How to find the solutions to a set of linear equations?

Matt J restored:

Hi All

I am currently trying to find the solutions to a set of linear equations by using Gauss elimination with partial pivoting in MATLAB

But when I run my script, I get the output of NaN. Why might this be so and how can I fix this issue?

Any form of help would be appreciated.

My code is shown below.

%Augmented matrix
Aug=[ 0  0       -2  0  0       0  0  0       0; 
      0 -0.8509   0  3  0       0  0  0       0; 
      0  0        0  0  0.8509  2  0  0       0; 
      1  0        0  0 -0.5253  0  0  0       0; 
      0  0.8509   0  0  0       0 -2  0.8509  0; 
      0 -0.8509   0 -4  0       0  0  0       12; 
      0  0       -1  0  0       3  0 -0.5253  0; 
      0  0        0  0  0       0  0  3       0];

[row,col]=size(Aug);%Obtain the size of A

%Conduct partial pivoting
[maxval,ind]=max(Aug((1:end),1)); %Find the max value and its index
if abs(maxval)>abs(Aug(1,1))
temp=Aug(ind,:); 
Aug(ind,:)=Aug(1,:);
Aug(1,:)=temp;
end

%Find the upper triangular matrix
for p=1:row-1
for i=p+1:row
    l(i,p)=Aug(i,p)/Aug(p,p);
    Aug(i,:)= Aug(i,:)-Aug(p,:)* l(i,p);
end
end

%Acquire coefficient matrix and column vector
for i=1:row
    for p=1:col-1
        coeff(i,p)=Aug(i,p);
        colvec(i)=Aug(i,col);
    end
end
colvec=colvec'; %transpose

%Back substitution to obtain results
sol(row)=colvec(row)/coeff(row,row);
tot=0;
for i=row-1:-1:1
    for p=i+1:row
        tot=tot+coeff(i,p)*sol(p);
        sol(i)=(colvec(i)-tot)/coeff(i,i)
    end
    tot=0;
end

[John D'Errico]

Just becauae you personally are not interested in the question anylonger, does not mean that others would not benefit from the answer. Effectively, you insult the person who spent the time answering your question,.

[Rik]

Question originally posted by aw007 retrieved from Google cache:

How to find the solutions to a set of linear equations?

Hi All

I am currently trying to find the solutions to a set of linear equations by using Gauss elimination with partial pivoting in MATLAB

But when I run my script, I get the output of NaN. Why might this be so and how can I fix this issue?

Any form of help would be appreciated.

My code is shown below.

%Augmented matrix
Aug=[ 0  0       -2  0  0       0  0  0       0; 
      0 -0.8509   0  3  0       0  0  0       0; 
      0  0        0  0  0.8509  2  0  0       0; 
      1  0        0  0 -0.5253  0  0  0       0; 
      0  0.8509   0  0  0       0 -2  0.8509  0; 
      0 -0.8509   0 -4  0       0  0  0       12; 
      0  0       -1  0  0       3  0 -0.5253  0; 
      0  0        0  0  0       0  0  3       0];

[row,col]=size(Aug);%Obtain the size of A

%Conduct partial pivoting
[maxval,ind]=max(Aug((1:end),1)); %Find the max value and its index
if abs(maxval)>abs(Aug(1,1))
temp=Aug(ind,:); 
Aug(ind,:)=Aug(1,:);
Aug(1,:)=temp;
end

%Find the upper triangular matrix
for p=1:row-1
for i=p+1:row
    l(i,p)=Aug(i,p)/Aug(p,p);
    Aug(i,:)= Aug(i,:)-Aug(p,:)* l(i,p);
end
end

%Acquire coefficient matrix and column vector
for i=1:row
    for p=1:col-1
        coeff(i,p)=Aug(i,p);
        colvec(i)=Aug(i,col);
    end
end
colvec=colvec'; %transpose

%Back substitution to obtain results
sol(row)=colvec(row)/coeff(row,row);
tot=0;
for i=row-1:-1:1
    for p=i+1:row
        tot=tot+coeff(i,p)*sol(p);
        sol(i)=(colvec(i)-tot)/coeff(i,i)
    end
    tot=0;
end

Answer 1

[Matt J]

You can easily trap the point where NaNs are introduced using

>>dbstop if naninf

https://www.mathworks.com/help/matlab/ref/dbstop.html#buz52rg

[JoBrr]

so where in my code would i write this?

[Matt J]

Just execute it at the command line and then re-run your code.

[JoBrr]

ok so when I do that a green arrow (what does this mean?) points to the line where is says:

 l(i,p)=Aug(i,p)/Aug(p,p);

[Matt J]

The code has stopped at this line because it is generating a NaN. You can examine the different variables at the K>> prompt and see what they contain. As you can see, the NaN is being generated by the fact that you are dividing by Aug(p,p) which is zero at this point in the code.

K>> i,p

i =

     4


p =

     3

K>> Aug(p,p)

ans =

     0

[JoBrr]

so how can i fix this?

[Matt J]

Well, I assume you didn't plan to be dividing by zero and that line of code isn't executing the step you intended. You should replace that line with what you did intend.

[JoBrr]

I intended to calculate the upper triangular matrix and I have been using this same portion of code to do so. I don't understand why it doesn't work with my current matrix. Are you familar with Gauss elimination with partial pivoting?

[Matt J]

I am only vaguely familiar with partial pivoting, but even if A were made upper triangular, I don't see how that would avoid the possibility that one of the elements A(p,p) would be equal to zero. What's supposed to happen if the whole matrix is zero to begin with?

[JoBrr]

Thats fine. If not sure what would happen if the whole matrix is zero to begin with, as then the solutions would just be zero.