From 1a009500f25c2f3f87effaf2700139f7a4ef9c52 Mon Sep 17 00:00:00 2001
From: Ian Bell <ian.bell@nist.gov>
Date: Wed, 20 Oct 2021 21:14:05 -0400
Subject: [PATCH] More attempts at critical tracing. Still not back to its old
reliability yet.
---
include/teqp/algorithms/critical_tracing.hpp | 119 +++++++++++++++----
interface/pybind11_wrapper.cpp | 10 ++
interface/pybind11_wrapper.hpp | 3 +-
src/tests/catch_test_multifluid.cxx | 3 +-
4 files changed, 109 insertions(+), 26 deletions(-)
diff --git a/include/teqp/algorithms/critical_tracing.hpp b/include/teqp/algorithms/critical_tracing.hpp
index d38676b..0f97b36 100644
--- a/include/teqp/algorithms/critical_tracing.hpp
+++ b/include/teqp/algorithms/critical_tracing.hpp
@@ -1,6 +1,8 @@
#pragma once
#include <fstream>
+#include <optional>
+
#include "nlohmann/json.hpp"
#include <Eigen/Dense>
@@ -9,6 +11,18 @@
// Imports from boost
#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/euler.hpp>
+
+// This has to be outside the critical tracing struct so that the pybind11 wrapper doesn't fight with the types
+struct TCABOptions {
+ double abs_err = 1.0e-6,
+ rel_err = 1.0e-6,
+ init_dt = 10, ///< The initial step size
+ max_dt = 10000000000,
+ T_tol = 1e-6; ///< The tolerance on temperature to indicate that it is converged
+ int small_T_count = 5; ///< How many small temperature steps indicates convergence
+ int integration_order = 5; ///<
+};
template<typename Model, typename Scalar = double, typename VecType = Eigen::ArrayXd>
struct CriticalTracing {
@@ -315,8 +329,25 @@ struct CriticalTracing {
Eigen::ArrayXd rho = x.tail(x.size() - 1);
return std::make_tuple(x[0], rho);
}
+ static auto critical_polish_fixedT(const Model& model, const Scalar T, const VecType& rhovec) {
+ auto polish_T_resid = [&model, &T](const auto& x) {
+ auto derivs = get_derivs(model, T, x);
+ return (Eigen::ArrayXd(2) << derivs.tot[2], derivs.tot[3]).finished();
+ };
+ Eigen::ArrayXd x0 = rhovec;
+ auto r0 = polish_T_resid(x0);
+ auto x = NewtonRaphson(polish_T_resid, x0, 1e-10);
+ auto r = polish_T_resid(x);
+ Eigen::ArrayXd change = x0 - x;
+ if (!std::isfinite(T) || !std::isfinite(x[1])) {
+ throw std::invalid_argument("Something not finite; aborting polishing");
+ }
+ return x;
+ }
- static auto trace_critical_arclength_binary(const Model& model, const Scalar &T0, const VecType& rhovec0, const std::string& filename) -> nlohmann::json {
+ static auto trace_critical_arclength_binary(const Model& model, const Scalar& T0, const VecType& rhovec0, const std::optional<std::string>& filename_ = std::nullopt, const std::optional<TCABOptions> &options_ = std::nullopt) -> nlohmann::json {
+ std::string filename = filename_.value_or("");
+ TCABOptions options = options_.value_or(TCABOptions{});
VecType last_drhodt;
@@ -333,25 +364,31 @@ struct CriticalTracing {
// x is [T, rhovec]
auto xprime = [&model, &c, norm](const state_type& x, state_type& dxdt, const double /* t */)
{
- const double& T = x[0];
+ // Unpack the inputs
+ const double T = x[0];
const auto rhovec = Eigen::Map<const Eigen::ArrayXd>(&(x[0]) + 1, x.size() - 1);
- auto drhodt = Eigen::Map<Eigen::ArrayXd>(&(dxdt[0]) + 1, dxdt.size() - 1);
+
auto drhodT = get_drhovec_dT_crit(model, T, rhovec).array().eval();
auto dTdt = 1.0 / norm(drhodT);
dxdt[0] = c*dTdt;
+ auto drhodt = Eigen::Map<Eigen::ArrayXd>(&(dxdt[0]) + 1, dxdt.size() - 1);
drhodt = c*(drhodT * dTdt).eval();
};
// Typedefs for the types
using namespace boost::numeric::odeint;
+
+ // Class for simple Euler integration
+ euler<state_type> eul;
+
typedef runge_kutta_cash_karp54< state_type > error_stepper_type;
typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
// Define the tolerances
- double abs_err = 1.0e-10, rel_err = 1.0e-6, a_x = 1.0, a_dxdt = 1.0;
+ double abs_err = options.abs_err, rel_err = options.rel_err, a_x = 1.0, a_dxdt = 1.0;
controlled_stepper_type controlled_stepper(default_error_checker< double, range_algebra, default_operations >(abs_err, rel_err, a_x, a_dxdt));
- double t = 0, dt = 0.1;
+ double t = 0, dt = options.init_dt;
// Build the initial state arrary, T, followed by rhovec
std::vector<double> x0(rhovec0.size() + 1);
@@ -359,27 +396,28 @@ struct CriticalTracing {
x0[0] = T0;
Eigen::Map<Eigen::ArrayXd>(&(x0[0]) + 1, x0.size() - 1) = rhovec0;
- ofs << "z0 / mole frac.,rho0 / mol/m^3,rho1 / mol/m^3,T / K,p / Pa,c,dT/dt,drho0/dT,drho1/dT,condition(1),condition(2)" << std::endl;
+ int counter_T_converged = 0, retry_count = 0;
+ ofs << "z0 / mole frac.,rho0 / mol/m^3,rho1 / mol/m^3,T / K,p / Pa,c,dt,condition(1),condition(2)" << std::endl;
for (auto iter = 0; iter < 1000; ++iter) {
// Make T and rhovec references to the contents of x0 vector
// The views are mutable (danger!)
- double& T = x0[0];
+ double &T = x0[0];
auto rhovec = Eigen::Map<Eigen::ArrayXd>(&(x0[0]) + 1, x0.size() - 1);
{
auto dxdt = x0;
xprime(x0, dxdt, -1.0);
- auto drhodt = Eigen::Map<Eigen::ArrayXd>(&(dxdt[0]) + 1, dxdt.size() - 1);
+ const auto drhodt = Eigen::Map<const Eigen::ArrayXd>(&(dxdt[0]) + 1, dxdt.size() - 1);
// Flip the sign if the tracing wants to go backwards, or if the first step would yield any negative concentrations
- auto this_drhodt = (c * drhodt).eval();
- auto step = rhovec + this_drhodt * dt;
+ const auto this_drhodt = drhodt.eval();
+ const auto step = rhovec + this_drhodt * dt;
Eigen::ArrayX<bool> negativestepvals = (step < 0).eval();
- if (iter == 0 && negativestepvals.any()) {
+ if (iter == 0 && retry_count == 0 && negativestepvals.any()) {
c *= -1;
}
- else if (iter > 1 && dot(this_drhodt, last_drhodt) < 0) {
+ else if (iter > 1 && retry_count == 0 && dot(this_drhodt, last_drhodt) < 0) {
c *= -1;
}
}
@@ -390,7 +428,7 @@ struct CriticalTracing {
double z0 = rhovec[0] / rhotot;
using id = IsochoricDerivatives<decltype(model)>;
auto conditions = get_criticality_conditions(model, T, rhovec);
- out << z0 << "," << rhovec[0] << "," << rhovec[1] << "," << T << "," << rhotot * model.R(rhovec / rhovec.sum()) * T + id::get_pr(model, T, rhovec) << "," << c << "," << conditions(0) << "," << conditions(1) << std::endl;
+ out << z0 << "," << rhovec[0] << "," << rhovec[1] << "," << T << "," << rhotot * model.R(rhovec / rhovec.sum()) * T + id::get_pr(model, T, rhovec) << "," << c << "," << dt << "," << conditions(0) << "," << conditions(1) << std::endl;
std::string sout(out.str());
std::cout << sout;
if (ofs.is_open()) {
@@ -403,17 +441,35 @@ struct CriticalTracing {
}
}
- controlled_step_result res;
- try {
- res = controlled_stepper.try_step(xprime, x0, t, dt);
+ double dtold = dt;
+ auto x0_previous = x0;
+
+ if (options.integration_order == 5) {
+ controlled_step_result res = controlled_step_result::fail;
+ try {
+ res = controlled_stepper.try_step(xprime, x0, t, dt);
+ }
+ catch (...) {
+ break;
+ }
+
+ if (res != controlled_step_result::success) {
+ // Try again, with a smaller step size
+ iter--;
+ retry_count++;
+ continue;
+ }
+ else {
+ retry_count = 0;
+ }
+ // Reduce step size if greater than the specified max step size
+ dt = std::min(dt, options.max_dt);
}
- catch(...){
- break;
+ else if (options.integration_order == 1) {
+ eul.do_step(xprime, x0, t, dt);
}
- if (res != controlled_step_result::success) {
- // Try again, with a smaller step size
- iter--;
- continue;
+ else {
+ throw std::invalid_argument("integration order is invalid:" + std::to_string(options.integration_order));
}
// Call the function again to get drho/dt in order
@@ -421,23 +477,34 @@ struct CriticalTracing {
auto dxdt = x0;
xprime(x0, dxdt, -1.0);
auto drhodt = Eigen::Map<Eigen::ArrayXd>(&(dxdt[0]) + 1, dxdt.size() - 1);
- last_drhodt = c * drhodt;
+ last_drhodt = drhodt;
+ auto absrelchange = std::abs(drhodt.sum()*dt/rhovec.sum());
auto conditions = get_criticality_conditions(model, T, rhovec);
auto z0 = rhovec[0] / rhovec.sum();
if (z0 < 0 || z0 > 1) {
break;
}
-
+
try {
int i = 0;
auto [Tnew, rhovecnew] = critical_polish_fixedrho(model, T, rhovec, i);
+ //int rrrr = 0;
T = Tnew; rhovec = rhovecnew;
}
catch (std::exception& e) {
std::cout << e.what() << std::endl;
}
+ auto actualstep = (Eigen::Map<Eigen::ArrayXd>(&(x0[0]), x0.size()) - Eigen::Map<Eigen::ArrayXd>(&(x0_previous[0]), x0_previous.size())).eval();
+ // Check if T has stopped changing
+ if (std::abs(actualstep[0]) < options.T_tol) {
+ counter_T_converged++;
+ }
+ else {
+ counter_T_converged = 0;
+ }
+
auto rhotot = rhovec.sum();
z0 = rhovec[0] / rhotot;
if (z0 < 0 || z0 > 1) {
@@ -467,6 +534,10 @@ struct CriticalTracing {
{"dirderiv(lambda1)/dalpha", conditions[1]},
};
JSONdata.push_back(point);
+
+ if (counter_T_converged > options.small_T_count) {
+ break;
+ }
}
return JSONdata;
}
diff --git a/interface/pybind11_wrapper.cpp b/interface/pybind11_wrapper.cpp
index d8d691f..408b70f 100644
--- a/interface/pybind11_wrapper.cpp
+++ b/interface/pybind11_wrapper.cpp
@@ -1,4 +1,5 @@
#include "pybind11_wrapper.hpp"
+#include "teqp/algorithms/critical_tracing.hpp"
#include "teqpversion.hpp"
@@ -27,6 +28,15 @@ void init_teqp(py::module& m) {
add_multifluid_mutant_invariant(m);
add_cubics(m);
+ // The options class for critical tracer, not tied to a particular model
+ py::class_<TCABOptions>(m, "TCABOptions")
+ .def(py::init<>())
+ .def_readwrite("abs_err", &TCABOptions::abs_err)
+ .def_readwrite("rel_err", &TCABOptions::rel_err)
+ .def_readwrite("init_dt", &TCABOptions::init_dt)
+ .def_readwrite("integration_order", &TCABOptions::integration_order)
+ ;
+
// Some functions for timing overhead of interface
m.def("___mysummer", [](const double &c, const Eigen::ArrayXd &x) { return c*x.sum(); });
using RAX = Eigen::Ref<Eigen::ArrayXd>;
diff --git a/interface/pybind11_wrapper.hpp b/interface/pybind11_wrapper.hpp
index 5d82d25..fc32062 100644
--- a/interface/pybind11_wrapper.hpp
+++ b/interface/pybind11_wrapper.hpp
@@ -40,7 +40,8 @@ void add_derivatives(py::module &m, Wrapper &cls) {
m.def("get_B12vir", &vd::get_B12vir, py::arg("model"), py::arg("T"), py::arg("molefrac").noconvert());
using ct = CriticalTracing<Model, double, Eigen::Array<double, Eigen::Dynamic, 1>>;
- m.def("trace_critical_arclength_binary", &ct::trace_critical_arclength_binary);
+
+ m.def("trace_critical_arclength_binary", &ct::trace_critical_arclength_binary, py::arg("model"), py::arg("T0"), py::arg("rhovec0").noconvert(), py::arg_v("path", std::nullopt, "None"), py::arg_v("options", std::nullopt, "None"));
m.def("get_criticality_conditions", &ct::get_criticality_conditions);
m.def("eigen_problem", &ct::eigen_problem);
m.def("get_minimum_eigenvalue_Psi_Hessian", &ct::get_minimum_eigenvalue_Psi_Hessian);
diff --git a/src/tests/catch_test_multifluid.cxx b/src/tests/catch_test_multifluid.cxx
index 226a583..f3180ae 100644
--- a/src/tests/catch_test_multifluid.cxx
+++ b/src/tests/catch_test_multifluid.cxx
@@ -20,7 +20,8 @@ TEST_CASE("Trace critical locus for nitrogen + ethane", "[crit],[multifluid]")
auto tic0 = std::chrono::steady_clock::now();
std::string filename = "h";
using ct = CriticalTracing<decltype(model), double, Eigen::ArrayXd>;
- auto j = ct::trace_critical_arclength_binary(model, T0, rhovec0, filename);
+ TCABOptions opt; opt.max_dt = 10000; opt.init_dt = 10; opt.abs_err = 1e-8; opt.rel_err = 1e-6; opt.small_T_count = 100;
+ auto j = ct::trace_critical_arclength_binary(model, T0, rhovec0, filename, opt);
CHECK(j.size() > 3);
auto tic1 = std::chrono::steady_clock::now();
}
--
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