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

org.apache.commons.math.linear.BiDiagonalTransformer
Class transforming any matrix to bi-diagonal shape.
Any m × n matrix A can be written as the product of three matrices: A = U × B × V^T with U an m × m orthogonal matrix, B an m × n bi-diagonal matrix (lower diagonal if m < n, upper diagonal otherwise), and V an n × n orthogonal matrix.

Transformation to bi-diagonal shape is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like {@link SingularValueDecomposition Singular Value Decomposition}. This class is therefore intended for internal use by the library and is not public. As a consequence of this explicitly limited scope, many methods directly returns references to internal arrays, not copies.
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 2.0

        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
        assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-14);        
    }


    public void testBBiDiagonal() {
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getB());
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getB());
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getB());
    }

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            }
        }
    }


    public void testMatricesValues() {
       BiDiagonalTransformer transformer =
            new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare));
       final double s17 = Math.sqrt(17.0);
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                {  -8 / (5 * s17), 19 / (5 * s17) },
                { -19 / (5 * s17), -8 / (5 * s17) }
        });
        RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] {
                { -3 * s17 / 5, 32 * s17 / 85 },
                {      0.0,     -5 * s17 / 17 }
        });
        RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1.0,  0.0 },
                { 0.0, -1.0 }
        });


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


        // check the same cached instance is returned the second time
        assertTrue(u == transformer.getU());
        assertTrue(b == transformer.getB());
        assertTrue(v == transformer.getV());
        
    }

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        assertTrue(v == transformer.getV());
        
    }


    public void testUpperOrLower() {
        assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).isUpperBiDiagonal());
        assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).isUpperBiDiagonal());
        assertFalse(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).isUpperBiDiagonal());
    }

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Related Classes of org.apache.commons.math.linear.BiDiagonalTransformer

org.apache.commons.math.linear.BiDiagonalTransformerTest

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