Average data points of different X,Y range

Dear all,

What is the correct technique to average curves of diferent X,Y ranges as shown by loosely dashed curves in the figure below? The solid blue curve, plotted by manual averaging of the parameters that fits the dashed curves does not seem to be representative.

Many thanks in advance.

AB

Answer 1

[Star Strider]

You have too interpolate all the curves to a single common independent variable. Then you can average them.

x1 = sort(rand(1,20))*20;
y1 = x1.^(1+rand);

x2 = sort(rand(1,15))*25;
y2 = x2.^(1+rand);

x3 = sort(rand(1,25))*30;
y3 = x3.^(1+rand);

xq = linspace(min([x1 x2 x3]), max([x1 x2 x3]), max([x1 x2 x3]));
y1i = interp1(x1, y1, xq);
y2i = interp1(x2, y2, xq);
y3i = interp1(x3, y3, xq);

ymean = mean([y1i; y2i; y3i], 'omitmissing');
Lv = xq <= min([max(x1)  max(x2) max(x3)]);

figure
plot(x1, y1, '.')
hold on
plot(x2, y2, '.')
plot(x3, y3, '.')
plot(xq(Lv), ymean(Lv), '-g', 'LineWidth',2)
hold off
grid

The mean value does not exist beyond the length of th shortest vector. This approach accounts for that.

.

[ArBio]

Thank you @Star Strider for the help.

[Star Strider]

As always, my pleasure!