Automatic Differentiation Example

ForwardDiff_example.jl

# testing the automatic differentiation capabilities
using Cairo;
using DataFrames;
using Gadfly;
using ForwardDiff;

f(x) = sin(x[1]);
x = [-pi:.1:pi];
outf=[f(i) for i in x];

g = forwarddiff_gradient(f, Float64, fadtype=:typed);
outg = [g([i])[1] for i in x];

# plot using dataframes + gadfly
n = length(x);
d=DataFrame(
  x=vcat(x, x),
  y=vcat(outf, outg),
  key = vcat(rep("f(x)",n),
               rep("grad(x)",n))
  );
p = plot(d,
     x="x",
     y="y",
     color="key",
     Geom.line);
# save it out

draw(PNG("myplot.png", 6inch, 3inch), p);