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<?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'); } }