Torch - 官方例子

require 'torch'

torch.manualSeed(1234) -- make sure the random seed is the same for everyone

N = 5 -- choose a dimension
A = torch.rand(N, N) -- create a random NxN matrix
A = A*A:t() -- make it symmetric positive
A:add(0.001, torch.eye(N)) -- make it definite
b = torch.rand(N) -- add a linear term


function J(x) -- create the quadratic form
   return 0.5*x:dot(A*x)-b:dot(x)
end
print(J(torch.rand(N))) -- print the function value

xs = torch.inverse(A)*b -- inverse the matrix
print(string.format('J(x^*) = %g', J(xs)))

function dJ(x) -- define the gradient w.r.t. x of J(x)
  return A*x-b
end

x = torch.rand(N) -- define some current solution
lr = 0.01 -- given learning rate lr
for i=1,20000 do
  x = x - dJ(x)*lr
  print(string.format('at iter %d J(x) = %f', i, J(x))) -- print the value of the objective function at each iteration
end

...
at iter 19995 J(x) = -3.135664
at iter 19996 J(x) = -3.135664
at iter 19997 J(x) = -3.135665
at iter 19998 J(x) = -3.135665
at iter 19999 J(x) = -3.135665
at iter 20000 J(x) = -3.135666

luarocks install optim

require 'optim'

state = { -- define a state for conjugate gradient
   verbose = true,
   maxIter = 100
}

x = torch.rand(N)
optim.cg(JdJ, x, state)

after 120 evaluation J(x) = -3.136835
after 121 evaluation J(x) = -3.136836
after 122 evaluation J(x) = -3.136837
after 123 evaluation J(x) = -3.136838
after 124 evaluation J(x) = -3.136840
after 125 evaluation J(x) = -3.136838

luarocks install gnuplot

evaluations = {}
time = {}
timer = torch.Timer()
neval = 0
function JdJ(x)
   local Jx = J(x)
   neval = neval + 1
   print(string.format('after %d evaluations, J(x) = %f', neval, Jx))
   table.insert(evaluations, Jx)
   table.insert(time, timer:time().real)
   return Jx, dJ(x)
end

-- trian
state = {
   verbose = true,
   maxIter = 100
}

x0 = torch.rand(N)
cgx = x0:clone() -- make a copy of x0
timer:reset()
optim.cg(JdJ, cgx, state)

-- convert the evaluations and time tables to tensors for plotting:
cgtime = torch.Tensor(time)
cgevaluations = torch.Tensor(evaluations)

-- add the training with stochastic gradient, using optim

evaluations = {}
time = {}
neval = 0
state = {
  lr = 0.1
}

-- start from the same starting point than for CG
x = x0:clone()

-- reset the timer!
timer:reset()

-- note that SGD optimizer requires to do the loop
for i=1,1000 do
  optim.sgd(JdJ, x, state)
  table.insert(evaluations, Jx)
end

sgdtime = torch.Tensor(time)
sgdevaluations = torch.Tensor(evaluations)

require 'gnuplot'

gnuplot.figure(1)
gnuplot.title('CG loss minimisation over time')
gnuplot.plot(cgtime, cgevaluations)

gnuplot.figure(2)
gnuplot.title('SGD loss minimisation over time')
gnuplot.plot(sgdtime, sgdevaluations)

require 'gnuplot'

gnuplot.pngfigure('plot.png')
gnuplot.plot(
   {'CG',  cgtime,  cgevaluations,  '-'},
   {'SGD', sgdtime, sgdevaluations, '-'})
gnuplot.xlabel('time (s)')
gnuplot.ylabel('J(x)')
gnuplot.plotflush()