From b446dff36a4816f4d5c800c171c89e7aef87cfc0 Mon Sep 17 00:00:00 2001
From: Andrew Johnson <andrew.johnson@arjohnsonau.com>
Date: Mon, 15 Jul 2024 12:30:29 +0300
Subject: [PATCH 1/2] Use Boost finite-diff implementation

---
 .../functor/finite_diff_gradient_auto.hpp     | 65 +++----------------
 1 file changed, 10 insertions(+), 55 deletions(-)

diff --git a/stan/math/prim/functor/finite_diff_gradient_auto.hpp b/stan/math/prim/functor/finite_diff_gradient_auto.hpp
index 66bc59b4e23..56c6a90f40b 100644
--- a/stan/math/prim/functor/finite_diff_gradient_auto.hpp
+++ b/stan/math/prim/functor/finite_diff_gradient_auto.hpp
@@ -2,7 +2,8 @@
 #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 {
@@ -10,35 +11,7 @@ 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
@@ -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;
   }
 }
 

From 43427a8c69b5f8983b830a97434946211df38251 Mon Sep 17 00:00:00 2001
From: Andrew Johnson <andrew.johnson@arjohnsonau.com>
Date: Mon, 15 Jul 2024 12:39:03 +0300
Subject: [PATCH 2/2] mix functor header

---
 stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp b/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp
index 108b059149c..fd6cde303c8 100644
--- a/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp
+++ b/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp
@@ -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>