write a function that takes any equation as an input

I saw that similar questions were asked previously by they were way too specific to be helpful for me.

I need to write a function that has inputs of a series of x values and an equation. This function should create an interpolating polynomial for this function using those given x values. It should then output the coefficients of this polynomial

My question is how do I write a function with an input of a function which outputs a matrix?

Code so far is just the one line:

function P(x) = splinecalc(Xlist, f(x))

And that line doesn't work. It should be able to take in things like sin(x) or x^3+15x-4 or e^x, etc. and it should output a 4×n matrix giving the coefficients of the natural (free) cubic spline through the n+1 points . The columns of the output matrix should correspond to the n cubic polynomials, in order. The kth row of your output matrix should give the coefficients of .

Answer 1

[the cyclist]

Are you familiar with anonymous functions? That would presumably be the best way to pass "any function" as an argument.

Then inside splinecalc you can do what manipulations you need to create the interpolating polynomial.

[Konrad Brine]

I was not familiar with anonymous functions, I am new to this. Following those guidelines I am able to continue. Thank you!

Answer 2

[Stephan]

You might to want to achieve this:

% Inputs
xvals = 0:0.01:10;
fun = @(x) x.^5 + sin(x);

% call function
res = splinecalc(xvals, fun)

% plot results
hold on
fplot(fun,[xvals(1) xvals(end)])
plot(xvals, polyval(res,xvals))
hold off    

% calculate cubic polynomial
function polynom = splinecalc(xvals, fun)
yvals = fun(xvals); 
polynom = polyfit(xvals,yvals,3);
end