Java EigenDecomposition.getEigenvector方法代码示例

import org.apache.commons.math3.linear.EigenDecomposition; //导入方法依赖的package包/类
private Matrix3d toOrientationMatrix(final EigenDecomposition decomposition) {
	final RealVector e1 = decomposition.getEigenvector(0);
	final RealVector e2 = decomposition.getEigenvector(1);
	final RealVector e3 = decomposition.getEigenvector(2);
	final Vector3d x = new Vector3d(e1.getEntry(0), e1.getEntry(1), e1.getEntry(
		2));
	final Vector3d y = new Vector3d(e2.getEntry(0), e2.getEntry(1), e2.getEntry(
		2));
	final Vector3d z = new Vector3d(e3.getEntry(0), e3.getEntry(1), e3.getEntry(
		2));
	final Matrix3d orientation = new Matrix3d();
	orientation.setColumn(0, x);
	orientation.setColumn(1, y);
	orientation.setColumn(2, z);
	return orientation;
}
 

import org.apache.commons.math3.linear.EigenDecomposition; //导入方法依赖的package包/类
/**
 * Fit points to the polynomial expression Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz
 * + 2Fyz + 2Gx + 2Hy + 2Iz = 1 and determine the center and radii of the
 * fit ellipsoid.
 * 
 * @param points
 *            the points to be fit to the ellipsoid.
 */
public void fitEllipsoid(ArrayList<ThreeSpacePoint> points)
{
	// Fit the points to Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz
	// + 2Fyz + 2Gx + 2Hy + 2Iz = 1 and solve the system.
	// v = (( d' * d )^-1) * ( d' * ones.mapAddToSelf(1));
	RealVector v = solveSystem(points);

	// Form the algebraic form of the ellipsoid.
	RealMatrix a = formAlgebraicMatrix(v);

	// Find the center of the ellipsoid.
	center = findCenter(a);

	// Translate the algebraic form of the ellipsoid to the center.
	RealMatrix r = translateToCenter(center, a);

	// Generate a submatrix of r.
	RealMatrix subr = r.getSubMatrix(0, 2, 0, 2);

	// subr[i][j] = subr[i][j] / -r[3][3]).
	double divr = -r.getEntry(3, 3);
	for (int i = 0; i < subr.getRowDimension(); i++)
	{
		for (int j = 0; j < subr.getRowDimension(); j++)
		{
			subr.setEntry(i, j, subr.getEntry(i, j) / divr);
		}
	}

	// Get the eigenvalues and eigenvectors.
	EigenDecomposition ed = new EigenDecomposition(subr, 0);
	evals = ed.getRealEigenvalues();
	evecs = ed.getEigenvector(0);
	evecs1 = ed.getEigenvector(1);
	evecs2 = ed.getEigenvector(2);

	// Find the radii of the ellipsoid.
	radii = findRadii(evals);
}
 

import org.apache.commons.math3.linear.EigenDecomposition; //导入方法依赖的package包/类
/**
 * Calculates the eigen decomposition of a real matrix. The eigen
 * decomposition of matrix A is a set of two matrices: V and D such that A =
 * V × D × VT. A, V and D are all m × m matrices.
 *
 * @param a Given matrix.
 * @return Result W/V arrays.
 */
public static Array[] eigen_bak(Array a) {
    int m = a.getShape()[0];
    Array Wa;
    Array Va = Array.factory(DataType.DOUBLE, new int[]{m, m});
    double[][] aa = (double[][]) ArrayUtil.copyToNDJavaArray(a);
    RealMatrix matrix = new Array2DRowRealMatrix(aa, false);
    EigenDecomposition decomposition = new EigenDecomposition(matrix);
    if (decomposition.hasComplexEigenvalues()) {
        Wa = Array.factory(DataType.OBJECT, new int[]{m});
        double[] rev = decomposition.getRealEigenvalues();
        double[] iev = decomposition.getImagEigenvalues();
        for (int i = 0; i < m; i++) {
            Wa.setObject(i, new Complex(rev[i], iev[i]));
            RealVector v = decomposition.getEigenvector(i);
            for (int j = 0; j < v.getDimension(); j++) {
                Va.setDouble(j * m + i, v.getEntry(j));
            }
        }
    } else {
        RealMatrix V = decomposition.getV();
        RealMatrix D = decomposition.getD();
        Wa = Array.factory(DataType.DOUBLE, new int[]{m});
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < m; j++) {
                Va.setDouble(i * m + (m - j - 1), V.getEntry(i, j));
                if (i == j) {
                    Wa.setDouble(m - i - 1, D.getEntry(i, j));
                }
            }
        }
    }

    return new Array[]{Wa, Va};
}
 

import org.apache.commons.math3.linear.EigenDecomposition; //导入方法依赖的package包/类
/**
 * Fit points to the polynomial expression Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz
 * + 2Fyz + 2Gx + 2Hy + 2Iz = 1 and determine the center and radii of the
 * fit ellipsoid.
 *
 * @param points the points to be fit to the ellipsoid.
 */
public boolean fitEllipsoid(List<? extends ThreeSpacePoint> points) {
    // Fit the points to Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz
    // + 2Fyz + 2Gx + 2Hy + 2Iz = 1 and solve the system.
    // v = (( d' * d )^-1) * ( d' * ones.mapAddToSelf(1));
    RealVector v = solveSystem(points);

    if (v == null) {
        return false;
    }

    // Form the algebraic form of the ellipsoid.
    RealMatrix a = formAlgebraicMatrix(v);

    // Find the center of the ellipsoid.
    center = findCenter(a);

    // Translate the algebraic form of the ellipsoid to the center.
    RealMatrix r = translateToCenter(center, a);

    // Generate a submatrix of r.
    RealMatrix subr = r.getSubMatrix(0, 2, 0, 2);

    // subr[i][j] = subr[i][j] / -r[3][3]).
    double divr = -r.getEntry(3, 3);
    for (int i = 0; i < subr.getRowDimension(); i++) {
        for (int j = 0; j < subr.getRowDimension(); j++) {
            subr.setEntry(i, j, subr.getEntry(i, j) / divr);
        }
    }

    // Get the eigenvalues and eigenvectors.
    EigenDecomposition ed = new EigenDecomposition(subr, 0);
    evals = ed.getRealEigenvalues();
    evecs = ed.getEigenvector(0);
    evecs1 = ed.getEigenvector(1);
    evecs2 = ed.getEigenvector(2);

    // Find the radii of the ellipsoid.
    radii = findRadii(evals);
    return true;
}