data upload

Eigen_Values.m

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+
+N= [5,6,10]-1;
+
+%Given constant values
+E=76e9;
+I=4e-9;
+L=5;
+
+%For loop that creates:
+    %1 - the lambda values 
+    %2 - number of segments
+    %3 - number of eignvalues
+i=1;
+for m=N
+    Dx=L/m;
+    p=10/(E*I);
+    a=Dx^2*p^2-2;
+    m=diag(ones(1,m-1),-1)+diag(a*ones(1,m))+ diag(ones(1,m-1),1)
+    e=eig(m);
+    i;
+    maxLam(i)= max(e);
+    minLam(i)=min(e);
+    i=i+1;
+end
+
+maxLam'
+minLam'
+N'
+nodes = N+1;
+nodes'
+

Spring_Mass.m

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+%This script solves the ODE Equation for the
+%Spring Mass System given in the HW
+
+%Values of System 
+stiff = [10,20,20,10];
+mass= [1;2;4;];
+
+%ODE Equations
+f1=[-1*(stiff(1)+stiff(2)), stiff(2), 0];
+f2=[stiff(2), -1*(stiff(2)+stiff(3)), stiff(3)];
+f3=[0,stiff(3), -1*(stiff(3)+stiff(4))];
+
+K= [f1;f2;f3];
+K= -1*K;
+
+M= diag(mass);
+
+K_tilde= (M^(-1/2))*(K)*(M^(-1/2));
+
+%Final lambda and omega
+e=eig(K_tilde)
+
+w= sqrt(e)

lu_tridiag.asv

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+function [ud, uo, lo ] = lu_tridiag( e,f,g )
+
+
+%This function carries out the LU decomposition
+% It takes in 3 vectors:
+% e subdiagonal, f diagonal, g superdiagonal
+
+A=diag(f)+diag(g,1)+diag(e,-1);
+B=eye(length(f));
+
+for j=1:length(e)
+
+x=A(j+1,j)/A(j,j);
+A(j+1,j)= (-e(j)/f(j))*f(j)+e(j);
+A(j+1,j+1)= (-x)*g(j)+f(j+1);
+B(j+1,j)=x;
+ud(1)=A(1,1);
+ud(j+1)= A(j+1,j+1);
+uo(j)=A(j,j+1);
+lo(j)=B(j+1,j);
+end
+
+%this will display the function results
+disp(ud)
+disp(uo)
+disp(lo)
+
+end
+

lu_tridiag.m

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+function [ud, uo, lo ] = lu_tridiag( e,f,g )
+
+
+%This function carries out the LU decomposition
+% It takes in 3 vectors:
+% e subdiagonal, f diagonal, g superdiagonal
+
+A=diag(f)+diag(g,1)+diag(e,-1);
+B=eye(length(f));
+
+for j=1:length(e)
+
+x=A(j+1,j)/A(j,j);
+A(j+1,j)= (-e(j)/f(j))*f(j)+e(j);
+A(j+1,j+1)= (-x)*g(j)+f(j+1);
+B(j+1,j)=x;
+lo(j)=B(j+1,j);
+ud(1)=A(1,1);
+ud(j+1)= A(j+1,j+1);
+uo(j)=A(j,j+1);
+
+end
+
+end
+

solve_tridiag.asv

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+function [x]=solve_tridiag(ud,uo,lo,b)
+
+%Input:  output of lu_tridiag function
+%Output:  x vector (Ax = B)
+
+M=ones(1,length(ud)); % initialisation
+
+for n = 1:(length(ud)-1)
+M(1)=b(1);
+M(n+1)= b(n+1)-(M(n)*lo(n));
+end
+
+
+x=ones(1,length(ud)); % initialisation
+
+for k =(length(ud):-1:2)
+    x(length(ud))=M(length(ud))/ud(length(ud));
+    x(k-1)= (M(k-1)-(uo(k-1)*x(k)))/(ud(k-1));
+end

solve_tridiag.m

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+function [x]=solve_tridiag(ud,uo,lo,b) %Input:  output of lu_tridiag function 
+                                       %Output:  x vector (Ax = B)
+
+T=ones(1,length(ud)); % initialisation
+
+for n = 1:(length(ud)-1)
+
+T(1)=b(1);
+
+T(n+1)= b(n+1)-(T(n)*lo(n));
+end
+
+
+x=ones(1,length(ud)); % initialisation
+
+
+
+
+for k =(length(ud):-1:2)
+
+x(length(ud))=T(length(ud))/ud(length(ud));
+
+x(k-1)= (T(k-1)-(uo(k-1)*x(k)))/(ud(k-1));
+
+end

test_array.m

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+rand('seed',1);
+
+for i = 3:10
+  e=sort(randi(6,[i-1,1]));
+  f=sort(randi(10,[i,1]));
+  g=sort(randi(9,[i-1,1]));
+  eval(['A',int2str(i),'=diag(f)+diag(e,-1)+diag(g,1);']);
+end