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--[[
This cg implementation is a rewrite of minimize.m written by Carl
E. Rasmussen. It is supposed to produce exactly same results (give
or take numerical accuracy due to some changed order of
operations). You can compare the result on rosenbrock with minimize.m.
http://www.gatsby.ucl.ac.uk/~edward/code/minimize/example.html
[x fx c] = minimize([0 0]', 'rosenbrock', -25)
Note that we limit the number of function evaluations only, it seems much
more important in practical use.
ARGS:
- `opfunc` : a function that takes a single input, the point of evaluation.
- `x` : the initial point
- `state` : a table of parameters and temporary allocations.
- `state.maxEval` : max number of function evaluations
- `state.maxIter` : max number of iterations
- `state.df[0,1,2,3]` : if you pass torch.Tensor they will be used for temp storage
- `state.[s,x0]` : if you pass torch.Tensor they will be used for temp storage
RETURN:
- `x*` : the new x vector, at the optimal point
- `f` : a table of all function values where
`f[1]` is the value of the function before any optimization and
`f[#f]` is the final fully optimized value, at x*
(Koray Kavukcuoglu, 2012)
--]]
function optim.cg(opfunc, x, config, state)
-- parameters
local config = config or {}
local state = state or config
local rho = config.rho or 0.01
local sig = config.sig or 0.5
local int = config.int or 0.1
local ext = config.ext or 3.0
local maxIter = config.maxIter or 20
local ratio = config.ratio or 100
local maxEval = config.maxEval or maxIter*1.25
local red = 1
local verbose = config.verbose or 0
local i = 0
local ls_failed = 0
local fx = {}
-- we need three points for the interpolation/extrapolation stuff
local z1,z2,z3 = 0,0,0
local d1,d2,d3 = 0,0,0
local f1,f2,f3 = 0,0,0
local df1 = state.df1 or x.new()
local df2 = state.df2 or x.new()
local df3 = state.df3 or x.new()
local tdf
df1:resizeAs(x)
df2:resizeAs(x)
df3:resizeAs(x)
-- search direction
local s = state.s or x.new()
s:resizeAs(x)
-- we need a temp storage for X
local x0 = state.x0 or x.new()
local f0 = 0
local df0 = state.df0 or x.new()
x0:resizeAs(x)
df0:resizeAs(x)
-- evaluate at initial point
f1,tdf = opfunc(x)
fx[#fx+1] = f1
df1:copy(tdf)
i=i+1
-- initial search direction
s:copy(df1):mul(-1)
d1 = -s:dot(s ) -- slope
z1 = red/(1-d1) -- initial step
while i < math.abs(maxEval) do
x0:copy(x)
f0 = f1
df0:copy(df1)
x:add(z1,s)
f2,tdf = opfunc(x)
df2:copy(tdf)
i=i+1
d2 = df2:dot(s)
f3,d3,z3 = f1,d1,-z1 -- init point 3 equal to point 1
local m = math.min(maxIter,maxEval-i)
local success = 0
local limit = -1
while true do
while (f2 > f1+z1*rho*d1 or d2 > -sig*d1) and m > 0 do
limit = z1
if f2 > f1 then
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3)
else
local A = 6*(f2-f3)/z3+3*(d2+d3)
local B = 3*(f3-f2)-z3*(d3+2*d2)
z2 = (math.sqrt(B*B-A*d2*z3*z3)-B)/A
end
if z2 ~= z2 or z2 == math.huge or z2 == -math.huge then
z2 = z3/2;
end
z2 = math.max(math.min(z2, int*z3),(1-int)*z3);
z1 = z1 + z2;
x:add(z2,s)
f2,tdf = opfunc(x)
df2:copy(tdf)
i=i+1
m = m - 1
d2 = df2:dot(s)
z3 = z3-z2;
end
if f2 > f1+z1*rho*d1 or d2 > -sig*d1 then
break
elseif d2 > sig*d1 then
success = 1;
break;
elseif m == 0 then
break;
end
local A = 6*(f2-f3)/z3+3*(d2+d3);
local B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+math.sqrt(B*B-A*d2*z3*z3))
if z2 ~= z2 or z2 == math.huge or z2 == -math.huge or z2 < 0 then
if limit < -0.5 then
z2 = z1 * (ext -1)
else
z2 = (limit-z1)/2
end
elseif (limit > -0.5) and (z2+z1) > limit then
z2 = (limit-z1)/2
elseif limit < -0.5 and (z2+z1) > z1*ext then
z2 = z1*(ext-1)
elseif z2 < -z3*int then
z2 = -z3*int
elseif limit > -0.5 and z2 < (limit-z1)*(1-int) then
z2 = (limit-z1)*(1-int)
end
f3=f2; d3=d2; z3=-z2;
z1 = z1+z2;
x:add(z2,s)
f2,tdf = opfunc(x)
df2:copy(tdf)
i=i+1
m = m - 1
d2 = df2:dot(s)
end
if success == 1 then
f1 = f2
fx[#fx+1] = f1;
local ss = (df2:dot(df2)-df2:dot(df1)) / df1:dot(df1)
s:mul(ss)
s:add(-1,df2)
local tmp = df1:clone()
df1:copy(df2)
df2:copy(tmp)
d2 = df1:dot(s)
if d2> 0 then
s:copy(df1)
s:mul(-1)
d2 = -s:dot(s)
end
z1 = z1 * math.min(ratio, d1/(d2-1e-320))
d1 = d2
ls_failed = 0
else
x:copy(x0)
f1 = f0
df1:copy(df0)
if ls_failed or i>maxEval then
break
end
local tmp = df1:clone()
df1:copy(df2)
df2:copy(tmp)
s:copy(df1)
s:mul(-1)
d1 = -s:dot(s)
z1 = 1/(1-d1)
ls_failed = 1
end
end
state.df0 = df0
state.df1 = df1
state.df2 = df2
state.df3 = df3
state.x0 = x0
state.s = s
return x,fx,i
end
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