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Use Boost finite-diff implementation for finite_diff_gradient_auto #3094

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Use Boost finite-diff implementation for finite_diff_gradient_auto #3094

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b446dff
Use Boost finite-diff implementation
andrjohns Jul 15, 2024
43427a8
mix functor header
andrjohns Jul 15, 2024
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2 changes: 1 addition & 1 deletion stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp
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Expand Up @@ -2,7 +2,7 @@
#define STAN_MATH_MIX_FUNCTOR_FINITE_DIFF_GRAD_HESSIAN_AUTO_HPP

#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/functor/finite_diff_gradient_auto.hpp>
#include <stan/math/prim/fun/finite_diff_stepsize.hpp>
#include <stan/math/rev/core.hpp>
#include <stan/math/mix/functor/hessian.hpp>
#include <vector>
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65 changes: 10 additions & 55 deletions stan/math/prim/functor/finite_diff_gradient_auto.hpp
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Expand Up @@ -2,43 +2,16 @@
#define STAN_MATH_PRIM_FUNCTOR_FINITE_DIFF_GRADIENT_AUTO_HPP

#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/finite_diff_stepsize.hpp>
#include <stan/math/prim/meta.hpp>
#include <boost/math/differentiation/finite_difference.hpp>
#include <cmath>

namespace stan {
namespace math {

/**
* Calculate the value and the gradient of the specified function
* at the specified argument using finite difference.
*
* <p>The functor must implement
*
* <code>
* double operator()(const Eigen::Matrix<double, -, 1>&) const;
* </code>
*
* <p>Error of derivative in dimension `i` should be on the should be on
* order of `epsilon(i)^6`, where `epsilon(i) = sqrt(delta) * abs(x(i))`
* for input `x` at dimension `i`.
*
* The reference for this algorithm is:
*
* <br />Robert de Levie. 2009. An improved numerical approximation
* for the first derivative. Journal of Chemical Sciences 121(5), page
* 3.
*
* <p>The reference for automatically setting the difference is this
* section of the Wikipedia,
*
* <br /><a
* href="https://en.wikipedia.org/wiki/Numerical_differentiation#Practical_considerations_using_floating-point_arithmetic">Numerical
* differentiation: practical considerations using floating point
* arithmetic</a>.
*
* <p>Evaluating this function involves 6 calls to the function being
* differentiated for each dimension in the input, plus one global
* evaluation. All evaluations will be for double-precision inputs.
* at the specified argument using finite differences.
*
* @tparam F Type of function
* @param[in] f function
Expand All @@ -50,36 +23,18 @@ template <typename F, typename VectorT,
typename ScalarT = return_type_t<VectorT>>
void finite_diff_gradient_auto(const F& f, const VectorT& x, ScalarT& fx,
VectorT& grad_fx) {
using boost::math::differentiation::finite_difference_derivative;
VectorT x_temp(x);
fx = f(x);
grad_fx.resize(x.size());
for (int i = 0; i < x.size(); ++i) {
double h = finite_diff_stepsize(value_of_rec(x[i]));

ScalarT delta_f = 0;

x_temp[i] = x[i] + 3 * h;
delta_f += f(x_temp);

x_temp[i] = x[i] + 2 * h;
delta_f -= 9 * f(x_temp);

x_temp[i] = x[i] + h;
delta_f += 45 * f(x_temp);

x_temp[i] = x[i] + -3 * h;
delta_f -= f(x_temp);

x_temp[i] = x[i] + -2 * h;
delta_f += 9 * f(x_temp);

x_temp[i] = x[i] - h;
delta_f -= 45 * f(x_temp);

delta_f /= 60 * h;

for (Eigen::Index i = 0; i < x.size(); ++i) {
auto fun = [&i, &x_temp, &f](const auto& y) {
x_temp[i] = y;
return f(x_temp);
};
grad_fx[i] = finite_difference_derivative(fun, x[i]);
x_temp[i] = x[i];
grad_fx[i] = delta_f;
}
}

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