polyfun.hpp

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// src/builtin/include/nk/builtin/polyfun.hpp
//
// Pure C++ Polynomials, interpolation, integration, and piecewise polynomials.
#pragma once
 
#include <functional>
#include <memory_resource>
#include <string>
#include <nk/value/value.hpp>
#include <nk/value/span.hpp>
#include <nk/value/fn_handle.hpp>
 
namespace nk::builtin {

 
 
using ::nk::FnHandle;

Value roots(const Value &p, std::pmr::memory_resource *mr = nullptr);

Value poly(const Value &r, std::pmr::memory_resource *mr = nullptr);

Value polyval(const Value &p, const Value &x, std::pmr::memory_resource *mr = nullptr);

Value polyder(const Value &p, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value> polyder(const Value &b, const Value &a, std::pmr::memory_resource *mr = nullptr);

Value polyint(const Value &p, double k = 0.0, std::pmr::memory_resource *mr = nullptr);

Value polyfit(const Value &x, const Value &y, int n, std::pmr::memory_resource *mr = nullptr);
 
#include <tuple>

struct PolyDiv {
    Value q; 
    Value r; 
};

struct PadeCoef {
    Value num; 
    Value den; 
};

Value polyvalm(const Value &p, const Value &A, std::pmr::memory_resource *mr = nullptr);

Value poly_of_matrix(const Value &A, std::pmr::memory_resource *mr = nullptr);

PadeCoef padecoef(double T, int N, std::pmr::memory_resource *mr = nullptr);

PolyDiv polydiv(const Value &b, const Value &a, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value, Value> tf2zp(const Value &b, const Value &a, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value> zp2tf(const Value &z, const Value &p, double k, std::pmr::memory_resource *mr = nullptr);

struct ResidueResult {
    Value r; 
    Value p; 
    Value k; 
};

ResidueResult residue(const Value &b, const Value &a, std::pmr::memory_resource *mr = nullptr);

ResidueResult residuez(const Value &b, const Value &a, std::pmr::memory_resource *mr = nullptr);
 
// ── Interpolation & Piecewise Polynomials ───────────────────────────────────

Value interp1(const Value &x, const Value &v, const Value &xq, const std::string &method = "linear", std::pmr::memory_resource *mr = nullptr);

Value interp2(const Value &V, const Value &Xq, const Value &Yq, const std::string &method = "linear", std::pmr::memory_resource *mr = nullptr);

Value interp2(const Value &x, const Value &y, const Value &v, const Value &xq, const Value &yq, const std::string &method = "linear", std::pmr::memory_resource *mr = nullptr);

Value interp3(const Value &V, const Value &Xq, const Value &Yq, const Value &Zq, const std::string &method = "linear", std::pmr::memory_resource *mr = nullptr);

Value interp3(const Value &X, const Value &Y, const Value &Z, const Value &V, const Value &Xq, const Value &Yq, const Value &Zq, const std::string &method = "linear", std::pmr::memory_resource *mr = nullptr);

Value spline(const Value &x, const Value &y, const Value &xq = Value(), std::pmr::memory_resource *mr = nullptr);

Value pchip(const Value &x, const Value &y, const Value &xq = Value(), std::pmr::memory_resource *mr = nullptr);

Value makima(const Value &x, const Value &y, const Value &xq, std::pmr::memory_resource *mr = nullptr);

Value mkpp(const Value &breaks, const Value &coefs, std::pmr::memory_resource *mr = nullptr);

Value unmkpp(const Value &pp, std::pmr::memory_resource *mr = nullptr);

Value ppval(const Value &pp, const Value &xq, std::pmr::memory_resource *mr = nullptr);

Value gradient(const Value &f, double h = 1.0, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value> gradient2(const Value &f, double hx = 1.0, double hy = 1.0, std::pmr::memory_resource *mr = nullptr);

Value del2(const Value &u, double h = 1.0, std::pmr::memory_resource *mr = nullptr);

Value trapz(const Value &y, std::pmr::memory_resource *mr = nullptr);

Value trapz(const Value &x, const Value &y, std::pmr::memory_resource *mr = nullptr);

Value trapz(const Value &x, const Value &y, int dim, std::pmr::memory_resource *mr = nullptr);

Value cumtrapz(const Value &y, std::pmr::memory_resource *mr = nullptr);

Value cumtrapz(const Value &x, const Value &y, std::pmr::memory_resource *mr = nullptr);

Value cumtrapz(const Value &x, const Value &y, int dim, std::pmr::memory_resource *mr = nullptr);

Value cumtrapzDim(const Value &y, int dim, std::pmr::memory_resource *mr = nullptr);

Value integral(FnHandle fn, double a, double b, double absTol = 1e-10, std::pmr::memory_resource *mr = nullptr);

Value integral2(FnHandle fn, double a, double b, double c, double d, double absTol = 1e-10, std::pmr::memory_resource *mr = nullptr);

Value integral3(FnHandle fn, double a, double b, double c, double d, double e, double f, double absTol = 1e-10, std::pmr::memory_resource *mr = nullptr);
 
// ── Computational Geometry ──────────────────────────────────────────────────

struct MatchpairsResult {
    Value M;   
    Value uR;  
    Value uC;  
};

struct InpolygonResult {
    Value in;  
    Value on;  
};

struct PolyxpolyResult {
    Value xi;        
    Value yi;        
    Value segments;  
};

Value polyarea(const Value &x, const Value &y, std::pmr::memory_resource *mr = nullptr);

Value inpolygon(const Value &xq, const Value &yq, const Value &xv, const Value &yv, std::pmr::memory_resource *mr = nullptr);

InpolygonResult inpolygon2(const Value &xq, const Value &yq, const Value &xv, const Value &yv, std::pmr::memory_resource *mr = nullptr);

Value convhull(const Value &x, const Value &y, std::pmr::memory_resource *mr = nullptr);

PolyxpolyResult polyxpoly(const Value &x1, const Value &y1, const Value &x2, const Value &y2, std::pmr::memory_resource *mr = nullptr);

MatchpairsResult matchpairs(const Value &C, double cU, const std::string &mode = "min", std::pmr::memory_resource *mr = nullptr);

Value boundary(const Value &x, const Value &y, double shrink = 0.5, std::pmr::memory_resource *mr = nullptr);

Value delaunay(const Value &x, const Value &y, std::pmr::memory_resource *mr = nullptr);

Value griddata(const Value &x, const Value &y, const Value &v, const Value &xq, const Value &yq, std::pmr::memory_resource *mr = nullptr);

Value griddata(const Value &x, const Value &y, const Value &v, const Value &xq, const Value &yq, const std::string &method, std::pmr::memory_resource *mr = nullptr);

Value griddatan(const Value &Xv, const Value &vv, const Value &xi, std::pmr::memory_resource *mr = nullptr);

Value griddatan(const Value &Xv, const Value &vv, const Value &xi, const std::string &method, std::pmr::memory_resource *mr = nullptr);

Value histcounts2(const Value &x, const Value &y, const Value &xedgesV, const Value &yedgesV, std::pmr::memory_resource *mr = nullptr);
 

} // namespace nk::builtin