LUP Decomp with Partial Pivoting

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Rebecca Berkawitz
Rebecca Berkawitz 2016-10-31
(1) Find L, U, and P using Gaussian Elimination with partial pivoting.
(2) Find the d, using forward substitution, by solving L d = P b
(3) Find the solution x using backward substitution by solving U x = d
Function: lup_decomp.m Write an m-file function called lup_decomp.m that decomposes a matrix A into L, U, and P. U is found using Gaussian Elimination with partial pivoting. To find P and L:
(1) Start with P = I, and L = 0
(2) We set the elements of L as we do in L U decomposition (using the factors calculated from Gaussian Elimination).
(3) Whenever we swap rows during the course of partial pivoting, we also swap the same rows in L and P.
(4) When we are all finished, we set the diagonal elements of L to 1. Inputs:
A The matrix to decompose
Outputs:
L The lower triangular matrix
U The upper triangular matrix
P The permutation matrix
Driver: ch2_1.m Solve the following system of equations using P
T L U decomposition:
−5 −3 −5 1 −2 1
5 1 −1 −4 3 −1
−4 −3 3 4 −4 3
0 −2 −3 2 −3 2
2 1 −2 −5 0 −1
1 3 1 2 4 0
x =
1 1 1 1
Print L, U, P, and x to the Command Window, and confirm you have the correct results using the lu built-in function in Ma t lab:
1 [ L U P ] = lu(A)
. . . . The driver isnt so important but this is what I have so far:
function [L, U, P]= lup_decomp(A)
%outputs of function L,U,P; function of matrix A
n= length(A);
L= eye(n);
U= zeros(n);
P= eye(n);
for k=1:n-1
[~,r]= max(abs(A(k:end,k)));
r= n-(n-k+1)+r;
A([k r], :)= A([r k],:);
P([k r],:)= P([r k],:);
L([k r],:)= L([r k],:);
L(k+1:n,k)= A(k+1:n,k)/A(k,k);
U(k,1:n)= A(k,1:n);
A(k+1:n,1:n)= A(k+1:n,1:n)- L(k+1:n,k)*A(k,1:n);
end
U(:,end)= A(:,end);
end . . . ... .. I just have no idea where to go from here

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