12345qiupeng
/
gtsam
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

refactor IncompleteGamma class

release/4.3a0
Varun Agrawal 2023-05-10 15:37:46 -04:00
parent d0b3f1dd25
commit 8201c77b30
1 changed files with 131 additions and 136 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

205
gtsam/nonlinear/GncHelpers.h
View File

@ -103,46 +103,41 @@ static const long double gauss_legendre_50_weights[50] = {
namespace internal { namespace internal {
/// 50 point Gauss-Legendre quadrature
template <typename T> template <typename T>
constexpr T incomplete_gamma_quad_inp_vals(const T lb, const T ub, class IncompleteGamma {
/// 50 point Gauss-Legendre quadrature
static constexpr T quadrature_inp_vals(const T lb, const T ub,
const int counter) noexcept { const int counter) noexcept {
return (ub - lb) * gauss_legendre_50_points[counter] / T(2) + return (ub - lb) * gauss_legendre_50_points[counter] / T(2) +
(ub + lb) / T(2); (ub + lb) / T(2);
} }
template <typename T> static constexpr T quadrature_weight_vals(const T lb, const T ub,
constexpr T incomplete_gamma_quad_weight_vals(const T lb, const T ub,
const int counter) noexcept { const int counter) noexcept {
return (ub - lb) * gauss_legendre_50_weights[counter] / T(2); return (ub - lb) * gauss_legendre_50_weights[counter] / T(2);
} }
template <typename T> static constexpr T quadrature_fn(const T x, const T a,
constexpr T incomplete_gamma_quad_fn(const T x, const T a,
const T lg_term) noexcept { const T lg_term) noexcept {
return exp(-x + (a - T(1)) * log(x) - lg_term); return exp(-x + (a - T(1)) * log(x) - lg_term);
} }
template <typename T> static constexpr T quadrature_recur(const T lb, const T ub, const T a,
constexpr T incomplete_gamma_quad_recur(const T lb, const T ub, const T a,
const T lg_term, const T lg_term,
const int counter) noexcept { const int counter) noexcept {
return (counter < 49 ? // if if (counter < 49) {
incomplete_gamma_quad_fn( return quadrature_fn(quadrature_inp_vals(lb, ub, counter), a, lg_term) *
incomplete_gamma_quad_inp_vals(lb, ub, counter), a, lg_term) * quadrature_weight_vals(lb, ub, counter) +
incomplete_gamma_quad_weight_vals(lb, ub, counter) + quadrature_recur(lb, ub, a, lg_term, counter + 1);
incomplete_gamma_quad_recur(lb, ub, a, lg_term, counter + 1) } else {
: return quadrature_fn(quadrature_inp_vals(lb, ub, counter), a, lg_term) *
// else quadrature_weight_vals(lb, ub, counter);
incomplete_gamma_quad_fn( }
incomplete_gamma_quad_inp_vals(lb, ub, counter), a, lg_term) * }
incomplete_gamma_quad_weight_vals(lb, ub, counter));
}
template <typename T> static constexpr T quadrature_lb(const T a, const T z) noexcept {
constexpr T incomplete_gamma_quad_lb(const T a, const T z) noexcept {
// break integration into ranges // break integration into ranges
return (a > T(1000) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a)) return a > T(1000) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a))
: a > T(800) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a)) : a > T(800) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a))
: a > T(500) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a)) : a > T(500) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a))
: a > T(300) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a)) : a > T(300) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a))
@ -152,12 +147,11 @@ constexpr T incomplete_gamma_quad_lb(const T a, const T z) noexcept {
: a > T(50) ? std::max(T(0), std::min(z, a) - 7 * sqrt(a)) : a > T(50) ? std::max(T(0), std::min(z, a) - 7 * sqrt(a))
: a > T(40) ? std::max(T(0), std::min(z, a) - 6 * sqrt(a)) : a > T(40) ? std::max(T(0), std::min(z, a) - 6 * sqrt(a))
: a > T(30) ? std::max(T(0), std::min(z, a) - 5 * sqrt(a)) : a > T(30) ? std::max(T(0), std::min(z, a) - 5 * sqrt(a))
: std::max(T(0), std::min(z, a) - 4 * sqrt(a))); : std::max(T(0), std::min(z, a) - 4 * sqrt(a));
} }
template <typename T> static constexpr T quadrature_ub(const T a, const T z) noexcept {
constexpr T incomplete_gamma_quad_ub(const T a, const T z) noexcept { return a > T(1000) ? std::min(z, a + 10 * sqrt(a))
return (a > T(1000) ? std::min(z, a + 10 * sqrt(a))
: a > T(800) ? std::min(z, a + 10 * sqrt(a)) : a > T(800) ? std::min(z, a + 10 * sqrt(a))
: a > T(500) ? std::min(z, a + 9 * sqrt(a)) : a > T(500) ? std::min(z, a + 9 * sqrt(a))
: a > T(300) ? std::min(z, a + 9 * sqrt(a)) : a > T(300) ? std::min(z, a + 9 * sqrt(a))
@ -165,92 +159,91 @@ constexpr T incomplete_gamma_quad_ub(const T a, const T z) noexcept {
: a > T(90) ? std::min(z, a + 8 * sqrt(a)) : a > T(90) ? std::min(z, a + 8 * sqrt(a))
: a > T(70) ? std::min(z, a + 7 * sqrt(a)) : a > T(70) ? std::min(z, a + 7 * sqrt(a))
: a > T(50) ? std::min(z, a + 6 * sqrt(a)) : a > T(50) ? std::min(z, a + 6 * sqrt(a))
: std::min(z, a + 5 * sqrt(a))); : std::min(z, a + 5 * sqrt(a));
} }
template <typename T> static constexpr T quadrature(const T a, const T z) noexcept {
constexpr T incomplete_gamma_quad(const T a, const T z) noexcept { return quadrature_recur(quadrature_lb(a, z), quadrature_ub(a, z), a,
return incomplete_gamma_quad_recur(incomplete_gamma_quad_lb(a, z),
incomplete_gamma_quad_ub(a, z), a,
lgamma(a), 0); lgamma(a), 0);
} }
// reverse cf expansion // reverse cf expansion
// see: https://functions.wolfram.com/GammaBetaErf/Gamma2/10/0003/ // see: https://functions.wolfram.com/GammaBetaErf/Gamma2/10/0003/
static constexpr T cf_2_recur(const T a, const T z,
template <typename T>
constexpr T incomplete_gamma_cf_2_recur(const T a, const T z,
const int depth) noexcept { const int depth) noexcept {
return (depth < 100 ? (1 + (depth - 1) * 2 - a + z) + if (depth < 100) {
depth * (a - depth) / return (1 + (depth - 1) * 2 - a + z) +
incomplete_gamma_cf_2_recur(a, z, depth + 1) depth * (a - depth) / cf_2_recur(a, z, depth + 1);
: (1 + (depth - 1) * 2 - a + z)); } else {
} return 1 + (depth - 1) * 2 - a + z;
}
}
template <typename T> /**
constexpr T incomplete_gamma_cf_2( * @brief Lower (regularized) incomplete gamma function
const T a, *
const T z) noexcept { // lower (regularized) incomplete gamma function * @param a
return (T(1.0) - exp(a * log(z) - z - lgamma(a)) / * @param z
incomplete_gamma_cf_2_recur(a, z, 1)); * @return constexpr T
} */
static constexpr T cf_2(const T a, const T z) noexcept {
return T(1.0) - exp(a * log(z) - z - lgamma(a)) / cf_2_recur(a, z, 1);
}
// cf expansion // continued fraction expansion
// see: http://functions.wolfram.com/GammaBetaErf/Gamma2/10/0009/ // see: http://functions.wolfram.com/GammaBetaErf/Gamma2/10/0009/
static constexpr T cf_1_coef(const T a, const T z, const int depth) noexcept {
template <typename T>
constexpr T incomplete_gamma_cf_1_coef(const T a, const T z,
const int depth) noexcept {
return (is_odd(depth) ? -(a - 1 + T(depth + 1) / T(2)) * z return (is_odd(depth) ? -(a - 1 + T(depth + 1) / T(2)) * z
: T(depth) / T(2) * z); : T(depth) / T(2) * z);
} }
template <typename T> static constexpr T cf_1_recur(const T a, const T z,
constexpr T incomplete_gamma_cf_1_recur(const T a, const T z,
const int depth) noexcept { const int depth) noexcept {
return (depth < 55 ? // if if (depth < 55) {
(a + depth - 1) + incomplete_gamma_cf_1_coef(a, z, depth) / return (a + depth - 1) +
incomplete_gamma_cf_1_recur(a, z, depth + 1) cf_1_coef(a, z, depth) / cf_1_recur(a, z, depth + 1);
: } else {
// else return (a + depth - 1);
(a + depth - 1)); }
} }
template <typename T> /**
constexpr T incomplete_gamma_cf_1( * @brief Lower (regularized) incomplete gamma function
const T a, *
const T z) noexcept { // lower (regularized) incomplete gamma function * @param a
return (exp(a * log(z) - z - lgamma(a)) / * @param z
incomplete_gamma_cf_1_recur(a, z, 1)); * @return constexpr T
} */
static constexpr T cf_1(const T a, const T z) noexcept {
return exp(a * log(z) - z - lgamma(a)) / cf_1_recur(a, z, 1);
}
// public:
/**
template <typename T> * @brief Compute the CDF for the Gamma distribution.
constexpr T incomplete_gamma_check(const T a, const T z) noexcept { *
return ( // NaN check * @param a
(is_nan(a) || is_nan(z)) ? LIM<T>::quiet_NaN() : * @param z
// * @return constexpr T
a < T(0) ? LIM<T>::quiet_NaN() */
: static constexpr T compute(const T a, const T z) noexcept {
// if (is_nan(a) || is_nan(z)) { // NaN check
LIM<T>::min() > z ? T(0) return LIM<T>::quiet_NaN();
: } else if (a < T(0)) {
// return LIM<T>::quiet_NaN();
LIM<T>::min() > a ? T(1) } else if (LIM<T>::min() > z) {
: return T(0);
// cf or quadrature } else if (LIM<T>::min() > a) {
(a < T(10)) && (z - a < T(10)) ? incomplete_gamma_cf_1(a, z) return T(1);
: (a < T(10)) || (z / a > T(3)) ? incomplete_gamma_cf_2(a, z) } else if (a < T(10) && z - a < T(10)) {
: return cf_1(a, z);
// else } else if (a < T(10) || z / a > T(3)) {
incomplete_gamma_quad(a, z)); return cf_2(a, z);
} } else {
return quadrature(a, z);
template <typename T1, typename T2, typename TC = common_return_t<T1, T2>> }
constexpr TC incomplete_gamma_type_check(const T1 a, const T2 p) noexcept { }
return incomplete_gamma_check(static_cast<TC>(a), static_cast<TC>(p)); };
}
} // namespace internal } // namespace internal
@ -274,7 +267,9 @@ constexpr TC incomplete_gamma_type_check(const T1 a, const T2 p) noexcept {
template <typename T1, typename T2> template <typename T1, typename T2>
constexpr common_return_t<T1, T2> incomplete_gamma(const T1 a, constexpr common_return_t<T1, T2> incomplete_gamma(const T1 a,
const T2 x) noexcept { const T2 x) noexcept {
return internal::incomplete_gamma_type_check(a, x); using TC = common_return_t<T1, T2>;
return internal::IncompleteGamma<TC>::compute(static_cast<TC>(a),
static_cast<TC>(x));
} }
namespace internal { namespace internal {