Java Code Examples for org.apache.commons.math3.linear.RealVector#getNorm()

@Override
public RealVector compose(List<RealVector> vectors) {
    RealVector sum = super.compose(vectors);
    if (vectors.size() > 1) {
        //norm is not calculated for single vectors.
        double norm = sum.getNorm();
        return sum.mapDivideToSelf(norm);
    }

    return sum;
}
 

/**
 * Find the first singular vector/value of a matrix A based on the Power method.
 * 
 * @see http://www.cs.yale.edu/homes/el327/datamining2013aFiles/07_singular_value_decomposition.pdf
 * @param A target matrix
 * @param x0 initial vector
 * @param nIter number of iterations for the Power method
 * @param u 1st left singular vector
 * @param v 1st right singular vector
 * @return 1st singular value
 */
public static double power1(@Nonnull final RealMatrix A, @Nonnull final double[] x0,
        final int nIter, @Nonnull final double[] u, @Nonnull final double[] v) {
    Preconditions.checkArgument(A.getColumnDimension() == x0.length,
        "Column size of A and length of x should be same");
    Preconditions.checkArgument(A.getRowDimension() == u.length,
        "Row size of A and length of u should be same");
    Preconditions.checkArgument(x0.length == v.length, "Length of x and u should be same");
    Preconditions.checkArgument(nIter >= 1, "Invalid number of iterations: " + nIter);

    RealMatrix AtA = A.transpose().multiply(A);

    RealVector x = new ArrayRealVector(x0);
    for (int i = 0; i < nIter; i++) {
        x = AtA.operate(x);
    }

    double xNorm = x.getNorm();
    for (int i = 0, n = v.length; i < n; i++) {
        v[i] = x.getEntry(i) / xNorm;
    }

    RealVector Av = new ArrayRealVector(A.operate(v));
    double s = Av.getNorm();

    for (int i = 0, n = u.length; i < n; i++) {
        u[i] = Av.getEntry(i) / s;
    }

    return s;
}
 

public double getObjective(double l2coef, List<RealVector> vars) {
    double objVal = 0.0;
    for (RealVector realVector : vars) {
        double l2norm = realVector.getNorm();
        objVal += l2norm * l2norm;
    }
    return objVal * l2coef;
}
 

/**
 * Lanczos tridiagonalization for a symmetric matrix C to make s * s tridiagonal matrix T.
 *
 * @see http://www.cas.mcmaster.ca/~qiao/publications/spie05.pdf
 * @param C target symmetric matrix
 * @param a initial vector
 * @param T result is stored here
 */
public static void lanczosTridiagonalization(@Nonnull final RealMatrix C,
        @Nonnull final double[] a, @Nonnull final RealMatrix T) {
    Preconditions.checkArgument(Arrays.deepEquals(C.getData(), C.transpose().getData()),
        "Target matrix C must be a symmetric matrix");
    Preconditions.checkArgument(C.getColumnDimension() == a.length,
        "Column size of A and length of a should be same");
    Preconditions.checkArgument(T.getRowDimension() == T.getColumnDimension(),
        "T must be a square matrix");

    int s = T.getRowDimension();

    // initialize T with zeros
    T.setSubMatrix(new double[s][s], 0, 0);

    RealVector a0 = new ArrayRealVector(a.length);
    RealVector r = new ArrayRealVector(a);

    double beta0 = 1.d;

    for (int i = 0; i < s; i++) {
        RealVector a1 = r.mapDivide(beta0);
        RealVector Ca1 = C.operate(a1);

        double alpha1 = a1.dotProduct(Ca1);

        r = Ca1.add(a1.mapMultiply(-1.d * alpha1)).add(a0.mapMultiply(-1.d * beta0));

        double beta1 = r.getNorm();

        T.setEntry(i, i, alpha1);
        if (i - 1 >= 0) {
            T.setEntry(i, i - 1, beta0);
        }
        if (i + 1 < s) {
            T.setEntry(i, i + 1, beta1);
        }

        a0 = a1.copy();
        beta0 = beta1;
    }
}
 

public double getObjective(double l2coef, RealVector var) {
    double l2norm = var.getNorm();
    return l2coef * l2norm * l2norm;
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}
 

/**
 * Compute the cosine of the angle between 2 vectors.
 *
 * @param v Vector.
 * @param w Vector.
 * @return the cosine of the angle between {@code v} and {@code w}.
 */
private double cosAngle(final RealVector v, final RealVector w) {
    return v.dotProduct(w) / (v.getNorm() * w.getNorm());
}