Improve performance of RF model

[charleskawczynski]

The RF model is suffering from heap allocations, based on looking at some flame graphs. In particular:

function non_dimensional_function(εδ_model::RFEntr, εδ_model_vars)
    # d inputs, p=2 outputs, m random features
    nondim_groups = collect(non_dimensional_groups(εδ_model, εδ_model_vars))
    d = size(nondim_groups)[1]

    # Learnable and fixed parameters
    c_rf_fix = εδ_model.c_rf_fix      # 2 x m x (1 + d), fix
    c_rf_fix = reshape(c_rf_fix, 2, :, 1 + d)
    m = size(c_rf_fix)[2]
    c_rf_opt = εδ_model.c_rf_opt      # 2 x (m + 1 + d), learn
    c_rf_opt = reshape(c_rf_opt, 2, m + 1 + d)

    # Random Features
    scale_x_entr = (c_rf_opt[1, (m + 2):(m + d + 1)] .^ 2) .* nondim_groups
    scale_x_detr = (c_rf_opt[2, (m + 2):(m + d + 1)] .^ 2) .* nondim_groups
    f_entr = c_rf_opt[1, m + 1]^2 * sqrt(2) * cos.(c_rf_fix[1, :, 2:(d + 1)] * scale_x_entr + c_rf_fix[1, :, 1])
    f_detr = c_rf_opt[2, m + 1]^2 * sqrt(2) * cos.(c_rf_fix[2, :, 2:(d + 1)] * scale_x_detr + c_rf_fix[2, :, 1])

    # Square output for nonnegativity for prediction
    nondim_ε = sum(c_rf_opt[1, 1:m] .* f_entr) / sqrt(m)
    nondim_δ = sum(c_rf_opt[2, 1:m] .* f_detr) / sqrt(m)
    return nondim_ε^2, nondim_δ^2
end

is allocating arrays. We can either:

• Try passing d, and m to the compiler, to see if it can stack allocate everything, or
• Write the result as the sum of a matrix-vector product, and avoid allocating the intermediate vector