Issue 949 complex step derivative

stan/math/prim/scal/functor/complex_step_derivative.hpp

@@ -0,0 +1,37 @@
+#ifndef STAN_MATH_PRIM_SCAL_FUNCTOR_COMPLEX_STEP_DERIVATIVE_HPP
+#define STAN_MATH_PRIM_SCAL_FUNCTOR_COMPLEX_STEP_DERIVATIVE_HPP
+
+#include <stan/math/prim/scal/fun/value_of.hpp>
+#include <stan/math/prim/scal/meta/return_type.hpp>
+
+#include <vector>
+#include <iostream>
+
+namespace stan {
+namespace math {
+
+/**
+ * Return a double that has value of given functor F with signature
+ * (complex, std::vector<double>, std::vector<int>, stream*) : complex
+ *
+ * @tparam F type of functor F
+ * @param[in] f functor for the complex number evaluation,
+ * must support @c std::complex<double> as arg.
+ * @param[in] theta parameter where f and df/d(theta) is requested.
+ * @param[in] x_r continuous data vector for the ODE.
+ * @param[in] x_i integer data vector for the ODE.
+ * @param[out] msgs the print stream for warning messages.
+ * @return a var with value f(theta.val()) and derivative at theta.
+ */
+template <typename F>
+double complex_step_derivative(const F& f, const double& theta,
+                               const std::vector<double>& x_r,
+                               const std::vector<int>& x_i,
+                               std::ostream* msgs) {
+  return f(theta, x_r, x_i, msgs);
+}
+
+}  // namespace math
+}  // namespace stan
+
+#endif

stan/math/rev/scal/functor/complex_step_derivative.hpp

@@ -0,0 +1,53 @@
+#ifndef STAN_MATH_REV_SCAL_FUNCTOR_COMPLEX_STEP_DERIVATIVE_HPP
+#define STAN_MATH_REV_SCAL_FUNCTOR_COMPLEX_STEP_DERIVATIVE_HPP
+
+#include <stan/math/prim/scal/fun/value_of.hpp>
+#include <stan/math/prim/scal/meta/return_type.hpp>
+#include <stan/math/prim/scal/functor/complex_step_derivative.hpp>
+#include <stan/math/rev/core/precomp_v_vari.hpp>
+#include <stan/math/rev/core/vari.hpp>
+#include <stan/math/rev/core/var.hpp>
+
+#include <vector>
+#include <complex>
+#include <iostream>
+
+namespace stan {
+namespace math {
+
+/**
+ * Return a var that has value of given functor F and derivative
+ * of df/d(theta), using complex step derivative
+ * approximation. "f" does not have to support "var"
+ * type, as its signature should be
+ * (complex, std::vector<double>, std::vector<int>, stream*) : complex
+ *
+ * @tparam F type of functor F
+ * @param[in] f functor for the complex number evaluation,
+ * must support @c std::complex<double> as arg.
+ * @param[in] theta parameter where f and df/d(theta) is requested.
+ * @param[in] x_r continuous data vector for the ODE.
+ * @param[in] x_i integer data vector for the ODE.
+ * @param[out] msgs the print stream for warning messages.
+ * @return a var with value f(theta.val()) and derivative at theta.
+ */
+template <typename F>
+stan::math::var complex_step_derivative(const F& f,
+                                        const stan::math::var& theta,
+                                        const std::vector<double>& x_r,
+                                        const std::vector<int>& x_i,
+                                        std::ostream* msgs) {
+  using stan::math::var;
+  using std::complex;
+  static double h = 1.e-32;
+  const double theta_d = theta.val();
+  const double res = complex_step_derivative(f, theta_d, x_r, x_i, msgs);
+  const double g
+      = std::imag(f(complex<double>(theta_d, h), x_r, x_i, msgs)) / h;
+  return var(new stan::math::precomp_v_vari(res, theta.vi_, g));
+}
+
+}  // namespace math
+}  // namespace stan
+
+#endif

test/unit/math/rev/scal/functor/complex_step_derivative_test.cpp

@@ -0,0 +1,44 @@
+#include <gtest/gtest.h>
+#include <stan/math.hpp>
+#include <stan/math/rev/scal/functor/complex_step_derivative.hpp>
+#include <test/unit/util.hpp>
+#include <iostream>
+#include <limits>
+#include <sstream>
+#include <vector>
+
+struct ComplexStepDerivativeScalTest : public ::testing::Test {
+  struct Fexp {
+    template <typename T>
+    inline T operator()(const T &theta, const std::vector<double> &x_r,
+                        const std::vector<int> &x_i, std::ostream *msgs) const {
+      return exp(theta) / sqrt(theta) - 0.5 * exp(theta) * pow(theta, -1.5);
+    }
+  };
+
+  void SetUp() {}
+  Fexp f;
+  const std::vector<double> x_r;
+  const std::vector<int> x_i;
+  std::ostream *msgs = nullptr;
+};
+
+TEST_F(ComplexStepDerivativeScalTest, func_exp_sqrt) {
+  using stan::math::complex_step_derivative;
+  using stan::math::var;
+
+  /* f near x = 0 has very large derivative */
+  var x = 0.01;
+  var y = complex_step_derivative(f, x, x_r, x_i, msgs);
+
+  ASSERT_FLOAT_EQ(y.val(), f(x.val(), x_r, x_i, msgs));
+
+  std::vector<stan::math::var> xv{x};
+  std::vector<double> g1, g;
+  var y1 = f(x, x_r, x_i, msgs);
+  stan::math::set_zero_all_adjoints();
+  y1.grad(xv, g1);
+  stan::math::set_zero_all_adjoints();
+  y.grad(xv, g);
+  ASSERT_FLOAT_EQ(g[0], g1[0]);
+}