diff --git a/src/stan/mcmc/hmc/hamiltonians/dense_e_metric.hpp b/src/stan/mcmc/hmc/hamiltonians/dense_e_metric.hpp
index 3f177b5a13e..7d99ae65e22 100644
--- a/src/stan/mcmc/hmc/hamiltonians/dense_e_metric.hpp
+++ b/src/stan/mcmc/hmc/hamiltonians/dense_e_metric.hpp
@@ -20,7 +20,7 @@ class dense_e_metric : public base_hamiltonian<Model, dense_e_point, BaseRNG> {
       : base_hamiltonian<Model, dense_e_point, BaseRNG>(model) {}
 
   double T(dense_e_point& z) {
-    return 0.5 * z.p.transpose() * z.inv_e_metric_ * z.p;
+    return 0.5 * z.p.transpose() * z.get_inv_metric() * z.p;
   }
 
   double tau(dense_e_point& z) { return T(z); }
@@ -35,7 +35,7 @@ class dense_e_metric : public base_hamiltonian<Model, dense_e_point, BaseRNG> {
     return Eigen::VectorXd::Zero(this->model_.num_params_r());
   }
 
-  Eigen::VectorXd dtau_dp(dense_e_point& z) { return z.inv_e_metric_ * z.p; }
+  Eigen::VectorXd dtau_dp(dense_e_point& z) { return z.get_inv_metric() * z.p; }
 
   Eigen::VectorXd dphi_dq(dense_e_point& z, callbacks::logger& logger) {
     return z.g;
@@ -51,7 +51,7 @@ class dense_e_metric : public base_hamiltonian<Model, dense_e_point, BaseRNG> {
     for (idx_t i = 0; i < u.size(); ++i)
       u(i) = rand_dense_gaus();
 
-    z.p = z.inv_e_metric_.llt().matrixU().solve(u);
+    z.p = z.get_transpose_llt_inv_metric().triangularView<Eigen::Upper>().solve(u);
   }
 };
 
diff --git a/src/stan/mcmc/hmc/hamiltonians/dense_e_point.hpp b/src/stan/mcmc/hmc/hamiltonians/dense_e_point.hpp
index 3b811e280e3..ca96eced6eb 100644
--- a/src/stan/mcmc/hmc/hamiltonians/dense_e_point.hpp
+++ b/src/stan/mcmc/hmc/hamiltonians/dense_e_point.hpp
@@ -11,11 +11,13 @@ namespace mcmc {
  * Euclidean manifold with dense metric
  */
 class dense_e_point : public ps_point {
- public:
+private:
   /**
    * Inverse mass matrix.
    */
   Eigen::MatrixXd inv_e_metric_;
+  Eigen::MatrixXd inv_e_metric_llt_matrixU_;
+public:
 
   /**
    * Construct a dense point in n-dimensional phase space
@@ -23,17 +25,40 @@ class dense_e_point : public ps_point {
    *
    * @param n number of dimensions
    */
-  explicit dense_e_point(int n) : ps_point(n), inv_e_metric_(n, n) {
+  explicit dense_e_point(int n) : ps_point(n),
+				  inv_e_metric_(n, n),
+				  inv_e_metric_llt_matrixU_(n, n) {
     inv_e_metric_.setIdentity();
+    inv_e_metric_llt_matrixU_.setIdentity();
   }
 
   /**
-   * Set elements of mass matrix
+   * Set inverse metric
    *
    * @param inv_e_metric initial mass matrix
    */
-  void set_metric(const Eigen::MatrixXd& inv_e_metric) {
+  void set_inv_metric(const Eigen::MatrixXd& inv_e_metric) {
     inv_e_metric_ = inv_e_metric;
+    inv_e_metric_llt_matrixU_ = inv_e_metric_.llt().matrixU();
+  }
+
+  /**
+   * Get inverse metric
+   *
+   * @return reference to the inverse metric
+   */
+  const Eigen::MatrixXd& get_inv_metric() {
+    return inv_e_metric_;
+  }
+
+  /**
+   * Get the transpose of the lower Cholesky factor
+   *  of the inverse metric
+   *
+   * @return reference to transpose of Cholesky factor
+   */
+  const Eigen::MatrixXd& get_transpose_llt_inv_metric() {
+    return inv_e_metric_llt_matrixU_;
   }
 
   /**
diff --git a/src/stan/mcmc/hmc/hamiltonians/diag_e_metric.hpp b/src/stan/mcmc/hmc/hamiltonians/diag_e_metric.hpp
index 98bfee84294..2762899f765 100644
--- a/src/stan/mcmc/hmc/hamiltonians/diag_e_metric.hpp
+++ b/src/stan/mcmc/hmc/hamiltonians/diag_e_metric.hpp
@@ -18,7 +18,7 @@ class diag_e_metric : public base_hamiltonian<Model, diag_e_point, BaseRNG> {
       : base_hamiltonian<Model, diag_e_point, BaseRNG>(model) {}
 
   double T(diag_e_point& z) {
-    return 0.5 * z.p.dot(z.inv_e_metric_.cwiseProduct(z.p));
+    return 0.5 * z.p.dot(z.get_inv_metric().cwiseProduct(z.p));
   }
 
   double tau(diag_e_point& z) { return T(z); }
@@ -34,7 +34,7 @@ class diag_e_metric : public base_hamiltonian<Model, diag_e_point, BaseRNG> {
   }
 
   Eigen::VectorXd dtau_dp(diag_e_point& z) {
-    return z.inv_e_metric_.cwiseProduct(z.p);
+    return z.get_inv_metric().cwiseProduct(z.p);
   }
 
   Eigen::VectorXd dphi_dq(diag_e_point& z, callbacks::logger& logger) {
@@ -46,7 +46,7 @@ class diag_e_metric : public base_hamiltonian<Model, diag_e_point, BaseRNG> {
         rand_diag_gaus(rng, boost::normal_distribution<>());
 
     for (int i = 0; i < z.p.size(); ++i)
-      z.p(i) = rand_diag_gaus() / sqrt(z.inv_e_metric_(i));
+      z.p(i) = rand_diag_gaus() / sqrt(z.get_inv_metric()(i));
   }
 };
 
diff --git a/src/stan/mcmc/hmc/hamiltonians/diag_e_point.hpp b/src/stan/mcmc/hmc/hamiltonians/diag_e_point.hpp
index eb2c2d9f5d5..af136812afd 100644
--- a/src/stan/mcmc/hmc/hamiltonians/diag_e_point.hpp
+++ b/src/stan/mcmc/hmc/hamiltonians/diag_e_point.hpp
@@ -11,12 +11,13 @@ namespace mcmc {
  * Euclidean manifold with diagonal metric
  */
 class diag_e_point : public ps_point {
- public:
+private:
   /**
    * Vector of diagonal elements of inverse mass matrix.
    */
   Eigen::VectorXd inv_e_metric_;
 
+public:
   /**
    * Construct a diag point in n-dimensional phase space
    * with vector of ones for diagonal elements of inverse mass matrix.
@@ -32,10 +33,19 @@ class diag_e_point : public ps_point {
    *
    * @param inv_e_metric initial mass matrix
    */
-  void set_metric(const Eigen::VectorXd& inv_e_metric) {
+  void set_inv_metric(const Eigen::VectorXd& inv_e_metric) {
     inv_e_metric_ = inv_e_metric;
   }
 
+  /**
+   * Get inverse metric
+   *
+   * @return reference to the inverse metric
+   */
+  const Eigen::VectorXd& get_inv_metric() {
+    return inv_e_metric_;
+  }
+
   /**
    * Write elements of mass matrix to string and handoff to writer.
    *
diff --git a/src/stan/mcmc/hmc/nuts/adapt_dense_e_nuts.hpp b/src/stan/mcmc/hmc/nuts/adapt_dense_e_nuts.hpp
index 05b6c80523f..e78f9440cd6 100644
--- a/src/stan/mcmc/hmc/nuts/adapt_dense_e_nuts.hpp
+++ b/src/stan/mcmc/hmc/nuts/adapt_dense_e_nuts.hpp
@@ -29,12 +29,15 @@ class adapt_dense_e_nuts : public dense_e_nuts<Model, BaseRNG>,
       this->stepsize_adaptation_.learn_stepsize(this->nom_epsilon_,
                                                 s.accept_stat());
 
-      bool update = this->covar_adaptation_.learn_covariance(
-          this->z_.inv_e_metric_, this->z_.q);
+      Eigen::MatrixXd inv_metric;
+      
+      bool update = this->covar_adaptation_.learn_covariance(inv_metric, this->z_.q);
 
       if (update) {
         this->init_stepsize(logger);
 
+	this->z_.set_inv_metric(inv_metric);
+
         this->stepsize_adaptation_.set_mu(log(10 * this->nom_epsilon_));
         this->stepsize_adaptation_.restart();
       }
diff --git a/src/stan/mcmc/hmc/nuts/adapt_diag_e_nuts.hpp b/src/stan/mcmc/hmc/nuts/adapt_diag_e_nuts.hpp
index 45e92380f57..94a05abc70a 100644
--- a/src/stan/mcmc/hmc/nuts/adapt_diag_e_nuts.hpp
+++ b/src/stan/mcmc/hmc/nuts/adapt_diag_e_nuts.hpp
@@ -29,12 +29,15 @@ class adapt_diag_e_nuts : public diag_e_nuts<Model, BaseRNG>,
       this->stepsize_adaptation_.learn_stepsize(this->nom_epsilon_,
                                                 s.accept_stat());
 
-      bool update = this->var_adaptation_.learn_variance(this->z_.inv_e_metric_,
-                                                         this->z_.q);
-
+      Eigen::VectorXd inv_metric;
+      
+      bool update = this->var_adaptation_.learn_variance(inv_metric, this->z_.q);
+      
       if (update) {
         this->init_stepsize(logger);
 
+	this->z_.set_inv_metric(inv_metric);
+
         this->stepsize_adaptation_.set_mu(log(10 * this->nom_epsilon_));
         this->stepsize_adaptation_.restart();
       }
diff --git a/src/stan/mcmc/hmc/nuts/base_nuts.hpp b/src/stan/mcmc/hmc/nuts/base_nuts.hpp
index 7b08ff8ce5d..a495a06754a 100644
--- a/src/stan/mcmc/hmc/nuts/base_nuts.hpp
+++ b/src/stan/mcmc/hmc/nuts/base_nuts.hpp
@@ -58,12 +58,12 @@ class base_nuts : public base_hmc<Model, Hamiltonian, Integrator, BaseRNG> {
 
   ~base_nuts() {}
 
-  void set_metric(const Eigen::MatrixXd& inv_e_metric) {
-    this->z_.set_metric(inv_e_metric);
+  void set_inv_metric(const Eigen::MatrixXd& inv_e_metric) {
+    this->z_.set_inv_metric(inv_e_metric);
   }
 
-  void set_metric(const Eigen::VectorXd& inv_e_metric) {
-    this->z_.set_metric(inv_e_metric);
+  void set_inv_metric(const Eigen::VectorXd& inv_e_metric) {
+    this->z_.set_inv_metric(inv_e_metric);
   }
 
   void set_max_depth(int d) {
diff --git a/src/stan/mcmc/hmc/static/adapt_dense_e_static_hmc.hpp b/src/stan/mcmc/hmc/static/adapt_dense_e_static_hmc.hpp
index 7691fc6f6e2..957c96ee390 100644
--- a/src/stan/mcmc/hmc/static/adapt_dense_e_static_hmc.hpp
+++ b/src/stan/mcmc/hmc/static/adapt_dense_e_static_hmc.hpp
@@ -32,12 +32,14 @@ class adapt_dense_e_static_hmc : public dense_e_static_hmc<Model, BaseRNG>,
                                                 s.accept_stat());
       this->update_L_();
 
-      bool update = this->covar_adaptation_.learn_covariance(
-          this->z_.inv_e_metric_, this->z_.q);
+      Eigen::MatrixXd inv_metric;
+      
+      bool update = this->covar_adaptation_.learn_covariance(inv_metric, this->z_.q);
 
       if (update) {
         this->init_stepsize(logger);
         this->update_L_();
+	this->z_.set_inv_metric(inv_metric);
 
         this->stepsize_adaptation_.set_mu(log(10 * this->nom_epsilon_));
         this->stepsize_adaptation_.restart();
diff --git a/src/stan/mcmc/hmc/static/adapt_diag_e_static_hmc.hpp b/src/stan/mcmc/hmc/static/adapt_diag_e_static_hmc.hpp
index a2098ef95f0..8f443b01cc3 100644
--- a/src/stan/mcmc/hmc/static/adapt_diag_e_static_hmc.hpp
+++ b/src/stan/mcmc/hmc/static/adapt_diag_e_static_hmc.hpp
@@ -32,12 +32,15 @@ class adapt_diag_e_static_hmc : public diag_e_static_hmc<Model, BaseRNG>,
                                                 s.accept_stat());
       this->update_L_();
 
-      bool update = this->var_adaptation_.learn_variance(this->z_.inv_e_metric_,
+      Eigen::VectorXd inv_metric;
+      
+      bool update = this->var_adaptation_.learn_variance(inv_metric,
                                                          this->z_.q);
 
       if (update) {
         this->init_stepsize(logger);
         this->update_L_();
+	this->z_.set_inv_metric(inv_metric);
 
         this->stepsize_adaptation_.set_mu(log(10 * this->nom_epsilon_));
         this->stepsize_adaptation_.restart();
diff --git a/src/stan/mcmc/hmc/static/base_static_hmc.hpp b/src/stan/mcmc/hmc/static/base_static_hmc.hpp
index 4dab52ad9b6..7d30447138f 100644
--- a/src/stan/mcmc/hmc/static/base_static_hmc.hpp
+++ b/src/stan/mcmc/hmc/static/base_static_hmc.hpp
@@ -30,12 +30,12 @@ class base_static_hmc
 
   ~base_static_hmc() {}
 
-  void set_metric(const Eigen::MatrixXd& inv_e_metric) {
-    this->z_.set_metric(inv_e_metric);
+  void set_inv_metric(const Eigen::MatrixXd& inv_e_metric) {
+    this->z_.set_inv_metric(inv_e_metric);
   }
 
-  void set_metric(const Eigen::VectorXd& inv_e_metric) {
-    this->z_.set_metric(inv_e_metric);
+  void set_inv_metric(const Eigen::VectorXd& inv_e_metric) {
+    this->z_.set_inv_metric(inv_e_metric);
   }
 
   sample transition(sample& init_sample, callbacks::logger& logger) {
diff --git a/src/stan/services/sample/hmc_nuts_dense_e.hpp b/src/stan/services/sample/hmc_nuts_dense_e.hpp
index f57466503db..671763279b7 100644
--- a/src/stan/services/sample/hmc_nuts_dense_e.hpp
+++ b/src/stan/services/sample/hmc_nuts_dense_e.hpp
@@ -73,7 +73,7 @@ int hmc_nuts_dense_e(Model& model, const stan::io::var_context& init,
 
   stan::mcmc::dense_e_nuts<Model, boost::ecuyer1988> sampler(model, rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
 
   sampler.set_nominal_stepsize(stepsize);
   sampler.set_stepsize_jitter(stepsize_jitter);
diff --git a/src/stan/services/sample/hmc_nuts_dense_e_adapt.hpp b/src/stan/services/sample/hmc_nuts_dense_e_adapt.hpp
index cb644a346c6..2c071d9199f 100644
--- a/src/stan/services/sample/hmc_nuts_dense_e_adapt.hpp
+++ b/src/stan/services/sample/hmc_nuts_dense_e_adapt.hpp
@@ -81,7 +81,7 @@ int hmc_nuts_dense_e_adapt(
 
   stan::mcmc::adapt_dense_e_nuts<Model, boost::ecuyer1988> sampler(model, rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
 
   sampler.set_nominal_stepsize(stepsize);
   sampler.set_stepsize_jitter(stepsize_jitter);
diff --git a/src/stan/services/sample/hmc_nuts_diag_e.hpp b/src/stan/services/sample/hmc_nuts_diag_e.hpp
index 3932a870dba..dc1f19724c0 100644
--- a/src/stan/services/sample/hmc_nuts_diag_e.hpp
+++ b/src/stan/services/sample/hmc_nuts_diag_e.hpp
@@ -73,7 +73,7 @@ int hmc_nuts_diag_e(Model& model, const stan::io::var_context& init,
 
   stan::mcmc::diag_e_nuts<Model, boost::ecuyer1988> sampler(model, rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
   sampler.set_nominal_stepsize(stepsize);
   sampler.set_stepsize_jitter(stepsize_jitter);
   sampler.set_max_depth(max_depth);
diff --git a/src/stan/services/sample/hmc_nuts_diag_e_adapt.hpp b/src/stan/services/sample/hmc_nuts_diag_e_adapt.hpp
index 8d03373e1a5..87211e6f2b2 100644
--- a/src/stan/services/sample/hmc_nuts_diag_e_adapt.hpp
+++ b/src/stan/services/sample/hmc_nuts_diag_e_adapt.hpp
@@ -81,7 +81,7 @@ int hmc_nuts_diag_e_adapt(
 
   stan::mcmc::adapt_diag_e_nuts<Model, boost::ecuyer1988> sampler(model, rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
   sampler.set_nominal_stepsize(stepsize);
   sampler.set_stepsize_jitter(stepsize_jitter);
   sampler.set_max_depth(max_depth);
diff --git a/src/stan/services/sample/hmc_static_dense_e.hpp b/src/stan/services/sample/hmc_static_dense_e.hpp
index 5ddb3d224eb..eead72689d9 100644
--- a/src/stan/services/sample/hmc_static_dense_e.hpp
+++ b/src/stan/services/sample/hmc_static_dense_e.hpp
@@ -70,7 +70,7 @@ int hmc_static_dense_e(
 
   stan::mcmc::dense_e_static_hmc<Model, boost::ecuyer1988> sampler(model, rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
   sampler.set_nominal_stepsize_and_T(stepsize, int_time);
   sampler.set_stepsize_jitter(stepsize_jitter);
 
diff --git a/src/stan/services/sample/hmc_static_dense_e_adapt.hpp b/src/stan/services/sample/hmc_static_dense_e_adapt.hpp
index 979e5ded1b8..6eec480bc6d 100644
--- a/src/stan/services/sample/hmc_static_dense_e_adapt.hpp
+++ b/src/stan/services/sample/hmc_static_dense_e_adapt.hpp
@@ -82,7 +82,7 @@ int hmc_static_dense_e_adapt(
   stan::mcmc::adapt_dense_e_static_hmc<Model, boost::ecuyer1988> sampler(model,
                                                                          rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
   sampler.set_nominal_stepsize_and_T(stepsize, int_time);
   sampler.set_stepsize_jitter(stepsize_jitter);
 
diff --git a/src/stan/services/sample/hmc_static_diag_e.hpp b/src/stan/services/sample/hmc_static_diag_e.hpp
index 57109395f5d..b1aa63465e7 100644
--- a/src/stan/services/sample/hmc_static_diag_e.hpp
+++ b/src/stan/services/sample/hmc_static_diag_e.hpp
@@ -75,7 +75,7 @@ int hmc_static_diag_e(Model& model, const stan::io::var_context& init,
 
   stan::mcmc::diag_e_static_hmc<Model, boost::ecuyer1988> sampler(model, rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
   sampler.set_nominal_stepsize_and_T(stepsize, int_time);
   sampler.set_stepsize_jitter(stepsize_jitter);
 
diff --git a/src/stan/services/sample/hmc_static_diag_e_adapt.hpp b/src/stan/services/sample/hmc_static_diag_e_adapt.hpp
index f374f205c62..86a4896988c 100644
--- a/src/stan/services/sample/hmc_static_diag_e_adapt.hpp
+++ b/src/stan/services/sample/hmc_static_diag_e_adapt.hpp
@@ -82,7 +82,7 @@ int hmc_static_diag_e_adapt(
   stan::mcmc::adapt_diag_e_static_hmc<Model, boost::ecuyer1988> sampler(model,
                                                                         rng);
 
-  sampler.set_metric(inv_metric);
+  sampler.set_inv_metric(inv_metric);
   sampler.set_nominal_stepsize_and_T(stepsize, int_time);
   sampler.set_stepsize_jitter(stepsize_jitter);
 
diff --git a/src/test/unit/mcmc/hmc/hamiltonians/dense_e_metric_test.cpp b/src/test/unit/mcmc/hmc/hamiltonians/dense_e_metric_test.cpp
index 2340609aebe..50dd3227f5a 100644
--- a/src/test/unit/mcmc/hmc/hamiltonians/dense_e_metric_test.cpp
+++ b/src/test/unit/mcmc/hmc/hamiltonians/dense_e_metric_test.cpp
@@ -25,7 +25,7 @@ TEST(McmcDenseEMetric, sample_p) {
 
   stan::mcmc::dense_e_metric<stan::mcmc::mock_model, rng_t> metric(model);
   stan::mcmc::dense_e_point z(2);
-  z.set_metric(m_inv);
+  z.set_inv_metric(m_inv);
 
   int n_samples = 1000;