Weird results using LU

Hi

Today I was testing my own implementation of the LU Descomposition

function [L,U]=LUDescomp(Coefs)
[N,~]=size(Coefs);
L=eye(N,N);%Genera una matriz identidad
%Eliminacion de variables

   for i=1:N-1
      %Proceso de Pivoteo Parcial
      Ai=Coefs(i:N,i);
      [~ ,Ind]=max(abs(Ai));
      Ind=Ind+i-1;

       if(Ind~=i)
       Temp=Coefs(i,:);
       Coefs(i,:)=Coefs(Ind,:);
       Coefs(Ind,:)=Temp;   
       end

      Piv=Coefs(i,i);
      for j=i+1:N
      ElementoPiv=Coefs(j,i)/Piv;
      L(j,i)=ElementoPiv;
      ModifiedRow=Coefs(i,:)*ElementoPiv;
      Coefs(j,:)=Coefs(j,:)-ModifiedRow;
      end
  end
  U=Coefs;
  end

So i try to compare the results with the lu function in Matlab, and something weird happen

 x =

     1     2     6
     4     8    -1
    -2     3    -5

>>[L,U,P]=lu(x)

   L =

      1.0000         0         0
     -0.5000    1.0000         0
      0.2500         0    1.0000

   U =

      4.0000    8.0000   -1.0000
           0    7.0000   -5.5000
           0         0    6.2500

   P =

       0     1     0
       0     0     1
       1     0     0

>> [L,U]=LUDescomp(x)

   L =

      1.0000         0         0
      0.2500    1.0000         0
     -0.5000         0    1.0000

   U =

      4.0000    8.0000   -1.0000
           0    7.0000   -5.5000
           0         0    6.2500

As you can see, the answers are almost same, except in the L matrix , the values 0.25 and -0.5 are interchanged in my matrix and i have checked my algorithm many times and i can´t find what's wrong.

I would appreciate all the help i could get.

Thank you

Answer 1

[John BG]

Fabio

your observation of a single case and then saying that the 1st column elements other than (1,1) are inverted or swapped is not correct.

Check for larger dimension with:

x=randi(13,6)
x =
    13     4     4     8     8     2
     8    11     9    12     1     8
     2     4     7     4     1     7
     2    13     5    10     7     1
     4     5    11    10    11     5
    11     3     8     5    13     3
>> [L,U,P]=lu(x)
L =
    1.0000         0         0         0         0         0
    0.1538    1.0000         0         0         0         0
    0.3077    0.3043    1.0000         0         0         0
    0.8462   -0.0311    0.5633    1.0000         0         0
    0.6154    0.6894    0.4168    0.2355    1.0000         0
    0.1538    0.2733    0.6149    0.6183    0.6685    1.0000
U =
   13.0000    4.0000    4.0000    8.0000    8.0000    2.0000
         0   12.3846    4.3846    8.7692    5.7692    0.6923
         0         0    8.4348    4.8696    6.7826    4.1739
         0         0         0   -4.2401    2.5891   -1.0221
         0         0         0         0  -11.3373    4.7930
         0         0         0         0         0    1.3646
P =
     1     0     0     0     0     0
     0     0     0     1     0     0
     0     0     0     0     1     0
     0     0     0     0     0     1
     0     1     0     0     0     0
     0     0     1     0     0     0
>> [L2,U2]=LUDescomp(x)
L2 =
    1.0000         0         0         0         0         0
    0.6154    1.0000         0         0         0         0
    0.1538    0.2733    1.0000         0         0         0
    0.1538    0.6894    0.4168    1.0000         0         0
    0.3077    0.3043    0.6149    0.6183    1.0000         0
    0.8462   -0.0311    0.5633    0.2355    0.6685    1.0000
U2 =
   13.0000    4.0000    4.0000    8.0000    8.0000    2.0000
         0   12.3846    4.3846    8.7692    5.7692    0.6923
         0    0.0000    8.4348    4.8696    6.7826    4.1739
         0   -0.0000         0   -4.2401    2.5891   -1.0221
         0   -0.0000         0         0  -11.3373    4.7930
         0    0.0000         0         0         0    1.3646

It's not L 1st column elements below 1 are swapped.

It's all elements below diagonal, of all columns are somehow shuffled.

Find out where in your function the shuffling takes place and fix it.

If you find this answer of any help solving your question, please click on the thumbs-up vote link,

thanks in advance

John

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