TensorOperator.hpp

#pragma once
#include "Angular/Wigner369j.hpp"
#include "Maths/Grid.hpp"
#include "Maths/NumCalc_quadIntegrate.hpp"
#include "Maths/SphericalBessel.hpp"
#include "Physics/PhysConst_constants.hpp"
#include "Potentials/NuclearPotentials.hpp"
#include "Wavefunction/DiracSpinor.hpp"
#include "qip/Vector.hpp"
#include <cmath>
#include <string>
#include <vector>
 
namespace DiracOperator {
 
enum class Parity { even, odd, blank };
enum class Realness { real, imaginary, blank };
 
//==============================================================================
struct IntM4x4
// 4x4 Integer matrix.
// Notation for elements:
//  (e00  e01)
//  (e10  e11)
{
  IntM4x4(int in00, int in01, int in10, int in11)
      : e00(in00), e01(in01), e10(in10), e11(in11) {}
 
  const int e00, e01, e10, e11;
};
 
//==============================================================================
class SpinorMatrix
// 2x2 matrix that acts in radial spinor space.
// Notation for elements:
//  (ff  fg)
//  (gf  gg)
{
  double ff{0.0}, fg{0.0}, gf{0.0}, gg{0.0};
 
public:
  // SpinorMatrix() = default;
  constexpr SpinorMatrix(double iff, double ifg, double igf, double igg)
      : ff(iff), fg(ifg), gf(igf), gg(igg) {}
  constexpr SpinorMatrix() {}
 
  constexpr SpinorMatrix &operator+=(const SpinorMatrix &rhs) {
    ff += rhs.ff;
    fg += rhs.fg;
    gf += rhs.gf;
    gg += rhs.gg;
    return *this;
  }
  constexpr SpinorMatrix &operator-=(const SpinorMatrix &rhs) {
    ff -= rhs.ff;
    fg -= rhs.fg;
    gf -= rhs.gf;
    gg -= rhs.gg;
    return *this;
  }
  friend SpinorMatrix operator+(SpinorMatrix lhs, const SpinorMatrix &rhs) {
    return lhs += rhs;
  }
  friend SpinorMatrix operator-(SpinorMatrix lhs, const SpinorMatrix &rhs) {
    return lhs -= rhs;
  }
  constexpr SpinorMatrix &operator*=(double x) {
    ff *= x;
    fg *= x;
    gf *= x;
    gg *= x;
    return *this;
  }
  friend SpinorMatrix operator*(SpinorMatrix lhs, double x) { return lhs *= x; }
  friend SpinorMatrix operator*(double x, SpinorMatrix rhs) { return rhs *= x; }
 
  DiracSpinor act(const DiracSpinor &Fa) const {
    using namespace qip::overloads;
    auto mFa = Fa;
    // mFa.f() = ff * Fa.f() + fg * Fa.g();
    // mFa.g() = gf * Fa.f() + gg * Fa.g();
 
    // since we start with a copy:
    if (ff != 1.0)
      mFa.f() *= ff;
    if (fg != 0.0)
      mFa.f() += fg * Fa.g();
    if (gg != 1.0)
      mFa.g() *= gg;
    if (gf != 0.0)
      mFa.g() += gf * Fa.f();
    return mFa;
  }
  DiracSpinor operator*(const DiracSpinor &Fa) const { return act(Fa); }
};
 
//==============================================================================
class TensorOperator {
protected:
  TensorOperator(int rank_k, Parity pi, double constant = 1.0,
                 const std::vector<double> &inv = {}, int diff_order = 0,
                 Realness RorI = Realness::real, bool freq_dep = false)
      : m_rank(rank_k),
        m_parity(pi),
        m_diff_order(diff_order),
        opC(RorI),
        m_freqDependantQ(freq_dep),
        m_constant(constant),
        m_vec(inv){};
 
public:
  virtual ~TensorOperator() = default;
 
protected:
  int m_rank;
  Parity m_parity;
  int m_diff_order;
  Realness opC;
  bool m_freqDependantQ{false};
 
protected:
  // these may be updated for frequency-dependant operators
  double m_constant; // included in radial integral
  std::vector<double> m_vec;
 
public:
  bool freqDependantQ() const { return m_freqDependantQ; }
 
public:
  bool isZero(const int ka, int kb) const;
  bool isZero(const DiracSpinor &Fa, const DiracSpinor &Fb) const;
 
  bool selectrion_rule(int twoJA, int piA, int twoJB, int piB) const {
    if (twoJA == twoJB && twoJA == 0.0)
      return false;
 
    if (Angular::triangle(twoJA, twoJB, 2 * m_rank) == 0)
      return false;
 
    // if (2 * m_rank < std::abs(twoJA - twoJB))
    //   return false;
    return (m_parity == Parity::even) == (piA == piB);
  }
 
  virtual void updateFrequency(const double){};
 
  void scale(double lambda);
 
  const std::vector<double> &getv() const { return m_vec; }
  double getc() const { return m_constant; }
  int get_d_order() const { return m_diff_order; }
 
  bool imaginaryQ() const { return (opC == Realness::imaginary); }
  int rank() const { return m_rank; }
  int parity() const { return (m_parity == Parity::even) ? 1 : -1; }
 
  int symm_sign(const DiracSpinor &Fa, const DiracSpinor &Fb) const {
    const auto sra_i = imaginaryQ() ? -1 : 1;
    const auto sra = Angular::neg1pow_2(Fa.twoj() - Fb.twoj());
    return sra_i * sra;
  }
 
  virtual std::string name() const { return "Operator"; };
  virtual std::string units() const { return "au"; };
 
public:
  // These are needed for radial integrals
  // Usually just constants, but can also be functions of kappa
  virtual double angularCff(int /*k_a*/, int /*k_b*/) const { return 1.0; }
  virtual double angularCgg(int, int) const { return 1.0; }
  virtual double angularCfg(int, int) const { return 0.0; }
  virtual double angularCgf(int, int) const { return 0.0; }
 
public:
  virtual double angularF(const int, const int) const = 0;
  virtual DiracSpinor radial_rhs(const int kappa_a,
                                 const DiracSpinor &Fb) const;
 
  virtual double radialIntegral(const DiracSpinor &Fa,
                                const DiracSpinor &Fb) const;
 
  double rme3js(const int twoja, const int twojb, int two_mb = 1,
                int two_q = 0) const;
 
  DiracSpinor reduced_rhs(const int ka, const DiracSpinor &Fb) const;
 
  DiracSpinor reduced_lhs(const int ka, const DiracSpinor &Fb) const;
 
  double reducedME(const DiracSpinor &Fa, const DiracSpinor &Fb) const;
 
  double fullME(const DiracSpinor &Fa, const DiracSpinor &Fb,
                std::optional<int> two_ma = std::nullopt,
                std::optional<int> two_mb = std::nullopt,
                std::optional<int> two_q = std::nullopt) const;
};
 
//============================================================================
//============================================================================
class ScalarOperator : public TensorOperator {
public:
  ScalarOperator(Parity pi, double in_coef,
                 const std::vector<double> &in_v = {},
                 const IntM4x4 &in_g = {1, 0, 0, 1}, int in_diff = 0,
                 Realness rori = Realness::real)
      : TensorOperator(0, pi, in_coef, in_v, in_diff, rori),
        c_ff(in_g.e00),
        c_fg(in_g.e01),
        c_gf(in_g.e10),
        c_gg(in_g.e11) {}
 
  ScalarOperator(const std::vector<double> &in_v)
      : TensorOperator(0, Parity::even, 1.0, in_v, 0),
        c_ff(1.0),
        c_fg(0.0),
        c_gf(0.0),
        c_gg(1.0) {}
 
  ScalarOperator(double in_coef, const std::vector<double> &in_v = {})
      : TensorOperator(0, Parity::even, in_coef, in_v, 0),
        c_ff(1.0),
        c_fg(0.0),
        c_gf(0.0),
        c_gg(1.0) {}
 
public:
  virtual double angularF(const int ka, const int kb) const override {
    // For scalar operators, <a||h||b> = RadInt / 3js
    // 3js:= 1/(Sqrt[2j+1]) ... depends on m???
    // |k| = j+1/2
    return (std::abs(ka) == std::abs(kb)) ? std::sqrt(2.0 * std::abs(ka)) : 0.0;
  }
 
private:
  const double c_ff, c_fg, c_gf, c_gg;
 
protected:
  double virtual angularCff(int, int) const override { return c_ff; }
  double virtual angularCgg(int, int) const override { return c_gg; }
  double virtual angularCfg(int, int) const override { return c_fg; }
  double virtual angularCgf(int, int) const override { return c_gf; }
};
 
//------------------------------------------------------------------------------
class NullOperator final : public ScalarOperator {
public:
  NullOperator() : ScalarOperator(Parity::even, 0, {}) {}
 
protected:
  double virtual angularCff(int, int) const override final { return 0.0; }
  double virtual angularCgg(int, int) const override final { return 0.0; }
  double virtual angularCfg(int, int) const override final { return 0.0; }
  double virtual angularCgf(int, int) const override final { return 0.0; }
};
 
} // namespace DiracOperator