LU decomposition

kevinsunParticipant 2010-05-24 at 3:15 am

How to use this class? Need examples please.

Haksun LiModerator 2010-05-25 at 4:04 pm

<br />
        Matrix A1 = new Matrix(new double[][]{<br />
                    {5, 2, 3, 4},<br />
                    {5, 6, 7, 4},<br />
                    {1, 3, 2, 3},<br />
                    {1, 7, 6, 2}<br />
                });<br />
        LU instance = new LU(A1);<br />
        LowerTriangularMatrix L = instance.L();<br />
        UpperTriangularMatrix U = instance.U();<br />
        PermutationMatrix P = instance.P();<br />
<br />
        Matrix A2 = P.times(A1);<br />
        Matrix A3 = L.times(U);<br />
<br />
        assertEquals(A2, A3);<br />
        assertEquals(24, Measure.det(A1), 1e-13);<br />

kevinsunParticipant 2010-05-29 at 5:55 am

I can’t do Inverse(L) for a LowerTriangularMatrix L. Please help.

Is there a linear system solver in the library to solve Lx=b if L is LowerTriangularMatrix? Same for UpperTriangularMatrix?

Haksun LiModerator 2010-05-31 at 1:26 pm

For a [tt:207ejgzd]LowerTriangularMatrix[/tt:207ejgzd], you can do

<br />
        LowerTriangularMatrix L = new LowerTriangularMatrix(new double[][]{<br />
                    {3},<br />
                    {7, 4}<br />
                });<br />
<br />
        Matrix Linv = new Inverse(L, 1e-15);//or a suitable epsilon<br />

For an [tt:207ejgzd]UpperTriangularMatrix[/tt:207ejgzd], you can do

<br />
        UpperTriangularMatrix U = new UpperTriangularMatrix(new double[][]{<br />
                    {7, 4},<br />
                    {3}<br />
                });<br />
<br />
        Matrix Ainv = new Inverse(U, 1e-15);//or a suitable epsilon<br />