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/*
* MIT No Attribution
*
* Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, KU Leuven.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of this
* software and associated documentation files (the "Software"), to deal in the Software
* without restriction, including without limitation the rights to use, copy, modify,
* merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
* PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <casadi/casadi.hpp>
#include <iostream>
#include <iomanip>
using namespace casadi;
struct Test {
SXDict dae;
double tf;
std::vector<double> x0;
double u0;
bool is_ode;
std::string name;
};
/** \brief Generate a simple ODE */
Test simpleODE(){
// Time
SX t = SX::sym("t");
// Parameter
SX u = SX::sym("u");
// Differential states
SX s = SX::sym("s"), v = SX::sym("v"), m = SX::sym("m");
SX x = vertcat(s, v, m);
// Constants
double alpha = 0.05; // friction
double beta = 0.1; // fuel consumption rate
// Differential equation
SX ode = vertcat(v, (u-alpha*v*v)/m, -beta*u*u);
// Quadrature
SX quad = pow(v,3) + pow((3-sin(t))-u,2);
// Return test problem
Test r;
r.dae = decltype(r.dae){{"t", t}, {"x", x}, {"p", u}, {"ode", ode}, {"quad", quad}}; // decltype because MSVC bug
r.tf = 0.5;
r.x0 = {0, 0, 1};
r.u0 = 0.4;
r.is_ode = true;
r.name = "simple_ode";
return r;
}
/** \brief Generate a simple DAE */
Test simpleDAE(){
// Parameter
SX u = SX::sym("u");
// Differential state
SX x = SX::sym("x");
// Algebraic variable
SX z = SX::sym("z");
// Differential equation
SX ode = -x + 0.5*x*x + u + 0.5*z;
// Algebraic constraint
SX alg = z + exp(z) - 1. + x;
// Quadrature
SX quad = x*x + 3.0*u*u;
// Return DAE
Test r;
r.dae = decltype(r.dae){{"x", x}, {"z", z}, {"p", u}, {"ode", ode}, {"alg", alg}, {"quad", quad}};
r.tf = 5;
r.x0 = {1};
r.u0 = 0.4;
r.is_ode = false;
r.name = "simple_dae";
return r;
}
struct Solver {
std::string plugin;
bool ode_only;
Dict opts;
};
int main(){
// Test problems
std::vector<Test> tests = {simpleODE(), simpleDAE()};
// ODE/DAE integrators
std::vector<Solver> solvers;
solvers.push_back({"cvodes", true, Dict()});
solvers.push_back({"idas", false, Dict()});
solvers.push_back({"rk", true, Dict()});
Dict kinsol_options = {{"linear_solver_type", "dense"}};
Dict coll_opts = {{"rootfinder", "kinsol"},
{"collocation_scheme", "legendre"},
{"rootfinder_options", kinsol_options}};
solvers.push_back({"collocation", false, coll_opts});
// Loop over all problems
for (auto&& test : tests) {
// Loop over all solvers
for (auto&& solver : solvers) {
// Test with or without multiple output times
for (int ntout : {1, 3}) {
// Skip if problem cannot be handled
if (solver.ode_only && !test.is_ode) continue;
// Printout
std::cout << "Solving \"" << test.name << "\" using \"" << solver.plugin << "\", " << ntout << " output times" << std::endl;
// Output time grid
std::vector<double> tout;
if (ntout == 1) {
tout = {test.tf};
} else {
tout = {0, 0.5 * test.tf, test.tf};
}
// Create integrator instance
Function I = integrator("I", solver.plugin, test.dae, 0, tout, solver.opts);
// Buffers for evaluation
std::map<std::string, DM> arg, res;
// Integrate to get results
arg = decltype(arg){{"x0", test.x0},
{"p", test.u0}};
res = I(arg);
DM xf(res.at("xf"));
DM qf(res.at("qf"));
std::cout << std::setw(50) << "Unperturbed solution: " << "xf = " << xf.nonzeros() << ", qf = " << qf.nonzeros() << std::endl;
// Perturb solution to get a finite difference approximation
double h = 0.001;
arg["p"] = test.u0+h;
res = I(arg);
DM fd_xf = (res.at("xf")-xf)/h;
DM fd_qf = (res.at("qf")-qf)/h;
std::cout << std::setw(50) << "Finite difference approximation: " << "d(xf)/d(p) = " << fd_xf.nonzeros() << ", d(qf)/d(p) = " << fd_qf.nonzeros() << std::endl;
// Calculate once, forward
Function I_fwd = I.factory("I_fwd", {"x0", "p", "fwd:x0", "fwd:p"},
{"fwd:xf", "fwd:qf"});
arg = decltype(arg){{"x0", test.x0},
{"p", test.u0},
{"fwd_x0", 0},
{"fwd_p", 1}};
res = I_fwd(arg);
DM fwd_xf = res.at("fwd_xf");
DM fwd_qf = res.at("fwd_qf");
std::cout << std::setw(50) << "Forward sensitivities: " << "d(xf)/d(p) = " << fwd_xf.nonzeros() << ", d(qf)/d(p) = " << fwd_qf.nonzeros() << std::endl;
// Calculate once, adjoint
std::vector<double> adj_qf(ntout, 0);
adj_qf.back() = 1;
Function I_adj = I.factory("I_adj", {"x0", "p", "adj:xf", "adj:qf"},
{"adj:p", "adj:x0"});
arg = decltype(arg){{"x0", test.x0}, {"p", test.u0}, {"adj_xf", 0}, {"adj_qf", adj_qf}};
res = I_adj(arg);
DM adj_x0 = res.at("adj_x0");
DM adj_p = res.at("adj_p");
std::cout << std::setw(50) << "Adjoint sensitivities: " << "d(qf)/d(x0) = " << adj_x0.nonzeros() << ", d(qf)/d(p) = " << adj_p.nonzeros() << std::endl;
// Perturb adjoint solution to get a finite difference approximation of the second order sensitivities
arg["p"] = test.u0+h;
res = I_adj(arg);
DM fd_adj_x0 = (res.at("adj_x0")-adj_x0)/h;
DM fd_adj_p = (res.at("adj_p")-adj_p)/h;
std::cout << std::setw(50) << "FD of adjoint sensitivities: " << "d2(qf)/d(x0)d(p) = " << fd_adj_x0.nonzeros() << ", d2(qf)/d(p)d(p) = " << fd_adj_p.nonzeros() << std::endl;
// Forward over adjoint to get the second order sensitivities
Function I_foa = I_adj.factory("I_foa",
{"x0", "p", "fwd:p", "adj_xf", "adj_qf"},
{"fwd:adj_x0", "fwd:adj_p"});
arg = decltype(arg){{"x0", test.x0},
{"p", test.u0},
{"fwd_p", 1},
{"adj_xf", 0},
{"adj_qf", adj_qf}};
res = I_foa(arg);
DM fwd_adj_x0 = res.at("fwd_adj_x0");
DM fwd_adj_p = res.at("fwd_adj_p");
std::cout << std::setw(50) << "Forward over adjoint sensitivities: " << "d2(qf)/d(x0)d(p) = " << fwd_adj_x0.nonzeros() << ", d2(qf)/d(p)d(p) = " << fwd_adj_p.nonzeros() << std::endl;
// Adjoint over adjoint to get the second order sensitivities
Function I_aoa = I_adj.factory("I_aoa", {"x0", "p", "adj_xf", "adj_qf", "adj:adj_p"},
{"adj:x0", "adj:p"});
arg = decltype(arg){{"x0", test.x0},
{"p", test.u0},
{"adj_xf", 0},
{"adj_qf", adj_qf},
{"adj_adj_p", 1}};
res = I_aoa(arg);
DM adj_adj_x0 = res.at("adj_x0");
DM adj_adj_p = res.at("adj_p");
std::cout << std::setw(50) << "Adjoint over adjoint sensitivities: " << "d2(qf)/d(x0)d(p) = " << adj_adj_x0.nonzeros() << ", d2(qf)/d(p)d(p) = " << adj_adj_p.nonzeros() << std::endl;
}
}
}
return 0;
}
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