Examples with Complex org.hipparchus.complex.Complex used on opensource projects

Example 61 with Complex

use of org.hipparchus.complex.Complex in project symja_android_library by axkr.

the class EllipticFunctionsJS method jacobiAmplitude.

public static Complex jacobiAmplitude(double x, double m) {
    if (m > 1) {
        return jacobiAmplitude(new Complex(x), new Complex(m));
    }
    Complex K = EllipticIntegralsJS.ellipticK(m);
    // ??? .getReal() inserted
    long n = Math.round(x / 2.0 / K.getReal());
    // ??? .getReal() inserted
    x = x - 2 * n * K.getReal();
    return Complex.valueOf(Math.asin(jacobiSN(x, m)) + (n * Math.PI));
}

Example 62 with Complex

use of org.hipparchus.complex.Complex in project symja_android_library by axkr.

the class EllipticFunctionsJS method weierstrassInvariants.

public static Complex[] weierstrassInvariants(Complex w1, Complex w3) {
    // order half periods by complex slope
    if (w3.getImaginary() / w3.getReal() < w1.getImaginary() / w1.getReal()) {
        Complex temp = w1;
        w1 = w3;
        w3 = temp;
    }
    Complex ratio = w3.divide(w1);
    boolean conjugate = false;
    if (ratio.getImaginary() < 0) {
        ratio = ratio.conjugate();
        conjugate = true;
    }
    Complex q = Complex.I.multiply(Math.PI).multiply(ratio).exp();
    // en.wikipedia.org/wiki/Weierstrass's_elliptic_functions
    // modified for input of half periods
    Complex a = jacobiTheta(2, Complex.ZERO, q);
    Complex b = jacobiTheta(3, Complex.ZERO, q);
    Complex aPow4 = a.multiply(a);
    aPow4 = aPow4.multiply(aPow4);
    Complex aPow8 = aPow4.multiply(aPow4);
    Complex bPow4 = b.multiply(b);
    bPow4 = bPow4.multiply(bPow4);
    Complex bPow8 = bPow4.multiply(bPow4);
    Complex g2 = w1.multiply(2).pow(-4).multiply(aPow8.add(aPow4.multiply(bPow4).negate()).add(bPow8)).multiply(4.0 / 3.0 * Math.pow(Math.PI, 4));
    Complex g3 = w1.multiply(2.0).pow(-6.0).multiply(8.0 / 27.0 * Math.pow(Math.PI, 6.0)).multiply(a.pow(12).add(aPow8.multiply(bPow4).multiply(-1.5)).add(aPow4.multiply(bPow8).multiply(-1.5)).add(b.pow(12)));
    if (conjugate) {
        g2 = g2.conjugate();
        g3 = g3.conjugate();
    }
    return new Complex[] { g2, g3 };
}

Example 63 with Complex

use of org.hipparchus.complex.Complex in project symja_android_library by axkr.

the class EllipticFunctionsJS method weierstrassRoots.

public static Complex[] weierstrassRoots(Complex g2, Complex g3) {
    g2 = g2.divide(4);
    g3 = g3.divide(4);
    Complex e1 = cubicTrigSolution(g2, g3, 0);
    Complex e2 = cubicTrigSolution(g2, g3, 1);
    Complex e3 = cubicTrigSolution(g2, g3, 2);
    return new Complex[] { e1, e2, e3 };
}

Example 64 with Complex

use of org.hipparchus.complex.Complex in project symja_android_library by axkr.

the class EllipticFunctionsJS method weierstrassHalfPeriods.

public static Complex[] weierstrassHalfPeriods(Complex g2, Complex g3) {
    Complex[] sol = weierstrassRoots(g2, g3);
    Complex e1 = sol[0];
    Complex e2 = sol[1];
    Complex e3 = sol[2];
    Complex lambda = e1.subtract(e3).sqrt();
    Complex m = e2.subtract(e3).divide(e1.subtract(e3));
    Complex w1 = ellipticK(m).divide(lambda);
    Complex w3 = Complex.I.multiply(ellipticK(Complex.ONE.subtract(m))).divide(lambda);
    return new Complex[] { w1, w3 };
// Complex e1 = sol[0];
// Complex e2 = sol[1];
// Complex e3 = sol[2];
// Complex w1 = inverseWeierstrassP(e1, g2, g3);
// Complex w2 = inverseWeierstrassP(e2, g2, g3);
// Complex w3 = inverseWeierstrassP(e3, g2, g3);
// 
// Complex[] w = new Complex[] { w1, w2, w3 };
// Arrays.sort(w, (a, b) -> (int) Math.signum((a.abs() - b.abs())));
// // w.sort( (a,b) => abs(a) - abs(b) );
// Complex smallest = w[0];
// Complex[] v = new Complex[] { w[1], w[2], //
// w[1].subtract(smallest), w[2].subtract(smallest) };
// // w.sort( (a,b) => abs(a) - abs(b) );
// Arrays.sort(v, (a, b) -> (int) Math.signum((a.abs() - b.abs())));
// return new Complex[] { smallest, v[0] };
}

Example 65 with Complex

use of org.hipparchus.complex.Complex in project symja_android_library by axkr.

the class EllipticFunctionsJS method jacobiAmplitude.

public static Complex jacobiAmplitude(Complex x, Complex m) {
    if (m.getImaginary() == 0.0 && m.getReal() <= 1) {
        Complex K = EllipticIntegralsJS.ellipticK(m.getReal());
        // ??? getReal() inserted
        long n = Math.round(x.getReal() / 2.0 / K.getReal());
        x = x.subtract(2.0 * n * K.getReal());
        if (m.getReal() < 0.0) {
            Complex Kp = EllipticIntegralsJS.ellipticK(1 - m.getReal());
            long p = Math.round(x.getImaginary() / 2.0 / Kp.getReal());
            // bitwise test for odd integer
            if ((p & 1) == 1) {
                return jacobiSN(x, m).asin().negate().add(n * Math.PI);
            }
        }
        return jacobiSN(x, m).asin().add(n * Math.PI);
    }
    return jacobiSN(x, m).asin();
// }
}