org.apache.commons.math3.linear.CholeskyDecomposition Java Examples

/**
 * Calculates the Cholesky decomposition of a matrix. The Cholesky
 * decomposition of a real symmetric positive-definite matrix A consists of
 * a lower triangular matrix L with same size such that: A = LLT. In a
 * sense, this is the square root of A.
 *
 * @param a The given matrix.
 * @return Result array.
 */
public static Array cholesky(Array a) {
    Array r = Array.factory(DataType.DOUBLE, a.getShape());
    double[][] aa = (double[][]) ArrayUtil.copyToNDJavaArray_Double(a);
    RealMatrix matrix = new Array2DRowRealMatrix(aa, false);
    CholeskyDecomposition decomposition = new CholeskyDecomposition(matrix);
    RealMatrix L = decomposition.getL();
    int n = L.getColumnDimension();
    int m = L.getRowDimension();
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            r.setDouble(i * n + j, L.getEntry(i, j));
        }
    }

    return r;
}
 

/**
 * Function to compute Cholesky decomposition of the given input matrix. 
 * The input must be a real symmetric positive-definite matrix.
 * 
 * @param in commons-math3 Array2DRowRealMatrix
 * @return matrix block
 */
private static MatrixBlock computeCholesky(Array2DRowRealMatrix in) {
	if ( !in.isSquare() )
		throw new DMLRuntimeException("Input to cholesky() must be square matrix -- given: a " + in.getRowDimension() + "x" + in.getColumnDimension() + " matrix.");
	CholeskyDecomposition cholesky = new CholeskyDecomposition(in, 1e-14,
		CholeskyDecomposition.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);
	RealMatrix rmL = cholesky.getL();
	return DataConverter.convertToMatrixBlock(rmL.getData());
}
 

/**
 * Constructor.
 * @param ch The result of the Cholesky decomposition.
 */
public CholeskyDecompositionCommonsResult(CholeskyDecomposition ch) {
  ArgChecker.notNull(ch, "Cholesky decomposition");
  _determinant = ch.getDeterminant();
  _l = CommonsMathWrapper.unwrap(ch.getL());
  _lt = CommonsMathWrapper.unwrap(ch.getLT());
  _solver = ch.getSolver();
}
 

void setCovariance(RealMatrix covariance) {
    this.covariance = covariance;
    CholeskyDecomposition decomposition = new CholeskyDecomposition(covariance);
    this.inverseCovariance = decomposition.getSolver().getInverse();
    RealMatrix lMatrix = decomposition.getL();
    double sum = 0;
    for (int i=0;i<lMatrix.getRowDimension();i++){
        sum += Math.log(lMatrix.getEntry(i,i));
    }
    this.logDeterminant = 2*sum;
}
 

@Override
protected RealVector solve(final RealMatrix jacobian,
                           final RealVector residuals) {
    try {
        final Pair<RealMatrix, RealVector> normalEquation =
                computeNormalMatrix(jacobian, residuals);
        final RealMatrix normal = normalEquation.getFirst();
        final RealVector jTr = normalEquation.getSecond();
        return new CholeskyDecomposition(
                normal, SINGULARITY_THRESHOLD, SINGULARITY_THRESHOLD)
                .getSolver()
                .solve(jTr);
    } catch (NonPositiveDefiniteMatrixException e) {
        throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM, e);
    }
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z
 *            the measurement vector
 * @throws NullArgumentException
 *             if the measurement vector is {@code null}
 * @throws DimensionMismatchException
 *             if the dimension of the measurement vector does not fit
 * @throws SingularMatrixException
 *             if the covariance matrix could not be inverted
 */
public void correct(final RealVector z)
        throws NullArgumentException, DimensionMismatchException, SingularMatrixException {

    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) - * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // invert S
    // as the error covariance matrix is a symmetric positive
    // semi-definite matrix, we can use the cholesky decomposition
    DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();
    RealMatrix invertedS = solver.getInverse();

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1
    RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z
 *            the measurement vector
 * @throws NullArgumentException
 *             if the measurement vector is {@code null}
 * @throws DimensionMismatchException
 *             if the dimension of the measurement vector does not fit
 * @throws SingularMatrixException
 *             if the covariance matrix could not be inverted
 */
public void correct(final RealVector z)
        throws NullArgumentException, DimensionMismatchException, SingularMatrixException {

    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) - * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // invert S
    // as the error covariance matrix is a symmetric positive
    // semi-definite matrix, we can use the cholesky decomposition
    DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();
    RealMatrix invertedS = solver.getInverse();

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1
    RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z the measurement vector
 * @throws DimensionMismatchException if the dimension of the
 * measurement vector does not fit
 * @throws org.apache.commons.math3.linear.SingularMatrixException
 * if the covariance matrix could not be inverted
 */
public void correct(final RealVector z) {
    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) - * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // invert S
    // as the error covariance matrix is a symmetric positive
    // semi-definite matrix, we can use the cholesky decomposition
    DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();
    RealMatrix invertedS = solver.getInverse();

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1
    RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z
 *            the measurement vector
 * @throws NullArgumentException
 *             if the measurement vector is {@code null}
 * @throws DimensionMismatchException
 *             if the dimension of the measurement vector does not fit
 * @throws SingularMatrixException
 *             if the covariance matrix could not be inverted
 */
public void correct(final RealVector z)
        throws NullArgumentException, DimensionMismatchException, SingularMatrixException {

    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) - * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // invert S
    // as the error covariance matrix is a symmetric positive
    // semi-definite matrix, we can use the cholesky decomposition
    DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();
    RealMatrix invertedS = solver.getInverse();

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1
    RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z the measurement vector
 * @throws DimensionMismatchException if the dimension of the
 * measurement vector does not fit
 * @throws org.apache.commons.math3.linear.SingularMatrixException
 * if the covariance matrix could not be inverted
 */
public void correct(final RealVector z) {
    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) - * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // invert S
    // as the error covariance matrix is a symmetric positive
    // semi-definite matrix, we can use the cholesky decomposition
    DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();
    RealMatrix invertedS = solver.getInverse();

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1
    RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z
 *            the measurement vector
 * @throws NullArgumentException
 *             if the measurement vector is {@code null}
 * @throws DimensionMismatchException
 *             if the dimension of the measurement vector does not fit
 * @throws SingularMatrixException
 *             if the covariance matrix could not be inverted
 */
public void correct(final RealVector z)
        throws NullArgumentException, DimensionMismatchException, SingularMatrixException {

    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) - * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // invert S
    // as the error covariance matrix is a symmetric positive
    // semi-definite matrix, we can use the cholesky decomposition
    DecompositionSolver solver = new CholeskyDecomposition(s).getSolver();
    RealMatrix invertedS = solver.getInverse();

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1
    RealMatrix kalmanGain = errorCovariance.multiply(measurementMatrixT).multiply(invertedS);

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

@Override
protected RealVector solve(final RealMatrix jacobian,
                           final RealVector residuals) {
    try {
        final Pair<RealMatrix, RealVector> normalEquation =
                computeNormalMatrix(jacobian, residuals);
        final RealMatrix normal = normalEquation.getFirst();
        final RealVector jTr = normalEquation.getSecond();
        return new CholeskyDecomposition(
                normal, SINGULARITY_THRESHOLD, SINGULARITY_THRESHOLD)
                .getSolver()
                .solve(jTr);
    } catch (NonPositiveDefiniteMatrixException e) {
        throw new ConvergenceException(LocalizedFormats.UNABLE_TO_SOLVE_SINGULAR_PROBLEM, e);
    }
}
 

/**
 * Function to compute Cholesky decomposition of the given input matrix. 
 * The input must be a real symmetric positive-definite matrix.
 * 
 * @param in commons-math3 Array2DRowRealMatrix
 * @return matrix block
 */
private static MatrixBlock computeCholesky(Array2DRowRealMatrix in) {
	if ( !in.isSquare() )
		throw new DMLRuntimeException("Input to cholesky() must be square matrix -- given: a " + in.getRowDimension() + "x" + in.getColumnDimension() + " matrix.");
	CholeskyDecomposition cholesky = new CholeskyDecomposition(in, 1e-14,
		CholeskyDecomposition.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);
	RealMatrix rmL = cholesky.getL();
	return DataConverter.convertToMatrixBlock(rmL.getData());
}
 

public void fit(List<Location> locations){
	setLocations(locations);
	int n = locations.size();
	double[][] K = new double[n][n];

	for(int i=0; i<n; i++){
		Location loc1 = locations.get(i);
		double[] x1 = ModelAdaptUtils.locationToVec(loc1);
		for(int j=i; j<n; j++){
			Location loc2 = locations.get(j);
			double[] x2 = ModelAdaptUtils.locationToVec(loc2);
			double k =kernel.computeKernel(x1, x2);
			K[i][j] = k;
			K[j][i] = k;
		}
	}
	RealMatrix Kmat = MatrixUtils.createRealMatrix(K);
	RealMatrix lambdamat = MatrixUtils.createRealIdentityMatrix(n).scalarMultiply(sigma_n*sigma_n); //Tentative treatment

	RealMatrix Kymat = Kmat.add(lambdamat);

	CholeskyDecomposition chol = new CholeskyDecomposition(Kymat);
	RealMatrix Lmat = chol.getL();

	double[] normalRands = new double[n];
	for(int i=0; i<n; i++){
		normalRands[i] = rand.nextGaussian();
	}
	this.y = Lmat.operate(normalRands);

	RealMatrix invKymat = (new LUDecomposition(Kymat)).getSolver().getInverse();
	this.alphas = invKymat.operate(y);
}
 

@Override
public SlopeCoefficients estimateCoefficients(final DerivationEquation eq)
    throws EstimationException {
  final double[][] sourceTriangleMatrix = eq.getCovarianceLowerTriangularMatrix();
  // Copy matrix and enhance it to a full matrix as expected by CholeskyDecomposition
  // FIXME: Avoid copy job to speed-up the solving process e.g. by extending the CholeskyDecomposition constructor
  final int length = sourceTriangleMatrix.length;
  final double[][] matrix = new double[length][];
  for (int i = 0; i < length; i++) {
    matrix[i] = new double[length];
    final double[] s = sourceTriangleMatrix[i];
    final double[] t = matrix[i];
    for (int j = 0; j <= i; j++) {
      t[j] = s[j];
    }
    for (int j = i + 1; j < length; j++) {
      t[j] = sourceTriangleMatrix[j][i];
    }
  }
  final RealMatrix coefficients =
      new Array2DRowRealMatrix(matrix, false);
  try {
    final DecompositionSolver solver = new CholeskyDecomposition(coefficients).getSolver();
    final RealVector constants = new ArrayRealVector(eq.getConstraints(), true);
    final RealVector solution = solver.solve(constants);
    return new DefaultSlopeCoefficients(solution.toArray());
  } catch (final NonPositiveDefiniteMatrixException e) {
    throw new EstimationException("Matrix inversion error due to data is linearly dependent", e);
  }
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z
 *            the measurement vector
 * @throws NullArgumentException
 *             if the measurement vector is {@code null}
 * @throws DimensionMismatchException
 *             if the dimension of the measurement vector does not fit
 * @throws SingularMatrixException
 *             if the covariance matrix could not be inverted
 */
public void correct(final RealVector z)
        throws NullArgumentException, DimensionMismatchException, SingularMatrixException {

    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1

    // instead of calculating the inverse of S we can rearrange the formula,
    // and then solve the linear equation A x X = B with A = S', X = K' and B = (H * P)'

    // K(k) * S = P(k)- * H'
    // S' * K(k)' = H * P(k)-'
    RealMatrix kalmanGain = new CholeskyDecomposition(s).getSolver()
            .solve(measurementMatrix.multiply(errorCovariance.transpose()))
            .transpose();

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Correct the current state estimate with an actual measurement.
 *
 * @param z
 *            the measurement vector
 * @throws NullArgumentException
 *             if the measurement vector is {@code null}
 * @throws DimensionMismatchException
 *             if the dimension of the measurement vector does not fit
 * @throws SingularMatrixException
 *             if the covariance matrix could not be inverted
 */
public void correct(final RealVector z)
        throws NullArgumentException, DimensionMismatchException, SingularMatrixException {

    // sanity checks
    MathUtils.checkNotNull(z);
    if (z.getDimension() != measurementMatrix.getRowDimension()) {
        throw new DimensionMismatchException(z.getDimension(),
                                             measurementMatrix.getRowDimension());
    }

    // S = H * P(k) * H' + R
    RealMatrix s = measurementMatrix.multiply(errorCovariance)
        .multiply(measurementMatrixT)
        .add(measurementModel.getMeasurementNoise());

    // Inn = z(k) - H * xHat(k)-
    RealVector innovation = z.subtract(measurementMatrix.operate(stateEstimation));

    // calculate gain matrix
    // K(k) = P(k)- * H' * (H * P(k)- * H' + R)^-1
    // K(k) = P(k)- * H' * S^-1

    // instead of calculating the inverse of S we can rearrange the formula,
    // and then solve the linear equation A x X = B with A = S', X = K' and B = (H * P)'

    // K(k) * S = P(k)- * H'
    // S' * K(k)' = H * P(k)-'
    RealMatrix kalmanGain = new CholeskyDecomposition(s).getSolver()
            .solve(measurementMatrix.multiply(errorCovariance.transpose()))
            .transpose();

    // update estimate with measurement z(k)
    // xHat(k) = xHat(k)- + K * Inn
    stateEstimation = stateEstimation.add(kalmanGain.operate(innovation));

    // update covariance of prediction error
    // P(k) = (I - K * H) * P(k)-
    RealMatrix identity = MatrixUtils.createRealIdentityMatrix(kalmanGain.getRowDimension());
    errorCovariance = identity.subtract(kalmanGain.multiply(measurementMatrix)).multiply(errorCovariance);
}
 

/**
 * Constructor
 * @param matrix    the input matrix
 */
XCD(RealMatrix matrix) {
    this.cd = new CholeskyDecomposition(matrix);
    this.l = LazyValue.of(() -> toDataFrame(cd.getL()));
}
 

/**
 * Calculate Cholesky decomposition {@code A = L L^T}
 * @param a
 * @return L
 */
public static Dataset calcCholeskyDecomposition(Dataset a) {
	CholeskyDecomposition cd = new CholeskyDecomposition(createRealMatrix(a));
	return createDataset(cd.getL());
}
 

/**
 * This will return the cholesky decomposition of
 * the given matrix
 * @param m the matrix to convert
 * @return the cholesky decomposition of the given
 * matrix.
 * See:
 * http://en.wikipedia.org/wiki/Cholesky_decomposition
 * @throws NonSquareMatrixException
 */
public CholeskyDecomposition choleskyFromMatrix(RealMatrix m) throws Exception {
    return new CholeskyDecomposition(m);
}