#include "p-spin.hpp"

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

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

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

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