interpolation1d

done single-threded 1d interpolations; linear, rational, cubic spline, polynomial and barycentric. Still not done test functions yet. Still missing multi-core options.

include/numerics/interpolation1d/interpolation1d_polynomial.h

@@ -0,0 +1,75 @@
+#pragma once
+
+#include "./numerics/interpolation1d_base.h"
+
+#include "./numerics/abs.h"
+#include "./utils/vector.h"
+
+
+namespace numerics{
+	
+	template <typename T>
+	struct interp_polynomial : 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_polynomial(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{
+
+			int64_t ns=0;
+			T y, den, dif, dift, ho, hp, w;
+			const T *xa = &xx[jl], *ya = &yy[jl];
+			utils::Vector<T> c(mm,0), d(mm,0);
+			dif = numerics::abs(x-xa[0]);
+
+			for (int64_t i = 0; i < mm; ++i){					// Here we find the index ns of the closest table entry,
+				dift = numerics::abs(x-xa[i]);
+				if (dift < dif){
+					ns = i;
+					dif=dift;
+				}
+				c[i]=ya[i];									// and initialize the tableau of c’s and d’s.
+				d[i]=ya[i];
+			}
+			y = ya[ns];										// This is the initial approximation to y.
+			ns -= 1;
+
+			for (int64_t m = 1; m < mm; ++m){				// For each column of the tableau,
+				for (int64_t i = 0; i < mm-m; ++i){		// we loop over the current c’s and d’s and update them.
+					ho = xa[i]-x;
+					hp = xa[i+m]-x;
+					w = c[i+1]-d[i];
+					den = ho-hp;
+					if (den == T{0.0}){
+						throw std::invalid_argument("interp_polynomial error"); // This error can occur only if two input xa’s are (to within roundoff identical.
+					}
+					den = w/den;							// Here the c’s and d’s are updated.
+					d[i] = hp*den;
+					c[i] = ho*den;
+				}
+				bool take_left = 2 * (ns + 1) < (mm - m);
+
+				if (take_left) {
+				    dy = c[ns + 1];
+				    y += dy;
+				} else {
+				    dy = d[ns];   
+				    y += dy;
+				    ns -= 1;
+				}
+			}
+			return y;
+		}
+
+	};
+
+} // namespace numerics
+