complex.h

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// Copyright (c) 2011, Hauke Strasdat
// Copyright (c) 2012, Steven Lovegrove
// Copyright (c) 2021, farm-ng, inc.
//
// Use of this source code is governed by an MIT-style
// license that can be found in the LICENSE file or at
// https://opensource.org/licenses/MIT.
 
#pragma once
#include "sophus/common/common.h"
#include "sophus/concepts/division_ring.h"
#include "sophus/linalg/vector_space.h"
 
namespace sophus {
 
template <class TScalar>
class ComplexImpl {
 public:
  using Scalar = TScalar;
  static int constexpr kNumParams = 2;
  static bool constexpr kIsCommutative = true;
 
  using Params = Eigen::Vector<Scalar, kNumParams>;
 
  template <class TCompatibleScalar>
  using ParamsReturn = Eigen::Vector<
      typename Eigen::ScalarBinaryOpTraits<Scalar, TCompatibleScalar>::
          ReturnType,
      2>;
 
  // factories
  static auto zero() -> Eigen::Vector<Scalar, 2> {
    return Eigen::Vector<Scalar, 2>::Zero();
  }
 
  static auto one() -> Eigen::Vector<Scalar, 2> {
    return Eigen::Vector<Scalar, 2>(1.0, 0.0);
  }
 
  static auto areParamsValid(Params const& /*unused*/)
      -> sophus::Expected<Success> {
    return sophus::Expected<Success>{};
  }
 
  static auto paramsExamples() -> std::vector<Params> {
    return pointExamples<Scalar, 2>();
  }
 
  static auto invalidParamsExamples() -> std::vector<Params> {
    return std::vector<Params>({});
  }
 
  // operations
 
  template <class TCompatibleScalar>
  static auto addition(
      Eigen::Vector<Scalar, 2> const& lhs_real_imag,
      Eigen::Vector<TCompatibleScalar, 2> const& rhs_real_imag)
      -> ParamsReturn<TCompatibleScalar> {
    return lhs_real_imag + rhs_real_imag;
  }
 
  template <class TCompatibleScalar>
  static auto multiplication(
      Eigen::Vector<Scalar, 2> const& lhs_real_imag,
      Eigen::Vector<TCompatibleScalar, 2> const& rhs_real_imag)
      -> ParamsReturn<TCompatibleScalar> {
    // complex multiplication
    return ParamsReturn<TCompatibleScalar>(
        lhs_real_imag.x() * rhs_real_imag.x() -
            lhs_real_imag.y() * rhs_real_imag.y(),
        lhs_real_imag.x() * rhs_real_imag.y() +
            lhs_real_imag.y() * rhs_real_imag.x());
  }
 
  static auto conjugate(Eigen::Vector<Scalar, 2> const& a)
      -> Eigen::Vector<Scalar, 2> {
    return Eigen::Vector<Scalar, 2>(a.x(), -a.y());
  }
 
  static auto inverse(Eigen::Vector<Scalar, 2> const& real_imag)
      -> Eigen::Vector<Scalar, 2> {
    return conjugate(real_imag) / squaredNorm(real_imag);
  }
 
  static auto norm(Eigen::Vector<Scalar, 2> const& real_imag) -> Scalar {
    using std::hypot;
    return hypot(real_imag.x(), real_imag.y());
  }
 
  static auto squaredNorm(Eigen::Vector<Scalar, 2> const& real_imag) -> Scalar {
    return real_imag.squaredNorm();
  }
};
 
template <class TScalar>
class Complex {
 public:
  using Scalar = TScalar;
  using Imag = Scalar;
  using Impl = ComplexImpl<Scalar>;
  static int constexpr kNumParams = 2;
 
  using Params = Eigen::Vector<Scalar, kNumParams>;
 
  template <class TCompatibleScalar>
  using ComplexReturn =
      Complex<typename Eigen::ScalarBinaryOpTraits<Scalar, TCompatibleScalar>::
                  ReturnType>;
 
  // constructors and factories
 
  Complex() : params_(Impl::zero()) {}
 
  Complex(Complex const&) = default;
  auto operator=(Complex const&) -> Complex& = default;
 
  static auto zero() -> Complex { return Complex::fromParams(Impl::zero()); }
 
  static auto one() -> Complex { return Complex::fromParams(Impl::one()); }
 
  static auto fromParams(Params const& params) -> Complex {
    Complex z(UninitTag{});
    z.setParams(params);
    return z;
  }
 
  [[nodiscard]] auto params() const -> Params const& { return params_; }
 
  void setParams(Params const& params) { params_ = params; }
 
  auto real() -> Scalar& { return params_[0]; }
  [[nodiscard]] auto real() const -> Scalar const& { return params_[0]; }
 
  auto imag() -> Scalar& { return params_[1]; }
  [[nodiscard]] auto imag() const -> Scalar const& { return params_[1]; }
 
  template <class TCompatibleScalar>
  auto operator+(Complex<TCompatibleScalar> const& other) const
      -> ComplexReturn<TCompatibleScalar> {
    return Complex::fromParams(Impl::addition(this->params_, other.params()));
  }
 
  template <class TCompatibleScalar>
  auto operator*(Complex<TCompatibleScalar> const& other) const
      -> ComplexReturn<TCompatibleScalar> {
    return ComplexReturn<TCompatibleScalar>::fromParams(
        Impl::multiplication(this->params_, other.params()));
  }
 
  [[nodiscard]] auto conjugate() const -> Complex {
    return Complex::fromParams(Impl::conjugate(this->params_));
  }
 
  [[nodiscard]] auto inverse() const -> Complex {
    return Complex::fromParams(Impl::inverse(this->params_));
  }
 
  [[nodiscard]] auto norm() const -> Scalar {
    return Impl::norm(this->params_);
  }
 
  [[nodiscard]] auto squaredNorm() const -> Scalar {
    return Impl::squaredNorm(this->params_);
  }
 
 private:
  Complex(UninitTag /*unused*/) {}
  Eigen::Vector2<Scalar> params_;
};
 
}  // namespace sophus