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AtomicFunctions
Joao Rui Leal edited this pageFeb 19, 2022 ·1 revision
This section describes how to use an atomic function (an inner reusable model) in another model (the outer model).
Both of these models are will be added to the same dynamic library.
First the model inner and outer models need to be defined:
std::vector<ADCGD>innerModel(const std::vector<ADCGD>& x) { std::vector<ADCGD>y(MInner);for (size_t i =0; i < x.size(); i++) { y[i] = x[i] * (i +2); }return y;}std::vector<ADCGD>outerModel(const std::vector<ADCGD>& x, atomic_base<CGD>& atomicfun) { std::vector<ADCGD>z(MOuter);for (size_t k =0; k <2; k++) { std::vector<ADCGD>y(MInner); std::vector<ADCGD>xInner(x.begin() + k, x.begin() + k + NInner);atomicfun(xInner, y);for (size_t i =0; i < y.size(); i++) { z[i + k * NInner] = y[i]; } } z[4] = x[1] * x[1]; z[5] = x[0] * x[2] +1;return z;}
As part of the process to generate the source code, anADFun needs to be generated for each of these models.
This involves:
- defining the independent variables
- calling the model
- creating an
ADFunand for the dependent variables provided by the models
std::unique_ptr<ADFun<CGD>>tapeInnerModel() { std::vector<ADCGD>ax(NInner);CppAD::Independent(ax); std::vector<ADCGD> ay =innerModel(ax); std::unique_ptr<ADFun<CGD>>funInner(new ADFun<CGD>()); funInner->Dependent(ay);return funInner;}std::unique_ptr<ADFun<CGD>>tapeOuterModel(CGAtomicFunBridge<double>& atomicFun) { std::vector<ADCGD>ax(NOuter);CppAD::Independent(ax); std::vector<ADCGD> az =outerModel(ax, atomicFun); std::unique_ptr<ADFun<CGD>>funOuter(new ADFun<CGD>()); funOuter->Dependent(az);return funOuter;}
Then, theseADFuns are used to create a dynamic library.
It is essential to configure the generation of source code for the Forward/Reverse modes for the inner model.
std::unique_ptr<ModelCSourceGen<double>>prepareInnerModelCompilation(ADFun<CGD>& funInner) {auto cSourceInner = std::make_unique<ModelCSourceGen<double>> (funInner,"my_inner_model"); cSourceInner->setCreateForwardZero(true); cSourceInner->setCreateForwardOne(true); cSourceInner->setCreateReverseOne(true); cSourceInner->setCreateReverseTwo(true);return cSourceInner;}std::unique_ptr<ModelCSourceGen<double>>prepareOuterModelCompilation(ADFun<CGD>& funOuter) {auto cSourceOuter = std::make_unique<ModelCSourceGen<double>>(funOuter,"my_outer_model"); cSourceOuter->setCreateForwardZero(true); cSourceOuter->setCreateSparseJacobian(true); cSourceOuter->setCreateSparseHessian(true);return cSourceOuter;}voidcompileLibrary() {auto funInner =tapeInnerModel(); CGAtomicFunBridge<double>atomicFun("my_inner_model", *funInner,true);auto funOuter =tapeOuterModel(atomicFun);auto cSourceInner =prepareInnerModelCompilation(*funInner);auto cSourceOuter =prepareOuterModelCompilation(*funOuter); ModelLibraryCSourceGen<double>libSourceGen(*cSourceInner, *cSourceOuter); GccCompiler<double> compiler;// the following options are used so that it is easier to debug generated sources compiler.setCompileFlags({"-O0","-g","-ggdb","-D_FORTIFY_SOURCE=2"}); compiler.setSaveToDiskFirst(true); DynamicModelLibraryProcessor<double>p(libSourceGen, LIBRARY_NAME);bool loadLib =false; p.createDynamicLibrary(compiler, loadLib);}
The dynamic library can now be used to compute derivatives.
Before the outer model can be called, the inner model must be configured as an atomic function by callingouterModel->addExternalModel().This is required since the atomic function could have been created in a different dynamic library.
voiduseLibrary() { LinuxDynamicLib<double>dynamicLib(LIBRARY_NAME_EXT); std::unique_ptr<GenericModel<double>> outerModel = dynamicLib.model("my_outer_model"); std::unique_ptr<GenericModel<double>> innerModel = dynamicLib.model("my_inner_model"); outerModel->addExternalModel(*innerModel); std::vector<double> xv{1.1,2.5,3.5}; std::vector<double> jac; std::vector<size_t> row, col; outerModel->SparseJacobian(xv, jac, row, col);// print out the resultfor (size_t i =0; i < jac.size(); ++i) std::cout <<"dz[" << row[i] <<"]/dx[" << col[i] <<"] =" << jac[i] <<";" << std::endl;}
The complete example is shown below:
#include<vector>#include<cppad/cg.hpp>usingnamespaceCppAD;usingnamespaceCppAD::cg;using CGD = CppAD::cg::CG<double>;using ADCGD = CppAD::AD<CGD>;constint MOuter =6;constint NOuter =3;constint MInner =2;constint NInner =2;const std::string LIBRARY_NAME ="./two_model_library";const std::string LIBRARY_NAME_EXT = LIBRARY_NAME + system::SystemInfo<>::DYNAMIC_LIB_EXTENSION;std::vector<ADCGD>innerModel(const std::vector<ADCGD>& x) { std::vector<ADCGD>y(MInner);for (size_t i =0; i < x.size(); i++) { y[i] = x[i] * (i +2); }return y;}std::vector<ADCGD>outerModel(const std::vector<ADCGD>& x, atomic_base<CGD>& atomicfun) { std::vector<ADCGD>z(MOuter);for (size_t k =0; k <2; k++) { std::vector<ADCGD>y(MInner); std::vector<ADCGD>xInner(x.begin() + k, x.begin() + k + NInner);atomicfun(xInner, y);for (size_t i =0; i < y.size(); i++) { z[i + k * NInner] = y[i]; } } z[4] = x[1] * x[1]; z[5] = x[0] * x[2] +1;return z;}std::unique_ptr<ADFun<CGD>>tapeInnerModel() { std::vector<ADCGD>ax(NInner);CppAD::Independent(ax); std::vector<ADCGD> ay =innerModel(ax); std::unique_ptr<ADFun<CGD>>funInner(new ADFun<CGD>()); funInner->Dependent(ay);return funInner;}std::unique_ptr<ADFun<CGD>>tapeOuterModel(CGAtomicFunBridge<double>& atomicFun) { std::vector<ADCGD>ax(NOuter);CppAD::Independent(ax); std::vector<ADCGD> az =outerModel(ax, atomicFun); std::unique_ptr<ADFun<CGD>>funOuter(new ADFun<CGD>()); funOuter->Dependent(az);return funOuter;}std::unique_ptr<ModelCSourceGen<double>>prepareInnerModelCompilation(ADFun<CGD>& funInner) {auto cSourceInner = std::make_unique<ModelCSourceGen<double>> (funInner,"my_inner_model"); cSourceInner->setCreateForwardZero(true); cSourceInner->setCreateForwardOne(true); cSourceInner->setCreateReverseOne(true); cSourceInner->setCreateReverseTwo(true);return cSourceInner;}std::unique_ptr<ModelCSourceGen<double>>prepareOuterModelCompilation(ADFun<CGD>& funOuter) {auto cSourceOuter = std::make_unique<ModelCSourceGen<double>>(funOuter,"my_outer_model"); cSourceOuter->setCreateForwardZero(true); cSourceOuter->setCreateSparseJacobian(true); cSourceOuter->setCreateSparseHessian(true);return cSourceOuter;}voidcompileLibrary() {auto funInner =tapeInnerModel(); CGAtomicFunBridge<double>atomicFun("my_inner_model", *funInner,true);auto funOuter =tapeOuterModel(atomicFun);auto cSourceInner =prepareInnerModelCompilation(*funInner);auto cSourceOuter =prepareOuterModelCompilation(*funOuter); ModelLibraryCSourceGen<double>libSourceGen(*cSourceInner, *cSourceOuter); GccCompiler<double> compiler;// the following options are used so that it is easier to debug generated sources compiler.setCompileFlags({"-O0","-g","-ggdb","-D_FORTIFY_SOURCE=2"}); compiler.setSaveToDiskFirst(true); DynamicModelLibraryProcessor<double>p(libSourceGen, LIBRARY_NAME);bool loadLib =false; p.createDynamicLibrary(compiler, loadLib);}voiduseLibrary() { LinuxDynamicLib<double>dynamicLib(LIBRARY_NAME_EXT); std::unique_ptr<GenericModel<double>> outerModel = dynamicLib.model("my_outer_model"); std::unique_ptr<GenericModel<double>> innerModel = dynamicLib.model("my_inner_model"); outerModel->addExternalModel(*innerModel); std::vector<double> xv{1.1,2.5,3.5}; std::vector<double> jac; std::vector<size_t> row, col; outerModel->SparseJacobian(xv, jac, row, col);// print out the resultfor (size_t i =0; i < jac.size(); ++i) std::cout <<"dz[" << row[i] <<"]/dx[" << col[i] <<"] =" << jac[i] <<";" << std::endl;}intmain() {if (!system::isFile(LIBRARY_NAME_EXT)) { std::cout <<"Creating a new library" << std::endl;compileLibrary(); }else { std::cout <<"Reusing existing library" << std::endl; }useLibrary();}