## Software documentation

#### High Level functions

 gpopt Sequential or batch optimization using GP algorithms bfgs_search_prior Optimize prior hyper-parameter with respect to the pseudo-likelihood using the BFGS algorithm

#### Chaining procedures

 chaining_tree Compute the chaining tree given the distance matrix chaining_ucb Compute the chaining UCB given the distance matrix enet_greedy Compute an $\epsilon$-net given the distance matrix

#### GP computing

 gp_dist Canonical GP distance $d^2(x,y)=V[f(x)-f(y)\mid X_t, Y_t]$ gp_downdate Posterior $\mu(x_i)$ and $\sigma^2(x_i)$ given $X_t\setminus\{x_i\}$ gp_inf Bayesian system resolution for computing posterior of GP given observations gp_inf_update Bayesian system update with new observations gp_lik Negative log likelihood gp_loolik Negative log pseudo-likelihood gp_pred Posterior mean and variance of GP given the kernel matrices and the Bayesian inferance gp_sample Sample a Gaussian process in a hypercube and perform Bayesian inferance

#### Predefined basis and kernel functions

 basis_cst Constant mean function basis_none Zero mean function kernel_matern Matern covariance function for $u \in\{1/2,3/2,5/2\}$ kernel_se Squared exponential covariance function kernel_se_normiso Isotropic squared exponential covariance function

#### Utils

 cholpsd Upper Cholesky decomposition of psd matrix cummax Cumulative maximum as used in simple regrets solve_chol Linear system resolution $MX=Y$ given upper Cholesky decomposition $M=R^\top R$