require 'torch'

require 'gnuplot'

local nData =

local kWidth =

local xTrain = torch.linspace(-, , nData)

local yTrain = torch.pow(xTrain, )

print(xTrain)

print(yTrain)

local yTrain = yTrain + torch.mul(torch.randn(nData), 0.1)

print(yTrain)

local function phi(x, y)

    return torch.exp(-(/kWidth)*torch.sum(torch.pow(x-y,)))

end

local Phi = torch.Tensor(nData, nData)

for i = , nData do

    for j = , nData do

        Phi[i][j] = phi(xTrain[{{i}}], xTrain[{{j}}])

    end

end

local regularizer = torch.mul(torch.eye(nData), 0.001)

local theta = torch.inverse((Phi:t()*Phi) + regularizer) * Phi:t() * yTrain

local nTestData =

local xTest = torch.linspace(-, , nTestData)

local PhiTest = torch.Tensor(nData, nTestData)

for i = , nData do

    for j = , nTestData do

        PhiTest[i][j] = phi(xTrain[{{i}}], xTest[{{j}}])

    end

end

local yPred = PhiTest:t() * theta

gnuplot.plot({'Data', xTrain, yTrain, '+'}, {'Prediction', xTest, yPred, '-'})