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POFitting data to a 3rd degree polynomial
 

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    <p>I'm currently writing a C++ program where I have vectors of independent and dependent data that I would like to fit to a cubic function. However, I'm having trouble generating a polynomial that can fit my data.</p> <p>Part of the problem is that I can't use various numerical packages, such as GSL (long story); it's possible that it might even be overkill for my case. I don't need a very generalized solution for least squares fitting. I specifically want to fit my data to a cubic function. I do have access to Sony's vector library, which supports 4x4 matrices and can calculate their inverses, among other things.</p> <p>While prototyping this in Scilab, I used a function like:</p> <pre><code>function p = polyfit(x, y, n) m = length(x); aa = zeros(m, n+1) aa(:,1) = ones(m,1) for k = 2:n+1 aa(:,k) = x.^(k-1) end p = aa\y endfunction </code></pre> <p>Unfortunately, this doesn't map well to my current environment. The above example needs to support a matrix of M x N+1 dimensions. In my case, that's M x 4, where M depends on how much sample data that I have. There's also the problem of left division. I would need a matrix library that supported the inverse of matrices of arbitrary dimensions.</p> <p>Is there an algorithm for least squares where I can avoid having to calculate aa\y, or at least limit it to a 4x4 matrix? I suppose that I'm trying to rewrite the above algorithm into a simpler case that works for fitting to a cubic polynomial. I'm not looking for a code solution, but if someone can point me in the right direction, I'd appreciate it.</p>
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    1. COEven if you can't use GSL or, say, uBLAS, you can look at their source to see how it's done.
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    2. CO"Looking at the source" doesn't really address my problem and misses the point completely. These libraries are already built on top of robust matrix libraries, and use the same techniques that I'm trying to work around. I'm looking to decompose my problem into a 4x4 matrix or something simpler altogether.
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    3. CO"I would need a matrix library that supported the inverse of matrices of arbitrary dimensions." This is asking a lot -- namely because inverses aren't defined for matrices that aren't square.
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