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package and depencies

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This commit is contained in:
RafficMohammed
2023-01-08 02:57:24 +05:30
parent d5332eb421
commit 1d54b8bc7f
4309 changed files with 193331 additions and 172289 deletions
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6
vendor/markbaker/complex/classes/src/Complex.php vendored
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@@ -377,13 +377,11 @@ class Complex
// Test for function calls
if (in_array($functionName, self::$functions, true)) {
$functionName = "\\" . __NAMESPACE__ . "\\{$functionName}";
return $functionName($this, ...$arguments);
return Functions::$functionName($this, ...$arguments);
}
// Test for operation calls
if (in_array($functionName, self::$operations, true)) {
$functionName = "\\" . __NAMESPACE__ . "\\{$functionName}";
return $functionName($this, ...$arguments);
return Operations::$functionName($this, ...$arguments);
}
throw new Exception('Complex Function or Operation does not exist');
}

823
vendor/markbaker/complex/classes/src/Functions.php vendored Normal file
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@@ -0,0 +1,823 @@
<?php
namespace Complex;
use InvalidArgumentException;
class Functions
{
/**
* Returns the absolute value (modulus) of a complex number.
* Also known as the rho of the complex number, i.e. the distance/radius
* from the centrepoint to the representation of the number in polar coordinates.
*
* This function is a synonym for rho()
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The absolute (or rho) value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*
* @see rho
*
*/
public static function abs($complex): float
{
return self::rho($complex);
}
/**
* Returns the inverse cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function acos($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex)));
$adjust = new Complex(
$complex->getReal() - $invsqrt->getImaginary(),
$complex->getImaginary() + $invsqrt->getReal()
);
$log = self::ln($adjust);
return new Complex(
$log->getImaginary(),
-1 * $log->getReal()
);
}
/**
* Returns the inverse hyperbolic cosine of a complex number.
*
* Formula from Wolfram Alpha:
* cosh^(-1)z = ln(z + sqrt(z + 1) sqrt(z - 1)).
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function acosh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal() && ($complex->getReal() > 1)) {
return new Complex(\acosh($complex->getReal()));
}
$acosh = self::ln(
Operations::add(
$complex,
Operations::multiply(
self::sqrt(Operations::add($complex, 1)),
self::sqrt(Operations::subtract($complex, 1))
)
)
);
return $acosh;
}
/**
* Returns the inverse cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function acot($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return self::atan(self::inverse($complex));
}
/**
* Returns the inverse hyperbolic cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function acoth($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return self::atanh(self::inverse($complex));
}
/**
* Returns the inverse cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function acsc($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::asin(self::inverse($complex));
}
/**
* Returns the inverse hyperbolic cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function acsch($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::asinh(self::inverse($complex));
}
/**
* Returns the argument of a complex number.
* Also known as the theta of the complex number, i.e. the angle in radians
* from the real axis to the representation of the number in polar coordinates.
*
* This function is a synonym for theta()
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The argument (or theta) value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*
* @see theta
*/
public static function argument($complex): float
{
return self::theta($complex);
}
/**
* Returns the inverse secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function asec($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::acos(self::inverse($complex));
}
/**
* Returns the inverse hyperbolic secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function asech($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::acosh(self::inverse($complex));
}
/**
* Returns the inverse sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function asin($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex)));
$adjust = new Complex(
$invsqrt->getReal() - $complex->getImaginary(),
$invsqrt->getImaginary() + $complex->getReal()
);
$log = self::ln($adjust);
return new Complex(
$log->getImaginary(),
-1 * $log->getReal()
);
}
/**
* Returns the inverse hyperbolic sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function asinh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal() && ($complex->getReal() > 1)) {
return new Complex(\asinh($complex->getReal()));
}
$asinh = clone $complex;
$asinh = $asinh->reverse()
->invertReal();
$asinh = self::asin($asinh);
return $asinh->reverse()
->invertImaginary();
}
/**
* Returns the inverse tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function atan($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\atan($complex->getReal()));
}
$t1Value = new Complex(-1 * $complex->getImaginary(), $complex->getReal());
$uValue = new Complex(1, 0);
$d1Value = clone $uValue;
$d1Value = Operations::subtract($d1Value, $t1Value);
$d2Value = Operations::add($t1Value, $uValue);
$uResult = $d1Value->divideBy($d2Value);
$uResult = self::ln($uResult);
$realMultiplier = -0.5;
$imaginaryMultiplier = 0.5;
if (abs($uResult->getImaginary()) === M_PI) {
// If we have an imaginary value at the max or min (PI or -PI), then we need to ensure
// that the primary is assigned for the correct quadrant.
$realMultiplier = (
($uResult->getImaginary() === M_PI && $uResult->getReal() > 0.0) ||
($uResult->getImaginary() === -M_PI && $uResult->getReal() < 0.0)
) ? 0.5 : -0.5;
}
return new Complex(
$uResult->getImaginary() * $realMultiplier,
$uResult->getReal() * $imaginaryMultiplier,
$complex->getSuffix()
);
}
/**
* Returns the inverse hyperbolic tangent of a complex number.
*
* Formula from Wolfram Alpha:
* tanh^(-1)z = 1/2 [ln(1 + z) - ln(1 - z)].
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function atanh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
$real = $complex->getReal();
if ($real >= -1.0 && $real <= 1.0) {
return new Complex(\atanh($real));
} else {
return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2));
}
}
$atanh = Operations::multiply(
Operations::subtract(
self::ln(Operations::add(1.0, $complex)),
self::ln(Operations::subtract(1.0, $complex))
),
0.5
);
return $atanh;
}
/**
* Returns the complex conjugate of a complex number
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The conjugate of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function conjugate($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return new Complex(
$complex->getReal(),
-1 * $complex->getImaginary(),
$complex->getSuffix()
);
}
/**
* Returns the cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function cos($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\cos($complex->getReal()));
}
return self::conjugate(
new Complex(
\cos($complex->getReal()) * \cosh($complex->getImaginary()),
\sin($complex->getReal()) * \sinh($complex->getImaginary()),
$complex->getSuffix()
)
);
}
/**
* Returns the hyperbolic cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function cosh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\cosh($complex->getReal()));
}
return new Complex(
\cosh($complex->getReal()) * \cos($complex->getImaginary()),
\sinh($complex->getReal()) * \sin($complex->getImaginary()),
$complex->getSuffix()
);
}
/**
* Returns the cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function cot($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::inverse(self::tan($complex));
}
/**
* Returns the hyperbolic cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function coth($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return self::inverse(self::tanh($complex));
}
/**
* Returns the cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function csc($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::inverse(self::sin($complex));
}
/**
* Returns the hyperbolic cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function csch($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return self::inverse(self::sinh($complex));
}
/**
* Returns the exponential of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The exponential of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function exp($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && (\abs($complex->getImaginary()) == M_PI)) {
return new Complex(-1.0, 0.0);
}
$rho = \exp($complex->getReal());
return new Complex(
$rho * \cos($complex->getImaginary()),
$rho * \sin($complex->getImaginary()),
$complex->getSuffix()
);
}
/**
* Returns the inverse of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws InvalidArgumentException If function would result in a division by zero
*/
public static function inverse($complex): Complex
{
$complex = clone Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
throw new InvalidArgumentException('Division by zero');
}
return $complex->divideInto(1.0);
}
/**
* Returns the natural logarithm of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The natural logarithm of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws InvalidArgumentException If the real and the imaginary parts are both zero
*/
public static function ln($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
throw new InvalidArgumentException();
}
return new Complex(
\log(self::rho($complex)),
self::theta($complex),
$complex->getSuffix()
);
}
/**
* Returns the base-2 logarithm of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The base-2 logarithm of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws InvalidArgumentException If the real and the imaginary parts are both zero
*/
public static function log2($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
throw new InvalidArgumentException();
} elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
return new Complex(\log($complex->getReal(), 2), 0.0, $complex->getSuffix());
}
return self::ln($complex)
->multiply(\log(Complex::EULER, 2));
}
/**
* Returns the common logarithm (base 10) of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The common logarithm (base 10) of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws InvalidArgumentException If the real and the imaginary parts are both zero
*/
public static function log10($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
throw new InvalidArgumentException();
} elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
return new Complex(\log10($complex->getReal()), 0.0, $complex->getSuffix());
}
return self::ln($complex)
->multiply(\log10(Complex::EULER));
}
/**
* Returns the negative of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The negative value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*
* @see rho
*
*/
public static function negative($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return new Complex(
-1 * $complex->getReal(),
-1 * $complex->getImaginary(),
$complex->getSuffix()
);
}
/**
* Returns a complex number raised to a power.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @param float|integer $power The power to raise this value to
* @return Complex The complex argument raised to the real power.
* @throws Exception If the power argument isn't a valid real
*/
public static function pow($complex, $power): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (!is_numeric($power)) {
throw new Exception('Power argument must be a real number');
}
if ($complex->getImaginary() == 0.0 && $complex->getReal() >= 0.0) {
return new Complex(\pow($complex->getReal(), $power));
}
$rValue = \sqrt(($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary()));
$rPower = \pow($rValue, $power);
$theta = $complex->argument() * $power;
if ($theta == 0) {
return new Complex(1);
}
return new Complex($rPower * \cos($theta), $rPower * \sin($theta), $complex->getSuffix());
}
/**
* Returns the rho of a complex number.
* This is the distance/radius from the centrepoint to the representation of the number in polar coordinates.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The rho value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function rho($complex): float
{
$complex = Complex::validateComplexArgument($complex);
return \sqrt(
($complex->getReal() * $complex->getReal()) +
($complex->getImaginary() * $complex->getImaginary())
);
}
/**
* Returns the secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function sec($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return self::inverse(self::cos($complex));
}
/**
* Returns the hyperbolic secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function sech($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return self::inverse(self::cosh($complex));
}
/**
* Returns the sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function sin($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\sin($complex->getReal()));
}
return new Complex(
\sin($complex->getReal()) * \cosh($complex->getImaginary()),
\cos($complex->getReal()) * \sinh($complex->getImaginary()),
$complex->getSuffix()
);
}
/**
* Returns the hyperbolic sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function sinh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\sinh($complex->getReal()));
}
return new Complex(
\sinh($complex->getReal()) * \cos($complex->getImaginary()),
\cosh($complex->getReal()) * \sin($complex->getImaginary()),
$complex->getSuffix()
);
}
/**
* Returns the square root of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The Square root of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function sqrt($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$theta = self::theta($complex);
$delta1 = \cos($theta / 2);
$delta2 = \sin($theta / 2);
$rho = \sqrt(self::rho($complex));
return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
}
/**
* Returns the tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws InvalidArgumentException If function would result in a division by zero
*/
public static function tan($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\tan($complex->getReal()));
}
$real = $complex->getReal();
$imaginary = $complex->getImaginary();
$divisor = 1 + \pow(\tan($real), 2) * \pow(\tanh($imaginary), 2);
if ($divisor == 0.0) {
throw new InvalidArgumentException('Division by zero');
}
return new Complex(
\pow(self::sech($imaginary)->getReal(), 2) * \tan($real) / $divisor,
\pow(self::sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor,
$complex->getSuffix()
);
}
/**
* Returns the hyperbolic tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
public static function tanh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$real = $complex->getReal();
$imaginary = $complex->getImaginary();
$divisor = \cos($imaginary) * \cos($imaginary) + \sinh($real) * \sinh($real);
if ($divisor == 0.0) {
throw new InvalidArgumentException('Division by zero');
}
return new Complex(
\sinh($real) * \cosh($real) / $divisor,
0.5 * \sin(2 * $imaginary) / $divisor,
$complex->getSuffix()
);
}
/**
* Returns the theta of a complex number.
* This is the angle in radians from the real axis to the representation of the number in polar coordinates.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The theta value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
public static function theta($complex): float
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0) {
if ($complex->isReal()) {
return 0.0;
} elseif ($complex->getImaginary() < 0.0) {
return M_PI / -2;
}
return M_PI / 2;
} elseif ($complex->getReal() > 0.0) {
return \atan($complex->getImaginary() / $complex->getReal());
} elseif ($complex->getImaginary() < 0.0) {
return -(M_PI - \atan(\abs($complex->getImaginary()) / \abs($complex->getReal())));
}
return M_PI - \atan($complex->getImaginary() / \abs($complex->getReal()));
}
}

210
vendor/markbaker/complex/classes/src/Operations.php vendored Normal file
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@@ -0,0 +1,210 @@
<?php
namespace Complex;
use InvalidArgumentException;
class Operations
{
/**
* Adds two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to add
* @return Complex
*/
public static function add(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
$real = $result->getReal() + $complex->getReal();
$imaginary = $result->getImaginary() + $complex->getImaginary();
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
/**
* Divides two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to divide
* @return Complex
*/
public static function divideby(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
throw new InvalidArgumentException('Division by zero');
}
$delta1 = ($result->getReal() * $complex->getReal()) +
($result->getImaginary() * $complex->getImaginary());
$delta2 = ($result->getImaginary() * $complex->getReal()) -
($result->getReal() * $complex->getImaginary());
$delta3 = ($complex->getReal() * $complex->getReal()) +
($complex->getImaginary() * $complex->getImaginary());
$real = $delta1 / $delta3;
$imaginary = $delta2 / $delta3;
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
/**
* Divides two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to divide
* @return Complex
*/
public static function divideinto(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
if ($result->getReal() == 0.0 && $result->getImaginary() == 0.0) {
throw new InvalidArgumentException('Division by zero');
}
$delta1 = ($complex->getReal() * $result->getReal()) +
($complex->getImaginary() * $result->getImaginary());
$delta2 = ($complex->getImaginary() * $result->getReal()) -
($complex->getReal() * $result->getImaginary());
$delta3 = ($result->getReal() * $result->getReal()) +
($result->getImaginary() * $result->getImaginary());
$real = $delta1 / $delta3;
$imaginary = $delta2 / $delta3;
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
/**
* Multiplies two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to multiply
* @return Complex
*/
public static function multiply(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
$real = ($result->getReal() * $complex->getReal()) -
($result->getImaginary() * $complex->getImaginary());
$imaginary = ($result->getReal() * $complex->getImaginary()) +
($result->getImaginary() * $complex->getReal());
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
/**
* Subtracts two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to subtract
* @return Complex
*/
public static function subtract(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
$real = $result->getReal() - $complex->getReal();
$imaginary = $result->getImaginary() - $complex->getImaginary();
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
}

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<?php
/**
*
* Function code for the complex abs() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the absolute value (modulus) of a complex number.
* Also known as the rho of the complex number, i.e. the distance/radius
* from the centrepoint to the representation of the number in polar coordinates.
*
* This function is a synonym for rho()
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The absolute (or rho) value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*
* @see rho
*
*/
if (!function_exists(__NAMESPACE__ . '\\abs')) {
function abs($complex): float
{
return rho($complex);
}
}

40
vendor/markbaker/complex/classes/src/functions/acos.php vendored
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<?php
/**
*
* Function code for the complex acos() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\acos')) {
function acos($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$square = clone $complex;
$square = multiply($square, $complex);
$invsqrt = new Complex(1.0);
$invsqrt = subtract($invsqrt, $square);
$invsqrt = sqrt($invsqrt);
$adjust = new Complex(
$complex->getReal() - $invsqrt->getImaginary(),
$complex->getImaginary() + $invsqrt->getReal()
);
$log = ln($adjust);
return new Complex(
$log->getImaginary(),
-1 * $log->getReal()
);
}
}

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<?php
/**
*
* Function code for the complex acosh() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse hyperbolic cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\acosh')) {
function acosh($complex)
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal() && ($complex->getReal() > 1)) {
return new Complex(\acosh($complex->getReal()));
}
$acosh = acos($complex)
->reverse();
if ($acosh->getReal() < 0.0) {
$acosh = $acosh->invertReal();
}
return $acosh;
}
}

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<?php
/**
*
* Function code for the complex acot() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\acot')) {
function acot($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return atan(inverse($complex));
}
}

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<?php
/**
*
* Function code for the complex acoth() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse hyperbolic cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\acoth')) {
function acoth($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return atanh(inverse($complex));
}
}

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<?php
/**
*
* Function code for the complex acsc() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\acsc')) {
function acsc($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return asin(inverse($complex));
}
}

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vendor/markbaker/complex/classes/src/functions/acsch.php vendored
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<?php
/**
*
* Function code for the complex acsch() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse hyperbolic cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\acsch')) {
function acsch($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return asinh(inverse($complex));
}
}

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vendor/markbaker/complex/classes/src/functions/argument.php vendored
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<?php
/**
*
* Function code for the complex argument() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the argument of a complex number.
* Also known as the theta of the complex number, i.e. the angle in radians
* from the real axis to the representation of the number in polar coordinates.
*
* This function is a synonym for theta()
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The argument (or theta) value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*
* @see theta
*/
if (!function_exists(__NAMESPACE__ . '\\argument')) {
function argument($complex): float
{
return theta($complex);
}
}

31
vendor/markbaker/complex/classes/src/functions/asec.php vendored
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<?php
/**
*
* Function code for the complex asec() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\asec')) {
function asec($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return acos(inverse($complex));
}
}

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vendor/markbaker/complex/classes/src/functions/asech.php vendored
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<?php
/**
*
* Function code for the complex asech() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse hyperbolic secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\asech')) {
function asech($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return acosh(inverse($complex));
}
}

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vendor/markbaker/complex/classes/src/functions/asin.php vendored
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<?php
/**
*
* Function code for the complex asin() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\asin')) {
function asin($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$square = multiply($complex, $complex);
$invsqrt = new Complex(1.0);
$invsqrt = subtract($invsqrt, $square);
$invsqrt = sqrt($invsqrt);
$adjust = new Complex(
$invsqrt->getReal() - $complex->getImaginary(),
$invsqrt->getImaginary() + $complex->getReal()
);
$log = ln($adjust);
return new Complex(
$log->getImaginary(),
-1 * $log->getReal()
);
}
}

35
vendor/markbaker/complex/classes/src/functions/asinh.php vendored
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<?php
/**
*
* Function code for the complex asinh() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse hyperbolic sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\asinh')) {
function asinh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal() && ($complex->getReal() > 1)) {
return new Complex(\asinh($complex->getReal()));
}
$asinh = clone $complex;
$asinh = $asinh->reverse()
->invertReal();
$asinh = asin($asinh);
return $asinh->reverse()
->invertImaginary();
}
}

47
vendor/markbaker/complex/classes/src/functions/atan.php vendored
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<?php
/**
*
* Function code for the complex atan() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
//include_once 'Math/Complex.php';
//include_once 'Math/ComplexOp.php';
/**
* Returns the inverse tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\atan')) {
function atan($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\atan($complex->getReal()));
}
$t1Value = new Complex(-1 * $complex->getImaginary(), $complex->getReal());
$uValue = new Complex(1, 0);
$d1Value = clone $uValue;
$d1Value = subtract($d1Value, $t1Value);
$d2Value = add($t1Value, $uValue);
$uResult = $d1Value->divideBy($d2Value);
$uResult = ln($uResult);
return new Complex(
(($uResult->getImaginary() == M_PI) ? -M_PI : $uResult->getImaginary()) * -0.5,
$uResult->getReal() * 0.5,
$complex->getSuffix()
);
}
}

40
vendor/markbaker/complex/classes/src/functions/atanh.php vendored
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<?php
/**
*
* Function code for the complex atanh() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse hyperbolic tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse hyperbolic tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\atanh')) {
function atanh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
$real = $complex->getReal();
if ($real >= -1.0 && $real <= 1.0) {
return new Complex(\atanh($real));
} else {
return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2));
}
}
$iComplex = clone $complex;
$iComplex = $iComplex->invertImaginary()
->reverse();
return atan($iComplex)
->invertReal()
->reverse();
}
}

30
vendor/markbaker/complex/classes/src/functions/conjugate.php vendored
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<?php
/**
*
* Function code for the complex conjugate() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the complex conjugate of a complex number
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The conjugate of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\conjugate')) {
function conjugate($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return new Complex(
$complex->getReal(),
-1 * $complex->getImaginary(),
$complex->getSuffix()
);
}
}

36
vendor/markbaker/complex/classes/src/functions/cos.php vendored
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<?php
/**
*
* Function code for the complex cos() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\cos')) {
function cos($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\cos($complex->getReal()));
}
return conjugate(
new Complex(
\cos($complex->getReal()) * \cosh($complex->getImaginary()),
\sin($complex->getReal()) * \sinh($complex->getImaginary()),
$complex->getSuffix()
)
);
}
}

34
vendor/markbaker/complex/classes/src/functions/cosh.php vendored
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<?php
/**
*
* Function code for the complex cosh() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the hyperbolic cosine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic cosine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\cosh')) {
function cosh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\cosh($complex->getReal()));
}
return new Complex(
\cosh($complex->getReal()) * \cos($complex->getImaginary()),
\sinh($complex->getReal()) * \sin($complex->getImaginary()),
$complex->getSuffix()
);
}
}

31
vendor/markbaker/complex/classes/src/functions/cot.php vendored
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<?php
/**
*
* Function code for the complex cot() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\cot')) {
function cot($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return inverse(tan($complex));
}
}

26
vendor/markbaker/complex/classes/src/functions/coth.php vendored
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<?php
/**
*
* Function code for the complex coth() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the hyperbolic cotangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic cotangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\coth')) {
function coth($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return inverse(tanh($complex));
}
}

31
vendor/markbaker/complex/classes/src/functions/csc.php vendored
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<?php
/**
*
* Function code for the complex csc() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\csc')) {
function csc($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return inverse(sin($complex));
}
}

31
vendor/markbaker/complex/classes/src/functions/csch.php vendored
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<?php
/**
*
* Function code for the complex csch() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the hyperbolic cosecant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic cosecant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\csch')) {
function csch($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return new Complex(INF);
}
return inverse(sinh($complex));
}
}

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<?php
/**
*
* Function code for the complex exp() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the exponential of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The exponential of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\exp')) {
function exp($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && (\abs($complex->getImaginary()) == M_PI)) {
return new Complex(-1.0, 0.0);
}
$rho = \exp($complex->getReal());
return new Complex(
$rho * \cos($complex->getImaginary()),
$rho * \sin($complex->getImaginary()),
$complex->getSuffix()
);
}
}

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vendor/markbaker/complex/classes/src/functions/inverse.php vendored
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<?php
/**
*
* Function code for the complex inverse() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the inverse of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The inverse of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\inverse')) {
function inverse($complex): Complex
{
$complex = clone Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
throw new \InvalidArgumentException('Division by zero');
}
return $complex->divideInto(1.0);
}
}

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vendor/markbaker/complex/classes/src/functions/ln.php vendored
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<?php
/**
*
* Function code for the complex ln() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the natural logarithm of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The natural logarithm of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If the real and the imaginary parts are both zero
*/
if (!function_exists(__NAMESPACE__ . '\\ln')) {
function ln($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
throw new \InvalidArgumentException();
}
return new Complex(
\log(rho($complex)),
theta($complex),
$complex->getSuffix()
);
}
}

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vendor/markbaker/complex/classes/src/functions/log10.php vendored
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<?php
/**
*
* Function code for the complex log10() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the common logarithm (base 10) of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The common logarithm (base 10) of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If the real and the imaginary parts are both zero
*/
if (!function_exists(__NAMESPACE__ . '\\log10')) {
function log10($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
throw new \InvalidArgumentException();
} elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
return new Complex(\log10($complex->getReal()), 0.0, $complex->getSuffix());
}
return ln($complex)
->multiply(\log10(Complex::EULER));
}
}

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<?php
/**
*
* Function code for the complex log2() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the base-2 logarithm of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The base-2 logarithm of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If the real and the imaginary parts are both zero
*/
if (!function_exists(__NAMESPACE__ . '\\log2')) {
function log2($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
throw new \InvalidArgumentException();
} elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
return new Complex(\log($complex->getReal(), 2), 0.0, $complex->getSuffix());
}
return ln($complex)
->multiply(\log(Complex::EULER, 2));
}
}

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vendor/markbaker/complex/classes/src/functions/negative.php vendored
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<?php
/**
*
* Function code for the complex negative() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the negative of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The negative value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*
* @see rho
*
*/
if (!function_exists(__NAMESPACE__ . '\\negative')) {
function negative($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return new Complex(
-1 * $complex->getReal(),
-1 * $complex->getImaginary(),
$complex->getSuffix()
);
}
}

42
vendor/markbaker/complex/classes/src/functions/pow.php vendored
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<?php
/**
*
* Function code for the complex pow() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns a complex number raised to a power.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @param float|integer $power The power to raise this value to
* @return Complex The complex argument raised to the real power.
* @throws Exception If the power argument isn't a valid real
*/
if (!function_exists(__NAMESPACE__ . '\\pow')) {
function pow($complex, $power): Complex
{
$complex = Complex::validateComplexArgument($complex);
if (!is_numeric($power)) {
throw new Exception('Power argument must be a real number');
}
if ($complex->getImaginary() == 0.0 && $complex->getReal() >= 0.0) {
return new Complex(\pow($complex->getReal(), $power));
}
$rValue = \sqrt(($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary()));
$rPower = \pow($rValue, $power);
$theta = $complex->argument() * $power;
if ($theta == 0) {
return new Complex(1);
}
return new Complex($rPower * \cos($theta), $rPower * \sin($theta), $complex->getSuffix());
}
}

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vendor/markbaker/complex/classes/src/functions/rho.php vendored
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<?php
/**
*
* Function code for the complex rho() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the rho of a complex number.
* This is the distance/radius from the centrepoint to the representation of the number in polar coordinates.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The rho value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\rho')) {
function rho($complex): float
{
$complex = Complex::validateComplexArgument($complex);
return \sqrt(
($complex->getReal() * $complex->getReal()) +
($complex->getImaginary() * $complex->getImaginary())
);
}
}

27
vendor/markbaker/complex/classes/src/functions/sec.php vendored
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<?php
/**
*
* Function code for the complex sec() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\sec')) {
function sec($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return inverse(cos($complex));
}
}

27
vendor/markbaker/complex/classes/src/functions/sech.php vendored
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<?php
/**
*
* Function code for the complex sech() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the hyperbolic secant of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic secant of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\sech')) {
function sech($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
return inverse(cosh($complex));
}
}

34
vendor/markbaker/complex/classes/src/functions/sin.php vendored
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<?php
/**
*
* Function code for the complex sin() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\sin')) {
function sin($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\sin($complex->getReal()));
}
return new Complex(
\sin($complex->getReal()) * \cosh($complex->getImaginary()),
\cos($complex->getReal()) * \sinh($complex->getImaginary()),
$complex->getSuffix()
);
}
}

34
vendor/markbaker/complex/classes/src/functions/sinh.php vendored
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<?php
/**
*
* Function code for the complex sinh() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the hyperbolic sine of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic sine of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\sinh')) {
function sinh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\sinh($complex->getReal()));
}
return new Complex(
\sinh($complex->getReal()) * \cos($complex->getImaginary()),
\cosh($complex->getReal()) * \sin($complex->getImaginary()),
$complex->getSuffix()
);
}
}

31
vendor/markbaker/complex/classes/src/functions/sqrt.php vendored
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@@ -1,31 +0,0 @@
<?php
/**
*
* Function code for the complex sqrt() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the square root of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The Square root of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\sqrt')) {
function sqrt($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$theta = theta($complex);
$delta1 = \cos($theta / 2);
$delta2 = \sin($theta / 2);
$rho = \sqrt(rho($complex));
return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
}
}

42
vendor/markbaker/complex/classes/src/functions/tan.php vendored
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@@ -1,42 +0,0 @@
<?php
/**
*
* Function code for the complex tan() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\tan')) {
function tan($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->isReal()) {
return new Complex(\tan($complex->getReal()));
}
$real = $complex->getReal();
$imaginary = $complex->getImaginary();
$divisor = 1 + \pow(\tan($real), 2) * \pow(\tanh($imaginary), 2);
if ($divisor == 0.0) {
throw new \InvalidArgumentException('Division by zero');
}
return new Complex(
\pow(sech($imaginary)->getReal(), 2) * \tan($real) / $divisor,
\pow(sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor,
$complex->getSuffix()
);
}
}

37
vendor/markbaker/complex/classes/src/functions/tanh.php vendored
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<?php
/**
*
* Function code for the complex tanh() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the hyperbolic tangent of a complex number.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return Complex The hyperbolic tangent of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
* @throws \InvalidArgumentException If function would result in a division by zero
*/
if (!function_exists(__NAMESPACE__ . '\\tanh')) {
function tanh($complex): Complex
{
$complex = Complex::validateComplexArgument($complex);
$real = $complex->getReal();
$imaginary = $complex->getImaginary();
$divisor = \cos($imaginary) * \cos($imaginary) + \sinh($real) * \sinh($real);
if ($divisor == 0.0) {
throw new \InvalidArgumentException('Division by zero');
}
return new Complex(
\sinh($real) * \cosh($real) / $divisor,
0.5 * \sin(2 * $imaginary) / $divisor,
$complex->getSuffix()
);
}
}

40
vendor/markbaker/complex/classes/src/functions/theta.php vendored
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@@ -1,40 +0,0 @@
<?php
/**
*
* Function code for the complex theta() function
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Returns the theta of a complex number.
* This is the angle in radians from the real axis to the representation of the number in polar coordinates.
*
* @param Complex|mixed $complex Complex number or a numeric value.
* @return float The theta value of the complex argument.
* @throws Exception If argument isn't a valid real or complex number.
*/
if (!function_exists(__NAMESPACE__ . '\\theta')) {
function theta($complex): float
{
$complex = Complex::validateComplexArgument($complex);
if ($complex->getReal() == 0.0) {
if ($complex->isReal()) {
return 0.0;
} elseif ($complex->getImaginary() < 0.0) {
return M_PI / -2;
}
return M_PI / 2;
} elseif ($complex->getReal() > 0.0) {
return \atan($complex->getImaginary() / $complex->getReal());
} elseif ($complex->getImaginary() < 0.0) {
return -(M_PI - \atan(\abs($complex->getImaginary()) / \abs($complex->getReal())));
}
return M_PI - \atan($complex->getImaginary() / \abs($complex->getReal()));
}
}

48
vendor/markbaker/complex/classes/src/operations/add.php vendored
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@@ -1,48 +0,0 @@
<?php
/**
*
* Function code for the complex addition operation
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Adds two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to add
* @return Complex
*/
if (!function_exists(__NAMESPACE__ . '\\add')) {
function add(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
$real = $result->getReal() + $complex->getReal();
$imaginary = $result->getImaginary() + $complex->getImaginary();
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
}

58
vendor/markbaker/complex/classes/src/operations/divideby.php vendored
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@@ -1,58 +0,0 @@
<?php
/**
*
* Function code for the complex division operation
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Divides two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to divide
* @return Complex
*/
if (!function_exists(__NAMESPACE__ . '\\divideby')) {
function divideby(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
throw new \InvalidArgumentException('Division by zero');
}
$delta1 = ($result->getReal() * $complex->getReal()) +
($result->getImaginary() * $complex->getImaginary());
$delta2 = ($result->getImaginary() * $complex->getReal()) -
($result->getReal() * $complex->getImaginary());
$delta3 = ($complex->getReal() * $complex->getReal()) +
($complex->getImaginary() * $complex->getImaginary());
$real = $delta1 / $delta3;
$imaginary = $delta2 / $delta3;
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
}

58
vendor/markbaker/complex/classes/src/operations/divideinto.php vendored
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@@ -1,58 +0,0 @@
<?php
/**
*
* Function code for the complex division operation
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Divides two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to divide
* @return Complex
*/
if (!function_exists(__NAMESPACE__ . '\\divideinto')) {
function divideinto(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
if ($result->getReal() == 0.0 && $result->getImaginary() == 0.0) {
throw new \InvalidArgumentException('Division by zero');
}
$delta1 = ($complex->getReal() * $result->getReal()) +
($complex->getImaginary() * $result->getImaginary());
$delta2 = ($complex->getImaginary() * $result->getReal()) -
($complex->getReal() * $result->getImaginary());
$delta3 = ($result->getReal() * $result->getReal()) +
($result->getImaginary() * $result->getImaginary());
$real = $delta1 / $delta3;
$imaginary = $delta2 / $delta3;
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
}

50
vendor/markbaker/complex/classes/src/operations/multiply.php vendored
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@@ -1,50 +0,0 @@
<?php
/**
*
* Function code for the complex multiplication operation
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Multiplies two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to multiply
* @return Complex
*/
if (!function_exists(__NAMESPACE__ . '\\multiply')) {
function multiply(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
$real = ($result->getReal() * $complex->getReal()) -
($result->getImaginary() * $complex->getImaginary());
$imaginary = ($result->getReal() * $complex->getImaginary()) +
($result->getImaginary() * $complex->getReal());
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
}

48
vendor/markbaker/complex/classes/src/operations/subtract.php vendored
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@@ -1,48 +0,0 @@
<?php
/**
*
* Function code for the complex subtraction operation
*
* @copyright Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
* @license https://opensource.org/licenses/MIT MIT
*/
namespace Complex;
/**
* Subtracts two or more complex numbers
*
* @param array of string|integer|float|Complex $complexValues The numbers to subtract
* @return Complex
*/
if (!function_exists(__NAMESPACE__ . '\\subtract')) {
function subtract(...$complexValues): Complex
{
if (count($complexValues) < 2) {
throw new \Exception('This function requires at least 2 arguments');
}
$base = array_shift($complexValues);
$result = clone Complex::validateComplexArgument($base);
foreach ($complexValues as $complex) {
$complex = Complex::validateComplexArgument($complex);
if ($result->isComplex() && $complex->isComplex() &&
$result->getSuffix() !== $complex->getSuffix()) {
throw new Exception('Suffix Mismatch');
}
$real = $result->getReal() - $complex->getReal();
$imaginary = $result->getImaginary() - $complex->getImaginary();
$result = new Complex(
$real,
$imaginary,
($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
);
}
return $result;
}
}