Add driver to compute parabolic fit to CALPHAD (#71)

drivers/CMakeLists.txt

@@ -38,6 +38,8 @@ add_executable(computeKKS3Ph2Sl
                ${CMAKE_SOURCE_DIR}/drivers/computeKKS3Ph2Sl.cc)
 add_executable(computeEqCompBinary2Ph1Sl
                ${CMAKE_SOURCE_DIR}/drivers/computeEqCompBinary2Ph1Sl.cc)
+add_executable(computeParabolicApproximation
+               ${CMAKE_SOURCE_DIR}/drivers/computeParabolicApproximation.cc)
 
 target_link_libraries(plotEnergyVsComposition thermo4pfm)
 target_link_libraries(plotEnergyVsCompositionThreePhase thermo4pfm)
@@ -47,6 +49,7 @@ target_link_libraries(computeKKSTernary thermo4pfm)
 target_link_libraries(computeTieLineTernary thermo4pfm)
 target_link_libraries(computeKKS3Ph2Sl thermo4pfm)
 target_link_libraries(computeEqCompBinary2Ph1Sl thermo4pfm)
+target_link_libraries(computeParabolicApproximation thermo4pfm)
 target_link_libraries(loopxlogx thermo4pfm)
 target_link_libraries(loopCALPHADSpeciesPhaseGibbsEnergy thermo4pfm)
 target_link_libraries(loopCALPHADConcSolverBinary thermo4pfm)
@@ -71,6 +74,7 @@ install(TARGETS plotEnergyVsComposition
                 computeKKSTernary
                 computeTieLineTernary
                 computeKKS3Ph2Sl
+                computeParabolicApproximation
                 loopxlogx
                 loopCALPHADSpeciesPhaseGibbsEnergy
                 loopCALPHADConcSolverBinary

drivers/computeParabolicApproximation.cc

@@ -0,0 +1,156 @@
+// Copyright (c) 2018, Lawrence Livermore National Security, LLC and
+// UT-Battelle, LLC.
+// Produced at the Lawrence Livermore National Laboratory and
+// the Oak Ridge National Laboratory
+// LLNL-CODE-747500
+// All rights reserved.
+// This file is part of AMPE.
+// For details, see https://github.com/LLNL/AMPE
+// Please also read AMPE/LICENSE.
+//
+#include "CALPHADFreeEnergyFunctionsBinary.h"
+
+#include <fstream>
+#include <iostream>
+#include <map>
+#include <string>
+
+#include <boost/property_tree/json_parser.hpp>
+#include <boost/property_tree/ptree.hpp>
+
+namespace pt = boost::property_tree;
+
+int main(int argc, char* argv[])
+{
+    if (argc < 4)
+    {
+        std::cerr
+            << "ERROR: program needs 2 argument (database + 2 temperatures "
+            << std::endl;
+        return 1;
+    }
+
+    std::string calphad_filename(argv[1]);
+    const double temperature_low  = atof(argv[2]);
+    const double temperature_high = atof(argv[3]);
+    // initial guesses
+    double init_guess[2];
+    init_guess[0] = atof(argv[4]);
+    init_guess[1] = atof(argv[5]);
+
+    {
+        Thermo4PFM::EnergyInterpolationType energy_interp_func_type
+            = Thermo4PFM::EnergyInterpolationType::PBG;
+        Thermo4PFM::ConcInterpolationType conc_interp_func_type
+            = Thermo4PFM::ConcInterpolationType::PBG;
+
+        boost::property_tree::ptree calphad_pt;
+        assert(calphad_filename.compare(calphad_filename.size() - 4, 4, "json")
+               == 0);
+        boost::property_tree::read_json(calphad_filename, calphad_pt);
+
+        pt::ptree newton_pt;
+
+        Thermo4PFM::CALPHADFreeEnergyFunctionsBinary cafe(calphad_pt, newton_pt,
+            energy_interp_func_type, conc_interp_func_type);
+
+        const int nT = 50;
+
+        std::vector<double> c0s(nT);
+        std::vector<double> c0l(nT);
+
+        std::vector<double> fs(nT);
+        std::vector<double> fl(nT);
+
+        std::vector<double> d2fs(nT);
+        std::vector<double> d2fl(nT);
+
+        double dT = (temperature_high - temperature_low) / 50;
+
+        const double tol = 1.e-8;
+        const int maxits = 50;
+
+        // loop over temperature range
+        for (int iT = 0; iT < nT; iT++)
+        {
+
+            double temperature = temperature_low + iT * dT;
+            std::clog << "T = " << temperature << std::endl;
+            // compute minimum using Newton iteration to solve for f'(x)=0
+            {
+                double conc = init_guess[0];
+                for (int it = 0; it < maxits; it++)
+                {
+                    double val = 0.;
+                    cafe.computeDerivFreeEnergy(temperature, &conc,
+                        Thermo4PFM::PhaseIndex::phaseL, &val);
+                    double deriv = 0.;
+                    cafe.computeSecondDerivativeFreeEnergy(temperature, &conc,
+                        Thermo4PFM::PhaseIndex::phaseL, &deriv);
+                    const double delta = val / deriv;
+                    conc -= delta;
+                    std::clog << conc << std::endl;
+
+                    if (std::abs(delta) < tol)
+                    {
+                        std::clog << "converged!" << std::endl;
+                        d2fl[iT] = deriv;
+                        fl[iT]   = cafe.computeFreeEnergy(
+                            temperature, &conc, Thermo4PFM::PhaseIndex::phaseL);
+                        break;
+                    }
+                }
+                c0l[iT] = conc;
+            }
+
+            {
+                double conc = init_guess[1];
+                for (int it = 0; it < maxits; it++)
+                {
+                    double val = 0.;
+                    cafe.computeDerivFreeEnergy(temperature, &conc,
+                        Thermo4PFM::PhaseIndex::phaseA, &val);
+                    double deriv = 0.;
+                    cafe.computeSecondDerivativeFreeEnergy(temperature, &conc,
+                        Thermo4PFM::PhaseIndex::phaseA, &deriv);
+                    const double delta = val / deriv;
+                    conc -= delta;
+                    std::clog << conc << std::endl;
+
+                    if (std::abs(delta) < tol)
+                    {
+                        std::clog << "converged!" << std::endl;
+                        d2fs[iT] = deriv;
+                        fs[iT]   = cafe.computeFreeEnergy(
+                            temperature, &conc, Thermo4PFM::PhaseIndex::phaseA);
+                        break;
+                    }
+                }
+                c0s[iT] = conc;
+            }
+        }
+
+        {
+            std::ofstream os("ParabolicDataLiquid.csv");
+            os << "T, c0, f(c0), d2f\n";
+            for (int iT = 0; iT < nT; iT++)
+            {
+                double temperature = temperature_low + iT * dT;
+                os << temperature << ", " << c0l[iT] << ", " << fl[iT] << ", "
+                   << d2fl[iT] << std::endl;
+            }
+        }
+        {
+            std::ofstream os("ParabolicDataSolid.csv");
+            os << "T, c0, f(c0), d2f\n";
+            for (int iT = 0; iT < nT; iT++)
+            {
+                double temperature = temperature_low + iT * dT;
+                os << temperature << ", " << c0s[iT] << ", " << fs[iT] << ", "
+                   << d2fs[iT] << std::endl;
+            }
+        }
+    }
+
+    return 0;
+}