I have an optimization problem that involves series of high order
derivatives of f(x).
So, to get a decent value, I need to calculate higher order derivative at
least to 40~50th order.
Initially, I tried to use ForwardDiff package with automatic
differentiation but kept facing the following error message
<div id="inner-editor"><br class="Apple-interchange-newline">using
DualNumbers using ForwardDiff f(x::Vector) = sum(sin, x) + prod(tan, x) *
sum(sqrt, x); x = rand(5) g = ForwardDiff.derivative(f);</div>
using DualNumbers
using ForwardDiff
f(x::Vector) = sum(sin, x) + prod(tan, x) * sum(sqrt, x);
x = rand(5)
g = ForwardDiff.derivative(f);
LoadError: MethodError: `derivative` has no method matching
derivative(::Function)
Closest candidates are:
derivative(::Any, !Matched::Any)
while loading In[28], in expression starting on line 4
So, I moved on to D(f) instead from Root package and it works quite well
for a small order (like 10th order derivative)
<div id="inner-editor"><br class="Apple-interchange-newline">using
DualNumbers using ForwardDiff using Roots using ForwardDiff using JuMP #
Need to say it whenever we use JuMP using Gadfly function hder(f, n::Real)
# subroutine to calculate higher order derivative temp = f; if n==0 return
temp else for i=1:1:n temp = D(temp) end return temp end end</div>
using DualNumbers
using ForwardDiff
using Roots
using ForwardDiff
using JuMP
using Gadfly
function hder(f, n::Real) # subroutine to calculate n-th order derivative
temp = f;
if n==0
return temp
else
for i=1:1:n
temp = D(temp)
end
return temp
end
end
Out[7]:
hder (generic function with 1 method)
f(x) = (cos(x)) * exp(-1/5 * x)
g0 = hder(f, 0)
g1 = hder(f, 1)
g2 = hder(f, 2)
g3 = hder(f, 3)
g4 = hder(f, 4)
g5 = hder(f, 5)
g6 = hder(f, 6)
g7 = hder(f, 7)
g8 = hder(f, 8)
plot([g0, g1, g2, g3, g4, g5, g6, g7, g8], 0, 5pi)
<https://lh3.googleusercontent.com/-RCrcnLVFPhE/V4tfcG9uSEI/AAAAAAAAGUU/unxjN7x60jgPaEcCmcRlykx8WpbMxJBnACLcB/s1600/Screen%2BShot%2B2016-07-17%2Bat%2B11.35.09.png>
However, if I push the limit and ask to calculate, like 30th order
derivative, the program never ends and keep calculating for hours.
Is there a better way to do this type of task? either by using ForwardDiff
package or by modifying my function?
I just learned Julia last week, so please understand if my question sounds
stupid.
