TPCFastTransformation: Fix runtime parameters on CPU for polynoms.

Author: fweig

GPU/TPCFastTransformation/MultivariatePolynomial.h

@@ -56,7 +56,7 @@ class MultivariatePolynomial : public FlatObject, public MultivariatePolynomialH
 
   /// constructor for compile time evaluation of polynomial formula
   template <bool IsEnabled = true, typename std::enable_if<(IsEnabled && (Dim != 0 && Degree != 0)), int32_t>::type = 0>
-  MultivariatePolynomial() : mNParams{this->getNParameters(Degree, Dim, InteractionOnly)}
+  MultivariatePolynomial() : mNParams{this->template getNParameters<Degree, Dim, InteractionOnly>()}
   {
     construct();
   }

GPU/TPCFastTransformation/MultivariatePolynomialHelper.h

@@ -57,7 +57,7 @@ struct MultivariatePolynomialContainer {
 class MultivariatePolynomialParametersHelper
 {
  public:
-  /// \returns number of parameters for given dimension and degree of polynomials
+  /// \returns number of parameters for given dimension and degree of polynomials at compile time
   /// calculates the number of parameters for a multivariate polynomial for given degree: nParameters = (n+d-1 d) -> binomial coefficient
   /// see: https://mathoverflow.net/questions/225953/number-of-polynomial-terms-for-certain-degree-and-certain-number-of-variables
   template <uint32_t Degree, uint32_t Dim>
@@ -70,7 +70,19 @@ class MultivariatePolynomialParametersHelper
     }
   }
 
-  /// \returns the number of parameters for interaction terms only (see: https://en.wikipedia.org/wiki/Combination)
+  /// \returns number of parameters for given dimension and degree of polynomials
+  /// calculates the number of parameters for a multivariate polynomial for given degree: nParameters = (n+d-1 d) -> binomial coefficient
+  /// see: https://mathoverflow.net/questions/225953/number-of-polynomial-terms-for-certain-degree-and-certain-number-of-variables
+  GPUd() static constexpr uint32_t getNParametersAllTerms(uint32_t degree, uint32_t dim)
+  {
+    if (degree == 0) {
+      return binomialCoeff(dim - 1, 0);
+    } else {
+      return binomialCoeff(dim - 1 + degree, degree) + getNParametersAllTerms(degree - 1, dim);
+    }
+  }
+
+  /// \returns the number of parameters at compile time for interaction terms only (see: https://en.wikipedia.org/wiki/Combination)
   template <uint32_t Degree, uint32_t Dim>
   GPUd() static constexpr uint32_t getNParametersInteractionOnly()
   {
@@ -81,6 +93,16 @@ class MultivariatePolynomialParametersHelper
     }
   }
 
+  /// \returns the number of parameters for interaction terms only (see: https://en.wikipedia.org/wiki/Combination)
+  GPUd() static constexpr uint32_t getNParametersInteractionOnly(uint32_t degree, uint32_t dim)
+  {
+    if (degree == 0) {
+      return binomialCoeff(dim - 1, 0);
+    } else {
+      return binomialCoeff(dim, degree) + getNParametersInteractionOnly(degree - 1, dim);
+    }
+  }
+
   template <uint32_t Degree, uint32_t Dim, bool InteractionOnly>
   GPUd() static constexpr uint32_t getNParameters()
   {
@@ -91,8 +113,17 @@ class MultivariatePolynomialParametersHelper
     }
   }
 
+  GPUd() static constexpr uint32_t getNParameters(uint32_t degree, uint32_t dim, bool interactionOnly)
+  {
+    if (interactionOnly) {
+      return getNParametersInteractionOnly(degree, dim);
+    } else {
+      return getNParametersAllTerms(degree, dim);
+    }
+  }
+
  private:
-  /// calculate factorial of n
+  /// calculate factorial of n at compile time
   /// \return returns n!
   template <uint32_t N>
   GPUd() static constexpr uint32_t factorial()
@@ -104,13 +135,24 @@ class MultivariatePolynomialParametersHelper
     }
   }
 
-  /// calculates binomial coefficient
+  /// calculate factorial of n
+  /// \return returns n!
+  GPUd() static constexpr uint32_t factorial(uint32_t n) { return n == 0 || n == 1 ? 1 : n * factorial(n - 1); }
+
+  /// calculates binomial coefficient at compile time
   /// \return returns (n k)
   template <uint32_t N, uint32_t K>
   GPUd() static constexpr uint32_t binomialCoeff()
   {
     return factorial<N>() / (factorial<K>() * factorial<N - K>());
   }
+
+  /// calculates binomial coefficient
+  /// \return returns (n k)
+  GPUd() static constexpr uint32_t binomialCoeff(uint32_t n, uint32_t k)
+  {
+    return factorial(n) / (factorial(k) * factorial(n - k));
+  }
 };
 
 /// Helper struct for evaluating a multidimensional polynomial using compile time evaluated formula

GPU/TPCFastTransformation/NDPiecewisePolynomials.inc

@@ -165,7 +165,7 @@ void NDPiecewisePolynomials<Dim, Degree, InteractionOnly>::performFits(const std
     // check if data points are in the grid
     if (index == indexClamped) {
       // index of the polyniomial
-      const uint32_t idx = getDataIndex(index.data()) / MultivariatePolynomialParametersHelper::getNParameters(Degree, Dim, InteractionOnly);
+      const uint32_t idx = getDataIndex(index.data()) / MultivariatePolynomialParametersHelper::getNParameters<Degree, Dim, InteractionOnly>();
 
       // store index to data point
       dataPointsIndices[idx].emplace_back(i);
@@ -216,7 +216,7 @@ void NDPiecewisePolynomials<Dim, Degree, InteractionOnly>::performFits(const std
     const auto params = MultivariatePolynomialHelper<0, 0, false>::fit(fitter, xCords, response, error, true);
 
     // store parameters
-    std::copy(params.begin(), params.end(), &mParams[i * MultivariatePolynomialParametersHelper::getNParameters(Degree, Dim, InteractionOnly)]);
+    std::copy(params.begin(), params.end(), &mParams[i * MultivariatePolynomialParametersHelper::getNParameters<Degree, Dim, InteractionOnly>()]);
   }
 }