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lu_tridiag.m

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+function [ud,uo,lo]=lu_tridiag(e,f,g);
+%lu_tridiag The purpose of this function is to perform a LU-decomposition
+%by creating a lower and upper matrix from three input vectors e,f,&g. This
+%function is to provide a method that creates linear equations to compute
+%the new matrix.
+%Note: the inputs of the function must be vectors of the same length
+%--------Linear equations-----------
+ud = zeros(length(f), 1); %set up empty vector for new upper diagonal
+uo = zeros(length(f)-1, 1); %empty vector for new upper-off diagonal matrix
+lo = zeros(length(f)-1, 1); %empty vector for new lower-off diagonal matrix
+
+lo = g;       %The value of the original upper matrix equals the new lower-off diagonal
+ud(1)=f(1);   %first element in new upper diagonal equals first in original diagonal 
+uo(1) = g(1); %first element in new upper-off diagonal equals that of first in g
+k = 2;        %Set index to initialize while loop.
+
+while k <= length(f)-1 %begin loop to assign values of generic vectors e f &g
+    lo(k-1) = e(k-1)/(ud(k-1)); %compute values for new lower-off digaonal
+    uo(k) = g(k); %assign values to new upper-off diagonal
+    ud(k) = f(k)-(lo(k-1)*uo(k-1));
+    k = k + 1; %repeat but shift to next column
+end
+lo(k-1) = e(k-1)/(ud(k-1)); %Due to indexing loop, equation is needed for final value of new lower-off diagonal
+ ud(k) = f(k)-(lo(k-1)*uo(k-1)); %same reasoning, needed to find final value of new upper diagonal
+
+