Examples of LUDecomposition

Jama.LUDecomposition
LU Decomposition.
For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.
The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.
org.apache.commons.math.linear.LUDecomposition
nist.gov/javanumerics/jama/">JAMA library.
- a {@link #getP() getP} method has been added,
- the det method has been renamed as {@link #getDeterminant() getDeterminant},
- the getDoublePivot method has been removed (but the int based {@link #getPivot() getPivot} method has been kept),
- the solve and isNonSingular methods have been replaced by a {@link #getSolver() getSolver} method and the equivalent methods provided bythe returned {@link DecompositionSolver}.
@see MathWorld @see Wikipedia @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ @since 2.0
org.apache.commons.math3.linear.LUDecomposition
nist.gov/javanumerics/jama/">JAMA library.
- a {@link #getP() getP} method has been added,
- the {@code det} method has been renamed as {@link #getDeterminant() getDeterminant},
- the {@code getDoublePivot} method has been removed (but the int based{@link #getPivot() getPivot} method has been kept),
- the {@code solve} and {@code isNonSingular} methods have been replacedby a {@link #getSolver() getSolver} method and the equivalent methodsprovided by the returned {@link DecompositionSolver}.
@see MathWorld @see Wikipedia @since 2.0 (changed to concrete class in 3.0)
org.ejml.factory.LUDecomposition

LU Decomposition refactors the original matrix such that:

P^T*L*U = A
where P is a pivot matrix, L is a lower triangular matrix, U is an upper triangular matrix and A is the original matrix.

LU Decomposition is useful since once the decomposition has been performed linear equations can be quickly solved and the original matrix A inverted. Different algorithms can be selected to perform the decomposition, all will have the same end result.

To use this class first specify the size of the matrix that will be decomposed by it in the constructor. Only square m by m matrices can be decomposed. Then to decompose a matrix call {@link #decompose}. If it encounters any problems an exception will be thrown. After that all the other functions will be available for solving and inverting matrices.
@author Peter Abeles
org.encog.mathutil.matrices.decomposition.LUDecomposition
nist.gov/javanumerics/jama/

Examples of Jama.LUDecomposition

        }
        int n = A.getColumnDimension();


        A = A.getMatrix(0, n - 1, 0, n - 1);
        A.set(0, 0, 0.);
        LUDecomposition LU = A.lu();


        try {
            check(A.getMatrix(LU.getPivot(), 0, n - 1),
                    LU.getL().times(LU.getU()));
            try_success("LUDecomposition...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount, "LUDecomposition...",
                    "incorrect LU decomposition calculation");
        }

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Examples of Jama.LUDecomposition

            print(
                    c < 1 / eps
                            ? fixedWidthDoubletoString(c, 12, 3)
                            : "         Inf");


            LUDecomposition LU = new LUDecomposition(M);
            Matrix L = LU.getL();
            Matrix U = LU.getU();
            int[] p = LU.getPivot();
            Matrix R = L.times(U).minus(M.getMatrix(p, 0, n - 1));
            double res = R.norm1() / (n * eps);


            print(fixedWidthDoubletoString(res, 12, 3));

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Examples of Jama.LUDecomposition

                    hessian[j][i] += r[i] * r[j] * weights[k];
                }
            }
        }


        final LUDecomposition lu = new LUDecomposition(new Matrix(hessian));


        if (lu.isNonsingular()) {
            deltas = lu.solve(gradient);
        } else {
            throw new AIFHError("Matrix Non singular");
        }


        final double[] prev = this.algorithm.getLongTermMemory().clone();

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Examples of Jama.LUDecomposition

   * for each <em>n</em>.
   */
  private Matrix actuallySolveMatrix() {
    MatrixPrimitive prim = this.toMatrixPrimitive();
    Matrix m = new Matrix(prim.body);
    LUDecomposition decomp = new LUDecomposition(m);
    Matrix solution = new Matrix(prim.solution);


    try {
      return decomp.solve(solution);
    } catch (RuntimeException e) {
      if (e.getMessage().equals("Matrix is singular.")) {
        throw new AmbiguousLayoutException();
      } else {
        throw e;

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

    }


    /** test dimensions */
    public void testDimensions() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        LUDecomposition LU = new LUDecompositionImpl(matrix);
        assertEquals(testData.length, LU.getL().getRowDimension());
        assertEquals(testData.length, LU.getL().getColumnDimension());
        assertEquals(testData.length, LU.getU().getRowDimension());
        assertEquals(testData.length, LU.getU().getColumnDimension());
        assertEquals(testData.length, LU.getP().getRowDimension());
        assertEquals(testData.length, LU.getP().getColumnDimension());


    }

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

    }


    /** test PA = LU */
    public void testPAEqualLU() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        LUDecomposition lu = new LUDecompositionImpl(matrix);
        RealMatrix l = lu.getL();
        RealMatrix u = lu.getU();
        RealMatrix p = lu.getP();
        double norm = l.multiply(u).subtract(p.multiply(matrix)).getNorm();
        assertEquals(0, norm, normTolerance);


        matrix = MatrixUtils.createRealMatrix(testDataMinus);
        lu = new LUDecompositionImpl(matrix);
        l = lu.getL();
        u = lu.getU();
        p = lu.getP();
        norm = l.multiply(u).subtract(p.multiply(matrix)).getNorm();
        assertEquals(0, norm, normTolerance);


        matrix = MatrixUtils.createRealIdentityMatrix(17);
        lu = new LUDecompositionImpl(matrix);
        l = lu.getL();
        u = lu.getU();
        p = lu.getP();
        norm = l.multiply(u).subtract(p.multiply(matrix)).getNorm();
        assertEquals(0, norm, normTolerance);


        matrix = MatrixUtils.createRealMatrix(singular);
        lu = new LUDecompositionImpl(matrix);
        assertFalse(lu.getSolver().isNonSingular());
        assertNull(lu.getL());
        assertNull(lu.getU());
        assertNull(lu.getP());


        matrix = MatrixUtils.createRealMatrix(bigSingular);
        lu = new LUDecompositionImpl(matrix);
        assertFalse(lu.getSolver().isNonSingular());
        assertNull(lu.getL());
        assertNull(lu.getU());
        assertNull(lu.getP());


    }

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

    }




    /** test singular */
    public void testSingular() {
        LUDecomposition lu =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData));
        assertTrue(lu.getSolver().isNonSingular());
        lu = new LUDecompositionImpl(MatrixUtils.createRealMatrix(singular));
        assertFalse(lu.getSolver().isNonSingular());
        lu = new LUDecompositionImpl(MatrixUtils.createRealMatrix(bigSingular));
        assertFalse(lu.getSolver().isNonSingular());
    }

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

        assertFalse(lu.getSolver().isNonSingular());
    }


    /** test matrices values */
    public void testMatricesValues1() {
       LUDecomposition lu =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData));
        RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1.0, 0.0, 0.0 },
                { 0.5, 1.0, 0.0 },
                { 0.5, 0.2, 1.0 }
        });
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                { 2.0,  5.0, 3.0 },
                { 0.0, -2.5, 6.5 },
                { 0.0,  0.0, 0.2 }
        });
        RealMatrix pRef = MatrixUtils.createRealMatrix(new double[][] {
                { 0.0, 1.0, 0.0 },
                { 0.0, 0.0, 1.0 },
                { 1.0, 0.0, 0.0 }
        });
        int[] pivotRef = { 1, 2, 0 };


        // check values against known references
        RealMatrix l = lu.getL();
        assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
        RealMatrix u = lu.getU();
        assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-13);
        RealMatrix p = lu.getP();
        assertEquals(0, p.subtract(pRef).getNorm(), 1.0e-13);
        int[] pivot = lu.getPivot();
        for (int i = 0; i < pivotRef.length; ++i) {
            assertEquals(pivotRef[i], pivot[i]);
        }


        // check the same cached instance is returned the second time
        assertTrue(l == lu.getL());
        assertTrue(u == lu.getU());
        assertTrue(p == lu.getP());
        
    }

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

        
    }


    /** test matrices values */
    public void testMatricesValues2() {
       LUDecomposition lu =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(luData));
        RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
                {    1.0,    0.0, 0.0 },
                {    0.0,    1.0, 0.0 },
                { 1.0 / 3.0, 0.0, 1.0 }
        });
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                { 6.0, 9.0,    8.0    },
                { 0.0, 5.0,    7.0    },
                { 0.0, 0.0, 1.0 / 3.0 }
        });
        RealMatrix pRef = MatrixUtils.createRealMatrix(new double[][] {
                { 0.0, 0.0, 1.0 },
                { 0.0, 1.0, 0.0 },
                { 1.0, 0.0, 0.0 }
        });
        int[] pivotRef = { 2, 1, 0 };


        // check values against known references
        RealMatrix l = lu.getL();
        assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
        RealMatrix u = lu.getU();
        assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-13);
        RealMatrix p = lu.getP();
        assertEquals(0, p.subtract(pRef).getNorm(), 1.0e-13);
        int[] pivot = lu.getPivot();
        for (int i = 0; i < pivotRef.length; ++i) {
            assertEquals(pivotRef[i], pivot[i]);
        }


        // check the same cached instance is returned the second time
        assertTrue(l == lu.getL());
        assertTrue(u == lu.getU());
        assertTrue(p == lu.getP());
        
    }

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

  @Override
  public double getDeterminant(final Matrix<?> m) {
    Validate.notNull(m, "m");
    if (m instanceof DoubleMatrix2D) {
      final RealMatrix temp = CommonsMathWrapper.wrap((DoubleMatrix2D) m);
      final LUDecomposition lud = new LUDecompositionImpl(temp);
      return lud.getDeterminant();
    }
    throw new IllegalArgumentException("Can only find determinant of DoubleMatrix2D; have " + m.getClass());
  }

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