How can I make curve form data?

Hi All,

I would like to make a convex curve from this (x,y) data that I have. The curve must connect the first and last points of y.

x= 7000,7050,7100,7150,7200

y= -92.9,-125.6,-158.5,-190.9,-223.5

The help would be apprecited,

Thanks in advance,

Riyadh

[Rik]

Do you want to fit a specific function to the data, or do you want to just have a smooth curve?

[John D'Errico]

@ Riyadh Muttaleb

There is no reason to use an answer to make a comment. Moved:

"I want to to have a smooth curve."

[Rik]

Your data is already a smooth curve:

p=polyfit(x,y,2);
polyval(p,x)-y

polyfit returns a warning and the second line shows the deviation from the fit is minimal.

So what is your goal?

[Riyadh Muttaleb]

My data is a smooth line! I want curve connect the first and last points.

[Walter Roberson]

After the polyfit,

xs = linspace(x(1), x(2));
ys = polyval(p, xs);
plot(xs, ys)

[Riyadh Muttaleb]

I got a straight line!

[Walter Roberson]

No you didn't -- you get a curved line that was sampled over a small enough region that it looked flat.

If you look at diff(y) you will see that the differences between adjacent y values is approximately constant, which is what you would expect for a straight line.

If you fit as a polynomial of degree 2, then the minimum of that polynomial is at 23425 and the zero crossings are at 6859 and 39990

Answer 1

[David Goodmanson]

Riyadh;

The differences from a straight line are small, so it make sense to look at that difference.

x = [7000,7050,7100,7150,7200]'
y = [-92.9,-125.6,-158.5,-190.9,-223.5]'
ylin = linspace(y(1),y(end),5)'
ydiff = y - ylin;
figure(1)
plot(x,ydiff,'o-');
grid on

The three differences are all negative, so absent any other information it can just be fit with a parabola that is zero at the end points. This will lead to a curve that is convex downwards.

p = (x-x(1)).*(x-x(end));  % parabola, zero at end points
c = p\ydiff;               % least squares fit
xnew = linspace(7000,7200,500);           % grid with more points
ydiffnew = c*(xnew-x(1)).*(xnew-x(end));  % fitted parabola, zero at end points
figure(2)
plot(x,ydiff,'o-',xnew,ydiffnew)
grid on

Then the final result ynew is this plus the linear line

slope = (y(end)-y(1))/(x(end)-x(1));
ylinnew = y(1) + slope*(xnew-x(1));
ynew = ylinnew + ydiffnew;
figure(3)
plot(x,y,'o-',xnew,ynew)
grid on

[Riyadh Muttaleb]

Thank you so much for your great work, However, the seconed part the curve is very good while in the third part it looks like a straight line!