Examples with Complex org.nfunk.jep.type.Complex used on opensource projects

Example 1 with Complex

use of org.nfunk.jep.type.Complex in project JWildfire by thargor6.

the class KleinGroupFunc method calcMaskitLeysModifiedGenerators.

/**
 * based on modified Maskit parameterization discussed in Jos Leys' article
 *     "A fast algorithm for limit sets of Kleinian groups with the Maskit parametrisation",
 *     section 4.1
 *  replaces b(z) = z + 2
 *      with b(z) = z + k
 *   where k = 2*cos(PI/n) and n is integer
 *   here we also allow imaginary component for k, to be set by b_im
 */
public Complex[][] calcMaskitLeysModifiedGenerators() {
    Complex mu = new Complex(a_re, a_im);
    Complex[] mat_a = new Complex[] { mu.mul(-1).mul(im1), im1.mul(-1), im1.mul(-1), zero };
    Complex b1 = new Complex(2 * cos(M_PI / b_re), b_im);
    Complex[] mat_b = new Complex[] { re1, b1, zero, re1 };
    Complex[][] generators = new Complex[2][4];
    generators[0] = mat_a;
    generators[1] = mat_b;
    return generators;
}

Example 2 with Complex

use of org.nfunk.jep.type.Complex in project JWildfire by thargor6.

the class KleinGroupFunc method calcGrandmaGenerators.

/**
 * using "Grandma's special parabolic commutator groups" recipe
 *   from the book "Indra's Pearls: the Vision of Felix Klein"
 */
public Complex[][] calcGrandmaGenerators() {
    Complex traceA = new Complex(a_re, a_im);
    Complex traceB = new Complex(b_re, b_im);
    // solve for traceAB:
    // traceAB^2 - (traceA * traceB * traceAB) + traceA^2 + traceB^2 = 0
    // x = (-b +- sqrt(b^2 - 4ac)) / 2a
    // x = traceAB
    // a = 1
    // b = -1 * traceA * traceB
    // c = traceA^2 + traceB^2
    Complex b = traceA.mul(traceB).mul(-1);
    Complex c = traceA.power(2).add(traceB.power(2));
    // Complex bsq = traceA.mul(traceB).power(2);
    Complex bsq = b.power(2);
    Complex ac4 = c.mul(4);
    Complex trABplus = b.mul(-1).add(bsq.sub(ac4).sqrt()).div(re2);
    Complex trABminus = b.mul(-1).sub(bsq.sub(ac4).sqrt()).div(re2);
    Complex traceAB = trABminus;
    // z0 = ((traceAB - 2) * traceB) / ((traceB * traceAB) - (2 * traceA) + (2i * traceAB))
    // z0 = traceAB.sub(2).mult(traceB).div(traceB.mult(traceAB).sub(traceA.mult(2)).add(traceAB.mult(Complex.I).mult(2)) )
    Complex znum = traceAB.sub(re2).mul(traceB);
    Complex zdenom = traceB.mul(traceAB).sub(traceA.mul(re2)).add(traceAB.mul(im2));
    Complex z0 = znum.div(zdenom);
    Complex a0 = traceA.div(re2);
    Complex a1num = traceA.mul(traceAB).sub(traceB.mul(re2)).add(im4);
    Complex a1denom = traceAB.mul(re2).add(re4).mul(z0);
    Complex a1 = a1num.div(a1denom);
    Complex a2num = traceA.mul(traceAB).sub(traceB.mul(re2)).sub(im4).mul(z0);
    Complex a2denom = traceAB.mul(re2).sub(re4);
    Complex a2 = a2num.div(a2denom);
    Complex a3 = traceA.div(re2);
    Complex b0 = traceB.sub(im2).div(re2);
    Complex b1 = traceB.div(re2);
    Complex b2 = traceB.div(re2);
    Complex b3 = traceB.add(im2).div(re2);
    mat_a = new Complex[] { a0, a1, a2, a3 };
    mat_b = new Complex[] { b0, b1, b2, b3 };
    Complex[][] generators = new Complex[2][4];
    generators[0] = mat_a;
    generators[1] = mat_b;
    return generators;
}

Example 3 with Complex

use of org.nfunk.jep.type.Complex in project JWildfire by thargor6.

the class KleinGroupFunc method calcModifiedMaskitGenerators.

public Complex[][] calcModifiedMaskitGenerators() {
    Complex mu = new Complex(a_re, a_im);
    // modifying Maskit to utilize b_re and b_im
    Complex b1 = new Complex(b_re, b_im);
    Complex[] mat_a = new Complex[] { mu.mul(-1).mul(im1), im1.mul(-1), im1.mul(-1), zero };
    // Complex[] mat_b = new Complex[]{ re1, re2, zero, re1};
    Complex[] mat_b = new Complex[] { re1, b1, zero, re1 };
    Complex[][] generators = new Complex[2][4];
    generators[0] = mat_a;
    generators[1] = mat_b;
    return generators;
}

Example 4 with Complex

use of org.nfunk.jep.type.Complex in project JWildfire by thargor6.

the class KleinGroupFunc method calcJorgensenGenerators.

public Complex[][] calcJorgensenGenerators() {
    Complex traceA = new Complex(a_re, a_im);
    Complex traceB = new Complex(b_re, b_im);
    // solve for traceAB:
    // traceAB^2 - (traceA * traceB * traceAB) + traceA^2 + traceB^2 = 0
    // x = (-b +- sqrt(b^2 - 4ac)) / 2a
    // x = traceAB
    // a = 1
    // b = -1 * traceA * traceB
    // c = traceA^2 + traceB^2
    Complex b = traceA.mul(traceB).mul(-1);
    Complex c = traceA.power(2).add(traceB.power(2));
    Complex bsq = b.power(2);
    Complex ac4 = c.mul(4);
    Complex trABplus = b.mul(-1).add(bsq.sub(ac4).sqrt()).div(re2);
    Complex trABminus = b.mul(-1).sub(bsq.sub(ac4).sqrt()).div(re2);
    Complex traceAB = trABminus;
    // a0 = ta - (tb/tab)
    Complex a0 = traceA.sub(traceB.div(traceAB));
    // a1 = ta / tab^2
    Complex a1 = traceA.div(traceAB.power(2));
    Complex a2 = traceA;
    Complex a3 = traceB.div(traceAB);
    // b0 = tb - (ta/tab)
    Complex b0 = traceB.sub(traceA.div(traceAB));
    // b1 = -tb/tab^2
    Complex b1 = traceB.mul(-1).div(traceAB.power(2));
    Complex b2 = traceB.mul(-1);
    Complex b3 = traceA.div(traceAB);
    mat_a = new Complex[] { a0, a1, a2, a3 };
    mat_b = new Complex[] { b0, b1, b2, b3 };
    Complex[][] generators = new Complex[2][4];
    generators[0] = mat_a;
    generators[1] = mat_b;
    return generators;
}

Example 5 with Complex

use of org.nfunk.jep.type.Complex in project JWildfire by thargor6.

the class KleinGroupFunc method calcModifiedRileyGenerators.

public Complex[][] calcModifiedRileyGenerators() {
    Complex c = new Complex(a_re, a_im);
    // modifying Riley to utilize b_re and b_im
    Complex b1 = new Complex(b_re, b_im);
    Complex[] mat_a = new Complex[] { re1, zero, c, re1 };
    // Complex[] mat_b = new Complex[]{ re1, re2, zero, re1 };
    Complex[] mat_b = new Complex[] { re1, b1, zero, re1 };
    Complex[][] generators = new Complex[2][4];
    generators[0] = mat_a;
    generators[1] = mat_b;
    return generators;
}