How can I smoothen my plots by removing sharp edges/points in the plots?

I have two codes for generating plots given below. The first code generate a plot from the data file attached. I need help to remove sharp edges/points that appear on the plots so that I get smooth curves. Below is the first code;

A=load('dataQ0.05t.txt');
y = A(:,2);
x = A(:,1);

plot(x,y,'b')
semilogx(x,y,'b')

The second code;

r = linspace(10^-2,10^2);
eta=zeros(size(r));
%hold on;
for delta= [0 1 2 3 4 5 6]
for k=1:numel(r)
  f=@(x,y) (1./pi).*(x.*exp(-3.44.*r(k).^(5/3).*x.*(sin(y/2)).^(5/3)).*cos(delta*y));
  eta(k) = integral2(f,0,1,0,2*pi).*exp(-10);
 % hold on
end

plot(r,eta)
axis([10^(-0.5) 10^2 10.^(-9) 10.^(-4)])
loglog(r,eta)
hold on
end

Answer 1

[Star Strider]

One option is to use vectors with increased resolutiuon (numbers of points), and then interpolate as necessary —

A=load('dataQ0.05t.txt');
y = A(:,2);
x = A(:,1);

plot(x,y,'b')

semilogx(x,y,'b')

xi = linspace(min(x), max(x), 250).';
yi = interp1(x, y, xi);

figure
semilogx(xi, yi, 'b')
title('Increased Resolution, Interpolated')

% r = linspace(10^-2,10^2);
r = logspace(-2, 2, 100);
eta=zeros(size(r));
%hold on;
for delta= [0 1 2 3 4 5 6]
for k=1:numel(r)
  f=@(x,y) (1./pi).*(x.*exp(-3.44.*r(k).^(5/3).*x.*(sin(y/2)).^(5/3)).*cos(delta*y));
  eta(k) = integral2(f,0,1,0,2*pi).*exp(-10);
 % hold on
end

plot(r,eta)
axis([10^(-0.5) 10^2 10.^(-9) 10.^(-4)])
loglog(r,eta)
hold on
end
title('Using ‘logspace’ With Increased Resolution')

The second plot uses the logspace function with 100 points to create much smoother curves.

.

[Comfort Sekga]

@Star Strider Thank you for the assistance. The revisions you made in the second code provide exactly the answer I was looking for. However, for the first plot I wanted to smoothen the curve at the points between 3*10^-5 and 4*10^-5 in the y-axis and then keep the same shape of the original plot.

[Star Strider]

My pleasure!

The interpolation functions work best on regularly-spaced, linear vectors. Your independent variable data are exponential, so the interpolation functions are going to have problems with them. The best I can do to smooth your curve is to provide a large number of interpolation points, and use the pchip interpolation method.

Try this —

A=load('dataQ0.05t.txt');
format shortG
y = A(:,2);
x = A(:,1);

plot(x,y,'b')

semilogx(x,y,'b')
title('Original')

xi = logspace(log10(min(x)), log10(max(x)), 5000).';
yi = interp1(x, y, xi, 'pchip');

figure
semilogx(xi, yi, 'b')
title('Increased Resolution, Interpolated')

It is still not perfect, however it is an improvement.

.

[Comfort Sekga]

@Star Strider Thank you very much. The plot looks good now.

[Star Strider]

As always, my pleasure!