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I'm trying to construct a multivariate likelihood function in c++ code with the aim of comparing multiple temperature simulations for consistency with observations but taking into account autocorrelation between the time steps. I am inexperienced in c++ and so have been struggling to understand how to write the equation in c++ form. I have the covariance matrix, the simulations I wish to judge and the observations to compare to. The equation is as follows:

f(x,μ,Σ) = (1/√(∣Σ∣(2π)^d))*exp(−1/2(x-μ)Σ^(-1)(x-μ)')

So I need to find the determinant and the inverse of the covariance matrix. Does anyone know how to do that in c++ if x,μ and Σ are all specified?

climatecode44
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    I guess you can implement some algorithm for calculating the determinant of a matrix and its inversion. Or you could use some linear algebra libraries like Eigen. – Quimby Aug 16 '22 at 20:05
  • I'm afraid I'm still very new with c++. Could you point me in the direction of any good example code? – climatecode44 Aug 16 '22 at 20:08
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    I am afraid not, neither algorithm is trivial to implement in any language. As I said, I would recommend a dedicated library. – Quimby Aug 16 '22 at 20:30
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