Example usage for org.apache.commons.math3.linear RealMatrix getFrobeniusNorm

Introduction

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

Prototype

double getFrobeniusNorm();

Source Link

Document

Returns the <a href="http://mathworld.wolfram.com/FrobeniusNorm.html"> Frobenius norm</a> of the matrix.

Usage

From source file:com.cloudera.oryx.common.math.RRQRDecomposition.java

/**
 * Return the effective numerical matrix rank.
 * <p>The effective numerical rank is the number of non-negligible
 * singular values.</p>/*from ww  w . ja v a 2 s  . c  om*/
 * <p>This implementation looks at Frobenius norms of the sequence of
 * bottom right submatrices.  When a large fall in norm is seen,
 * the rank is returned. The drop is computed as:</p>
 * {@code (thisNorm/lastNorm) * rNorm < dropThreshold }
 * <p>
 * where thisNorm is the Frobenius norm of the current submatrix,
 * lastNorm is the Frobenius norm of the previous submatrix,
 * rNorm is is the Frobenius norm of the complete matrix
 * </p>
 *
 * @param dropThreshold threshold triggering rank computation
 * @return effective numerical matrix rank
 */
public int getRank(final double dropThreshold) {
    RealMatrix r = getR();
    int rows = r.getRowDimension();
    int columns = r.getColumnDimension();
    int rank = 1;
    double lastNorm = r.getFrobeniusNorm();
    double rNorm = lastNorm;
    while (rank < Math.min(rows, columns)) {
        double thisNorm = r.getSubMatrix(rank, rows - 1, rank, columns - 1).getFrobeniusNorm();
        if (thisNorm == 0 || (thisNorm / lastNorm) * rNorm < dropThreshold) {
            break;
        }
        lastNorm = thisNorm;
        rank++;
    }
    return rank;
}

---

From source file:edu.cudenver.bios.matrix.GramSchmidtOrthonormalization.java

/**
 * Perform Gram Schmidt Orthonormalization on the specified 
 * matrix. The matrix A (mxn) is decomposed into two matrices 
 * Q (mxn), R (nxn) such that/*from w  w  w .j  a  v a 2  s  .c  om*/
 * <ul>
 * <li>A = QR
 * <li>Q'Q = Identity
 * <li>R is upper triangular
 * </ul> 
 * The resulting Q, R matrices can be retrieved with the getQ()
 * and getR() functions.
 * 
 * @param matrix
 */
public GramSchmidtOrthonormalization(RealMatrix matrix) {
    if (matrix == null)
        throw new IllegalArgumentException("Null matrix");

    // create the Q, R matrices
    int m = matrix.getRowDimension();
    int n = matrix.getColumnDimension();
    Q = MatrixUtils.createRealMatrix(m, n);
    R = MatrixUtils.createRealMatrix(n, n);

    // perform Gram Schmidt process using the following algorithm
    // let w<n> be the resulting orthonormal column vectors
    // let v<n> be the columns of the incoming matrix
    // w1 = (1/norm(v1))*v1
    // ...
    // wj = 1/norm(vj - projectionVj-1Vj)*[vj - projectionVj-1Vj]
    // where projectionVj-1Vj = (w1 * vj) * w1 + (w2 * vj) * w2 + ... + (wj-1 * vj) * wj-1
    //
    for (int i = 0; i < n; i++) {
        RealMatrix v = matrix.getColumnMatrix(i);
        for (int j = 0; j < i; j++) {
            RealMatrix Qj = Q.getColumnMatrix(j);
            double value = Qj.transpose().multiply(v).getEntry(0, 0);
            R.setEntry(j, i, value);
            v = v.subtract(Qj.scalarMultiply(value));
        }
        double norm = v.getFrobeniusNorm();
        R.setEntry(i, i, norm);
        Q.setColumnMatrix(i, v.scalarMultiply(1 / norm));
    }
}

---

From source file:org.ojalgo.benchmark.lab.library.ACM.java

@Override
protected double norm(final RealMatrix matrix) {
    return matrix.getFrobeniusNorm();
}

---