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Lua explaining the structure of two functions in Lua


New Coder
Hi everyone,

I am trying to integrate a code which is a variational auto encoder model (where the prior of the VAE is a mixture of Gaussians) from Lua (torch) to pytorch as part of my model and I have a hard time to fully understand the Lua script (I didn't find a tutorial of the language). These two following functions are vague for me:
First starting from this line which is computing the loglikelihood.

require 'layers/GaussianLogLikelihood'
function Likelihood(K, D, M)
    local x_sample = - nn.Identity() -- [(MxN)xD]
    local mean = - nn.Identity()  -- {[(MxN)xD]}k
    local logVar = - nn.Identity() -- {[(MxN)xD]}k

    local llh_table = nn.ConcatTable()
    for k =1, K do
        local x = - nn.Identity()
        local mean_k_in = - nn.Identity()
        local logVar_k_in = - nn.Identity()

        local mean_k = mean_k_in
                        - nn.SelectTable(k)

        local logVar_k = logVar_k_in
                        - nn.SelectTable(k)

        local llh = {x, mean_k, logVar_k}
                        - nn.GaussianLogLikelihood()

        local llh_module = nn.gModule({x, mean_k_in, logVar_k_in}, {llh})

    local out = {x_sample, mean, logVar}
                            - llh_table -- {[MxN,1]}k
                            - nn.JoinTable(2) -- [MxN,K]  -- log unNorm P
                            - nn.SoftMax()

    return nn.gModule({x_sample, mean, logVar},{out})
The likelihood function requires GaussianLogLikelihood function too:

function GaussianLogLikelihood:__init(name,display)
self.gradInput = {}

function GaussianLogLikelihood:updateOutput(input)
-- input[1] : x [NxD]
-- input[2] : mean [NxD]
-- input[3] : logVar [NxD]
-- llh = -0.5 sum_d { (x_i - mu_i)^2/var_i } - 1/2 sum_d (logVar_i) - D/2 ln(2pi) [N]
local N = input[1]:size(1)
local D = input[1]:size(2)

self._x = self._x or torch.Tensor():typeAs(input[1]):resizeAs(input[1])
self._var = self._var or torch.Tensor():typeAs(input[3]):resizeAs(input[3])

self.output = self.output or input[1].new()
self.output:typeAs(input[1]):resize(N, 1):zero()

self.output:copy( self._x:add(-1, input[2]):pow(2):cdiv(self._var):sum(2) )
self.output:add( input[3]:sum(2) )
self.output:add( D * torch.log(2*math.pi) )

return self.output

I am confused about the inputs and the outputs of each function. I appreciate if someone can describe them in terms of a pseudo code. Thanks in advance.