解线性方程组的直接法matlab实现

function [x,XA]= GaussXQAllMain (A,b) N = size(A); n = N(1); index_l = 0; index_r = 0; order = 1:n; %记录未知数顺序的向量 for i=1:(n-1) me = max(max(abs(A(i:n,i:n)))); %选取全主元 for k=i:n for r=i:n if(abs(A(k,r))==me) index_l = k; index_r = r; %保存主元所在的行和列 k=n; break; end end end temp = A(i,1:n); A(i,1:n) = A(index_l,1:n); A(index_l,1:n) = temp; bb = b(index_l); b(index_l)=b(i); b(i) = bb; %交换主行 temp = A(1:n,i); A(1:n,i) = A(1:n,index_r); A(1:n,index_r) = temp; %交换主列 pos = order(i); order(i) = order(index_r); order(index_r) = pos; %主列的交换会造成未知数顺序的变化 for j=(i+1):n if(A(i,i)==0) disp('对角元素为0！'); return; end l = A(j,i); m = A(i,i); A(j,1:n)=A(j,1:n)-l*A(i,1:n)/m; b(j)=b(j)-l*b(i)/m; end end x=SolveUpTriangle(A,b); y=zeros(n,1); for i=1:n for j=1:n if(order(j)==i) y(i)=x(j); end end end %恢复未知数原来的顺序 x=y; XA = A;