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

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

    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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    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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    /** 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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                {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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        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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        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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            {  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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  @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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  @Override
  public DoubleMatrix2D getInverse(final Matrix<?> m) {
    Validate.notNull(m, "matrix was null");
    if (m instanceof DoubleMatrix2D) {
      final RealMatrix temp = CommonsMathWrapper.wrap((DoubleMatrix2D) m);
      final SingularValueDecomposition sv = new SingularValueDecompositionImpl(temp);
      final RealMatrix inv = sv.getSolver().getInverse();
      return CommonsMathWrapper.unwrap(inv);
    }
    throw new IllegalArgumentException("Can only find inverse of DoubleMatrix2D; have " + m.getClass());
  }

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    if (m instanceof DoubleMatrix1D) {
      final RealVector temp = CommonsMathWrapper.wrap((DoubleMatrix1D) m);
      return temp.getNorm();
    } else if (m instanceof DoubleMatrix2D) {
      final RealMatrix temp = CommonsMathWrapper.wrap((DoubleMatrix2D) m);
      final SingularValueDecomposition svd = new SingularValueDecompositionImpl(temp);
      return svd.getNorm();
    }
    throw new IllegalArgumentException("Can only find norm2 of DoubleMatrix2D; have " + m.getClass());
  }

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