391 lines
11 KiB
PHP
391 lines
11 KiB
PHP
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<?php
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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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* 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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* @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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* @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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* @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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* @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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* 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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// 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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// 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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$complexParts
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);
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if (!$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, $complexParts[2]];
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}
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// If we don't have an imaginary part, identify whether it should be +1 or -1...
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if (($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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// 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]) ? $complexParts[9] : 'i'
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];
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}
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public function __construct($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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$suffix = 'i';
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} elseif ($imaginaryPart == 0.0 && !empty($suffix)) {
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$suffix = '';
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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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* 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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* 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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* 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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* 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 $this->imaginaryPart == 0.0;
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}
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/**
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* Returns true if this is a complex value, false if a real value
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*
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* @return Bool
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*/
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public function isComplex()
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{
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return !$this->isReal();
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}
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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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return $str;
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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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* 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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return $complex;
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}
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/**
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* Returns the reverse of this complex number
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*
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* @return Complex
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*/
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public function reverse()
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{
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return new Complex(
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$this->imaginaryPart,
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$this->realPart,
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($this->realPart == 0.0) ? null : $this->suffix
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);
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}
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public function invertImaginary()
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{
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return new Complex(
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$this->realPart,
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$this->imaginaryPart * -1,
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($this->imaginaryPart == 0.0) ? null : $this->suffix
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);
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}
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public function invertReal()
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{
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return new Complex(
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$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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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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protected static $operations = [
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'add',
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'subtract',
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'multiply',
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'divideby',
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'divideinto',
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];
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/**
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* Returns the result of the function call or operation
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*
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* @return Complex|float
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* @throws Exception|\InvalidArgumentException
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*/
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public function __call($functionName, $arguments)
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{
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$functionName = strtolower(str_replace('_', '', $functionName));
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// Test for function calls
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if (in_array($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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