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Simple Checkpointing: Example and Test

Purpose
Break a large computation into pieces and only store values at the interface of the pieces. In actual applications, there may be many functions, but for this example there are only two. The functions $F : \B{R}^2 \rightarrow \B{R}^2$ and $G : \B{R}^2 \rightarrow \B{R}^2$ defined by $$F(y) = \left( \begin{array}{c} y_0 + y_0 + y_0 \\ y_1 + y_1 + y_1 \end{array} \right) \; , \; G(x) = \left( \begin{array}{c} x_0 \cdot x_0 \cdot x_0 \\ x_1 \cdot x_1 \cdot x_1 \end{array} \right)$$  # include <cppad/cppad.hpp> namespace { using CppAD::AD; typedef CPPAD_TESTVECTOR(AD<double>) ADVector; typedef CppAD::atomic_base<double>::option_enum option_enum; void f_algo(const ADVector& y, ADVector& z) { z[0] = 0.0; z[1] = 0.0; for(size_t k = 0; k < 3; k++) { z[0] += y[0]; z[1] += y[1]; } return; } void g_algo(const ADVector& x, ADVector& y) { y[0] = 1.0; y[1] = 1.0; for(size_t k = 0; k < 3; k++) { y[0] *= x[0]; y[1] *= x[1]; } return; } bool test_case( option_enum f_sparsity, option_enum g_sparsity, bool optimize ) { bool ok = true; using CppAD::checkpoint; using CppAD::ADFun; using CppAD::NearEqual; size_t i, j, k, n = 2, m = n; double eps = 10. * std::numeric_limits<double>::epsilon(); // checkpoint version of the function F(x) ADVector ax(n), ay(n), az(m); for(j = 0; j < n; j++) ax[j] = double(j + 1); // could also use bool_sparsity_enum or set_sparsity_enum checkpoint<double> atom_f("atom_f", f_algo, ax, ay, f_sparsity); checkpoint<double> atom_g("atom_g", g_algo, ay, az, g_sparsity); // Record a version of z = g[f(x)] without checkpointing Independent(ax); f_algo(ax, ay); g_algo(ay, az); ADFun<double> check_not(ax, az); // Record a version of z = g[f(x)] with checkpointing Independent(ax); atom_f(ax, ay); atom_g(ay, az); ADFun<double> check_yes(ax, az); // checkpointing should use fewer operations ok &= check_yes.size_var() < check_not.size_var(); // this does not really save space because f and g are only used once ok &= check_not.size_var() <= check_yes.size_var() + atom_f.size_var() + atom_g.size_var(); // compare forward mode results for orders 0, 1, 2 size_t q = 2; CPPAD_TESTVECTOR(double) x_q(n*(q+1)), z_not(m*(q+1)), z_yes(m*(q+1)); for(j = 0; j < n; j++) { for(k = 0; k <= q; k++) x_q[ j * (q+1) + k ] = 1.0 / double(q + 1 - k); } z_not = check_not.Forward(q, x_q); z_yes = check_yes.Forward(q, x_q); for(i = 0; i < m; i++) { for(k = 0; k <= q; k++) { double zik_not = z_not[ i * (q+1) + k]; double zik_yes = z_yes[ i * (q+1) + k]; ok &= NearEqual(zik_not, zik_yes, eps, eps); } } // compare reverse mode results CPPAD_TESTVECTOR(double) w(m*(q+1)), dw_not(n*(q+1)), dw_yes(n*(q+1)); for(i = 0; i < m * (q + 1); i++) w[i] = 1.0 / double(i + 1); dw_not = check_not.Reverse(q+1, w); dw_yes = check_yes.Reverse(q+1, w); for(j = 0; j < n; j++) { for(k = 0; k <= q; k++) { double dwjk_not = dw_not[ j * (q+1) + k]; double dwjk_yes = dw_yes[ j * (q+1) + k]; ok &= NearEqual(dwjk_not, dwjk_yes, eps, eps); } } // compare forward mode Jacobian sparsity patterns CppAD::vector< std::set<size_t> > r(n), s_not(m), s_yes(m); for(j = 0; j < n; j++) r[j].insert(j); s_not = check_not.ForSparseJac(n, r); s_yes = check_yes.ForSparseJac(n, r); for(i = 0; i < m; i++) ok &= s_not[i] == s_yes[i]; // compare reverse mode Jacobian sparsity patterns CppAD::vector< std::set<size_t> > s(m), r_not(m), r_yes(m); for(i = 0; i < m; i++) s[i].insert(i); r_not = check_not.RevSparseJac(m, s); r_yes = check_yes.RevSparseJac(m, s); for(i = 0; i < m; i++) ok &= r_not[i] == r_yes[i]; // compare reverse mode Hessian sparsity patterns CppAD::vector< std::set<size_t> > s_one(1), h_not(n), h_yes(n); for(i = 0; i < m; i++) s_one[0].insert(i); h_not = check_not.RevSparseHes(n, s_one); h_yes = check_yes.RevSparseHes(n, s_one); for(i = 0; i < n; i++) ok &= h_not[i] == h_yes[i]; return ok; } } bool checkpoint(void) { bool ok = true; // different types of sparsity option_enum pack_sparsity = CppAD::atomic_base<double>::pack_sparsity_enum; option_enum bool_sparsity = CppAD::atomic_base<double>::bool_sparsity_enum; option_enum set_sparsity = CppAD::atomic_base<double>::set_sparsity_enum; // test some different cases ok &= test_case(pack_sparsity, pack_sparsity, true); ok &= test_case(pack_sparsity, bool_sparsity, false); ok &= test_case(bool_sparsity, set_sparsity, true); ok &= test_case(set_sparsity, set_sparsity, false); return ok; } 
Input File: example/atomic/checkpoint.cpp