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remove recursion for Halley update

release/4.3a0
Varun Agrawal 2023-05-10 16:16:20 -04:00
parent d5771609a4
commit 7ce5684e05
1 changed files with 32 additions and 55 deletions
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87
gtsam/nonlinear/GncHelpers.h
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@ -168,7 +168,7 @@ class IncompleteGamma {
* @brief Reverse continued fraction expansion
* See: https://functions.wolfram.com/GammaBetaErf/Gamma2/10/0003/
*
* @param a
* @param a Degrees of freedom
* @param z
* @param depth
* @return constexpr T
@ -186,7 +186,7 @@ class IncompleteGamma {
/**
* @brief Lower (regularized) incomplete gamma function
*
* @param a
* @param a Degrees of freedom
* @param z
* @return constexpr T
*/
@ -198,7 +198,7 @@ class IncompleteGamma {
* @brief Continued fraction expansion of Gamma function
* See: http://functions.wolfram.com/GammaBetaErf/Gamma2/10/0009/
*
* @param a
* @param a Degrees of freedom
* @param z
* @param depth
* @return constexpr T
@ -217,7 +217,7 @@ class IncompleteGamma {
/**
* @brief Lower (regularized) incomplete gamma function
*
* @param a
* @param a Degrees of freedom
* @param z
* @return constexpr T
*/
@ -229,7 +229,7 @@ class IncompleteGamma {
/**
* @brief Compute the CDF for the Gamma distribution.
*
* @param a
* @param a Degrees of freedom
* @param z
* @return constexpr T
*/
@ -287,7 +287,7 @@ class IncompleteGammaInverse {
* @brief Compute an initial value for the inverse gamma function which is
* then iteratively updated.
*
* @param a
* @param a Degrees of freedom
* @param p
* @return constexpr T
*/
@ -322,7 +322,7 @@ class IncompleteGammaInverse {
* @brief Compute the error value `f(x)` which we can use for root-finding.
*
* @param value
* @param a
* @param a Degrees of freedom
* @param p
* @return constexpr T
*/
@ -334,12 +334,12 @@ class IncompleteGammaInverse {
* @brief Derivative of the incomplete gamma function w.r.t. value
*
* @param value
* @param a
* @param a Degrees of freedom
* @param log_val
* @return constexpr T
*/
static constexpr T derivative(const T value, const T a,
const T lg_val) noexcept {
static constexpr T first_derivative(const T value, const T a,
const T lg_val) noexcept {
return (exp(-value + (a - T(1)) * log(value) - lg_val));
}
@ -347,7 +347,7 @@ class IncompleteGammaInverse {
* @brief Second derivative of the incomplete gamma function w.r.t. value
*
* @param value
* @param a
* @param a Degrees of freedom
* @param derivative
* @return constexpr T
*/
@ -361,7 +361,7 @@ class IncompleteGammaInverse {
* of the update denominator.
*
* @param value
* @param a
* @param a Degrees of freedom
* @param p
* @param derivative
* @return constexpr T
@ -376,7 +376,7 @@ class IncompleteGammaInverse {
* of the update denominator.
*
* @param value
* @param a
* @param a Degrees of freedom
* @param derivative
* @return constexpr T
*/
@ -386,7 +386,7 @@ class IncompleteGammaInverse {
}
/**
* @brief Halley's method update step
* @brief Halley's method update delta
*
* @param ratio_val_1
* @param ratio_val_2
@ -397,60 +397,37 @@ class IncompleteGammaInverse {
std::max(T(0.8), std::min(T(1.2), T(1) - T(0.5) * ratio_val_1 *
ratio_val_2)));
}
/**
* @brief Recursive method for computing the iterative solution for the
* @brief Compute the iterative solution for the
* incomplete inverse gamma function.
*
* @param value
* @param a
* @param p
* @param derivative
* @param lg_val
* @param iter_count
* @return constexpr T
*/
static constexpr T recurse(const T value, const T a, const T p,
const T derivative, const T lg_val,
const int iter_count) noexcept {
return decision(value, a, p,
halley(ratio_val_1(value, a, p, derivative),
ratio_val_2(value, a, derivative)),
lg_val, iter_count);
}
static constexpr T decision(const T value, const T a, const T p,
const T direc, const T lg_val,
const int iter_count) noexcept {
const int GAMMA_INV_MAX_ITER = 35;
if (iter_count <= GAMMA_INV_MAX_ITER) {
return recurse(value - direc, a, p, derivative(value, a, lg_val), lg_val,
iter_count + 1);
} else {
return value - direc;
}
}
/**
* @brief Start point for numerical computation of the incomplete gamma
* inverse funtion.
*
* @param initial_val Initial value guess
* @param a
* @param a Degrees of freedom
* @param p
* @param lg_val
* @return constexpr T
*/
static constexpr T begin(const T initial_val, const T a, const T p,
const T lg_val) noexcept {
return recurse(initial_val, a, p, derivative(initial_val, a, lg_val),
lg_val, 1);
static constexpr T find_root(const T initial_val, const T a, const T p,
const T lg_val) noexcept {
const int GAMMA_INV_MAX_ITER = 35;
T x = initial_val;
T derivative = first_derivative(initial_val, a, lg_val);
for (size_t counter = 1; counter <= GAMMA_INV_MAX_ITER; counter++) {
T direc = halley(ratio_val_1(x, a, p, derivative),
ratio_val_2(x, a, derivative));
derivative = first_derivative(x, a, lg_val);
x = x - direc;
}
return x - halley(ratio_val_1(x, a, p, derivative),
ratio_val_2(x, a, derivative));
}
public:
/**
* @brief Compute the percent point function for the Gamma distribution.
*
* @param a
* @param a Degrees of freedom
* @param p
* @return constexpr T
*/
@ -467,7 +444,7 @@ class IncompleteGammaInverse {
} else if (LIM<T>::min() > a) { // Check lower bound for degrees of freedom
return T(0);
} else {
return begin(initial_val(a, p), a, p, lgamma(a));
return find_root(initial_val(a, p), a, p, lgamma(a));
}
}
};