Package org.apache.mahout.math

Examples of org.apache.mahout.math.Matrix.times()

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    a = a.transpose().times(a);

    EigenDecomposition eig = new EigenDecomposition(a);
    Matrix d = eig.getD();
    Matrix v = eig.getV();
    check("EigenvalueDecomposition (rank deficient)...", a.times(v), v.times(d));

    assertEquals(0, eig.getImagEigenvalues().norm(1), 1e-10);
    assertEquals(3, eig.getRealEigenvalues().norm(0), 1e-10);
  }
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      }
    }
    EigenDecomposition eig = new EigenDecomposition(a);
    Matrix d = eig.getD();
    Matrix v = eig.getV();
    check("EigenvalueDecomposition (nonsymmetric)...", a.times(v), v.times(d));
  }

  @Test
  public void testSequential() {
    int validld = 3;
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    }

    EigenDecomposition Eig = new EigenDecomposition(A);
    Matrix D = Eig.getD();
    Matrix V = Eig.getV();
    check("EigenvalueDecomposition (nonsymmetric)...", A.times(V), V.times(D));

    A = A.transpose().times(A);
    Eig = new EigenDecomposition(A);
    D = Eig.getD();
    V = Eig.getV();
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    A = A.transpose().times(A);
    Eig = new EigenDecomposition(A);
    D = Eig.getD();
    V = Eig.getV();
    check("EigenvalueDecomposition (symmetric)...", A.times(V), V.times(D));

  }

  private void check(String msg, Matrix a, Matrix b) {
    assertEquals(msg, 0, a.minus(b).aggregate(Functions.PLUS, Functions.ABS), 1e-10);
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    Vector x = new DenseVector(new double[]{5, -120, 630, -1120, 630});

    Vector b = new DenseVector(5);
    b.assign(1);

    assertEquals(0, m.times(x).minus(b).norm(2), 1.0e-9);

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

    // the ideal solution is  [5  -120   630 -1120   630] but the 5x5 hilbert matrix
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    // has a condition number of almost 500,000 and the normal equation condition
    // number is that squared.  This means that we don't get the exact answer with
    // a fast iterative solution.
    // Thus, we have to check the residuals rather than testing that the answer matched
    // the ideal.
    assertEquals(0, m.times(x1).minus(b).norm(2), 1.0e-2);
    assertEquals(0, m.transpose().times(m).times(x1).minus(m.transpose().times(b)).norm(2), 1.0e-7);

    // and we need to check that the error estimates are pretty good.
    assertEquals(m.times(x1).minus(b).norm(2), r.getResidualNorm(), 1.0e-5);
    assertEquals(m.transpose().times(m).times(x1).minus(m.transpose().times(b)).norm(2), r.getNormalEquationResidual(), 1.0e-9);
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    // the ideal.
    assertEquals(0, m.times(x1).minus(b).norm(2), 1.0e-2);
    assertEquals(0, m.transpose().times(m).times(x1).minus(m.transpose().times(b)).norm(2), 1.0e-7);

    // and we need to check that the error estimates are pretty good.
    assertEquals(m.times(x1).minus(b).norm(2), r.getResidualNorm(), 1.0e-5);
    assertEquals(m.transpose().times(m).times(x1).minus(m.transpose().times(b)).norm(2), r.getNormalEquationResidual(), 1.0e-9);
  }
 
  private static Matrix hilbert(int n) {
    Matrix r = new DenseMatrix(n, n);
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      }
      v.assign(Functions.MULT, 1/((row + 1) * v.norm(2)));
      matrix.assignRow(row, v);
    }
    if (symmetric) {
      return matrix.times(matrix.transpose());
    }
    return matrix;
  }

  public static Matrix randomHierarchicalSymmetricMatrix(int size) {
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    Vector v = new RandomAccessSparseVector(50);
    v.assign(1.0);
    Matrix m = SolverTest.randomSequentialAccessSparseMatrix(100, 90, 50, 20, 1.0);
    DistributedRowMatrix dm = randomDistributedMatrix(100, 90, 50, 20, 1.0, false);

    Vector expected = m.times(v);
    Vector actual = dm.times(v);
    assertEquals(0.0, expected.getDistanceSquared(actual), EPSILON);
  }

  @Test
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                                                      boolean isSymmetric,
                                                      String baseTmpDirSuffix) throws IOException {
    Path baseTmpDirPath = getTestTempDirPath(baseTmpDirSuffix);
    Matrix c = SolverTest.randomSequentialAccessSparseMatrix(numRows, nonNullRows, numCols, entriesPerRow, entryMean);
    if (isSymmetric) {
      c = c.times(c.transpose());
    }
    return saveToFs(c, baseTmpDirPath);
  }

  private static DistributedRowMatrix saveToFs(final Matrix m, Path baseTmpDirPath) throws IOException {
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