B = 212;431;615;编写matlab程序使用克洛特分解求解并输出原矩阵、L、U矩阵自己定义函数不要使用内置函数是克洛特分

function [L,U]=crout_decomposition(A) % CR_OUT_DECOMPOSITION is a function that uses Crout's method % to decompose a matrix A into its lower and upper triangular % matrices L and U respectively. % Input: % A - a square matrix of order n % % Output: % L - lower triangular matrix of order n % U - upper triangular matrix of order n

n=size(A,1); L=zeros(n); U=zeros(n);

for k=1:n L(k,k)=1; for i=k:n sum=0; for p=1:k-1 sum=sum+L(i,p)*U(p,k); end L(i,k)=A(i,k)-sum; end for j=k+1:n sum=0; for p=1:k-1 sum=sum+L(k,p)*U(p,j); end U(k,j)=(A(k,j)-sum)/L(k,k); end end

end

%Test the function with matrix B B=[2,1,2;4,3,1;6,1,5]; [L,U]=crout_decomposition(B);

%Print L and U matrices fprintf('L matrix = \n'); disp(L); fprintf('U matrix = \n'); disp(U);

%Verify that LU = B fprintf('LU = \n'); disp(L*U);

%Print the original matrix B fprintf('Original matrix B = \n'); disp(B)