Examples of org.apache.commons.math3.linear.RealMatrix

org.apache.commons.math3.linear.RealMatrix
Interface defining a real-valued matrix with basic algebraic operations.
Matrix element indexing is 0-based -- e.g., getEntry(0, 0) returns the element in the first row, first column of the matrix.
@version $Id: RealMatrix.java 1244107 2012-02-14 16:17:55Z erans $

     * @return covariance matrix
     */
    public RealMatrix getResult() {


        int dimension = sums.length;
        RealMatrix result = MatrixUtils.createRealMatrix(dimension, dimension);


        if (n > 1) {
            double c = 1.0 / (n * (isBiasCorrected ? (n - 1) : n));
            int k = 0;
            for (int i = 0; i < dimension; ++i) {
                for (int j = 0; j <= i; ++j) {
                    double e = c * (n * productsSums[k++] - sums[i] * sums[j]);
                    result.setEntry(i, j, e);
                    result.setEntry(j, i, e);
                }
            }
        }


        return result;

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        generationLoop:
        for (iterations = 1; iterations <= maxIterations; iterations++) {
            incrementIterationCount();


            // Generate and evaluate lambda offspring
            final RealMatrix arz = randn1(dimension, lambda);
            final RealMatrix arx = zeros(dimension, lambda);
            final double[] fitness = new double[lambda];
            final ValuePenaltyPair[] valuePenaltyPairs = new ValuePenaltyPair[lambda];
            // generate random offspring
            for (int k = 0; k < lambda; k++) {
                RealMatrix arxk = null;
                for (int i = 0; i < checkFeasableCount + 1; i++) {
                    if (diagonalOnly <= 0) {
                        arxk = xmean.add(BD.multiply(arz.getColumnMatrix(k))
                                         .scalarMultiply(sigma)); // m + sig * Normal(0,C)
                    } else {
                        arxk = xmean.add(times(diagD,arz.getColumnMatrix(k))
                                         .scalarMultiply(sigma));
                    }
                    if (i >= checkFeasableCount ||
                        fitfun.isFeasible(arxk.getColumn(0))) {
                        break;
                    }
                    // regenerate random arguments for row
                    arz.setColumn(k, randn(dimension));
                }
                copyColumn(arxk, 0, arx, k);
                try {
                    valuePenaltyPairs[k] = fitfun.value(arx.getColumn(k)); // compute fitness
                } catch (TooManyEvaluationsException e) {
                    break generationLoop;
                }
            }


            // Compute fitnesses by adding value and penalty after scaling by value range.
            double valueRange = valueRange(valuePenaltyPairs);
            for (int iValue=0;iValue<valuePenaltyPairs.length;iValue++) {
                 fitness[iValue] = valuePenaltyPairs[iValue].value + valuePenaltyPairs[iValue].penalty*valueRange;
            }


            // Sort by fitness and compute weighted mean into xmean
            final int[] arindex = sortedIndices(fitness);
            // Calculate new xmean, this is selection and recombination
            final RealMatrix xold = xmean; // for speed up of Eq. (2) and (3)
            final RealMatrix bestArx = selectColumns(arx, MathArrays.copyOf(arindex, mu));
            xmean = bestArx.multiply(weights);
            final RealMatrix bestArz = selectColumns(arz, MathArrays.copyOf(arindex, mu));
            final RealMatrix zmean = bestArz.multiply(weights);
            final boolean hsig = updateEvolutionPaths(zmean, xold);
            if (diagonalOnly <= 0) {
                updateCovariance(hsig, bestArx, arz, arindex, xold);
            } else {
                updateCovarianceDiagonalOnly(hsig, bestArz);

View Full Code Here

        // initialize sigma
        final double[][] sigmaArray = new double[guess.length][1];
        for (int i = 0; i < guess.length; i++) {
            sigmaArray[i][0] = inputSigma[i];
        }
        final RealMatrix insigma = new Array2DRowRealMatrix(sigmaArray, false);
        sigma = max(insigma); // overall standard deviation


        // initialize termination criteria
        stopTolUpX = 1e3 * max(insigma);
        stopTolX = 1e-11 * max(insigma);
        stopTolFun = 1e-12;
        stopTolHistFun = 1e-13;


        // initialize selection strategy parameters
        mu = lambda / 2; // number of parents/points for recombination
        logMu2 = FastMath.log(mu + 0.5);
        weights = log(sequence(1, mu, 1)).scalarMultiply(-1).scalarAdd(logMu2);
        double sumw = 0;
        double sumwq = 0;
        for (int i = 0; i < mu; i++) {
            double w = weights.getEntry(i, 0);
            sumw += w;
            sumwq += w * w;
        }
        weights = weights.scalarMultiply(1 / sumw);
        mueff = sumw * sumw / sumwq; // variance-effectiveness of sum w_i x_i


        // initialize dynamic strategy parameters and constants
        cc = (4 + mueff / dimension) /
                (dimension + 4 + 2 * mueff / dimension);
        cs = (mueff + 2) / (dimension + mueff + 3.);
        damps = (1 + 2 * FastMath.max(0, FastMath.sqrt((mueff - 1) /
                                                       (dimension + 1)) - 1)) *
            FastMath.max(0.3,
                         1 - dimension / (1e-6 + maxIterations)) + cs; // minor increment
        ccov1 = 2 / ((dimension + 1.3) * (dimension + 1.3) + mueff);
        ccovmu = FastMath.min(1 - ccov1, 2 * (mueff - 2 + 1 / mueff) /
                              ((dimension + 2) * (dimension + 2) + mueff));
        ccov1Sep = FastMath.min(1, ccov1 * (dimension + 1.5) / 3);
        ccovmuSep = FastMath.min(1 - ccov1, ccovmu * (dimension + 1.5) / 3);
        chiN = FastMath.sqrt(dimension) *
                (1 - 1 / ((double) 4 * dimension) + 1 / ((double) 21 * dimension * dimension));
        // intialize CMA internal values - updated each generation
        xmean = MatrixUtils.createColumnRealMatrix(guess); // objective variables
        diagD = insigma.scalarMultiply(1 / sigma);
        diagC = square(diagD);
        pc = zeros(dimension, 1); // evolution paths for C and sigma
        ps = zeros(dimension, 1); // B defines the coordinate system
        normps = ps.getFrobeniusNorm();

View Full Code Here

    private void updateCovariance(boolean hsig, final RealMatrix bestArx,
                                  final RealMatrix arz, final int[] arindex,
                                  final RealMatrix xold) {
        double negccov = 0;
        if (ccov1 + ccovmu > 0) {
            final RealMatrix arpos = bestArx.subtract(repmat(xold, 1, mu))
                .scalarMultiply(1 / sigma); // mu difference vectors
            final RealMatrix roneu = pc.multiply(pc.transpose())
                .scalarMultiply(ccov1); // rank one update
            // minor correction if hsig==false
            double oldFac = hsig ? 0 : ccov1 * cc * (2 - cc);
            oldFac += 1 - ccov1 - ccovmu;
            if (isActiveCMA) {
                // Adapt covariance matrix C active CMA
                negccov = (1 - ccovmu) * 0.25 * mueff /
                    (FastMath.pow(dimension + 2, 1.5) + 2 * mueff);
                // keep at least 0.66 in all directions, small popsize are most
                // critical
                final double negminresidualvariance = 0.66;
                // where to make up for the variance loss
                final double negalphaold = 0.5;
                // prepare vectors, compute negative updating matrix Cneg
                final int[] arReverseIndex = reverse(arindex);
                RealMatrix arzneg = selectColumns(arz, MathArrays.copyOf(arReverseIndex, mu));
                RealMatrix arnorms = sqrt(sumRows(square(arzneg)));
                final int[] idxnorms = sortedIndices(arnorms.getRow(0));
                final RealMatrix arnormsSorted = selectColumns(arnorms, idxnorms);
                final int[] idxReverse = reverse(idxnorms);
                final RealMatrix arnormsReverse = selectColumns(arnorms, idxReverse);
                arnorms = divide(arnormsReverse, arnormsSorted);
                final int[] idxInv = inverse(idxnorms);
                final RealMatrix arnormsInv = selectColumns(arnorms, idxInv);
                // check and set learning rate negccov
                final double negcovMax = (1 - negminresidualvariance) /
                    square(arnormsInv).multiply(weights).getEntry(0, 0);
                if (negccov > negcovMax) {
                    negccov = negcovMax;
                }
                arzneg = times(arzneg, repmat(arnormsInv, dimension, 1));
                final RealMatrix artmp = BD.multiply(arzneg);
                final RealMatrix Cneg = artmp.multiply(diag(weights)).multiply(artmp.transpose());
                oldFac += negalphaold * negccov;
                C = C.scalarMultiply(oldFac)
                    .add(roneu) // regard old matrix
                    .add(arpos.scalarMultiply( // plus rank one update
                                              ccovmu + (1 - negalphaold) * negccov) // plus rank mu update
                         .multiply(times(repmat(weights, 1, dimension),
                                         arpos.transpose())))
                    .subtract(Cneg.scalarMultiply(negccov));
            } else {
                // Adapt covariance matrix C - nonactive
                C = C.scalarMultiply(oldFac) // regard old matrix
                    .add(roneu) // plus rank one update
                    .add(arpos.scalarMultiply(ccovmu) // plus rank mu update

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    public void testTransitionMeasurementMatrixMismatch() {
        
        // A and H matrix do not match in dimensions
        
        // A = [ 1 ]
        RealMatrix A = new Array2DRowRealMatrix(new double[] { 1d });
        // no control input
        RealMatrix B = null;
        // H = [ 1 1 ]
        RealMatrix H = new Array2DRowRealMatrix(new double[] { 1d, 1d });
        // Q = [ 0 ]
        RealMatrix Q = new Array2DRowRealMatrix(new double[] { 0 });
        // R = [ 0 ]
        RealMatrix R = new Array2DRowRealMatrix(new double[] { 0 });


        ProcessModel pm
            = new DefaultProcessModel(A, B, Q,
                                      new ArrayRealVector(new double[] { 0 }), null);
        MeasurementModel mm = new DefaultMeasurementModel(H, R);

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    public void testTransitionControlMatrixMismatch() {
        
        // A and B matrix do not match in dimensions
        
        // A = [ 1 ]
        RealMatrix A = new Array2DRowRealMatrix(new double[] { 1d });
        // B = [ 1 1 ]
        RealMatrix B = new Array2DRowRealMatrix(new double[] { 1d, 1d });
        // H = [ 1 ]
        RealMatrix H = new Array2DRowRealMatrix(new double[] { 1d });
        // Q = [ 0 ]
        RealMatrix Q = new Array2DRowRealMatrix(new double[] { 0 });
        // R = [ 0 ]
        RealMatrix R = new Array2DRowRealMatrix(new double[] { 0 });


        ProcessModel pm
            = new DefaultProcessModel(A, B, Q,
                                      new ArrayRealVector(new double[] { 0 }), null);
        MeasurementModel mm = new DefaultMeasurementModel(H, R);

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        double constantValue = 10d;
        double measurementNoise = 0.1d;
        double processNoise = 1e-5d;


        // A = [ 1 ]
        RealMatrix A = new Array2DRowRealMatrix(new double[] { 1d });
        // no control input
        RealMatrix B = null;
        // H = [ 1 ]
        RealMatrix H = new Array2DRowRealMatrix(new double[] { 1d });
        // x = [ 10 ]
        RealVector x = new ArrayRealVector(new double[] { constantValue });
        // Q = [ 1e-5 ]
        RealMatrix Q = new Array2DRowRealMatrix(new double[] { processNoise });
        // R = [ 0.1 ]
        RealMatrix R = new Array2DRowRealMatrix(new double[] { measurementNoise });


        ProcessModel pm
            = new DefaultProcessModel(A, B, Q,
                                      new ArrayRealVector(new double[] { constantValue }), null);
        MeasurementModel mm = new DefaultMeasurementModel(H, R);

View Full Code Here

        // acceleration noise (meter/sec^2)
        double accelNoise = 0.2d;


        // A = [ 1 dt ]
        //     [ 0  1 ]
        RealMatrix A = new Array2DRowRealMatrix(new double[][] { { 1, dt }, { 0, 1 } });


        // B = [ dt^2/2 ]
        //     [ dt     ]
        RealMatrix B = new Array2DRowRealMatrix(
                new double[][] { { FastMath.pow(dt, 2d) / 2d }, { dt } });


        // H = [ 1 0 ]
        RealMatrix H = new Array2DRowRealMatrix(new double[][] { { 1d, 0d } });


        // x = [ 0 0 ]
        RealVector x = new ArrayRealVector(new double[] { 0, 0 });


        RealMatrix tmp = new Array2DRowRealMatrix(
                new double[][] { { FastMath.pow(dt, 4d) / 4d, FastMath.pow(dt, 3d) / 2d },
                                 { FastMath.pow(dt, 3d) / 2d, FastMath.pow(dt, 2d) } });


        // Q = [ dt^4/4 dt^3/2 ]
        //     [ dt^3/2 dt^2   ]
        RealMatrix Q = tmp.scalarMultiply(FastMath.pow(accelNoise, 2));


        // P0 = [ 1 1 ]
        //      [ 1 1 ]
        RealMatrix P0 = new Array2DRowRealMatrix(new double[][] { { 1, 1 }, { 1, 1 } });


        // R = [ measurementNoise^2 ]
        RealMatrix R = new Array2DRowRealMatrix(
                new double[] { FastMath.pow(measurementNoise, 2) });


        // constant control input, increase velocity by 0.1 m/s per cycle
        RealVector u = new ArrayRealVector(new double[] { 0.1d });

View Full Code Here


        // A = [ 1, dt, 0,  0 ]  =>  x(n+1) = x(n) + vx(n)
        //     [ 0,  1, 0,  0 ]  => vx(n+1) =        vx(n)
        //     [ 0,  0, 1, dt ]  =>  y(n+1) =              y(n) + vy(n)
        //     [ 0,  0, 0,  1 ]  => vy(n+1) =                     vy(n)
        final RealMatrix A = MatrixUtils.createRealMatrix(new double[][] {
                { 1, dt, 0,  0 },
                { 0,  1, 0,  0 },
                { 0,  0, 1, dt },
                { 0,  0, 0,  1 }       
        });


        // The control vector, which adds acceleration to the kinematic equations.
        // 0          =>  x(n+1) =  x(n+1)
        // 0          => vx(n+1) = vx(n+1)
        // -9.81*dt^2 =>  y(n+1) =  y(n+1) - 1/2 * 9.81 * dt^2
        // -9.81*dt   => vy(n+1) = vy(n+1) - 9.81 * dt
        final RealVector controlVector =
                MatrixUtils.createRealVector(new double[] { 0, 0, 0.5 * -9.81 * dt * dt, -9.81 * dt } );


        // The control matrix B only expects y and vy, see control vector
        final RealMatrix B = MatrixUtils.createRealMatrix(new double[][] {
                { 0, 0, 0, 0 },
                { 0, 0, 0, 0 },
                { 0, 0, 1, 0 },
                { 0, 0, 0, 1 }
        });


        // We only observe the x/y position of the cannonball
        final RealMatrix H = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 0, 0, 0 },
                { 0, 0, 0, 0 },
                { 0, 0, 1, 0 },
                { 0, 0, 0, 0 }
        });
        
        // our guess of the initial state.
        final RealVector initialState = MatrixUtils.createRealVector(new double[] { 0, speedX, 0, speedY } );


        // the initial error covariance matrix, the variance = noise^2
        final double var = measurementNoise * measurementNoise;
        final RealMatrix initialErrorCovariance = MatrixUtils.createRealMatrix(new double[][] {
                { var,    0,   0,    0 },
                {   0, 1e-3,   0,    0 },
                {   0,    0, var,    0 },
                {   0,    0,   0, 1e-3 }
        });


        // we assume no process noise -> zero matrix
        final RealMatrix Q = MatrixUtils.createRealMatrix(4, 4);
        
        // the measurement covariance matrix
        final RealMatrix R = MatrixUtils.createRealMatrix(new double[][] {
                { var,    0,   0,    0 },
                {   0, 1e-3,   0,    0 },
                {   0,    0, var,    0 },
                {   0,    0,   0, 1e-3 }
        });

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            messageBuffer.append("\nexpected " + expected.getRowDimension() +
                    " x " + expected.getColumnDimension());
            Assert.fail(messageBuffer.toString());
        }


        RealMatrix delta = expected.subtract(observed);
        if (delta.getNorm() >= tolerance) {
            StringBuilder messageBuffer = new StringBuilder(msg);
            messageBuffer.append("\nExpected: " + expected);
            messageBuffer.append("\nObserved: " + observed);
            messageBuffer.append("\nexpected - observed: " + delta);
            Assert.fail(messageBuffer.toString());

View Full Code Here

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