Example usage for org.apache.commons.math3.linear QRDecomposition QRDecomposition

Introduction

In this page you can find the example usage for org.apache.commons.math3.linear QRDecomposition QRDecomposition.

Prototype

public QRDecomposition(RealMatrix matrix, double threshold) 

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Document

Calculates the QR-decomposition of the given matrix.

Usage

From source file:io.yields.math.concepts.operator.Smoothness.java

private RealMatrix computeDistance(List<Tuple> normalizedData) {
    RealMatrix a = new Array2DRowRealMatrix(normalizedData.size(), order + 1);
    RealMatrix b = new Array2DRowRealMatrix(normalizedData.size(), 1);
    int row = 0;/*  ww w  . j  a  v  a2s.  c o m*/
    for (Tuple tuple : normalizedData) {
        final int currentRow = row;
        IntStream.rangeClosed(0, order)
                .forEach(power -> a.setEntry(currentRow, power, Math.pow(tuple.getX(), power)));
        b.setEntry(currentRow, 0, tuple.getY());
        row++;
    }
    DecompositionSolver solver = new QRDecomposition(a, EPS).getSolver();
    if (solver.isNonSingular() && !isConstant(b)) {
        RealMatrix solution = solver.solve(b);
        return a.multiply(solution).subtract(b);
    } else {
        return new Array2DRowRealMatrix(normalizedData.size(), 1);
    }
}

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From source file:org.orekit.utils.AngularCoordinates.java

/** Find a vector from two known cross products.
 * <p>//from  w  w  w  .  j a v  a2s  .co m
 * We want to find  such that:   v? = c? and   v = c
 * </p>
 * <p>
 * The first equation (  v? = c?) will always be fulfilled exactly,
 * and the second one will be fulfilled if possible.
 * </p>
 * @param v1 vector forming the first known cross product
 * @param c1 know vector for cross product   v?
 * @param v2 vector forming the second known cross product
 * @param c2 know vector for cross product   v
 * @param tolerance relative tolerance factor used to check singularities
 * @return vector  such that:   v? = c? and   v = c
 * @exception MathIllegalArgumentException if vectors are inconsistent and
 * no solution can be found
 */
private static Vector3D inverseCrossProducts(final Vector3D v1, final Vector3D c1, final Vector3D v2,
        final Vector3D c2, final double tolerance) throws MathIllegalArgumentException {

    final double v12 = v1.getNormSq();
    final double v1n = FastMath.sqrt(v12);
    final double v22 = v2.getNormSq();
    final double v2n = FastMath.sqrt(v22);
    final double threshold = tolerance * FastMath.max(v1n, v2n);

    Vector3D omega;

    try {
        // create the over-determined linear system representing the two cross products
        final RealMatrix m = MatrixUtils.createRealMatrix(6, 3);
        m.setEntry(0, 1, v1.getZ());
        m.setEntry(0, 2, -v1.getY());
        m.setEntry(1, 0, -v1.getZ());
        m.setEntry(1, 2, v1.getX());
        m.setEntry(2, 0, v1.getY());
        m.setEntry(2, 1, -v1.getX());
        m.setEntry(3, 1, v2.getZ());
        m.setEntry(3, 2, -v2.getY());
        m.setEntry(4, 0, -v2.getZ());
        m.setEntry(4, 2, v2.getX());
        m.setEntry(5, 0, v2.getY());
        m.setEntry(5, 1, -v2.getX());

        final RealVector rhs = MatrixUtils.createRealVector(
                new double[] { c1.getX(), c1.getY(), c1.getZ(), c2.getX(), c2.getY(), c2.getZ() });

        // find the best solution we can
        final DecompositionSolver solver = new QRDecomposition(m, threshold).getSolver();
        final RealVector v = solver.solve(rhs);
        omega = new Vector3D(v.getEntry(0), v.getEntry(1), v.getEntry(2));

    } catch (SingularMatrixException sme) {

        // handle some special cases for which we can compute a solution
        final double c12 = c1.getNormSq();
        final double c1n = FastMath.sqrt(c12);
        final double c22 = c2.getNormSq();
        final double c2n = FastMath.sqrt(c22);

        if (c1n <= threshold && c2n <= threshold) {
            // simple special case, velocities are cancelled
            return Vector3D.ZERO;
        } else if (v1n <= threshold && c1n >= threshold) {
            // this is inconsistent, if v? is zero, c? must be 0 too
            throw new NumberIsTooLargeException(c1n, 0, true);
        } else if (v2n <= threshold && c2n >= threshold) {
            // this is inconsistent, if v is zero, c must be 0 too
            throw new NumberIsTooLargeException(c2n, 0, true);
        } else if (Vector3D.crossProduct(v1, v2).getNorm() <= threshold && v12 > threshold) {
            // simple special case, v is redundant with v?, we just ignore it
            // use the simplest : orthogonal to both v? and c?
            omega = new Vector3D(1.0 / v12, Vector3D.crossProduct(v1, c1));
        } else {
            throw sme;
        }

    }

    // check results
    final double d1 = Vector3D.distance(Vector3D.crossProduct(omega, v1), c1);
    if (d1 > threshold) {
        throw new NumberIsTooLargeException(d1, 0, true);
    }

    final double d2 = Vector3D.distance(Vector3D.crossProduct(omega, v2), c2);
    if (d2 > threshold) {
        throw new NumberIsTooLargeException(d2, 0, true);
    }

    return omega;

}

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