#include "p-spin.hpp"

inline Real fP(unsigned p, Real q) {
  return 0.5 * pow(q, p);
}

inline Real dfP(unsigned p, Real q) {
  return 0.5 * p * pow(q, p - 1);
}

inline Real ddfP(unsigned p, Real q) {
  return 0.5 * p * (p - 1) * pow(q, p - 2);
}

Real f(Real λ, unsigned p, unsigned s, Real q) {
  return (1 - λ) * fP(p, q) + λ * fP(s, q);
}

Real df(Real λ, unsigned p, unsigned s, Real q) {
  return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
}

Real ddf(Real λ, unsigned p, unsigned s, Real q) {
  return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
}