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.mahout.math.SingularValueDecomposition


    // L L' = B B'
    cd2 = new CholeskyDecomposition(b.times(b.transpose()));


    // U_0 D V_0' = L
    svd = new SingularValueDecomposition(cd2.getL());
  }

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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

      for (int j = 0; j < n; j++) {
        a[i][j] -= xi.getQuick(j);
      }
    }


    SingularValueDecomposition svd2 =
      new SingularValueDecomposition(new DenseMatrix(a));


    Vector svalues2 = new DenseVector(svd2.getSingularValues());
    LocalSSVDSolverSparseSequentialTest.dumpSv(svalues2);


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

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Examples of org.apache.mahout.math.SingularValueDecomposition

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


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


    Vector svalues2 = new DenseVector(svd2.getSingularValues());
    dumpSv(svalues2);


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

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Examples of org.apache.mahout.math.SingularValueDecomposition

    });
    // Verify all errors are nearly zero.
    assertEquals(0, columnNorms.norm(1) / columnNorms.size(), 0.1);


    // Verify that the centroids are a permutation of the original ones.
    SingularValueDecomposition svd = new SingularValueDecomposition(x);
    Vector s = svd.getS().viewDiagonal().assign(Functions.div(6));
    assertEquals(5, s.getLengthSquared(), 0.05);
    assertEquals(5, s.norm(1), 0.05);
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

  @Test
  public void testSingularValues() {
    Matrix A = lowRankMatrix();


    SequentialBigSvd s = new SequentialBigSvd(A, 8);
    SingularValueDecomposition svd = new SingularValueDecomposition(A);


    Vector reference = new DenseVector(svd.getSingularValues()).viewPart(0, 8);
    assertEquals(reference, s.getSingularValues());


    assertEquals(A, s.getU().times(new DiagonalMatrix(s.getSingularValues())).times(s.getV().transpose()));
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

  @Test
  public void testLeftVectors() {
    Matrix A = lowRankMatrix();


    SequentialBigSvd s = new SequentialBigSvd(A, 8);
    SingularValueDecomposition svd = new SingularValueDecomposition(A);


    // can only check first few singular vectors because once the singular values
    // go to zero, the singular vectors are not uniquely determined
    Matrix u1 = svd.getU().viewPart(0, 20, 0, 4).assign(Functions.ABS);
    Matrix u2 = s.getU().viewPart(0, 20, 0, 4).assign(Functions.ABS);
    assertEquals(0, u1.minus(u2).aggregate(Functions.PLUS, Functions.ABS), 1.0e-9);
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

  @Test
  public void testRightVectors() {
    Matrix A = lowRankMatrix();


    SequentialBigSvd s = new SequentialBigSvd(A, 6);
    SingularValueDecomposition svd = new SingularValueDecomposition(A);


    Matrix v1 = svd.getV().viewPart(0, 20, 0, 3).assign(Functions.ABS);
    Matrix v2 = s.getV().viewPart(0, 20, 0, 3).assign(Functions.ABS);
    assertEquals(v1, v2);
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition


        b2.assign(bTmp.get().times(bTmp.get().transpose()), Functions.PLUS);
      }
    }
    l2 = new CholeskyDecomposition(b2);
    svd = new SingularValueDecomposition(l2.getL());
  }

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Examples of org.apache.mahout.math.SingularValueDecomposition

  @Test
  public void testLeftVectors() throws IOException {
    Matrix A = lowRankMatrixInMemory(20, 20);


    SequentialBigSvd s = new SequentialBigSvd(A, 6);
    SingularValueDecomposition svd = new SingularValueDecomposition(A);


    // can only check first few singular vectors
    Matrix u1 = svd.getU().viewPart(0, 20, 0, 3).assign(Functions.ABS);
    Matrix u2 = s.getU().viewPart(0, 20, 0, 3).assign(Functions.ABS);
    assertEquals(u1, u2);
  }

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