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function [sigma_z]=boussinesq_lookup(q,a,b,z) | ||
fmn= [0.1,0.02926,0.03007,0.03058 | ||
0.2,0.05733,0.05894,0.05994 | ||
0.3,0.08323,0.08561,0.08709 | ||
0.4,0.10631,0.10941,0.11135 | ||
0.5,0.12626,0.13003,0.13241 | ||
0.6,0.14309,0.14749,0.15027 | ||
0.7,0.15703,0.16199,0.16515 | ||
0.8,0.16843,0.17389,0.17739]; | ||
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m = a/z; | ||
n = b/z; | ||
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if (n>1.5) | ||
n=1.6; | ||
elseif (1.3<=n) | ||
if (n<=1.5) | ||
n=1.4; | ||
end | ||
elseif 1.3<=n | ||
n=1.2; | ||
end | ||
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c = ones(1,4); | ||
d = ones(1,4); | ||
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for i=1:4 | ||
[~,p]=min(abs(m-fmn(:,1))); | ||
M =fmn(p,1); | ||
fmn(p,1)=0; | ||
if n==1.2 | ||
t=fmn(p,2); | ||
elseif n==1.4 | ||
t=fmn(p,3); | ||
elseif n==1.6 | ||
t=fmn(p,4); | ||
end | ||
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d(i) = M; | ||
c(i) = t; | ||
end | ||
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b1=c(1); | ||
b2=(c(2)-c(1))/(d(2)-d(1)); | ||
b3=(((c(3)-c(2))/(d(3)-d(2)))-((c(2)-c(1))/(d(2)-d(1)))/(d(3)-d(1))); | ||
b4=(((c(4)-c(3))/(d(4)-d(3)))-((c(3)-c(2))/(d(3)-d(2)))-((c(2)-c(1))/(d(2)-d(1))))/(d(4)-d(1)); | ||
f3=b1+(b2*(m-d(1)))+(b3*(m-d(1))*(m-d(2)))+(b4*(m-d(1))*(m-d(2))*(m-d(3))); | ||
sigma_z=q*f3; | ||
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end |
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function [cost, gradient] = cost_logistic(a, x, y) | ||
cost = 0; | ||
gradient = 0; | ||
t = a(1)+a(2).*x; | ||
sigma = 1./(1+exp(-t)); | ||
cost = sum(-y.*log(sigma)- (1-y).*log(1-sigma)); | ||
costFun = @ (a) sum(-y.*log((1./(1+exp(-(a(1)+a(2).*x)))))-(1-y).*log(1-(1./(1+exp(-(a(1)+a(2).*x)))))); | ||
gradient = (1/length(x))*sum((sigma-y).*t); | ||
ai = [0 0]; | ||
% Set options for fminunc | ||
options = optimset('GradObj','on','MaxIter',400); | ||
% Run fminunc to obtain the optimal theta | ||
% This function will return theta and the cost | ||
[theta, cost] = fminunc(costFun, ai); | ||
t = theta(1)+theta(2).*x; | ||
sigma = 1./(1+exp(-t)); | ||
plot(x,y,'xb', x, sigma); | ||
title('Regression') | ||
xlabel('Temp (Degrees F)') | ||
ylabel('Pass or Fail (1 or 0)') | ||
end |
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c = [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]; | ||
a = c(:,1); | ||
x = c(:,2); | ||
y = c(:,3); |
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function [a,fx,r2] = least_squares(Z,y) | ||
a = Z\y; | ||
Sr = sum((y-Z*a).^2); | ||
r2 = 1-Sr/sum((y-mean(y)).^2); | ||
x = Z(:,2); | ||
fx = a(1)+(a(2)*x)+(a(3)*x.^2); | ||
end | ||
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clear | ||
clc | ||
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% part a | ||
xa=[1 2 3 4 5]'; | ||
ya=[2.2 2.8 3.6 4.5 5.5]'; | ||
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Za = [ones(size(xa)), xa, xa.^-1]; | ||
[a1,fx1,r2_1] = least_squares(Za,ya); | ||
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% part b | ||
xb=[3 4 5 7 8 9 11 12]'; | ||
yb=[1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6]'; | ||
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Zb = [ones(size(xb)), xb, xb.^2, xb.^3]; | ||
[a2,fx2,r2_2] = least_squares(Zb,yb); | ||
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% part c | ||
xc=[0.5 1 2 3 4 5 6 7 9]'; | ||
yc=[6 4.4 3.2 2.7 2.2 1.9 1.7 1.4 1.1]'; | ||
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Zc = [exp(-1.5*xc),exp(-0.3*xc), exp(-0.05*xc)]; | ||
[a3,fx3,r2_3] = least_squares(Zc,yc); |
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set(0, 'defaultAxesFontSize', 16) | ||
set(0,'defaultTextFontSize',14) | ||
set(0,'defaultLineLineWidth',3) |