Matrix\Decomposition\LU Class Reference

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.

References Matrix\Decomposition\LU\buildPivot(), Matrix\Matrix\columns(), Matrix\Matrix\rows(), and Matrix\Matrix\toArray().

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

        $this->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.

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

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

                                                                   : 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;
        }
    }

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buildPivot()

Matrix\Decomposition\LU::buildPivot ( )

private

Definition at line 118 of file LU.php.

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().

                                 : 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);
        }
    }

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computeMultipliers()

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

private

Definition at line 190 of file LU.php.

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

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

                                                  : 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];
            }
        }
    }

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findPivot()

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

private

Definition at line 165 of file LU.php.

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

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

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

        return $pivot;
    }

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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.

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

                          : 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);
    }

getP()

Matrix\Decomposition\LU::getP

(

)

Return pivot permutation vector.

Returns

Matrix Pivot matrix

Definition at line 78 of file LU.php.

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

                          : 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);
    }

getPivot()

Matrix\Decomposition\LU::getPivot

(

)

Return pivot permutation vector.

Returns

array Pivot vector

Definition at line 97 of file LU.php.

References Matrix\Decomposition\LU\$pivot.

                              : array
    {
        return $this->pivot;
    }

getU()

Matrix\Decomposition\LU::getU

(

)

Get upper triangular factor.

Returns

Matrix Upper triangular factor

Definition at line 55 of file LU.php.

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

                          : 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);
    }

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.

References Matrix\Decomposition\LU\$columns.

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

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

        return true;
    }

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localisedReferenceColumn()

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

private

Definition at line 140 of file LU.php.

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

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

                                                      : array
    {
        $luColumn = [];

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

        return $luColumn;
    }

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pivotB()

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

private

Definition at line 199 of file LU.php.

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

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

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

        return $X;
    }

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pivotExchange()

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

private

Definition at line 177 of file LU.php.

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

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

                                                   : 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;
    }

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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.

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

                                    : 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);
    }

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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().

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

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