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

$matrix

The matrix whose adjoint we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 32 of file Functions.php.

References Matrix\Matrix\isSquare().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Adjoint can only be calculated for a square matrix');
        }

        return self::getAdjoint($matrix);
    }

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antidiagonal()

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

static

Return the antidiagonal of this matrix.

Parameters

Matrix

$matrix

The matrix whose antidiagonal we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 188 of file Functions.php.

References $grid, $i, Matrix\Matrix\getValue(), Matrix\Matrix\isSquare(), and Matrix\Matrix\rows().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Anti-Diagonal can only be extracted from a square matrix');
        }

        $dimensions = $matrix->rows;
        $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
            ->toArray();

        for ($i = 0; $i < $dimensions; ++$i) {
            $grid[$i][$dimensions - $i - 1] = $matrix->getValue($i + 1, $dimensions - $i);
        }

        return new Matrix($grid);
    }

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cofactors()

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

static

Return the cofactors of this matrix.

Parameters

Matrix

$matrix

The matrix whose cofactors we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 75 of file Functions.php.

References Matrix\Matrix\isSquare().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Cofactors can only be calculated for a square matrix');
        }

        return self::getCofactors($matrix);
    }

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determinant()

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

static

Return the determinant of this matrix.

Parameters

Matrix

$matrix

The matrix whose determinant we wish to calculate

Returns

float

Exceptions

Exception

Definition at line 148 of file Functions.php.

References Matrix\Matrix\isSquare().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Determinant can only be calculated for a square matrix');
        }

        return self::getDeterminant($matrix);
    }

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diagonal()

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

static

Return the diagonal of this matrix.

Parameters

Matrix

$matrix

The matrix whose diagonal we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 164 of file Functions.php.

References $grid, $i, Matrix\Matrix\getValue(), Matrix\Matrix\isSquare(), and Matrix\Matrix\rows().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Diagonal can only be extracted from a square matrix');
        }

        $dimensions = $matrix->rows;
        $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
            ->toArray();

        for ($i = 0; $i < $dimensions; ++$i) {
            $grid[$i][$i] = $matrix->getValue($i + 1, $i + 1);
        }

        return new Matrix($grid);
    }

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getAdjoint()

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

staticprivate

Calculate the adjoint of the matrix.

Parameters

Matrix

$matrix

The matrix whose adjoint we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 15 of file Functions.php.

    {
        return self::transpose(
            self::getCofactors($matrix)
        );
    }

getCofactors()

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

staticprivate

Calculate the cofactors of the matrix.

Parameters

Matrix

$matrix

The matrix whose cofactors we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 49 of file Functions.php.

References $i, and Matrix\Matrix\rows().

    {
        $cofactors = self::getMinors($matrix);
        $dimensions = $matrix->rows;

        $cof = 1;
        for ($i = 0; $i < $dimensions; ++$i) {
            $cofs = $cof;
            for ($j = 0; $j < $dimensions; ++$j) {
                $cofactors[$i][$j] *= $cofs;
                $cofs = -$cofs;
            }
            $cof = -$cof;
        }

        return new Matrix($cofactors);
    }

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getDeterminant()

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

staticprivate

Calculate the determinant of the matrix.

Parameters

Matrix

$matrix

The matrix whose determinant we wish to calculate

Returns

float

Exceptions

Exception

Definition at line 113 of file Functions.php.

References $i, Matrix\Matrix\getValue(), and Matrix\Matrix\rows().

    {
        $dimensions = $matrix->rows;
        $determinant = 0;

        switch ($dimensions) {
            case 1:
                $determinant = $matrix->getValue(1, 1);
                break;
            case 2:
                $determinant = $matrix->getValue(1, 1) * $matrix->getValue(2, 2) -
                    $matrix->getValue(1, 2) * $matrix->getValue(2, 1);
                break;
            default:
                for ($i = 1; $i <= $dimensions; ++$i) {
                    $det = $matrix->getValue(1, $i) * self::getDeterminantSegment($matrix, 0, $i - 1);
                    if (($i % 2) == 0) {
                        $determinant -= $det;
                    } else {
                        $determinant += $det;
                    }
                }
                break;
        }

        return $determinant;
    }

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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.

References $row, and Matrix\Matrix\toArray().

    {
        $tmpMatrix = $matrix->toArray();
        unset($tmpMatrix[$row]);
        array_walk(
            $tmpMatrix,
            function (&$row) use ($column) {
                unset($row[$column]);
            }
        );

        return self::getDeterminant(new Matrix($tmpMatrix));
    }

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getMinors()

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

staticprotected

Calculate the minors of the matrix.

Parameters

Matrix

$matrix

The matrix whose minors we wish to calculate

Returns

array[]

Exceptions

Exception

Definition at line 259 of file Functions.php.

References $i, Matrix\Matrix\rows(), and Matrix\Matrix\toArray().

    {
        $minors = $matrix->toArray();
        $dimensions = $matrix->rows;
        if ($dimensions == 1) {
            return $minors;
        }

        for ($i = 0; $i < $dimensions; ++$i) {
            for ($j = 0; $j < $dimensions; ++$j) {
                $minors[$i][$j] = self::getDeterminantSegment($matrix, $i, $j);
            }
        }

        return $minors;
    }

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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

$matrix

The matrix whose identity we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 214 of file Functions.php.

References Matrix\Matrix\isSquare(), and Matrix\Matrix\rows().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Identity can only be created for a square matrix');
        }

        $dimensions = $matrix->rows;

        return Builder::createIdentityMatrix($dimensions);
    }

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inverse()

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

static

Return the inverse of this matrix.

Parameters

Matrix

$matrix

The matrix whose inverse we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 232 of file Functions.php.

References $type, Matrix\Matrix\getValue(), Matrix\Matrix\isSquare(), and Matrix\Matrix\rows().

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

    {
        if (!$matrix->isSquare()) {
            throw new Exception(ucfirst($type) . ' can only be calculated for a square matrix');
        }

        $determinant = self::getDeterminant($matrix);
        if ($determinant == 0.0) {
            throw new Div0Exception(ucfirst($type) . ' can only be calculated for a matrix with a non-zero determinant');
        }

        if ($matrix->rows == 1) {
            return new Matrix([[1 / $matrix->getValue(1, 1)]]);
        }

        return self::getAdjoint($matrix)
            ->multiply(1 / $determinant);
    }

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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

$matrix

The matrix whose minors we wish to calculate

Returns

Matrix

Exceptions

Exception

Definition at line 288 of file Functions.php.

References Matrix\Matrix\isSquare().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Minors can only be calculated for a square matrix');
        }

        return new Matrix(self::getMinors($matrix));
    }

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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

$matrix

The matrix whose trace we wish to calculate

Returns

float

Exceptions

Exception

Definition at line 306 of file Functions.php.

References $i, $result, Matrix\Matrix\getValue(), Matrix\Matrix\isSquare(), and Matrix\Matrix\rows().

    {
        if (!$matrix->isSquare()) {
            throw new Exception('Trace can only be extracted from a square matrix');
        }

        $dimensions = $matrix->rows;
        $result = 0;
        for ($i = 1; $i <= $dimensions; ++$i) {
            $result += $matrix->getValue($i, $i);
        }

        return $result;
    }

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transpose()

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

static

Return the transpose of this matrix.

Parameters

Matrix

$matrix

The matrix whose transpose we wish to calculate

Returns

Matrix

Definition at line 327 of file Functions.php.

References $grid, and Matrix\Matrix\toArray().

    {
        $array = array_values(array_merge([null], $matrix->toArray()));
        $grid = call_user_func_array(
            'array_map',
            $array
        );

        return new Matrix($grid);
    }

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

• libs/composer/vendor/markbaker/matrix/classes/src/Functions.php