions; ++$i) {
268 for ($j = 0; $j < $dimensions; ++$j) {
269 $minors[$i][$j] = self::getDeterminantSegment($matrix, $i, $j);
270 }
271 }
272
273 return $minors;
274 }

References $i, and $matrix.

◆ identity()

static Matrix\Functions::identity ( Matrix  $matrix)
static

Return the identity matrix The identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

Parameters
Matrix$matrixThe matrix whose identity we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 214 of file Functions.php.

215 {
216 if (!$matrix->isSquare()) {
217 throw new Exception('Identity can only be created for a square matrix');
218 }
219
220 $dimensions = $matrix->rows;
221
222 return Builder::createIdentityMatrix($dimensions);
223 }
Matrix\Builder\createIdentityMatrix
static createIdentityMatrix($dimensions, $fillValue=null)
Create a new identity matrix of specified dimensions This will always be a square matrix,...
Definition: Builder.php:60

References $matrix.

◆ inverse()

static Matrix\Functions::inverse ( Matrix  $matrix,
string  $type = 'inverse' 
)
static

Return the inverse of this matrix.

Parameters
Matrix$matrixThe matrix whose inverse we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 232 of file Functions.php.

233 {
234 if (!$matrix->isSquare()) {
235 throw new Exception(ucfirst($type) . ' can only be calculated for a square matrix');
236 }
237
238 $determinant = self::getDeterminant($matrix);
239 if ($determinant == 0.0) {
240 throw new Div0Exception(ucfirst($type) . ' can only be calculated for a matrix with a non-zero determinant');
241 }
242
243 if ($matrix->rows == 1) {
244 return new Matrix([[1 / $matrix->getValue(1, 1)]]);
245 }
246
247 return self::getAdjoint($matrix)
248 ->multiply(1 / $determinant);
249 }
$type
$type
Definition: proxy_ylocal.php:10

References $matrix, and $type.

Referenced by Matrix\Operators\Division\execute().

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◆ minors()

static Matrix\Functions::minors ( Matrix  $matrix)
static

Return the minors of the matrix The minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows or columns.

Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of square matrices.

Parameters
Matrix$matrixThe matrix whose minors we wish to calculate
Returns
Matrix
Exceptions
Exception

Definition at line 288 of file Functions.php.

289 {
290 if (!$matrix->isSquare()) {
291 throw new Exception('Minors can only be calculated for a square matrix');
292 }
293
294 return new Matrix(self::getMinors($matrix));
295 }

References $matrix.

◆ trace()

static Matrix\Functions::trace ( Matrix  $matrix)
static

Return the trace of this matrix The trace is defined as the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of the matrix.

Parameters
Matrix$matrixThe matrix whose trace we wish to calculate
Returns
float
Exceptions
Exception

Definition at line 306 of file Functions.php.

307 {
308 if (!$matrix->isSquare()) {
309 throw new Exception('Trace can only be extracted from a square matrix');
310 }
311
312 $dimensions = $matrix->rows;
313 $result = 0;
314 for ($i = 1; $i <= $dimensions; ++$i) {
315 $result += $matrix->getValue($i, $i);
316 }
317
318 return $result;
319 }
$result
$result
Definition: CleanUpTest.php:463

References $i, $matrix, and $result.

◆ transpose()

static Matrix\Functions::transpose ( Matrix  $matrix)
static

Return the transpose of this matrix.

Parameters
Matrix$matrixThe matrix whose transpose we wish to calculate
Returns
Matrix

Definition at line 327 of file Functions.php.

328 {
329 $array = array_values(array_merge([null], $matrix->toArray()));
330 $grid = call_user_func_array(
331 'array_map',
332 $array
333 );
334
335 return new Matrix($grid);
336 }

References $grid, and $matrix.

The documentation for this class was generated from the following file: