Sync public subset from Flux (private)

include/numerics/interpolation1d/interpolation1d_rational.h

@@ -0,0 +1,79 @@
+#pragma once
+
+#include "./numerics/interpolation1d/interpolation1d_base.h"
+
+#include "./utils/vector.h"
+#include "./numerics/abs.h"
+
+namespace numerics{
+	
+	template <typename T>
+	struct interp_rational : 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::mm;
+
+	  	T dy;
+
+
+
+		interp_rational(const utils::Vector<T> &xv, const utils::Vector<T> &yv, uint64_t m)
+		: Base_interp<T>(xv, &yv[0], m), dy(T{0}){}
+
+		T rawinterp(int64_t jl, T x) override{
+
+			const T TINY = T{1.0e-99};
+			int64_t ns=0;
+			T y, w, t, hh, h, dd;
+			const T *xa = &xx[jl], *ya = &yy[jl];
+			utils::Vector<T> c(mm, T{0}), d(mm, T{0});
+
+			hh = numerics::abs(x - xa[0]);
+
+			for (int64_t i = 0; i < mm; ++i){
+				h = numerics::abs(x-xa[i]);
+				if (h == T{0}){
+					dy = T{0};
+					return ya[i];
+				}else if (h < hh){
+					ns = i;
+					hh = h;
+				}
+				c[i] = ya[i];
+				d[i] = ya[i] + TINY;					// The TINY part is needed to prevent a rare zero-over-zero condition.
+			}
+			y = ya[ns];
+			ns -= 1;
+			for (int64_t m = 1; m < mm; ++m){
+				for (int64_t i = 0; i < mm-m; ++i){
+					w = c[i+1] - d[i];
+					h = xa[i+m] - x;					// h will never be zero, since this was tested in the initializing loop.
+					t = (xa[i] - x)*d[i]/h;
+					dd = t - c[i+1];
+					if (dd == T{0}){					// This error condition indicates that the interpolating function has a pole at the requested value of x.
+						throw std::invalid_argument("Error in routine interp_rational"); // 
+					}
+					dd = w/dd;
+					d[i] = c[i+1]*dd;
+					c[i] = t*dd;
+				}
+				const bool take_left = (2 * (ns + 1) < (mm - m));
+
+				if (take_left) {
+					dy = c[ns + 1];
+				} else {
+					dy = d[ns];
+					ns -= 1;
+				}
+				y += dy;
+			}
+			return y;
+		}
+
+	};
+
+} // namespace numerics
+