Fixed bug #702 and added unit test.

Thanks to Alexander Werner for the report.

3 files changed, 48 insertions, 5 deletions

diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index 8d42e69b9..590797973 100644
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -599,12 +599,10 @@ atan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b)
   PlainADS ret;
   ret.value() = atan2(a.value(), b.value());
   
-  Scalar tmp2 = a.value() * a.value();
-  Scalar tmp3 = b.value() * b.value();
-  Scalar tmp4 = tmp3/(tmp2+tmp3);
+  Scalar squared_hypot = a.value() * a.value() + b.value() * b.value();
   
-  if (tmp4!=0)
-    ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) * (tmp2+tmp3);
+  // if (squared_hypot==0) the derivation is undefined and the following results in a NaN:
+  ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) / squared_hypot;
 
   return ret;
 }
diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt
index a94a3b5e5..38c89a234 100644
--- a/unsupported/test/CMakeLists.txt
+++ b/unsupported/test/CMakeLists.txt
@@ -28,6 +28,7 @@ endif(ADOLC_FOUND)
 ei_add_test(NonLinearOptimization)
 
 ei_add_test(NumericalDiff)
+ei_add_test(autodiff_scalar)
 ei_add_test(autodiff)
 
 if (NOT CMAKE_CXX_COMPILER MATCHES "clang\\+\\+$")
diff --git a/unsupported/test/autodiff_scalar.cpp b/unsupported/test/autodiff_scalar.cpp
new file mode 100644
index 000000000..ba4b5aec4
--- /dev/null
+++ b/unsupported/test/autodiff_scalar.cpp
@@ -0,0 +1,44 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christoph Hertzberg <chtz@informatik.uni-bremen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/AutoDiff>
+
+/*
+ * In this file scalar derivations are tested for correctness.
+ * TODO add more tests!
+ */
+
+template<typename Scalar> void check_atan2()
+{
+  typedef Matrix<Scalar, 1, 1> Deriv1;
+  typedef AutoDiffScalar<Deriv1> AD;
+  
+  AD x(internal::random<Scalar>(-3.0, 3.0), Deriv1::UnitX());
+  
+  using std::exp;
+  Scalar r = exp(internal::random<Scalar>(-10, 10));
+  
+  AD s = sin(x), c = cos(x);
+  AD res = atan2(r*s, r*c);
+  
+  VERIFY_IS_APPROX(res.value(), x.value());
+  VERIFY_IS_APPROX(res.derivatives(), x.derivatives());
+}
+
+
+
+
+void test_autodiff_scalar()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( check_atan2<float>() );
+    CALL_SUBTEST_2( check_atan2<double>() );
+  }
+}