Using Matlab to get maximum values from many polyfitted curves in one figure - matlab

Question

x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12];
z1 = [1, 4, 9, 16, 25, 36, 49, 36, 25, 16, 8, 1];
z2 = [1, 5, 10, 17, 26, 38, 26, 17, 10, 9, 7, 1];
z3 = [1, 8, 18, 30, 40, 30, 18, 8, 7, 4, 3, 1];
plot(x, z1, '*');
hold on;
p1 = polyfit(x, z1, 5);
z1fit = polyval(p1, x);
plot(x, z1fit);
hold on;
plot(x, z2, '*');
p2 = polyfit(x, z2, 5);
z2fit = polyval(p2, x);
plot(x, z2fit);
hold on;
plot(x, z3,'*');
p3 = polyfit(x, z3, 5);
z3fit = polyval(p3, x);
plot(x, z3fit);
My question is, how to find every maximum value of each curve and display them? The maximum points are not the maximum values that I gave , It should be the peak points after fitting. I can simply read these peak points from the plotted figure, just want to know how to get the exact coordinate of the highest peak of the polynomial fit and return them. The degree of n (in my code 5) from polyfit is changeable.

Answer 1

To get the exact value of the maximum in the range of x, you can use the optimization toolbox.
x=[1,2,3,4,5,6,7,8,9,10,11,12];
z1=[1,4,9,16,25,36,49,36,25,16,8,1];
p1=polyfit(x, z1, 5);
fun = #(x) -polyval(p1,x);
x_max = fminbnd(fun,x(1),x(end))
figure; hold on;
plot(x,z1,'*');
fplot(#(x) polyval(p1,x),[x(1) x(end)],':');
plot(x_max,polyval(p1,x_max),'o');
legend('data','fit','max')
Use the polyfit function to get the coefficients of the fitted polynomial, use the polyval function to create a function handle to the polynomial you created and the fminbnd to "Find minimum of single-variable function on fixed interval". With the function handle, you can use the fplot function to plot the fit.
Edit:
If you want to calculate and plot the fitted curves in the same figure, you can:
x=[1,2,3,4,5,6,7,8,9,10,11,12];
z1 = [1, 4, 9, 16, 25, 36, 49, 36, 25, 16, 8, 1];
z2 = [1, 5, 10, 17, 26, 38, 26, 17, 10, 9, 7, 1];
z3 = [1, 8, 18, 30, 40, 30, 18, 8, 7, 4, 3, 1];
z = [z1;z2;z3];
figure; hold on;
for ii=1:size(z,1)
p1=polyfit(x, z(ii,:), 5);
fun = #(x) -polyval(p1,x);
x_max = fminbnd(fun,x(1),x(end))
plot(x,z(ii,:),'*');
fplot(#(x) polyval(p1,x),[x(1) x(end)],':');
plot(x_max,polyval(p1,x_max),'o');
end
The result, however, will not be that good, because you will have a lot of information in the same figure. Depending on what you want, that may be good. But I suggest you plot on different figures different data, maybe using subplots.