From b2d008a927f6915e60e30007c6181215ec7e8068 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fl=C3=A1vio=20Ribeiro?= <flavioluiz@gmail.com>
Date: Sun, 16 Aug 2015 01:12:28 +0200
Subject: [PATCH 1/2] included complex step finite  method for the gradient
 computation

---
 src/finite_difference.jl | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/src/finite_difference.jl b/src/finite_difference.jl
index 34a39e4..03937fe 100644
--- a/src/finite_difference.jl
+++ b/src/finite_difference.jl
@@ -129,8 +129,17 @@ function finite_difference!{S <: Number, T <: Number}(f::Function,
             x[i] = oldx
             g[i] = (f_xplusdx - f_xminusdx) / (epsilon + epsilon)
         end
+    elseif dtype == :complex
+        xcomplex = x + 0.*im
+        for i = 1:n
+            @complexrule x[i] epsilon
+            oldxi = xcomplex[i]
+            xcomplex[i] = oldxi + epsilon * im
+            g[i] = imag(f(xcomplex)) / epsilon
+            xcomplex[i] = oldxi
+        end	
     else
-        error("dtype must be :forward or :central")
+        error("dtype must be :forward, :central or :complex")
     end
 
     return

From 6a5f47812156dcabf328ff42d7dd43285a2effbf Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fl=C3=A1vio=20Ribeiro?= <flavioluiz@gmail.com>
Date: Tue, 18 Aug 2015 23:18:06 +0200
Subject: [PATCH 2/2] solves a problem for derivative when x = 0

---
 src/finite_difference.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/finite_difference.jl b/src/finite_difference.jl
index 03937fe..669b328 100644
--- a/src/finite_difference.jl
+++ b/src/finite_difference.jl
@@ -38,7 +38,7 @@ end
 macro complexrule(x, e)
     x, e = esc(x), esc(e)
     quote
-        $e = eps($x)
+        $e = eps($x + 1e-200)
     end
 end