Examples of SingularValueDecomposition

Jama.SingularValueDecomposition
Singular Value Decomposition.
For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'.
The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
cern.colt.matrix.linalg.SingularValueDecomposition
For an m x n matrix A with m >= n, the singular value decomposition is an m x n orthogonal matrix U, an n x n diagonal matrix S, and an n x n orthogonal matrix V so that A = U*S*V'.
The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
edu.ucla.sspace.matrix.factorization.SingularValueDecomposition
A refinement of the {@link MatrixFactorization} interface for algorithms thatcompute the Singular Value Decomposition. This interface exposes the three matrices that are generated as a result of the decomposition. @author David Jurgens
org.apache.commons.math.linear.SingularValueDecomposition
nist.gov/javanumerics/jama/">JAMA library, with the following changes:
- the norm2 method which has been renamed as {@link #getNorm() getNorm},
- the cond method which has been renamed as {@link #getConditionNumber() getConditionNumber},
- the rank method which has been renamed as {@link #getRank() getRank},
- a {@link #getUT() getUT} method has been added,
- a {@link #getVT() getVT} method has been added,
- a {@link #getSolver() getSolver} method has been added,
- a {@link #getCovariance(double) getCovariance} method has been added.
@see MathWorld @see Wikipedia @version $Revision: 928081 $ $Date: 2010-03-26 23:36:38 +0100 (ven. 26 mars 2010) $ @since 2.0
org.apache.mahout.math.SingularValueDecomposition
org.ejml.factory.SingularValueDecomposition

This is an abstract class for computing the singular value decomposition (SVD) of a matrix, which is defined as:

A = U * W * V ^T

where A is m by n, and U and V are orthogonal matrices, and W is a diagonal matrix.

The dimension of U,W,V depends if it is a compact SVD or not. If not compact then U is m by m, W is m by n, V is n by n. If compact then let s be the number of singular values, U is m by s, W is s by s, and V is n by s.

Accessor functions for decomposed matrices can return an internally constructed matrix if null is passed in for the optional storage parameter. The exact behavior is implementation specific. If an internally maintained matrix is returned then on the next call to decompose the matrix will be modified. The advantage of this approach is reduced memory overhead.

To create a new instance of SingularValueDecomposition see {@link DecompositionFactory#svd(int,int,boolean,boolean,boolean)}and {@link org.ejml.ops.SingularOps} contains additional helpful SVD related functions.

*Note* that the ordering of singular values is not guaranteed, unless done so by a specific implementation. The singular values can be put into descending order while adjusting U and V using {@link org.ejml.ops.SingularOps#descendingOrder(org.ejml.data.DenseMatrix64F,boolean,org.ejml.data.DenseMatrix64F,org.ejml.data.DenseMatrix64F,boolean)} SingularOps.descendingOrder()}.
@author Peter Abeles
org.encog.mathutil.matrices.decomposition.SingularValueDecomposition
nist.gov/javanumerics/jama/
weka.core.matrix.SingularValueDecomposition
nist.gov/javanumerics/jama/" target="_blank">JAMA package. @author The Mathworks and NIST @author Fracpete (fracpete at waikato dot ac dot nz) @version $Revision: 1.5 $

Examples of Jama.SingularValueDecomposition

    if ((y.length < ndata) || (x.length < ndata) || ((sd != null) && (sd.length < ndata))) {
      throw new IllegalArgumentException("data paramenters incorrect too short vector");
    }
    Matrix A = new Matrix(ndata, order + 1);
    double[] b = new double[ndata];
    SingularValueDecomposition SVD;
    double[] a = new double[order + 1];
    double xVal;
    double yVal;
    double small = 0.0000000001 * ndata;
    double[] coeff = new double[order + 1];
    double[][] U;
    double[][] V;
    double[] w;


    if (sd == null) {
      sd = new double[ndata];
      for (int i = 0; i < ndata; i++) {
        sd[i] = 1;
      }
    }


    for (int i = 0; i < ndata; i++) {
      A.set(i, 0, 1 / sd[i]);
    }
    for (int i = 0; i < ndata; i++) {
      xVal = 1;
      yVal = 1;
      for (int j = 1; j <= order; j++) {
        xVal *= x[i];
        yVal += xVal;
        A.set(i, j, xVal / sd[i]);
      }
      b[i] = yVal / sd[i];
    }
    SVD = A.svd();
    U = (SVD.getU()).getArray();
    V = (SVD.getV()).getArray();
    w = SVD.getSingularValues();


    for (int j = 0; j <= order; j++) {
      coeff[j] = 0;
      if (w[j] > small) {
        for (int i = 0; i < ndata; i++) {

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Examples of Jama.SingularValueDecomposition

            try_success("QRDecomposition...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount, "QRDecomposition...",
                    "incorrect QR decomposition calculation");
        }
        SingularValueDecomposition SVD = A.svd();


        try {
            check(A, SVD.getU().times(SVD.getS().times(SVD.getV().transpose())));
            try_success("SingularValueDecomposition...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount, "SingularValueDecomposition...",
                    "incorrect singular value decomposition calculation");
        }
        DEF = new Matrix(rankdef);
        try {
            check(DEF.rank(),
                    Math.min(DEF.getRowDimension(), DEF.getColumnDimension())
                    - 1);
            try_success("rank()...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount, "rank()...",
                    "incorrect rank calculation");
        }
        B = new Matrix(condmat);
        SVD = B.svd(); 
        double[] singularvalues = SVD.getSingularValues();


        try {
            check(B.cond(),
                    singularvalues[0]
                    / singularvalues[Math.min(B.getRowDimension(), B.getColumnDimension()) - 1]);

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Examples of cern.colt.matrix.linalg.SingularValueDecomposition

 */
public class MultinormalPCAGen extends MultinormalGen {
   private double[] lambda;


   private static SingularValueDecomposition getSvd (DoubleMatrix2D sigma) {
      return (new SingularValueDecomposition (sigma));
   }

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Examples of cern.colt.matrix.linalg.SingularValueDecomposition

   public static DoubleMatrix2D decompPCA (DoubleMatrix2D sigma)   {
      // L'objet SingularValueDecomposition permet de recuperer la matrice
      // des valeurs propres en ordre decroissant et celle des vecteurs propres de
      // sigma (pour une matrice symetrique et definie-positive seulement).


      SingularValueDecomposition sv = getSvd (sigma);
      // D contient les valeurs propres sur la diagonale
      DoubleMatrix2D D = sv.getS ();
      // Calculer la racine carree des valeurs propres
      for (int i = 0; i < D.rows(); ++i)
         D.setQuick (i, i, Math.sqrt (D.getQuick (i, i)));
      DoubleMatrix2D P = sv.getV();
      // Multiplier par la matrice orthogonale (ici P)
      return P.zMult (D, null);
   }

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Examples of cern.colt.matrix.linalg.SingularValueDecomposition

    * Computes and returns the eigenvalues of <TT>sigma</TT> in
    *  decreasing order.
    * 
    */
   public static double[] getLambda (DoubleMatrix2D sigma) {
      SingularValueDecomposition sv = getSvd (sigma);
      DoubleMatrix2D D = sv.getS ();
      double[] lambd = new double[D.rows()];
      for (int i = 0; i < D.rows(); ++i)
         lambd[i] = D.getQuick (i, i);
      return lambd;
   }

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Examples of edu.ucla.sspace.matrix.factorization.SingularValueDecomposition

            Transform transform = new LogEntropyTransform();
            if (argOptions.hasOption("preprocess"))
                transform = ReflectionUtil.getObjectInstance(
                        argOptions.getStringOption("preprocess"));
            String algName = argOptions.getStringOption("svdAlgorithm", "ANY");
            SingularValueDecomposition factorization = SVD.getFactorization(
                    Algorithm.valueOf(algName.toUpperCase()));
            basis = new StringBasisMapping();


            return new LatentSemanticAnalysis(
                false, dimensions, transform, factorization, false, basis);

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Examples of org.apache.commons.math.linear.SingularValueDecomposition

    public void testMoreRows() {
        final double[] singularValues = { 123.456, 2.3, 1.001, 0.999 };
        final int rows    = singularValues.length + 2;
        final int columns = singularValues.length;
        Random r = new Random(15338437322523l);
        SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

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Examples of org.apache.commons.math.linear.SingularValueDecomposition

    public void testMoreColumns() {
        final double[] singularValues = { 123.456, 2.3, 1.001, 0.999 };
        final int rows    = singularValues.length;
        final int columns = singularValues.length + 2;
        Random r = new Random(732763225836210l);
        SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

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Examples of org.apache.commons.math.linear.SingularValueDecomposition

    /** test dimensions */
    public void testDimensions() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testSquare);
        final int m = matrix.getRowDimension();
        final int n = matrix.getColumnDimension();
        SingularValueDecomposition svd = new SingularValueDecompositionImpl(matrix);
        assertEquals(m, svd.getU().getRowDimension());
        assertEquals(m, svd.getU().getColumnDimension());
        assertEquals(m, svd.getS().getColumnDimension());
        assertEquals(n, svd.getS().getColumnDimension());
        assertEquals(n, svd.getV().getRowDimension());
        assertEquals(n, svd.getV().getColumnDimension());


    }

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Examples of org.apache.commons.math.linear.SingularValueDecomposition

                {15.0 / 2.0,  5.0 / 2.0,  9.0 / 2.0,  3.0 / 2.0 },
                { 5.0 / 2.0, 15.0 / 2.0,  3.0 / 2.0,  9.0 / 2.0 },
                { 9.0 / 2.0,  3.0 / 2.0, 15.0 / 2.0,  5.0 / 2.0 },
                { 3.0 / 2.0,  9.0 / 2.0,  5.0 / 2.0, 15.0 / 2.0 }
        }, false);
        SingularValueDecomposition svd = new SingularValueDecompositionImpl(matrix);
        assertEquals(16.0, svd.getSingularValues()[0], 1.0e-14);
        assertEquals( 8.0, svd.getSingularValues()[1], 1.0e-14);
        assertEquals( 4.0, svd.getSingularValues()[2], 1.0e-14);
        assertEquals( 2.0, svd.getSingularValues()[3], 1.0e-14);


        RealMatrix fullCovariance = new Array2DRowRealMatrix(new double[][] {
                {  85.0 / 1024, -51.0 / 1024, -75.0 / 1024,  45.0 / 1024 },
                { -51.0 / 1024,  85.0 / 1024,  45.0 / 1024, -75.0 / 1024 },
                { -75.0 / 1024,  45.0 / 1024,  85.0 / 1024, -51.0 / 1024 },
                {  45.0 / 1024, -75.0 / 1024, -51.0 / 1024,  85.0 / 1024 }
        }, false);
        assertEquals(0.0,
                     fullCovariance.subtract(svd.getCovariance(0.0)).getNorm(),
                     1.0e-14);


        RealMatrix halfCovariance = new Array2DRowRealMatrix(new double[][] {
                {   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024 },
                {  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024 },
                {   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024 },
                {  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024 }
        }, false);
        assertEquals(0.0,
                     halfCovariance.subtract(svd.getCovariance(6.0)).getNorm(),
                     1.0e-14);


    }

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