Data commit

Task/Gaussian-elimination/MATLAB/gaussian-elimination.m

@@ -0,0 +1,70 @@
+function [ x ] = GaussElim( A, b)
+
+% Ensures A is n by n
+sz = size(A);
+if sz(1)~=sz(2)
+    fprintf('A is not n by n\n');
+    clear x;
+    return;
+end
+
+n = sz(1);
+
+% Ensures b is n x 1.
+if n~=sz(1)
+    fprintf('b is not 1 by n.\n');
+    return
+end
+
+x = zeros(n,1);
+aug = [A b];
+tempmatrix = aug;
+
+for i=2:sz(1)
+
+
+    % Find maximum of row and divide by the maximum
+    tempmatrix(1,:) = tempmatrix(1,:)/max(tempmatrix(1,:));
+
+    % Finds the maximum in column
+    temp = find(abs(tempmatrix) - max(abs(tempmatrix(:,1))));
+    if length(temp)>2
+        for j=1:length(temp)-1
+            if j~=temp(j)
+                maxi = j; %maxi = column number of maximum
+                break;
+            end
+        end
+    else % length(temp)==2
+        maxi=1;
+    end
+
+    % Row swap if maxi is not 1
+    if maxi~=1
+        temp = tempmatrix(maxi,:);
+        tempmatrix(maxi,:) = tempmatrix(1,:);
+        tempmatrix(1,:) = temp;
+    end
+
+    % Row reducing
+    for j=2:length(tempmatrix)-1
+        tempmatrix(j,:) = tempmatrix(j,:)-tempmatrix(j,1)/tempmatrix(1,1)*tempmatrix(1,:);
+        if tempmatrix(j,j)==0 || isnan(tempmatrix(j,j)) || abs(tempmatrix(j,j))==Inf
+            fprintf('Error: Matrix is singular.\n');
+            clear x;
+            return
+        end
+    end
+    aug(i-1:end,i-1:end) = tempmatrix;
+
+    % Decrease matrix size
+    tempmatrix = tempmatrix(2:end,2:end);
+end
+
+% Backwards Substitution
+x(end) = aug(end,end)/aug(end,end-1);
+for i=n-1:-1:1
+    x(i) = (aug(i,end)-dot(aug(i,1:end-1),x))/aug(i,i);
+end
+
+end