new functions to return the final gradient information

CHANGELOG.md

@@ -1,3 +1,12 @@
+## Unrealeased
+
+### Added
+- Added functions `final_grad()` and `final_grad_norm()` to `LBFGSSolver`
+  and `LBFGSBSolver` to retrieve the final gradient information
+  ([#12](https://github.com/yixuan/LBFGSpp/issues/12))
+
+
+
 ## [0.2.0] - 2022-05-20
 
 ### Added

examples/example-rosenbrock-box.cpp

@@ -58,6 +58,8 @@ int main()
     std::cout << niter << " iterations" << std::endl;
     std::cout << "x = \n" << x.transpose() << std::endl;
     std::cout << "f(x) = " << fx << std::endl;
+    std::cout << "grad = " << solver.final_grad().transpose() << std::endl;
+    std::cout << "projected grad norm = " << solver.final_grad_norm() << std::endl;
 
     return 0;
 }

examples/example-rosenbrock.cpp

@@ -41,6 +41,8 @@ int main()
     std::cout << niter << " iterations" << std::endl;
     std::cout << "x = \n" << x.transpose() << std::endl;
     std::cout << "f(x) = " << fx << std::endl;
+    std::cout << "grad = " << solver.final_grad().transpose() << std::endl;
+    std::cout << "||grad|| = " << solver.final_grad_norm() << std::endl;
 
     return 0;
 }

include/LBFGS.h

@@ -30,6 +30,7 @@ class LBFGSSolver
     Vector m_fx;                        // History of the objective function values
     Vector m_xp;                        // Old x
     Vector m_grad;                      // New gradient
+    Scalar m_gnorm;                     // Norm of the gradient
     Vector m_gradp;                     // Old gradient
     Vector m_drt;                       // Moving direction
 
@@ -87,12 +88,12 @@ class LBFGSSolver
 
         // Evaluate function and compute gradient
         fx = f(x, m_grad);
-        Scalar gnorm = m_grad.norm();
+        m_gnorm = m_grad.norm();
         if (fpast > 0)
             m_fx[0] = fx;
 
         // Early exit if the initial x is already a minimizer
-        if (gnorm <= m_param.epsilon || gnorm <= m_param.epsilon_rel * x.norm())
+        if (m_gnorm <= m_param.epsilon || m_gnorm <= m_param.epsilon_rel * x.norm())
         {
             return 1;
         }
@@ -114,10 +115,10 @@ class LBFGSSolver
             LineSearch<Scalar>::LineSearch(f, fx, x, m_grad, step, m_drt, m_xp, m_param);
 
             // New gradient norm
-            gnorm = m_grad.norm();
+            m_gnorm = m_grad.norm();
 
             // Convergence test -- gradient
-            if (gnorm <= m_param.epsilon || gnorm <= m_param.epsilon_rel * x.norm())
+            if (m_gnorm <= m_param.epsilon || m_gnorm <= m_param.epsilon_rel * x.norm())
             {
                 return k;
             }
@@ -151,6 +152,20 @@ class LBFGSSolver
 
         return k;
     }
+
+    ///
+    /// Returning the gradient vector on the last iterate.
+    /// Typically used to debug and test convergence.
+    /// Should only be called after the `minimize()` function.
+    ///
+    /// \return A const reference to the gradient vector.
+    ///
+    const Vector& final_grad() const { return m_grad; }
+
+    ///
+    /// Returning the Euclidean norm of the final gradient.
+    ///
+    Scalar final_grad_norm() const { return m_gnorm; }
 };
 
 }  // namespace LBFGSpp

include/LBFGSB.h

@@ -33,6 +33,7 @@ class LBFGSBSolver
     Vector m_fx;                         // History of the objective function values
     Vector m_xp;                         // Old x
     Vector m_grad;                       // New gradient
+    Scalar m_projgnorm;                  // Projected gradient norm
     Vector m_gradp;                      // Old gradient
     Vector m_drt;                        // Moving direction
 
@@ -134,15 +135,15 @@ class LBFGSBSolver
 
         // Evaluate function and compute gradient
         fx = f(x, m_grad);
-        Scalar projgnorm = proj_grad_norm(x, m_grad, lb, ub);
+        m_projgnorm = proj_grad_norm(x, m_grad, lb, ub);
         if (fpast > 0)
             m_fx[0] = fx;
 
         // std::cout << "x0 = " << x.transpose() << std::endl;
-        // std::cout << "f(x0) = " << fx << ", ||proj_grad|| = " << projgnorm << std::endl << std::endl;
+        // std::cout << "f(x0) = " << fx << ", ||proj_grad|| = " << m_projgnorm << std::endl << std::endl;
 
         // Early exit if the initial x is already a minimizer
-        if (projgnorm <= m_param.epsilon || projgnorm <= m_param.epsilon_rel * x.norm())
+        if (m_projgnorm <= m_param.epsilon || m_projgnorm <= m_param.epsilon_rel * x.norm())
         {
             return 1;
         }
@@ -181,14 +182,14 @@ class LBFGSBSolver
             LineSearch<Scalar>::LineSearch(f, fx, x, m_grad, step, step_max, m_drt, m_xp, m_param);
 
             // New projected gradient norm
-            projgnorm = proj_grad_norm(x, m_grad, lb, ub);
+            m_projgnorm = proj_grad_norm(x, m_grad, lb, ub);
 
             /* std::cout << "** Iteration " << k << std::endl;
             std::cout << "   x = " << x.transpose() << std::endl;
-            std::cout << "   f(x) = " << fx << ", ||proj_grad|| = " << projgnorm << std::endl << std::endl; */
+            std::cout << "   f(x) = " << fx << ", ||proj_grad|| = " << m_projgnorm << std::endl << std::endl; */
 
             // Convergence test -- gradient
-            if (projgnorm <= m_param.epsilon || projgnorm <= m_param.epsilon_rel * x.norm())
+            if (m_projgnorm <= m_param.epsilon || m_projgnorm <= m_param.epsilon_rel * x.norm())
             {
                 return k;
             }
@@ -238,6 +239,23 @@ class LBFGSBSolver
 
         return k;
     }
+
+    ///
+    /// Returning the gradient vector on the last iterate.
+    /// Typically used to debug and test convergence.
+    /// Should only be called after the `minimize()` function.
+    ///
+    /// \return A const reference to the gradient vector.
+    ///
+    const Vector& final_grad() const { return m_grad; }
+
+    ///
+    /// Returning the infinity norm of the final projected gradient.
+    /// The projected gradient is defined as \f$P(x-g,l,u)-x\f$, where \f$P(v,l,u)\f$ stands for
+    /// the projection of a vector \f$v\f$ onto the box specified by the lower bound vector \f$l\f$ and
+    /// upper bound vector \f$u\f$.
+    ///
+    Scalar final_grad_norm() const { return m_projgnorm; }
 };
 
 }  // namespace LBFGSpp