列主元消去法例题详解_线性方程组的分解法——列主元消去法

1.代码

%%列主元消去法

function ECPE = Elimination_of_column_pivot_entries(M,b)

global n;

[n,n] = size(M);

B =[M,b];

R_A = rank(M);R_B = rank(B);

if R_A ~= R_B

disp('方程无解');

elseif (R_A == R_B)&&(R_A == n)

disp('此方程有唯一解');

for k = 1:n-1

B = Column_pivot_transformation(B,k);

B = Elimination_method(B,k);

end

X = Upper_trig_iterative_solution(B);

else

disp('方程有无穷多组解');

end

disp('解向量为：');

ECPE = X;

%%列主元变换

%%指定p列，找出列最大值，以此值为主元进行行变换

function CPT = Column_pivot_transformation(M,p)

[m,n] = size(M);

s = max(M(p:m,p));

[x,y] = find(M(p:m,p) == s);

H = x+p-1;

Ch1 = M(H,:);

Ch2 = M(p,:);

M(H,:) = Ch2;

M(p,:) = Ch1;

CPT = M;

end

%%p列消元函数

function EM = Elimination_method(M,p)

[m,n] =