public function testAbsReturnsAbsoluteValue()
{
$c1 = new ComplexType($this->createRationalType(1), $this->createRationalType(2));
$c2 = new ComplexType($this->createRationalType(-1), $this->createRationalType(2));
$c3 = new ComplexType($this->createRationalType(1), $this->createRationalType(-2));
$c4 = new ComplexType($this->createRationalType(-1), $this->createRationalType(-2));
$this->assertEquals($c1->modulus(), $c1->abs());
$this->assertEquals($c1->modulus(), $c2->abs());
$this->assertEquals($c1->modulus(), $c3->abs());
$this->assertEquals($c1->modulus(), $c4->abs());
}
/**
* @param ComplexType $a first operand
* @param ComplexType $exp second operand
*
* @return array [real, imaginary]
*/
protected function getPowExponentPartsFromPolar(ComplexType $a, ComplexType $exp)
{
$eReal = $exp->r()->get();
$eImaginary = $exp->i()->get();
$logr = log($a->modulus()->get());
$theta = $a->theta()->get();
$rho = exp($logr * $eReal - $eImaginary * $theta);
$beta = $theta * $eReal + $eImaginary * $logr;
return [$rho * cos($beta), $rho * sin($beta)];
}
/**
* 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;
}
