update columns dot product for complex types

stan/math/rev/fun/columns_dot_product.hpp

@@ -14,6 +14,35 @@
 namespace stan {
 namespace math {
 
+/**
+ * Returns the dot product of columns of the specified matrices.
+ *
+ * @tparam Mat1 type of the first matrix (must be derived from \c
+ * Eigen::MatrixBase)
+ * @tparam Mat2 type of the second matrix (must be derived from \c
+ * Eigen::MatrixBase)
+ *
+ * @param v1 Matrix of first vectors.
+ * @param v2 Matrix of second vectors.
+ * @return Dot product of the vectors.
+ * @throw std::domain_error If the vectors are not the same
+ * size or if they are both not vector dimensioned.
+ */
+template <typename Mat1, typename Mat2,
+          require_all_eigen_t<Mat1, Mat2>* = nullptr,
+          require_any_eigen_vt<is_var, Mat1, Mat2>* = nullptr,
+          require_vt_complex<Mat1>* = nullptr,
+          require_vt_complex<Mat2>* = nullptr>
+inline Eigen::Matrix<return_type_t<Mat1, Mat2>, 1, Mat1::ColsAtCompileTime>
+columns_dot_product(const Mat1& v1, const Mat2& v2) {
+  check_matching_sizes("dot_product", "v1", v1, "v2", v2);
+  Eigen::Matrix<var, 1, Mat1::ColsAtCompileTime> ret(1, v1.cols());
+  for (size_type j = 0; j < v1.cols(); ++j) {
+    ret.coeffRef(j) = dot_product(v1.col(j), v2.col(j));
+  }
+  return ret;
+}
+
 /**
  * Returns the dot product of columns of the specified matrices.
  *
@@ -27,7 +56,9 @@ namespace math {
  * size or if they are both not vector dimensioned.
  */
 template <typename Mat1, typename Mat2,
-          require_all_matrix_t<Mat1, Mat2>* = nullptr>
+          require_all_matrix_t<Mat1, Mat2>* = nullptr,
+          require_not_st_complex<Mat1>* = nullptr,
+          require_not_st_complex<Mat2>* = nullptr>
 inline auto columns_dot_product(Mat1&& v1, Mat2&& v2) {
   check_matching_sizes("columns_dot_product", "v1", v1, "v2", v2);
   using inner_return_t = decltype(

stan/math/rev/meta/return_var_matrix.hpp

@@ -23,8 +23,11 @@ using return_var_matrix_t = std::conditional_t<
     is_any_var_matrix<ReturnType, Types...>::value,
     stan::math::var_value<
         stan::math::promote_scalar_t<double, plain_type_t<ReturnType>>>,
-    stan::math::promote_scalar_t<stan::math::var_value<double>,
-                                 plain_type_t<ReturnType>>>;
+    std::conditional_t<is_complex<scalar_type_t<ReturnType>>::value, 
+    stan::math::promote_scalar_t<std::complex<stan::math::var_value<double>>,
+                                 plain_type_t<ReturnType>>,
+                                 stan::math::promote_scalar_t<stan::math::var_value<double>,
+                                 plain_type_t<ReturnType>>>>;
 }  // namespace stan
 
 #endif