Examples of org.apache.commons.math.complex.Complex

org.apache.commons.math.complex.Complex
Representation of a Complex number - a number which has both a real and imaginary part.
Implementations of arithmetic operations handle NaN and infinite values according to the rules for {@link java.lang.Double}arithmetic, applying definitional formulas and returning NaN or infinite values in real or imaginary parts as these arise in computation. See individual method javadocs for details.

{@link #equals} identifies all values with NaN in either realor imaginary part - e.g.,
```
 1 + NaNi  == NaN + i == NaN + NaNi.
```
implements Serializable since 2.0 @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $

        if (f.value(min) == 0.0) { return min; }
        if (f.value(max) == 0.0) { return max; }
        verifyBracketing(min, max, f);


        double coefficients[] = ((PolynomialFunction) f).getCoefficients();
        Complex c[] = new Complex[coefficients.length];
        for (int i = 0; i < coefficients.length; i++) {
            c[i] = new Complex(coefficients[i], 0.0);
        }
        Complex initial = new Complex(0.5 * (min + max), 0.0);
        Complex z = solve(c, initial);
        if (isRootOK(min, max, z)) {
            setResult(z.getReal(), iterationCount);
            return result;
        }


        // solve all roots and select the one we're seeking
        Complex[] root = solveAll(c, initial);

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     */
    @Deprecated
    public Complex[] solveAll(double coefficients[], double initial) throws
        ConvergenceException, FunctionEvaluationException {


        Complex c[] = new Complex[coefficients.length];
        Complex z = new Complex(initial, 0.0);
        for (int i = 0; i < c.length; i++) {
            c[i] = new Complex(coefficients[i], 0.0);
        }
        return solveAll(c, z);
    }

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        int iterationCount = 0;
        if (n < 1) {
            throw MathRuntimeException.createIllegalArgumentException(
                  LocalizedFormats.NON_POSITIVE_POLYNOMIAL_DEGREE, n);
        }
        Complex c[] = new Complex[n+1];    // coefficients for deflated polynomial
        for (int i = 0; i <= n; i++) {
            c[i] = coefficients[i];
        }


        // solve individual root successively
        Complex root[] = new Complex[n];
        for (int i = 0; i < n; i++) {
            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]));
            }
            iterationCount += this.iterationCount;
        }


        resultComputed = true;

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        int n = coefficients.length - 1;
        if (n < 1) {
            throw MathRuntimeException.createIllegalArgumentException(
                  LocalizedFormats.NON_POSITIVE_POLYNOMIAL_DEGREE, n);
        }
        Complex N  = new Complex(n,     0.0);
        Complex N1 = new Complex(n - 1, 0.0);


        int i = 1;
        Complex pv = null;
        Complex dv = null;
        Complex d2v = null;
        Complex G = null;
        Complex G2 = null;
        Complex H = null;
        Complex delta = null;
        Complex denominator = null;
        Complex z = initial;
        Complex oldz = new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
        while (i <= maximalIterationCount) {
            // Compute pv (polynomial value), dv (derivative value), and
            // d2v (second derivative value) simultaneously.
            pv = coefficients[n];
            dv = Complex.ZERO;
            d2v = Complex.ZERO;
            for (int j = n-1; j >= 0; j--) {
                d2v = dv.add(z.multiply(d2v));
                dv = pv.add(z.multiply(dv));
                pv = coefficients[j].add(z.multiply(pv));
            }
            d2v = d2v.multiply(new Complex(2.0, 0.0));


            // check for convergence
            double tolerance = FastMath.max(relativeAccuracy * z.abs(),
                                        absoluteAccuracy);
            if ((z.subtract(oldz)).abs() <= tolerance) {
                resultComputed = true;
                iterationCount = i;
                return z;
            }
            if (pv.abs() <= functionValueAccuracy) {
                resultComputed = true;
                iterationCount = i;
                return z;
            }


            // now pv != 0, calculate the new approximation
            G = dv.divide(pv);
            G2 = G.multiply(G);
            H = G2.subtract(d2v.divide(pv));
            delta = N1.multiply((N.multiply(H)).subtract(G2));
            // choose a denominator larger in magnitude
            Complex deltaSqrt = delta.sqrt();
            Complex dplus = G.add(deltaSqrt);
            Complex dminus = G.subtract(deltaSqrt);
            denominator = dplus.abs() > dminus.abs() ? dplus : dminus;
            // Perturb z if denominator is zero, for instance,
            // p(x) = x^3 + 1, z = 0.
            if (denominator.equals(new Complex(0.0, 0.0))) {
                z = z.add(new Complex(absoluteAccuracy, absoluteAccuracy));
                oldz = new Complex(Double.POSITIVE_INFINITY,
                                   Double.POSITIVE_INFINITY);
            } else {
                oldz = z;
                z = z.subtract(N.divide(denominator));
            }

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    super(imaginaryCharacter);
    // TODO Auto-generated constructor stub
  }


  public org.zkoss.zss.engine.Complex parse(String source, String suffix) throws ParseException {
    Complex c = super.parse(source);
    org.zkoss.zss.engine.Complex result = new org.zkoss.zss.engine.Complex(c.getReal(), c.getImaginary(), suffix);
    return result;
  }

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            x[i] = a - b;
            x[n-i] = a + b;
            t1 += c;
        }
        FastFourierTransformer transformer = new FastFourierTransformer();
        Complex y[] = transformer.transform(x);


        // reconstruct the FCT result for the original array
        transformed[0] = y[0].getReal();
        transformed[1] = t1;
        for (int i = 1; i < (n >> 1); i++) {

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    /**
     * Test of solver for the quintic function using solveAll().
     */
    public void testQuinticFunction2() throws MathException {
        double initial = 0.0, tolerance;
        Complex expected, result[];


        // p(x) = x^5 + 4x^3 + x^2 + 4 = (x+1)(x^2-x+1)(x^2+4)
        double coefficients[] = { 4.0, 0.0, 1.0, 4.0, 0.0, 1.0 };
        LaguerreSolver solver = new LaguerreSolver();
        result = solver.solveAll(coefficients, initial);


        expected = new Complex(0.0, -2.0);
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(0.0, 2.0);
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(0.5, 0.5 * FastMath.sqrt(3.0));
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(-1.0, 0.0);
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(0.5, -0.5 * FastMath.sqrt(3.0));
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);
    }

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    /**
     * Test of solver for the quintic function using solveAll().
     */
    public void testQuinticFunction2() throws MathException {
        double initial = 0.0, tolerance;
        Complex expected, result[];


        // p(x) = x^5 + 4x^3 + x^2 + 4 = (x+1)(x^2-x+1)(x^2+4)
        double coefficients[] = { 4.0, 0.0, 1.0, 4.0, 0.0, 1.0 };
        LaguerreSolver solver = new LaguerreSolver();
        result = solver.solveAll(coefficients, initial);


        expected = new Complex(0.0, -2.0);
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(0.0, 2.0);
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(0.5, 0.5 * Math.sqrt(3.0));
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);


        expected = new Complex(-1.0, 0.0);
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);
        
        expected = new Complex(0.5, -0.5 * Math.sqrt(3.0));
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected.abs() * solver.getRelativeAccuracy()));
        TestUtils.assertContains(result, expected, tolerance);
    }

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            x[i] = A - B;
            x[N-i] = A + B;
            F1 += C;
        }
        FastFourierTransformer transformer = new FastFourierTransformer();
        Complex y[] = transformer.transform(x);


        // reconstruct the FCT result for the original array
        F[0] = y[0].getReal();
        F[1] = F1;
        for (int i = 1; i < (N >> 1); i++) {

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     */
    protected Complex[] fft(double f[], boolean isInverse)
        throws IllegalArgumentException {


        verifyDataSet(f);
        Complex F[] = new Complex[f.length];
        if (f.length == 1) {
            F[0] = new Complex(f[0], 0.0);
            return F;
        }


        // Rather than the naive real to complex conversion, pack 2N
        // real numbers into N complex numbers for better performance.
        int N = f.length >> 1;
        Complex c[] = new Complex[N];
        for (int i = 0; i < N; i++) {
            c[i] = new Complex(f[2*i], f[2*i+1]);
        }
        roots.computeOmega(isInverse ? -N : N);
        Complex z[] = fft(c);


        // reconstruct the FFT result for the original array
        roots.computeOmega(isInverse ? -2*N : 2*N);
        F[0] = new Complex(2 * (z[0].getReal() + z[0].getImaginary()), 0.0);
        F[N] = new Complex(2 * (z[0].getReal() - z[0].getImaginary()), 0.0);
        for (int i = 1; i < N; i++) {
            Complex A = z[N-i].conjugate();
            Complex B = z[i].add(A);
            Complex C = z[i].subtract(A);
            //Complex D = roots.getOmega(i).multiply(Complex.I);
            Complex D = new Complex(-roots.getOmegaImaginary(i),
                                    roots.getOmegaReal(i));
            F[i] = B.subtract(C.multiply(D));
            F[2*N-i] = F[i].conjugate();
        }

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