71 lines
1.5 KiB
Matlab
71 lines
1.5 KiB
Matlab
function [ x ] = GaussElim( A, b)
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% Ensures A is n by n
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sz = size(A);
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if sz(1)~=sz(2)
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fprintf('A is not n by n\n');
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clear x;
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return;
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end
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n = sz(1);
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% Ensures b is n x 1.
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if n~=sz(1)
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fprintf('b is not 1 by n.\n');
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return
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end
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x = zeros(n,1);
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aug = [A b];
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tempmatrix = aug;
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for i=2:sz(1)
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% Find maximum of row and divide by the maximum
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tempmatrix(1,:) = tempmatrix(1,:)/max(tempmatrix(1,:));
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% Finds the maximum in column
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temp = find(abs(tempmatrix) - max(abs(tempmatrix(:,1))));
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if length(temp)>2
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for j=1:length(temp)-1
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if j~=temp(j)
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maxi = j; %maxi = column number of maximum
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break;
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end
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end
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else % length(temp)==2
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maxi=1;
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end
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% Row swap if maxi is not 1
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if maxi~=1
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temp = tempmatrix(maxi,:);
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tempmatrix(maxi,:) = tempmatrix(1,:);
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tempmatrix(1,:) = temp;
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end
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% Row reducing
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for j=2:length(tempmatrix)-1
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tempmatrix(j,:) = tempmatrix(j,:)-tempmatrix(j,1)/tempmatrix(1,1)*tempmatrix(1,:);
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if tempmatrix(j,j)==0 || isnan(tempmatrix(j,j)) || abs(tempmatrix(j,j))==Inf
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fprintf('Error: Matrix is singular.\n');
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clear x;
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return
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end
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end
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aug(i-1:end,i-1:end) = tempmatrix;
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% Decrease matrix size
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tempmatrix = tempmatrix(2:end,2:end);
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end
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% Backwards Substitution
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x(end) = aug(end,end)/aug(end,end-1);
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for i=n-1:-1:1
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x(i) = (aug(i,end)-dot(aug(i,1:end-1),x))/aug(i,i);
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end
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end
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