From 8b6f53222b84d1e4f0f1e86b1d321777b58a28dc Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 2 Jun 2016 15:29:59 +0200
Subject: [PATCH] bug #1193: fix lpNorm<Infinity> for empty input.

---
 Eigen/src/Core/Dot.h      |  7 ++++++-
 Eigen/src/Core/Redux.h    |  4 +++-
 test/array_for_matrix.cpp | 16 +++++++++++++++-
 3 files changed, 24 insertions(+), 3 deletions(-)

diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
index 82d58fc0b..f3c869635 100644
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -227,9 +227,12 @@ struct lpNorm_selector<Derived, 2>
 template<typename Derived>
 struct lpNorm_selector<Derived, Infinity>
 {
+  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
   EIGEN_DEVICE_FUNC
-  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+  static inline RealScalar run(const MatrixBase<Derived>& m)
   {
+    if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==Dynamic && m.size()==0))
+      return RealScalar(0);
     return m.cwiseAbs().maxCoeff();
   }
 };
@@ -240,6 +243,8 @@ struct lpNorm_selector<Derived, Infinity>
   *          of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
   *          norm, that is the maximum of the absolute values of the coefficients of \c *this.
   *
+  * In all cases, if \c *this is empty, then the value 0 is returned.
+  *
   * \note For matrices, this function does not compute the <a href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
   *
   * \sa norm()
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
index 3a47edf79..7984cd6e1 100644
--- a/Eigen/src/Core/Redux.h
+++ b/Eigen/src/Core/Redux.h
@@ -438,7 +438,9 @@ DenseBase<Derived>::maxCoeff() const
   return derived().redux(Eigen::internal::scalar_max_op<Scalar>());
 }
 
-/** \returns the sum of all coefficients of *this
+/** \returns the sum of all coefficients of \c *this
+  *
+  * If \c *this is empty, then the value 0 is returned.
   *
   * \sa trace(), prod(), mean()
   */
diff --git a/test/array_for_matrix.cpp b/test/array_for_matrix.cpp
index db5f3b34a..75e6a778f 100644
--- a/test/array_for_matrix.cpp
+++ b/test/array_for_matrix.cpp
@@ -144,9 +144,21 @@ template<typename MatrixType> void comparisons(const MatrixType& m)
 template<typename VectorType> void lpNorm(const VectorType& v)
 {
   using std::sqrt;
+  typedef typename VectorType::RealScalar RealScalar;
   VectorType u = VectorType::Random(v.size());
 
-  VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());
+  if(v.size()==0)
+  {
+    VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), RealScalar(0));
+    VERIFY_IS_APPROX(u.template lpNorm<1>(), RealScalar(0));
+    VERIFY_IS_APPROX(u.template lpNorm<2>(), RealScalar(0));
+    VERIFY_IS_APPROX(u.template lpNorm<5>(), RealScalar(0));
+  }
+  else
+  {
+    VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());
+  }
+
   VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum());
   VERIFY_IS_APPROX(u.template lpNorm<2>(), sqrt(u.array().abs().square().sum()));
   VERIFY_IS_APPROX(numext::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum());
@@ -255,6 +267,8 @@ void test_array_for_matrix()
     CALL_SUBTEST_5( lpNorm(VectorXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
     CALL_SUBTEST_4( lpNorm(VectorXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
   }
+  CALL_SUBTEST_5( lpNorm(VectorXf(0)) );
+  CALL_SUBTEST_4( lpNorm(VectorXcf(0)) );
   for(int i = 0; i < g_repeat; i++) {
     CALL_SUBTEST_4( resize(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
     CALL_SUBTEST_5( resize(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );