问在MATLAB中执行不旋转的LU分解

EN

function [L, U] = lu_nopivot(A)

n = size(A, 1); % Obtain number of rows (should equal number of columns)
L = eye(n); % Start L off as identity and populate the lower triangular half slowly
for k = 1 : n
    % For each row k, access columns from k+1 to the end and divide by
    % the diagonal coefficient at A(k ,k)
    L(k + 1 : n, k) = A(k + 1 : n, k) / A(k, k);

    % For each row k+1 to the end, perform Gaussian elimination
    % In the end, A will contain U
    for l = k + 1 : n
        A(l, :) = A(l, :) - L(l, k) * A(k, :);
    end
end
U = A;

end

>> rng(123)
>> A = randi(10, 3, 3)

A =

     7     6    10
     3     8     7
     3     5     5

>> [L,U] = lu_nopivot(A)

L =

    1.0000         0         0
    0.4286    1.0000         0
    0.4286    0.4474    1.0000   

U =

    7.0000    6.0000   10.0000
         0    5.4286    2.7143
         0         0   -0.5000

>> L*U

ans =

     7     6    10
     3     8     7
     3     5     5

[L, U] = lu(sparse(A), 0)