--[[ ADAGRAD implementation for SGD

ARGS:
- `opfunc` : a function that takes a single input (X), the point of
         evaluation, and returns f(X) and df/dX
- `x` : the initial point
- `state` : a table describing the state of the optimizer; after each
         call the state is modified
- `state.learningRate` : learning rate
- `state.paramVariance` : vector of temporal variances of parameters
- `state.weightDecay` : scalar that controls weight decay
RETURN:
- `x` : the new x vector
- `f(x)` : the function, evaluated before the update

]]
function optim.adagrad(opfunc, x, config, state)
   -- (0) get/update state
   if config == nil and state == nil then
      print('no state table, ADAGRAD initializing')
   end
   local config = config or {}
   local state = state or config
   local lr = config.learningRate or 1e-3
   local lrd = config.learningRateDecay or 0
   local wd = config.weightDecay or 0
   state.evalCounter = state.evalCounter or 0
   local nevals = state.evalCounter

   -- (1) evaluate f(x) and df/dx
   local fx,dfdx = opfunc(x)

   -- (2) weight decay with a single parameter
   if wd ~= 0 then
       dfdx:add(wd, x)
   end

   -- (3) learning rate decay (annealing)
   local clr = lr / (1 + nevals*lrd)

   -- (4) parameter update with single or individual learning rates
   if not state.paramVariance then
      state.paramVariance = torch.Tensor():typeAs(x):resizeAs(dfdx):zero()
      state.paramStd = torch.Tensor():typeAs(x):resizeAs(dfdx)
   end
   state.paramVariance:addcmul(1,dfdx,dfdx)
   state.paramStd:resizeAs(state.paramVariance):copy(state.paramVariance):sqrt()
   x:addcdiv(-clr, dfdx,state.paramStd:add(1e-10))

   -- (5) update evaluation counter
   state.evalCounter = state.evalCounter + 1

   -- return x*, f(x) before optimization
   return x,{fx}
end