Fix bug in the sign of the gradient.

experimental/include/scalfmm/matrix_kernels/laplace.hpp

@@ -191,7 +191,7 @@ namespace scalfmm::matrix_kernels::laplace
     /// grad_one_over_r\f$ k(x,y) : R -> R^{d}\f$ with \f$d \f$ the space
     /// dimension.
     ///
-    ///           \f$k(x,y) = \grad | x - y |^{-1}\f$
+    ///           \f$k(x,y) = \grad | x - y |^{-1} = -(x-y) | x - y |^{-3}\f$
     ///
     /// scale factor  \f$k(ax,ay)= 1/a^2 k(x,y)\f$
     template<std::size_t Dim = 3>
@@ -242,7 +242,7 @@ namespace scalfmm::matrix_kernels::laplace
             using std::sqrt;
             ValueType tmp = ValueType(1.0) / sqrt((((xs.at(Is) - ys.at(Is)) * (xs.at(Is) - ys.at(Is))) + ...));
             ValueType r3{pow(tmp, int(3))};
-            return std::make_tuple((r3 * (xs.at(Is) - ys.at(Is)))...);
+            return std::make_tuple((r3 * (ys.at(Is) - xs.at(Is)))...);
             //-r3 * (xs - ys);
         }
 
@@ -257,6 +257,8 @@ namespace scalfmm::matrix_kernels::laplace
     /// val_grad_one_over_r \f$k(x,y) : R^{km} -> R^{kn}\f$  with \f$ km = 1\f$ and \f$kn = d+1\f$  with \f$ d\f$ the
     /// space dimension.
     ///
+    /// \f$k(x,y) = ( | x - y |^{-1}, \grad | x - y |^{-1} ) =(| x - y |^{-1}, -(x-y) | x - y |^{-3}\f)$
+    ///
     ///  Is a specific kernel used to compute the  value of the kernel and its gradient
     ///
     /// scale factor \f$ k(ax,ay)= (1/a, 1/a^2 ... 1/a^2) k(x,y)\f$
@@ -302,7 +304,7 @@ namespace scalfmm::matrix_kernels::laplace
             using std::sqrt;
             ValueType tmp = ValueType(1.0) / sqrt((((xs.at(Is) - ys.at(Is)) * (xs.at(Is) - ys.at(Is))) + ...));
             ValueType r3{pow(tmp, int(3))};
-            return std::make_tuple(tmp, (r3 * (xs.at(Is) - ys.at(Is)))...);   //-r3 * (xs - ys);
+            return std::make_tuple(tmp, (r3 * (ys.at(Is) - xs.at(Is)))...);   //-r3 * (xs - ys);
         }
 
         const std::size_t separation_criterion{1};