/home/mip/mip/public/img/credit/datatables/classes.tar
src/Operations.php 0000644 00000010116 15152054524 0010171 0 ustar 00 <?php
namespace Matrix;
use Matrix\Operators\Addition;
use Matrix\Operators\DirectSum;
use Matrix\Operators\Division;
use Matrix\Operators\Multiplication;
use Matrix\Operators\Subtraction;
class Operations
{
public static function add(...$matrixValues): Matrix
{
if (count($matrixValues) < 2) {
throw new Exception('Addition operation requires at least 2 arguments');
}
$matrix = array_shift($matrixValues);
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('Addition arguments must be Matrix or array');
}
$result = new Addition($matrix);
foreach ($matrixValues as $matrix) {
$result->execute($matrix);
}
return $result->result();
}
public static function directsum(...$matrixValues): Matrix
{
if (count($matrixValues) < 2) {
throw new Exception('DirectSum operation requires at least 2 arguments');
}
$matrix = array_shift($matrixValues);
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('DirectSum arguments must be Matrix or array');
}
$result = new DirectSum($matrix);
foreach ($matrixValues as $matrix) {
$result->execute($matrix);
}
return $result->result();
}
public static function divideby(...$matrixValues): Matrix
{
if (count($matrixValues) < 2) {
throw new Exception('Division operation requires at least 2 arguments');
}
$matrix = array_shift($matrixValues);
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('Division arguments must be Matrix or array');
}
$result = new Division($matrix);
foreach ($matrixValues as $matrix) {
$result->execute($matrix);
}
return $result->result();
}
public static function divideinto(...$matrixValues): Matrix
{
if (count($matrixValues) < 2) {
throw new Exception('Division operation requires at least 2 arguments');
}
$matrix = array_pop($matrixValues);
$matrixValues = array_reverse($matrixValues);
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('Division arguments must be Matrix or array');
}
$result = new Division($matrix);
foreach ($matrixValues as $matrix) {
$result->execute($matrix);
}
return $result->result();
}
public static function multiply(...$matrixValues): Matrix
{
if (count($matrixValues) < 2) {
throw new Exception('Multiplication operation requires at least 2 arguments');
}
$matrix = array_shift($matrixValues);
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('Multiplication arguments must be Matrix or array');
}
$result = new Multiplication($matrix);
foreach ($matrixValues as $matrix) {
$result->execute($matrix);
}
return $result->result();
}
public static function subtract(...$matrixValues): Matrix
{
if (count($matrixValues) < 2) {
throw new Exception('Subtraction operation requires at least 2 arguments');
}
$matrix = array_shift($matrixValues);
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('Subtraction arguments must be Matrix or array');
}
$result = new Subtraction($matrix);
foreach ($matrixValues as $matrix) {
$result->execute($matrix);
}
return $result->result();
}
}
src/Functions.php 0000644 00000025222 15152054524 0010022 0 ustar 00 <?php
namespace Matrix;
class Functions
{
/**
* Validates an array of matrix, converting an array to a matrix if required.
*
* @param Matrix|array $matrix Matrix or an array to treat as a matrix.
* @return Matrix The new matrix
* @throws Exception If argument isn't a valid matrix or array.
*/
private static function validateMatrix($matrix)
{
if (is_array($matrix)) {
$matrix = new Matrix($matrix);
}
if (!$matrix instanceof Matrix) {
throw new Exception('Must be Matrix or array');
}
return $matrix;
}
/**
* Calculate the adjoint of the matrix
*
* @param Matrix $matrix The matrix whose adjoint we wish to calculate
* @return Matrix
*
* @throws Exception
*/
private static function getAdjoint(Matrix $matrix)
{
return self::transpose(
self::getCofactors($matrix)
);
}
/**
* 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.
*
* @param Matrix|array $matrix The matrix whose adjoint we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function adjoint($matrix)
{
$matrix = self::validateMatrix($matrix);
if (!$matrix->isSquare()) {
throw new Exception('Adjoint can only be calculated for a square matrix');
}
return self::getAdjoint($matrix);
}
/**
* Calculate the cofactors of the matrix
*
* @param Matrix $matrix The matrix whose cofactors we wish to calculate
* @return Matrix
*
* @throws Exception
*/
private static function getCofactors(Matrix $matrix)
{
$cofactors = self::getMinors($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);
}
/**
* Return the cofactors of this matrix
*
* @param Matrix|array $matrix The matrix whose cofactors we wish to calculate
* @return Matrix
*
* @throws Exception
*/
public static function cofactors($matrix)
{
$matrix = self::validateMatrix($matrix);
if (!$matrix->isSquare()) {
throw new Exception('Cofactors can only be calculated for a square matrix');
}
return self::getCofactors($matrix);
}
/**
* @param Matrix $matrix
* @param int $row
* @param int $column
* @return float
* @throws Exception
*/
private static function getDeterminantSegment(Matrix $matrix, $row, $column)
{
$tmpMatrix = $matrix->toArray();
unset($tmpMatrix[$row]);
array_walk(
$tmpMatrix,
function (&$row) use ($column) {
unset($row[$column]);
}
);
return self::getDeterminant(new Matrix($tmpMatrix));
}
/**
* Calculate the determinant of the matrix
*
* @param Matrix $matrix The matrix whose determinant we wish to calculate
* @return float
*
* @throws Exception
*/
private static function getDeterminant(Matrix $matrix)
{
$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;
}
/**
* Return the determinant of this matrix
*
* @param Matrix|array $matrix The matrix whose determinant we wish to calculate
* @return float
* @throws Exception
**/
public static function determinant($matrix)
{
$matrix = self::validateMatrix($matrix);
if (!$matrix->isSquare()) {
throw new Exception('Determinant can only be calculated for a square matrix');
}
return self::getDeterminant($matrix);
}
/**
* Return the diagonal of this matrix
*
* @param Matrix|array $matrix The matrix whose diagonal we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function diagonal($matrix)
{
$matrix = self::validateMatrix($matrix);
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);
}
/**
* Return the antidiagonal of this matrix
*
* @param Matrix|array $matrix The matrix whose antidiagonal we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function antidiagonal($matrix)
{
$matrix = self::validateMatrix($matrix);
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);
}
/**
* 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
*
* @param Matrix|array $matrix The matrix whose identity we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function identity($matrix)
{
$matrix = self::validateMatrix($matrix);
if (!$matrix->isSquare()) {
throw new Exception('Identity can only be created for a square matrix');
}
$dimensions = $matrix->rows;
return Builder::createIdentityMatrix($dimensions);
}
/**
* Return the inverse of this matrix
*
* @param Matrix|array $matrix The matrix whose inverse we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function inverse($matrix, string $type = 'inverse')
{
$matrix = self::validateMatrix($matrix);
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);
}
/**
* Calculate the minors of the matrix
*
* @param Matrix $matrix The matrix whose minors we wish to calculate
* @return array[]
*
* @throws Exception
*/
protected static function getMinors(Matrix $matrix)
{
$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;
}
/**
* 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.
*
* @param Matrix|array $matrix The matrix whose minors we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function minors($matrix)
{
$matrix = self::validateMatrix($matrix);
if (!$matrix->isSquare()) {
throw new Exception('Minors can only be calculated for a square matrix');
}
return new Matrix(self::getMinors($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
*
* @param Matrix|array $matrix The matrix whose trace we wish to calculate
* @return float
* @throws Exception
**/
public static function trace($matrix)
{
$matrix = self::validateMatrix($matrix);
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;
}
/**
* Return the transpose of this matrix
*
* @param Matrix|\a $matrix The matrix whose transpose we wish to calculate
* @return Matrix
**/
public static function transpose($matrix)
{
$matrix = self::validateMatrix($matrix);
$array = array_values(array_merge([null], $matrix->toArray()));
$grid = call_user_func_array(
'array_map',
$array
);
return new Matrix($grid);
}
}
src/Complex.php 0000644 00000026017 15152054524 0007464 0 ustar 00 <?php
/**
*
* Class for the management of Complex numbers
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Complex Number object.
*
* @package Complex
*
* @method float abs()
* @method Complex acos()
* @method Complex acosh()
* @method Complex acot()
* @method Complex acoth()
* @method Complex acsc()
* @method Complex acsch()
* @method float argument()
* @method Complex asec()
* @method Complex asech()
* @method Complex asin()
* @method Complex asinh()
* @method Complex atan()
* @method Complex atanh()
* @method Complex conjugate()
* @method Complex cos()
* @method Complex cosh()
* @method Complex cot()
* @method Complex coth()
* @method Complex csc()
* @method Complex csch()
* @method Complex exp()
* @method Complex inverse()
* @method Complex ln()
* @method Complex log2()
* @method Complex log10()
* @method Complex negative()
* @method Complex pow(int|float $power)
* @method float rho()
* @method Complex sec()
* @method Complex sech()
* @method Complex sin()
* @method Complex sinh()
* @method Complex sqrt()
* @method Complex tan()
* @method Complex tanh()
* @method float theta()
* @method Complex add(...$complexValues)
* @method Complex subtract(...$complexValues)
* @method Complex multiply(...$complexValues)
* @method Complex divideby(...$complexValues)
* @method Complex divideinto(...$complexValues)
*/
class Complex
{
/**
* @constant Euler's Number.
*/
const EULER = 2.7182818284590452353602874713526624977572;
/**
* @constant Regexp to split an input string into real and imaginary components and suffix
*/
const NUMBER_SPLIT_REGEXP =
'` ^
( # Real part
[-+]?(\d+\.?\d*|\d*\.?\d+) # Real value (integer or float)
([Ee][-+]?[0-2]?\d{1,3})? # Optional real exponent for scientific format
)
( # Imaginary part
[-+]?(\d+\.?\d*|\d*\.?\d+) # Imaginary value (integer or float)
([Ee][-+]?[0-2]?\d{1,3})? # Optional imaginary exponent for scientific format
)?
( # Imaginary part is optional
([-+]?) # Imaginary (implicit 1 or -1) only
([ij]?) # Imaginary i or j - depending on whether mathematical or engineering
)
$`uix';
/**
* @var float $realPart The value of of this complex number on the real plane.
*/
protected $realPart = 0.0;
/**
* @var float $imaginaryPart The value of of this complex number on the imaginary plane.
*/
protected $imaginaryPart = 0.0;
/**
* @var string $suffix The suffix for this complex number (i or j).
*/
protected $suffix;
/**
* Validates whether the argument is a valid complex number, converting scalar or array values if possible
*
* @param mixed $complexNumber The value to parse
* @return array
* @throws Exception If the argument isn't a Complex number or cannot be converted to one
*/
private static function parseComplex($complexNumber)
{
// Test for real number, with no imaginary part
if (is_numeric($complexNumber)) {
return [$complexNumber, 0, null];
}
// Fix silly human errors
$complexNumber = str_replace(
['+-', '-+', '++', '--'],
['-', '-', '+', '+'],
$complexNumber
);
// Basic validation of string, to parse out real and imaginary parts, and any suffix
$validComplex = preg_match(
self::NUMBER_SPLIT_REGEXP,
$complexNumber,
$complexParts
);
if (!$validComplex) {
// Neither real nor imaginary part, so test to see if we actually have a suffix
$validComplex = preg_match('/^([\-\+]?)([ij])$/ui', $complexNumber, $complexParts);
if (!$validComplex) {
throw new Exception('Invalid complex number');
}
// We have a suffix, so set the real to 0, the imaginary to either 1 or -1 (as defined by the sign)
$imaginary = 1;
if ($complexParts[1] === '-') {
$imaginary = 0 - $imaginary;
}
return [0, $imaginary, $complexParts[2]];
}
// If we don't have an imaginary part, identify whether it should be +1 or -1...
if (($complexParts[4] === '') && ($complexParts[9] !== '')) {
if ($complexParts[7] !== $complexParts[9]) {
$complexParts[4] = 1;
if ($complexParts[8] === '-') {
$complexParts[4] = -1;
}
} else {
// ... or if we have only the real and no imaginary part
// (in which case our real should be the imaginary)
$complexParts[4] = $complexParts[1];
$complexParts[1] = 0;
}
}
// Return real and imaginary parts and suffix as an array, and set a default suffix if user input lazily
return [
$complexParts[1],
$complexParts[4],
!empty($complexParts[9]) ? $complexParts[9] : 'i'
];
}
public function __construct($realPart = 0.0, $imaginaryPart = null, $suffix = 'i')
{
if ($imaginaryPart === null) {
if (is_array($realPart)) {
// We have an array of (potentially) real and imaginary parts, and any suffix
list ($realPart, $imaginaryPart, $suffix) = array_values($realPart) + [0.0, 0.0, 'i'];
} elseif ((is_string($realPart)) || (is_numeric($realPart))) {
// We've been given a string to parse to extract the real and imaginary parts, and any suffix
list($realPart, $imaginaryPart, $suffix) = self::parseComplex($realPart);
}
}
if ($imaginaryPart != 0.0 && empty($suffix)) {
$suffix = 'i';
} elseif ($imaginaryPart == 0.0 && !empty($suffix)) {
$suffix = '';
}
// Set parsed values in our properties
$this->realPart = (float) $realPart;
$this->imaginaryPart = (float) $imaginaryPart;
$this->suffix = strtolower($suffix ?? '');
}
/**
* Gets the real part of this complex number
*
* @return Float
*/
public function getReal(): float
{
return $this->realPart;
}
/**
* Gets the imaginary part of this complex number
*
* @return Float
*/
public function getImaginary(): float
{
return $this->imaginaryPart;
}
/**
* Gets the suffix of this complex number
*
* @return String
*/
public function getSuffix(): string
{
return $this->suffix;
}
/**
* Returns true if this is a real value, false if a complex value
*
* @return Bool
*/
public function isReal(): bool
{
return $this->imaginaryPart == 0.0;
}
/**
* Returns true if this is a complex value, false if a real value
*
* @return Bool
*/
public function isComplex(): bool
{
return !$this->isReal();
}
public function format(): string
{
$str = "";
if ($this->imaginaryPart != 0.0) {
if (\abs($this->imaginaryPart) != 1.0) {
$str .= $this->imaginaryPart . $this->suffix;
} else {
$str .= (($this->imaginaryPart < 0.0) ? '-' : '') . $this->suffix;
}
}
if ($this->realPart != 0.0) {
if (($str) && ($this->imaginaryPart > 0.0)) {
$str = "+" . $str;
}
$str = $this->realPart . $str;
}
if (!$str) {
$str = "0.0";
}
return $str;
}
public function __toString(): string
{
return $this->format();
}
/**
* Validates whether the argument is a valid complex number, converting scalar or array values if possible
*
* @param mixed $complex The value to validate
* @return Complex
* @throws Exception If the argument isn't a Complex number or cannot be converted to one
*/
public static function validateComplexArgument($complex): Complex
{
if (is_scalar($complex) || is_array($complex)) {
$complex = new Complex($complex);
} elseif (!is_object($complex) || !($complex instanceof Complex)) {
throw new Exception('Value is not a valid complex number');
}
return $complex;
}
/**
* Returns the reverse of this complex number
*
* @return Complex
*/
public function reverse(): Complex
{
return new Complex(
$this->imaginaryPart,
$this->realPart,
($this->realPart == 0.0) ? null : $this->suffix
);
}
public function invertImaginary(): Complex
{
return new Complex(
$this->realPart,
$this->imaginaryPart * -1,
($this->imaginaryPart == 0.0) ? null : $this->suffix
);
}
public function invertReal(): Complex
{
return new Complex(
$this->realPart * -1,
$this->imaginaryPart,
($this->imaginaryPart == 0.0) ? null : $this->suffix
);
}
protected static $functions = [
'abs',
'acos',
'acosh',
'acot',
'acoth',
'acsc',
'acsch',
'argument',
'asec',
'asech',
'asin',
'asinh',
'atan',
'atanh',
'conjugate',
'cos',
'cosh',
'cot',
'coth',
'csc',
'csch',
'exp',
'inverse',
'ln',
'log2',
'log10',
'negative',
'pow',
'rho',
'sec',
'sech',
'sin',
'sinh',
'sqrt',
'tan',
'tanh',
'theta',
];
protected static $operations = [
'add',
'subtract',
'multiply',
'divideby',
'divideinto',
];
/**
* Returns the result of the function call or operation
*
* @return Complex|float
* @throws Exception|\InvalidArgumentException
*/
public function __call($functionName, $arguments)
{
$functionName = strtolower(str_replace('_', '', $functionName));
// Test for function calls
if (in_array($functionName, self::$functions, true)) {
return Functions::$functionName($this, ...$arguments);
}
// Test for operation calls
if (in_array($functionName, self::$operations, true)) {
return Operations::$functionName($this, ...$arguments);
}
throw new Exception('Complex Function or Operation does not exist');
}
}
src/Exception.php 0000644 00000000357 15152054524 0010012 0 ustar 00 <?php
/**
* Exception.
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Matrix;
class Exception extends \Exception
{
}
src/Builder.php 0000644 00000003260 15152066446 0007444 0 ustar 00 <?php
/**
*
* Class for the creating "special" Matrices
*
* @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Matrix;
/**
* Matrix Builder class.
*
* @package Matrix
*/
class Builder
{
/**
* Create a new matrix of specified dimensions, and filled with a specified value
* If the column argument isn't provided, then a square matrix will be created
*
* @param mixed $fillValue
* @param int $rows
* @param int|null $columns
* @return Matrix
* @throws Exception
*/
public static function createFilledMatrix($fillValue, $rows, $columns = null)
{
if ($columns === null) {
$columns = $rows;
}
$rows = Matrix::validateRow($rows);
$columns = Matrix::validateColumn($columns);
return new Matrix(
array_fill(
0,
$rows,
array_fill(
0,
$columns,
$fillValue
)
)
);
}
/**
* Create a new identity matrix of specified dimensions
* This will always be a square matrix, with the number of rows and columns matching the provided dimension
*
* @param int $dimensions
* @return Matrix
* @throws Exception
*/
public static function createIdentityMatrix($dimensions, $fillValue = null)
{
$grid = static::createFilledMatrix($fillValue, $dimensions)->toArray();
for ($x = 0; $x < $dimensions; ++$x) {
$grid[$x][$x] = 1;
}
return new Matrix($grid);
}
}
src/Div0Exception.php 0000644 00000000362 15152066446 0010537 0 ustar 00 <?php
/**
* Exception.
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Matrix;
class Div0Exception extends Exception
{
}
src/Decomposition/QR.php 0000644 00000012757 15152066446 0011227 0 ustar 00 <?php
namespace Matrix\Decomposition;
use Matrix\Exception;
use Matrix\Matrix;
class QR
{
private $qrMatrix;
private $rows;
private $columns;
private $rDiagonal = [];
public function __construct(Matrix $matrix)
{
$this->qrMatrix = $matrix->toArray();
$this->rows = $matrix->rows;
$this->columns = $matrix->columns;
$this->decompose();
}
public function getHouseholdVectors(): Matrix
{
$householdVectors = [];
for ($row = 0; $row < $this->rows; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
if ($row >= $column) {
$householdVectors[$row][$column] = $this->qrMatrix[$row][$column];
} else {
$householdVectors[$row][$column] = 0.0;
}
}
}
return new Matrix($householdVectors);
}
public function getQ(): Matrix
{
$qGrid = [];
$rowCount = $this->rows;
for ($k = $this->columns - 1; $k >= 0; --$k) {
for ($i = 0; $i < $this->rows; ++$i) {
$qGrid[$i][$k] = 0.0;
}
$qGrid[$k][$k] = 1.0;
if ($this->columns > $this->rows) {
$qGrid = array_slice($qGrid, 0, $this->rows);
}
for ($j = $k; $j < $this->columns; ++$j) {
if (isset($this->qrMatrix[$k], $this->qrMatrix[$k][$k]) && $this->qrMatrix[$k][$k] != 0.0) {
$s = 0.0;
for ($i = $k; $i < $this->rows; ++$i) {
$s += $this->qrMatrix[$i][$k] * $qGrid[$i][$j];
}
$s = -$s / $this->qrMatrix[$k][$k];
for ($i = $k; $i < $this->rows; ++$i) {
$qGrid[$i][$j] += $s * $this->qrMatrix[$i][$k];
}
}
}
}
array_walk(
$qGrid,
function (&$row) use ($rowCount) {
$row = array_reverse($row);
$row = array_slice($row, 0, $rowCount);
}
);
return new Matrix($qGrid);
}
public function getR(): Matrix
{
$rGrid = [];
for ($row = 0; $row < $this->columns; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
if ($row < $column) {
$rGrid[$row][$column] = $this->qrMatrix[$row][$column] ?? 0.0;
} elseif ($row === $column) {
$rGrid[$row][$column] = $this->rDiagonal[$row] ?? 0.0;
} else {
$rGrid[$row][$column] = 0.0;
}
}
}
if ($this->columns > $this->rows) {
$rGrid = array_slice($rGrid, 0, $this->rows);
}
return new Matrix($rGrid);
}
private function hypo($a, $b): float
{
if (abs($a) > abs($b)) {
$r = $b / $a;
$r = abs($a) * sqrt(1 + $r * $r);
} elseif ($b != 0.0) {
$r = $a / $b;
$r = abs($b) * sqrt(1 + $r * $r);
} else {
$r = 0.0;
}
return $r;
}
/**
* QR Decomposition computed by Householder reflections.
*/
private function decompose(): void
{
for ($k = 0; $k < $this->columns; ++$k) {
// Compute 2-norm of k-th column without under/overflow.
$norm = 0.0;
for ($i = $k; $i < $this->rows; ++$i) {
$norm = $this->hypo($norm, $this->qrMatrix[$i][$k]);
}
if ($norm != 0.0) {
// Form k-th Householder vector.
if ($this->qrMatrix[$k][$k] < 0.0) {
$norm = -$norm;
}
for ($i = $k; $i < $this->rows; ++$i) {
$this->qrMatrix[$i][$k] /= $norm;
}
$this->qrMatrix[$k][$k] += 1.0;
// Apply transformation to remaining columns.
for ($j = $k + 1; $j < $this->columns; ++$j) {
$s = 0.0;
for ($i = $k; $i < $this->rows; ++$i) {
$s += $this->qrMatrix[$i][$k] * $this->qrMatrix[$i][$j];
}
$s = -$s / $this->qrMatrix[$k][$k];
for ($i = $k; $i < $this->rows; ++$i) {
$this->qrMatrix[$i][$j] += $s * $this->qrMatrix[$i][$k];
}
}
}
$this->rDiagonal[$k] = -$norm;
}
}
public function isFullRank(): bool
{
for ($j = 0; $j < $this->columns; ++$j) {
if ($this->rDiagonal[$j] == 0.0) {
return false;
}
}
return true;
}
/**
* Least squares solution of A*X = B.
*
* @param Matrix $B a Matrix with as many rows as A and any number of columns
*
* @throws Exception
*
* @return Matrix matrix that minimizes the two norm of Q*R*X-B
*/
public function solve(Matrix $B): Matrix
{
if ($B->rows !== $this->rows) {
throw new Exception('Matrix row dimensions are not equal');
}
if (!$this->isFullRank()) {
throw new Exception('Can only perform this operation on a full-rank matrix');
}
// Compute Y = transpose(Q)*B
$Y = $this->getQ()->transpose()
->multiply($B);
// Solve R*X = Y;
return $this->getR()->inverse()
->multiply($Y);
}
}
src/Decomposition/Decomposition.php 0000644 00000001022 15152066446 0013500 0 ustar 00 <?php
namespace Matrix\Decomposition;
use Matrix\Exception;
use Matrix\Matrix;
class Decomposition
{
const LU = 'LU';
const QR = 'QR';
/**
* @throws Exception
*/
public static function decomposition($type, Matrix $matrix)
{
switch (strtoupper($type)) {
case self::LU:
return new LU($matrix);
case self::QR:
return new QR($matrix);
default:
throw new Exception('Invalid Decomposition');
}
}
}
src/Decomposition/LU.php 0000644 00000015471 15152066446 0011221 0 ustar 00 <?php
namespace Matrix\Decomposition;
use Matrix\Exception;
use Matrix\Matrix;
class LU
{
private $luMatrix;
private $rows;
private $columns;
private $pivot = [];
public function __construct(Matrix $matrix)
{
$this->luMatrix = $matrix->toArray();
$this->rows = $matrix->rows;
$this->columns = $matrix->columns;
$this->buildPivot();
}
/**
* Get lower triangular factor.
*
* @return Matrix Lower triangular factor
*/
public function getL(): 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);
}
/**
* Get upper triangular factor.
*
* @return Matrix Upper triangular factor
*/
public function getU(): 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);
}
/**
* Return pivot permutation vector.
*
* @return Matrix Pivot matrix
*/
public function getP(): 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);
}
/**
* Return pivot permutation vector.
*
* @return array Pivot vector
*/
public function getPivot(): array
{
return $this->pivot;
}
/**
* Is the matrix nonsingular?
*
* @return bool true if U, and hence A, is nonsingular
*/
public function isNonsingular(): bool
{
for ($diagonal = 0; $diagonal < $this->columns; ++$diagonal) {
if ($this->luMatrix[$diagonal][$diagonal] === 0.0) {
return false;
}
}
return true;
}
private function buildPivot(): void
{
for ($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($luColumn);
}
}
private function localisedReferenceColumn($column): array
{
$luColumn = [];
for ($row = 0; $row < $this->rows; ++$row) {
$luColumn[$row] = &$this->luMatrix[$row][$column];
}
return $luColumn;
}
private function applyTransformations($column, array $luColumn): void
{
for ($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] -= $sValue;
}
}
private function findPivot($column, array $luColumn): int
{
$pivot = $column;
for ($row = $column + 1; $row < $this->rows; ++$row) {
if (abs($luColumn[$row]) > abs($luColumn[$pivot])) {
$pivot = $row;
}
}
return $pivot;
}
private function pivotExchange($pivot, $column): void
{
for ($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] = $lValue;
}
private function computeMultipliers($diagonal): 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];
}
}
}
private function pivotB(Matrix $B): array
{
$X = [];
foreach ($this->pivot as $rowId) {
$row = $B->getRows($rowId + 1)->toArray();
$X[] = array_pop($row);
}
return $X;
}
/**
* Solve A*X = B.
*
* @param Matrix $B a Matrix with as many rows as A and any number of columns
*
* @throws Exception
*
* @return Matrix X so that L*U*X = B(piv,:)
*/
public function solve(Matrix $B): Matrix
{
if ($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);
}
}
src/Operators/DirectSum.php 0000644 00000003577 15152066446 0011746 0 ustar 00 <?php
namespace Matrix\Operators;
use Matrix\Matrix;
use Matrix\Exception;
class DirectSum extends Operator
{
/**
* Execute the addition
*
* @param mixed $value The matrix or numeric value to add to the current base value
* @return $this The operation object, allowing multiple additions to be chained
* @throws Exception If the provided argument is not appropriate for the operation
*/
public function execute($value): Operator
{
if (is_array($value)) {
$value = new Matrix($value);
}
if ($value instanceof Matrix) {
return $this->directSumMatrix($value);
}
throw new Exception('Invalid argument for addition');
}
/**
* Execute the direct sum for a matrix
*
* @param Matrix $value The numeric value to concatenate/direct sum with the current base value
* @return $this The operation object, allowing multiple additions to be chained
**/
private function directSumMatrix($value): Operator
{
$originalColumnCount = count($this->matrix[0]);
$originalRowCount = count($this->matrix);
$valColumnCount = $value->columns;
$valRowCount = $value->rows;
$value = $value->toArray();
for ($row = 0; $row < $this->rows; ++$row) {
$this->matrix[$row] = array_merge($this->matrix[$row], array_fill(0, $valColumnCount, 0));
}
$this->matrix = array_merge(
$this->matrix,
array_fill(0, $valRowCount, array_fill(0, $originalColumnCount, 0))
);
for ($row = $originalRowCount; $row < $originalRowCount + $valRowCount; ++$row) {
array_splice(
$this->matrix[$row],
$originalColumnCount,
$valColumnCount,
$value[$row - $originalRowCount]
);
}
return $this;
}
}
src/Operators/Multiplication.php 0000644 00000005544 15152066446 0013040 0 ustar 00 <?php
namespace Matrix\Operators;
use Matrix\Matrix;
use \Matrix\Builder;
use Matrix\Exception;
use Throwable;
class Multiplication extends Operator
{
/**
* Execute the multiplication
*
* @param mixed $value The matrix or numeric value to multiply the current base value by
* @throws Exception If the provided argument is not appropriate for the operation
* @return $this The operation object, allowing multiple multiplications to be chained
**/
public function execute($value, string $type = 'multiplication'): Operator
{
if (is_array($value)) {
$value = new Matrix($value);
}
if (is_object($value) && ($value instanceof Matrix)) {
return $this->multiplyMatrix($value, $type);
} elseif (is_numeric($value)) {
return $this->multiplyScalar($value, $type);
}
throw new Exception("Invalid argument for $type");
}
/**
* Execute the multiplication for a scalar
*
* @param mixed $value The numeric value to multiply with the current base value
* @return $this The operation object, allowing multiple mutiplications to be chained
**/
protected function multiplyScalar($value, string $type = 'multiplication'): Operator
{
try {
for ($row = 0; $row < $this->rows; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
$this->matrix[$row][$column] *= $value;
}
}
} catch (Throwable $e) {
throw new Exception("Invalid argument for $type");
}
return $this;
}
/**
* Execute the multiplication for a matrix
*
* @param Matrix $value The numeric value to multiply with the current base value
* @return $this The operation object, allowing multiple mutiplications to be chained
* @throws Exception If the provided argument is not appropriate for the operation
**/
protected function multiplyMatrix(Matrix $value, string $type = 'multiplication'): Operator
{
$this->validateReflectingDimensions($value);
$newRows = $this->rows;
$newColumns = $value->columns;
$matrix = Builder::createFilledMatrix(0, $newRows, $newColumns)
->toArray();
try {
for ($row = 0; $row < $newRows; ++$row) {
for ($column = 0; $column < $newColumns; ++$column) {
$columnData = $value->getColumns($column + 1)->toArray();
foreach ($this->matrix[$row] as $key => $valueData) {
$matrix[$row][$column] += $valueData * $columnData[$key][0];
}
}
}
} catch (Throwable $e) {
throw new Exception("Invalid argument for $type");
}
$this->matrix = $matrix;
return $this;
}
}
src/Operators/Addition.php 0000644 00000004000 15152066446 0011560 0 ustar 00 <?php
namespace Matrix\Operators;
use Matrix\Matrix;
use Matrix\Exception;
class Addition extends Operator
{
/**
* Execute the addition
*
* @param mixed $value The matrix or numeric value to add to the current base value
* @throws Exception If the provided argument is not appropriate for the operation
* @return $this The operation object, allowing multiple additions to be chained
**/
public function execute($value): Operator
{
if (is_array($value)) {
$value = new Matrix($value);
}
if (is_object($value) && ($value instanceof Matrix)) {
return $this->addMatrix($value);
} elseif (is_numeric($value)) {
return $this->addScalar($value);
}
throw new Exception('Invalid argument for addition');
}
/**
* Execute the addition for a scalar
*
* @param mixed $value The numeric value to add to the current base value
* @return $this The operation object, allowing multiple additions to be chained
**/
protected function addScalar($value): Operator
{
for ($row = 0; $row < $this->rows; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
$this->matrix[$row][$column] += $value;
}
}
return $this;
}
/**
* Execute the addition for a matrix
*
* @param Matrix $value The numeric value to add to the current base value
* @return $this The operation object, allowing multiple additions to be chained
* @throws Exception If the provided argument is not appropriate for the operation
**/
protected function addMatrix(Matrix $value): Operator
{
$this->validateMatchingDimensions($value);
for ($row = 0; $row < $this->rows; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
$this->matrix[$row][$column] += $value->getValue($row + 1, $column + 1);
}
}
return $this;
}
}
src/Operators/Subtraction.php 0000644 00000004100 15152066446 0012323 0 ustar 00 <?php
namespace Matrix\Operators;
use Matrix\Matrix;
use Matrix\Exception;
class Subtraction extends Operator
{
/**
* Execute the subtraction
*
* @param mixed $value The matrix or numeric value to subtract from the current base value
* @throws Exception If the provided argument is not appropriate for the operation
* @return $this The operation object, allowing multiple subtractions to be chained
**/
public function execute($value): Operator
{
if (is_array($value)) {
$value = new Matrix($value);
}
if (is_object($value) && ($value instanceof Matrix)) {
return $this->subtractMatrix($value);
} elseif (is_numeric($value)) {
return $this->subtractScalar($value);
}
throw new Exception('Invalid argument for subtraction');
}
/**
* Execute the subtraction for a scalar
*
* @param mixed $value The numeric value to subtracted from the current base value
* @return $this The operation object, allowing multiple additions to be chained
**/
protected function subtractScalar($value): Operator
{
for ($row = 0; $row < $this->rows; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
$this->matrix[$row][$column] -= $value;
}
}
return $this;
}
/**
* Execute the subtraction for a matrix
*
* @param Matrix $value The numeric value to subtract from the current base value
* @return $this The operation object, allowing multiple subtractions to be chained
* @throws Exception If the provided argument is not appropriate for the operation
**/
protected function subtractMatrix(Matrix $value): Operator
{
$this->validateMatchingDimensions($value);
for ($row = 0; $row < $this->rows; ++$row) {
for ($column = 0; $column < $this->columns; ++$column) {
$this->matrix[$row][$column] -= $value->getValue($row + 1, $column + 1);
}
}
return $this;
}
}
src/Operators/Operator.php 0000644 00000003721 15152066446 0011631 0 ustar 00 <?php
namespace Matrix\Operators;
use Matrix\Matrix;
use Matrix\Exception;
abstract class Operator
{
/**
* Stored internally as a 2-dimension array of values
*
* @property mixed[][] $matrix
**/
protected $matrix;
/**
* Number of rows in the matrix
*
* @property integer $rows
**/
protected $rows;
/**
* Number of columns in the matrix
*
* @property integer $columns
**/
protected $columns;
/**
* Create an new handler object for the operation
*
* @param Matrix $matrix The base Matrix object on which the operation will be performed
*/
public function __construct(Matrix $matrix)
{
$this->rows = $matrix->rows;
$this->columns = $matrix->columns;
$this->matrix = $matrix->toArray();
}
/**
* Compare the dimensions of the matrices being operated on to see if they are valid for addition/subtraction
*
* @param Matrix $matrix The second Matrix object on which the operation will be performed
* @throws Exception
*/
protected function validateMatchingDimensions(Matrix $matrix): void
{
if (($this->rows != $matrix->rows) || ($this->columns != $matrix->columns)) {
throw new Exception('Matrices have mismatched dimensions');
}
}
/**
* Compare the dimensions of the matrices being operated on to see if they are valid for multiplication/division
*
* @param Matrix $matrix The second Matrix object on which the operation will be performed
* @throws Exception
*/
protected function validateReflectingDimensions(Matrix $matrix): void
{
if ($this->columns != $matrix->rows) {
throw new Exception('Matrices have mismatched dimensions');
}
}
/**
* Return the result of the operation
*
* @return Matrix
*/
public function result(): Matrix
{
return new Matrix($this->matrix);
}
}
src/Operators/Division.php 0000644 00000001755 15152066446 0011627 0 ustar 00 <?php
namespace Matrix\Operators;
use Matrix\Div0Exception;
use Matrix\Exception;
use \Matrix\Matrix;
use \Matrix\Functions;
class Division extends Multiplication
{
/**
* Execute the division
*
* @param mixed $value The matrix or numeric value to divide the current base value by
* @throws Exception If the provided argument is not appropriate for the operation
* @return $this The operation object, allowing multiple divisions to be chained
**/
public function execute($value, string $type = 'division'): Operator
{
if (is_array($value)) {
$value = new Matrix($value);
}
if (is_object($value) && ($value instanceof Matrix)) {
$value = Functions::inverse($value, $type);
return $this->multiplyMatrix($value, $type);
} elseif (is_numeric($value)) {
return $this->multiplyScalar(1 / $value, $type);
}
throw new Exception('Invalid argument for division');
}
}
src/Matrix.php 0000644 00000026450 15152066446 0007330 0 ustar 00 <?php
/**
*
* Class for the management of Matrices
*
* @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Matrix;
use Generator;
use Matrix\Decomposition\LU;
use Matrix\Decomposition\QR;
/**
* Matrix object.
*
* @package Matrix
*
* @property-read int $rows The number of rows in the matrix
* @property-read int $columns The number of columns in the matrix
* @method Matrix antidiagonal()
* @method Matrix adjoint()
* @method Matrix cofactors()
* @method float determinant()
* @method Matrix diagonal()
* @method Matrix identity()
* @method Matrix inverse()
* @method Matrix minors()
* @method float trace()
* @method Matrix transpose()
* @method Matrix add(...$matrices)
* @method Matrix subtract(...$matrices)
* @method Matrix multiply(...$matrices)
* @method Matrix divideby(...$matrices)
* @method Matrix divideinto(...$matrices)
* @method Matrix directsum(...$matrices)
*/
class Matrix
{
protected $rows;
protected $columns;
protected $grid = [];
/*
* Create a new Matrix object from an array of values
*
* @param array $grid
*/
final public function __construct(array $grid)
{
$this->buildFromArray(array_values($grid));
}
/*
* Create a new Matrix object from an array of values
*
* @param array $grid
*/
protected function buildFromArray(array $grid): void
{
$this->rows = count($grid);
$columns = array_reduce(
$grid,
function ($carry, $value) {
return max($carry, is_array($value) ? count($value) : 1);
}
);
$this->columns = $columns;
array_walk(
$grid,
function (&$value) use ($columns) {
if (!is_array($value)) {
$value = [$value];
}
$value = array_pad(array_values($value), $columns, null);
}
);
$this->grid = $grid;
}
/**
* Validate that a row number is a positive integer
*
* @param int $row
* @return int
* @throws Exception
*/
public static function validateRow(int $row): int
{
if ((!is_numeric($row)) || (intval($row) < 1)) {
throw new Exception('Invalid Row');
}
return (int)$row;
}
/**
* Validate that a column number is a positive integer
*
* @param int $column
* @return int
* @throws Exception
*/
public static function validateColumn(int $column): int
{
if ((!is_numeric($column)) || (intval($column) < 1)) {
throw new Exception('Invalid Column');
}
return (int)$column;
}
/**
* Validate that a row number falls within the set of rows for this matrix
*
* @param int $row
* @return int
* @throws Exception
*/
protected function validateRowInRange(int $row): int
{
$row = static::validateRow($row);
if ($row > $this->rows) {
throw new Exception('Requested Row exceeds matrix size');
}
return $row;
}
/**
* Validate that a column number falls within the set of columns for this matrix
*
* @param int $column
* @return int
* @throws Exception
*/
protected function validateColumnInRange(int $column): int
{
$column = static::validateColumn($column);
if ($column > $this->columns) {
throw new Exception('Requested Column exceeds matrix size');
}
return $column;
}
/**
* Return a new matrix as a subset of rows from this matrix, starting at row number $row, and $rowCount rows
* A $rowCount value of 0 will return all rows of the matrix from $row
* A negative $rowCount value will return rows until that many rows from the end of the matrix
*
* Note that row numbers start from 1, not from 0
*
* @param int $row
* @param int $rowCount
* @return static
* @throws Exception
*/
public function getRows(int $row, int $rowCount = 1): Matrix
{
$row = $this->validateRowInRange($row);
if ($rowCount === 0) {
$rowCount = $this->rows - $row + 1;
}
return new static(array_slice($this->grid, $row - 1, (int)$rowCount));
}
/**
* Return a new matrix as a subset of columns from this matrix, starting at column number $column, and $columnCount columns
* A $columnCount value of 0 will return all columns of the matrix from $column
* A negative $columnCount value will return columns until that many columns from the end of the matrix
*
* Note that column numbers start from 1, not from 0
*
* @param int $column
* @param int $columnCount
* @return Matrix
* @throws Exception
*/
public function getColumns(int $column, int $columnCount = 1): Matrix
{
$column = $this->validateColumnInRange($column);
if ($columnCount < 1) {
$columnCount = $this->columns + $columnCount - $column + 1;
}
$grid = [];
for ($i = $column - 1; $i < $column + $columnCount - 1; ++$i) {
$grid[] = array_column($this->grid, $i);
}
return (new static($grid))->transpose();
}
/**
* Return a new matrix as a subset of rows from this matrix, dropping rows starting at row number $row,
* and $rowCount rows
* A negative $rowCount value will drop rows until that many rows from the end of the matrix
* A $rowCount value of 0 will remove all rows of the matrix from $row
*
* Note that row numbers start from 1, not from 0
*
* @param int $row
* @param int $rowCount
* @return static
* @throws Exception
*/
public function dropRows(int $row, int $rowCount = 1): Matrix
{
$this->validateRowInRange($row);
if ($rowCount === 0) {
$rowCount = $this->rows - $row + 1;
}
$grid = $this->grid;
array_splice($grid, $row - 1, (int)$rowCount);
return new static($grid);
}
/**
* Return a new matrix as a subset of columns from this matrix, dropping columns starting at column number $column,
* and $columnCount columns
* A negative $columnCount value will drop columns until that many columns from the end of the matrix
* A $columnCount value of 0 will remove all columns of the matrix from $column
*
* Note that column numbers start from 1, not from 0
*
* @param int $column
* @param int $columnCount
* @return static
* @throws Exception
*/
public function dropColumns(int $column, int $columnCount = 1): Matrix
{
$this->validateColumnInRange($column);
if ($columnCount < 1) {
$columnCount = $this->columns + $columnCount - $column + 1;
}
$grid = $this->grid;
array_walk(
$grid,
function (&$row) use ($column, $columnCount) {
array_splice($row, $column - 1, (int)$columnCount);
}
);
return new static($grid);
}
/**
* Return a value from this matrix, from the "cell" identified by the row and column numbers
* Note that row and column numbers start from 1, not from 0
*
* @param int $row
* @param int $column
* @return mixed
* @throws Exception
*/
public function getValue(int $row, int $column)
{
$row = $this->validateRowInRange($row);
$column = $this->validateColumnInRange($column);
return $this->grid[$row - 1][$column - 1];
}
/**
* Returns a Generator that will yield each row of the matrix in turn as a vector matrix
* or the value of each cell if the matrix is a column vector
*
* @return Generator|Matrix[]|mixed[]
*/
public function rows(): Generator
{
foreach ($this->grid as $i => $row) {
yield $i + 1 => ($this->columns == 1)
? $row[0]
: new static([$row]);
}
}
/**
* Returns a Generator that will yield each column of the matrix in turn as a vector matrix
* or the value of each cell if the matrix is a row vector
*
* @return Generator|Matrix[]|mixed[]
*/
public function columns(): Generator
{
for ($i = 0; $i < $this->columns; ++$i) {
yield $i + 1 => ($this->rows == 1)
? $this->grid[0][$i]
: new static(array_column($this->grid, $i));
}
}
/**
* Identify if the row and column dimensions of this matrix are equal,
* i.e. if it is a "square" matrix
*
* @return bool
*/
public function isSquare(): bool
{
return $this->rows === $this->columns;
}
/**
* Identify if this matrix is a vector
* i.e. if it comprises only a single row or a single column
*
* @return bool
*/
public function isVector(): bool
{
return $this->rows === 1 || $this->columns === 1;
}
/**
* Return the matrix as a 2-dimensional array
*
* @return array
*/
public function toArray(): array
{
return $this->grid;
}
/**
* Solve A*X = B.
*
* @param Matrix $B Right hand side
*
* @throws Exception
*
* @return Matrix ... Solution if A is square, least squares solution otherwise
*/
public function solve(Matrix $B): Matrix
{
if ($this->columns === $this->rows) {
return (new LU($this))->solve($B);
}
return (new QR($this))->solve($B);
}
protected static $getters = [
'rows',
'columns',
];
/**
* Access specific properties as read-only (no setters)
*
* @param string $propertyName
* @return mixed
* @throws Exception
*/
public function __get(string $propertyName)
{
$propertyName = strtolower($propertyName);
// Test for function calls
if (in_array($propertyName, self::$getters)) {
return $this->$propertyName;
}
throw new Exception('Property does not exist');
}
protected static $functions = [
'adjoint',
'antidiagonal',
'cofactors',
'determinant',
'diagonal',
'identity',
'inverse',
'minors',
'trace',
'transpose',
];
protected static $operations = [
'add',
'subtract',
'multiply',
'divideby',
'divideinto',
'directsum',
];
/**
* Returns the result of the function call or operation
*
* @param string $functionName
* @param mixed[] $arguments
* @return Matrix|float
* @throws Exception
*/
public function __call(string $functionName, $arguments)
{
$functionName = strtolower(str_replace('_', '', $functionName));
// Test for function calls
if (in_array($functionName, self::$functions, true)) {
return Functions::$functionName($this, ...$arguments);
}
// Test for operation calls
if (in_array($functionName, self::$operations, true)) {
return Operations::$functionName($this, ...$arguments);
}
throw new Exception('Function or Operation does not exist');
}
}
