Task: computeDrudeTemperature (openmm/openmm#3512)

org: openmm
repo: openmm
pr_number: 3512
issue_title: computeDrudeTemperature
issue_body: Adds a convenience function to compute the instantaneous Drude temperature in the `DrudeNoseHooverIntegrator` and `DrudeLangevinIntegrator`.


resolved_issues: title: computeDrudeTemperature
body: ### Issue Description

#### Problem
Currently, there is no direct way to compute the instantaneous temperature of the Drude system in simulations that involve Drude particle pairs. This temperature, which reflects the kinetic energy of the internal motion of Drude pairs, is critical for monitoring and validating the behavior of simulations, particularly when using integrators designed for systems with Drude particles. Without this functionality, users must rely on indirect or manual calculations, which can be cumbersome and error-prone.

#### Expected Behavior
The software should provide a convenient method to compute the instantaneous Drude temperature directly during simulations. This value should be readily accessible and accurately reflect the internal kinetic energy of Drude pairs, allowing users to verify that the Drude temperature remains close to the prescribed value. This functionality would enhance usability and improve the ability to monitor simulation performance and stability.

## IMPORTANT INSTRUCTIONS

1. If you edit a python file, you MUST run 'make PythonInstall' inside the build directory
2. If you edit a c++ file, you MUST run 'make -j4 && make install" inside the build directory

Reference solution:
fix_patch: diff --git a/plugins/drude/openmmapi/include/openmm/DrudeLangevinIntegrator.h b/plugins/drude/openmmapi/include/openmm/DrudeLangevinIntegrator.h
index 8f39c6e075..5b26adcfbc 100644
--- a/plugins/drude/openmmapi/include/openmm/DrudeLangevinIntegrator.h
+++ b/plugins/drude/openmmapi/include/openmm/DrudeLangevinIntegrator.h
@@ -126,6 +126,12 @@ class OPENMM_EXPORT_DRUDE DrudeLangevinIntegrator : public DrudeIntegrator {
      * getTemperature().
      */
     double computeSystemTemperature();
+    /**
+     * Compute the instantaneous temperature of the Drude system, measured in Kelvin.
+     * This is calculated based on the kinetic energy of the internal motion of Drude pairs
+     * and should remain close to the prescribed Drude temperature.
+     */
+    double computeDrudeTemperature();
 protected:
     /**
      * This will be called by the Context when it is created.  It informs the Integrator
diff --git a/plugins/drude/openmmapi/include/openmm/DrudeNoseHooverIntegrator.h b/plugins/drude/openmmapi/include/openmm/DrudeNoseHooverIntegrator.h
index 475b3378fc..7bc87a8738 100644
--- a/plugins/drude/openmmapi/include/openmm/DrudeNoseHooverIntegrator.h
+++ b/plugins/drude/openmmapi/include/openmm/DrudeNoseHooverIntegrator.h
@@ -106,6 +106,12 @@ class OPENMM_EXPORT_DRUDE DrudeNoseHooverIntegrator : public NoseHooverIntegrato
      * getTemperature().
      */
     double computeSystemTemperature();
+    /**
+     * Compute the instantaneous temperature of the Drude system, measured in Kelvin.
+     * This is calculated based on the kinetic energy of the internal motion of Drude pairs
+     * and should remain close to the prescribed Drude temperature.
+     */ 
+     double computeDrudeTemperature();
 protected:
     /**
      * Return a list of velocities normally distributed around a target temperature, with the Drude
diff --git a/plugins/drude/openmmapi/src/DrudeHelpers.cpp b/plugins/drude/openmmapi/src/DrudeHelpers.cpp
index da5823bf02..b3eb941cf0 100644
--- a/plugins/drude/openmmapi/src/DrudeHelpers.cpp
+++ b/plugins/drude/openmmapi/src/DrudeHelpers.cpp
@@ -127,12 +127,16 @@ vector<Vec3> assignDrudeVelocities(const System &system, double temperature, dou
     return velocities;
 }
 
-double computeSystemTemperatureFromVelocities(const System& system, const vector<Vec3>& velocities) {
+
+/**
+ * Computes the instantaneous temperatures of the system and the internal Drude motion and returns a pair (T_system, T_drude)
+ */
+pair<double, double> computeTemperaturesFromVelocities(const System& system, const vector<Vec3>& velocities) {
     vector<int> normalParticles;
     vector<pair<int, int> > pairParticles;
     findParticlesAndPairs(system, normalParticles, pairParticles);
-    double energy = 0.0;
-    int dof = 0;
+    double energy = 0.0, drudeEnergy = 0;
+    int dof = 0, drudeDof = 0;
     
     // Kinetic energy and degrees of freedom from normal particles.
     
@@ -151,10 +155,14 @@ double computeSystemTemperatureFromVelocities(const System& system, const vector
         int p2 = pair.second;
         double mass1 = system.getParticleMass(p1);
         double mass2 = system.getParticleMass(p2);
+	double reducedMass = (mass1*mass2)/(mass1+mass2);
         if (mass1 != 0 || mass2 != 0) {
             Vec3 momentum = mass1*velocities[p1] + mass2*velocities[p2];
             energy += momentum.dot(momentum)/(mass1+mass2);
-            dof += 3;
+	    Vec3 drudeVelocity = velocities[p1] - velocities[p2];
+            drudeEnergy += reducedMass*drudeVelocity.dot(drudeVelocity);
+	    dof += 3;
+	    drudeDof += 3;
         }
     }
     
@@ -176,7 +184,10 @@ double computeSystemTemperatureFromVelocities(const System& system, const vector
             break;
         }
     energy *= 0.5;
-    return 2*energy/(dof*BOLTZ);
+    drudeEnergy *= 0.5;
+    if (drudeDof == 0)
+        drudeDof = 1; // so that the drude temperature is reported as 0
+    return make_pair<double, double>(2*energy/(dof*BOLTZ), 2*drudeEnergy/(drudeDof*BOLTZ));
 }
 
 }
diff --git a/plugins/drude/openmmapi/src/DrudeLangevinIntegrator.cpp b/plugins/drude/openmmapi/src/DrudeLangevinIntegrator.cpp
index 793f65c593..8665fe3653 100644
--- a/plugins/drude/openmmapi/src/DrudeLangevinIntegrator.cpp
+++ b/plugins/drude/openmmapi/src/DrudeLangevinIntegrator.cpp
@@ -42,9 +42,10 @@
 using namespace OpenMM;
 using std::string;
 using std::vector;
+using std::pair;
 
 namespace OpenMM {
-    double computeSystemTemperatureFromVelocities(const System& system, const vector<Vec3>& velocities);
+	pair<double, double> computeTemperaturesFromVelocities(const System& system, const vector<Vec3>& velocities);
 }
 
 DrudeLangevinIntegrator::DrudeLangevinIntegrator(double temperature, double frictionCoeff, double drudeTemperature, double drudeFrictionCoeff, double stepSize) : DrudeIntegrator(stepSize) {
@@ -126,5 +127,15 @@ double DrudeLangevinIntegrator::computeSystemTemperature() {
     context->calcForcesAndEnergy(true, false, getIntegrationForceGroups());
     vector<Vec3> velocities;
     context->computeShiftedVelocities(getVelocityTimeOffset(), velocities);
-    return computeSystemTemperatureFromVelocities(context->getSystem(), velocities);
+    return computeTemperaturesFromVelocities(context->getSystem(), velocities).first;
 }
+
+double DrudeLangevinIntegrator::computeDrudeTemperature() {
+    if (context == NULL)
+        throw OpenMMException("This Integrator is not bound to a context!");  
+    context->calcForcesAndEnergy(true, false, getIntegrationForceGroups());
+    vector<Vec3> velocities;
+    context->computeShiftedVelocities(getVelocityTimeOffset(), velocities);
+    return computeTemperaturesFromVelocities(context->getSystem(), velocities).second;
+} 
+
diff --git a/plugins/drude/openmmapi/src/DrudeNoseHooverIntegrator.cpp b/plugins/drude/openmmapi/src/DrudeNoseHooverIntegrator.cpp
index 6a2943a374..feae183c70 100644
--- a/plugins/drude/openmmapi/src/DrudeNoseHooverIntegrator.cpp
+++ b/plugins/drude/openmmapi/src/DrudeNoseHooverIntegrator.cpp
@@ -30,6 +30,7 @@
  * -------------------------------------------------------------------------- */
 
 #include "openmm/DrudeNoseHooverIntegrator.h"
+#include "SimTKOpenMMRealType.h"
 #include "openmm/Context.h"
 #include "openmm/OpenMMException.h"
 #include "openmm/internal/ContextImpl.h"
@@ -45,12 +46,14 @@
 using namespace OpenMM;
 using std::string;
 using std::vector;
+using std::pair;
 
 namespace OpenMM {
     extern std::vector<Vec3> assignDrudeVelocities(const System &system, double temperature, double drudeTemperature, int randomSeed);
-    double computeSystemTemperatureFromVelocities(const System& system, const vector<Vec3>& velocities);
+    pair<double, double> computeTemperaturesFromVelocities(const System& system, const vector<Vec3>& velocities);
 }
 
+
 DrudeNoseHooverIntegrator::DrudeNoseHooverIntegrator(double temperature, double collisionFrequency, 
                                                      double drudeTemperature, double drudeCollisionFrequency,
                                                      double stepSize, int chainLength, int numMTS, int numYoshidaSuzuki) :
@@ -151,8 +154,20 @@ double DrudeNoseHooverIntegrator::computeSystemTemperature() {
     context->calcForcesAndEnergy(true, false, getIntegrationForceGroups());
     vector<Vec3> velocities;
     context->computeShiftedVelocities(getVelocityTimeOffset(), velocities);
-    return computeSystemTemperatureFromVelocities(context->getSystem(), velocities);
+    return computeTemperaturesFromVelocities(context->getSystem(), velocities).first;
+}
+
+double DrudeNoseHooverIntegrator::computeDrudeTemperature() {
+    if (context == NULL)
+        throw OpenMMException("This Integrator is not bound to a context!");  
+    double kE = computeDrudeKineticEnergy();
+    size_t num_dofs = 0;
+    for (const auto &nhc: noseHooverChains){
+       num_dofs += 3 * nhc.getThermostatedPairs().size();
+    }
+    return kE/(0.5 * num_dofs * BOLTZ);
 }
+
 std::vector<Vec3> DrudeNoseHooverIntegrator::getVelocitiesForTemperature(const System &system, double temperature,
                                                                          int randomSeedIn) const {
     return assignDrudeVelocities(system, temperature, drudeTemperature, randomSeedIn);
diff --git a/wrappers/python/src/swig_doxygen/swigInputConfig.py b/wrappers/python/src/swig_doxygen/swigInputConfig.py
index 702bd3d328..b88b1c24cd 100755
--- a/wrappers/python/src/swig_doxygen/swigInputConfig.py
+++ b/wrappers/python/src/swig_doxygen/swigInputConfig.py
@@ -226,6 +226,7 @@
 ("*", "getGlobalParameterDefaultValue") : (None, ()),
 ("*", "getPermutationMode") : (None, ()),
 ("*", "computeSystemTemperature") : ("unit.kelvin", ()),
+("*", "computeDrudeTemperature") : ("unit.kelvin", ()),
 ("LocalCoordinatesSite", "getOriginWeights") : (None, ()),
 ("LocalCoordinatesSite", "getXWeights") : (None, ()),
 ("LocalCoordinatesSite", "getYWeights") : (None, ()),