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

Example 41 with Complex

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

the class BesselJS method airyAiPrime.

public static Complex airyAiPrime(Complex x) {
    if (F.isZero(x)) {
        return new Complex(-1.0 / Math.pow(3.0, 1.0 / 3.0) / GammaJS.gamma(1.0 / 3.0));
    }
    if (x.getReal() < 0) {
        Complex xMinus = x.negate();
        Complex z = xMinus.pow(1.5).multiply(2.0 / 3.0);
        return x.divide(3.0).multiply(besselJ(-2.0 / 3.0, z).subtract(besselJ(2.0 / 3.0, z)));
    }
    Complex z = x.pow(1.5).multiply(2.0 / 3.0);
    return besselK(2.0 / 3.0, z).multiply(x).multiply(-1.0 / Math.PI / Math.sqrt(3.0));
}

Example 42 with Complex

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

the class EllipticIntegralsJS method carlsonRF.

private static Complex carlsonRF(Complex x, Complex y, Complex z, double tolerance) {
    // if ( isComplex(x) || isComplex(y) || isComplex(z) ) {
    // if (y.getImaginary()==0.0) {
    // y = new Complex(y.getReal());
    // }
    Complex xm = x;
    Complex ym = y;
    Complex zm = z;
    Complex A0 = x.add(y).add(z).divide(3.0);
    Complex Am = A0;
    double Q = Math.pow(3.0 * tolerance, -1.0 / 6.0) * Math.max(A0.subtract(x).norm(), Math.max(A0.subtract(y).norm(), A0.subtract(z).norm()));
    double g = 0.25;
    double pow4 = 1.0;
    while (true) {
        double absAm = Am.norm();
        if (Double.isNaN(absAm) || Double.isInfinite(absAm)) {
            throw new ArgumentTypeException("carlsonRF: Am is undefined");
        }
        Complex xs = xm.sqrt();
        Complex ys = ym.sqrt();
        Complex zs = zm.sqrt();
        Complex lm = xs.multiply(ys).add(xs.multiply(zs)).add(ys.multiply(zs));
        // Complex Am1 = Am.add(lm).multiply(g);
        xm = xm.add(lm).multiply(g);
        ym = ym.add(lm).multiply(g);
        zm = zm.add(lm).multiply(g);
        if (pow4 * Q < absAm) {
            break;
        }
        // Am=Am1;
        Am = Am.add(lm).multiply(g);
        pow4 *= g;
    }
    Complex t = new Complex(pow4).divide(Am);
    Complex X = A0.subtract(x).multiply(t);
    Complex Y = A0.subtract(y).multiply(t);
    Complex Z = X.add(Y).negate();
    Complex E2 = X.multiply(Y).subtract(Z.multiply(Z));
    Complex E3 = X.multiply(Y).multiply(Z);
    // Am.pow(-0.5)
    Complex AmPow = Am.pow(-0.5);
    return AmPow.multiply(E2.multiply(-924.0).add(E2.multiply(E2).multiply(385.0)).add(E3.multiply(660.0)).add(E2.multiply(E3).multiply(-630.0)).add(9240.0)).multiply(1.0 / 9240.0);
}

Example 43 with Complex

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

the class EllipticIntegralsJS method kleinJ.

public static Complex kleinJ(Complex x) {
    // from mpmath / elliptic.py
    Complex q = new Complex(0, Math.PI).multiply(x).exp();
    // TODO add Chop()
    Complex t2 = EllipticFunctionsJS.jacobiTheta(2, Complex.ZERO, q);
    Complex t3 = EllipticFunctionsJS.jacobiTheta(3, Complex.ZERO, q);
    Complex t4 = EllipticFunctionsJS.jacobiTheta(4, Complex.ZERO, q);
    Complex P = t2.pow(8.0).add(t3.pow(8.0)).add(t4.pow(8)).pow(3.0);
    Complex Q = t2.multiply(t3).multiply(t4).pow(8.0).multiply(54.0);
    return P.divide(Q);
}

Example 44 with Complex

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

the class EllipticIntegralsJS method ellipticPi.

public static Complex ellipticPi(Complex n, Complex x, Complex m) {
    // return LegendreEllipticIntegral.bigPi(n, x, m);
    Complex period = Complex.ZERO;
    if (Math.abs(x.getReal()) > Math.PI / 2.0) {
        long p = Math.round(x.getReal() / Math.PI);
        x = new Complex(x.getReal() - p * Math.PI, x.getImaginary());
        period = ellipticPi(n, new Complex(Math.PI / 2.0), m).multiply(p + p);
    }
    Complex sinX = x.sin();
    Complex cosX = x.cos();
    Complex sqrSinX = sinX.multiply(sinX);
    Complex sqrCosX = cosX.multiply(cosX);
    Complex p3SinX = sqrSinX.multiply(sinX);
    Complex a2;
    if (sinX.equals(Complex.ZERO)) {
        a2 = Complex.ONE;
    } else {
        a2 = Complex.ONE.subtract(m.multiply(sqrSinX));
    }
    return sinX.multiply(carlsonRF(sqrCosX, a2, Complex.ONE)).add(n.multiply(1.0 / 3.0).multiply(p3SinX).multiply(carlsonRJ(sqrCosX, Complex.ONE.subtract(m.multiply(sqrSinX)), Complex.ONE, Complex.ONE.subtract(n.multiply(sqrSinX))))).add(period);
}

Example 45 with Complex

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

the class EllipticIntegralsJS method ellipticF.

// elliptic integrals
public static Complex ellipticF(Complex x, Complex m) {
    // https://github.com/Hipparchus-Math/hipparchus/issues/151
    // return LegendreEllipticIntegral.bigF(x, m);
    Complex period = Complex.ZERO;
    if (Math.abs(x.getReal()) > (Math.PI / 2)) {
        long p = Math.round(x.getReal() / Math.PI);
        x = new Complex(x.getReal() - p * Math.PI, x.getImaginary());
        period = ellipticK(m).multiply(p + p);
    }
    Complex sinX = x.sin();
    Complex cosX = x.cos();
    if (cosX.getImaginary() == 0.0) {
        cosX = new Complex(cosX.getReal());
    }
    Complex sqrSinX = sinX.multiply(sinX);
    Complex sqrCosX = cosX.multiply(cosX);
    return sinX.multiply(carlsonRF(sqrCosX, Complex.ONE.subtract(m.multiply(sqrSinX)), Complex.ONE)).add(period);
}