Use PDF for impact parameter weight

This commit uses the PDF of a half-Gaussian distribution to determine
the weight of the impact factor in the track finding. This changes makes
it so that weights are strictly positive and negates the "cut-off"
effect caused by the confirmation weight.

Author: stephenswat

core/include/traccc/definitions/common.hpp

@@ -21,6 +21,10 @@ using unit = detray::unit<scalar_t>;
 template <typename scalar_t>
 using constant = detray::constant<scalar_t>;
 
+namespace constants {
+constexpr scalar sqrt_pi = 1.772453851f;
+}
+
 // epsilon for float variables
 constexpr scalar float_epsilon = 1e-5f;
 

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 +112,22 @@ 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.
+            scalar impactParameterProb =
+                constant<scalar>::sqrt2 /
+                (filter_config.impactSigma * constants::sqrt_pi) *
+                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()});
         }
     }
 }