% Class 13 Optimization
% Coded by Nigel F. Reuel on 2.26.19
%
close all
clc
% In class exercise
F1 = @(x) 2*x^2+4*x+6*x^3-7;
%fplot(F1) %to find guess value of 0.6
% Derivative for Newton Raphson
D1 = @(x) 4*x+4+18*x^2;
[NR_root,~,~]=newtraph(F1,D1,.6)
% For roots function, must order coefficients in descending order
Ans_RootFunc = roots([6 2 4 -7])
% Fzero
FZ_root = fzero(F1,0.6)
%
% Class notes
% 
F1 = @(x) x^4+2*x^3+8*x^2+5*x;
fplot(F1,[-2 1])
[x,~,~,~]=goldmin(F1,-2,1,1)
% Example using fminbnd 
% Remember that this works for a single variable
% with a single function (limited)
%
X_sol = fminbnd(F1,-2,1)
% For optimization with one or more variables
% (but still with ONE objective function)
% use the fminsearch
% Let's do example 7.11, make contour plot
% then solve for minimum
F2 = @(x,y) 2*x.^2+3*y.^2-4*x.*y-y-3*x;
xvec = linspace(-10,10,100);
yvec = linspace(-10,10,100);
[xmat ymat] = meshgrid(xvec,yvec);
zmat = F2(xmat,ymat);
contourf(xvec,yvec,zmat)
% Matlab solution to minimum location
% V(1) = x, V(2) = y
% Recast equation so it has one variable (array)
F3 = @(V) 2*V(1).^2+3*V(2).^2-4*V(1).*V(2)...
    -V(2)-3*V(1);
F4 = @(T) F2(T(1),T(2));
S = fminsearch(F3,[4 4]);
hold on
plot(S(1),S(2),'r+')
% Example 7.38 from the textbook 
%
alpha_vec = (45:1:135);
np = length(alpha_vec);
% Preallocate memory for the answers
L_vec = zeros(np,1);
for i = 1:np
    % Now, the value of alpha changes 
    alpha = alpha_vec(i);
    a_rad = alpha/180*pi;
    w1 = 2; %m
    w2 = 2; %m
    Lfunc = @(theta) w1/sin(theta)+...
        w2/sin(pi-a_rad-theta);
    [theta_min, L] = fminsearch(Lfunc,30/180*pi);
    L_vec(i,1) = L;
end
% Now we have the solution vector, we can plot
figure
plot(alpha_vec,L_vec)
xlabel('Alpha (deg)')
ylabel('Length of Ladder (m)')