Create levmarq.lua

levmarq.lua

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+--[[
+inputs:
+F - vector function at x. (torch.Tensor(m))
+J - Jacobian of F at x. (torch.Tensor(m,n)) 
+lamda - damping parameter
+--]]
+calc_lm_step=function(F,J,lamda)
+  --F: R^n -> R^m
+  m=J:size(1) 
+  n=J:size(2) 
+  --define M1:=J*J_tr-lambda*I
+  --local M1,Id=torch.Tensor(n,n),torch.Tensor(n,n)
+  --local d=torch.Tensor(n,1),torch.Tensor(n,1) 
+  Id=torch.eye(n)
+  M1=torch.mm(J:t(),J)
+  M1:add(lamda,Id)
+  -- right side:
+  g=torch.mv(J:t(),F)
+  -- in order to solve linear system with gesv we need to make RS 2-dimensional
+  g:resize(g:size(1),1)
+  -- solve M1*d=RS
+  d=-torch.gesv(g,M1)
+  return d,g
+  end
+
+
+  --[[
+levenberg-marquart optimization algorithm:
+-- for a vector function F: R^n -> R^m  the goal is to minimize the function
+f(x)=norm(F(x))^2
+--at a given point x the levmar-step d is given by:
+(J*J_tr+lambda*I)d=-J_tr*F(x)
+where J is the jacobian of F
+  perform lm step
+  input:
+  x - current point (should be torch.Tensor(n))
+  Feval - vector function F (should return torch.Tensor(m))
+  Jeval - Jacobian of F (should return torch.Tensor(m))
+  --]]
+  function optim.levmar(Feval,Jeval,x,config)
+   if config == nil then
+      print('no state table, LEVMAR initializing')
+   end
+  F=Feval(x)
+  J=Jeval(x)
+  d,g=calc_lm_step(F,J,config.lamda) 
+  nrmd=torch.norm(d)
+  --print('norm_d='..nrmd)
+  fx=torch.norm(Feval(x))^2
+  tmp=x+d
+  fxnew=torch.norm(Feval(tmp))^2
+  if fxnew<fx then
+    x:copy(tmp)
+    if (config.lamda > config.lamda_min) then
+      config.lamda=config.lamda*config.lamda_down
+    end
+  else
+    config.lamda=config.lamda*config.lamda_up
+    print('no step in lm_step()')
+  end
+  --tmp2, tmp3 = model:parameters()
+  return fxnew,g
+  end
+