/**
* 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]]);
}
public function testPolarStringForNonZeroComplexReturnsNonZeroString()
{
$c = new ComplexType($this->createRationalType(1), $this->createRationalType(0));
$this->assertEquals('cos 0 + i⋅sin 0', $c->polarString());
$c = new ComplexType($this->createRationalType(5), $this->createRationalType(0));
$this->assertEquals('5(cos 0 + i⋅sin 0)', $c->polarString());
$c = new ComplexType($this->createRationalType(5), $this->createRationalType(2));
$this->assertEquals('5.385165(cos 0.380506 + i⋅sin 0.380506)', $c->polarString());
}
/**
* 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));
}
/**
* Compare complex numbers.
* If both operands are real then compare the real parts
* else compare the modulii of the two numbers
*
* @param ComplexType $a
* @param ComplexType $b
*
* @return boolean
*/
protected function complexCompare(ComplexType $a, ComplexType $b)
{
if ($a->isReal() && $b->isReal()) {
return $this->rationalCompare($a->r(), $b->r());
}
//hack to get around native php integer limitations
//what we should be doing here is to return $this->rationalCompare($a->modulus(), $b->modulus())
//but this blows up because of the big rationals it produces
$am = $a->modulus()->asFloatType()->get();
$bm = $b->modulus()->asFloatType()->get();
if ($am == $bm) {
return 0;
}
if ($am < $bm) {
return -1;
}
return 1;
}
