Package com.opengamma.analytics.math.number

Examples of com.opengamma.analytics.math.number.ComplexNumber

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  }
 
  @Override
  public ComplexNumber getValue(ComplexNumber u, double t) {
    if (u.getReal() == 0.0 && u.getImaginary() == 0.0) {
      return new ComplexNumber(0.0);
    }

    final ComplexNumber ui = multiply(I, u);

    //handle small lambda properly
    if (2 * mod(u) * _lambda * _lambda / _kappa / _kappa < 1e-6) {
      final double d = _theta * t + (1 - _theta) * (1 - Math.exp(-_kappa * t)) / _kappa;
      return multiply(d, ui);
    }

    ComplexNumber temp = subtract(_kappa * _kappa, multiply(2 * _lambda * _lambda, ui));
    final ComplexNumber gamma = sqrt(temp);
    final ComplexNumber gammaHalfT = multiply(gamma, t / 2.0);
    temp = divide(multiply(2, ui), add(_kappa, divide(gamma, TrigonometricFunctionUtils.tanh(gammaHalfT))));
    final ComplexNumber kappaOverGamma = divide(_kappa, gamma);
    final double power = 2 * _kappa * _theta / _lambda / _lambda;
    final ComplexNumber res = add(multiply(power, subtract(_kappa * t / 2, getLogCoshSinh(gammaHalfT, kappaOverGamma))), temp);
    return res;
  }
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    return res;
  }

  // ln(cosh(a) + bsinh(a)
  private ComplexNumber getLogCoshSinh(final ComplexNumber a, final ComplexNumber b) {
    final ComplexNumber temp = add(TrigonometricFunctionUtils.cosh(a), multiply(b, TrigonometricFunctionUtils.sinh(a)));
    return log(temp);
  }
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    return new Function1D<Double, Double>() {

      @Override
      public Double evaluate(Double x) {
        final ComplexNumber z = new ComplexNumber(x, -1 - alpha);
        ComplexNumber[] ajoint = ajointFunctions.evaluate(z);
        ComplexNumber num = exp(add(new ComplexNumber(0, -x * kappa), ajoint[0]));
        if (index > 0) {
          num = multiply(num, ajoint[index]);
        }
        final ComplexNumber denom = multiply(z, subtract(MINUS_I, z));
        final ComplexNumber res = divide(num, denom);
        return res.getReal();
      }
    };

  }
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      return ZERO;
    }

    //non-stochastic vol limit
    if (_omega == 0.0 || mod(multiply(multiply(_omega / _kappa, u), add(I, u))) < 1e-6) {
      final ComplexNumber z = multiply(u, add(I, u));
      if (_kappa * t < 1e-6) {
        return multiply(-_vol0 / 2 * t, z);
      }
      final double var = _theta * t + (_vol0 - _theta) * (1 - Math.exp(-_kappa * t)) / _kappa;
      return multiply(-var / 2, z);
    }

    final ComplexNumber c = getC(u, t);
    final ComplexNumber dv0 = multiply(_vol0, getD(u, t));
    return add(c, dv0);
  }
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    };
  }

  private ComplexNumber[] forwardSweep(final ComplexNumber u, final double t) {
    ComplexNumber[] w = new ComplexNumber[19];
    w[0] = new ComplexNumber(_kappa * _theta / _omega / _omega);
    w[1] = multiply(u, new ComplexNumber(0, _rho * _omega));
    w[2] = subtract(w[1], _kappa);
    w[3] = square(w[2]);
    w[4] = multiply(u, new ComplexNumber(0, _omega * _omega));
    w[5] = square(multiply(u, _omega));
    w[6] = add(w[3], w[4], w[5]);
    w[7] = sqrt(w[6]);
    w[8] = subtract(w[7], w[2]);
    w[9] = multiply(-1.0, add(w[7], w[2]));
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  }

  private ComplexNumber[] backwardsSweep(final ComplexNumber[] w, final double t) {
    final double oneOverOmega2 = 1 / _omega / _omega;
    final ComplexNumber[] wBar = new ComplexNumber[19];
    wBar[18] = new ComplexNumber(1.0); //formal start
    wBar[17] = new ComplexNumber(_vol0); //Suppressing the multiple by wBar18
    wBar[16] = wBar[18];
    wBar[15] = multiply(oneOverOmega2, w[8], wBar[17]);
    wBar[14] = multiply(-2, w[0], wBar[16]);
    wBar[13] = divide(wBar[14], w[13]);
    ComplexNumber temp1 = subtract(1.0, w[10]);
    ComplexNumber temp2 = subtract(w[10], w[12]);
    ComplexNumber temp3 = square(temp2);
    wBar[12] = add(multiply(wBar[15], divide(temp1, temp3)), divide(wBar[13], temp1));
    wBar[11] = multiply(w[0], wBar[16]);
    wBar[10] = add(multiply(divide(subtract(w[12], 1), temp3), wBar[15]), multiply(divide(subtract(w[12], 1), square(temp1)), wBar[13]));
    wBar[9] = subtract(multiply(t, wBar[11]), multiply(divide(w[8], square(w[9])), wBar[10]));
    wBar[8] = add(multiply(oneOverOmega2, w[15], wBar[17]), divide(wBar[10], w[9]));
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      return res;
    }

    //non-stochastic vol limit
    if (_omega == 0.0 || mod(multiply(_omega / _kappa, u, add(I, u))) < 1e-6) {
      final ComplexNumber z = multiply(u, add(I, u));

      //      //TODO calculate the omega -> 0 sensitivity without resorting to this hack
      //      HestonCharacteristicExponent ceTemp = this.withOmega(1.1e-6 * _kappa / mod(z));
      //      ComplexNumber[] temp = ceTemp.getCharacteristicExponentAdjoint(u, t);

      final double var;
      if (_kappa * t < 1e-6) {
        var = _vol0 * t + (_vol0 - _theta) * _kappa * t * t / 2;
        res[1] = multiply(-0.5 * (_vol0 - _theta) * t * t / 2, z);
        res[2] = multiply(_kappa * t * t / 4, z);
        res[3] = multiply(-0.5 * (t + _kappa * t * t / 2), z);
        res[4] = ZERO; //TODO this is wrong
        res[5] = ZERO;
      } else {
        final double expKappaT = Math.exp(-_kappa * t);
        var = _theta * t + (_vol0 - _theta) * (1 - expKappaT) / _kappa;
        res[1] = multiply(-0.5 * (_vol0 - _theta) * (expKappaT * (1 + t * _kappa) - 1) / _kappa / _kappa, z);
        res[2] = multiply(-0.5 * (t - (1 - expKappaT) / _kappa), z);
        res[3] = multiply(-0.5 * (1 - expKappaT) / _kappa, z);
        res[4] = ZERO; //TODO this is wrong
        res[5] = ZERO;
      }
      res[0] = multiply(-var / 2, z);
      return res;
    }

    final double oneOverOmega2 = 1 / _omega / _omega;
    final double w0 = _kappa * _theta * oneOverOmega2;

    final ComplexNumber w1 = multiply(u, new ComplexNumber(0, _rho * _omega)); //w1
    final ComplexNumber w2 = subtract(w1, _kappa); //w2
    final ComplexNumber w3 = square(w2); //w3
    final ComplexNumber w4 = multiply(u, new ComplexNumber(0, _omega * _omega));
    final ComplexNumber w5 = square(multiply(u, _omega));
    final ComplexNumber w6 = add(w3, w4, w5);
    final ComplexNumber w7 = sqrt(w6);

    final ComplexNumber w8 = subtract(w7, w2);
    final ComplexNumber w9 = multiply(-1.0, add(w7, w2));
    final ComplexNumber w10 = divide(w8, w9);

    final ComplexNumber w11 = multiply(t, w9);
    final ComplexNumber w12 = exp(multiply(w7, -t));
    final ComplexNumber w13 = divide(subtract(w10, w12), subtract(w10, 1));

    final ComplexNumber w14 = log(w13);
    final ComplexNumber w15 = divide(subtract(1, w12), subtract(w10, w12));

    final ComplexNumber w16 = multiply(w0, subtract(w11, multiply(2, w14)));
    final ComplexNumber w17 = multiply(oneOverOmega2, w8, w15);
    final ComplexNumber w18 = add(w16, multiply(_vol0, w17));

    res[0] = w18; //value of CE

    //backwards sweep
    final ComplexNumber wBar16 = new ComplexNumber(1.0);
    final ComplexNumber wBar17 = new ComplexNumber(_vol0);
    final ComplexNumber wBar15 = multiply(oneOverOmega2, wBar17, w8);
    final ComplexNumber wBar14 = multiply(-2 * w0, wBar16);
    final ComplexNumber wBar13 = divide(wBar14, w13);
    final ComplexNumber wBar12a = multiply(wBar15, divide(subtract(1, w10), square(subtract(w10, w12))));
    final ComplexNumber wBar12b = multiply(wBar13, divide(1.0, subtract(1.0, w10)));
    final ComplexNumber wBar12 = add(wBar12a, wBar12b);
    final ComplexNumber wBar11 = multiply(w0, wBar16);
    final ComplexNumber wBar10a = multiply(wBar15, divide(w15, subtract(w12, w10)));
    final ComplexNumber wBar10b = multiply(wBar13, divide(subtract(w12, 1.0), square(subtract(w10, 1.0))));
    final ComplexNumber wBar10 = add(wBar10a, wBar10b);
    final ComplexNumber wBar9a = multiply(t, wBar11);
    final ComplexNumber wBar9b = multiply(-1.0, wBar10, divide(w10, w9));
    final ComplexNumber wBar9 = add(wBar9a, wBar9b);
    final ComplexNumber wBar8a = multiply(oneOverOmega2, wBar17, w15);
    final ComplexNumber wBar8b = divide(wBar10, w9);
    final ComplexNumber wBar8 = add(wBar8a, wBar8b);
    final ComplexNumber wBar7 = subtract(add(multiply(wBar12, multiply(-t, w12)), wBar8), wBar9);
    final ComplexNumber wBar6 = multiply(wBar7, divide(0.5, w7));
    final ComplexNumber wBar5 = wBar6;
    final ComplexNumber wBar4 = wBar6;
    final ComplexNumber wBar3 = wBar6;
    final ComplexNumber wBar2 = subtract(multiply(wBar3, multiply(2.0, w2)), add(wBar8, wBar9));
    final ComplexNumber wBar1 = wBar2;
    final ComplexNumber wBar0 = multiply(wBar16, subtract(w11, multiply(2, w14)));

    res[1] = subtract(multiply(wBar0, _theta / _omega / _omega), wBar2); //kappaBar
    res[2] = multiply(wBar0, _kappa / _omega / _omega); //thetaBar
    res[3] = w17; //vol0

    final ComplexNumber omegaBar1 = multiply(-2 / _omega, w17, wBar17);
    final ComplexNumber omegaBar2 = multiply(-2.0 * w0 / _omega, wBar0);
    final ComplexNumber omegaBar3 = multiply(1 / _omega, w1, wBar1);
    final ComplexNumber omegaBar4 = multiply(2 / _omega, w4, wBar4);
    final ComplexNumber omegaBar5 = multiply(2 / _omega, w5, wBar5);
    res[4] = add(omegaBar1, omegaBar2, omegaBar3, omegaBar4, omegaBar5);

    res[5] = multiply(_omega, u, I, wBar1);

    return res;
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    return res;
  }

  private ComplexNumber getC(final ComplexNumber u, final double t) {
    final ComplexNumber c1 = multiply(u, new ComplexNumber(0, _rho * _omega));
    final ComplexNumber c = c(u);
    final ComplexNumber d = d(u);
    final ComplexNumber c3 = multiply(t, subtract(_kappa, add(d, c1)));
    final ComplexNumber e = exp(multiply(d, -t));
    ComplexNumber c4 = divide(subtract(c, e), subtract(c, 1));
    c4 = log(c4);
    return multiply(_kappa * _theta / _omega / _omega, subtract(c3, multiply(2, c4)));
  }
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    c4 = log(c4);
    return multiply(_kappa * _theta / _omega / _omega, subtract(c3, multiply(2, c4)));
  }

  private ComplexNumber getD(final ComplexNumber u, final double t) {
    final ComplexNumber c1 = multiply(u, new ComplexNumber(0, _rho * _omega));
    final ComplexNumber c = c(u);
    final ComplexNumber d = d(u);
    final ComplexNumber c3 = add(_kappa, subtract(d, c1));
    final ComplexNumber e = exp(multiply(d, -t));
    final ComplexNumber c4 = divide(subtract(1, e), subtract(c, e));
    return divide(multiply(c3, c4), _omega * _omega);
  }
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    final ComplexNumber c4 = divide(subtract(1, e), subtract(c, e));
    return divide(multiply(c3, c4), _omega * _omega);
  }

  private ComplexNumber c(final ComplexNumber u) {
    final ComplexNumber c1 = multiply(u, new ComplexNumber(0, _rho * _omega));
    final ComplexNumber c2 = d(u);
    final ComplexNumber num = add(_kappa, subtract(c2, c1));
    final ComplexNumber denom = subtract(_kappa, add(c2, c1));
    return divide(num, denom);
  }
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