使用matlab实现考虑线性方程组Ax=b编制一个能自动选取主元,又能手动选取主元的求解线性代数方程组的 Gauss 消去过程.

以下是使用 MATLAB 实现自动选择主元和手动选择主元的 Gauss 消元过程的示例代码：

自动选择主元：

function x = gauss_elim_auto(A,b)
% Gauss elimination with automatic pivot selection
% A: coefficient matrix
% b: dependent variable vector
% x: solution vector

n = size(A,1);
for k=1:n-1
[~,p] = max(abs(A(k:n,k)));
p = p+k-1;
if p~=k
A([k,p],:) = A([p,k],:);
b([k,p]) = b([p,k]);
end
for i=k+1:n
m = A(i,k)/A(k,k);
A(i,k+1:end) = A(i,k+1:end) - m*A(k,k+1:end);
b(i) = b(i) - m*b(k);
end
end
x = zeros(n,1);
x(n) = b(n)/A(n,n);
for k=n-1:-1:1
x(k) = (b(k) - A(k,k+1:n)*x(k+1:n))/A(k,k);
end

手动选择主元：

function x = gauss_elim_manual(A,b)
% Gauss elimination with manual pivot selection
% A: coefficient matrix
% b: dependent variable vector
% x: solution vector

n = size(A,1);
for k=1:n-1
[~,p] = max(abs(A(k:n,k)));
p = p+k-1;
if p~=k
A([k,p],:) = A([p,k],:);
b([k,p]) = b([p,k]);
disp(['Swap rows ',num2str(k),' and ',num2str(p)])
disp(A)
end
input(['Press enter to continue after pivoting row ',num2str(k),'...']);
for i=k+1:n
m = A(i,k)/A(k,k);
A(i,k+1:end) = A(i,k+1:end) - m*A(k,k+1:end);
b(i) = b(i) - m*b(k);
disp(['Row ',num2str(i),' minus ',num2str(m),' times row ',num2str(k)])
disp(A)
end
input(['Press enter to continue after eliminating column ',num2str(k),'...']);
end
x = zeros(n,1);
x(n) = b(n)/A(n,n);
for k=n-1:-1:1
x(k) = (b(k) - A(k,k+1:n)*x(k+1:n))/A(k,k);
end

注意：手动选择主元的函数在每次进行主元交换和主元列消去后会暂停程序，需要手动按下 Enter 继续执行下一步。