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%Generating uniform acceleration data for homework
b = 5;
a = 20;
t = (0:0.1:12).';
n = 10*randn(size(t));

x = a + b.*t + n;

load mollycar

E = [ones(size(t)) t];
vec = inv(E.'*E)*(E.'*x);
model = vec(1) + vec(2).*t;

rms = sqrt(mean((model-x).^2));
num = find(x>model-2*rms & x<model+2*rms);

atst = 18.9:0.05:21.1;
btst = 4:0.05:6;
atst = 10:0.1:30;
btst = 0:0.1:10;
clear RMS
for jn = 1:length(atst)
    for kn = 1:length(btst)
        model2 = atst(jn) + btst(kn).*t;
        RMS(jn,kn) = sqrt(mean((model2 - x).^2));
    end
end

[xx,yy] = find(RMS==min(min(RMS)));
model2 = atst(xx) + btst(yy).*t;

disp(['RMS from matrices         RMS from nested loops']);
disp([num2str(rms),'                    ',num2str(RMS(xx,yy))]);
figure(1)
clf
pcolorjw(atst,btst,RMS.')
colorbar
hold on
plot(atst(xx),btst(yy),'r.')
plot(vec(1),vec(2),'g+')
plot(a,b,'y.')

figure(2)
clf
pcolorjw(atst,btst,RMS.')
colorbar
hold on
plot(atst(xx),btst(yy),'r.')
plot(vec(1),vec(2),'g+')
plot(a,b,'y.')
axis([18 20.1 4.5 5.5]); caxis([9.3 10])
axis([17 21 4 6]); caxis([9.3 12]); shading faceted



%clf
%plot(t,x,'.')
%hold on
%plot(t,model,'r')
%plot(t,model-2*rms,'g')
%plot(t,model+2*rms,'g')
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