Add Hypergeometric 1F0 function and gradients

stan/math/fwd/fun.hpp

@@ -41,6 +41,7 @@
 #include <stan/math/fwd/fun/gamma_p.hpp>
 #include <stan/math/fwd/fun/gamma_q.hpp>
 #include <stan/math/fwd/fun/grad_inc_beta.hpp>
+#include <stan/math/fwd/fun/hypergeometric_1F0.hpp>
 #include <stan/math/fwd/fun/hypergeometric_2F1.hpp>
 #include <stan/math/fwd/fun/hypergeometric_pFq.hpp>
 #include <stan/math/fwd/fun/hypot.hpp>

stan/math/fwd/fun/hypergeometric_1F0.hpp

@@ -0,0 +1,46 @@
+#ifndef STAN_MATH_FWD_FUN_HYPERGEOMETRIC_1F0_HPP
+#define STAN_MATH_FWD_FUN_HYPERGEOMETRIC_1F0_HPP
+
+#include <stan/math/prim/meta.hpp>
+#include <stan/math/prim/fun/hypergeometric_1F0.hpp>
+#include <stan/math/fwd/core.hpp>
+
+namespace stan {
+namespace math {
+
+/**
+ * Returns the Hypergeometric 1F0 function applied to the
+ * input arguments:
+ * \f$ _1F_0(a;;z) = \sum_{k=1}^{\infty}\frac{\left(a\right)_kz^k}{k!}\f$
+ *
+ * \f$ \frac{\partial _1F_0\left(a;;z\right)}{\partial a} =
+ *    -\left(1-z\right)^{-a}\log\left(1 - z\right) \f$
+ *
+ * \f$ \frac{\partial _1F_0\left(a;;z\right)}{\partial z} =
+ *    a\left(1-z\right)^{-a-1} \f$
+ *
+ * @tparam Ta Fvar or arithmetic type of 'a' argument
+ * @tparam Tz Fvar or arithmetic type of 'z' argument
+ * @param[in] a Scalar 'a' argument
+ * @param[in] z Scalar z argument
+ * @return Hypergeometric 1F0 function
+ */
+template <typename Ta, typename Tz, require_any_fvar_t<Ta, Tz>* = nullptr>
+auto hypergeometric_1f0(const Ta& a, const Tz& z) {
+  using FvarT = return_type_t<Ta, Tz>;
+
+  auto a_val = value_of(a);
+  auto z_val = value_of(z);
+  FvarT rtn = FvarT(hypergeometric_1f0(a_val, z_val), 0.0);
+  if (!is_constant_all<Ta>::value) {
+    rtn.d_ += forward_as<FvarT>(a).d() * -rtn.val() * log1m(z_val);
+  }
+  if (!is_constant_all<Tz>::value) {
+    rtn.d_ += forward_as<FvarT>(z).d() * rtn.val() * a_val * inv(1 - z_val);
+  }
+  return rtn;
+}
+
+}  // namespace math
+}  // namespace stan
+#endif

stan/math/prim/fun.hpp

@@ -134,6 +134,7 @@
 #include <stan/math/prim/fun/grad_reg_inc_gamma.hpp>
 #include <stan/math/prim/fun/grad_reg_lower_inc_gamma.hpp>
 #include <stan/math/prim/fun/head.hpp>
+#include <stan/math/prim/fun/hypergeometric_1F0.hpp>
 #include <stan/math/prim/fun/hypergeometric_2F1.hpp>
 #include <stan/math/prim/fun/hypergeometric_2F2.hpp>
 #include <stan/math/prim/fun/hypergeometric_3F2.hpp>

stan/math/prim/fun/hypergeometric_1F0.hpp

@@ -0,0 +1,40 @@
+#ifndef STAN_MATH_PRIM_FUN_HYPERGEOMETRIC_1F0_HPP
+#define STAN_MATH_PRIM_FUN_HYPERGEOMETRIC_1F0_HPP
+
+#include <stan/math/prim/meta.hpp>
+#include <stan/math/prim/err/check_less.hpp>
+#include <stan/math/prim/fun/boost_policy.hpp>
+#include <boost/math/special_functions/hypergeometric_1F0.hpp>
+#include <cmath>
+
+namespace stan {
+namespace math {
+
+/**
+ * Returns the Hypergeometric 1F0 function applied to the
+ * input arguments:
+ * \f$ _1F_0(a;;z) = \sum_{k=1}^{\infty}\frac{\left(a\right)_kz^k}{k!}\f$
+ *
+ * \f$ \frac{\partial _1F_0\left(a;;z\right)}{\partial a} =
+ *    -\left(1-z\right)^{-a}\log\left(1 - z\right) \f$
+ *
+ * \f$ \frac{\partial _1F_0\left(a;;z\right)}{\partial z} =
+ *    a\left(1-z\right)^{-a-1} \f$
+ *
+ * @tparam Ta Arithmetic type of 'a' argument
+ * @tparam Tz Arithmetic type of 'z' argument
+ * @param[in] a Scalar 'a' argument
+ * @param[in] z Scalar z argument
+ * @return Hypergeometric 1F0 function
+ */
+template <typename Ta, typename Tz, require_all_arithmetic_t<Ta, Tz>* = nullptr>
+auto hypergeometric_1f0(const Ta& a, const Tz& z) {
+  constexpr const char* function = "hypergeometric_1f0";
+  check_less("hypergeometric_1f0", "abs(z)", std::abs(z), 1.0);
+
+  return boost::math::hypergeometric_1F0(a, z, boost_policy_t<>());
+}
+
+}  // namespace math
+}  // namespace stan
+#endif

stan/math/rev/fun.hpp

@@ -76,6 +76,7 @@
 #include <stan/math/rev/fun/gp_periodic_cov.hpp>
 #include <stan/math/rev/fun/grad.hpp>
 #include <stan/math/rev/fun/grad_inc_beta.hpp>
+#include <stan/math/rev/fun/hypergeometric_1F0.hpp>
 #include <stan/math/rev/fun/hypergeometric_2F1.hpp>
 #include <stan/math/rev/fun/hypergeometric_pFq.hpp>
 #include <stan/math/rev/fun/hypot.hpp>

stan/math/rev/fun/hypergeometric_1F0.hpp

@@ -0,0 +1,48 @@
+#ifndef STAN_MATH_REV_FUN_HYPERGEOMETRIC_1F0_HPP
+#define STAN_MATH_REV_FUN_HYPERGEOMETRIC_1F0_HPP
+
+#include <stan/math/prim/meta.hpp>
+#include <stan/math/prim/fun/hypergeometric_1F0.hpp>
+#include <stan/math/prim/fun/value_of.hpp>
+#include <stan/math/prim/fun/log1m.hpp>
+#include <stan/math/prim/fun/inv.hpp>
+#include <stan/math/rev/core.hpp>
+
+namespace stan {
+namespace math {
+
+/**
+ * Returns the Hypergeometric 1F0 function applied to the
+ * input arguments:
+ * \f$ _1F_0(a;;z) = \sum_{k=1}^{\infty}\frac{\left(a\right)_kz^k}{k!}\f$
+ *
+ * \f$ \frac{\partial _1F_0\left(a;;z\right)}{\partial a} =
+ *    -\left(1-z\right)^{-a}\log\left(1 - z\right) \f$
+ *
+ * \f$ \frac{\partial _1F_0\left(a;;z\right)}{\partial z} =
+ *    a\left(1-z\right)^{-a-1} \f$
+ *
+ * @tparam Ta Var or arithmetic type of 'a' argument
+ * @tparam Tz Var or arithmetic type of 'z' argument
+ * @param[in] a Scalar 'a' argument
+ * @param[in] z Scalar z argument
+ * @return Hypergeometric 1F0 function
+ */
+template <typename Ta, typename Tz, require_any_var_t<Ta, Tz>* = nullptr>
+var hypergeometric_1f0(const Ta& a, const Tz& z) {
+  double a_val = value_of(a);
+  double z_val = value_of(z);
+  double rtn = hypergeometric_1f0(a_val, z_val);
+  return make_callback_var(rtn, [rtn, a, z, a_val, z_val](auto& vi) mutable {
+    if (!is_constant_all<Ta>::value) {
+      forward_as<var>(a).adj() += vi.adj() * -rtn * log1m(z_val);
+    }
+    if (!is_constant_all<Tz>::value) {
+      forward_as<var>(z).adj() += vi.adj() * rtn * a_val * inv(1 - z_val);
+    }
+  });
+}
+
+}  // namespace math
+}  // namespace stan
+#endif

test/unit/math/mix/fun/hypergeometric_1F0_test.cpp

@@ -0,0 +1,15 @@
+#include <test/unit/math/test_ad.hpp>
+
+TEST(mathMixScalFun, hypergeometric_1f0) {
+  auto f = [](const auto& x1, const auto& x2) {
+    using stan::math::hypergeometric_1f0;
+    return hypergeometric_1f0(x1, x2);
+  };
+
+  stan::test::expect_ad(f, 5, 0.3);
+  stan::test::expect_ad(f, 3.4, 0.9);
+  stan::test::expect_ad(f, 3.4, 0.1);
+  stan::test::expect_ad(f, 5, -0.7);
+  stan::test::expect_ad(f, 7, -0.1);
+  stan::test::expect_ad(f, 2.8, 0.8);
+}

test/unit/math/prim/fun/hypergeometric_1F0_test.cpp

@@ -0,0 +1,23 @@
+#include <stan/math/prim.hpp>
+#include <gtest/gtest.h>
+#include <cmath>
+#include <limits>
+
+TEST(MathFunctions, hypergeometric_1f0Double) {
+  using stan::math::hypergeometric_1f0;
+  using stan::math::inv;
+
+  EXPECT_FLOAT_EQ(4.62962962963, hypergeometric_1f0(3, 0.4));
+  EXPECT_FLOAT_EQ(0.510204081633, hypergeometric_1f0(2, -0.4));
+  EXPECT_FLOAT_EQ(300.906354890, hypergeometric_1f0(16.0, 0.3));
+  EXPECT_FLOAT_EQ(0.531441, hypergeometric_1f0(-6.0, 0.1));
+}
+
+TEST(MathFunctions, hypergeometric_1f0_throw) {
+  using stan::math::hypergeometric_1f0;
+
+  EXPECT_THROW(hypergeometric_1f0(2.1, 1.0), std::domain_error);
+  EXPECT_THROW(hypergeometric_1f0(0.5, 1.5), std::domain_error);
+  EXPECT_THROW(hypergeometric_1f0(0.5, -1.0), std::domain_error);
+  EXPECT_THROW(hypergeometric_1f0(0.5, -1.5), std::domain_error);
+}