The "plot" and "polyfit".

I want to plot a graph of a function fitted by two list of t and fp. A dependent variable fp is gotten by a independent variable t with a fitting function using "ployfit". I don't know how to plot a graph of the function ,even if I got "fp"s from "t" given arbitrarily.The code is shown below.

function y=fp(t)
t_1=[0 0.15 0.49 2.1126];
t_2=[2.27 3.53 8.78 25.45 42.80 43.68 44.08];
p_1=9.80665*[331.2 614.3 505.4 607.8];
p_2=9.80665*[48.65 43.97 42.01 41 40.8 40.79 2.22];
y=polyfit(t_2,p_2,2)*[t.*t;t;1]*(t>=2.1126)+polyfit(t_1,p_1,2)*[t.*t;t;1]*(t>=0&&t<2.1126);
end

Actually,the "plot" seems workable, but I need help to plot;

[John D'Errico]

Please learn to format your code so it will be readable. I've done that for you this time.

You do realize that this is not actually a spline that you are building? It is not even a continuous function across the breakpoint.

Answer 1

[John D'Errico]

It looks like you are trying to build a VERY simple spline, but not doing a very credible job of it. (Sorry.) This is a piecewise quadratic function, but it is one that will not even be continuous across the breakpoint.

t_1=[0 0.15 0.49 2.1126];
t_2=[2.27 3.53 8.78 25.45 42.80 43.68 44.08];
p_1=9.80665*[331.2 614.3 505.4 607.8];
p_2=9.80665*[48.65 43.97 42.01 41 40.8 40.79 2.22];

poly1 = polyfit(t_1,p_1,2);
poly2 = polyfit(t_2,p_2,2);

plot(t_1,p_1,'bo',t_2,p_2,'ro')
hold on

t = linspace(0,2.1126,100);
plot(t,polyval(poly1,t),'b-')

t = linspace(2.1126,44.08,100);
plot(t,polyval(poly2,t),'r-')

plot([2.1126 2.1126],[0 607.8],'g-')
grid on

In fact, the entire modeling effort is (again, sorry) rather insane. That first piece with only 4 wildly scattered points does not even justify a quadratic polynomial for that fit.

I don't know what you are trying to do here, nor why you are trying to force a quadratic polynomial through that mess. But I'm not sure that you know why either.

[Zhengsong Liao]

Thank you for your answer to the question.

The whole work I have tried is to build a spline for these discerete data so that an ODE can be solved with the spline. Actually, these show the force of jet engine from launch, and I want to solve an ODE to get the trajectory with a continuous force function. However ,it is no easy to build a fit function. Quadratic polynomial might be not good so I want to find a BETTER one which at least should be continuous at break point.