ME_3255_Extra_Credit_Problem

Extra Credit Assignment 2

User	Radius (cm)	Angle (deg)
bra15003	3	260
bra15003	8.5	50
bra15003	4.2	195
bra15003	4	10
bra15003	10	60
bra15003	2	160
bra15003	0	0
bra15003	3.5	165
bra15003	8	111.5
bra15003	6.3	327.2

Extra Credit Assignment 3

data=[1.0000 ,  53.0000 ,   1.0000
    2.0000 ,  57.0000 ,   1.0000
    3.0000  , 58.0000 ,   1.0000
    4.0000,  63.0000  ,  1.0000
    5.0000 ,  66.0000  ,       0
    6.0000 ,  66.8000  ,       0
    7.0000 ,  67.0000 ,        0
    8.0000 ,  67.2000  ,       0
    9.0000  , 68.0000 ,        0
    10.0000 ,  69.0000  ,       0
    11.0000 ,  69.8000 ,   1.0000
    12.0000 ,  69.8000  ,       0
    13.0000,   70.2000  ,  1.0000
    14.0000 ,  70.2000  ,       0
    15.0000 ,  72.0000  ,       0
    16.0000  , 73.0000  ,       0
    17.0000  , 75.0000  ,       0
    18.0000 ,  75.0000  ,  1.0000
    19.0000 ,  75.8000   ,      0
    20.0000  , 76.2000  ,       0
    21.0000 ,  78.0000    ,     0
    22.0000  , 79.0000,         0
    23.0000  , 81.0000   ,      0];

n=23;
x=data(:,3);
y=data(:,2);

initial_a=[0,0];
options = optimset('GradObj', 'on', 'MaxIter', 400);
% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[a] = ...
fminunc(@(a) sum(-y.*log(1./(1+exp(-a(1)-a(2).*x)))-(1-y).*log(1./(1+exp(-a(1)-a(2).*x)))), initial_a, options);

Part A

function [cost,grad]=cost_logistic(a,x,y)

n=23;
x=data(:,3);
y=data(:,2);

options = optimset('GradObj', 'on', 'MaxIter', 400);
% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = ...
fminunc(@(a)(sum(-y.*log(1./(1+exp(-a.*x)))-(1-y).*log(1./(1+exp(-a.*x))))), initial_a, options);


t=a.*x;
sigma=1./(1+exp(-t));
cost=zeros(1,n);
grad=zeros(1,n);
for i=1:n
    cost(i)=sum(-y(i).*log(sigma(i))-(1-y(i)).*log(1-sigma(i)))
    grad(i)=sum(sigma(i)-y(i)).*x(i)
end
end

Part B

Output

• a0 = 137.8472
• a1 = 210.1783

Part C

plot(x,y, x, sigma(a(1)+a(2)*x))