Package org.apache.commons.math.linear

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

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    }

    /** test A = LLT */
    @Test
    public void testAEqualLLT() throws MathException {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        CholeskyDecomposition llt = new CholeskyDecompositionImpl(matrix);
        RealMatrix l  = llt.getL();
        RealMatrix lt = llt.getLT();
        double norm = l.multiply(lt).subtract(matrix).getNorm();
        assertEquals(0, norm, 1.0e-15);
    }
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    }

    /** test that L is lower triangular */
    @Test
    public void testLLowerTriangular() throws MathException {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        RealMatrix l = new CholeskyDecompositionImpl(matrix).getL();
        for (int i = 0; i < l.getRowDimension(); i++) {
            for (int j = i + 1; j < l.getColumnDimension(); j++) {
                assertEquals(0.0, l.getEntry(i, j), 0.0);
            }
        }
    }
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    }

    /** test that LT is transpose of L */
    @Test
    public void testLTTransposed() throws MathException {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        CholeskyDecomposition llt = new CholeskyDecompositionImpl(matrix);
        RealMatrix l  = llt.getL();
        RealMatrix lt = llt.getLT();
        double norm = l.subtract(lt.transpose()).getNorm();
        assertEquals(0, norm, 1.0e-15);
    }
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    }

    /** test matrices values */
    @Test
    public void testMatricesValues() throws MathException {
        RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
                {  1,  0,  0,  0,  0 },
                {  2,  3,  0,  0,  0 },
                {  4,  5,  6,  0,  0 },
                {  7,  8,  9, 10,  0 },
                { 11, 12, 13, 14, 15 }
        });
       CholeskyDecomposition llt =
            new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(testData));

        // check values against known references
        RealMatrix l = llt.getL();
        assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
        RealMatrix lt = llt.getLT();
        assertEquals(0, lt.subtract(lRef.transpose()).getNorm(), 1.0e-13);

        // check the same cached instance is returned the second time
        assertTrue(l  == llt.getL());
        assertTrue(lt == llt.getLT());

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    public void testSimplistic() throws DimensionMismatchException {
        VectorialCovariance stat = new VectorialCovariance(2, true);
        stat.increment(new double[] {-1.0,  1.0});
        stat.increment(new double[] { 1.0, -1.0});
        RealMatrix c = stat.getResult();
        assertEquals( 2.0, c.getEntry(0, 0), 1.0e-12);
        assertEquals(-2.0, c.getEntry(1, 0), 1.0e-12);
        assertEquals( 2.0, c.getEntry(1, 1), 1.0e-12);
    }
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            stat.increment(points[i]);
        }

        assertEquals(points.length, stat.getN());

        RealMatrix c = stat.getResult();
        double[][] refC    = new double[][] {
                { 8.0470, -1.9195, -3.4445},
                {-1.9195,  1.0470,  3.2795},
                {-3.4445,  3.2795, 12.2070}
        };

        for (int i = 0; i < c.getRowDimension(); ++i) {
            for (int j = 0; j <= i; ++j) {
                assertEquals(refC[i][j], c.getEntry(i, j), 1.0e-12);
            }
        }

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

    private void checkAEqualUSVt(RealMatrix matrix) {
        BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix);
        RealMatrix u = transformer.getU();
        RealMatrix b = transformer.getB();
        RealMatrix v = transformer.getV();
        double norm = u.multiply(b).multiply(v.transpose()).subtract(matrix).getNorm();
        Assert.assertEquals(0, norm, 1.0e-14);
    }
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        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getV());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getV());
    }

    private void checkOrthogonal(RealMatrix m) {
        RealMatrix mTm = m.transpose().multiply(m);
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
        Assert.assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-14);
    }
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                { 3.0, 5.0, 7.0 }
            }));
       final double s3  = FastMath.sqrt(3.0);
       final double s14 = FastMath.sqrt(14.0);
       final double s1553 = FastMath.sqrt(1553.0);
       RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
           {  -1.0 / s14,  5.0 / (s3 * s14),  1.0 / s3 },
           {  -2.0 / s14, -4.0 / (s3 * s14),  1.0 / s3 },
           {  -3.0 / s14,  1.0 / (s3 * s14), -1.0 / s3 }
       });
       RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] {
           { -s14, s1553 / s14,   0.0 },
           {  0.0, -87 * s3 / (s14 * s1553), -s3 * s14 / s1553 },
           {  0.0, 0.0, 0.0 }
       });
       RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
           { 1.0,   0.0,         0.0        },
           { 0.0,  -23 / s1553,  32 / s1553 },
           { 0.0,  -32 / s1553, -23 / s1553 }
       });

       // check values against known references
       RealMatrix u = transformer.getU();
       Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14);
       RealMatrix b = transformer.getB();
       Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14);
       RealMatrix v = transformer.getV();
       Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14);

       // check the same cached instance is returned the second time
       Assert.assertTrue(u == transformer.getU());
       Assert.assertTrue(b == transformer.getB());
       Assert.assertTrue(v == transformer.getV());
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  @Test
  public void testLeastSquares1()
  throws FunctionEvaluationException, ConvergenceException {

      final RealMatrix factors =
          new Array2DRowRealMatrix(new double[][] {
              { 1.0, 0.0 },
              { 0.0, 1.0 }
          }, false);
      LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
          public double[] value(double[] variables) {
              return factors.operate(variables);
          }
      }, new double[] { 2.0, -3.0 });
      NelderMead optimizer = new NelderMead();
      optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
      optimizer.setMaxIterations(200);
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  • org.apache.commons.math.estimation.AbstractEstimator
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  • org.apache.commons.math.linear.BiDiagonalTransformerTest
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