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require 'torch'
-- rosenbrock.m This function returns the function value, partial derivatives
-- and Hessian of the (general dimension) rosenbrock function, given by:
--
-- f(x) = sum_{i=1:D-1} 100*(x(i+1) - x(i)^2)^2 + (1-x(i))^2
--
-- where D is the dimension of x. The true minimum is 0 at x = (1 1 ... 1).
--
-- Carl Edward Rasmussen, 2001-07-21.
function rosenbrock(x)
-- (1) compute f(x)
local d = x:size(1)
-- x1 = x(i)^2
local x1 = x.new(d-1):copy(x:narrow(1,1,d-1))
-- x(i+1) - x(i)^2
x1:cmul(x1):mul(-1):add(x:narrow(1,2,d-1))
-- 100*(x(i+1) - x(i)^2)^2
x1:cmul(x1):mul(100)
-- x(i)
local x0 = x.new(d-1):copy(x:narrow(1,1,d-1))
-- 1-x(i)
x0:mul(-1):add(1)
-- (1-x(i))^2
x0:cmul(x0)
-- 100*(x(i+1) - x(i)^2)^2 + (1-x(i))^2
x1:add(x0)
local fout = x1:sum()
-- (2) compute f(x)/dx
local dxout = x.new():resizeAs(x):zero()
-- df(1:D-1) = - 400*x(1:D-1).*(x(2:D)-x(1:D-1).^2) - 2*(1-x(1:D-1));
x1:copy(x:narrow(1,1,d-1))
x1:cmul(x1):mul(-1):add(x:narrow(1,2,d-1)):cmul(x:narrow(1,1,d-1)):mul(-400)
x0:copy(x:narrow(1,1,d-1)):mul(-1):add(1):mul(-2)
x1:add(x0)
dxout:narrow(1,1,d-1):copy(x1)
-- df(2:D) = df(2:D) + 200*(x(2:D)-x(1:D-1).^2);
x0:copy(x:narrow(1,1,d-1))
x0:cmul(x0):mul(-1):add(x:narrow(1,2,d-1)):mul(200)
dxout:narrow(1,2,d-1):add(x0)
return fout,dxout
end
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