Sync public subset from Flux (private)

include/numerics/interpolation1d/interpolation1d_barycentric.h

@@ -0,0 +1,88 @@
+#pragma once
+
+#include "./numerics/interpolation1d/interpolation1d_base.h"
+
+#include "./utils/vector.h"
+#include "./numerics/min.h"
+#include "./numerics/max.h"
+
+
+namespace numerics{
+	
+	template <typename T>
+	struct interp_barycentric : Base_interp<T> {
+		using Base   = Base_interp<T>;
+
+	  	// bring base data members into scope (or use this->xx / this->yy below)
+	  	using Base::xx;
+	  	using Base::yy;
+	  	using Base::n;
+
+	  	utils::Vector<T> w;
+	  	int64_t d;
+
+		interp_barycentric(const utils::Vector<T> &xv, const utils::Vector<T> &yv, uint64_t dd)
+		: Base_interp<T>(xv, &yv[0], xv.size()), w(n,T{0}), d(dd) {
+			// Constructor arguments are x and y vectors of length n, and order d of desired approximation.
+			if (n <= d){
+				throw std::invalid_argument("d too large for number of points in interp_barycentric");
+			}
+			for (int64_t k = 0; k < n; ++k){
+				int64_t imin = numerics::max(k-d, static_cast<int64_t>(0));
+				int64_t imax;
+				if (k >= n - d) {
+				    imax = n - d - 1;
+				} else {
+				    imax = k;
+				}
+				T temp;
+				if ( (imin & 1) != 0 ) {   // odd?
+				    temp = T{-1};
+				} else {                   // even
+				    temp = T{1};
+				}
+				T sum = T{0};
+
+				for (int64_t i = imin; i <= imax; ++i){
+					int64_t jmax = numerics::min(i+d, n-1);
+					T term = T{1};
+					for (int64_t j = i; j <= jmax; ++j){
+						if (j == k){
+							continue;
+						}
+						term *= (xx[k] - xx[j]);
+					}
+					term = temp/term;
+					temp = -temp;
+					sum += term;
+				}
+				w[k] = sum;
+			}
+		}
+
+		T rawinterp(int64_t jl, T x) override{
+
+			T num{T{0}}, den{T{0}};
+			
+			for (int64_t i = 0; i < n; ++i){
+				T h = x - xx[i];
+				if (h == T{0}){
+					return yy[i];
+				}else{
+					T temp = w[i]/h;
+					num += temp*yy[i];
+					den += temp;
+				}
+			}
+			return num/den;
+		}
+
+
+		T interp(T x) {
+			return rawinterp(1, x);
+		}
+
+	};
+
+} // namespace numerics
+