Complex numbers problem...

[kepler]

Hi

I have a C++ code which I'm trying to convert to a php routine. Some parts seemed easy...but others are not. The main function is (in C++):

 

function solve(const double al, const complex<double> &z, 
                     const double u, complex<double> &zto, double &r)
{
    const double ex = abs(z);
    const double ex2 = ex*ex;
    const double ex3 = ex2*ex;

    double e = (al + (ex - ex3/8)*sin(al) + 0.5 * ex2 * sin(2*al) 
                + 0.375 * ex3 * sin(3*al));

    complex<double> z1 = conj(z);

    for (int k = 0; k < 10; k++)
    {
        const complex<double> z2(0, e);
        const complex<double> zteta = exp(z2);

        const complex<double> z3 = z1*zteta;

        const double dl = al - e + z3.imag();
        r = 1 - z3.real();
        if (fabs(dl) < 1e-12)
        {
            z1 = u * z * z3.imag();
            const complex<double> z2(z1.imag(), -z1.real());
            zto = (-z + zteta + z2)/r;
            return;
        }
        e += dl/r;
    }
    xpWarn("can't converge\n", __FILE__, __LINE__);
}

 

The function is called like this:

 

    complex<double> z(xk, xh);
    complex<double> zto;
    double r;

    solve(xl, z, u, zto, r); //xl, u and r are doubles

    const double xcw = zto.real();
    const double xsw = zto.imag();
    
    const double xm = xp*xcw - xq*xsw;
    const double xxx = xa*r;

So, function Solve returns the complex number zto and the double r which are necessary to the calculations to proceed.

Can someone help me out here?

Kind regards

 

Kepler

 

 

 

[requinix]

Probably the first thing you need to do is find a PHP library for handling complex numbers. I'll bet PEAR has something...

[kepler]

3 hours ago, requinix said:

Probably the first thing you need to do is find a PHP library for handling complex numbers. I'll bet PEAR has something...

Hi

Thanks for the reply. I found this small class. Maybe you can help me understand some things?...

class Complex {

    private $real = 0;
    private $imag = 0;

    public function __construct($real, $imag = null) {
        if ($imag === null) {
        } else {
            $this->real = (float)$real;
            $this->imag = (float)$imag;
        }
    }

    public function __toString() {
        $str = "";
        if (round($this->imag, 12) != 0) $str .= sprintf("%.12f", $this->imag) . "i";
        if ($str) $str .= "+";
        if (round($this->real, 12) != 0) $str .= sprintf("%.12f", $this->real);
        if (!$str) $str = "0";
        return $str;
    }

    public function abs() {
        return sqrt($this->real * $this->real + $this->imag * $this->imag);
    }

    public function add(Complex $c) {
        $this->real += $c->real;
        $this->imag += $c->imag;
    }

} 

Tell me if this is right please:

$z1 = new Complex(2,1);
$z2 = new Complex(7,5);
$z3 = new Complex;

$x1 = $z1->abs(); //$x1 has now the absolute value of the complex var. $z1 = sqrt(2*2+1*1)?...
$z3 = $z1->add($z2); //$z3 is now equal to (2+7,1+5)?...

Cheers

Kepler

[requinix]

That's right.