I would like to use code of SOR method. Here is the code:
% SOR ALGORITHM 7.3
%
% To solve Ax = b given the parameter w and an initial approximation
% x(0):
%% INPUT: the number of equations and unknowns n; the entries
% A(I,J), 1<=I, J<=n, of the matrix A; the entries
% B(I), 1<=I<=n, of the inhomogeneous term b; the
% entries XO(I), 1<=I<=n, of x(0); tolerance TOL;
% maximum number of iterations N; parameter w (omega).
%% OUTPUT: the approximate solution X(1),...,X(n) or a message
% that the number of iterations was exceeded.
syms('OK', 'AA', 'NAME', 'INP', 'N', 'I', 'J', 'A', 'X1'); syms('TOL', 'NN', 'W', 'K', 'ERR', 'S', 'FLAG', 'OUP'); TRUE = 1; FALSE = 0; fprintf(1,'This is the SOR Method for Linear Systems.\n'); OK = FALSE; fprintf(1,'The array will be input from a text file in the order:\n'); fprintf(1,'A(1,1), A(1,2), ..., A(1,n+1) \n'); fprintf(1,'A(2,1), A(2,2), ..., A(2,n+1),\n'); fprintf(1,'..., A(n,1), A(n,2), ..., A(n,n+1)\n\n'); fprintf(1,'Place as many entries as desired on each line, but \n'); fprintf(1,'separate entries with at least one blank.\n'); fprintf(1,'The initial approximation should follow in same format.\n\n\n'); fprintf(1,'Has the input file been created? - enter Y or N.\n'); AA = input(' ','s'); if AA == 'Y' | AA == 'y' fprintf(1,'Input the file name in the form - drive:\\name.ext\n'); fprintf(1,'for example: A:\\DATA.DTA\n'); NAME = input(' ','s'); INP = fopen(NAME,'rt'); OK = FALSE; while OK == FALSE fprintf(1,'Input the number of equations - an integer.\n'); N = input(' '); if N > 0 A = zeros(N,N+1); X1 = zeros(1,N); for I = 1 : N for J = 1 : N+1 A(I,J) = fscanf(INP, '%f',1); end; end; for I = 1 : N X1(I) = fscanf(INP, '%f',1); end;% use X1 for X0
OK = TRUE; fclose(INP); else fprintf(1,'The number must be a positive integer.\n'); end; end; OK = FALSE; while OK == FALSE fprintf(1,'Input the tolerance.\n'); TOL = input(' '); if TOL > 0 OK = TRUE; else fprintf(1,'Tolerance must be a positive number.\n'); end; end; OK = FALSE; while OK == FALSE fprintf(1,'Input maximum number of iterations.\n'); NN = input(' '); if NN > 0 OK = TRUE; else fprintf(1,'Number must be a positive integer.\n'); end; end; fprintf(1,'Input parameter w (omega)\n'); W = input(' ');% use W for omega
else fprintf(1,'The program will end so the input file can be created.\n'); end; if OK == TRUE % STEP 1
K = 1; OK = FALSE;% STEP 2
while OK == FALSE & K <= NN % ERR is used to test accuracy - it measures the infinity norm
ERR = 0;% STEP 3
for I = 1 : N S = 0; for J = 1 : N S = S-A(I,J)*X1(J); end; S = W*(S+A(I,N+1))/A(I,I); if abs(S) > ERR ERR = abs(S); end; X1(I) = X1(I)+S; end;% STEP 4
if ERR <= TOL OK = TRUE;% process is complete
else% STEP 5
K = K+1;% STEP 6 - is not used since only one vector is required
end; end; if OK == FALSE fprintf(1,'Maximum Number of Iterations Exceeded.\n');% STEP 7
% procedure completed unsuccessfully
else 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, 'SOR ITERATIVE METHOD FOR LINEAR SYSTEMS\n\n'); fprintf(OUP, 'The solution vector is :\n'); for I = 1 : N fprintf(OUP, ' %11.8f', X1(I)); end; fprintf(OUP, '\nusing %d iterations with\n', K); fprintf(OUP, 'Tolerance %.10e in infinity-norm\n', TOL); fprintf(OUP, 'with Parameter %.10e\n', W); if OUP ~= 1 fclose(OUP); fprintf(1,'Output file %s created successfully \n',NAME); end; end; end;
And my data matrix is:
1 -0.5 0 0 0 0 0-0.5 1 -0.5 0 0 0 00 -0.5 1 -0.5 0 0 00 0 -0.5 1 -0.5 0 00 0 0 -0.5 1 -0.5 0 0 0 0 0 -0.5 1 -0.50 0 0 0 0 -0.5 1
But I got error like this:
Has the input file been created? - enter Y or N. YInput the file name in the form - drive:\name.extfor example: A:\DATA.DTA ALG073.DTAInput the number of equations - an integer. 7Unable to perform assignment because the left and right sides have a different number of elements.Error in ALG073 (line 47) X1(I) = fscanf(INP, '%f',1);
Can anyone help?
Best Answer