Collaboration diagram for Matrix\Decomposition\LU:

Public Member Functions
	__construct (Matrix $matrix)

	getL ()
	Get lower triangular factor. More...

	getU ()
	Get upper triangular factor. More...

	getP ()
	Return pivot permutation vector. More...

	getPivot ()
	Return pivot permutation vector. More...

	isNonsingular ()
	Is the matrix nonsingular? More...

	solve (Matrix $B)
	Solve A*X = B. More...

Private Member Functions
	buildPivot ()

	localisedReferenceColumn ($column)

	applyTransformations ($column, array $luColumn)

	findPivot ($column, array $luColumn)

	pivotExchange ($pivot, $column)

	computeMultipliers ($diagonal)

	pivotB (Matrix $B)

Private Attributes
	$luMatrix

	$rows

	$columns

	$pivot = []

Detailed Description

Definition at line 8 of file LU.php.

Constructor & Destructor Documentation

◆ __construct()

Matrix\Decomposition\LU::__construct ( Matrix $matrix )

Definition at line 16 of file LU.php.

    {
        $this->luMatrix = $matrix->toArray();
        $this->rows = $matrix->rows;
        $this->columns = $matrix->columns;
 
        $this->buildPivot();
    }

References $matrix, and Matrix\Decomposition\LU\buildPivot().

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Member Function Documentation

◆ applyTransformations()

Matrix\Decomposition\LU::applyTransformations	(		$column,
		array	$luColumn
	)

private

Definition at line 151 of file LU.php.

                                                                   : void
    {
        for ($row = 0; $row < $this->rows; ++$row) {
            $luRow = $this->luMatrix[$row];
            // Most of the time is spent in the following dot product.
            $kmax = min($row, $column);
            $sValue = 0.0;
            for ($kValue = 0; $kValue < $kmax; ++$kValue) {
                $sValue += $luRow[$kValue] * $luColumn[$kValue];
            }
            $luRow[$column] = $luColumn[$row] -= $sValue;
        }
    }

References $row, and Matrix\Decomposition\LU\$rows.

Referenced by Matrix\Decomposition\LU\buildPivot().

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◆ buildPivot()

Matrix\Decomposition\LU::buildPivot ( )

private

Definition at line 118 of file LU.php.

                                 : void
    {
        for ($row = 0; $row < $this->rows; ++$row) {
            $this->pivot[$row] = $row;
        }
 
        for ($column = 0; $column < $this->columns; ++$column) {
            $luColumn = $this->localisedReferenceColumn($column);
 
            $this->applyTransformations($column, $luColumn);
 
            $pivot = $this->findPivot($column, $luColumn);
            if ($pivot !== $column) {
                $this->pivotExchange($pivot, $column);
            }
 
            $this->computeMultipliers($column);
 
            unset($luColumn);
        }
    }

References Matrix\Decomposition\LU\$columns, Matrix\Decomposition\LU\$pivot, $row, Matrix\Decomposition\LU\$rows, Matrix\Decomposition\LU\applyTransformations(), Matrix\Decomposition\LU\computeMultipliers(), Matrix\Decomposition\LU\findPivot(), Matrix\Decomposition\LU\localisedReferenceColumn(), and Matrix\Decomposition\LU\pivotExchange().

Referenced by Matrix\Decomposition\LU\__construct().

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◆ computeMultipliers()

Matrix\Decomposition\LU::computeMultipliers ( $diagonal )

private

Definition at line 190 of file LU.php.

                                                  : void
    {
        if (($diagonal < $this->rows) && ($this->luMatrix[$diagonal][$diagonal] != 0.0)) {
            for ($row = $diagonal + 1; $row < $this->rows; ++$row) {
                $this->luMatrix[$row][$diagonal] /= $this->luMatrix[$diagonal][$diagonal];
            }
        }
    }

References $row, and Matrix\Decomposition\LU\$rows.

Referenced by Matrix\Decomposition\LU\buildPivot().

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◆ findPivot()

Matrix\Decomposition\LU::findPivot	(		$column,
		array	$luColumn
	)

private

Definition at line 165 of file LU.php.

                                                        : int
    {
        $pivot = $column;
        for ($row = $column + 1; $row < $this->rows; ++$row) {
            if (abs($luColumn[$row]) > abs($luColumn[$pivot])) {
                $pivot = $row;
            }
        }
 
        return $pivot;
    }

References Matrix\Decomposition\LU\$pivot, $row, and Matrix\Decomposition\LU\$rows.

Referenced by Matrix\Decomposition\LU\buildPivot().

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◆ getL()

Matrix\Decomposition\LU::getL ( )

Get lower triangular factor.

Returns: Matrix Lower triangular factor

Definition at line 30 of file LU.php.

                          : Matrix
    {
        $lower = [];
 
        $columns = min($this->rows, $this->columns);
        for ($row = 0; $row < $this->rows; ++$row) {
            for ($column = 0; $column < $columns; ++$column) {
                if ($row > $column) {
                    $lower[$row][$column] = $this->luMatrix[$row][$column];
                } elseif ($row === $column) {
                    $lower[$row][$column] = 1.0;
                } else {
                    $lower[$row][$column] = 0.0;
                }
            }
        }
 
        return new Matrix($lower);
    }

References Matrix\Decomposition\LU\$columns, $row, and Matrix\Decomposition\LU\$rows.

◆ getP()

Matrix\Decomposition\LU::getP ( )

Return pivot permutation vector.

Returns: Matrix Pivot matrix

Definition at line 78 of file LU.php.

                          : Matrix
    {
        $pMatrix = [];
 
        $pivots = $this->pivot;
        $pivotCount = count($pivots);
        foreach ($pivots as $row => $pivot) {
            $pMatrix[$row] = array_fill(0, $pivotCount, 0);
            $pMatrix[$row][$pivot] = 1;
        }
 
        return new Matrix($pMatrix);
    }

References Matrix\Decomposition\LU\$pivot, and $row.

◆ getPivot()

Matrix\Decomposition\LU::getPivot ( )

Return pivot permutation vector.

Returns: array Pivot vector

Definition at line 97 of file LU.php.

                              : array
    {
        return $this->pivot;
    }

References Matrix\Decomposition\LU\$pivot.

◆ getU()

Matrix\Decomposition\LU::getU ( )

Get upper triangular factor.

Returns: Matrix Upper triangular factor

Definition at line 55 of file LU.php.

                          : Matrix
    {
        $upper = [];
 
        $rows = min($this->rows, $this->columns);
        for ($row = 0; $row < $rows; ++$row) {
            for ($column = 0; $column < $this->columns; ++$column) {
                if ($row <= $column) {
                    $upper[$row][$column] = $this->luMatrix[$row][$column];
                } else {
                    $upper[$row][$column] = 0.0;
                }
            }
        }
 
        return new Matrix($upper);
    }

References Matrix\Decomposition\LU\$columns, $row, and Matrix\Decomposition\LU\$rows.

◆ isNonsingular()

Matrix\Decomposition\LU::isNonsingular ( )

Is the matrix nonsingular?

Returns: bool true if U, and hence A, is nonsingular

Definition at line 107 of file LU.php.

                                   : bool
    {
        for ($diagonal = 0; $diagonal < $this->columns; ++$diagonal) {
            if ($this->luMatrix[$diagonal][$diagonal] === 0.0) {
                return false;
            }
        }
 
        return true;
    }

References Matrix\Decomposition\LU\$columns.

Referenced by Matrix\Decomposition\LU\solve().

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◆ localisedReferenceColumn()

Matrix\Decomposition\LU::localisedReferenceColumn ( $column )

private

Definition at line 140 of file LU.php.

                                                      : array
    {
        $luColumn = [];
 
        for ($row = 0; $row < $this->rows; ++$row) {
            $luColumn[$row] = &$this->luMatrix[$row][$column];
        }
 
        return $luColumn;
    }

References $row, and Matrix\Decomposition\LU\$rows.

Referenced by Matrix\Decomposition\LU\buildPivot().

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◆ pivotB()

Matrix\Decomposition\LU::pivotB ( Matrix $B )

private

Definition at line 199 of file LU.php.

                                      : array
    {
        $X = [];
        foreach ($this->pivot as $rowId) {
            $row = $B->getRows($rowId + 1)->toArray();
            $X[] = array_pop($row);
        }
 
        return $X;
    }

References $row, $X, and Matrix\Matrix\getRows().

Referenced by Matrix\Decomposition\LU\solve().

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◆ pivotExchange()

Matrix\Decomposition\LU::pivotExchange	(	$pivot,
		$column
	)

private

Definition at line 177 of file LU.php.

                                                   : void
    {
        for ($kValue = 0; $kValue < $this->columns; ++$kValue) {
            $tValue = $this->luMatrix[$pivot][$kValue];
            $this->luMatrix[$pivot][$kValue] = $this->luMatrix[$column][$kValue];
            $this->luMatrix[$column][$kValue] = $tValue;
        }
 
        $lValue = $this->pivot[$pivot];
        $this->pivot[$pivot] = $this->pivot[$column];
        $this->pivot[$column] = $lValue;
    }

References Matrix\Decomposition\LU\$columns, and Matrix\Decomposition\LU\$pivot.

Referenced by Matrix\Decomposition\LU\buildPivot().

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◆ solve()

Matrix\Decomposition\LU::solve ( Matrix $B )

Solve A*X = B.

Parameters

Matrix $B a Matrix with as many rows as A and any number of columns

Exceptions

Exception

Returns: Matrix X so that L*U*X = B(piv,:)

Definition at line 219 of file LU.php.

                                    : Matrix
    {
        if ($B->rows !== $this->rows) {
            throw new Exception('Matrix row dimensions are not equal');
        }
 
        if ($this->rows !== $this->columns) {
            throw new Exception('LU solve() only works on square matrices');
        }
 
        if (!$this->isNonsingular()) {
            throw new Exception('Can only perform operation on singular matrix');
        }
 
        // Copy right hand side with pivoting
        $nx = $B->columns;
        $X = $this->pivotB($B);
 
        // Solve L*Y = B(piv,:)
        for ($k = 0; $k < $this->columns; ++$k) {
            for ($i = $k + 1; $i < $this->columns; ++$i) {
                for ($j = 0; $j < $nx; ++$j) {
                    $X[$i][$j] -= $X[$k][$j] * $this->luMatrix[$i][$k];
                }
            }
        }
 
        // Solve U*X = Y;
        for ($k = $this->columns - 1; $k >= 0; --$k) {
            for ($j = 0; $j < $nx; ++$j) {
                $X[$k][$j] /= $this->luMatrix[$k][$k];
            }
            for ($i = 0; $i < $k; ++$i) {
                for ($j = 0; $j < $nx; ++$j) {
                    $X[$i][$j] -= $X[$k][$j] * $this->luMatrix[$i][$k];
                }
            }
        }
 
        return new Matrix($X);
    }

References Matrix\Decomposition\LU\$columns, $i, $X, Matrix\Matrix\columns(), Matrix\Decomposition\LU\isNonsingular(), Matrix\Decomposition\LU\pivotB(), and Matrix\Matrix\rows().

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Field Documentation

◆ $columns

Matrix\Decomposition\LU::$columns

private

Definition at line 12 of file LU.php.

Referenced by Matrix\Decomposition\LU\buildPivot(), Matrix\Decomposition\LU\getL(), Matrix\Decomposition\LU\getU(), Matrix\Decomposition\LU\isNonsingular(), Matrix\Decomposition\LU\pivotExchange(), and Matrix\Decomposition\LU\solve().

◆ $luMatrix

Matrix\Decomposition\LU::$luMatrix

private

Definition at line 10 of file LU.php.

◆ $pivot

Matrix\Decomposition\LU::$pivot = []

private

Definition at line 14 of file LU.php.

Referenced by Matrix\Decomposition\LU\buildPivot(), Matrix\Decomposition\LU\findPivot(), Matrix\Decomposition\LU\getP(), Matrix\Decomposition\LU\getPivot(), and Matrix\Decomposition\LU\pivotExchange().

◆ $rows

Matrix\Decomposition\LU::$rows

private

Definition at line 11 of file LU.php.

Referenced by Matrix\Decomposition\LU\applyTransformations(), Matrix\Decomposition\LU\buildPivot(), Matrix\Decomposition\LU\computeMultipliers(), Matrix\Decomposition\LU\findPivot(), Matrix\Decomposition\LU\getL(), Matrix\Decomposition\LU\getU(), and Matrix\Decomposition\LU\localisedReferenceColumn().

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

libs/composer/vendor/markbaker/matrix/classes/src/Decomposition/LU.php

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ __construct()

Member Function Documentation

◆ applyTransformations()

◆ buildPivot()

◆ computeMultipliers()

◆ findPivot()

◆ getL()

◆ getP()

◆ getPivot()

◆ getU()

◆ isNonsingular()

◆ localisedReferenceColumn()

◆ pivotB()

◆ pivotExchange()

◆ solve()

Field Documentation

◆ $columns

◆ $luMatrix

◆ $pivot

◆ $rows