Use PDF for impact parameter weight

core/include/traccc/seeding/detail/seeding_config.hpp

@@ -192,6 +192,9 @@ struct seedfilter_config {
     // the impact parameters (d0) is multiplied by this factor and subtracted
     // from weight
     float impactWeightFactor = 1.f;
+    // assumed variance of the half-Gaussian distribution of the impact
+    // parameter $d_0$ in mm
+    float impactSigma = 5.f;
     // seed weight increased by this value if a compatible seed has been found.
     float compatSeedWeight = 200.f;
     // minimum distance between compatible seeds to be considered for weight
@@ -211,7 +214,7 @@ struct seedfilter_config {
     float good_spB_min_weight = 380.f;
 
     // seed cut
-    float seed_min_weight = 200.f;
+    float seed_min_weight = 400.f;
     float spB_min_radius = 43.f * unit<float>::mm;
 };
 

device/common/include/traccc/seeding/device/impl/find_triplets.ipp

@@ -112,11 +112,35 @@ inline void find_triplets(
                 spM, lb, lt, config, iSinTheta2, scatteringInRegion2, curvature,
                 impact_parameter)) {
 
+            // Compute the weight attributed by the impact factor as the PDF of
+            // a half-Gaussian distribution, i.e. we compute:
+            //
+            // w' = \frac{\sqrt{2}}{\sigma\sqrt{\pi}}
+            //      \exp\left(\frac{-x^2}{2\sigma^2}\right)
+            //
+            // However, we would like the weight to be normalized to the range
+            // [0, 1], so we divide by the maximum probability density which
+            // is easily found as:
+            //
+            // w_{max} = \frac{\sqrt{2}}{\sigma\sqrt{\pi}}
+            //
+            // Thus normalizing gives:
+            //
+            // w = \frac{w'}{w_{max}} = \exp\left(\frac{-x^2}{2\sigma^2}\right)
+            //
+            // Conveniently, this normalization also reduces the number of
+            // operations to be performed.
+            scalar impactParameterProb = math::exp(
+                -(impact_parameter * impact_parameter) /
+                (2.f * filter_config.impactSigma * filter_config.impactSigma));
+
+            scalar weight =
+                impactParameterProb * filter_config.impactWeightFactor;
+
             // Add triplet to jagged vector
-            triplets.at(posTriplets++) = device_triplet(
-                {spB_idx, spM_idx, spT_idx, globalIndex, curvature,
-                 -impact_parameter * filter_config.impactWeightFactor,
-                 lb.Zo()});
+            triplets.at(posTriplets++) =
+                device_triplet({spB_idx, spM_idx, spT_idx, globalIndex,
+                                curvature, weight, lb.Zo()});
         }
     }
 }