HW_3 Script

%HW_3
%Script calls functions and outputs tables and plots relevant to HW3.

 [root(1),fx(1),ea(1),iter(1)]=falsepos(@(x) projectile_HW3(x),1,50,.00001);
 [root(2),ea(2),iter(2)]=mod_secant(@(x) projectile_HW3(x),1,50,.00001);
 [root(3), ea(3), iter(3)]= newtraph(@(x) projectile_HW3(x),@(x) dh_dtheta(x),50,.00001,1000);
 [root(4),fx(4),ea(4),iter(4)]=bisect(@(x) projectile_HW3(x),0,50,.00001);
 
for k=1:4;
    Table(k,1)=root(k);
    Table(k,2)=ea(k);
    Table(k,3)=iter(k);
    Table(k,4)=fx(k);
end

%Root=[root(1);root(2);root(3);root(4)];
%Initial_Guess=[50;50;50;50]
%Ea=[ea(1);ea(2);ea(3);ea(4)];
%Iter=[iter(1);iter(2);iter(3);iter(4)];


%Labels={'Falsepos','Mod_Secant','Bisect','Newtraph'};
%table(Initial_Guess,Root,Ea,Iter,'RowNames',Labels)

%This would be the table function used to create a table in MATLAB 2016a.
%Unfortunately in my 2013 MATLAB version there is no table function. This
%stores values for each column of the table and I saved the row labels as a
%matrix. The table function puts it in a table.


fprintf('\n\n\n');
fprintf('Solver     Initial Guess    Root        Ea       Iterations\n');
fprintf('Falsepos         50       %4.4f     %4.2s      %4.0f\n', Table(1,1),Table(1,2),Table(1,3))
fprintf('Bisect           50       %4.4f     %4.2s      %4.0f\n', Table(2,1),Table(2,2),Table(2,3))
fprintf('Mod_Secant       50       %4.4f     %4.2s      %4.0f\n', Table(3,1),Table(3,2),Table(3,3))
fprintf('Newtraph         50       %4.4f     %4.2s      %4.0f\n', Table(4,1),Table(4,2),Table(4,3))
fprintf('\n\n\n\n');
for k=1:4;
    iter(k)=log10(iter(k));
end
scatter(iter,ea)
for k=1:4
points(1,k)=iter(1,k);
points(2,k)=ea(1,k);
end
labels={'Falsepos','Bisect', 'Mod Secant', 'Newtraph'};
text(points(1,:),points(2,:),labels,'horizontal','left','vertical','bottom');
xlabel('Iterations (log10 base)');
ylabel('Relative Accuracy');
title('Roots and Optimization');


[x_i,Iter,Ea]=newtraph_edit(@(x) Y_Function_HW3(x),@(x) Derivative_HW3(x),2,.00001,5);



fprintf('Divergence of Newton-Raphson Method\n');
fprintf('Iteration    x_i       Approximate Error\n');
fprintf('%4.0f       %4.4f           %4.2s\n', Iter(1),x_i(1),Ea(1));
fprintf('%4.0f       %4.4f           %4.2s\n', Iter(2),x_i(2),Ea(2));
fprintf('%4.0f       %4.4f           %4.2s\n', Iter(3),x_i(3),Ea(3));
fprintf('%4.0f       %4.4f           %4.2s\n', Iter(4),x_i(4),Ea(4));
fprintf('%4.0f       %4.4f           %4.2s\n', Iter(5),x_i(5),Ea(5));
fprintf('%4.0f       %4.4f           %4.2s\n', Iter(6),x_i(6),Ea(6));


[x_i,Iter,Ea]=newtraph_edit2(@(x) Y_Function_HW3(x),@(x) Derivative_HW3(x),.2,.00001,5);

fprintf('\n\n\n');
fprintf('Convergence of Newton-Raphson Method\n');
fprintf('Iteration    x_i            Approximate Error\n');
fprintf('%4.0f       %4.6f               %4.2s\n', Iter(1),x_i(1),Ea(1));
fprintf('%4.0f       %4.6f               %4.2s\n', Iter(2),x_i(2),Ea(2));
fprintf('%4.0f       %4.6f               %4.2s\n', Iter(3),x_i(3),Ea(3));
fprintf('%4.0f       %4.6f               %4.2s\n', Iter(4),x_i(4),Ea(4));
fprintf('%4.0f       %4.6f               %4.2s\n', Iter(5),x_i(5),Ea(5));
fprintf('%4.0f       %4.6f               %4.2s\n', Iter(6),x_i(6),Ea(6));