在没有abs函数的Matlab中进行数据透视的LU分解

Question

任何帮助都会受到赞赏，输出没有意义，我不确定是什么问题。我正在尝试执行标题中列出的功能。

function [L,U,P]=lufactor(A);

A= [2 1 1 0;
4 3 3 1;
8 7 9 5;
6 7 9 8];

[Row1,~] = size(A); 
L=eye(Row1); 
P=eye(Row1); 
U=A;

for i=1:Row1
nrow(i)=i;
end
nrow=nrow';

for k=1:Row1-1;
max=0;
for j = k:Row1 %Go through vector one value at a time
  if abs(nrow(j))>max; %Determine if value in vector is greater than the          current value
      max=abs(nrow(j));
  if max ~= k %perform row exchange
      U([max,j],:) =  U([j,max], :);   % interchange rows m and j in U
      P([max,j],:) =  P([j,max], :);   % interchange rows m and j in P
  if j >= 2    
      L([max,j],1:j-1) =  L([j,max], 1:j-1);   % interchange rows m and j in columns 1:j-1 of L
  end
  end
  end
 for i = j+1:Row1      
      L(i, j) = U(i, j) / U(j, j);
      U(i, :) =  U(i, :) - L(i, j)*U(j, :);
     end
    end
    end

[L，U，P]

当前输出，结果组织为[L，U，P]：

 1     0     0     0     2     1     1     0     1     0     0     0
 2     1     0     0     0     1     1     1     0     1     0     0
 4     0     1     0     0     0     2     2     0     0     1     0
 3     0     0     1     0     0     0     2     0     0     0     1

预期产出：

L =

1.0000         0         0         0
0.7500    1.0000         0         0
0.5000   -0.2857    1.0000         0
0.2500   -0.4286    0.3333    1.0000

U =

8.0000    7.0000    9.0000    5.0000
     0    1.7500    2.2500    4.2500
     0         0   -0.8571   -0.2857
     0         0         0    0.6667

P =

 0     0     1     0
 0     0     0     1
 0     1     0     0
 1     0     0     0