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 org.apache.commons.math.linear.SingularValueDecomposition

        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare).transpose());
    }


    public void checkAEqualUSVt(final RealMatrix matrix) {
        SingularValueDecomposition svd = new SingularValueDecompositionImpl(matrix);
        RealMatrix u = svd.getU();
        RealMatrix s = svd.getS();
        RealMatrix v = svd.getV();
        double norm = u.multiply(s).multiply(v.transpose()).subtract(matrix).getNorm();
        assertEquals(0, norm, normTolerance);


    }

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

        assertEquals(0, mTm.subtract(id).getNorm(), normTolerance);
    }


    /** test matrices values */
    public void testMatricesValues1() {
       SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare));
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                { 3.0 / 5.0, -4.0 / 5.0 },
                { 4.0 / 5.0,  3.0 / 5.0 }
        });
        RealMatrix sRef = MatrixUtils.createRealMatrix(new double[][] {
                { 3.0, 0.0 },
                { 0.0, 1.0 }
        });
        RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
                { 4.0 / 5.0,  3.0 / 5.0 },
                { 3.0 / 5.0, -4.0 / 5.0 }
        });


        // check values against known references
        RealMatrix u = svd.getU();
        assertEquals(0, u.subtract(uRef).getNorm(), normTolerance);
        RealMatrix s = svd.getS();
        assertEquals(0, s.subtract(sRef).getNorm(), normTolerance);
        RealMatrix v = svd.getV();
        assertEquals(0, v.subtract(vRef).getNorm(), normTolerance);


        // check the same cached instance is returned the second time
        assertTrue(u == svd.getU());
        assertTrue(s == svd.getS());
        assertTrue(v == svd.getV());
        
    }

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

            {  24.0 / 125.0,  107.0 / 125.0, 60.0 / 125.0 },
            { -93.0 / 125.0,  -24.0 / 125.0, 80.0 / 125.0 }
        });


        // check values against known references
        SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testNonSquare));
        RealMatrix u = svd.getU();
        assertEquals(0, u.subtract(uRef).getNorm(), normTolerance);
        RealMatrix s = svd.getS();
        assertEquals(0, s.subtract(sRef).getNorm(), normTolerance);
        RealMatrix v = svd.getV();
        assertEquals(0, v.subtract(vRef).getNorm(), normTolerance);


        // check the same cached instance is returned the second time
        assertTrue(u == svd.getU());
        assertTrue(s == svd.getS());
        assertTrue(v == svd.getV());


    }

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

  @Override
  public double getCondition(final Matrix<?> m) {
    Validate.notNull(m, "m");
    if (m instanceof DoubleMatrix2D) {
      final RealMatrix temp = CommonsMathWrapper.wrap((DoubleMatrix2D) m);
      final SingularValueDecomposition svd = new SingularValueDecompositionImpl(temp);
      return svd.getConditionNumber();
    }
    throw new IllegalArgumentException("Can only find condition number of DoubleMatrix2D; have " + m.getClass());
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

      throw new CardinalityException(m.numRows(), m.numCols());
    }
    // See http://www.mlahanas.de/Math/svd.htm for details,
    // which specifically details the case of covariance matrix inversion
    // Complexity: O(min(nm2,mn2))
    SingularValueDecomposition svd = new SingularValueDecomposition(m);
    Matrix sInv = svd.getS();
    // Inverse Diagonal Elems
    for (int i = 0; i < sInv.numRows(); i++) {
      double diagElem = sInv.get(i,i);
      if (diagElem > 0.0) {
        sInv.set(i, i, 1 / diagElem);
      } else {
        throw new IllegalStateException("Eigen Value equals to 0 found.");
      }
    }
    inverseCovarianceMatrix = svd.getU().times(sInv.times(svd.getU().transpose()));
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

      throw new CardinalityException(m.numRows(), m.numCols());
    }
    // See http://www.mlahanas.de/Math/svd.htm for details,
    // which specifically details the case of covariance matrix inversion
    // Complexity: O(min(nm2,mn2))
    SingularValueDecomposition svd = new SingularValueDecomposition(m);
    Matrix sInv = svd.getS();
    // Inverse Diagonal Elems
    for (int i = 0; i < sInv.numRows(); i++) {
      double diagElem = sInv.get(i, i);
      if (diagElem > 0.0) {
        sInv.set(i, i, 1 / diagElem);
      } else {
        throw new IllegalStateException("Eigen Value equals to 0 found.");
      }
    }
    inverseCovarianceMatrix = svd.getU().times(sInv.times(svd.getU().transpose()));
    Preconditions.checkArgument(inverseCovarianceMatrix != null, "inverseCovarianceMatrix not initialized");
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

    mx.setQuick(1, 2, 6);
    mx.setQuick(2, 0, 7);
    mx.setQuick(2, 1, 8);
    mx.setQuick(2, 2, 9);


    SingularValueDecomposition svd2 = new SingularValueDecomposition(mx);
    double[] svaluesControl = svd2.getSingularValues();


    for (int i = 0; i < kp; i++) {
      System.out.printf("%.3e ", svaluesControl[i]);
    }
    System.out.println();

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Examples of org.apache.mahout.math.SingularValueDecomposition

    mx.setQuick(1, 2, 6);
    mx.setQuick(2, 0, 7);
    mx.setQuick(2, 1, 8);
    mx.setQuick(2, 2, 9);


    SingularValueDecomposition svd2 = new SingularValueDecomposition(mx);
    double[] svaluesControl = svd2.getSingularValues();


    for (int i = 0; i < kp; i++) {
      System.out.printf("%e ", svaluesControl[i]);
    }
    System.out.println();

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Examples of org.apache.mahout.math.SingularValueDecomposition

    // try to run the same thing without stochastic algo
    double[][] a = SSVDSolver.loadDistributedRowMatrix(fs, aPath, conf);


    // SingularValueDecompositionImpl svd=new SingularValueDecompositionImpl(new
    // Array2DRowRealMatrix(a));
    SingularValueDecomposition svd2 =
      new SingularValueDecomposition(new DenseMatrix(a));


    double[] svalues2 = svd2.getSingularValues();
    dumpSv(svalues2);


    for (int i = 0; i < k + p; i++) {
      assertTrue(Math.abs(svalues2[i] - stochasticSValues[i]) <= s_epsilon);
    }

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Examples of org.apache.mahout.math.SingularValueDecomposition


    LSMR r = new LSMR();
    Vector x1 = r.solve(m, b);


//    assertEquals(0, m.times(x1).minus(b).norm(2), 1.0e-2);
    double norm = new SingularValueDecomposition(m).getS().viewDiagonal().norm(2);
    double actual = m.transpose().times(m).times(x1).minus(m.transpose().times(b)).norm(2);
    System.out.printf("%.4f\n", actual / norm * 1.0e6);
    assertEquals(0, actual, norm * 1.0e-5);


    // and we need to check that the error estimates are pretty good.

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