How can I reduce the time for this Gaussian Elimination Code

I am relatively new to MATlab and have been given a code, however I think the time that the code runs could be reduced by a significant amount. When I ran the profile command on this code just about 80% of the time used comes from one line of code. The code is a little bit on the long side, but the line that I am talking about is %Step 6

TRUE = 1;
 FALSE = 0;
 fprintf(1,'This is Gaussian Elimination to solve a linear system.\n');
 fprintf(1,'The array shall be written in the code in advance.\n');
 fprintf(1,'Has the array been written? - enter Y or N.\n');
 AA = input(' ','s');
 OK = FALSE;
 if AA == 'Y' || AA == 'y' 
 while OK == FALSE
% Matrix dimension N 
M = 146;
N = 4*M;

   A = zeros(N,N+1);
   X = zeros(1,N);
   for I = 1:N
   for J = 1:N
     if I==J,
      A(I,J) = 2;
     end;
     if J==I+1,
      A(I,J)=-1;
     end;
     if J==I-1,
      A(I,J)=-1;
     end; 
   end;
   end;
  % right-hand-side
     A(1,N+1)=1;
     for I = 2:N-1
      A(I,N+1)=0;
     end;
     A(N,N+1)=1;

   OK = TRUE;
   end;
   else 
   fprintf(1,'The program will end so the matrix can be written.\n');
   end;

   if OK == TRUE 

   fprintf(1,'The code is executing now.\n');

   t = cputime; %Starting time

% STEP 1
% Elimination Process 
 NN = N-1;
 M = N+1;
 ICHG = 0;
 I = 1;
 while OK == TRUE && I <= NN 
% STEP 2
% use IP instead of p
 IP = I;
 while abs(A(IP,I)) <= 1.0e-20&& IP <= N 
 IP = IP+1;
 end;
 if IP == M 
 OK = FALSE;
 else
% STEP 3
 if IP ~= I 
 for JJ = 1:M
 C = A(I,JJ);
 A(I,JJ) = A(IP,JJ);
 A(IP,JJ) = C;
 end;
 ICHG = ICHG+1;
 end;
% STEP 4
 JJ = I+1;
 for J = JJ:N
% STEP 5
% use XM in place of m(J,I)
 XM = A(J,I)/A(I,I);
% STEP 6
 for K = JJ:M
 A(J,K) = A(J,K) - XM * A(I,K);
 end;
% Multiplier XM could be saved in A(J,I).
 A(J,I) = 0;
 end;
 end;
 I = I+1;
 end;
 if OK == TRUE
% STEP 7
 if abs(A(N,N)) <= 1.0e-20 
 OK = FALSE;
 else
% STEP 8
% start backward substitution
 X(N) = A(N,M) / A(N,N);
% STEP 9
 for K = 1:NN
 I = NN-K+1;
 JJ = I+1;
 SUM = 0;
 for KK = JJ:N
 SUM = SUM - A(I,KK) * X(KK);
 end;
 X(I) = (A(I,M)+SUM) / A(I,I);
 end;

   eltime = cputime-t; %total elapse time

% STEP 10
% procedure completed successfully
 fprintf(1,'Choice of output method:\n');
 fprintf(1,'1. Output to screen\n');
 fprintf(1,'2. Output to text file\n');
 fprintf(1,'Please enter 1 or 2.\n');
 FLAG = input(' ');
 if FLAG == 2 
 fprintf(1,'Input the file name in the form - drive:\\name.ext\n');
 fprintf(1,'for example:  A:\\OUTPUT.DTA\n');
 NAME = input(' ','s');
 OUP = fopen(NAME,'wt');
 else
 OUP = 1;
 end;
 fprintf(OUP, 'GAUSSIAN ELIMINATION\n\n');
 fprintf(OUP, 'The reduced system - output by rows:\n');
%   for I = 1:N
%   for J = 1:M
%   fprintf(OUP, ' %11.8f', A(I,J));
%   end;
%   fprintf(OUP, '\n');
%   end;
 fprintf(OUP, '\n\nHas solution vector:\n');
 for I = 1:N
 fprintf(OUP, '  %12.8f\n', X(I));
 end;
 fprintf (OUP, '\n\nwith %d row interchange(s)\n', ICHG);
 fprintf(OUP, 'cpu time \n'); 
 fprintf(OUP, '%12.8f\n',eltime);

   if OUP ~= 1 
   fclose(OUP);
   fprintf(1,'Output file %s created successfully \n',NAME);
   end;
   end;
   end;
   if OK == FALSE 
   fprintf(1,'System has no unique solution\n');
   end;
   end;

Thank you for any help!

Answer 1

[Torsten]

n=4*146;
S=sparse(gallery('tridiag',n,-1,2,-1));
b=sparse(1;zeros(n-2,1);1);
x=S\b;

should do the same as your program.

Best wishes

Torsten.

[Connor Oliver]

Thanks for the reply, unfortunately I cannot get this code to execute properly.

It comes up with the error for line 3, saying it is unbalanced or unexpected parenthesis or bracket.

I will play with this code a little bit more to see if I cannot get it to work.

[Connor Oliver]

Ok, I ended up getting it to work with a little more knowledge on sparse command than I had previously, so thank you. This is the code I ended up using, that does give the right values.

n=4*146;
S=sparse(gallery('tridiag',n,-1,2,-1));
i=[1,n];
j=[1,1];
s=[1,1];
b=sparse(i,j,s,n,1);
x=S\b;

[Torsten]

And does it execute faster than the code you've been given ?

Best wishes

Torsten.