function pleac_Using_Complex_Numbers()
{
// PHP offers no native support for complex numbers. However, a 'Math_Complex' class
// is available for download from PEAR: [http://pear.php.net/package/Math_Complex].
// Note the following 'include' directives are required:
//
// include_once('Math/Complex.php');
// include_once('Math/TrigOp.php');
// include_once('Math/ComplexOp.php');
$a = new Math_Complex(3, 5);
$b = new Math_Complex(2, -2);
$c = Math_ComplexOp::mult($a, $b);
echo $c->toString() . "\n";
// ----------------------------
$d = new Math_Complex(3, 4);
$r = Math_ComplexOp::sqrt($d);
echo $r->toString() . "\n";
}
/**
* Returns the exponentiation of a complex numbers to a real power: z = c1^(real)
*
* @param Math_Complex $c1
* @param float $real
* @return Math_Complex A valid Math_Complex number on success
* @throws InvalidArgumentException
*/
public static function powReal(Math_Complex $c1, $real)
{
if (!Math_ComplexOp::isComplex($c1)) {
throw new InvalidArgumentException('First arguments must be Math_Complex object');
} elseif (!is_numeric($real)) {
throw new InvalidArgumentException("An real number is needed as second parameter");
} else {
$ar = $c1->getReal();
$ai = $c1->getIm();
if ($ar == 0 && $ai == 0) {
$r = $i = 0.0;
} else {
$logr = log($c1->abs());
$theta = $c1->arg();
$rho = exp($logr * $real);
$beta = $theta * $real;
$r = $rho * cos($beta);
$i = $rho * sin($beta);
}
return new Math_Complex($r, $i);
}
}
function testPowReal()
{
/*{{{*/
$tmp = Math_ComplexOp::powReal($this->cnum1, M_E);
$this->assertEquals('-0.217519902849 + 0.0771254874156i', $tmp->toString());
}
if (!Math_ComplexOp::areEqual($a, $b)) {
echo "a != b\n";
}
$z = Math_ComplexOp::add($a, $b);
echo "add(a, b) = " . $z->toString() . "\n";
$z = Math_ComplexOp::sub($a, $b);
echo "sub(a,b) = a - b = " . $z->toString() . "\n";
$t = Math_ComplexOp::sub($b, $a);
echo "b - a: " . $t->toString() . "\n";
$t = Math_ComplexOp::sub($b, Math_ComplexOp::conjugate($a));
echo "b - a': " . $t->toString() . "\n";
$v = Math_ComplexOp::conjugate($b);
$t = Math_ComplexOp::sub($v, $a);
echo "b' - a: " . $t->toString() . "\n";
$v = Math_ComplexOp::conjugate($b);
$t = Math_ComplexOp::sub($v, Math_ComplexOp::conjugate($a));
echo "b' - a': " . $t->toString() . "\n";
$z = Math_ComplexOp::mult($a, $b);
echo "mult(a, b) = " . $z->toString() . "\n";
$z = Math_ComplexOp::div($a, $b);
echo "div(a, b) = " . $z->toString() . "\n";
$z = Math_ComplexOp::pow($a, $b);
echo "pow(a, b) = " . $z->toString() . "\n";
$z = Math_ComplexOp::logBase($a, $b);
echo "logBase(a, b) = " . $z->toString() . "\n";
$z = Math_ComplexOp::multReal($a, M_PI);
echo "multReal(a, M_PI) = " . $z->toString() . "\n";
$z = Math_ComplexOp::multIm($a, $im);
echo "multIm(a, i) = " . $z->toString() . "\n";
$z = Math_ComplexOp::powReal($a, M_E);
echo "powReal(a, M_E) = " . $z->toString() . "\n";
