Java Code Examples for org.apache.commons.math3.complex.Complex#add()

public Complex response(final double normalizedFrequency) {
    final double w = 2 * Math.PI * normalizedFrequency;
    final Complex czn1 = ComplexUtils.polar2Complex(1., -w);
    final Complex czn2 = ComplexUtils.polar2Complex(1., -2 * w);
    Complex ch = new Complex(1);
    Complex cbot = new Complex(1);

    for (int i = 0; i < mNumBiquads; i++) {
        final Biquad stage = mBiquads[i];

        Complex ct = new Complex(stage.getB0() / stage.getA0()); // NOPMD
        ct = ct.add(czn1.multiply(stage.getB1() / stage.getA0()));
        ct = ct.add(czn2.multiply(stage.getB2() / stage.getA0()));

        Complex cb = new Complex(1); // NOPMD
        cb = cb.add(czn1.multiply(stage.getA1() / stage.getA0()));
        cb = cb.add(czn2.multiply(stage.getA2() / stage.getA0()));

        ch = ch.multiply(ct);
        cbot = cbot.multiply(cb);
    }

    return ch.divide(cbot);
}
 

private static ComplexPair transform(final Complex in, final double a, final double b) {
    if (in.isInfinite()) {
        return new ComplexPair(new Complex(-1), new Complex(1));
    }

    final Complex c = new Complex(1).add(in).divide(new Complex(1).subtract(in)); // bilinear

    final double a2 = a * a;
    final double b2 = b * b;
    final double ab = a * b;
    final double ab2 = 2 * ab;
    Complex v = new Complex(0).add(c.multiply(4 * (b2 * (a2 - 1) + 1)));
    v = v.add(8 * (b2 * (a2 - 1) - 1));
    v = v.multiply(c);
    v = v.add(4 * (b2 * (a2 - 1) + 1));
    v = v.sqrt();

    final Complex u = v.multiply(-1).add(c.multiply(ab2)).add(ab2);

    v = v.add(c.multiply(ab2)).add(ab2);

    final Complex d = new Complex(0).add(c.multiply(2 * (b - 1))).add(2 * (1 + b));

    return new ComplexPair(u.divide(d), v.divide(d));
}
 

/**
 * Compute Zernike moments at specified order.
 *
 * @param w Width of the bounding box of the shape.
 * @param h Height of the bounding box of the shape.
 * @param n 1st order of the moment.
 * @param m 2nd order of the moment.
 *
 * @return Zernike moment of data in f[][].
 */
public static Complex calculateZernikeMoment(double[][] f, int w, int h, int n, int m){
    int diff = n-Math.abs(m);
    if ((n<0) || (Math.abs(m) > n) || (diff%2!=0)){
        throw new IllegalArgumentException("zer_mom: n="+n+", m="+m+", n-|m|="+diff);
    }

    final double c = -1;
    final double d = 1;


    ZernikeBasisFunction zernike = new ZernikeBasisFunction(n,m);
    Complex res = new Complex(0.0, 0.0);
    for (int i=0;i<w;i++){
        for (int j=0;j<h;j++) {
            Complex v = new Complex(c+(i*(d-c))/(w-1), d-(j*(d-c))/(h-1));
            res = res.add(zernike.value(v).conjugate().multiply(f[i][j]));
        }
    }

    return res.multiply((n+1)/Math.PI);
}
 

@Override
public Complex apply(final Complex argument) {
	final Complex iargument = argument.multiply(Complex.I);
	final Complex exponent = iargument.add(1.0);
	final Complex numerator = (new Complex(strike)).pow(exponent.subtract(1.0)).multiply(exponent);
	final Complex denominator = (argument.multiply(argument)).subtract(iargument);

	return numerator.divide(denominator);
}
 

/**
 * Find all complex roots for the polynomial with the given
 * coefficients, starting from the given initial value.
 *
 * @param coefficients Polynomial coefficients.
 * @param initial Start value.
 * @return the point at which the function value is zero.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximum number of evaluations is exceeded.
 * @throws NullArgumentException if the {@code coefficients} is
 * {@code null}.
 * @throws NoDataException if the {@code coefficients} array is empty.
 */
public Complex[] solveAll(Complex coefficients[], Complex initial)
    throws NullArgumentException,
           NoDataException,
           TooManyEvaluationsException {
    if (coefficients == null) {
        throw new NullArgumentException();
    }
    final int n = coefficients.length - 1;
    if (n == 0) {
        throw new NoDataException(LocalizedFormats.POLYNOMIAL);
    }
    // Coefficients for deflated polynomial.
    final Complex c[] = new Complex[n + 1];
    for (int i = 0; i <= n; i++) {
        c[i] = coefficients[i];
    }

    // Solve individual roots successively.
    final Complex root[] = new Complex[n];
    for (int i = 0; i < n; i++) {
        final Complex subarray[] = new Complex[n - i + 1];
        System.arraycopy(c, 0, subarray, 0, subarray.length);
        root[i] = solve(subarray, initial);
        // Polynomial deflation using synthetic division.
        Complex newc = c[n - i];
        Complex oldc = null;
        for (int j = n - i - 1; j >= 0; j--) {
            oldc = c[j];
            c[j] = newc;
            newc = oldc.add(newc.multiply(root[i]));
        }
    }

    return root;
}
 

/**
 * Find all complex roots for the polynomial with the given
 * coefficients, starting from the given initial value.
 *
 * @param coefficients Polynomial coefficients.
 * @param initial Start value.
 * @return the point at which the function value is zero.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximum number of evaluations is exceeded.
 * @throws NullArgumentException if the {@code coefficients} is
 * {@code null}.
 * @throws NoDataException if the {@code coefficients} array is empty.
 */
public Complex[] solveAll(Complex coefficients[], Complex initial)
    throws NullArgumentException,
           NoDataException,
           TooManyEvaluationsException {
    if (coefficients == null) {
        throw new NullArgumentException();
    }
    final int n = coefficients.length - 1;
    if (n == 0) {
        throw new NoDataException(LocalizedFormats.POLYNOMIAL);
    }
    // Coefficients for deflated polynomial.
    final Complex c[] = new Complex[n + 1];
    for (int i = 0; i <= n; i++) {
        c[i] = coefficients[i];
    }

    // Solve individual roots successively.
    final Complex root[] = new Complex[n];
    for (int i = 0; i < n; i++) {
        final Complex subarray[] = new Complex[n - i + 1];
        System.arraycopy(c, 0, subarray, 0, subarray.length);
        root[i] = solve(subarray, initial);
        // Polynomial deflation using synthetic division.
        Complex newc = c[n - i];
        Complex oldc = null;
        for (int j = n - i - 1; j >= 0; j--) {
            oldc = c[j];
            c[j] = newc;
            newc = oldc.add(newc.multiply(root[i]));
        }
    }

    return root;
}
 

/**
 * Find all complex roots for the polynomial with the given
 * coefficients, starting from the given initial value.
 *
 * @param coefficients Polynomial coefficients.
 * @param initial Start value.
 * @return the point at which the function value is zero.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximum number of evaluations is exceeded.
 * @throws NullArgumentException if the {@code coefficients} is
 * {@code null}.
 * @throws NoDataException if the {@code coefficients} array is empty.
 */
public Complex[] solveAll(Complex coefficients[], Complex initial) {
    if (coefficients == null) {
        throw new NullArgumentException();
    }
    final int n = coefficients.length - 1;
    if (n == 0) {
        throw new NoDataException(LocalizedFormats.POLYNOMIAL);
    }
    // Coefficients for deflated polynomial.
    final Complex c[] = new Complex[n + 1];
    for (int i = 0; i <= n; i++) {
        c[i] = coefficients[i];
    }

    // Solve individual roots successively.
    final Complex root[] = new Complex[n];
    for (int i = 0; i < n; i++) {
        final Complex subarray[] = new Complex[n - i + 1];
        System.arraycopy(c, 0, subarray, 0, subarray.length);
        root[i] = solve(subarray, initial);
        // Polynomial deflation using synthetic division.
        Complex newc = c[n - i];
        Complex oldc = null;
        for (int j = n - i - 1; j >= 0; j--) {
            oldc = c[j];
            c[j] = newc;
            newc = oldc.add(newc.multiply(root[i]));
        }
    }

    return root;
}
 

/**
 * Find all complex roots for the polynomial with the given
 * coefficients, starting from the given initial value.
 *
 * @param coefficients Polynomial coefficients.
 * @param initial Start value.
 * @return the point at which the function value is zero.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximum number of evaluations is exceeded.
 * @throws NullArgumentException if the {@code coefficients} is
 * {@code null}.
 * @throws NoDataException if the {@code coefficients} array is empty.
 */
public Complex[] solveAll(Complex coefficients[], Complex initial)
    throws NullArgumentException,
           NoDataException,
           TooManyEvaluationsException {
    if (coefficients == null) {
        throw new NullArgumentException();
    }
    final int n = coefficients.length - 1;
    if (n == 0) {
        throw new NoDataException(LocalizedFormats.POLYNOMIAL);
    }
    // Coefficients for deflated polynomial.
    final Complex c[] = new Complex[n + 1];
    for (int i = 0; i <= n; i++) {
        c[i] = coefficients[i];
    }

    // Solve individual roots successively.
    final Complex root[] = new Complex[n];
    for (int i = 0; i < n; i++) {
        final Complex subarray[] = new Complex[n - i + 1];
        System.arraycopy(c, 0, subarray, 0, subarray.length);
        root[i] = solve(subarray, initial);
        // Polynomial deflation using synthetic division.
        Complex newc = c[n - i];
        Complex oldc = null;
        for (int j = n - i - 1; j >= 0; j--) {
            oldc = c[j];
            c[j] = newc;
            newc = oldc.add(newc.multiply(root[i]));
        }
    }

    return root;
}
 

/**
 * Find all complex roots for the polynomial with the given
 * coefficients, starting from the given initial value.
 *
 * @param coefficients Polynomial coefficients.
 * @param initial Start value.
 * @return the point at which the function value is zero.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximum number of evaluations is exceeded.
 * @throws NullArgumentException if the {@code coefficients} is
 * {@code null}.
 * @throws NoDataException if the {@code coefficients} array is empty.
 */
public Complex[] solveAll(Complex coefficients[], Complex initial)
    throws NullArgumentException,
           NoDataException,
           TooManyEvaluationsException {
    if (coefficients == null) {
        throw new NullArgumentException();
    }
    final int n = coefficients.length - 1;
    if (n == 0) {
        throw new NoDataException(LocalizedFormats.POLYNOMIAL);
    }
    // Coefficients for deflated polynomial.
    final Complex c[] = new Complex[n + 1];
    for (int i = 0; i <= n; i++) {
        c[i] = coefficients[i];
    }

    // Solve individual roots successively.
    final Complex root[] = new Complex[n];
    for (int i = 0; i < n; i++) {
        final Complex subarray[] = new Complex[n - i + 1];
        System.arraycopy(c, 0, subarray, 0, subarray.length);
        root[i] = solve(subarray, initial);
        // Polynomial deflation using synthetic division.
        Complex newc = c[n - i];
        Complex oldc = null;
        for (int j = n - i - 1; j >= 0; j--) {
            oldc = c[j];
            c[j] = newc;
            newc = oldc.add(newc.multiply(root[i]));
        }
    }

    return root;
}
 

/**
 * Tests if orthogonality relation that exists between two Zernike Polynoms holds true
 * for all n between 1 and 5.
 */
@Test
@DisplayName("Test Orthogonality")
void testOrthogonality() {
    final double increment = 0.25e-2;
    final double n_max = 5;
    for (int n1=1;n1<=n_max;n1++) {
        for (int m1=0; m1<=n1;m1++) {
            for (int n2=1;n2<=n_max;n2++) {
                for (int m2=0;m2<=n2;m2++) {
                    if (((n1-Math.abs(m1)) % 2 == 0) && ((n2-Math.abs(m2)) % 2 == 0)) {
                        Complex result = new Complex(0, 0);

                        /* Initialize ZernikeBasisFunctions for n1,m1 and n2,m2. */
                        final ZernikeBasisFunction ZF1 = new ZernikeBasisFunction(n1, m1);
                        final ZernikeBasisFunction ZF2 = new ZernikeBasisFunction(n2, m2);
                        final double expected = ((Math.PI) / (n1 + 1)) * MathHelper.kronecker(n1,n2) * MathHelper.kronecker(m1,m2);

                        /* Calculate integral (approximation). */
                        for (double theta = 0.0; theta <= 2 * Math.PI; theta += increment) {
                            for (double r = 0.0; r <= 1.0f; r += increment) {
                                Complex v = new Complex(r * FastMath.cos(theta), r * FastMath.sin(theta));
                                Complex res1 = ZF1.value(v);
                                Complex res2 = ZF2.value(v);
                                result = result.add(res1.conjugate().multiply(res2).multiply(r * increment * increment));
                            }
                        }

                        /* Result of integral must be equal to expected value. */
                        assertEquals(expected, result.abs(), 1e-2);
                    }
                }
            }
        }
    }
}
 

public StateVariable toSv1(StateVariable sv2) {
    Complex s2 = new Complex(-sv2.p, -sv2.q); // s2=p2+jq2
    Complex u2 = ComplexUtils.polar2Complex(sv2.u, Math.toRadians(sv2.theta));
    Complex v2 = u2.divide(SQUARE_3); // v2=u2/sqrt(3)
    Complex i2 = s2.divide(v2.multiply(3)).conjugate(); // i2=conj(s2/(3*v2))
    Complex v1p = v2.add(z.multiply(i2)); // v1'=v2+z*i2
    Complex i1p = i2.negate().add(y.multiply(v1p)); // i1'=-i2+v1'*y
    Complex i1 = i1p.multiply(ratio); // i1=i1p*ration
    Complex v1 = v1p.divide(ratio); // v1=v1p/ration
    Complex s1 = v1.multiply(3).multiply(i1.conjugate()); // s1=3*v1*conj(i1)
    Complex u1 = v1.multiply(SQUARE_3);
    return new StateVariable(-s1.getReal(), -s1.getImaginary(), u1.abs(), Math.toDegrees(u1.getArgument()));
}
 

@Override
public Complex apply(final Complex argument) {
	final Complex iargument = argument.multiply(Complex.I);
	final Complex exponent = iargument.add(1.0);
	final Complex numerator = (new Complex(strike)).pow(exponent.subtract(1.0)).multiply(exponent);
	final Complex denominator = (argument.multiply(argument)).subtract(iargument);

	return numerator.divide(denominator);
}
 

/**
 * Find all complex roots for the polynomial with the given
 * coefficients, starting from the given initial value.
 *
 * @param coefficients Polynomial coefficients.
 * @param initial Start value.
 * @return the point at which the function value is zero.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximum number of evaluations is exceeded.
 * @throws NullArgumentException if the {@code coefficients} is
 * {@code null}.
 * @throws NoDataException if the {@code coefficients} array is empty.
 */
public Complex[] solveAll(Complex coefficients[], Complex initial)
    throws NullArgumentException,
           NoDataException,
           TooManyEvaluationsException {
    if (coefficients == null) {
        throw new NullArgumentException();
    }
    final int n = coefficients.length - 1;
    if (n == 0) {
        throw new NoDataException(LocalizedFormats.POLYNOMIAL);
    }
    // Coefficients for deflated polynomial.
    final Complex c[] = new Complex[n + 1];
    for (int i = 0; i <= n; i++) {
        c[i] = coefficients[i];
    }

    // Solve individual roots successively.
    final Complex root[] = new Complex[n];
    for (int i = 0; i < n; i++) {
        final Complex subarray[] = new Complex[n - i + 1];
        System.arraycopy(c, 0, subarray, 0, subarray.length);
        root[i] = solve(subarray, initial);
        // Polynomial deflation using synthetic division.
        Complex newc = c[n - i];
        Complex oldc = null;
        for (int j = n - i - 1; j >= 0; j--) {
            oldc = c[j];
            c[j] = newc;
            newc = oldc.add(newc.multiply(root[i]));
        }
    }

    return root;
}
 

public Complex response(final double normalizedFrequency) {
    final double a0 = getA0();
    final double a1 = getA1();
    final double a2 = getA2();
    final double b0 = getB0();
    final double b1 = getB1();
    final double b2 = getB2();

    final double w = 2 * Math.PI * normalizedFrequency;
    final Complex czn1 = ComplexUtils.polar2Complex(1., -w);
    final Complex czn2 = ComplexUtils.polar2Complex(1., -2 * w);
    Complex ch = new Complex(1);
    Complex cbot = new Complex(1);

    Complex ct = new Complex(b0 / a0);

    ct = ct.add(czn1.multiply(b1 / a0));
    ct = ct.add(czn2.multiply(b2 / a0));

    Complex cb = new Complex(1);
    cb = cb.add(czn1.multiply(a1 / a0));
    cb = cb.add(czn2.multiply(a2 / a0));

    ch = ch.multiply(ct);
    cbot = cbot.multiply(cb);

    return ch.divide(cbot);
}
 

@Override
public void fit(final double[] input) {

	if (this.numberOfDisieredCoefficients > input.length) {
		throw new IllegalArgumentException("There cannot be more DFT coefficents calcualated than there entrys in the basis instance.");
	}

	if (input.length == 0) {
		throw new IllegalArgumentException("The to transform instance can not be of length zero.");
	}

	if (this.rekursivFirstInstance) {
		this.startingpoint = 0;
	}
	// The buffer for the calculated DFT coefficeients
	this.dftCoefficientsInstance = new double[this.numberOfDisieredCoefficients * 2 - (this.startingpoint * 2)];

	// Variable used to make steps of size two in a loop that makes setps of size one
	int loopcounter = 0;

	for (int coefficient = this.startingpoint; coefficient < this.numberOfDisieredCoefficients; coefficient++) {

		Complex result = new Complex(0.0, 0.0);

		for (int entry = 0; entry < input.length; entry++) {

			// calculates the real and imaginary part of the entry according to the desired coefficient
			// c.f. p. 1510 "The BOSS is concerned with time series classification in the presence of noise" by Patrick Sch�fer
			double realpart = Math.cos(-(1.0 / input.length) * 2.0 * Math.PI * entry * coefficient);
			double imaginarypart = Math.sin(-(1.0 / input.length) * 2.0 * Math.PI * entry * coefficient);

			Complex tmp = new Complex(realpart, imaginarypart);
			tmp = tmp.multiply(input[entry]);

			result = result.add(tmp);
		}

		// saves the calculated coefficient in the buffer with first the real part and than the imaginary
		this.dftCoefficientsInstance[loopcounter] = result.getReal();
		this.dftCoefficientsInstance[loopcounter + 1] = result.getImaginary();
		loopcounter += 2;
	}
	if (this.rekursivFirstInstance && this.meanCorrected) {
		this.startingpoint = 1;
	}
	this.fittedInstance = true;
}
 

private double gotoLimit2(AclfNetwork net) throws InterpssException {
		
		int busi = 9;
		System.out.println("============ Go to Limit ============");
		LoadflowAlgorithm algo = CoreObjectFactory.createLoadflowAlgorithm(net);
		algo.loadflow();
//		LFOut.showlf(net);
		
		
		AclfBus bus = net.getBusList().get(9);
		Complex base = bus.getLoadPQ();
		oBase = bus.getLoadPQ();
		Complex delta = base.multiply(10);
		Complex result = base;

//		System.out.println("base = "+base+", delta = "+delta);
		bus.getContributeLoadList().get(0).setLoadCP(base.add(delta));
//		System.out.println("\tbus load pq = "+bus.getLoadPQ());
		
		int iter = 0;
		while(delta.abs() > 1e-10) {
			iter += 1;
			//��ǰ��������
//			System.out.println("base = "+base+", delta = "+delta);
			
			//��̽�е�
			delta = delta.multiply(0.5);
			bus.getContributeLoadList().get(0).setLoadCP(base.add(delta));
			//�����
//			System.out.println("bus 9 load pq = "+bus.getLoadPQ());
			
			//����̽�ɹ���...
			if (algo.loadflow()) {
				base = base.add(delta);
				result = base;
//				System.out.println("a success bus 9 load PQ = "+bus.getLoadPQ());
			}
//			System.out.println(AclfOutFunc.loadFlowSummary(net));
		}
		
//		System.out.println("iter = "+iter);
		bus.getContributeLoadList().get(0).setLoadCP(result);
//		System.out.println("after searching, bus 9 load PQ = "+result+", lf result = "+algo.loadflow());
//		System.out.println(AclfOutFunc.loadFlowSummary(net));
		
		return result.divide(oBase).abs();
	}
 

private double gotoLimit2(AclfNetwork net) throws InterpssException {
		
		int busi = 15;
		System.out.println("============ Go to Limit ============");
		LoadflowAlgorithm algo = CoreObjectFactory.createLoadflowAlgorithm(net);
		algo.loadflow();
//		LFOut.showlf(net);
		
		
		AclfBus bus = net.getBusList().get(busi);
		Complex base = bus.getLoadPQ();
		oBase = bus.getLoadPQ();
		Complex delta = base.multiply(100);
		Complex result = base;

//		System.out.println("base = "+base+", delta = "+delta);
		bus.getContributeLoadList().get(0).setLoadCP(base.add(delta));
		System.out.println("\tbus 16 load pq = "+bus.getLoadPQ());
		
		int iter = 0;
		while(delta.abs() > 1e-10) {
			iter += 1;
			//��ǰ��������
//			System.out.println("base = "+base+", delta = "+delta);
			
			//��̽�е�
			delta = delta.multiply(0.5);
			bus.getContributeLoadList().get(0).setLoadCP(base.add(delta));
			//�����
//			System.out.println("bus 9 load pq = "+bus.getLoadPQ());
			
			//����̽�ɹ���...
			if (algo.loadflow()) {
				base = base.add(delta);
				result = base;
//				System.out.println("a success bus 9 load PQ = "+bus.getLoadPQ());
			}
//			System.out.println(AclfOutFunc.loadFlowSummary(net));
		}
		
//		System.out.println("iter = "+iter);
		bus.getContributeLoadList().get(0).setLoadCP(result);
		System.out.println("after searching, bus 16 load PQ = "+result+", lf result = "+algo.loadflow());
//		System.out.println(AclfOutFunc.loadFlowSummary(net));
		
		return result.divide(oBase).abs();
	}
 

protected void gotoLimit(AclfNetwork net) throws InterpssException {
		
		int busi = 9;
		System.out.println("============ Go to Limit ============");
		LoadflowAlgorithm algo = CoreObjectFactory.createLoadflowAlgorithm(net);
		
		AclfBus bus = net.getBusList().get(9);
		Complex base = bus.getLoadPQ();
		Complex delta = base.multiply(10);
		Complex result = base;

		System.out.println("base = "+base+", delta = "+delta);
		if (bus.getContributeLoadList().size() == 0)
			return;//������cpf39����Э
		bus.getContributeLoadList().get(0).setLoadCP(base.add(delta));
		System.out.println("\tbus load pq = "+bus.getLoadPQ());
		
		int iter = 0;
		while(delta.abs() > 1e-10) {
			iter += 1;
			//��ǰ��������
			System.out.println("base = "+base+", delta = "+delta);
			
			//��̽�е�
			delta = delta.multiply(0.5);
			bus.getContributeLoadList().get(0).setLoadCP(base.add(delta));
			//�����
			System.out.println("bus load pq = "+bus.getLoadPQ());
			
			//����̽�ɹ���...
			if (algo.loadflow()) {
				base = base.add(delta);
				result = base;
				System.out.println("a success bus 9 load PQ = "+bus.getLoadPQ());
			}
//			System.out.println(AclfOutFunc.loadFlowSummary(net));
		}
		
		System.out.println("iter = "+iter);
		bus.getContributeLoadList().get(0).setLoadCP(result);
		System.out.println("after searching, bus 9 load PQ = "+result+", lf result = "+algo.loadflow());
		System.out.println(AclfOutFunc.loadFlowSummary(net));
		
	}
 

public Complex characteristicFunctionByMonteCarlo(final Complex zeta, final RandomVariable processAtTime) {

		final int states = processAtTime.getRealizations().length;

		Complex runningSum = new Complex(0.0,0.0);

		for(int i = 0; i< states; i++) {
			runningSum = runningSum.add((Complex.I.multiply(zeta.multiply(processAtTime.get(i)))).exp());
		}

		return runningSum.divide(states);
	}
 

public Complex characteristicFunctionByMonteCarlo(final Complex zeta, final RandomVariable processAtTime) {

		final int states = processAtTime.getRealizations().length;

		Complex runningSum = new Complex(0.0,0.0);

		for(int i = 0; i< states; i++) {
			runningSum = runningSum.add((Complex.I.multiply(zeta.multiply(processAtTime.get(i)))).exp());
		}

		return runningSum.divide(states);
	}