atan2.hpp

Go to the documentation of this file.

#ifndef STAN_MATH_REV_FUN_ATAN2_HPP
#define STAN_MATH_REV_FUN_ATAN2_HPP
 
#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
inline var atan2(const var& a, const var& b) {
  return make_callback_var(
      std::atan2(a.val(), b.val()), [a, b](const auto& vi) mutable {
        double a_sq_plus_b_sq = (a.val() * a.val()) + (b.val() * b.val());
        a.adj() += vi.adj_ * b.val() / a_sq_plus_b_sq;
        b.adj() += -vi.adj_ * a.val() / a_sq_plus_b_sq;
      });
}
 
inline var atan2(const var& a, double b) {
  return make_callback_var(
      std::atan2(a.val(), b), [a, b](const auto& vi) mutable {
        double a_sq_plus_b_sq = (a.val() * a.val()) + (b * b);
        a.adj() += vi.adj_ * b / a_sq_plus_b_sq;
      });
}
 
inline var atan2(double a, const var& b) {
  return make_callback_var(
      std::atan2(a, b.val()), [a, b](const auto& vi) mutable {
        double a_sq_plus_b_sq = (a * a) + (b.val() * b.val());
        b.adj() += -vi.adj_ * a / a_sq_plus_b_sq;
      });
}
 
template <typename Mat1, typename Mat2,
          require_any_var_matrix_t<Mat1, Mat2>* = nullptr,
          require_all_matrix_t<Mat1, Mat2>* = nullptr>
inline auto atan2(const Mat1& a, const Mat2& b) {
  if (!is_constant<Mat1>::value && !is_constant<Mat2>::value) {
    arena_t<promote_scalar_t<var, Mat1>> arena_a = a;
    arena_t<promote_scalar_t<var, Mat2>> arena_b = b;
    auto atan2_val = atan2(arena_a.val(), arena_b.val());
    auto a_sq_plus_b_sq
        = to_arena((arena_a.val().array() * arena_a.val().array())
                   + (arena_b.val().array() * arena_b.val().array()));
    return make_callback_var(
        atan2(arena_a.val(), arena_b.val()),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_a.adj().array()
              += vi.adj().array() * arena_b.val().array() / a_sq_plus_b_sq;
          arena_b.adj().array()
              += -vi.adj().array() * arena_a.val().array() / a_sq_plus_b_sq;
        });
  } else if (!is_constant<Mat1>::value) {
    arena_t<promote_scalar_t<var, Mat1>> arena_a = a;
    arena_t<promote_scalar_t<double, Mat2>> arena_b = value_of(b);
    auto a_sq_plus_b_sq
        = to_arena((arena_a.val().array() * arena_a.val().array())
                   + (arena_b.array() * arena_b.array()));
 
    return make_callback_var(
        atan2(arena_a.val(), arena_b),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_a.adj().array()
              += vi.adj().array() * arena_b.array() / a_sq_plus_b_sq;
        });
  } else if (!is_constant<Mat2>::value) {
    arena_t<promote_scalar_t<double, Mat1>> arena_a = value_of(a);
    arena_t<promote_scalar_t<var, Mat2>> arena_b = b;
    auto a_sq_plus_b_sq
        = to_arena((arena_a.array() * arena_a.array())
                   + (arena_b.val().array() * arena_b.val().array()));
 
    return make_callback_var(
        atan2(arena_a, arena_b.val()),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_b.adj().array()
              += -vi.adj().array() * arena_a.array() / a_sq_plus_b_sq;
        });
  }
}
 
template <typename Scalar, typename VarMat,
          require_var_matrix_t<VarMat>* = nullptr,
          require_stan_scalar_t<Scalar>* = nullptr>
inline auto atan2(const Scalar& a, const VarMat& b) {
  if (!is_constant<Scalar>::value && !is_constant<VarMat>::value) {
    var arena_a = a;
    arena_t<promote_scalar_t<var, VarMat>> arena_b = b;
    auto atan2_val = atan2(arena_a.val(), arena_b.val());
    auto a_sq_plus_b_sq
        = to_arena((arena_a.val() * arena_a.val())
                   + (arena_b.val().array() * arena_b.val().array()));
    return make_callback_var(
        atan2(arena_a.val(), arena_b.val()),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_a.adj()
              += (vi.adj().array() * arena_b.val().array() / a_sq_plus_b_sq)
                     .sum();
          arena_b.adj().array()
              += -vi.adj().array() * arena_a.val() / a_sq_plus_b_sq;
        });
  } else if (!is_constant<Scalar>::value) {
    var arena_a = a;
    arena_t<promote_scalar_t<double, VarMat>> arena_b = value_of(b);
    auto a_sq_plus_b_sq = to_arena((arena_a.val() * arena_a.val())
                                   + (arena_b.array() * arena_b.array()));
 
    return make_callback_var(
        atan2(arena_a.val(), arena_b),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_a.adj()
              += (vi.adj().array() * arena_b.array() / a_sq_plus_b_sq).sum();
        });
  } else if (!is_constant<VarMat>::value) {
    double arena_a = value_of(a);
    arena_t<promote_scalar_t<var, VarMat>> arena_b = b;
    auto a_sq_plus_b_sq = to_arena(
        (arena_a * arena_a) + (arena_b.val().array() * arena_b.val().array()));
 
    return make_callback_var(
        atan2(arena_a, arena_b.val()),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_b.adj().array() += -vi.adj().array() * arena_a / a_sq_plus_b_sq;
        });
  }
}
 
template <typename VarMat, typename Scalar,
          require_var_matrix_t<VarMat>* = nullptr,
          require_stan_scalar_t<Scalar>* = nullptr>
inline auto atan2(const VarMat& a, const Scalar& b) {
  if (!is_constant<VarMat>::value && !is_constant<Scalar>::value) {
    arena_t<promote_scalar_t<var, VarMat>> arena_a = a;
    var arena_b = b;
    auto atan2_val = atan2(arena_a.val(), arena_b.val());
    auto a_sq_plus_b_sq
        = to_arena((arena_a.val().array() * arena_a.val().array())
                   + (arena_b.val() * arena_b.val()));
    return make_callback_var(
        atan2(arena_a.val(), arena_b.val()),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_a.adj().array()
              += vi.adj().array() * arena_b.val() / a_sq_plus_b_sq;
          arena_b.adj()
              += -(vi.adj().array() * arena_a.val().array() / a_sq_plus_b_sq)
                      .sum();
        });
  } else if (!is_constant<VarMat>::value) {
    arena_t<promote_scalar_t<var, VarMat>> arena_a = a;
    double arena_b = value_of(b);
    auto a_sq_plus_b_sq = to_arena(
        (arena_a.val().array() * arena_a.val().array()) + (arena_b * arena_b));
 
    return make_callback_var(
        atan2(arena_a.val(), arena_b),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_a.adj().array() += vi.adj().array() * arena_b / a_sq_plus_b_sq;
        });
  } else if (!is_constant<Scalar>::value) {
    arena_t<promote_scalar_t<double, VarMat>> arena_a = value_of(a);
    var arena_b = b;
    auto a_sq_plus_b_sq = to_arena((arena_a.array() * arena_a.array())
                                   + (arena_b.val() * arena_b.val()));
 
    return make_callback_var(
        atan2(arena_a, arena_b.val()),
        [arena_a, arena_b, a_sq_plus_b_sq](auto& vi) mutable {
          arena_b.adj()
              += -(vi.adj().array() * arena_a.array() / a_sq_plus_b_sq).sum();
        });
  }
}
 
}  // namespace math
}  // namespace stan
#endif