/**
* Create complex power from natural base and complex exponent
*
* @param int|float $base base
* @param ComplexType $exp exponent
*
* @return NI|ComplexType
*/
private function complexExponent($base, ComplexType $exp)
{
if ($exp->isReal()) {
return $this->rationalPow(RationalTypeFactory::fromFloat($base), $exp->r());
}
//do the imaginary part
//n^bi = cos(b.lg(n)) + i.sin(b.lg(n))
$b = $exp->i()->get();
$n = log($base);
$r = cos($b * $n);
$i = sin($b * $n);
//no real part
if ($exp->r()->get() == 0) {
return new ComplexType(RationalTypeFactory::fromFloat($r), RationalTypeFactory::fromFloat($i));
}
//real and imaginary part
//n^a+bi = n^a(cos(b.lg(n)) + i.sin(b.lg(n)))
$na = pow($base, $exp->r()->get());
$rr = $na * $r;
$ii = $na * $i;
return new ComplexType(RationalTypeFactory::fromFloat($rr), RationalTypeFactory::fromFloat($ii));
}
/**
* Create a matrix representation of a complex number
* For z = a+bi
* Returns [[a, -b]
* [b, a]]
*
* @param \Chippyash\Type\Number\Complex\ComplexType $c
* @return \Chippyash\Math\Matrix\RationalMatrix
*/
public static function createFromComplex(ComplexType $c)
{
$a = clone $c->r();
$b = clone $c->i();
$b2 = clone $c->i();
$bi = new RationalType($b2->numerator()->negate(), $b->denominator());
return self::createRational([[$a, $bi], [$b, $a]]);
}
/**
* |c1 * c2| = |c1| * |c2|
*/
public function testCommutativeMultiplicationAttributeForModulus()
{
$c1 = new ComplexType($this->createRationalType(1), $this->createRationalType(2));
$c2 = new ComplexType($this->createRationalType(3), $this->createRationalType(4));
$c1R = $c1->r()->get();
$c1I = $c1->i()->get();
$c2R = $c2->r()->get();
$c2I = $c2->i()->get();
$nR = $c1R * $c2R - $c1I * $c2I;
$nI = $c1I * $c2R + $c1R * $c2I;
$c1mulc2 = new ComplexType(RationalTypeFactory::fromFloat($nR), RationalTypeFactory::fromFloat($nI));
$mod1 = $c1->modulus();
$mod2 = $c2->modulus();
$modc1mulc2 = $c1mulc2->modulus();
$this->assertEquals($modc1mulc2(), $mod1() * $mod2());
}