[Matlab]Upper Triangularization & Back Substitution代码

用来做数值计算作业的代码，来自Numerical Methods Using Matlab (4th Edition) [John H. Mathews, Kurtis K. Fink]，改了一下注释，并添加输出消元过程的代码

uptrbk.m

function X = uptrbk(A, B)
    % initialization
    [N N] = size(A);
    X = zeros(N, );
    C = zeros(, N+);

    % construct augmented matrix
    Aug = [A B];

    disp('Aug before elimination');
    disp(Aug);

    for p=:N-
        % partial pivoting
        [Y,j] = max(abs(Aug(p:N, p)));
        C = Aug(p,:);
        Aug(p,:) = Aug(j+p-,:);
        Aug(j+p-,:) = C;

        disp('Aug after pivoting');
        disp(Aug);

        if Aug(p, p) ==
            'A was singular';
            break
        end

        % Elimination
        for k = p+:N
            m = Aug(k, p) / Aug(p,p);
            Aug(k, p:N+) = Aug(k, p:N+) - m*Aug(p,p:N+);
        end

        disp(['Aug after ', num2str(p), ' elimination']);
        disp(Aug);
    end

    X = backsub(Aug(:N, :N), Aug(:N, N+));
end

backsub.m

function X = backsub(A, B)
    n = length(B);
    X = zeros(n, );
    X(n) = B(n)/A(n, n);

    for k = n-:-:
        X(k) = (B(k) - A(k, k+:n) * X(k+:n)) / A(k,k);
    end
end

Note: 如果要使用分数输出结果，需要用format rat设置输出格式，默认是short（上次作业为了这个精度问题还换了C++……原来完全没必要，设format long就行了- -b）

参考连接： http://www.mathworks.cn/cn/help/matlab/ref/format.html