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<?php |
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|
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/** |
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* |
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* Class for the management of Complex numbers |
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* |
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* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex) |
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* @license https://opensource.org/licenses/MIT MIT |
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*/ |
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namespace Complex; |
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|
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/** |
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* Complex Number object. |
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* |
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* @package Complex |
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* |
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* @method float abs() |
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* @method Complex acos() |
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* @method Complex acosh() |
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* @method Complex acot() |
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* @method Complex acoth() |
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* @method Complex acsc() |
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* @method Complex acsch() |
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* @method float argument() |
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* @method Complex asec() |
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* @method Complex asech() |
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* @method Complex asin() |
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* @method Complex asinh() |
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* @method Complex atan() |
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* @method Complex atanh() |
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* @method Complex conjugate() |
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* @method Complex cos() |
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* @method Complex cosh() |
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* @method Complex cot() |
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* @method Complex coth() |
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* @method Complex csc() |
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* @method Complex csch() |
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* @method Complex exp() |
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* @method Complex inverse() |
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* @method Complex ln() |
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* @method Complex log2() |
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* @method Complex log10() |
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* @method Complex negative() |
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* @method Complex pow(int|float $power) |
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* @method float rho() |
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* @method Complex sec() |
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* @method Complex sech() |
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* @method Complex sin() |
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* @method Complex sinh() |
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* @method Complex sqrt() |
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* @method Complex tan() |
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* @method Complex tanh() |
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* @method float theta() |
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* @method Complex add(...$complexValues) |
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* @method Complex subtract(...$complexValues) |
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* @method Complex multiply(...$complexValues) |
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* @method Complex divideby(...$complexValues) |
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* @method Complex divideinto(...$complexValues) |
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*/ |
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class Complex |
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{ |
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/** |
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* @constant Euler's Number. |
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*/ |
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const EULER = 2.7182818284590452353602874713526624977572; |
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|
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/** |
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* @constant Regexp to split an input string into real and imaginary components and suffix |
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*/ |
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const NUMBER_SPLIT_REGEXP = |
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'` ^ |
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( # Real part |
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[-+]?(\d+\.?\d*|\d*\.?\d+) # Real value (integer or float) |
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([Ee][-+]?[0-2]?\d{1,3})? # Optional real exponent for scientific format |
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) |
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( # Imaginary part |
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[-+]?(\d+\.?\d*|\d*\.?\d+) # Imaginary value (integer or float) |
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([Ee][-+]?[0-2]?\d{1,3})? # Optional imaginary exponent for scientific format |
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)? |
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( # Imaginary part is optional |
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([-+]?) # Imaginary (implicit 1 or -1) only |
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([ij]?) # Imaginary i or j - depending on whether mathematical or engineering |
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) |
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$`uix'; |
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|
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/** |
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* @var float $realPart The value of of this complex number on the real plane. |
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*/ |
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protected $realPart = 0.0; |
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|
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/** |
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* @var float $imaginaryPart The value of of this complex number on the imaginary plane. |
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*/ |
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protected $imaginaryPart = 0.0; |
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|
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/** |
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* @var string $suffix The suffix for this complex number (i or j). |
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*/ |
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protected $suffix; |
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|
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|
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/** |
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* Validates whether the argument is a valid complex number, converting scalar or array values if possible |
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* |
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* @param mixed $complexNumber The value to parse |
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* @return array |
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* @throws Exception If the argument isn't a Complex number or cannot be converted to one |
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*/ |
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private static function parseComplex($complexNumber) |
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{ |
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// Test for real number, with no imaginary part |
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if (is_numeric($complexNumber)) { |
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return [$complexNumber, 0, null]; |
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} |
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|
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// Fix silly human errors |
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$complexNumber = str_replace( |
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['+-', '-+', '++', '--'], |
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['-', '-', '+', '+'], |
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$complexNumber |
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); |
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|
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// Basic validation of string, to parse out real and imaginary parts, and any suffix |
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$validComplex = preg_match( |
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self::NUMBER_SPLIT_REGEXP, |
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$complexNumber, |
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$complexParts |
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); |
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|
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if (!$validComplex) { |
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// Neither real nor imaginary part, so test to see if we actually have a suffix |
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$validComplex = preg_match('/^([\-\+]?)([ij])$/ui', $complexNumber, $complexParts); |
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if (!$validComplex) { |
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throw new Exception('Invalid complex number'); |
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} |
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// We have a suffix, so set the real to 0, the imaginary to either 1 or -1 (as defined by the sign) |
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$imaginary = 1; |
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if ($complexParts[1] === '-') { |
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$imaginary = 0 - $imaginary; |
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} |
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return [0, $imaginary, $complexParts[2]]; |
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} |
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|
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// If we don't have an imaginary part, identify whether it should be +1 or -1... |
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if (($complexParts[4] === '') && ($complexParts[9] !== '')) { |
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if ($complexParts[7] !== $complexParts[9]) { |
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$complexParts[4] = 1; |
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if ($complexParts[8] === '-') { |
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$complexParts[4] = -1; |
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} |
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} else { |
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// ... or if we have only the real and no imaginary part |
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// (in which case our real should be the imaginary) |
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$complexParts[4] = $complexParts[1]; |
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$complexParts[1] = 0; |
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} |
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} |
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|
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// Return real and imaginary parts and suffix as an array, and set a default suffix if user input lazily |
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return [ |
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$complexParts[1], |
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$complexParts[4], |
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!empty($complexParts[9]) ? $complexParts[9] : 'i' |
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]; |
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} |
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|
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|
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public function __construct($realPart = 0.0, $imaginaryPart = null, $suffix = 'i') |
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{ |
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if ($imaginaryPart === null) { |
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if (is_array($realPart)) { |
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// We have an array of (potentially) real and imaginary parts, and any suffix |
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list ($realPart, $imaginaryPart, $suffix) = array_values($realPart) + [0.0, 0.0, 'i']; |
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} elseif ((is_string($realPart)) || (is_numeric($realPart))) { |
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// We've been given a string to parse to extract the real and imaginary parts, and any suffix |
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list($realPart, $imaginaryPart, $suffix) = self::parseComplex($realPart); |
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} |
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} |
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if ($imaginaryPart <> 0.0 && empty($suffix)) { |
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$suffix = 'i'; |
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} |
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|
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// Set parsed values in our properties |
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$this->realPart = (float) $realPart; |
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$this->imaginaryPart = (float) $imaginaryPart; |
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$this->suffix = strtolower($suffix); |
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} |
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|
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/** |
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* Gets the real part of this complex number |
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* |
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* @return Float |
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*/ |
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public function getReal() |
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{ |
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return $this->realPart; |
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} |
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|
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/** |
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* Gets the imaginary part of this complex number |
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* |
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* @return Float |
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*/ |
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public function getImaginary() |
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{ |
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return $this->imaginaryPart; |
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} |
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|
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/** |
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* Gets the suffix of this complex number |
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* |
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* @return String |
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*/ |
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public function getSuffix() |
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{ |
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return $this->suffix; |
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} |
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|
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/** |
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* Returns true if this is a real value, false if a complex value |
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* |
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* @return Bool |
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*/ |
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public function isReal() |
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{ |
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return $this->imaginaryPart == 0.0; |
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} |
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|
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/** |
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* Returns true if this is a complex value, false if a real value |
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* |
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* @return Bool |
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*/ |
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public function isComplex() |
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{ |
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return !$this->isReal(); |
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} |
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|
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public function format() |
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{ |
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$str = ""; |
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if ($this->imaginaryPart != 0.0) { |
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if (\abs($this->imaginaryPart) != 1.0) { |
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$str .= $this->imaginaryPart . $this->suffix; |
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} else { |
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$str .= (($this->imaginaryPart < 0.0) ? '-' : '') . $this->suffix; |
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} |
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} |
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if ($this->realPart != 0.0) { |
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if (($str) && ($this->imaginaryPart > 0.0)) { |
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$str = "+" . $str; |
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} |
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$str = $this->realPart . $str; |
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} |
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if (!$str) { |
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$str = "0.0"; |
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} |
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|
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return $str; |
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} |
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|
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public function __toString() |
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{ |
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return $this->format(); |
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} |
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|
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/** |
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* Validates whether the argument is a valid complex number, converting scalar or array values if possible |
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* |
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* @param mixed $complex The value to validate |
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* @return Complex |
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* @throws Exception If the argument isn't a Complex number or cannot be converted to one |
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*/ |
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public static function validateComplexArgument($complex) |
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{ |
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if (is_scalar($complex) || is_array($complex)) { |
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$complex = new Complex($complex); |
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} elseif (!is_object($complex) || !($complex instanceof Complex)) { |
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throw new Exception('Value is not a valid complex number'); |
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} |
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|
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return $complex; |
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} |
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|
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/** |
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* Returns the reverse of this complex number |
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* |
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* @return Complex |
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*/ |
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public function reverse() |
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{ |
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return new Complex( |
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$this->imaginaryPart, |
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$this->realPart, |
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($this->realPart == 0.0) ? null : $this->suffix |
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); |
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} |
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|
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public function invertImaginary() |
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{ |
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return new Complex( |
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$this->realPart, |
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$this->imaginaryPart * -1, |
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($this->imaginaryPart == 0.0) ? null : $this->suffix |
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); |
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} |
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|
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public function invertReal() |
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{ |
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return new Complex( |
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$this->realPart * -1, |
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$this->imaginaryPart, |
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($this->imaginaryPart == 0.0) ? null : $this->suffix |
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); |
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} |
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|
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protected static $functions = [ |
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'abs', |
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'acos', |
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'acosh', |
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'acot', |
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'acoth', |
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'acsc', |
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'acsch', |
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'argument', |
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'asec', |
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'asech', |
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'asin', |
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'asinh', |
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'atan', |
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'atanh', |
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'conjugate', |
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'cos', |
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'cosh', |
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'cot', |
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'coth', |
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'csc', |
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'csch', |
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'exp', |
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'inverse', |
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'ln', |
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'log2', |
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'log10', |
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'negative', |
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'pow', |
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'rho', |
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'sec', |
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'sech', |
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'sin', |
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'sinh', |
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'sqrt', |
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'tan', |
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'tanh', |
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'theta', |
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]; |
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|
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protected static $operations = [ |
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'add', |
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'subtract', |
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'multiply', |
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'divideby', |
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'divideinto', |
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]; |
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|
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/** |
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* Returns the result of the function call or operation |
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* |
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* @return Complex|float |
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* @throws Exception|\InvalidArgumentException |
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*/ |
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public function __call($functionName, $arguments) |
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{ |
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$functionName = strtolower(str_replace('_', '', $functionName)); |
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|
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// Test for function calls |
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if (in_array($functionName, self::$functions)) { |
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$functionName = "\\" . __NAMESPACE__ . "\\{$functionName}"; |
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return $functionName($this, ...$arguments); |
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} |
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// Test for operation calls |
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if (in_array($functionName, self::$operations)) { |
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$functionName = "\\" . __NAMESPACE__ . "\\{$functionName}"; |
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return $functionName($this, ...$arguments); |
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} |
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throw new Exception('Function or Operation does not exist'); |
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} |
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} |
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|
