Smoothing of an error curve

Hello guys

I am working on my dissertation and I have a few graphs that I need to smooth out. Those are error graphs so they cannot go below 0. I used to use excel to smooth them out giving the following graph:

But now I must recreate the graph in MATLAB to stay consistent throughout the document. I have tried the smooth(x,y) function but it does not smooth the graph out at all, it just messes it up. I have tried the curve fitting tool as well as csaps and interp1 spline fitting functions but they cause the values to go below 0, which I cannot have as I will be using a log scale to plot the graph. The data from the above graph looks as follows:

A1=[0.31077 0.53279 0.021153 0.011143 0.001778 0.000642];
B1=[780 1560 3924 7344 11820 17352];
A2=[0.076948 0.119 0.009376 0.000887 4.27*10^(-5) 7.56*10^(-6)];
B2=[2368 4736 11928 22336 35960 52800];
A3=[0.039363 0.040862 0.002222 6.42*10^(-5) 1.73*10^(-6) 3.10*10^(-8)];
B3=[10059 20118 50391 94140 151365 222066];

With A vectors being the Error values and B vectors being the NDOF values for each curve. I have tried the following code using the interp1 function:

xq=B1(1,1):100:B1(1,6);
vq=interp1(B1,A1,xq,'spline');
plot(xq,vq);
hold on
xq=B2(1,1):100:B2(1,6);
vq=interp1(B2,A2,xq,'spline');
plot(xq,vq)
hold on
xq=B3(1,1):100:B3(1,6);
vq=interp1(B3,A3,xq,'spline');
plot(xq,vq)
set(gca,'XScale','log');
set(gca,'YScale','log');

But as I said, the spline fitting method causes the values to go into negative, and then they get ignored by the plot because of the log scale. I have tried cubic methods but the graphs really do not look right with them, and when I tried the cftool most graphs there did not converge to the final value of the graphs from excel, which is important as I am trying to show error convergence.

Does anyone know any technique that can recreate these graphs in a smooth way using this data ? I have researched the excel algorithm used for smoothing the graphs and it is apparently called a Bezier spline, but I do not know how to apply it for curve fitting in matlab. The only thing I managed to find is a mention of a bspline function, but it seems to only plot the spline for some non-decreasing value array, rather than use it to smooth out curves.

Answer 1

[Ameer Hamza]

Use 'pchip' interpolation

A1=[0.31077 0.53279 0.021153 0.011143 0.001778 0.000642];
B1=[780 1560 3924 7344 11820 17352];
A2=[0.076948 0.119 0.009376 0.000887 4.27*10^(-5) 7.56*10^(-6)];
B2=[2368 4736 11928 22336 35960 52800];
A3=[0.039363 0.040862 0.002222 6.42*10^(-5) 1.73*10^(-6) 3.10*10^(-8)];
B3=[10059 20118 50391 94140 151365 222066];

xq=B1(1,1):100:B1(1,6);
vq=interp1(B1,A1,xq,'pchip');
loglog(xq,vq,'-', B1,A1,'+');
hold on
xq=B2(1,1):100:B2(1,6);
vq=interp1(B2,A2,xq,'pchip');
loglog(xq,vq,'-', B2,A2,'+');
hold on
xq=B3(1,1):100:B3(1,6);
vq=interp1(B3,A3,xq,'pchip');
loglog(xq,vq,'-', B3,A3,'+');

[nth24601]

Thank you, I have used the pchip method as well. I was hoping that there could be another way to more accurately smooth these out (they seem to behave quite weird around the exact data points) but if there is no closer way I will probably use it.