diff --git a/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp b/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp index b41a54e0320..beeeff4c3ac 100644 --- a/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp +++ b/stan/math/mix/functor/finite_diff_grad_hessian_auto.hpp @@ -58,7 +58,7 @@ inline void finite_diff_grad_hessian_auto( for (int i = 0; i < d; ++i) { double dummy_fx_eval; - double epsilon = finite_diff_stepsize(x(i)); + double epsilon = finite_diff_stepsize<2>(x(i)); hess_diff.setZero(); x_temp(i) = x(i) + 2 * epsilon; diff --git a/stan/math/mix/functor/laplace_base_rng.hpp b/stan/math/mix/functor/laplace_base_rng.hpp index 1923de477c2..db14a894d94 100644 --- a/stan/math/mix/functor/laplace_base_rng.hpp +++ b/stan/math/mix/functor/laplace_base_rng.hpp @@ -38,12 +38,13 @@ inline Eigen::VectorXd laplace_base_rng( LLFunc&& ll_fun, LLArgs&& ll_args, CovarFun&& covariance_function, CovarArgs&& covar_args, const laplace_options& options, RNG& rng, std::ostream* msgs) { + Eigen::MatrixXd covariance_train = stan::math::apply( + [msgs, &covariance_function](auto&&... args) { + return covariance_function(std::forward(args)..., msgs); + }, + std::forward(covar_args)); auto md_est = internal::laplace_marginal_density_est( - ll_fun, std::forward(ll_args), - std::forward(covariance_function), - to_ref(std::forward(covar_args)), options, msgs); - // Modified R&W method - auto&& covariance_train = md_est.covariance; + ll_fun, std::forward(ll_args), covariance_train, options, msgs); Eigen::VectorXd mean_train = covariance_train * md_est.theta_grad; if (options.solver == 1 || options.solver == 2) { Eigen::MatrixXd V_dec diff --git a/stan/math/mix/functor/laplace_likelihood.hpp b/stan/math/mix/functor/laplace_likelihood.hpp index b044112bd52..0fd8b7d1c70 100644 --- a/stan/math/mix/functor/laplace_likelihood.hpp +++ b/stan/math/mix/functor/laplace_likelihood.hpp @@ -8,11 +8,49 @@ namespace stan { namespace math { +namespace internal { +/** + * Set all adjoints of the output to zero. + */ +template +inline void set_zero_adjoint(Output&& output) { + if constexpr (is_all_arithmetic_scalar_v) { + return; + } else { + return iter_tuple_nested( + [](auto&& output_i) { + using output_i_t = std::decay_t; + if constexpr (is_all_arithmetic_scalar_v) { + return; + } else if constexpr (is_std_vector::value) { + for (Eigen::Index i = 0; i < output_i.size(); ++i) { + output_i[i].adj() = 0; + } + } else if constexpr (is_eigen_v) { + output_i.adj().setZero(); + } else if constexpr (is_stan_scalar_v) { + output_i.adj() = 0; + } else { + static_assert( + sizeof(std::decay_t*) == 0, + "INTERNAL ERROR:(laplace_marginal_lpdf) set_zero_adjoints was " + "not able to deduce the actions needed for the given type. " + "This is an internal error, please report it: " + "https://github.com/stan-dev/math/issues"); + } + }, + std::forward(output)); + } +} + +} // namespace internal + /** * functions to compute the log density, first, second, * and third-order derivatives for a likelihoood specified by the user. */ namespace laplace_likelihood { + namespace internal { /** * @tparam F A functor with `opertor()(Args&&...)` returning a scalar @@ -106,6 +144,126 @@ inline auto shallow_copy_vargs(Args&&... args) { std::forward(args)...); } +/** + * Computes theta gradient `f` wrt `theta` and `args...` + * @note If `Args` contains \ref var types then their adjoints will be + * calculated as a side effect. + * @tparam F A functor with `opertor()(Args&&...)` returning a scalar + * @tparam Theta A class assignable to an Eigen vector type + * @tparam Stream Type of stream for messages. + * @tparam Args Type of variadic arguments. + * @param f Log likelihood function. + * @param theta Latent Gaussian model. + * @param msgs Stream for messages. + * @param args Variadic arguments for the likelihood function. + */ +template * = nullptr> +inline auto theta_grad(F&& f, Theta&& theta, Stream* msgs, Args&&... args) { + using Eigen::Dynamic; + using Eigen::Matrix; + nested_rev_autodiff nested; + Matrix theta_var = theta; + var f_var = f(theta_var, args..., msgs); + grad(f_var.vi_); + return theta_var.adj().eval(); +} + +/** + * Computes likelihood argument gradient of `f` + * @note If `Args` contains \ref var types then their adjoints will be + * calculated as a side effect. + * @tparam F A functor with `opertor()(Args&&...)` returning a scalar + * @tparam Theta A class assignable to an Eigen vector type + * @tparam Stream Type of stream for messages. + * @tparam Args Type of variadic arguments. + * @param f Log likelihood function. + * @param theta Latent Gaussian model. + * @param msgs Stream for messages. + * @param args Variadic arguments for the likelihood function. + */ +template * = nullptr> +inline void ll_arg_grad(F&& f, Theta&& theta, Stream* msgs, Args&&... args) { + using Eigen::Dynamic; + using Eigen::Matrix; + nested_rev_autodiff nested; + var f_var = f(theta, args..., msgs); + grad(f_var.vi_); +} + +/** + * Computes negative block diagonal Hessian of `f` wrt`theta` and `args...` + * @note If `Args` contains \ref var types then their adjoints will be + * calculated as a side effect. + * @tparam F A functor with `opertor()(Args&&...)` returning a scalar + * @tparam Theta A class assignable to an Eigen vector type + * @tparam Stream Type of stream for messages. + * @tparam Args Type of variadic arguments. + * @param f Log likelihood function. + * @param theta Latent Gaussian model. + * @param hessian_block_size If the Hessian of the log likelihood function w.r.t + * the latent Gaussian variable is block-diagonal, + * size of each block. + * @param msgs Stream for messages. + * @param args Variadic arguments for the likelihood function. + */ +template * = nullptr> +inline auto diagonal_hessian(F&& f, Theta&& theta, Stream* msgs, + Args&&... args) { + using Eigen::Dynamic; + using Eigen::Matrix; + const Eigen::Index theta_size = theta.size(); + auto v = Eigen::VectorXd::Ones(theta_size); + Eigen::VectorXd hessian_v = Eigen::VectorXd::Zero(theta_size); + hessian_times_vector(f, hessian_v, std::forward(theta), std::move(v), + value_of(args)..., msgs); + return (-hessian_v).eval(); +} + +/** + * Computes negative block diagonal Hessian of `f` wrt`theta` and `args...` + * @note If `Args` contains \ref var types then their adjoints will be + * calculated as a side effect. + * @tparam F A functor with `opertor()(Args&&...)` returning a scalar + * @tparam Theta A class assignable to an Eigen vector type + * @tparam Stream Type of stream for messages. + * @tparam Args Type of variadic arguments. + * @param f Log likelihood function. + * @param theta Latent Gaussian model. + * @param hessian_block_size If the Hessian of the log likelihood function w.r.t + * the latent Gaussian variable is block-diagonal, + * size of each block. + * @param msgs Stream for messages. + * @param args Variadic arguments for the likelihood function. + */ +template * = nullptr> +inline auto block_hessian(F&& f, Theta&& theta, + const Eigen::Index hessian_block_size, Stream* msgs, + Args&&... args) { + using Eigen::Dynamic; + using Eigen::Matrix; + const Eigen::Index theta_size = theta.size(); + if (hessian_block_size == 1) { + auto v = Eigen::VectorXd::Ones(theta_size); + Eigen::VectorXd hessian_v = Eigen::VectorXd::Zero(theta_size); + hessian_times_vector(f, hessian_v, std::forward(theta), std::move(v), + value_of(args)..., msgs); + Eigen::SparseMatrix hessian_theta(theta_size, theta_size); + hessian_theta.reserve(Eigen::VectorXi::Constant(theta_size, 1)); + for (Eigen::Index i = 0; i < theta_size; i++) { + hessian_theta.insert(i, i) = hessian_v(i); + } + return (-hessian_theta).eval(); + } else { + return (-hessian_block_diag(f, std::forward(theta), + hessian_block_size, value_of(args)..., msgs)) + .eval(); + } +} + /** * Computes theta gradient and negative block diagonal Hessian of `f` wrt * `theta` and `args...` @@ -301,6 +459,79 @@ inline auto diff_eta_implicit(F&& f, V_t&& v, Theta&& theta, Stream* msgs, } // namespace internal +/** + * A wrapper that accepts a tuple as arguments. + * @tparam F A functor with `opertor()(Args&&...)` returning a scalar + * @tparam Theta A class assignable to an Eigen vector type + * @tparam TupleArgs Type of arguments for covariance function. + * @tparam Stream Type of stream for messages. + * @param f Log likelihood function. + * @param theta Latent Gaussian model. + * @param ll_tup Arguments for likelihood function + * @param msgs stream messages. + */ +template * = nullptr, + require_tuple_t* = nullptr> +inline auto theta_grad(F&& f, Theta&& theta, TupleArgs&& ll_tup, + Stream* msgs = nullptr) { + return apply( + [](auto&& f, auto&& theta, auto&& msgs, auto&&... args) { + return internal::theta_grad(std::forward(f), + std::forward(theta), msgs, + std::forward(args)...); + }, + std::forward(ll_tup), std::forward(f), + std::forward(theta), msgs); +} + +template * = nullptr, + require_tuple_t* = nullptr> +inline auto ll_arg_grad(F&& f, Theta&& theta, TupleArgs&& ll_tup, + Stream* msgs = nullptr) { + return apply( + [](auto&& f, auto&& theta, auto&& msgs, auto&&... args) { + return internal::ll_arg_grad(std::forward(f), + std::forward(theta), msgs, + std::forward(args)...); + }, + std::forward(ll_tup), std::forward(f), + std::forward(theta), msgs); +} + +template * = nullptr, + require_tuple_t* = nullptr> +inline auto diagonal_hessian(F&& f, Theta&& theta, TupleArgs&& ll_tuple, + Stream* msgs) { + return apply( + [](auto&& f, auto&& theta, auto* msgs, auto&&... args) { + return internal::diagonal_hessian( + std::forward(f), std::forward(theta), + msgs, std::forward(args)...); + }, + std::forward(ll_tuple), std::forward(f), + std::forward(theta), msgs); +} + +template * = nullptr, + require_tuple_t* = nullptr> +inline auto block_hessian(F&& f, Theta&& theta, + const Eigen::Index hessian_block_size, + TupleArgs&& ll_tuple, Stream* msgs) { + return apply( + [](auto&& f, auto&& theta, auto hessian_block_size, auto* msgs, + auto&&... args) { + return internal::block_hessian( + std::forward(f), std::forward(theta), + hessian_block_size, msgs, std::forward(args)...); + }, + std::forward(ll_tuple), std::forward(f), + std::forward(theta), hessian_block_size, msgs); +} + /** * A wrapper that accepts a tuple as arguments. * @tparam F A functor with `opertor()(Args&&...)` returning a scalar diff --git a/stan/math/mix/functor/laplace_marginal_density.hpp b/stan/math/mix/functor/laplace_marginal_density.hpp index 3ceb6a403ab..325f469a593 100644 --- a/stan/math/mix/functor/laplace_marginal_density.hpp +++ b/stan/math/mix/functor/laplace_marginal_density.hpp @@ -1,7 +1,9 @@ + #ifndef STAN_MATH_MIX_FUNCTOR_LAPLACE_MARGINAL_DENSITY_HPP #define STAN_MATH_MIX_FUNCTOR_LAPLACE_MARGINAL_DENSITY_HPP #include #include +#include #include #include #include @@ -12,7 +14,6 @@ #include #include #include -#include /** * @file @@ -38,13 +39,14 @@ struct laplace_options_base { * using an LU decomposition (more general, but slower) */ int solver{1}; - /* Maximum number of steps in line search */ - int max_steps_line_search{0}; - /* iterations end when difference in objective function is less than tolerance + /** + * iterations end when difference in objective function is less than tolerance + * Default is sqrt(machine_epsilon) */ - double tolerance{1e-6}; + double tolerance{1.49012e-08}; /* Maximum number of steps*/ - int max_num_steps{100}; + int max_num_steps{500}; + laplace_line_search_options line_search; }; template @@ -63,13 +65,11 @@ using laplace_options_default = laplace_options; using laplace_options_user_supplied = laplace_options; namespace internal { -template +template struct laplace_density_estimates { /* log marginal density */ double lmd{std::numeric_limits::infinity()}; - /* Evaluated covariance function for the latent gaussian variable */ - Covar covariance; /* ThetaVec at the mode */ ThetaVec theta; /* negative hessian or sqrt of negative hessian */ @@ -84,19 +84,19 @@ struct laplace_density_estimates { LU_t LU; /* Cholesky of the covariance matrix */ KRoot K_root; - laplace_density_estimates(double lmd_, Covar&& covariance_, ThetaVec&& theta_, - WR&& W_r_, L_t&& L_, A_vec&& a_, - ThetaGrad&& theta_grad_, LU_t&& LU_, - KRoot&& K_root_) + int solver_used{1}; + laplace_density_estimates(double lmd_, ThetaVec&& theta_, WR&& W_r_, L_t&& L_, + A_vec&& a_, ThetaGrad&& theta_grad_, LU_t&& LU_, + KRoot&& K_root_, int solver_used_) : lmd(lmd_), - covariance(std::move(covariance_)), theta(std::move(theta_)), W_r(std::move(W_r_)), L(std::move(L_)), a(std::move(a_)), theta_grad(std::move(theta_grad_)), LU(std::move(LU_)), - K_root(std::move(K_root_)) {} + K_root(std::move(K_root_)), + solver_used(solver_used_) {} }; /** @@ -238,106 +238,6 @@ inline void block_matrix_chol_L(WRootMat& W_root, } } -/** - * @brief Performs a simple line search - * - * @tparam AVec Type of the parameter update vector (`a`), e.g. - * Eigen::VectorXd. - * @tparam APrev Type of the previous parameter vector (`a_prev`), same shape - * as AVec. - * @tparam ThetaVec Type of the transformed vector (`theta`), e.g. Σ·a. - * @tparam LLFun Functor type for computing the log‐likelihood. - * @tparam LLArgs Tuple or pack type forwarded to `ll_fun`. - * @tparam Covar Matrix type for the covariance Σ, e.g. Eigen::MatrixXd. - * @tparam Msgs Diagnostics container type for capturing warnings/errors. - * - * @param[in,out] objective_new On entry: objective at the full‐step `a` (must - * satisfy objective_new < objective_old). On exit: best objective found. - * @param[in,out] a On entry: candidate parameter vector. On exit: updated to - * the step achieving the lowest objective. - * @param[in,out] theta On entry: Σ·a for the initial candidate. On exit: Σ·a - * for the accepted best step. - * @param[in,out] a_prev On entry: previous parameter vector, with objective - * `objective_old`. On exit: rolled forward to each newly accepted step. - * @param[in] ll_fun Callable that computes the log‐likelihood given `(theta, - * ll_args, msgs)`. - * @param[in] ll_args Arguments forwarded to `ll_fun` at each evaluation. - * @param[in] covariance Covariance matrix Σ used to compute `theta = Σ·a`. - * @param[in] max_steps_line_search Maximum number of iterations. - * @param[in] objective_old Objective value at the initial `a_prev` (used as f₀ - * for the first pass). - * @param[in] tolerance Minimum tolerance to accept a step - * @param[in,out] msgs Pointer to a diagnostics container; may be used by - * `ll_fun` to record warnings. - */ -template -inline void line_search(double& objective_new, AVec& a, ThetaVec& theta, - APrev& a_prev, LLFun&& ll_fun, LLArgs&& ll_args, - Covar&& covariance, const int max_steps_line_search, - const double objective_old, double tolerance, - Msgs* msgs) { - Eigen::VectorXd a_tmp(a.size()); - double objective_new_tmp = 0.0; - double objective_old_tmp = objective_old; - Eigen::VectorXd theta_tmp(covariance.rows()); - for (int j = 0; - j < max_steps_line_search && (objective_new < objective_old_tmp); ++j) { - a_tmp.noalias() = a_prev + 0.5 * (a - a_prev); - theta_tmp.noalias() = covariance * a_tmp; - if (!theta_tmp.allFinite()) { - break; - } else { - objective_new_tmp = -0.5 * a_tmp.dot(theta_tmp) - + laplace_likelihood::log_likelihood( - ll_fun, theta_tmp, ll_args, msgs); - if (objective_new_tmp < objective_new) { - a_prev.swap(a); - a.swap(a_tmp); - theta.swap(theta_tmp); - objective_old_tmp = objective_new; - objective_new = objective_new_tmp; - } else { - break; - } - } - } -} - -/** - * Set all adjoints of the output to zero. - */ -template -inline void set_zero_adjoint(Output&& output) { - if constexpr (is_all_arithmetic_scalar_v) { - return; - } else { - return iter_tuple_nested( - [](auto&& output_i) { - using output_i_t = std::decay_t; - if constexpr (is_all_arithmetic_scalar_v) { - return; - } else if constexpr (is_std_vector::value) { - for (Eigen::Index i = 0; i < output_i.size(); ++i) { - output_i[i].adj() = 0; - } - } else if constexpr (is_eigen_v) { - output_i.adj().setZero(); - } else if constexpr (is_stan_scalar_v) { - output_i.adj() = 0; - } else { - static_assert( - sizeof(std::decay_t*) == 0, - "INTERNAL ERROR:(laplace_marginal_lpdf) set_zero_adjoints was " - "not able to deduce the actions needed for the given type. " - "This is an internal error, please report it: " - "https://github.com/stan-dev/math/issues"); - } - }, - std::forward(output)); - } -} - /** * Collect the adjoints from the input and add them to the output. * @tparam ZeroInput If true, the adjoints of the input will be set to zero @@ -398,13 +298,13 @@ inline STAN_COLD_PATH void throw_nan(NameStr&& name_str, ParamStr&& param_str, Param&& param) { std::string msg = std::string("Error in ") + name_str + ": " + std::string(param_str) + " contains NaN values"; - if ((Eigen::isnan(param.array()) || Eigen::isinf(param.array())).all()) { + if ((param.array().isNaN() || !param.array().isFinite()).all()) { msg += " for all values."; throw std::domain_error(msg); } msg += " at indices ["; for (int i = 0; i < param.size(); ++i) { - if (std::isnan(param(i) || std::isinf(param(i)))) { + if (std::isnan(param(i)) || std::isinf(param(i))) { msg += std::to_string(i) + ", "; } } @@ -414,6 +314,120 @@ inline STAN_COLD_PATH void throw_nan(NameStr&& name_str, ParamStr&& param_str, throw std::domain_error(msg); } +/** + * @brief Curvature-aware Barzilai–Borwein (BB) step length with robust + * safeguards. + * + * Given successive parameter displacements \f$s = x_k - x_{k-1}\f$ and + * gradients \f$g_k\f$, \f$g_{k-1}\f$, this routine forms + * \f$y = g_k - g_{k-1}\f$ and computes the two classical BB candidates + * + * \f{align*}{ + * \alpha_{\text{BB1}} &= \frac{\langle s,s\rangle}{\langle s,y\rangle},\\ + * \alpha_{\text{BB2}} &= \frac{\langle s,y\rangle}{\langle y,y\rangle}, + * \f} + * + * then chooses between them using the **spectral cosine** + * \f$r = \cos^2\!\angle(s,y) = \dfrac{\langle s,y\rangle^2} + * {\langle s,s\rangle\,\langle + * y,y\rangle}\in[0,1]\f$: + * + * - if \f$r > 0.9\f$ (well-aligned curvature) and the previous line search + * did **≤ 1** backtrack, prefer the “long” step \f$\alpha_{\text{BB1}}\f$; + * - if \f$0.1 \le r \le 0.9\f$, take the neutral geometric mean + * \f$\sqrt{\alpha_{\text{BB1}}\alpha_{\text{BB2}}}\f$; + * - otherwise default to the “short” step \f$\alpha_{\text{BB2}}\f$. + * + * All candidates are clamped into \f$[\text{min\_alpha},\,\text{max\_alpha}]\f$ + * and must be finite and positive. + * If the curvature scalars are ill-posed (non-finite or too small), + * \f$\langle s,y\rangle \le \varepsilon\f$, or if `last_backtracks == 99` + * (explicitly disabling BB for this iteration), the function falls back to a + * **safe** step: + * use `prev_step` when finite and positive, otherwise \f$1.0\f$, then clamp to + * \f$[\text{min\_alpha},\,\text{max\_alpha}]\f$. + * + * @param s Displacement between consecutive iterates + * (\f$s = x_k - x_{k-1}\f$). + * @param g_curr Gradient at the current iterate \f$g_k\f$. + * @param g_prev Gradient at the previous iterate \f$g_{k-1}\f$. + * @param prev_step Previously accepted step length (used by the fallback). + * @param last_backtracks + * Number of backtracking contractions performed by the most + * recent line search; set to 99 to force the safe fallback. + * @param min_alpha Lower bound for the returned step length. + * @param max_alpha Upper bound for the returned step length. + * + * @return A finite, positive BB-style step length \f$\alpha \in + * [\text{min\_alpha},\,\text{max\_alpha}]\f$ suitable for seeding a + * line search or as a spectral preconditioner scale. + * + * @note Uses \f$\varepsilon=10^{-16}\f$ to guard against division by very + * small curvature terms, and applies `std::abs` to BB ratios to avoid + * negative steps; descent is enforced by the line search. + * @warning The vectors must have identical size. Non-finite inputs yield the + * safe fallback. + */ +inline double barzilai_borwein_step_size(const Eigen::VectorXd& s, + const Eigen::VectorXd& g_curr, + const Eigen::VectorXd& g_prev, + double prev_step, int last_backtracks, + double min_alpha, double max_alpha) { + // Fallbacks + auto safe_fallback = [&]() -> double { + double a = std::clamp( + prev_step > 0.0 && std::isfinite(prev_step) ? prev_step : 1.0, + min_alpha, max_alpha); + return a; + }; + + const Eigen::VectorXd y = g_curr - g_prev; + const double sty = s.dot(y); + const double sts = s.squaredNorm(); + const double yty = y.squaredNorm(); + + // Basic validity checks + constexpr double eps = 1e-16; + if (!(std::isfinite(sty) && std::isfinite(sts) && std::isfinite(yty)) + || sts <= eps || yty <= eps || sty <= eps || last_backtracks == 99) { + return safe_fallback(); + } + + // BB candidates + double alpha_bb1 = std::clamp(std::abs(sts / sty), min_alpha, max_alpha); + double alpha_bb2 = std::clamp(std::abs(sty / yty), min_alpha, max_alpha); + + // Safeguard candidates + if (!std::isfinite(alpha_bb1) || !std::isfinite(alpha_bb2) || alpha_bb1 <= 0.0 + || alpha_bb2 <= 0.0) { + return safe_fallback(); + } + + // Spectral cosine r = cos^2(angle(s, y)) in [0,1] + const double r = (sty * sty) / (sts * yty); + + // Heuristic thresholds (robust defaults) + constexpr double kLoose = 0.9; // "nice" curvature + constexpr double kTight = 0.1; // "dodgy" curvature + + double alpha0 = alpha_bb2; // default to short BB for robustness + if (r > kLoose && last_backtracks <= 1) { + // Spectrum looks friendly and line search was not harsh -> try long BB + alpha0 = alpha_bb1; + } else if (r >= kTight && r <= kLoose) { + // Neither clearly friendly nor clearly dodgy -> neutral middle + alpha0 = std::sqrt(alpha_bb1 * alpha_bb2); + } // else keep alpha_bb2 + + // Clip to user bounds + alpha0 = std::clamp(alpha0, min_alpha, max_alpha); + + if (!std::isfinite(alpha0) || alpha0 <= 0.0) { + return safe_fallback(); + } + return alpha0; +} + /** * For a latent Gaussian model with hyperparameters phi and * latent variables theta, and observations y, this function computes @@ -446,6 +460,7 @@ inline STAN_COLD_PATH void throw_nan(NameStr&& name_str, ParamStr&& param_str, * \laplace_common_template_args * @param[in] ll_fun A log likelihood functor * @param[in] ll_args Tuple containing parameters for `LLFun` + * @param[in] covariance The covariance matrix for the latent Gaussian * \laplace_common_args * @param[in] options A set of options for tuning the solver * \msg_arg @@ -462,16 +477,12 @@ inline STAN_COLD_PATH void throw_nan(NameStr&& name_str, ParamStr&& param_str, * 7. l_grad the log density of the likelihood, evaluated at the mode * */ -template >* = nullptr> +template >* = nullptr> inline auto laplace_marginal_density_est( - LLFun&& ll_fun, LLTupleArgs&& ll_args, CovarFun&& covariance_function, - CovarArgs&& covar_args, const laplace_options& options, - std::ostream* msgs) { - using Eigen::MatrixXd; - using Eigen::SparseMatrix; - using Eigen::VectorXd; + LLFun&& ll_fun, LLTupleArgs&& ll_args, CovarMat&& covariance, + const laplace_options& options, std::ostream* msgs) { if constexpr (InitTheta) { check_nonzero_size("laplace_marginal", "initial guess", options.theta_0); check_finite("laplace_marginal", "initial guess", options.theta_0); @@ -480,14 +491,6 @@ inline auto laplace_marginal_density_est( check_positive("laplace_marginal", "max_num_steps", options.max_num_steps); check_positive("laplace_marginal", "hessian_block_size", options.hessian_block_size); - check_nonnegative("laplace_marginal", "max_steps_line_search", - options.max_steps_line_search); - - Eigen::MatrixXd covariance = stan::math::apply( - [msgs, &covariance_function](auto&&... args) { - return covariance_function(args..., msgs); - }, - covar_args); check_square("laplace_marginal", "covariance", covariance); const Eigen::Index theta_size = covariance.rows(); @@ -511,6 +514,23 @@ inline auto laplace_marginal_density_est( msg << "]."; throw std::domain_error(msg.str()); }(); + } else if (unlikely(theta_size < options.hessian_block_size)) { + [&]() STAN_COLD_PATH { + std::stringstream msg; + msg << "laplace_marginal_density: The hessian size (" << theta_size + << ", " << theta_size << ") is smaller than the hessian block size (" + << options.hessian_block_size + << "). Try a hessian block size such as [1, "; + for (int i = 2; i < theta_size; ++i) { + if (theta_size % i == 0) { + msg << i << ", "; + } + } + msg.str().pop_back(); + msg.str().pop_back(); + msg << "]."; + throw std::domain_error(msg.str()); + }(); } auto throw_overstep = [](const auto max_num_steps) STAN_COLD_PATH { @@ -518,245 +538,380 @@ inline auto laplace_marginal_density_est( std::string("laplace_marginal_density: max number of iterations: ") + std::to_string(max_num_steps) + " exceeded."); }; - auto ll_args_vals = value_of(ll_args); - Eigen::VectorXd theta = [theta_size, &options]() { - if constexpr (InitTheta) { - return options.theta_0; - } else { - return Eigen::VectorXd::Zero(theta_size); - } - }(); - double objective_old = std::numeric_limits::lowest(); - double objective_new = std::numeric_limits::lowest() + 1; - Eigen::VectorXd a_prev = Eigen::VectorXd::Zero(theta_size); + // Wolfe optimizes over the latent 'a' space + auto obj_fun = [&](const Eigen::VectorXd& a_val, auto&& theta_val) -> double { + return -0.5 * a_val.dot(theta_val) + + laplace_likelihood::log_likelihood(ll_fun, theta_val, ll_args, + msgs); + }; + auto theta_grad_f = [&ll_fun, &ll_args, &msgs](auto&& theta_val) { + return laplace_likelihood::theta_grad(ll_fun, theta_val, ll_args, msgs); + }; + internal::WolfeInfo wolfe_info( + obj_fun, theta_size, + [theta_size, &options]() -> decltype(auto) { + if constexpr (InitTheta) { + return options.theta_0; + } else { + return Eigen::VectorXd::Zero(theta_size); + } + }(), + theta_grad_f); + auto&& curr = wolfe_info.curr_; + auto&& prev = wolfe_info.prev_; Eigen::MatrixXd B(theta_size, theta_size); - Eigen::VectorXd a(theta_size); Eigen::VectorXd b(theta_size); - if (options.solver == 1) { - if (options.hessian_block_size == 1) { - for (Eigen::Index i = 0; i <= options.max_num_steps; i++) { - auto [theta_grad, W] = laplace_likelihood::diff( - ll_fun, theta, options.hessian_block_size, ll_args, msgs); - Eigen::VectorXd W_r(W.rows()); - // Compute matrix square-root of W. If all elements of W are positive, - // do an element wise square-root. Else try a matrix square-root - for (Eigen::Index i = 0; i < W.rows(); i++) { - if (W.coeff(i, i) < 0) { - throw std::domain_error( - "laplace_marginal_density: Hessian matrix is not positive " - "definite"); + // 'a' gradient + auto grad_fun = [&covariance](auto&& step) { + return -covariance * step.a() + covariance * step.theta_grad(); + }; + auto update_step = [&covariance, &obj_fun, &theta_grad_f, &grad_fun]( + auto& step_info, auto&& /* curr */, auto&& prev, + auto& eval_in, auto&& p) { + step_info.a() = prev.a() + eval_in.alpha() * p; + step_info.theta().noalias() = covariance * step_info.a(); + step_info.theta_grad() = theta_grad_f(step_info.theta()); + eval_in.obj() = obj_fun(step_info.a(), step_info.theta()); + eval_in.dir() = grad_fun(step_info).dot(p); + }; + Eigen::VectorXd prev_g(theta_size); + auto update_line_search = [&grad_fun, &covariance, &prev_g, &update_step, + &theta_grad_f, &options, + &msgs](auto&& wolfe_status, auto&& wolfe_info, + auto&& curr, auto&& prev) { + wolfe_info.p_ = curr.a() - prev.a(); + prev_g.noalias() = grad_fun(prev); + wolfe_info.init_dir_ = prev_g.dot(wolfe_info.p_); + // Flip direction if not ascending + if (wolfe_info.init_dir_ < 0) { + wolfe_info.p_ = -wolfe_info.p_; + wolfe_info.init_dir_ = -wolfe_info.init_dir_; + } + auto scratch = wolfe_info.scratch_; + scratch.alpha() = 1.0; + while (scratch.alpha() > options.line_search.min_alpha) { + try { + update_step(scratch, curr, prev, scratch.eval_, wolfe_info.p_); + if (std::isnan(scratch.eval_.obj()) || std::isinf(scratch.eval_.obj()) + || std::isnan(scratch.eval_.dir()) + || std::isinf(scratch.eval_.dir())) { + scratch.alpha() *= options.line_search.tau; + continue; + } + } catch (const std::exception& e) { + scratch.alpha() *= options.line_search.tau; + continue; + } + break; + } + if (scratch.alpha() <= options.line_search.min_alpha) { + wolfe_status.success_ = false; + return true; + } + if (options.line_search.max_iterations == 0) { + if (scratch.alpha() > options.line_search.min_alpha) { + curr.update(scratch); + wolfe_status.success_ = true; + return false; + } + } else { + curr.alpha() = barzilai_borwein_step_size( + wolfe_info.p_, grad_fun(scratch), prev_g, prev.alpha(), + wolfe_status.num_backtracks_, options.line_search.min_alpha, + options.line_search.max_alpha); + wolfe_status = internal::wolfe_line_search(wolfe_info, update_step, + options.line_search, msgs); + } + return abs(curr.obj() - prev.obj()) < options.tolerance + || (!wolfe_status.success_ && curr.obj() <= prev.obj()); + }; + auto set_next_iter = [&options](auto&& curr, auto&& prev) { + prev.update(curr); + curr.alpha() = std::clamp(curr.alpha(), 0.0, options.line_search.max_alpha); + }; + /** + * On the final loop if we found a better wolfe step, but we are going to + * exit, we want to make sure all of our return values are with the most + * recent wolfe step that was accepted. So we do one final loop to update + * our return values. + */ + bool allow_bounce = false; + bool final_loop = false; + bool finish_update = false; + WolfeStatus wolfe_status; + // Start with safe step size + wolfe_status.num_backtracks_ = 99; + Eigen::Index i = 0; + try { + if (options.solver == 1) { + if (options.hessian_block_size == 1) { + // std::cout << "Solver: 1Diag" << std::endl; + Eigen::VectorXd W_r(theta_size); + for (; i <= options.max_num_steps; i++) { + auto W = laplace_likelihood::diagonal_hessian(ll_fun, prev.theta(), + ll_args, msgs); + for (Eigen::Index j = 0; j < W.size(); j++) { + if (W.coeff(j) < 0) { + throw std::domain_error( + "laplace_marginal_density: Hessian matrix is not positive " + "definite"); + } else { + W_r.coeffRef(j) = std::sqrt(W.coeff(j)); + } + } + B.noalias() = Eigen::MatrixXd::Identity(theta_size, theta_size) + + W_r.asDiagonal() * covariance * W_r.asDiagonal(); + Eigen::LLT> llt_B(B); + if (llt_B.info() != Eigen::Success) { + double jitter_try = 1e-10; + for (; jitter_try < 1e-5; jitter_try *= 10) { + B.diagonal().array() += jitter_try; + llt_B.compute(B); + if (llt_B.info() == Eigen::Success) { + break; + } + } + if (llt_B.info() != Eigen::Success) { + throw std::domain_error( + "laplace_marginal_density: Cholesky failed in iteration " + + std::to_string(i)); + } + } + auto L = llt_B.matrixL(); + auto LT = llt_B.matrixU(); + b.noalias() + = (W.array() * prev.theta().array()).matrix() + prev.theta_grad(); + curr.a().noalias() + = b + - W_r.asDiagonal() + * LT.solve(L.solve(W_r.cwiseProduct(covariance * b))); + if (!final_loop) { + finish_update + = update_line_search(wolfe_status, wolfe_info, curr, prev); + } + if (finish_update) { + if (!final_loop && wolfe_status.success_) { + // Do one final loop with exact wolfe conditions + final_loop = true; + // NOTE: Swapping here so we need to swap prev and curr later + set_next_iter(curr, prev); + continue; + } + const double B_log_determinant + = 2.0 * llt_B.matrixLLT().diagonal().array().log().sum(); + /** + * NOTE: At this point we are return prev because either + * 1. Line search + tolerance passed and we swapped prev<->curr + * 2. Line search failed and we want to return the previous step + */ + return laplace_density_estimates{ + prev.obj() - 0.5 * B_log_determinant, + std::move(prev.theta()), + Eigen::SparseMatrix(W_r.asDiagonal()), + Eigen::MatrixXd(L), + std::move(prev.a()), + std::move(prev.theta_grad()), + Eigen::PartialPivLU{}, + Eigen::MatrixXd(0, 0), + 1}; } else { - W_r.coeffRef(i) = std::sqrt(W.coeff(i, i)); + set_next_iter(curr, prev); } } - B.noalias() = MatrixXd::Identity(theta_size, theta_size) - + W_r.asDiagonal() * covariance * W_r.asDiagonal(); - Eigen::LLT> llt_B(B); - auto L = llt_B.matrixL(); - auto LT = llt_B.matrixU(); - b.noalias() = W.diagonal().cwiseProduct(theta) + theta_grad; - a.noalias() - = b - - W_r.asDiagonal() - * LT.solve(L.solve(W_r.cwiseProduct(covariance * b))); - // Simple Newton step - theta.noalias() = covariance * a; - objective_old = objective_new; - if (unlikely( - (Eigen::isinf(theta.array()) || Eigen::isnan(theta.array())) - .any())) { - throw_nan("laplace_marginal_density", "theta", theta); - } - objective_new = -0.5 * a.dot(theta) - + laplace_likelihood::log_likelihood( - ll_fun, theta, ll_args_vals, msgs); - if (options.max_steps_line_search) { - line_search(objective_new, a, theta, a_prev, ll_fun, ll_args_vals, - covariance, options.max_steps_line_search, objective_old, - options.tolerance, msgs); - } - // Check for convergence - if (abs(objective_new - objective_old) < options.tolerance) { - const double B_log_determinant - = 2.0 * llt_B.matrixLLT().diagonal().array().log().sum(); - // Overwrite W instead of making a new sparse matrix - W.diagonal() = W_r; - return laplace_density_estimates{ - objective_new - 0.5 * B_log_determinant, - std::move(covariance), - std::move(theta), - std::move(W), - Eigen::MatrixXd(L), - std::move(a), - std::move(theta_grad), - Eigen::PartialPivLU{}, - Eigen::MatrixXd(0, 0)}; - } else { - a_prev = std::move(a); - set_zero_adjoint(ll_args); + } else { + Eigen::SparseMatrix W_r(theta_size, theta_size); + Eigen::Index block_size = options.hessian_block_size; + W_r.reserve(Eigen::VectorXi::Constant(W_r.cols(), block_size)); + const Eigen::Index n_block = W_r.cols() / block_size; + // Prefill W_r so we only make space once + for (Eigen::Index ii = 0; ii < n_block; ii++) { + for (Eigen::Index k = 0; k < block_size; k++) { + for (Eigen::Index j = 0; j < block_size; j++) { + W_r.insert(ii * block_size + j, ii * block_size + k) = 1.0; + } + } } - } - } else { - Eigen::SparseMatrix W_r(theta_size, theta_size); - Eigen::Index block_size = options.hessian_block_size; - W_r.reserve(Eigen::VectorXi::Constant(W_r.cols(), block_size)); - const Eigen::Index n_block = W_r.cols() / block_size; - // Prefill W_r so we only make space once - for (Eigen::Index i = 0; i < n_block; i++) { - for (Eigen::Index k = 0; k < block_size; k++) { - for (Eigen::Index j = 0; j < block_size; j++) { - W_r.insert(i * block_size + j, i * block_size + k) = 1.0; + W_r.makeCompressed(); + for (; i <= options.max_num_steps; i++) { + auto W = laplace_likelihood::block_hessian( + ll_fun, prev.theta(), options.hessian_block_size, ll_args, msgs); + for (Eigen::Index j = 0; j < W.rows(); j++) { + if (W.coeff(j, j) < 0) { + throw std::domain_error( + "laplace_marginal_density: Hessian matrix is not positive " + "definite"); + } + } + block_matrix_sqrt(W_r, W, options.hessian_block_size); + B.noalias() = Eigen::MatrixXd::Identity(theta_size, theta_size) + + W_r * (covariance * W_r); + Eigen::LLT llt_B(B); + if (llt_B.info() != Eigen::Success) { + double jitter_try = 1e-10; + for (; jitter_try < 1e-5; jitter_try *= 10) { + B.diagonal().array() += jitter_try; + llt_B.compute(B); + if (llt_B.info() == Eigen::Success) { + break; + } + } + if (llt_B.info() != Eigen::Success) { + throw std::domain_error( + "laplace_marginal_density: Cholesky failed in iteration " + + std::to_string(i)); + } + } + auto L = llt_B.matrixL(); + auto LT = llt_B.matrixU(); + b.noalias() = W * prev.theta() + prev.theta_grad(); + curr.a().noalias() + = b - W_r * LT.solve(L.solve(W_r * (covariance * b))); + if (!final_loop) { + finish_update + = update_line_search(wolfe_status, wolfe_info, curr, prev); + } + if (finish_update) { + if (!final_loop && wolfe_status.success_) { + // Do one final loop with exact wolfe conditions + final_loop = true; + set_next_iter(curr, prev); + continue; + } + const double B_log_determinant + = 2.0 * llt_B.matrixLLT().diagonal().array().log().sum(); + return laplace_density_estimates{ + prev.obj() - 0.5 * B_log_determinant, + std::move(prev.theta()), + std::move(W_r), + Eigen::MatrixXd(L), + std::move(prev.a()), + std::move(prev.theta_grad()), + Eigen::PartialPivLU{}, + Eigen::MatrixXd(0, 0), + 1}; + } else { + set_next_iter(curr, prev); } } } - W_r.makeCompressed(); - for (Eigen::Index i = 0; i <= options.max_num_steps; i++) { - auto [theta_grad, W] = laplace_likelihood::diff( - ll_fun, theta, options.hessian_block_size, ll_args, msgs); - for (Eigen::Index i = 0; i < W.rows(); i++) { - if (W.coeff(i, i) < 0) { + throw_overstep(options.max_num_steps); + } + } catch (const std::exception& e) { + allow_bounce = true; + if (msgs != nullptr) { + (*msgs) << "Solver 1 failed at iteration " << i + << " with error: " << e.what() << std::endl; + (*msgs) << "Attempting to switch to solver 2 (LLT decomposition)." + << std::endl; + } + } + try { + if (options.solver == 2 || allow_bounce) { + Eigen::MatrixXd K_root + = covariance.template selfadjointView().llt().matrixL(); + for (; i <= options.max_num_steps; i++) { + debug::print("======Iter", i); + auto W = laplace_likelihood::block_hessian( + ll_fun, prev.theta(), options.hessian_block_size, ll_args, msgs); + B.noalias() = Eigen::MatrixXd::Identity(theta_size, theta_size) + + K_root.transpose() * W * K_root; + Eigen::LLT> llt_B(B); + if (llt_B.info() != Eigen::Success) { + double jitter_try = 1e-10; + for (; jitter_try < 1e-5; jitter_try *= 10) { + B.diagonal().array() += jitter_try; + llt_B.compute(B); + if (llt_B.info() == Eigen::Success) { + break; + } + } + if (llt_B.info() != Eigen::Success) { throw std::domain_error( - "laplace_marginal_density: Hessian matrix is not positive " - "definite"); + "laplace_marginal_density: Cholesky failed in iteration " + + std::to_string(i)); } } - block_matrix_chol_L(W_r, W, options.hessian_block_size); - B.noalias() = MatrixXd::Identity(theta_size, theta_size) - + W_r * (covariance * W_r); - Eigen::LLT> llt_B(B); auto L = llt_B.matrixL(); auto LT = llt_B.matrixU(); - b.noalias() = W * theta + theta_grad; - a.noalias() = b - W_r * LT.solve(L.solve(W_r * (covariance * b))); - // Simple Newton step - theta.noalias() = covariance * a; - objective_old = objective_new; - if (unlikely( - (Eigen::isinf(theta.array()) || Eigen::isnan(theta.array())) - .any())) { - throw_nan("laplace_marginal_density", "theta", theta); + b.noalias() = W * prev.theta() + prev.theta_grad(); + curr.a().noalias() + = K_root.transpose().template triangularView().solve( + LT.solve(L.solve(K_root.transpose() * b))); + if (!final_loop) { + finish_update + = update_line_search(wolfe_status, wolfe_info, curr, prev); } - objective_new = -0.5 * a.dot(value_of(theta)) - + laplace_likelihood::log_likelihood( - ll_fun, value_of(theta), ll_args_vals, msgs); - if (options.max_steps_line_search > 0) { - line_search(objective_new, a, theta, a_prev, ll_fun, ll_args_vals, - covariance, options.max_steps_line_search, objective_old, - options.tolerance, msgs); - } - // Check for convergence - if (abs(objective_new - objective_old) < options.tolerance) { + if (finish_update) { + if (!final_loop && wolfe_status.success_) { + // Do one final loop with exact wolfe conditions + final_loop = true; + // NOTE: Swapping here so we need to swap prev and curr later + set_next_iter(curr, prev); + continue; + } const double B_log_determinant = 2.0 * llt_B.matrixLLT().diagonal().array().log().sum(); return laplace_density_estimates{ - objective_new - 0.5 * B_log_determinant, - std::move(covariance), - std::move(theta), - std::move(W_r), - Eigen::MatrixXd(L), - std::move(a), - std::move(theta_grad), + prev.obj() - 0.5 * B_log_determinant, + std::move(prev.theta()), + std::move(W), + std::move(Eigen::MatrixXd(L)), + std::move(prev.a()), + std::move(prev.theta_grad()), Eigen::PartialPivLU{}, - Eigen::MatrixXd(0, 0)}; + std::move(K_root), + 2}; } else { - a_prev = a; - set_zero_adjoint(ll_args); + set_next_iter(curr, prev); } } + throw_overstep(options.max_num_steps); } - throw_overstep(options.max_num_steps); - } else if (options.solver == 2) { - Eigen::MatrixXd K_root - = covariance.template selfadjointView().llt().matrixL(); - for (Eigen::Index i = 0; i <= options.max_num_steps; i++) { - auto [theta_grad, W] = laplace_likelihood::diff( - ll_fun, theta, options.hessian_block_size, ll_args, msgs); - B.noalias() = MatrixXd::Identity(theta_size, theta_size) - + K_root.transpose() * W * K_root; - Eigen::LLT> llt_B(B); - auto L = llt_B.matrixL(); - auto LT = llt_B.matrixU(); - b.noalias() = W * theta + theta_grad; - a.noalias() - = K_root.transpose().template triangularView().solve( - LT.solve(L.solve(K_root.transpose() * b))); - // Simple Newton step - theta.noalias() = covariance * a; - objective_old = objective_new; - if (unlikely((Eigen::isinf(theta.array()) || Eigen::isnan(theta.array())) - .any())) { - throw_nan("laplace_marginal_density", "theta", theta); - } - objective_new = -0.5 * a.dot(theta) - + laplace_likelihood::log_likelihood(ll_fun, theta, - ll_args_vals, msgs); - // linesearch - if (options.max_steps_line_search > 0) { - line_search(objective_new, a, theta, a_prev, ll_fun, ll_args_vals, - covariance, options.max_steps_line_search, objective_old, - options.tolerance, msgs); - } - // Check for convergence - if (abs(objective_new - objective_old) < options.tolerance) { - const double B_log_determinant - = 2.0 * llt_B.matrixLLT().diagonal().array().log().sum(); - return laplace_density_estimates{ - objective_new - 0.5 * B_log_determinant, - std::move(covariance), - std::move(theta), - std::move(W), - std::move(Eigen::MatrixXd(L)), - std::move(a), - std::move(theta_grad), - Eigen::PartialPivLU{}, - std::move(K_root)}; - } else { - a_prev = a; - set_zero_adjoint(ll_args); - } + } catch (const std::exception& e) { + allow_bounce = true; + if (msgs != nullptr) { + (*msgs) << "Solver 2 failed at iteration " << i + << " with error: " << e.what() << std::endl; + (*msgs) << "Attempting to switch to solver 3 (LU decomposition)." + << std::endl; } - throw_overstep(options.max_num_steps); - } else if (options.solver == 3) { - for (Eigen::Index i = 0; i <= options.max_num_steps; i++) { - auto [theta_grad, W] = laplace_likelihood::diff( - ll_fun, theta, options.hessian_block_size, ll_args, msgs); - Eigen::PartialPivLU LU( - MatrixXd::Identity(theta_size, theta_size) + covariance * W); - // L on upper and U on lower triangular - b.noalias() = W * theta + theta_grad; - a.noalias() = b - W * LU.solve(covariance * b); - // Simple Newton step - theta.noalias() = covariance * a; - objective_old = objective_new; - if (((Eigen::isinf(theta.array()) || Eigen::isnan(theta.array())) - .any())) { - throw_nan("laplace_marginal_density", "theta", theta); - } - objective_new = -0.5 * a.dot(value_of(theta)) - + laplace_likelihood::log_likelihood( - ll_fun, value_of(theta), ll_args_vals, msgs); - - if (options.max_steps_line_search > 0) { - line_search(objective_new, a, theta, a_prev, ll_fun, ll_args_vals, - covariance, options.max_steps_line_search, objective_old, - options.tolerance, msgs); + } + if (options.solver == 3 || allow_bounce) { + // std::cout << "Solver: 3" << std::endl; + Eigen::PartialPivLU LU(theta_size); + for (; i <= options.max_num_steps; i++) { + auto W = laplace_likelihood::block_hessian( + ll_fun, prev.theta(), options.hessian_block_size, ll_args, msgs); + LU.compute(Eigen::MatrixXd::Identity(theta_size, theta_size) + + covariance * W); + // L on lower and U on upper triangular + b.noalias() = W * prev.theta() + prev.theta_grad(); + curr.a().noalias() = b - W * LU.solve(covariance * b); + if (!final_loop) { + finish_update + = update_line_search(wolfe_status, wolfe_info, curr, prev); } - if (abs(objective_new - objective_old) < options.tolerance) { - // TODO(Charles): There has to be a simple trick for this - const double B_log_determinant = log(LU.determinant()); - return laplace_density_estimates{ - objective_new - 0.5 * B_log_determinant, - std::move(covariance), - std::move(theta), - std::move(W), - Eigen::MatrixXd(0, 0), - std::move(a), - std::move(theta_grad), - std::move(LU), - Eigen::MatrixXd(0, 0)}; + if (finish_update) { + if (!final_loop && wolfe_status.success_) { + // Do one final loop with exact wolfe conditions + final_loop = true; + // NOTE: Swapping here so we need to swap prev and curr later + set_next_iter(curr, prev); + continue; + } + const double B_log_determinant + = LU.matrixLU().diagonal().array().log().sum(); + return laplace_density_estimates{prev.obj() - 0.5 * B_log_determinant, + std::move(prev.theta()), + std::move(W), + Eigen::MatrixXd(0, 0), + std::move(prev.a()), + std::move(prev.theta_grad()), + std::move(LU), + Eigen::MatrixXd(0, 0), + 3}; } else { - a_prev = a; - set_zero_adjoint(ll_args); + set_next_iter(curr, prev); } } throw_overstep(options.max_num_steps); @@ -801,10 +956,14 @@ inline double laplace_marginal_density( LLFun&& ll_fun, LLTupleArgs&& ll_args, CovarFun&& covariance_function, CovarArgs&& covar_args, const laplace_options& options, std::ostream* msgs) { + Eigen::MatrixXd covariance = stan::math::apply( + [msgs, &covariance_function](auto&&... args) { + return covariance_function(std::forward(args)..., msgs); + }, + std::forward(covar_args)); return internal::laplace_marginal_density_est( std::forward(ll_fun), std::forward(ll_args), - std::forward(covariance_function), - std::forward(covar_args), options, msgs) + std::move(covariance), options, msgs) .lmd; } @@ -1054,20 +1213,30 @@ inline auto laplace_marginal_density(const LLFun& ll_fun, LLTupleArgs&& ll_args, nested_rev_autodiff nested; // Make one hard copy here - using laplace_likelihood::internal::conditional_copy_and_promote; using laplace_likelihood::internal::COPY_TYPE; - auto ll_args_copy - = conditional_copy_and_promote( - ll_args_refs); - + using laplace_likelihood::internal::deep_copy_vargs; + auto ll_args_copy = deep_copy_vargs(ll_args_refs); + auto covar_args_copy = deep_copy_vargs(covar_args_refs); + auto covariance = stan::math::apply( + [&covariance_function, &msgs](auto&&... args) { + if constexpr (is_any_var_scalar_v) { + return to_var_value(covariance_function(args..., msgs)); + } else { + return covariance_function(args..., msgs); + } + }, + covar_args_copy); auto md_est = internal::laplace_marginal_density_est( - ll_fun, ll_args_copy, covariance_function, value_of(covar_args_refs), - options, msgs); - + ll_fun, value_of(ll_args_copy), value_of(covariance), options, msgs); + if constexpr (ll_args_contain_var) { + laplace_likelihood::ll_arg_grad(ll_fun, md_est.theta, ll_args_copy, msgs); + } // Solver 1, 2 arena_t R(md_est.theta.size(), md_est.theta.size()); // Solver 3 - arena_t LU_solve_covariance; + arena_t LU_solve_covariance( + covariance.rows() * (md_est.solver_used == 3), + covariance.cols() * (md_est.solver_used == 3)); // Solver 1, 2, 3 arena_t s2(md_est.theta.size()); @@ -1080,24 +1249,23 @@ inline auto laplace_marginal_density(const LLFun& ll_fun, LLTupleArgs&& ll_args, } }, partial_parm, ll_args_filter); - if (options.solver == 1) { + if (md_est.solver_used == 1) { if (options.hessian_block_size == 1) { - // TODO(Steve): Solve without casting from sparse to dense - Eigen::MatrixXd tmp - = md_est.L.template triangularView().solve( - md_est.W_r.toDense()); - R = tmp.transpose() * tmp; + arena_t tmp = md_est.W_r.toDense(); + md_est.L.template triangularView().solveInPlace(tmp); + R.noalias() = tmp.transpose() * tmp; arena_t C = md_est.L.template triangularView().solve( - md_est.W_r * md_est.covariance); + md_est.W_r * value_of(covariance)); if constexpr (!ll_args_contain_var) { s2.deep_copy( (0.5 - * (md_est.covariance.diagonal() - (C.transpose() * C).diagonal()) + * (value_of(covariance).diagonal() + - (C.transpose() * C).diagonal()) .cwiseProduct(laplace_likelihood::third_diff( ll_fun, md_est.theta, value_of(ll_args_copy), msgs)))); } else { - arena_t A = md_est.covariance - C.transpose() * C; + arena_t A = value_of(covariance) - C.transpose() * C; auto s2_tmp = laplace_likelihood::compute_s2( ll_fun, md_est.theta, A, options.hessian_block_size, ll_args_copy, msgs); @@ -1106,21 +1274,20 @@ inline auto laplace_marginal_density(const LLFun& ll_fun, LLTupleArgs&& ll_args, } } else { - Eigen::MatrixXd tmp - = md_est.L.template triangularView().solve( - md_est.W_r.toDense()); - R = tmp.transpose() * tmp; + arena_t tmp = md_est.W_r.toDense(); + md_est.L.template triangularView().solveInPlace(tmp); + R.noalias() = tmp.transpose() * tmp; arena_t C = md_est.L.template triangularView().solve( - md_est.W_r * md_est.covariance); - arena_t A = md_est.covariance - C.transpose() * C; + md_est.W_r * value_of(covariance)); + arena_t A = value_of(covariance) - C.transpose() * C; auto s2_tmp = laplace_likelihood::compute_s2(ll_fun, md_est.theta, A, options.hessian_block_size, ll_args_copy, msgs); s2.deep_copy(s2_tmp); internal::copy_compute_s2(partial_parm, ll_args_filter); } - } else if (options.solver == 2) { + } else if (md_est.solver_used == 2) { R = md_est.W_r - md_est.W_r * md_est.K_root * md_est.L.transpose() @@ -1138,11 +1305,14 @@ inline auto laplace_marginal_density(const LLFun& ll_fun, LLTupleArgs&& ll_args, s2.deep_copy(s2_tmp); internal::copy_compute_s2(partial_parm, ll_args_filter); } else { // options.solver with LU decomposition - LU_solve_covariance = md_est.LU.solve(md_est.covariance); - R = md_est.W_r - md_est.W_r * LU_solve_covariance * md_est.W_r; + LU_solve_covariance = md_est.LU.solve(value_of(covariance)); + auto I_minus_BinvKW + = Eigen::MatrixXd::Identity(md_est.W_r.rows(), md_est.W_r.cols()) + - LU_solve_covariance * md_est.W_r; + R = md_est.W_r * I_minus_BinvKW; // == W - W B^{-1} K W arena_t A - = md_est.covariance - - md_est.covariance * md_est.W_r * LU_solve_covariance; + = value_of(covariance) + - value_of(covariance) * md_est.W_r * LU_solve_covariance; auto s2_tmp = laplace_likelihood::compute_s2(ll_fun, md_est.theta, A, options.hessian_block_size, ll_args_copy, msgs); @@ -1151,37 +1321,24 @@ inline auto laplace_marginal_density(const LLFun& ll_fun, LLTupleArgs&& ll_args, } lmd = md_est.lmd; if constexpr (is_any_var_scalar_v>) { - [&covar_args_refs, &covar_args_adj, &md_est, &R, &s2, - &covariance_function, &msgs]() mutable { - const nested_rev_autodiff nested; - auto covar_args_copy - = laplace_likelihood::internal::conditional_copy_and_promote< - is_any_var_scalar, var, - laplace_likelihood::internal::COPY_TYPE::DEEP>(covar_args_refs); - - var_value K_var = to_var_value(stan::math::apply( - [&covariance_function, &msgs](auto&&... args) { - return covariance_function(args..., msgs); - }, - covar_args_copy)); - arena_t K_adj_arena - = 0.5 * md_est.a * md_est.a.transpose() - 0.5 * R - + s2 * md_est.theta_grad.transpose() - - (R * (K_var.val() * s2)) * md_est.theta_grad.transpose(); - var Z = make_callback_var(0.0, [K_var, K_adj_arena](auto&& vi) mutable { - K_var.adj().array() += vi.adj() * K_adj_arena.array(); - }); - grad(Z.vi_); - auto covar_args_filter - = internal::filter_var_scalar_types(covar_args_copy); - internal::collect_adjoints(covar_args_adj, covar_args_filter); - }(); + arena_t K_adj_arena + = 0.5 * md_est.a * md_est.a.transpose() - 0.5 * R + + s2 * md_est.theta_grad.transpose() + - (R * (covariance.val() * s2)) * md_est.theta_grad.transpose(); + var Z = make_callback_var( + 0.0, [covariance, K_adj_arena](auto&& vi) mutable { + covariance.adj().array() += vi.adj() * K_adj_arena.array(); + }); + grad(Z.vi_); + auto covar_args_filter + = internal::filter_var_scalar_types(covar_args_copy); + internal::collect_adjoints(covar_args_adj, covar_args_filter); } if constexpr (ll_args_contain_var) { arena_t v; - if (options.solver == 1 || options.solver == 2) { - v = md_est.covariance * s2 - - md_est.covariance * R * md_est.covariance * s2; + if (md_est.solver_used == 1 || md_est.solver_used == 2) { + v = value_of(covariance) * s2 + - value_of(covariance) * R * value_of(covariance) * s2; } else { v = LU_solve_covariance * s2; } diff --git a/stan/math/mix/functor/wolfe_line_search.hpp b/stan/math/mix/functor/wolfe_line_search.hpp new file mode 100644 index 00000000000..46890038355 --- /dev/null +++ b/stan/math/mix/functor/wolfe_line_search.hpp @@ -0,0 +1,1016 @@ +#ifndef STAN_MATH_MIX_FUNCTOR_WOLFE_LINE_SEARCH_HPP +#define STAN_MATH_MIX_FUNCTOR_WOLFE_LINE_SEARCH_HPP + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +// #define LAPLACE_DEBUG +#ifdef LAPLACE_DEBUG +#include +#include +#include +#include +#include +#endif + +namespace stan::math { + +/** + * @brief Options for Wolfe line search during optimization. + * + * These parameters control the behavior of the line search, + * including the Wolfe condition thresholds, step size bounds, + * and numerical tolerances. + */ +struct laplace_line_search_options { + constexpr explicit laplace_line_search_options(int max_iter) + : max_iterations(max_iter) {} + constexpr laplace_line_search_options() = default; + int max_iterations{1000}; + /** + * @brief Armijo condition parameter (sufficient decrease). + * + * Controls how much the objective function must decrease + * relative to the step length and gradient. Must be in (0, 1). + * Smaller values make the condition easier to satisfy. + */ + double c1{1e-4}; + + /** + * @brief Curvature condition parameter. + * + * Ensures that the step length provides a sufficient reduction + * in the gradient magnitude. Must satisfy c1 < c2 < 1. + * Larger values enforce stronger curvature requirements. + */ + double c2{0.9}; + + /** + * @brief Backtracking shrinkage factor. + * + * When the Wolfe conditions are not met, the step size is + * multiplied by this factor (0 < tau < 1) to reduce it. + */ + double tau{0.5}; + + /** + * @brief Minimum allowable step size. + * + * Prevents the line search from shrinking the step length + * below this threshold, which helps avoid numerical issues. + */ + double min_alpha{1e-8}; + + /** + * @brief Maximum allowable step size. + * + * Caps the growth of the step length to ensure stability. + */ + double max_alpha{16.0}; + + /** + * @brief Step size expansion factor. + * + * If the Wolfe conditions are satisfied and further progress + * seems possible, the step size may be multiplied by this factor + * to accelerate convergence. + */ + double scale_up{2.0}; + + /** + * @brief Absolute gradient tolerance. + * + * If the gradient norm falls below this threshold, the line + * search may terminate early since further progress is negligible. + */ + double abs_grad_threshold{1e-12}; + + /** + * @brief Absolute objective tolerance. + * + * If the change in objective function value falls below this + * threshold, the line search may terminate as improvements are + * considered insignificant. + */ + double abs_obj_threshold{1e-12}; + + double rel_grad_threshold{1e-3}; // off by default + double rel_obj_threshold{1e-10}; // off by default +}; +namespace internal { +namespace debug { + +constexpr void print(int tabs) {} + +#ifdef LAPLACE_DEBUG +std::ofstream csv_file("../wolfe_line_search_debug.csv"); +template +void print(int tabs, const char* name, Val&& val, Types&&... args) { + csv_file << name << ", " << std::setprecision(13) << std::fixed + << stan::math::eval(val) << "\n"; + print(tabs, std::forward(args)...); +} + +template +void print(const char* msg, int tabs, const char* name, Val&& val, + Types&&... args) { + csv_file << name << ", " << std::setprecision(13) << std::fixed + << stan::math::eval(val) << "\n"; + print(tabs, std::forward(args)...); +} + +void print(const char* msg) { + // std::cout << msg << "\n"; +} + +template +void print(const char* msg, Val&& val) { + csv_file << msg << ", " << std::setprecision(13) << std::fixed + << stan::math::eval(val) << "\n"; +} + +#else +template +constexpr void print(int tabs, const char* name, Val&& val, Types&&... args) {} + +template +constexpr void print(const char* msg, int tabs, const char* name, Val&& val, + Types&&... args) {} + +constexpr void print(const char* msg) {} + +template +constexpr void print(const char* msg, Val&& val) {} +#endif +} // namespace debug + +/* + * Safeguarded cubic-or-bisection step chooser for MAXIMIZATION. + * Given a bracket [a, b] with values and directional derivatives + * (fa, fpa) at a and (fb, fpb) at b, returns a trial point in (a, b). + * + * Preconditions (recommended for a well-formed maximum bracket): + * a < b, fpa > 0, fpb < 0. + * If inputs are degenerate or non-finite, falls back to the midpoint. + * + * The routine internally normalizes the interval to s in [0, 1], fits a + * cubic Hermite model F(s), and selects among: + * - stationary points of F(s) (cubic argmax), + * - a secant estimate for the derivative root, + * - pure bisection (midpoint), + * then clamps away from edges by `edge_guard`. + */ +template +inline Scalar cubic_or_bisect_max(Scalar a, Scalar fa, Scalar fpa, Scalar b, + Scalar fb, Scalar fpb) { + // Basic validation. + if (!(b > a) || !std::isfinite(fa) || !std::isfinite(fb) + || !std::isfinite(fpa) || !std::isfinite(fpb)) { + return (a + b) / Scalar(2.0); + } + + const Scalar width = b - a; + const Scalar fpa_s = width * fpa; // slope w.r.t. s at s=0 + const Scalar fpb_s = width * fpb; // slope w.r.t. s at s=1 + + // Cubic Hermite coefficients in s \in [0,1]: + // F(s) = a3*s^3 + a2*s^2 + a1*s + a0 + // with F(0)=fa, F'(0)=fpa_s, F(1)=fb, F'(1)=fpb_s. + const Scalar a0 = fa; + const Scalar a1 = fpa_s; + const Scalar a2 = (Scalar(3) * (fb - fa)) - (Scalar(2) * fpa_s) - fpb_s; + const Scalar a3 = (Scalar(2) * (fa - fb)) + fpa_s + fpb_s; + + auto eval = [&](Scalar s) -> Scalar { + // Horner evaluation of F(s). + return ((a3 * s + a2) * s + a1) * s + a0; + }; + + // Helper: push candidate s if it's inside (0,1). + struct Candidate { + Scalar s; + Scalar val; + }; + Candidate best{Scalar(0.5), eval(Scalar(0.5))}; // start with bisection + + auto consider = [&](Scalar s) { + if (!(s > Scalar(0) && s < Scalar(1)) || !std::isfinite(s)) + return; + const Scalar v = eval(s); + if (v > best.val) + best = {s, v}; + }; + + // 1) Stationary points of the cubic model (argmax/min candidates). + // F'(s) = 3*a3*s^2 + 2*a2*s + a1 = 0. + { + const Scalar A = Scalar(3) * a3; + const Scalar B = Scalar(2) * a2; + const Scalar C = a1; + + const Scalar eps = std::numeric_limits::epsilon(); + if (std::abs(A) <= eps * (std::abs(B) + std::abs(C))) { + // Degenerates to linear: B*s + C = 0. + if (std::abs(B) > eps * std::abs(C)) { + consider(-C / B); + } + } else { + const Scalar disc = std::fma(-Scalar(4) * A, C, B * B); // B^2 - 4AC + if (disc >= 0) { + const Scalar r = std::sqrt(disc); + // q-formula for numerical stability. + const Scalar q = -Scalar(0.5) * (B + std::copysign(r, B)); + const Scalar s1 = q / A; + const Scalar s2 = (q == Scalar(0)) + ? std::numeric_limits::quiet_NaN() + : C / q; + consider(s1); + consider(s2); + } + } + } + + // 2) Secant estimate for the derivative root (More–Thuente often uses + // a secant/minimizer mix; we add the secant root for robustness). + // Derivative across s is linearly interpolated from fpa to fpb: + // D(s) ~ fpa + (fpb - fpa)*s; root at s = fpa / (fpa - fpb). + if (std::isfinite(fpa) && std::isfinite(fpb) && (fpa != fpb)) { + const Scalar s_secant = fpa / (fpa - fpb); + consider(s_secant); + } + + // Edge guard: keep away from exact ends. + constexpr Scalar edge_guard = Scalar(1e-3); + constexpr Scalar lo = 0.0 * (1.0 - edge_guard) + (1.0 * edge_guard); + constexpr Scalar hi = Scalar(0.0) * (1.0 - (Scalar(1) - edge_guard)) + + (1.0 * (Scalar(1) - edge_guard)); + const Scalar s_star = std::clamp(best.s, lo, hi); + // Map back to alpha-space. + return a + s_star * width; +} + +template +inline auto cubic_or_bisect_max(Eval&& low, Eval&& high, Options&& opt) { + auto alpha = cubic_or_bisect_max(low.alpha(), low.obj(), low.dir(), + high.alpha(), high.obj(), high.dir()); + const double width = high.alpha() - low.alpha(); + const double guard = 1e-3 * width; // or make this an option + alpha = std::clamp(alpha, low.alpha() + guard, high.alpha() - guard); + return alpha; +} + +template +inline auto check_armijo(double obj_next, double obj_init, double alpha_next, + double dir0, Option&& opt) { + debug::print( + "check_armijo: ", 2, "armijo: ", + (obj_next >= obj_init + alpha_next * dir0 * opt.c1 ? 1 : 0), + "obj_next: ", obj_next, "obj_init: ", obj_init, + "alpha_next: ", alpha_next, "dir0: ", dir0, "c1: ", opt.c1, + "obj + alpha * dir0 * c1: ", (obj_init + alpha_next * dir0 * opt.c1)); + return (obj_next >= obj_init) + && (obj_next >= obj_init + alpha_next * dir0 * opt.c1); +} + +template +inline bool check_armijo(const Eval& eval, const WolfeT& prev, + const Option& opt) { + return check_armijo(eval.obj(), prev.obj(), eval.alpha(), prev.dir(), opt); +} + +template +inline auto check_wolfe_curve(double dir_deriv_next, double dir_deriv_init, + Option&& opt) { + debug::print( + "check_wolfe_curve: ", 2, "wolfe: ", + (std::abs(dir_deriv_next) <= (opt.c2 * std::abs(dir_deriv_init)) ? 1 : 0), + "deriv_next: ", dir_deriv_next, "deriv_init: ", dir_deriv_init, + "c2: ", opt.c2, "abs(d_next): ", std::abs(dir_deriv_next), + "abs(d_init)*c2 ", (std::abs(dir_deriv_init) * opt.c2)); + return std::abs(dir_deriv_next) <= (opt.c2 * std::abs(dir_deriv_init)); +} + +template +inline bool check_wolfe(const Eval& eval, const WolfeT& prev, + const Option& opt) { + return check_wolfe_curve(eval.dir(), prev.dir(), opt); +} + +enum class WolfeReturn : uint8_t { + // both conditions true + Wolfe, + // Armijo true, curvature false + Armijo, + // |phi'| small + ConvergedGradient, + // |phi - phi0| small + ConvergedObjective, + // |phi - phi0| and |phi'| small + ConvergedObjectiveAndGradient, + // high and low became too small + IntervalTooSmall, + // alpha < min_alpha + StepTooSmall, + // max iters reached + ReachedMaxStep, + // failed to find a step + NumericalIssue, + // All other failures + Fail, + Continue +}; + +/** + * Struct to hold the result status of the Wolfe line search. + */ +struct WolfeStatus { + // total updates/evaluations + int num_evals_{0}; + int num_backtracks_{0}; + WolfeReturn stop_{WolfeReturn::Fail}; + // Whether a valid new step was found + bool success_{false}; + WolfeStatus() = default; + WolfeStatus(WolfeReturn stop, int evals, int back) + : num_evals_(evals), + num_backtracks_(back), + stop_(stop), + success_{false} {} + WolfeStatus(WolfeReturn stop, int evals, int back, bool success) + : num_evals_(evals), + num_backtracks_(back), + stop_(stop), + success_{success} {} +}; + +/** + * Helper function for pretty printing + */ +inline auto wolfe_status_str(WolfeStatus s) { + switch (s.stop_) { + case WolfeReturn::Wolfe: + return "Wolfe"; + case WolfeReturn::Armijo: + return "Armijo"; + case WolfeReturn::ConvergedGradient: + return "ConvergedGradient"; + case WolfeReturn::ConvergedObjective: + return "ConvergedObjective"; + case WolfeReturn::ConvergedObjectiveAndGradient: + return "ConvergedObjectiveAndGradient"; + case WolfeReturn::IntervalTooSmall: + return "IntervalTooSmall"; + case WolfeReturn::StepTooSmall: + return "StepTooSmall"; + case WolfeReturn::ReachedMaxStep: + return "ReachedMaxStep"; + case WolfeReturn::NumericalIssue: + return "NumericalIssue"; + case WolfeReturn::Fail: + return "Fail"; + case WolfeReturn::Continue: + return "Continue"; + default: + return "UNKNOWN"; + } +} + +/** + * evaluation struct for Wolfe line search + */ +struct Eval { + // alpha + double alpha_{0.0}; + // obj + double obj_{0.0}; + // directional derivative + double dir_{0.0}; + inline auto&& alpha() { return alpha_; } + inline const auto& alpha() const { return alpha_; } + inline auto&& obj() { return obj_; } + inline const auto& obj() const { return obj_; } + inline auto&& dir() { return dir_; } + inline const auto& dir() const { return dir_; } + constexpr Eval(double alpha, double obj, double dir) + : alpha_(alpha), obj_(obj), dir_(dir) {} + constexpr Eval() = default; +}; + +/** + * Data used in current evaluation of wolfe line search at a particular stepsize + */ +struct WolfeData { + // current parameter values + Eigen::VectorXd theta_; + // parameter gradients + Eigen::VectorXd theta_grad_; + // latent variable + Eigen::VectorXd a_; + // evaluation data + Eval eval_; + explicit WolfeData(Eigen::Index n) + : theta_(Eigen::VectorXd::Zero(n)), + theta_grad_(Eigen::VectorXd::Zero(n)), + a_(Eigen::VectorXd::Zero(n)), + eval_() {} + + template + WolfeData(ObjFun&& obj_fun, const Eigen::VectorXd& a, const Theta0& theta0, + ThetaGradF&& theta_grad_f) + : theta_(theta0), + theta_grad_(theta_grad_f(theta_)), + a_(a), + eval_(1.0, obj_fun(a_, theta_), 0.0) {} + + template + WolfeData(ObjFun&& obj_fun, Eigen::Index n, const Theta0& theta0, + ThetaGradF&& theta_grad_f) + : theta_(theta0), + theta_grad_(theta_grad_f(theta_)), + a_(Eigen::VectorXd::Zero(n)), + eval_(1.0, obj_fun(a_, theta_), 0.0) {} + + // Initialize with theta = 0 + template + WolfeData(Eigen::Index n, const LLFun& ll_fun, const LLArgs& ll_args, + const Msgs& msgs) + : WolfeData(n, Eigen::VectorXd::Zero(n), ll_fun, ll_args, msgs) {} + + void update(WolfeData& other) { + theta_.swap(other.theta_); + theta_grad_.swap(other.theta_grad_); + a_.swap(other.a_); + eval_ = other.eval_; + } + void update(WolfeData& other, Eval& eval) { + theta_.swap(other.theta_); + a_.swap(other.a_); + theta_grad_.swap(other.theta_grad_); + eval_ = eval; + } + inline auto&& theta() { return theta_; } + inline const auto& theta() const { return theta_; } + inline auto&& theta_grad() { return theta_grad_; } + inline const auto& theta_grad() const { return theta_grad_; } + inline auto&& a() { return a_; } + inline const auto& a() const { return a_; } + inline auto&& obj() { return eval_.obj(); } + inline const auto& obj() const { return eval_.obj(); } + inline auto&& alpha() { return eval_.alpha(); } + inline const auto& alpha() const { return eval_.alpha(); } + inline auto&& dir() { return eval_.dir(); } + inline const auto& dir() const { return eval_.dir(); } +}; + +/** + * Data object used in wolfe line search + */ +struct WolfeInfo { + // Current step data. On output will be the proposal step + WolfeData curr_; + // Previous step data + WolfeData prev_; + // Scratch space for evaluations of proposal steps + WolfeData scratch_; + // Search direction + Eigen::VectorXd p_; + // Initial directional derivative + double init_dir_; + template + WolfeInfo(ObjFun&& obj_fun, Eigen::Index n, Theta0&& theta0, + ThetaGradF&& theta_grad_f) + : curr_(std::forward(obj_fun), n, std::forward(theta0), + std::forward(theta_grad_f)), + prev_(curr_), + scratch_(n) { + if (!std::isfinite(curr_.obj())) { + throw std::domain_error( + "laplace_marginal_density: log likelihood is not finite at initial " + "theta and likelihood arguments."); + } + } + WolfeInfo(WolfeData&& curr, WolfeData&& prev) + : curr_(std::move(curr)), + prev_(std::move(prev)), + scratch_(curr_.theta().size()), + p_(Eigen::VectorXd::Zero(curr_.theta().size())), + init_dir_(0.0) {} + explicit WolfeInfo(Eigen::Index n) + : curr_(n), + prev_(curr_), + scratch_(n), + p_(Eigen::VectorXd::Zero(n)), + init_dir_(0.0) {} +}; + +/** + * @brief Strong-Wolfe line search with expansion, bracketing, and + * cubic/bisection zoom + * + * This routine searches along the ray + * \f[ + * a(\alpha) = a_0 + \alpha\,p,\qquad p = a_1 - a_0, + * \f] + * to find the largest step \f$\alpha\f$ that satisfies the **strong-Wolfe** + * conditions + * + * \f{align*}{ + * \phi(\alpha) &\le \phi(0) + c_1\,\alpha\,\phi'(0) \quad\text{(Armijo)},\\ + * |\phi'(\alpha)| &\le c_2\,|\phi'(0)| \quad\text{(curvature)}, + * \f} + * + * where \f$\phi(\alpha)\f$ is the objective at \f$a(\alpha)\f$ and + * \f$\phi'(\alpha)=\nabla\phi(a(\alpha))^\top p\f$ is the directional + * derivative. + * + * ## How the search proceeds (phases) + * + * The algorithm works with a *left* point `low` and a *right* point `high`, + * stores the “best so far” Armijo-OK point `best`, and reuses a scratch buffer + * to avoid recomputation when a step is finally accepted. + * + * 1. **Numerical contraction (pre-check).** + * Start from \f$\alpha_0=\mathrm{clamp}( \text{curr.alpha} \cdot + * \text{opt.scale_up}, \text{opt.min_alpha}, \text{opt.max_alpha})\f$. Evaluate + * \f$\phi(\alpha_0)\f$ and the derived state. If either the objective or + * derived quantities (e.g. \f$\theta(\alpha)\f$, its gradient) are non-finite, + * shrink \f$\alpha \leftarrow \alpha \cdot \text{opt.tau}\f$ until + * everything is finite. + * **Ends when** values become finite → continue, or + * \f$\alpha<\text{opt.min_alpha}\f$ → **returns** `StepTooSmall`. + * + * 2. **Quick accept & “zoom-up”.** + * If the current `high` satisfies **both** Armijo and curvature, repeatedly + * *expand* \f$\alpha \leftarrow \alpha \cdot \text{opt.scale_up}\f$ while + * the strong-Wolfe tests continue to pass, keeping the last valid step as + * `best`. + * **Ends when** a test fails, \f$\alpha>\text{opt.max_alpha}\f$, or + * iteration limit is reached. The function **returns** the last passing step + * with `Wolfe`. + * + * 3. **Expansion & right-bracketing.** + * Otherwise, continue evaluating larger \f$\alpha\f$ values: + * - If Armijo holds and \f$\phi'(\alpha)>0\f$, promote the left endpoint + * `low ← high` and *expand* again. + * (We are on the “far side” of the minimum.) + * - If Armijo holds but \f$\phi'(\alpha)\le 0\f$, or if Armijo fails, a + * right endpoint has been found -> stop expanding and proceed to zoom. + * **Ends when** a right endpoint is found, + * \f$\alpha>\text{opt.max_alpha}\f$, or iteration limit is reached. + * + * 4. **Safety bisection (optional).** + * If both endpoints currently have positive directional derivatives, take + * pure bisection steps until a sign change is observed or the interval is + * small. + * + * 5. **Cubic/bisection zoom.** + * Repeatedly propose an interior point \f$\alpha_m\f$ using a cubic + * interpolation of the bracket end-points (falling back to bisection when the + * cubic is degenerate), evaluate there, and shrink the bracket according to: + * - If Armijo and curvature hold → **returns** `Wolfe`. + * - If Armijo holds but curvature fails → keep the better side; prefer the + * sub-interval with a derivative sign change. + * - If Armijo fails → move the right endpoint left. + * Throughout zoom we remember the best Armijo-OK point `best` in case + * strong-Wolfe cannot be satisfied. + * **Ends when** the interval width is \f$\le\text{opt.min_alpha}\f$, a + * convergence tolerance triggers, or the iteration limit is reached. + * + * 6. **Convergence/guard rails.** + * After each evaluation we check: + * - Gradient tolerance: \f$|\phi'(\alpha)| \le + * \max(\text{opt.abs\_grad\_threshold},\ + * \text{opt.rel\_grad\_threshold}\,|\phi'(0)|)\f$. + * - Objective change tolerance (for very small steps): + * \f$|\phi(\alpha)-\phi(0)| \le + * \max(\text{opt.abs\_obj\_threshold},\ + * \text{opt.rel\_obj\_threshold}\,(1+|\phi(0)|))\f$ and \f$\alpha < + * \text{opt.min_alpha}\f$. If triggered, the routine returns one of + * `ConvergedGradient`, `ConvergedObjective`, or + * `ConvergedObjectiveAndGradient`. If neither test is met but the bracket + * becomes too small, it returns `IntervalTooSmall` (accepting the current point + * only if it satisfies Armijo). + * + * If zoom exits without a strong-Wolfe point but an Armijo-OK point was seen, + * the routine **returns** `Armijo` at that best point; otherwise it **returns** + * `Fail`. + * + * ### Contract for the step evaluator `UpdateFun` + * + * The line search delegates *all* numerical work to a user-supplied callable + * `update_fun` that evaluates the objective and its directional derivative at a + * trial step and prepares the candidate state for acceptance. + * + * **Required signature** + * @code + * void update_fun(WolfeData& out, Eval& e, const Direction& p); + * @endcode + * + * **Inputs** + * - `e.alpha()` is the trial step \f$\alpha\f$ to evaluate. + * - `p` is the search direction. + * - The baseline (point at \f$\alpha=0\f$) and its values live in + * `wolfe_info.prev_` (made available when you constructed/captured + * `update_fun`). + * + * **You must:** + * - Form the trial point \f$a(\alpha)=a_0+\alpha p\f$ and any derived + * quantities your model needs (e.g., + * \f$\theta(\alpha)\f$, \f$\nabla\theta(\alpha)\f$). + * - Compute the objective \f$\phi(\alpha)\f$ and set `e.obj()`. + * - Compute the directional derivative + * \f$\phi'(\alpha)=\nabla\phi(a(\alpha))^\top p\f$ and set `e.dir()`. + * - Populate `out` with the *entire* candidate state corresponding to + * \f$\alpha\f$ (e.g., parameters, `theta()`, `theta_grad()`, cached factors, + * etc.). The search will call `out.swap(...)` to accept this state; **do not** + * mutate `curr_`/`prev_`. + * + * **Postconditions** + * - `e.obj()` and `e.dir()` are finite when the step is numerically valid. + * - `out.theta()` and `out.theta_grad()` are finite (used by the search to + * detect numerical trouble). + * + * `update_fun` is free to close over `ll_fun` and `ll_args`. This routine + * itself does not call `ll_fun` directly; it simply invokes `update_fun` + * whenever it needs an evaluation. + * + * ### Options and tolerances + * The `opt` object must provide: + * - `double c1, c2;` // Wolfe constants (0 < c1 < c2 < 1) + * - `double tau;` // contraction factor (0 < tau < 1) + * - `double scale_up;` // expansion factor (> 1) + * - `double min_alpha, max_alpha;` // step bounds + * - `int max_iterations;` // max number of calls to + * `update_fun` + * - `double abs_grad_threshold, rel_grad_threshold;` + * - `double abs_obj_threshold, rel_obj_threshold;` + * + * @tparam Info Type providing the fields documented under *Wolfe line search + * data*. + * @tparam UpdateFun Callable used to evaluate a trial step; must satisfy the + * contract above. + * @tparam Options Type providing the fields documented under *Options and + * tolerances*. + * @tparam Stream Output stream type for diagnostics (e.g., `std::ostream`); may + * be `nullptr`. + * + * @param wolfe_info Line-search working set (holds `prev_`, `curr_`, + * `scratch_`, the direction `p_`, and the initial directional derivative). + * @param update_fun Callable that evaluates \f$\phi(\alpha)\f$, + * \f$\phi'(\alpha)\f$, and prepares the candidate state (see contract above). + * @param opt Wolfe and algorithmic options. + * @param msgs Optional stream for debug messages; pass `nullptr` to disable. + * + * @return `WolfeStatus` describing how the search ended: + * - `Wolfe` — Found a step satisfying **both** Armijo and curvature; `curr_` + * updated. + * - `Armijo` — Could not satisfy curvature; returns the best Armijo-OK step; + * `curr_` updated. + * - `ConvergedGradient` — \f$|\phi'(\alpha)|\f$ below tolerance at a tiny + * step; `curr_` may be updated iff that point also satisfies Armijo. + * - `ConvergedObjective` — Objective improvement below tolerance at a tiny + * step; same acceptance rule. + * - `ConvergedObjectiveAndGradient` — Both tests met; same acceptance rule. + * - `IntervalTooSmall` — Bracket is smaller than `min_alpha` without meeting + * strong-Wolfe; accepts the current point only if Armijo holds. + * - `StepTooSmall` — Numerical contraction drove \f$\alpha<\text{min_alpha}\f$ + * before a finite evaluation. + * - `ReachedMaxStep` — Exceeded `max_iterations`; if the best Armijo-OK point + * exists it is returned (and may be `Wolfe` or `Armijo`), otherwise search + * aborts without updating `curr_`. + * - `Fail` — No Armijo-OK point was found; `curr_` is left unchanged. + * + * The status also reports: + * - `num_evals` — total calls to `update_fun`. + * - `num_backtracks` — times the step was reduced during bracketing/zoom. + * - `accepted` — whether `curr_` was updated to a new point. + */ +template +inline WolfeStatus wolfe_line_search(Info& wolfe_info, UpdateFun&& update_fun, + Options&& opt, Stream* msgs) { + auto& curr = wolfe_info.curr_; + auto& prev = wolfe_info.prev_; + auto& scratch = wolfe_info.scratch_; + auto&& p = wolfe_info.p_; + auto&& dir_deriv_init = wolfe_info.init_dir_; + Eval low{0.0, prev.obj(), dir_deriv_init}; + prev.dir() = dir_deriv_init; + auto armijo_ok = [&prev, &opt](const Eval& eval) -> bool { + return check_armijo(eval, prev, opt); + }; + auto wolfe_ok = [&prev, &opt](const Eval& eval) -> bool { + return check_wolfe(eval, prev, opt); + }; + int total_updates = 0; + auto assign_step + = [](WolfeData& out, WolfeData& buf, Eval& e) { out.update(buf, e); }; + auto update_with_tick = [&total_updates, &update_fun, &prev, &curr]( + WolfeData& buf, Eval& e, auto&& p) { + update_fun(buf, curr, prev, e, p); + ++total_updates; + }; + auto check_max_steps = [&assign_step, &p, &total_updates, &armijo_ok, + &wolfe_ok, &update_with_tick, + &msgs](auto&& scratch, auto&& curr, auto&& prev, + auto&& best, auto&& opt) { + if (total_updates > opt.max_iterations) { + debug::print("Exit on precheck max iterations", 1); + debug::print("total_updates", total_updates); + if (armijo_ok(best)) { + update_with_tick(scratch, best, p); + assign_step(curr, scratch, best); + if (wolfe_ok(best)) { + return WolfeStatus{WolfeReturn::Wolfe, total_updates, 0, true}; + } else { + return WolfeStatus{WolfeReturn::Armijo, total_updates, 0, true}; + } + } + return WolfeStatus{WolfeReturn::ReachedMaxStep, total_updates, 0, false}; + } else { + return WolfeStatus{WolfeReturn::Continue, total_updates, 0, false}; + } + }; + double alpha_start + = std::clamp(curr.alpha() * opt.scale_up, opt.min_alpha, opt.max_alpha); + Eval high{alpha_start, curr.obj(), dir_deriv_init}; + update_with_tick(scratch, high, p); + Eval best = low; // keep the best Armijo-OK in case strong-Wolfe fails + { + while (!(std::isfinite(high.obj()) && scratch.theta().allFinite())) { + high.alpha() *= opt.tau; + if (high.alpha() < opt.min_alpha) { + debug::print("Exit on precheck numerical trouble", 1); + debug::print("total_updates", total_updates); + return WolfeStatus{WolfeReturn::StepTooSmall, total_updates, 0, false}; + } + update_with_tick(scratch, high, p); + auto check_steps = check_max_steps(scratch, curr, prev, high, opt); + if (check_steps.stop_ != WolfeReturn::Continue) { + return check_steps; + } + } + debug::print("First precheck: ", 1, "high.alpha(): ", high.alpha(), + "high.obj(): ", high.obj(), "deriv_high: ", high.dir(), + "deriv_init: ", dir_deriv_init); + // Quick accept if Armijo and Wolfe conditions are satisfied + if (armijo_ok(high)) { + if (wolfe_ok(high)) { + // Try zooming up till we hit a fail + best = high; + while (armijo_ok(high) && wolfe_ok(high)) { + best = high; + auto check_steps = check_max_steps(scratch, curr, prev, best, opt); + if (check_steps.stop_ != WolfeReturn::Continue) { + return check_steps; + } + high.alpha() *= opt.scale_up; + if (high.alpha() > opt.max_alpha) { + break; + } + update_with_tick(scratch, high, p); + debug::print("Zoom up: ", 1, "high.alpha(): ", high.alpha(), + "high.obj(): ", high.obj(), "deriv_high: ", high.dir(), + "deriv_init: ", dir_deriv_init); + } + debug::print("Exit on first precheck", 1); + update_with_tick(scratch, best, p); + assign_step(curr, scratch, best); + debug::print("total_updates", total_updates); + return WolfeStatus{WolfeReturn::Wolfe, total_updates, 0, true}; + } else { + if (best.obj() < high.obj()) { + best = high; + } + } + } + } + // If current alpha fails, backtrack down till we find a good point + debug::print("Begin Loop: ", 1, "Initial alpha: ", high.alpha()); + int loop_iter = 0; + const double grad_tol + = std::max(opt.abs_grad_threshold, + opt.rel_grad_threshold * std::abs(dir_deriv_init)); + const double obj_tol + = std::max(opt.abs_obj_threshold, + opt.rel_obj_threshold * (1.0 + std::abs(prev.obj()))); + // If true we have already found a good first point + bool found_right = false; + int num_backtracks = 0; + /** + * For each case + * | armijo | wolfe | sign(g) | Action + * -------+-------+---------+-------------------------------- + * | [1] T | T | | Accept alpha + * | [2] T | F | > 0 | set low=high, expand high + * | [3] T | F | < 0 | Set alpha_high <- alpha, stop + * | [4] F | T | | Set alpha_high <- alpha, stop + * | [5] F | F | | Set alpha_high <- alpha, stop + **/ + while (!found_right && high.alpha() < opt.max_alpha) { + num_backtracks++; + // 1. Evaluate f(alpha) and g(alpha) + update_with_tick(scratch, high, p); + debug::print("First While", 1, "Second Iter: ", loop_iter++, + "high.alpha(): ", high.alpha(), "high.obj(): ", high.obj(), + "deriv_high: ", high.dir(), "deriv_init: ", dir_deriv_init, + "scratch.theta(): ", scratch.theta().transpose()); + const bool finite_ok + = std::isfinite(high.obj()) && scratch.theta().allFinite(); + // 2. Handle numerical trouble first + if (!finite_ok) { // f or g is NaN/Inf → shrink + high.alpha() *= 0.5; + if (high.alpha() < opt.min_alpha) { + break; + } + continue; + } + if (armijo_ok(high)) { + // [1] + if (wolfe_ok(high)) { + assign_step(curr, scratch, high); + debug::print("Exit on first while", 1); + debug::print("total_updates", total_updates); + return WolfeStatus{WolfeReturn::Wolfe, total_updates, num_backtracks, + true}; + } else { + if (best.obj() < high.obj()) { + best = high; + } + // [2] + if (high.dir() > 0) { + low = high; + high.alpha() *= opt.scale_up; + continue; + } else { + // [3] + found_right = true; + } + } + } + // [4,5] + found_right = true; + auto check_steps = check_max_steps(scratch, curr, prev, best, opt); + if (check_steps.stop_ != WolfeReturn::Continue) { + return check_steps; + } + } + auto check_bounds = [&](auto&& curr_eval) { + // Check for grad convergence + if (std::abs(curr_eval.dir()) <= grad_tol || // tiny slope + std::abs(curr_eval.obj() - prev.obj()) <= obj_tol + && curr_eval.alpha() < opt.min_alpha) { // tiny gain + bool step_ok = curr_eval.obj() != low.obj() && armijo_ok(curr_eval); + if (step_ok) { + update_with_tick(scratch, curr_eval, p); + assign_step(curr, scratch, curr_eval); + } + debug::print("total_updates", total_updates); + if (std::abs(curr_eval.dir()) <= grad_tol && // tiny slope + std::abs(curr_eval.obj() - prev.obj()) <= obj_tol) { + debug::print("Exit on grad_tol and obj_tol", 1); + return WolfeStatus{WolfeReturn::ConvergedObjectiveAndGradient, + total_updates, num_backtracks, step_ok}; + } else if (std::abs(curr_eval.dir()) <= grad_tol) { + debug::print("Exit on grad_tol", 1); + return WolfeStatus{WolfeReturn::ConvergedGradient, total_updates, + num_backtracks, step_ok}; + } else if (std::abs(curr_eval.obj() - prev.obj()) <= obj_tol) { + debug::print("Exit on obj_tol", 1); + return WolfeStatus{WolfeReturn::ConvergedObjective, total_updates, + num_backtracks, step_ok}; + } else { + debug::print("Exit on alpha failure", 1); + return WolfeStatus{WolfeReturn::IntervalTooSmall, total_updates, + num_backtracks, step_ok}; + } + } + return WolfeStatus{WolfeReturn::Continue, total_updates, num_backtracks, + false}; + }; + auto check_b = check_bounds(high); + if (check_b.stop_ != WolfeReturn::Continue) { + return check_b; + } + update_with_tick(scratch, high, p); + loop_iter = 0; + // Pure bisection to try to get a sign change. + while ((low.dir() > 0 && high.dir() > 0) + && (high.alpha() - low.alpha() > opt.min_alpha)) { + Eval mid{0.5 * (low.alpha() + high.alpha()), 0.0, 0.0}; + update_with_tick(scratch, mid, p); + if (!std::isfinite(mid.obj()) || !std::isfinite(mid.dir()) + || !scratch.theta().allFinite() || !scratch.theta_grad().allFinite()) { + high.alpha() *= opt.tau; + if (high.alpha() < opt.min_alpha) + break; + continue; + } + if (best.obj() < mid.obj()) { + best = mid; + } + if (mid.dir() > 0) { + low = mid; + } else { + high = mid; + } + } + Eval mid{high}; + while (mid.alpha() > opt.min_alpha) { + num_backtracks++; + const double diff_alpha = high.alpha() - low.alpha(); + mid.alpha() = cubic_or_bisect_max(low, high, opt); + if (mid.alpha() <= opt.min_alpha) { + break; + } + update_with_tick(scratch, mid, p); + if (mid.alpha() <= opt.min_alpha) { + break; + } + const bool finite_ok + = std::isfinite(mid.obj()) && scratch.theta().allFinite(); + if (!finite_ok) { + high = mid; + continue; + } + /** + * |Armijo|Wolfe|mid.obj > low.obj|mid.dir < 0|Action| + * | T | T | | | Accept | + * | T | F | T | T | high = mid | + * | T | F | T | F | low = mid | + * | T | F | F | F | low = mid | + * | T | F | F | F | high = mid | + * | F | F | F | F | high = mid | + */ + if (armijo_ok(mid)) { + if (wolfe_ok(mid)) { + assign_step(curr, scratch, mid); + debug::print("Exit on safe on zoom", 1); + debug::print("total_updates", total_updates); + return WolfeStatus{WolfeReturn::Wolfe, total_updates, num_backtracks, + true}; + } else { + if (best.obj() < mid.obj()) { + best = mid; + } + if (mid.obj() > low.obj()) { + // sign change + if (mid.dir() * low.dir() < 0) { + high = mid; + } else { + low = mid; + } + } else { + high = mid; + } + } + } else { + if (best.obj() < high.obj()) { + best = high; + } + high = mid; + } + auto check_bb = check_bounds(mid); + if (check_bb.stop_ != WolfeReturn::Continue) { + return check_bb; + } + auto check_steps = check_max_steps(scratch, curr, prev, best, opt); + if (check_steps.stop_ != WolfeReturn::Continue) { + return check_steps; + } + } + debug::print("Failed zoom: ", 1, "Failed zoom:", 1, + "low.alpha(): ", low.alpha(), "low.obj(): ", low.obj(), + "deriv_low: ", low.dir(), "high.alpha():", high.alpha(), + "high.obj(): ", high.obj(), "deriv_high:", high.dir()); + // On failure, use the best point we have found so far that at least satisfies + // armijo + const bool armijo_ok_best = armijo_ok(best); + const bool curve_ok_best = wolfe_ok(best); + if (armijo_ok_best) { + update_with_tick(scratch, best, p); + assign_step(curr, scratch, best); + debug::print("Exit on only satisfying armijo", 1); + debug::print("total_updates", total_updates); + return WolfeStatus{WolfeReturn::Armijo, total_updates, num_backtracks, + true}; + } else { + debug::print("Exit on failure", 1); + debug::print("total_updates", total_updates); + return WolfeStatus{WolfeReturn::Fail, total_updates, num_backtracks, false}; + } +} +} // namespace internal + +} // namespace stan::math +#endif diff --git a/stan/math/mix/prob/laplace_latent_bernoulli_logit_rng.hpp b/stan/math/mix/prob/laplace_latent_bernoulli_logit_rng.hpp index 8d3cde2a36d..2f3c530faeb 100644 --- a/stan/math/mix/prob/laplace_latent_bernoulli_logit_rng.hpp +++ b/stan/math/mix/prob/laplace_latent_bernoulli_logit_rng.hpp @@ -39,9 +39,13 @@ inline Eigen::VectorXd laplace_latent_tol_bernoulli_logit_rng( const double tolerance, const int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, RNG& rng, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_base_rng( bernoulli_logit_likelihood{}, std::forward_as_tuple(to_vector(y), n_samples, std::forward(mean)), diff --git a/stan/math/mix/prob/laplace_latent_neg_binomial_2_log_rng.hpp b/stan/math/mix/prob/laplace_latent_neg_binomial_2_log_rng.hpp index ccdf4675c28..7b0ad1cf8f0 100644 --- a/stan/math/mix/prob/laplace_latent_neg_binomial_2_log_rng.hpp +++ b/stan/math/mix/prob/laplace_latent_neg_binomial_2_log_rng.hpp @@ -44,9 +44,13 @@ inline Eigen::VectorXd laplace_latent_tol_neg_binomial_2_log_rng( ThetaVec&& theta_0, const double tolerance, const int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, RNG& rng, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_base_rng( neg_binomial_2_log_likelihood{}, std::forward_as_tuple(std::forward(eta), y, y_index, diff --git a/stan/math/mix/prob/laplace_latent_poisson_log_rng.hpp b/stan/math/mix/prob/laplace_latent_poisson_log_rng.hpp index 802f2dde8e4..e392ffcbd7f 100644 --- a/stan/math/mix/prob/laplace_latent_poisson_log_rng.hpp +++ b/stan/math/mix/prob/laplace_latent_poisson_log_rng.hpp @@ -39,9 +39,13 @@ inline Eigen::VectorXd laplace_latent_tol_poisson_log_rng( const double tolerance, const int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, RNG& rng, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_base_rng( poisson_log_likelihood{}, std::forward_as_tuple(y, y_index, std::forward(mean)), diff --git a/stan/math/mix/prob/laplace_latent_rng.hpp b/stan/math/mix/prob/laplace_latent_rng.hpp index 1d6291b2e56..b1c87e2c4ec 100644 --- a/stan/math/mix/prob/laplace_latent_rng.hpp +++ b/stan/math/mix/prob/laplace_latent_rng.hpp @@ -37,8 +37,12 @@ inline auto laplace_latent_tol_rng( const int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, RNG& rng, std::ostream* msgs) { const laplace_options_user_supplied ops{ - hessian_block_size, solver, max_steps_line_search, - tolerance, max_num_steps, value_of(theta_0)}; + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_base_rng(std::forward(L_f), std::forward(ll_args), std::forward(covariance_function), diff --git a/stan/math/mix/prob/laplace_marginal.hpp b/stan/math/mix/prob/laplace_marginal.hpp index 5296d104d9f..ad0ad525064 100644 --- a/stan/math/mix/prob/laplace_marginal.hpp +++ b/stan/math/mix/prob/laplace_marginal.hpp @@ -33,9 +33,13 @@ inline auto laplace_marginal_tol( CovarArgs&& covar_args, const ThetaVec& theta_0, double tolerance, int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_marginal_density( std::forward(L_f), std::forward(l_args), std::forward(covariance_function), diff --git a/stan/math/mix/prob/laplace_marginal_bernoulli_logit_lpmf.hpp b/stan/math/mix/prob/laplace_marginal_bernoulli_logit_lpmf.hpp index c0af114da54..09691964c58 100644 --- a/stan/math/mix/prob/laplace_marginal_bernoulli_logit_lpmf.hpp +++ b/stan/math/mix/prob/laplace_marginal_bernoulli_logit_lpmf.hpp @@ -8,11 +8,13 @@ #include #include #include +#include #include #include #include #include #include +#include #include #include @@ -25,9 +27,8 @@ struct bernoulli_logit_likelihood { const std::vector& delta_int, Mean&& mean, std::ostream* pstream) const { auto theta_offset = to_ref(add(theta, mean)); - return sum( - elt_multiply(theta_offset, y) - - elt_multiply(to_vector(delta_int), log(add(1.0, exp(theta_offset))))); + return sum(elt_multiply(theta_offset, y) + - elt_multiply(to_vector(delta_int), log1p_exp(theta_offset))); } }; @@ -60,9 +61,13 @@ inline auto laplace_marginal_tol_bernoulli_logit_lpmf( const ThetaVec& theta_0, double tolerance, int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_marginal_density( bernoulli_logit_likelihood{}, std::forward_as_tuple(to_vector(y), n_samples, std::forward(mean)), diff --git a/stan/math/mix/prob/laplace_marginal_neg_binomial_2_log_lpmf.hpp b/stan/math/mix/prob/laplace_marginal_neg_binomial_2_log_lpmf.hpp index 9da39279b52..4ba134eb477 100644 --- a/stan/math/mix/prob/laplace_marginal_neg_binomial_2_log_lpmf.hpp +++ b/stan/math/mix/prob/laplace_marginal_neg_binomial_2_log_lpmf.hpp @@ -11,12 +11,14 @@ #include #include #include +#include #include #include #include #include #include #include +#include #include #include @@ -39,14 +41,17 @@ struct neg_binomial_2_log_likelihood { } Eigen::Map y_map(y.data(), y.size()); - auto theta_offset = to_ref(add(theta, mean)); - auto log_eta_plus_exp_theta = eval(log(add(eta, exp(theta_offset)))); - return sum(binomial_coefficient_log(subtract(add(y_map, eta), 1), y_map)) - + sum( - add(elt_multiply(counts_per_group, - subtract(theta_offset, log_eta_plus_exp_theta)), - elt_multiply(multiply(n_per_group, eta), - subtract(log(eta), log_eta_plus_exp_theta)))); + auto theta_offset = add(theta, mean); + auto log_eta = log(eta); + auto lse = to_ref(log_sum_exp(theta_offset, log_eta)); + + return sum(binomial_coefficient_log(subtract(add(y_map, eta), 1.0), y_map)) + + sum(add( + // counts_per_group * (theta - log(eta + exp(theta))) + elt_multiply(counts_per_group, subtract(theta_offset, lse)), + // n_per_group * eta * (log(eta) - log(eta + exp(theta))) + elt_multiply(multiply(n_per_group, eta), + subtract(log_eta, lse)))); } }; @@ -80,9 +85,13 @@ inline auto laplace_marginal_tol_neg_binomial_2_log_lpmf( const ThetaVec& theta_0, double tolerance, int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_marginal_density( neg_binomial_2_log_likelihood{}, std::forward_as_tuple(eta, y, y_index, std::forward(mean)), @@ -135,15 +144,17 @@ struct neg_binomial_2_log_likelihood_summary { Eigen::Map counts_per_group_map( counts_per_group.data(), counts_per_group.size()); - auto theta_offset = to_ref(add(theta, mean)); - auto log_eta_plus_exp_theta = eval(log(add(eta, exp(theta_offset)))); + auto theta_offset = add(theta, mean); + auto log_eta = log(eta); + auto lse = to_ref(log_sum_exp(theta_offset, log_eta)); return sum(binomial_coefficient_log(subtract(add(y_map, eta), 1.0), y_map)) - + sum( - add(elt_multiply(counts_per_group_map, - subtract(theta_offset, log_eta_plus_exp_theta)), - elt_multiply(multiply(n_per_group_map, eta), - subtract(log(eta), log_eta_plus_exp_theta)))); + + sum(add( + // counts_per_group * (theta - log(eta + exp(theta))) + elt_multiply(counts_per_group_map, subtract(theta_offset, lse)), + // n_per_group * eta * (log(eta) - log(eta + exp(theta))) + elt_multiply(multiply(n_per_group_map, eta), + subtract(log_eta, lse)))); } }; @@ -178,9 +189,13 @@ inline auto laplace_marginal_tol_neg_binomial_2_log_summary_lpmf( const ThetaVec& theta_0, double tolerance, int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_marginal_density( neg_binomial_2_log_likelihood_summary{}, std::forward_as_tuple(eta, y, n_per_group, counts_per_group, diff --git a/stan/math/mix/prob/laplace_marginal_poisson_log_lpmf.hpp b/stan/math/mix/prob/laplace_marginal_poisson_log_lpmf.hpp index 5652bac7f01..3b5fa9f829d 100644 --- a/stan/math/mix/prob/laplace_marginal_poisson_log_lpmf.hpp +++ b/stan/math/mix/prob/laplace_marginal_poisson_log_lpmf.hpp @@ -77,9 +77,13 @@ inline auto laplace_marginal_tol_poisson_log_lpmf( const ThetaVec& theta_0, double tolerance, int max_num_steps, const int hessian_block_size, const int solver, const int max_steps_line_search, std::ostream* msgs) { - laplace_options_user_supplied ops{hessian_block_size, solver, - max_steps_line_search, tolerance, - max_num_steps, value_of(theta_0)}; + laplace_options_user_supplied ops{ + hessian_block_size, + solver, + tolerance, + max_num_steps, + laplace_line_search_options{max_steps_line_search}, + value_of(theta_0)}; return laplace_marginal_density( poisson_log_likelihood{}, std::forward_as_tuple(y, y_index, std::forward(mean)), diff --git a/stan/math/prim/fun/finite_diff_stepsize.hpp b/stan/math/prim/fun/finite_diff_stepsize.hpp index b32ec098462..d652306345c 100644 --- a/stan/math/prim/fun/finite_diff_stepsize.hpp +++ b/stan/math/prim/fun/finite_diff_stepsize.hpp @@ -3,25 +3,86 @@ #include #include +#include #include namespace stan { namespace math { +namespace internal { +template +inline constexpr auto eps_root_calc() { + constexpr T eps = std::numeric_limits::epsilon(); + if constexpr (StencilOrder == 2) { + // ε^(1/3) + return std::cbrt(eps); + } else if constexpr (StencilOrder == 3) { + // ε^(1/4) = sqrt(sqrt(ε)) + return std::sqrt(std::sqrt(eps)); + } else if constexpr (StencilOrder == 5) { + // ε^(1/6) = sqrt(cbrt(ε)) + return std::sqrt(std::cbrt(eps)); + } else { + // General fallback: ε^(1/(p+1)) + return std::pow(eps, T(1) / T(StencilOrder + 1)); + } +} +} // namespace internal /** - * Return the stepsize for finite difference evaluations at the - * specified scalar. + * @brief Compute a finite-difference step size suitable for a stencil with + * leading truncation order \p StencilOrder. + * + * This implements the standard balance between truncation error + * \f$A\,h^{p}\f$ and floating-point rounding error \f$B\,\varepsilon/h\f$, + * whose minimizer is \f$h_\star \propto \varepsilon^{1/(p+1)}\f$, where + * \f$p = \texttt{StencilOrder}\f$ and \f$\varepsilon\f$ is machine epsilon + * for the scalar type \p T. We additionally scale by \f$\max(1, |u|)\f$ to + * obtain an absolute step size near the point being perturbed. + * + * For the common second-order (3-point central) stencil, the function uses an + * `if constexpr` branch to compute \f$\varepsilon^{1/3}\f$ via `std::cbrt` + * (avoids a `pow` and is numerically tidy). For higher orders it uses + * \f$\varepsilon^{1/(p+1)}\f` via `std::pow`. + * + * @tparam T Floating-point scalar type (e.g., float, double). + * @tparam StencilOrder Leading truncation order \f$p\f$ of your stencil: + * - first-derivative 3-point central → \f$p=2\f$ + * - first-derivative 5-point central → \f$p=4\f$ + * - first-derivative 6-point central → \f$p=6\f$ + * - “derivative of Hessian” via 5-point diff → \f$p=4\f$ + * + * @param u The coordinate value (or local scale) at which the step will be + * applied; the step is scaled by \f$\max(1, |u|)\f$. + * @param c Dimensionless tuning constant multiplying the theoretically + * optimal step. Default is 1.0. In practice, \f$c \in [0.5, 2]\f$ + * works well: + * - Increase \p c (larger h) if round-off/cancellation dominates + * (noisy function values, very large |f|, many subtractions). + * - Decrease \p c (smaller h) if truncation dominates (very smooth + * function with large higher derivatives or low curvature scale). + * If your problem has a known physical scale S (not |u|), prefer + * passing \p u scaled by S or modify the scaling accordingly. * - *

The formula used is `stepsize(u) = cbrt(epsilon) * max(1, - * abs(u)).` + * @return A step size \f$h\f$ such that \f$u+h \neq u\f$; if the theoretical + * step underflows at \p u, the function falls back to the next + * representable increment. * - * @param u initial value to increment - * @return stepsize away from u for finite differences + * @note The step computed here assumes smooth (at least \(p{+}1\) times + * differentiable) behavior along the perturbed coordinate. */ -inline double finite_diff_stepsize(double u) { - using std::fabs; - static const double cbrt_epsilon = std::cbrt(EPSILON); - return cbrt_epsilon * std::fmax(1, fabs(u)); +template +inline auto finite_diff_stepsize(T u_, T c = T(1)) { + using fp_t = std::conditional_t, double, T>; + const fp_t u = static_cast(u_); + const fp_t scale = std::max(fp_t{1}, std::abs(u)); + const fp_t eps_root = internal::eps_root_calc(); + const fp_t h = static_cast(c) * eps_root * scale; + // Ensure perturbation isn’t rounded away at u. + if (u + h == u) { + const fp_t next = std::nextafter(u, std::numeric_limits::infinity()); + return std::max(h, next - u); + } + return h; } } // namespace math diff --git a/stan/math/prim/functor/finite_diff_gradient_auto.hpp b/stan/math/prim/functor/finite_diff_gradient_auto.hpp index 8c9951ae37b..4f6caec77a2 100644 --- a/stan/math/prim/functor/finite_diff_gradient_auto.hpp +++ b/stan/math/prim/functor/finite_diff_gradient_auto.hpp @@ -59,7 +59,7 @@ inline void finite_diff_gradient_auto(const F& f, VectorT&& x, ScalarT& fx, Eigen::Map grad_map(grad_fx.data(), grad_fx.size()); grad_map = EigT::NullaryExpr(x.size(), [&f, &x](Eigen::Index i) { - double h = finite_diff_stepsize(value_of_rec(x[i])); + double h = finite_diff_stepsize<2>(value_of_rec(x[i])); ScalarT delta_f = 0; for (int j = 0; j < 6; ++j) { auto x_temp diff --git a/stan/math/prim/meta/is_autodiff.hpp b/stan/math/prim/meta/is_autodiff.hpp index 91acf9a92ef..a5eec9f62e3 100644 --- a/stan/math/prim/meta/is_autodiff.hpp +++ b/stan/math/prim/meta/is_autodiff.hpp @@ -57,13 +57,16 @@ template struct is_autodiff : internal::is_autodiff {}; template -inline constexpr bool is_autodiff_v = internal::is_autodiff::value; +inline constexpr bool is_autodiff_v + = internal::is_autodiff>::value; template -inline constexpr bool is_all_autodiff_v = (is_autodiff_v && ...); +inline constexpr bool is_all_autodiff_v + = (is_autodiff_v> && ...); template -inline constexpr bool is_any_autodiff_v = (is_autodiff_v || ...); +inline constexpr bool is_any_autodiff_v + = (is_autodiff_v> || ...); /*! \ingroup require_stan_scalar_real */ /*! \defgroup autodiff_types autodiff */ diff --git a/test/unit/math/ad_tolerances.hpp b/test/unit/math/ad_tolerances.hpp index 268767b2192..08da13c7278 100644 --- a/test/unit/math/ad_tolerances.hpp +++ b/test/unit/math/ad_tolerances.hpp @@ -6,6 +6,17 @@ namespace stan { namespace test { +/** + * Helper struct for setting the gradient tolerances used for reverse mode. + */ +struct ad_gradient_tols { + relative_tolerance val_{1e-8}; + relative_tolerance grad_{1e-4}; + constexpr ad_gradient_tols() = default; + constexpr ad_gradient_tols(relative_tolerance val, relative_tolerance grad) + : val_(val), grad_(grad) {} +}; + /** * Simple struct to hold the complete set of tolerances used to test a * function. The default constructor uses default values for all @@ -33,42 +44,24 @@ namespace test { * `grad_hessian_grad_hessian_`: 1e-2 */ struct ad_tolerances { - relative_tolerance gradient_val_; - relative_tolerance gradient_grad_; - relative_tolerance gradient_grad_varmat_matvar_; - relative_tolerance gradient_fvar_val_; - relative_tolerance gradient_fvar_grad_; - relative_tolerance hessian_val_; - relative_tolerance hessian_grad_; - relative_tolerance hessian_hessian_; - relative_tolerance hessian_fvar_val_; - relative_tolerance hessian_fvar_grad_; - relative_tolerance hessian_fvar_hessian_; - relative_tolerance grad_hessian_val_; - relative_tolerance grad_hessian_hessian_; - relative_tolerance grad_hessian_grad_hessian_; - constexpr ad_tolerances() - : gradient_val_(1e-8), - gradient_grad_(1e-4), - - gradient_grad_varmat_matvar_(1e-8), - - gradient_fvar_val_(1e-8), - gradient_fvar_grad_(1e-4), - - hessian_val_(1e-8), - hessian_grad_(1e-4), - hessian_hessian_(1e-4, 1e-3), - - hessian_fvar_val_(1e-8), - hessian_fvar_grad_(1e-4), - hessian_fvar_hessian_(1e-4, 1e-3), - - grad_hessian_val_(1e-8), - grad_hessian_hessian_(1e-3), - grad_hessian_grad_hessian_(1e-2) {} + relative_tolerance gradient_val_{1e-8}; + relative_tolerance gradient_grad_{1e-4}; + relative_tolerance gradient_grad_varmat_matvar_{1e-8}; + relative_tolerance gradient_fvar_val_{1e-8}; + relative_tolerance gradient_fvar_grad_{1e-4}; + relative_tolerance hessian_val_{1e-8}; + relative_tolerance hessian_grad_{1e-4}; + relative_tolerance hessian_hessian_{1e-4, 1e-3}; + relative_tolerance hessian_fvar_val_{1e-8}; + relative_tolerance hessian_fvar_grad_{1e-4}; + relative_tolerance hessian_fvar_hessian_{1e-4, 1e-3}; + relative_tolerance grad_hessian_val_{1e-8}; + relative_tolerance grad_hessian_hessian_{1e-3}; + relative_tolerance grad_hessian_grad_hessian_{1e-2}; + constexpr ad_tolerances() = default; + constexpr explicit ad_tolerances(ad_gradient_tols grad_tols) + : gradient_val_(grad_tols.val_), gradient_grad_(grad_tols.grad_) {} }; - } // namespace test } // namespace stan #endif diff --git a/test/unit/math/laplace/aki_ex_test.cpp b/test/unit/math/laplace/aki_ex_test.cpp new file mode 100644 index 00000000000..bc9dd1f0502 --- /dev/null +++ b/test/unit/math/laplace/aki_ex_test.cpp @@ -0,0 +1,209 @@ +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include + +struct poisson_re_log_ll_functor { + template + stan::return_type_t, stan::base_type_t> operator()( + const T0& theta_arg, const T1& y_arg, const T2& mu_arg, + std::ostream* pstream) const { + using local_scalar_t + = stan::return_type_t, stan::base_type_t>; + auto&& theta = stan::math::to_ref(theta_arg); + auto&& mu = stan::math::to_ref(mu_arg); + auto mu_theta = stan::math::eval( + stan::math::add(stan::math::as_column_vector_or_scalar(mu), theta)); + return stan::math::poisson_log_lpmf(y_arg, mu_theta); + } +}; + +struct integrand_functor { + template + stan::return_type_t, stan::base_type_t> + operator()(const T0& theta, const T1& notused, const T2& phi, const T3& X_i, + const T4& y_i, std::ostream* pstream) const { + using local_scalar_t = stan::return_type_t, + stan::base_type_t>; + // suppress unused var warning + static constexpr bool propto = true; + local_scalar_t sigma = phi[0]; + local_scalar_t mu = phi[1]; + local_scalar_t p = stan::math::exp( + (stan::math::normal_lpdf(theta, 0, sigma) + + stan::math::poisson_log_lpmf(y_i, (theta + mu)))); + return p; + } +}; +struct integrand_vec_functor { + template + stan::return_type_t, stan::base_type_t> + operator()(const T0& theta, const T1& notused, const T2& phi, const T3& X_i, + const T4& y_i, std::ostream* pstream) const { + using local_scalar_t = stan::return_type_t, + stan::base_type_t>; + // suppress unused var warning + static constexpr bool propto = true; + auto sigma = phi[0]; + auto mu + = stan::math::as_column_vector_or_scalar(phi).tail(theta.size()).eval(); + auto p = stan::math::exp((stan::math::normal_lpdf(theta, 0, sigma) + + stan::math::poisson_log_lpmf( + y_i, stan::math::add(theta, mu)))); + return p; + } +}; +struct cov_fun_functor { + template + Eigen::Matrix, -1, -1> operator()( + const T0& sigma, const int& N, std::ostream* pstream) const { + using local_scalar_t = stan::return_type_t; + return stan::math::diag_matrix( + stan::math::rep_vector(stan::math::pow(sigma, 2), N)); + } +}; + +TEST(WriteArrayBodySimple, ExceededIteration) { + stan::test::relative_tolerance rel_tol(5e-2); + const double integrate_1d_reltol = 1e-8; + auto mu_samples = stan::math::test::laplace::read_matrix_csv( + "./test/unit/math/laplace/roach_data/mu_bad.csv"); + auto sigmaz_samples = stan::math::test::laplace::read_matrix_csv( + "./test/unit/math/laplace/roach_data/sigma_bad.csv"); + auto y_samples_dbl = stan::math::test::laplace::read_matrix_csv( + "./test/unit/math/laplace/roach_data/y_bad.csv"); + auto y_samples = y_samples_dbl.cast(); + const int num_samples = mu_samples.cols(); + const int N = mu_samples.rows(); + std::ostream* pstream = nullptr; + for (int i = 1; i <= N; ++i) { + auto y = y_samples(i - 1, 0); + auto mu = mu_samples(i - 1, 0); + auto sigmaz = sigmaz_samples(i - 1, 0); + + double ll_laplace_val{0}; + try { + ll_laplace_val = stan::math::laplace_marginal( + poisson_re_log_ll_functor(), std::forward_as_tuple(y, mu), + cov_fun_functor(), std::tuple(sigmaz, 1), pstream); + } catch (const std::domain_error& e) { + // Log bad values to CSV files + ADD_FAILURE() << "Laplace failed" + << "(i, y, mu, sigma) = (" << i << ", " << y << ", " << mu + << ", " << sigmaz << ")" + << "\nerror: " << e.what(); + continue; + } + double piece{0}; + try { + piece = stan::math::integrate_1d( + integrand_functor(), stan::math::negative_infinity(), + stan::math::positive_infinity(), std::vector{sigmaz, mu}, + std::vector{0}, std::vector{y}, pstream, + integrate_1d_reltol); + std::string msg = std::string("for (i) = (") + std::to_string(i) + + "), laplace and integrated results should be close"; + expect_near_rel(msg, ll_laplace_val, std::log(piece), rel_tol, + "laplace_val", "integrated_val"); + } catch (const std::domain_error& e) { + // NOTE: Failures for integration our fine since we are testing laplace. + continue; + } + } +} + +TEST(WriteArrayBodySimple, ExecutesBodyWithHardcodedData) { + stan::test::relative_tolerance rel_tol(5e-1); + const double integrate_1d_reltol = 1e-8; + auto&& y = stan::math::test::roaches::y; + auto&& sigmaz_samples = stan::math::test::roaches::sigmaz; + auto mu_samples = stan::math::test::laplace::read_matrix_csv( + "./test/unit/math/laplace/roach_data/mu.csv"); + const int num_samples = mu_samples.cols(); + const int N = mu_samples.rows(); + std::ostream* pstream = nullptr; + for (int iter = 0; iter < num_samples; ++iter) { + std::vector ll_laplace_vec; + double ll_integrate_1d = 0; + double ll_laplace = 0; + std::vector ll_integrate_1d_vec; + auto mu = mu_samples.col(iter); + auto sigmaz = sigmaz_samples(0, iter); + for (int i = 1; i <= N; ++i) { + // std::cout << "y and mu for (i, iter) = (" << i << ", " << iter << + // "): (" + // << y[i - 1] << ", " << mu[i - 1] << ")" << std::endl; + double ll_laplace_val{0}; + try { + ll_laplace_val = stan::math::laplace_marginal( + poisson_re_log_ll_functor(), + std::forward_as_tuple(y[i - 1], mu[i - 1]), cov_fun_functor(), + std::tuple(sigmaz, 1), pstream); + } catch (const std::domain_error& e) { + // Log bad values to CSV files + + /* + std::ofstream + y_bad("./test/unit/math/laplace/roach_data/y_bad.csv", + std::ios::app); std::ofstream + mu_bad("./test/unit/math/laplace/roach_data/mu_bad.csv", + std::ios::app); std::ofstream + sigma_bad("./test/unit/math/laplace/roach_data/sigma_bad.csv", + std::ios::app); if (y_bad && mu_bad && sigma_bad) { y_bad << y[i - 1] + << '\n'; mu_bad << mu[i - 1] << '\n'; sigma_bad << sigmaz << '\n'; + } + */ + ADD_FAILURE() << "LAPLACE FAILURE: y and mu for i = " << i << ": (" + << y[i - 1] << ", " << mu[i - 1] << ")" + << "\nerror: " << e.what() << std::endl; + continue; + } + double piece{0}; + try { + piece = stan::math::integrate_1d( + integrand_functor(), stan::math::negative_infinity(), + stan::math::positive_infinity(), + std::vector{sigmaz, mu[i - 1]}, std::vector{0}, + std::vector{y[i - 1]}, pstream, integrate_1d_reltol); + ll_laplace_vec.push_back(ll_laplace_val); + ll_integrate_1d_vec.push_back(std::log(piece)); + ll_integrate_1d += std::log(piece); + ll_laplace += ll_laplace_val; + std::string msg = std::string("for (i) = (") + std::to_string(i) + + "), laplace and integrated results should be close"; + expect_near_rel(msg, ll_laplace_val, std::log(piece), rel_tol, + "laplace_val", "integrated_val"); + } catch (const std::domain_error& e) { + // Note: Integration failures are fine since we are testing laplace. + continue; + } + } + auto ll_laplace_all = stan::math::laplace_marginal( + poisson_re_log_ll_functor(), std::forward_as_tuple(y, mu), + cov_fun_functor(), std::tuple(sigmaz, N), pstream); + // Assertions + // std::cout << "ll_laplace: " << ll_laplace << "\nll_laplace_all: " << + // ll_laplace_all << "\nll_integrate_1d: " << ll_integrate_1d << + // std::endl; + stan::test::relative_tolerance sum_rel_tol(3e-2); + expect_near_rel("sum laplace vs integrated sum", ll_laplace, + ll_integrate_1d, sum_rel_tol, "laplace_sum", + "integrated_sum"); + expect_near_rel("total laplace vs integrated sum", ll_laplace_all, + ll_integrate_1d, sum_rel_tol, "laplace_sum", + "integrated_sum"); + EXPECT_TRUE(std::isfinite(ll_laplace)) << "Laplace result should be finite"; + EXPECT_TRUE(std::isfinite(ll_integrate_1d)) + << "Integrated result should be finite"; + } +} diff --git a/test/unit/math/laplace/csv_reader.hpp b/test/unit/math/laplace/csv_reader.hpp new file mode 100644 index 00000000000..71b9b7693fe --- /dev/null +++ b/test/unit/math/laplace/csv_reader.hpp @@ -0,0 +1,66 @@ +#pragma once +#include // or +#include +#include +#include +#include +#include + +namespace stan::math::test::laplace { + +/** + * Reads a CSV of doubles into a dynamically sized Eigen::Matrix. + * + * @param file_path Path to a CSV file with R-style numeric matrix + * (no header, no row names, comma-separated). + * @return Matrix(rows, cols) filled from the file. + * @throws std::runtime_error on I/O error or inconsistent column counts. + */ +inline Eigen::Matrix read_matrix_csv( + const std::string& file_path) { + std::ifstream in(file_path); + if (!in.is_open()) { + throw std::runtime_error("Could not open CSV file: " + file_path); + } + + std::vector> buffer; + std::string line; + while (std::getline(in, line)) { + if (line.empty()) { + continue; // skip blank lines + } + std::vector row; + std::stringstream ss(line); + std::string cell; + while (std::getline(ss, cell, ',')) { + try { + row.push_back(std::stod(cell)); + } catch (const std::invalid_argument&) { + throw std::runtime_error("Non-numeric value in CSV at line: " + line); + } + } + if (!buffer.empty() && row.size() != buffer[0].size()) { + throw std::runtime_error("Inconsistent column count in CSV: expected " + + std::to_string(buffer[0].size()) + " but got " + + std::to_string(row.size())); + } + buffer.push_back(std::move(row)); + } + + // If empty file, return a 0×0 matrix + if (buffer.empty()) { + return Eigen::Matrix(0, 0); + } + + const int rows = static_cast(buffer.size()); + const int cols = static_cast(buffer[0].size()); + Eigen::Matrix mat(rows, cols); + for (int i = 0; i < rows; ++i) { + for (int j = 0; j < cols; ++j) { + mat(i, j) = buffer[i][j]; + } + } + return mat; +} + +} // namespace stan::math::test::laplace diff --git a/test/unit/math/laplace/laplace_bernoulli_logit_rng_test.cpp b/test/unit/math/laplace/laplace_bernoulli_logit_rng_test.cpp index 9ad613894c2..4442bcf7066 100644 --- a/test/unit/math/laplace/laplace_bernoulli_logit_rng_test.cpp +++ b/test/unit/math/laplace/laplace_bernoulli_logit_rng_test.cpp @@ -64,16 +64,12 @@ TEST(laplace_bernoulli_logit_rng, two_dim_diag) { using stan::math::sqrt; using stan::math::square; - Eigen::VectorXd theta_0(2); - theta_0 << 0, 0; - Eigen::VectorXd phi(2); - phi << 3, 2; + Eigen::VectorXd theta_0{{0, 0}}; + Eigen::VectorXd phi{{3, 2}}; std::vector n_samples = {1, 1}; std::vector sums = {1, 0}; - Eigen::VectorXd ye(2); - ye << 1, 1; - Eigen::VectorXd mean(2); - mean << 0, 0; + Eigen::VectorXd ye{{1, 1}}; + Eigen::VectorXd mean{{0, 0}}; std::vector d0; std::vector di0; std::vector x_dummy; diff --git a/test/unit/math/laplace/laplace_marginal_bernoulli_logit_lpmf_test.cpp b/test/unit/math/laplace/laplace_marginal_bernoulli_logit_lpmf_test.cpp index 3445a6d1591..f9804d4b90e 100644 --- a/test/unit/math/laplace/laplace_marginal_bernoulli_logit_lpmf_test.cpp +++ b/test/unit/math/laplace/laplace_marginal_bernoulli_logit_lpmf_test.cpp @@ -15,40 +15,31 @@ TEST(laplace_marginal_bernoulli_logit_lpmf, phi_dim500) { using stan::math::to_vector; using stan::math::var; using stan::math::test::flag_test; - int dim_theta = 500; - int n_observations = 500; + constexpr int dim_theta = 500; auto x1 = stan::test::laplace::x1; auto x2 = stan::test::laplace::x2; auto y = stan::test::laplace::y; - - int dim_x = 2; std::vector x(dim_theta); for (int i = 0; i < dim_theta; i++) { - Eigen::VectorXd coordinate(dim_x); - coordinate << x1[i], x2[i]; - x[i] = coordinate; + x[i] = Eigen::VectorXd{{x1[i], x2[i]}}; } std::vector n_samples = stan::math::rep_array(1, dim_theta); Eigen::VectorXd theta_0 = Eigen::VectorXd::Zero(dim_theta); Eigen::VectorXd mean = Eigen::VectorXd::Zero(dim_theta); std::vector delta; std::vector delta_int; - int dim_phi = 2; - double tol = 8e-5; - Eigen::Matrix phi_dbl(dim_phi); - phi_dbl << 1.6, 1; + Eigen::Matrix phi_dbl{{1.6, 1}}; using stan::math::test::sqr_exp_kernel_functor; double target = laplace_marginal_bernoulli_logit_lpmf( y, n_samples, 0, sqr_exp_kernel_functor{}, std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1)), nullptr); // Benchmark against gpstuff. + constexpr double tol = 8e-4; EXPECT_NEAR(-195.368, target, tol); - constexpr double tolerance = 1e-8; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 1000; - // solver_num, max_steps_line_search, hessian_block_size - using stan::math::test::laplace_issue; - constexpr std::array known_issues{ - laplace_issue{1, 1, 1}, laplace_issue{1, 2, 1}, laplace_issue{1, 2, 3}}; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-3}}; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -59,11 +50,6 @@ TEST(laplace_marginal_bernoulli_logit_lpmf, phi_dim500) { max_num_steps, hessian_block_size, solver_num, max_steps_line_search, nullptr); }; - stan::test::ad_tolerances tols; - if (flag_test(known_issues, solver_num, max_steps_line_search, - hessian_block_size)) { - tols.gradient_grad_ = 0.005; - } stan::test::expect_ad(tols, f, phi_dbl[0], phi_dbl[1]); }, theta_0); diff --git a/test/unit/math/laplace/laplace_marginal_lpdf_moto_test.cpp b/test/unit/math/laplace/laplace_marginal_lpdf_moto_test.cpp new file mode 100644 index 00000000000..487a8f6701b --- /dev/null +++ b/test/unit/math/laplace/laplace_marginal_lpdf_moto_test.cpp @@ -0,0 +1,277 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +struct normal_likelihood { + template + auto operator()(const Theta& theta, const YVec& y, const int delta_int, + std::ostream* pstream) const { + int n_obs = delta_int; + Eigen::Matrix, -1, 1> mu(n_obs); + Eigen::Matrix, -1, 1> sigma(n_obs); + stan::return_type_t lp = 0; + for (Eigen::Index i = 0; i < n_obs; i++) { + mu(i) = theta(2 * i); + // TODO(Charles): Theta can be a large negative value so sigma can be 0 + sigma(i) = stan::math::lb_constrain( + stan::math::multiply(0.5, theta(2 * i + 1)), 1e-14, lp); + } + try { + return stan::math::normal_lpdf(y, mu, sigma) + lp; + } catch (const std::domain_error& e) { + std::cout << "Error in normal_lpdf: " << e.what() << std::endl; + std::cout << "theta: \n" << theta.transpose() << std::endl; + std::cout << "y: \n" << y.transpose() << std::endl; + std::cout << "mu: \n" << mu.transpose() << std::endl; + std::cout << "sigma: \n" << sigma.transpose() << std::endl; + return stan::math::normal_lpdf(y, mu, sigma) + lp; + } + } +}; + +struct covariance_motorcycle_functor { + template + auto operator()(const TX& x, const LengthF& length_scale_f, + const LengthG& length_scale_g, const SigmaF& sigma_f, + const SigmaG& sigma_g, const int n_obs, + std::ostream* msgs = nullptr) const { + using Eigen::Matrix; + using stan::math::gp_exp_quad_cov; + using scalar_t = stan::return_type_t; + + constexpr double jitter = 1e-8; + Matrix kernel_f + = gp_exp_quad_cov(x, sigma_f, length_scale_f); + Matrix kernel_g + = gp_exp_quad_cov(x, sigma_g, length_scale_g); + + Matrix kernel_all + = Eigen::MatrixXd::Zero(2 * n_obs, 2 * n_obs); + for (Eigen::Index i = 0; i < n_obs; i++) { + for (Eigen::Index j = 0; j <= i; j++) { + kernel_all(2 * i, 2 * j) = kernel_f(i, j); + kernel_all(2 * i + 1, 2 * j + 1) = kernel_g(i, j); + if (i != j) { + kernel_all(2 * j, 2 * i) = kernel_all(2 * i, 2 * j); + kernel_all(2 * j + 1, 2 * i + 1) = kernel_all(2 * i + 1, 2 * j + 1); + } + } + } + for (Eigen::Index i = 0; i < 2 * n_obs; i++) { + kernel_all(i, i) += jitter; + } + return kernel_all; + } +}; + +class laplace_motorcyle_gp_test : public ::testing::Test { + protected: + void SetUp() override { + using stan::math::gp_exp_quad_cov; + using stan::math::value_of; + Eigen::MatrixXd K_plus_I + = gp_exp_quad_cov(x, value_of(sigma_f), value_of(length_scale_f)) + + Eigen::MatrixXd::Identity(n_obs, n_obs); + Eigen::VectorXd mu_hat = K_plus_I.colPivHouseholderQr().solve(y); + // Remark: finds optimal point with or without informed initial guess. + // Better θ0: μ at GP posterior mean; g at a stable constant σ from + // residuals + for (int i = 0; i < n_obs; ++i) { + theta0(2 * i) = mu_hat(i); + } + // After computing mu_hat as you already do + Eigen::VectorXd r = (y - mu_hat).cwiseAbs(); + + // Optional tiny smoothing to avoid zeros / spikes (window radius = 2) + Eigen::VectorXd r_smooth = r; + for (int i = 0; i < n_obs; ++i) { + double acc = 0.0; + int cnt = 0; + for (int j = std::max(0, i - 2); j <= std::min(n_obs - 1, i + 2); ++j) { + acc += r(j); + ++cnt; + } + r_smooth(i) = acc / cnt; + } + + // Baseline scale for clamping + double s0 = std::max(1e-3, std::sqrt(r.array().square().mean())); + + // Choose sigma_i0 close to |residual|, and clamp to a sane band + for (int i = 0; i < n_obs; ++i) { + double si = std::min(2.0 * s0, std::max(0.5 * s0, r_smooth(i))); + // sigma = lb + exp(0.5 * theta) => theta = 2 * log(sigma - lb) + theta0(2 * i + 1) = 2.0 * std::log(std::max(si - 1e-14, 1e-12)); + } + } + + static constexpr int n_obs{133}; + static constexpr int dim_phi{4}; + std::vector x{stan::test::laplace::moto::x}; + Eigen::VectorXd y{stan::test::laplace::moto::y}; + + static constexpr double length_scale_f{0.3}; + static constexpr double length_scale_g{0.5}; + static constexpr double sigma_f{0.25}; + static constexpr double sigma_g{0.25}; + Eigen::VectorXd theta0{Eigen::VectorXd::Zero(2 * n_obs)}; + Eigen::Matrix eta{{1.0}}; + static constexpr double sigma_global{1.0}; + Eigen::VectorXd eta_dbl{{sigma_global}}; + static constexpr int solver{2}; + static constexpr double eps{1e-7}; + Eigen::VectorXd phi_dbl{{length_scale_f, length_scale_g, sigma_f, sigma_g}}; +}; + +TEST_F(laplace_motorcyle_gp_test, gp_motorcycle_val) { + // logger->current_test_name_ = "gp_motorcycle"; + using stan::math::laplace_marginal_tol; + constexpr double tolerance = 1e-12; + constexpr int max_num_steps = 1000; + constexpr int hessian_block_size = 2; + constexpr int do_line_search = 1; + constexpr int max_steps_line_search = 10; + + double target = laplace_marginal_tol( + normal_likelihood{}, std::forward_as_tuple(y, n_obs), + covariance_motorcycle_functor{}, + std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1), phi_dbl(2), phi_dbl(3), + n_obs), + theta0, tolerance, max_num_steps, hessian_block_size, 3, + max_steps_line_search, nullptr); +} + +TEST_F(laplace_motorcyle_gp_test, gp_motorcycle_ad) { + using stan::math::gp_exp_quad_cov; + using stan::math::value_of; + // logger->current_test_name_ = "gp_motorcycle"; + using stan::math::laplace_marginal_tol; + + // TODO(Steve): benchmark this result against GPStuff. + constexpr double tolerance = 1e-8; + constexpr int max_num_steps = 1000; + auto phi_0 = phi_dbl(0); + auto phi_1 = phi_dbl(1); + Eigen::VectorXd phi_rest = phi_dbl.tail(2); + Eigen::VectorXd phi_01{{phi_0, phi_1}}; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-1}}; + stan::math::test::run_solver_grid( + [&](int solver_num, int hessian_block_size, int max_steps_line_search, + auto&& theta_0) { + auto f = [&](auto&& phi_01_v, auto&& phi_rest_v) { + return laplace_marginal_tol( + normal_likelihood{}, std::forward_as_tuple(y, n_obs), + covariance_motorcycle_functor{}, + std::forward_as_tuple(x, phi_01_v(0), phi_01_v(1), phi_rest_v(0), + phi_rest_v(1), n_obs), + theta_0, tolerance, max_num_steps, hessian_block_size, solver_num, + max_steps_line_search, nullptr); + }; + try { + stan::test::expect_ad(tols, f, phi_01, phi_rest); + } catch (const std::domain_error e) { + ADD_FAILURE() << "Exception: " << e.what() + << "\n\tsolver_num: " << solver_num + << "\n\tmax_steps_line_search: " + << max_steps_line_search + << "\n\thessian_block_size: " << hessian_block_size + << std::endl; + stan::math::recover_memory(); + } + }, + theta0); +} + +struct normal_likelihood2 { + template + auto operator()(const Theta& theta, const Eigen::VectorXd& y, const int n_obs, + const SigmaGlobal& sigma_global, + std::ostream* pstream) const { + using stan::math::multiply; + Eigen::Matrix, -1, 1> mu(n_obs); + Eigen::Matrix, -1, 1> sigma(n_obs); + stan::return_type_t lp = 0; + for (int i = 0; i < n_obs; i++) { + mu(i) = theta(2 * i); + sigma(i) = stan::math::lb_constrain(multiply(0.5, theta(2 * i + 1)), + 0.0, lp); // * sigma_global; + } + // return stan::math::normal_lpdf(y, mu, sigma); + return stan::math::normal_lpdf(y, mu, stan::math::add(sigma_global, sigma)) + + lp; + } +}; + +TEST_F(laplace_motorcyle_gp_test, gp_motorcycle2_val) { + using stan::math::gp_exp_quad_cov; + using stan::math::value_of; + Eigen::MatrixXd K_plus_I + = gp_exp_quad_cov(x, value_of(sigma_f), value_of(length_scale_f)) + + Eigen::MatrixXd::Identity(n_obs, n_obs); + Eigen::VectorXd mu_hat = K_plus_I.colPivHouseholderQr().solve(y); + // Remark: finds optimal point with or without informed initial guess. + for (int i = 0; i < n_obs - 1; i++) { + theta0(2 * i) = mu_hat(i); + theta0(2 * i + 1) = -1.0; + } + using stan::math::laplace_marginal_tol; + Eigen::VectorXd length_scale_vec = phi_dbl.head(2); + Eigen::VectorXd sigma_vec = phi_dbl.tail(2); + constexpr double tolerance = 1e-12; + constexpr int max_num_steps = 300; + constexpr int hessian_block_size = 2; + constexpr int do_line_search = 1; + constexpr int max_steps_line_search = 200; + double target = laplace_marginal_tol( + normal_likelihood2{}, std::forward_as_tuple(y, n_obs, sigma_global), + covariance_motorcycle_functor{}, + std::forward_as_tuple(x, length_scale_f, length_scale_g, sigma_f, sigma_g, + n_obs), + theta0, tolerance, max_num_steps, hessian_block_size, 3, + max_steps_line_search, nullptr); +} + +TEST_F(laplace_motorcyle_gp_test, gp_motorcycle2_ad) { + using stan::math::gp_exp_quad_cov; + using stan::math::laplace_marginal_tol; + using stan::math::value_of; + Eigen::MatrixXd K_plus_I + = gp_exp_quad_cov(x, value_of(sigma_f), value_of(length_scale_f)) + + Eigen::MatrixXd::Identity(n_obs, n_obs); + Eigen::VectorXd mu_hat = K_plus_I.colPivHouseholderQr().solve(y); + // TODO(Charles): benchmark this result against GPStuff. + constexpr double tolerance = 1e-8; + constexpr int max_num_steps = 1000; + Eigen::VectorXd length_scale_vec = phi_dbl.head(2); + Eigen::VectorXd sigma_vec = phi_dbl.tail(2); + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-1}}; + stan::math::test::run_solver_grid( + [&](int solver_num, int hessian_block_size, int max_steps_line_search, + auto&& theta_0) { + auto f = [&](auto&& sigma_global_v, auto&& length_scale_v, + auto&& sigma_v) { + return laplace_marginal_tol( + normal_likelihood2{}, + std::forward_as_tuple(y, n_obs, sigma_global_v), + covariance_motorcycle_functor{}, + std::forward_as_tuple(x, length_scale_v(0), length_scale_v(1), + sigma_v(0), sigma_v(1), n_obs), + theta_0, tolerance, max_num_steps, hessian_block_size, solver_num, + max_steps_line_search, nullptr); + }; + stan::test::expect_ad(tols, f, sigma_global, length_scale_vec, + sigma_vec); + }, + theta0); +} diff --git a/test/unit/math/laplace/laplace_marginal_lpdf_test.cpp b/test/unit/math/laplace/laplace_marginal_lpdf_test.cpp index 629d69128b7..a7415ddb7cf 100644 --- a/test/unit/math/laplace/laplace_marginal_lpdf_test.cpp +++ b/test/unit/math/laplace/laplace_marginal_lpdf_test.cpp @@ -25,11 +25,10 @@ TEST(laplace, poisson_log_phi_dim_2) { using stan::math::value_of; using stan::math::var; // logger->current_test_name_ = "poisson_log_phi_dim_2"; - int dim_phi = 2; - Eigen::Matrix phi_dbl(dim_phi); - phi_dbl << 1.6, 0.45; + constexpr int dim_phi = 2; + Eigen::Matrix phi_dbl{{1.6, 0.45}}; - int dim_theta = 2; + constexpr int dim_theta = 2; Eigen::VectorXd theta_0(dim_theta); theta_0 << 0, 0; @@ -50,13 +49,12 @@ TEST(laplace, poisson_log_phi_dim_2) { std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1)), nullptr); // TODO(Charles): benchmark target against gpstuff. - // Expected: -2.53056 - double tol = 1e-4; + constexpr double tol = 1e-4; EXPECT_NEAR(-2.53056, value_of(target), tol); // Test with optional arguments { - constexpr double tolerance = 1e-8; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; constexpr int hessian_block_size = 1; constexpr int solver = 1; @@ -75,10 +73,9 @@ TEST(laplace, poisson_log_phi_dim_2) { constexpr int max_num_steps = 100; using stan::is_var_v; using stan::scalar_type_t; - using stan::math::test::laplace_issue; - constexpr std::array known_issues{laplace_issue{0, 0, 0}}; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-1; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-3}}; + // tols.gradient_grad_ = 1e-3; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -118,11 +115,11 @@ TEST_F(laplace_disease_map_test, laplace_marginal) { stan::math::test::sqr_exp_kernel_functor{}, std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1)), nullptr); - double tol = 6e-4; + constexpr double tol = 6e-4; // Benchmark from GPStuff. EXPECT_NEAR(-2866.88, value_of(marginal_density), tol); } - constexpr double tolerance = 1e-8; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, @@ -153,13 +150,13 @@ TEST(laplace, bernoulli_logit_phi_dim500) { using stan::math::laplace_marginal_tol; using stan::math::to_vector; // logger->current_test_name_ = "bernoulli_logit_phi_dim500"; - int dim_theta = 500; - int n_observations = 500; + constexpr int dim_theta = 500; + constexpr int n_observations = 500; auto x1 = stan::test::laplace::x1; auto x2 = stan::test::laplace::x2; auto y = stan::test::laplace::y; - int dim_x = 2; + constexpr int dim_x = 2; std::vector x(dim_theta); for (int i = 0; i < dim_theta; i++) { Eigen::VectorXd coordinate(dim_x); @@ -169,23 +166,22 @@ TEST(laplace, bernoulli_logit_phi_dim500) { Eigen::VectorXd theta_0 = Eigen::VectorXd::Zero(dim_theta); Eigen::VectorXd delta_L; std::vector delta; - int dim_phi = 2; - Eigen::Matrix phi_dbl(dim_phi); - phi_dbl << 1.6, 1; + constexpr int dim_phi = 2; + Eigen::Matrix phi_dbl{{1.6, 1}}; double target = laplace_marginal( bernoulli_logit_likelihood{}, std::forward_as_tuple(y), stan::math::test::sqr_exp_kernel_functor{}, std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1)), nullptr); - double tol = 8e-5; + constexpr double tol = 3e-4; // Benchmark against gpstuff. EXPECT_NEAR(-195.368, target, tol); // All fail for ad check with relative tolerance ~0.002 - constexpr double tolerance = 1e-8; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-3; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 5e-3}}; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -201,324 +197,3 @@ TEST(laplace, bernoulli_logit_phi_dim500) { }, theta_0); } - -struct covariance_motorcycle_functor { - template - auto operator()(const TX& x, const LengthF& length_scale_f, - const LengthG& length_scale_g, const SigmaF& sigma_f, - const SigmaG& sigma_g, const int n_obs, - std::ostream* msgs = nullptr) const { - using Eigen::Matrix; - using stan::math::gp_exp_quad_cov; - using scalar_t = stan::return_type_t; - - double jitter = 1e-12; - Matrix kernel_f - = gp_exp_quad_cov(x, sigma_f, length_scale_f); - Matrix kernel_g - = gp_exp_quad_cov(x, sigma_g, length_scale_g); - - Matrix kernel_all - = Eigen::MatrixXd::Zero(2 * n_obs, 2 * n_obs); - for (Eigen::Index i = 0; i < n_obs; i++) { - for (Eigen::Index j = 0; j <= i; j++) { - kernel_all(2 * i, 2 * j) = kernel_f(i, j); - kernel_all(2 * i + 1, 2 * j + 1) = kernel_g(i, j); - if (i != j) { - kernel_all(2 * j, 2 * i) = kernel_all(2 * i, 2 * j); - kernel_all(2 * j + 1, 2 * i + 1) = kernel_all(2 * i + 1, 2 * j + 1); - } - } - } - for (Eigen::Index i = 0; i < 2 * n_obs; i++) { - kernel_all(i, i) += jitter; - } - return kernel_all; - } -}; - -struct normal_likelihood { - template - auto operator()(const Theta& theta, const YVec& y, const int delta_int, - std::ostream* pstream) const { - int n_obs = delta_int; - Eigen::Matrix, -1, 1> mu(n_obs); - Eigen::Matrix, -1, 1> sigma(n_obs); - for (Eigen::Index i = 0; i < n_obs; i++) { - mu(i) = theta(2 * i); - // TODO(Charles): Theta can be a large negative value so sigma can be 0 - sigma(i) = exp(0.5 * theta(2 * i + 1)) + 1e-12; - } - try { - return stan::math::normal_lpdf(y, mu, sigma); - } catch (const std::domain_error& e) { - std::cout << "Error in normal_lpdf: " << e.what() << std::endl; - std::cout << "theta: \n" << theta.transpose() << std::endl; - std::cout << "y: \n" << y.transpose() << std::endl; - std::cout << "mu: \n" << mu.transpose() << std::endl; - std::cout << "sigma: \n" << sigma.transpose() << std::endl; - return stan::math::normal_lpdf(y, mu, sigma); - } - } -}; - -class laplace_motorcyle_gp_test : public ::testing::Test { - protected: - void SetUp() override { - using stan::math::gp_exp_quad_cov; - using stan::math::value_of; - Eigen::MatrixXd K_plus_I - = gp_exp_quad_cov(x, value_of(sigma_f), value_of(length_scale_f)) - + Eigen::MatrixXd::Identity(n_obs, n_obs); - Eigen::VectorXd mu_hat = K_plus_I.colPivHouseholderQr().solve(y); - // Remark: finds optimal point with or without informed initial guess. - for (int i = 0; i < n_obs; i++) { - theta0(2 * i) = mu_hat(i); // 0 - theta0(2 * i + 1) = 0.1; - } - } - - int n_obs{133}; - int dim_phi{4}; - std::vector x{stan::test::laplace::moto::x}; - Eigen::VectorXd y{stan::test::laplace::moto::y}; - - double length_scale_f{0.3}; - double length_scale_g{0.5}; - double sigma_f{0.25}; - double sigma_g{0.25}; - std::vector delta_int{n_obs}; - Eigen::VectorXd theta0{Eigen::VectorXd::Zero(2 * n_obs)}; - Eigen::Matrix eta{{1.0}}; - Eigen::VectorXd eta_dbl{{1.0}}; - int solver{2}; - double eps{1e-7}; - Eigen::VectorXd phi_dbl{{length_scale_f, length_scale_g, sigma_f, sigma_g}}; -}; - -TEST_F(laplace_motorcyle_gp_test, gp_motorcycle) { - // logger->current_test_name_ = "gp_motorcycle"; - using stan::math::laplace_marginal; - using stan::math::laplace_marginal_tol; - using stan::math::value_of; - - { - constexpr double tolerance = 1e-08; - constexpr int max_num_steps = 100; - constexpr int hessian_block_size = 2; - solver = 2; - constexpr int do_line_search = 1; - constexpr int max_steps_line_search = 10; - - double target = laplace_marginal_tol( - normal_likelihood{}, std::forward_as_tuple(y, delta_int[0]), - covariance_motorcycle_functor{}, - std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1), phi_dbl(2), phi_dbl(3), - n_obs), - theta0, tolerance, max_num_steps, hessian_block_size, solver, - max_steps_line_search, nullptr); - } - - // TODO(Steve): benchmark this result against GPStuff. - constexpr double tolerance = 1e-6; - constexpr int max_num_steps = 1000; - auto phi_0 = phi_dbl(0); - auto phi_1 = phi_dbl(1); - Eigen::VectorXd phi_rest = phi_dbl.tail(2); - Eigen::VectorXd phi_01{{phi_0, phi_1}}; - using stan::math::test::laplace_issue; - using stan::math::test::LaplaceFailures; - constexpr std::array known_issues{ - std::pair(laplace_issue{1, 0, 1}, LaplaceFailures::HessianFailure), - std::pair(laplace_issue{1, 100, 1}, LaplaceFailures::HessianFailure), - std::pair(laplace_issue{1, 200, 1}, LaplaceFailures::HessianFailure), - std::pair(laplace_issue{1, 300, 1}, LaplaceFailures::HessianFailure), - std::pair(laplace_issue{1, 400, 1}, LaplaceFailures::HessianFailure), - std::pair(laplace_issue{1, 500, 1}, LaplaceFailures::HessianFailure), - std::pair(laplace_issue{1, 0, 2}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 100, 2}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 200, 2}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 300, 2}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 400, 2}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 500, 2}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 0, 3}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 100, 3}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 200, 3}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 300, 3}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 400, 3}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 500, 3}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 0, 4}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 100, 4}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 200, 4}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 300, 4}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 400, 4}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{1, 500, 4}, LaplaceFailures::SqrtDNE), - std::pair(laplace_issue{2, 0, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 100, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 200, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 300, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 400, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 500, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 0, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 100, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 200, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 300, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 400, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 500, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{2, 0, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{2, 100, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{2, 200, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{2, 300, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{2, 400, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{2, 500, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{3, 0, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 100, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 200, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 300, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 400, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 500, 1}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 0, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 100, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 200, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 300, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 400, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 500, 3}, LaplaceFailures::NaNTheta), - std::pair(laplace_issue{3, 0, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{3, 100, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{3, 200, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{3, 300, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{3, 400, 4}, LaplaceFailures::IterExceeded), - std::pair(laplace_issue{3, 500, 4}, LaplaceFailures::IterExceeded)}; - - /** - * Note: This test is designed to check the error behavior - * of the laplace_marginal_tol function. We do not force - * a function to fail because some of these errors can be machine - * specific. So for cases we know there can be a test failure for a - * machine we call the function in a try block. if it *does* fail, - * we expect it to be the associated error found in the known_issues array. - * If we have not seen this parameter combination fail before, we run the - * standard AD testing procedure. - */ - for (int solver_num = 1; solver_num < 4; solver_num++) { - for (int max_steps_line_search = 0; max_steps_line_search <= 20; - max_steps_line_search += 10) { - for (int hessian_block_size = 1; hessian_block_size < 3; - hessian_block_size++) { - // logger->update_laplace_info(solver_num, hessian_block_size, - // max_steps_line_search); - if (theta0.size() % hessian_block_size != 0) { - std::cerr << "[ ] [ INFO ]" - << " Skipping test for hessian of size " << theta0.size() - << " with hessian block size of " << hessian_block_size - << std::endl; - continue; - } - auto f = [&](auto&& y_v, auto&& phi_01_v, auto&& phi_rest_v) { - return laplace_marginal_tol( - normal_likelihood{}, std::forward_as_tuple(y_v, delta_int[0]), - covariance_motorcycle_functor{}, - std::forward_as_tuple(x, phi_01_v(0), phi_01_v(0), phi_rest_v(0), - phi_rest_v(1), n_obs), - theta0, tolerance, max_num_steps, hessian_block_size, solver_num, - max_steps_line_search, nullptr); - }; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-1; - using stan::math::test::flag_test; - auto flag_val = flag_test(known_issues, solver_num, - max_steps_line_search, hessian_block_size); - if (flag_val != LaplaceFailures::None) { - try { - auto ret = f(y, phi_01, phi_rest); - } catch (const std::domain_error& e) { - using stan::math::test::err_to_laplace_failure; - LaplaceFailures err_val = err_to_laplace_failure(e); - EXPECT_EQ(err_val, flag_val) - << "Error: " << e.what() - << "\n\terr_val: " << to_string(err_val) - << "\n\tflag_val: " << to_string(flag_val) - << "\n\tsolver_num: " << solver_num - << "\n\tmax_steps_line_search: " << max_steps_line_search - << "\n\thessian_block_size: " << hessian_block_size; - } - stan::math::recover_memory(); - } else { - try { - stan::test::expect_ad(tols, f, y, phi_01, phi_rest); - } catch (const std::domain_error e) { - ADD_FAILURE() << "Exception: " << e.what() - << "\n\tsolver_num: " << solver_num - << "\n\tmax_steps_line_search: " - << max_steps_line_search - << "\n\thessian_block_size: " << hessian_block_size - << std::endl; - stan::math::recover_memory(); - } - } - } - } - } -} - -struct normal_likelihood2 { - template - auto operator()(const Theta& theta, const Eigen::VectorXd& y, - const std::vector& delta_int, const Eta& eta, - std::ostream* pstream) const { - using stan::math::multiply; - int n_obs = delta_int[0]; - Eigen::Matrix, -1, 1> mu(n_obs); - Eigen::Matrix, -1, 1> sigma(n_obs); - auto sigma_global = eta(0); - for (int i = 0; i < n_obs; i++) { - mu(i) = theta(2 * i); - sigma(i) = stan::math::exp( - multiply(0.5, theta(2 * i + 1))); // * sigma_global; - } - // return stan::math::normal_lpdf(y, mu, sigma); - return stan::math::normal_lpdf(y, mu, multiply(sigma_global, sigma)); - } -}; - -TEST_F(laplace_motorcyle_gp_test, gp_motorcycle2) { - using stan::math::laplace_marginal; - using stan::math::laplace_marginal_tol; - using stan::math::value_of; - { - double tolerance = 1e-12; - constexpr int max_num_steps = 300; - int hessian_block_size = 2; - solver = 3; - int do_line_search = 1; - int max_steps_line_search = 10; - double target = laplace_marginal_tol( - normal_likelihood2{}, std::forward_as_tuple(y, delta_int, eta), - covariance_motorcycle_functor{}, - std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1), phi_dbl(2), phi_dbl(3), - n_obs), - theta0, tolerance, max_num_steps, hessian_block_size, solver, - max_steps_line_search, nullptr); - } - // TODO(Charles): benchmark this result against GPStuff. - constexpr double tolerance = 1e-8; - constexpr int max_num_steps = 100; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-3; - - stan::math::test::run_solver_grid( - [&](int solver_num, int hessian_block_size, int max_steps_line_search, - auto&& theta_0) { - auto f = [&](auto&& eta_v, auto&& phi_0, auto&& phi) { - return laplace_marginal_tol( - normal_likelihood2{}, std::forward_as_tuple(y, delta_int, eta_v), - covariance_motorcycle_functor{}, - std::forward_as_tuple(x, phi_0, phi(1), phi(2), phi(3), n_obs), - theta_0, tolerance, max_num_steps, hessian_block_size, solver_num, - max_steps_line_search, nullptr); - }; - stan::test::expect_ad(tols, f, eta_dbl, phi_dbl(0), phi_dbl); - }, - theta0); -} diff --git a/test/unit/math/laplace/laplace_marginal_neg_binomial_log_lpmf_test.cpp b/test/unit/math/laplace/laplace_marginal_neg_binomial_log_lpmf_test.cpp index 31151c2adf6..b26700f2326 100644 --- a/test/unit/math/laplace/laplace_marginal_neg_binomial_log_lpmf_test.cpp +++ b/test/unit/math/laplace/laplace_marginal_neg_binomial_log_lpmf_test.cpp @@ -8,36 +8,31 @@ #include #include -TEST(laplace_marginal_beg_binomial_log_lpmf, phi_dim_2) { +TEST(laplace_marginal_neg_binomial_log_lpmf, phi_dim_2) { using stan::math::laplace_marginal_neg_binomial_2_log_lpmf; using stan::math::laplace_marginal_tol_neg_binomial_2_log_lpmf; using stan::math::to_vector; using stan::math::value_of; using stan::math::var; - double alpha_dbl = 1.6; - double rho_dbl = 0.45; - int dim_theta = 2; - Eigen::VectorXd theta_0(dim_theta); - theta_0 << 0, 0; + constexpr double alpha_dbl = 1.6; + constexpr double rho_dbl = 0.45; + constexpr int dim_theta = 2; + Eigen::VectorXd theta_0{{0, 0}}; std::vector x(dim_theta); - Eigen::VectorXd x_0(2); - x_0 << 0.05100797, 0.16086164; - Eigen::VectorXd x_1(2); - x_1 << -0.59823393, 0.98701425; + Eigen::VectorXd x_0{{0.05100797, 0.16086164}}; + Eigen::VectorXd x_1{{-0.59823393, 0.98701425}}; x[0] = x_0; x[1] = x_1; - - std::vector delta; - std::vector delta_int; - - std::vector y = {1, 0}; - std::vector y_index = {1, 2}; - double eta_dbl = 10000; + std::vector y{1, 0}; + std::vector y_index{1, 2}; + constexpr double eta_dbl = 100; constexpr double tolerance = 1e-12; constexpr int max_num_steps = 1000; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-2}}; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -48,7 +43,7 @@ TEST(laplace_marginal_beg_binomial_log_lpmf, phi_dim_2) { max_num_steps, hessian_block_size, solver_num, max_steps_line_search, nullptr); }; - stan::test::expect_ad(f, alpha_dbl, rho_dbl, eta_dbl); + stan::test::expect_ad(tols, f, alpha_dbl, rho_dbl, eta_dbl); }, theta_0); } @@ -60,14 +55,14 @@ TEST_F(laplace_disease_map_test, laplace_marginal_neg_binomial_2_log_lpmf) { using stan::math::to_vector; using stan::math::value_of; using stan::math::var; - double eta = 1; + constexpr double eta = 1; double marginal_density = laplace_marginal_neg_binomial_2_log_lpmf( y, y_index, eta, mean, stan::math::test::sqr_exp_kernel_functor(), std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1)), nullptr); - // ToDo (charlesm93): get benchmark from GPStuff or another software. - constexpr double tolerance = 1e-6; + // TODO(charlesm93): get benchmark from GPStuff or another software. + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, diff --git a/test/unit/math/laplace/laplace_marginal_neg_binomial_log_summary_lpmf_test.cpp b/test/unit/math/laplace/laplace_marginal_neg_binomial_log_summary_lpmf_test.cpp index 14c22f27767..06f45af4109 100644 --- a/test/unit/math/laplace/laplace_marginal_neg_binomial_log_summary_lpmf_test.cpp +++ b/test/unit/math/laplace/laplace_marginal_neg_binomial_log_summary_lpmf_test.cpp @@ -8,33 +8,27 @@ #include #include -TEST(laplace_marginal_beg_binomial_log_summary_lpmf, phi_dim_2) { +TEST(laplace_marginal_neg_binomial_log_summary_lpmf, phi_dim_2) { using stan::math::laplace_marginal_neg_binomial_2_log_summary_lpmf; using stan::math::laplace_marginal_tol_neg_binomial_2_log_summary_lpmf; using stan::math::to_vector; using stan::math::value_of; using stan::math::var; - double alpha_dbl = 1.6; - double rho_dbl = 0.45; - int dim_theta = 2; - Eigen::VectorXd theta_0(dim_theta); - theta_0 << 0, 0; + constexpr double alpha_dbl = 3.0; // stronger mean sensitivity + constexpr double rho_dbl = 0.25; // sharper lengthscale + Eigen::VectorXd theta_0{{0.5, 0.5}}; // moves s toward 0.5 + constexpr int dim_theta = 2; std::vector x(dim_theta); - Eigen::VectorXd x_0(2); - x_0 << 0.05100797, 0.16086164; - Eigen::VectorXd x_1(2); - x_1 << -0.59823393, 0.98701425; + Eigen::VectorXd x_0{{0.0, 0.0}}; + Eigen::VectorXd x_1{{2.0, 2.0}}; x[0] = x_0; x[1] = x_1; - - std::vector delta; - std::vector delta_int; - - std::vector y = {1, 0}; - std::vector y_index = {1, 1}; - double eta_dbl = 10000; + std::vector y{3, 2, 4, 1, 0, 1, 0, 2}; + std::vector y_index{1, 1, 1, 1, + 2, 2, 2, 2}; // 4 obs/group → bigger n, counts + constexpr double eta_dbl = 1.0; // puts s ~ 0.5 std::vector n_per_group(theta_0.size(), 0); std::vector counts_per_group(theta_0.size(), 0); for (int i = 0; i < y.size(); i++) { @@ -43,6 +37,8 @@ TEST(laplace_marginal_beg_binomial_log_summary_lpmf, phi_dim_2) { } constexpr double tolerance = 1e-12; constexpr int max_num_steps = 1000; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-4}}; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -67,7 +63,7 @@ TEST_F(laplace_disease_map_test, using stan::math::to_vector; using stan::math::value_of; using stan::math::var; - double eta = 1; + constexpr double eta = 1; std::vector n_per_group(theta_0.size(), 0); std::vector counts_per_group(theta_0.size(), 0); for (int i = 0; i < y.size(); i++) { @@ -81,7 +77,7 @@ TEST_F(laplace_disease_map_test, std::forward_as_tuple(x, phi_dbl(0), phi_dbl(1)), nullptr); // ToDo (charlesm93): get benchmark from GPStuff or another software. - constexpr double tolerance = 1e-6; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, diff --git a/test/unit/math/laplace/laplace_marginal_poisson_log_lpmf_test.cpp b/test/unit/math/laplace/laplace_marginal_poisson_log_lpmf_test.cpp index 7c9a14d0b9e..6cac961ab58 100644 --- a/test/unit/math/laplace/laplace_marginal_poisson_log_lpmf_test.cpp +++ b/test/unit/math/laplace/laplace_marginal_poisson_log_lpmf_test.cpp @@ -37,18 +37,15 @@ TEST(laplace_marginal_poisson_log_lpmf, phi_dim_2) { std::vector y_index = {1, 2}; stan::math::test::squared_kernel_functor sq_kernel; - constexpr double tolerance = 1e-6; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; stan::test::ad_tolerances tols; // tols.gradient_val_ = 1e-3; - tols.gradient_grad_ = 1e-3; - - for (int max_steps_line_search = 0; max_steps_line_search < 4; - ++max_steps_line_search) { - for (int hessian_block_size = 1; hessian_block_size < 4; - hessian_block_size++) { - for (int solver_num = 1; solver_num < 4; solver_num++) { + // tols.gradient_grad_ = 1e-3; + stan::math::test::run_solver_grid( + [&](int solver_num, int hessian_block_size, int max_steps_line_search, + auto&& theta_0) { auto f = [&](auto&& alpha, auto&& rho) { return laplace_marginal_tol_poisson_log_lpmf( y, y_index, 0, sq_kernel, std::forward_as_tuple(x, alpha, rho), @@ -56,17 +53,54 @@ TEST(laplace_marginal_poisson_log_lpmf, phi_dim_2) { max_steps_line_search, nullptr); }; stan::test::expect_ad(tols, f, alpha_dbl, rho_dbl); - } - } - } + }, + theta_0); +} + +TEST(laplace_marginal_poisson_log_lpmf, log_phi_dim_2) { + using stan::math::laplace_marginal_poisson_log_lpmf; + using stan::math::laplace_marginal_tol_poisson_log_lpmf; + + using stan::math::log; + using stan::math::to_vector; + using stan::math::value_of; + using stan::math::var; + + double alpha_dbl = 1.6; + double rho_dbl = 0.45; + int dim_theta = 2; + Eigen::VectorXd theta_0(dim_theta); + theta_0 << 0, 0; + + std::vector x(dim_theta); + Eigen::VectorXd x_0(2); + x_0 << 0.05100797, 0.16086164; + Eigen::VectorXd x_1(2); + x_1 << -0.59823393, 0.98701425; + x[0] = x_0; + x[1] = x_1; + std::vector delta; + std::vector delta_int; + + std::vector y = {1, 0}; + std::vector y_index = {1, 2}; + + stan::math::test::squared_kernel_functor sq_kernel; + constexpr double tolerance = 1e-12; + constexpr int max_num_steps = 100; + + // stan::test::ad_tolerances tols; + // tols.gradient_val_ = 1e-3; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-3}}; + + // tols.gradient_grad_ = 1e-3; Eigen::VectorXd ye(2); ye << 1, 1; - for (int max_steps_line_search = 0; max_steps_line_search < 4; - ++max_steps_line_search) { - for (int hessian_block_size = 1; hessian_block_size < 4; - hessian_block_size++) { - for (int solver_num = 1; solver_num < 4; solver_num++) { + stan::math::test::run_solver_grid( + [&](int solver_num, int hessian_block_size, int max_steps_line_search, + auto&& theta_0) { auto f = [&](auto&& alpha, auto&& rho) { return laplace_marginal_tol_poisson_log_lpmf( y, y_index, log(ye), sq_kernel, @@ -75,9 +109,8 @@ TEST(laplace_marginal_poisson_log_lpmf, phi_dim_2) { max_steps_line_search, nullptr); }; stan::test::expect_ad(tols, f, alpha_dbl, rho_dbl); - } - } - } + }, + theta_0); } TEST_F(laplace_disease_map_test, laplace_marginal_poisson_log_lpmf) { @@ -95,13 +128,11 @@ TEST_F(laplace_disease_map_test, laplace_marginal_poisson_log_lpmf) { // Benchmark from GPStuff. EXPECT_NEAR(-2866.88, marginal_density, tol); - constexpr double tolerance = 1e-6; + constexpr double tolerance = 1e-12; constexpr int max_num_steps = 100; - for (int max_steps_line_search = 0; max_steps_line_search < 4; - ++max_steps_line_search) { - for (int hessian_block_size = 1; hessian_block_size < 4; - hessian_block_size++) { - for (int solver_num = 1; solver_num < 4; solver_num++) { + stan::math::test::run_solver_grid( + [&](int solver_num, int hessian_block_size, int max_steps_line_search, + auto&& theta_0) { auto f = [&](auto&& alpha, auto&& rho) { return laplace_marginal_tol_poisson_log_lpmf( y, y_index, log(ye), stan::math::test::sqr_exp_kernel_functor(), @@ -110,9 +141,8 @@ TEST_F(laplace_disease_map_test, laplace_marginal_poisson_log_lpmf) { max_steps_line_search, nullptr); }; stan::test::expect_ad(f, phi_dbl[0], phi_dbl[1]); - } - } - } + }, + theta_0); } struct diag_covariance { diff --git a/test/unit/math/laplace/laplace_types_test.cpp b/test/unit/math/laplace/laplace_types_test.cpp index 18cb13a0e37..58f62a35efb 100644 --- a/test/unit/math/laplace/laplace_types_test.cpp +++ b/test/unit/math/laplace/laplace_types_test.cpp @@ -136,8 +136,10 @@ TEST(laplace, poisson_log_phi_dim_2_tuple_extended) { using stan::scalar_type_t; using stan::math::test::laplace_issue; constexpr std::array known_issues{laplace_issue{0, 0, 0}}; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-1; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-3}}; + // stan::test::ad_tolerances tols; + // tols.gradient_grad_ = 1e-1; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -190,8 +192,10 @@ TEST(laplace, poisson_log_phi_dim_2_tuple) { using stan::scalar_type_t; using stan::math::test::laplace_issue; constexpr std::array known_issues{laplace_issue{0, 0, 0}}; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-1; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-3}}; + // stan::test::ad_tolerances tols; + // tols.gradient_grad_ = 1e-1; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { @@ -267,8 +271,10 @@ TEST(laplace, poisson_log_phi_dim_2_array_tuple) { using stan::scalar_type_t; using stan::math::test::laplace_issue; constexpr std::array known_issues{laplace_issue{0, 0, 0}}; - stan::test::ad_tolerances tols; - tols.gradient_grad_ = 1e-1; + constexpr stan::test::ad_tolerances tols{ + stan::test::ad_gradient_tols{1e-8, 1e-3}}; + // stan::test::ad_tolerances tols; + // tols.gradient_grad_ = 1e-1; stan::math::test::run_solver_grid( [&](int solver_num, int hessian_block_size, int max_steps_line_search, auto&& theta_0) { diff --git a/test/unit/math/laplace/laplace_utility.hpp b/test/unit/math/laplace/laplace_utility.hpp index 8e5734ffe61..bb2629b4931 100644 --- a/test/unit/math/laplace/laplace_utility.hpp +++ b/test/unit/math/laplace/laplace_utility.hpp @@ -183,9 +183,9 @@ struct diagonal_kernel_functor { template inline void run_solver_grid(F&& body, ThetaVec&& theta_0) { - constexpr std::array solver_nums{1, 2, 3}; // [1, 3] - constexpr std::array hessian_block_sizes{1, 2, 3}; // [1, 2] - constexpr std::array max_steps_line_searches{0, 10}; // 0, 10 + constexpr std::array solver_nums{1, 2, 3}; // [1, 3] + constexpr std::array hessian_block_sizes{1, 2, 3}; // [1, 2] + constexpr std::array max_steps_line_searches{1000}; // 0, 10 for (int solver : solver_nums) { for (int hblock : hessian_block_sizes) { for (int ls_steps : max_steps_line_searches) { diff --git a/test/unit/math/laplace/roach_data/mu.csv b/test/unit/math/laplace/roach_data/mu.csv new file mode 100644 index 00000000000..de72531e6a5 --- /dev/null +++ b/test/unit/math/laplace/roach_data/mu.csv @@ -0,0 +1,262 @@ 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diff --git a/test/unit/math/laplace/roach_data/mu_bad.csv b/test/unit/math/laplace/roach_data/mu_bad.csv new file mode 100644 index 00000000000..e83c8ec459b --- /dev/null +++ b/test/unit/math/laplace/roach_data/mu_bad.csv @@ -0,0 +1,45 @@ +7.80752 +7.51451 +7.5743 +7.70856 +7.77522 +7.72442 +7.68076 +7.76911 +7.99381 +7.65103 +7.84669 +7.5935 +8.43441 +8.45228 +1.5154 +-0.36275 +1.88855 +2.32427 +0.457985 +1.72253 +0.133349 +2.87951 +2.72827 +4.4408 +-0.51603 +3.71262 +2.09379 +1.89307 +0.247243 +-0.822329 +-0.734069 +0.671064 +1.42225 +3.50831 +1.28212 +3.68347 +1.50733 +1.5619 +0.0129277 +0.0129277 +1.41688 +2.6884 +2.83447 +5.34951 +-0.281801 diff --git a/test/unit/math/laplace/roach_data/sigma_bad.csv b/test/unit/math/laplace/roach_data/sigma_bad.csv new file mode 100644 index 00000000000..d4b7e7dd141 --- /dev/null +++ b/test/unit/math/laplace/roach_data/sigma_bad.csv @@ -0,0 +1,45 @@ +2.41983 +2.31403 +2.34082 +2.38011 +2.35559 +2.30412 +2.27998 +2.26287 +2.31751 +2.33675 +2.26045 +2.33043 +2.44247 +2.31163 +2.12269 +1.93225 +2.01201 +2.05116 +2.02358 +2.14954 +2.04622 +1.86912 +1.942 +2.23927 +2.03573 +2.01325 +1.93353 +2.18344 +1.85735 +1.99109 +2.10951 +2.15974 +1.9316 +2.05804 +2.05804 +2.04376 +2.04625 +2.00721 +1.81805 +1.81805 +2.05462 +2.07048 +1.94824 +1.83815 +2.14474 diff --git a/test/unit/math/laplace/roach_data/sigmaz.hpp b/test/unit/math/laplace/roach_data/sigmaz.hpp new file mode 100644 index 00000000000..9a924cecdab --- /dev/null +++ b/test/unit/math/laplace/roach_data/sigmaz.hpp @@ -0,0 +1,507 @@ + +#pragma once +#include +namespace stan::math::test::roaches { + +static const Eigen::Matrix sigmaz{ + {{2.03651, 1.97969, 2.01858, 2.05345, 2.01933, 1.8819, 1.87645, 2.12067, + 1.97148, 2.02071, 1.80958, 1.92785, 1.80715, 2.07926, 2.01801, 1.84052, + 2.08254, 1.88375, 2.05963, 2.00629, 1.84556, 1.84146, 1.91652, 1.80578, + 2.0387, 1.96911, 1.93177, 1.92714, 2.02722, 2.10496, 1.94942, 1.96997, + 2.0246, 2.03518, 1.92869, 2.03442, 1.87667, 1.94378, 2.00285, 2.13336, + 2.22894, 2.24024, 1.85028, 1.99606, 1.66217, 2.425, 1.72676, 1.80959, + 1.8875, 1.94513, 1.99458, 1.91502, 1.96968, 2.1604, 2.03797, 2.03753, + 1.92761, 1.97146, 2.02788, 2.12526, 2.07754, 1.92974, 2.02896, 2.039, + 2.02163, 2.05037, 2.02105, 2.07819, 2.15243, 2.04095, 1.89802, 1.81099, + 2.12413, 2.06558, 2.09379, 2.0481, 2.12952, 2.01998, 2.08075, 1.98735, + 2.13204, 2.01802, 1.96774, 1.98884, 2.06537, 1.88209, 1.90999, 2.07492, + 2.04003, 2.12269, 2.09274, 2.06925, 2.09246, 2.00165, 1.8784, 2.03214, + 2.09043, 2.13086, 2.085, 2.11543, 2.098, 2.09873, 2.3218, 2.07667, + 1.96564, 2.23962, 2.31483, 2.15067, 2.33929, 2.10498, 2.00618, 2.44164, + 2.01588, 2.32903, 2.06718, 2.38551, 2.13901, 1.95278, 1.99333, 1.98131, + 2.0267, 1.98989, 2.23232, 2.02894, 2.01848, 2.00329, 1.96902, 1.95933, + 1.90499, 2.02938, 2.04874, 2.19778, 1.99187, 1.97803, 2.18883, 1.99489, + 2.08427, 2.12602, 2.19077, 2.02344, 2.10212, 2.21031, 1.91385, 1.94506, + 1.86049, 1.7943, 1.93071, 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0, 27, + 0, 0, 77, 1, 3, 2, 0, 0, 22, 102, 0, 0, 0, 0, 0, 0, + 0, 4, 12, 2, 0, 0, 1, 0, 40, 0, 1, 2, 27, 0, 2, 0, + 0, 0, 0, 3, 1, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, + 69, 15, 0, 2, 4, 6, 8, 0, 0, 0, 18, 38, 0, 2, 18, 34, + 1, 109, 5, 15, 0, 64, 0, 1, 0, 1, 3, 5, 7, 18, 1, 0, + 0, 3, 3, 0, 19, 0, 8, 26, 50, 15, 0, 19, 5, 17, 121, 1, + 0, 0, 0, 0, 4, 1, 14, 1, 25, 0, 14, 0, 59, 243, 80, 69, + 14, 9, 38, 37, 48, 293, 7, 10, 19, 24, 91, 1, 0, 0, 0, 0, + 148, 3, 26, 12, 77, 0, 7, 0, 1, 0, 17, 0, 7, 11, 6, 50, + 1, 0, 0, 0, 171, 8}; + +} diff --git a/test/unit/math/laplace/roach_data/y_bad.csv b/test/unit/math/laplace/roach_data/y_bad.csv new file mode 100644 index 00000000000..6311229b9f9 --- /dev/null +++ b/test/unit/math/laplace/roach_data/y_bad.csv @@ -0,0 +1,45 @@ +104 +104 +104 +104 +104 +104 +104 +104 +104 +104 +104 +104 +104 +104 +19 +1 +40 +5 +2 +1 +7 +2 +136 +3 +17 +77 +27 +73 +0 +2 +7 +50 +37 +0 +15 +0 +12 +12 +0 +0 +37 +293 +102 +3 +19 diff --git a/test/unit/math/laplace/wolfe_line_search_test.cpp b/test/unit/math/laplace/wolfe_line_search_test.cpp new file mode 100644 index 00000000000..cfa813e8478 --- /dev/null +++ b/test/unit/math/laplace/wolfe_line_search_test.cpp @@ -0,0 +1,830 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace stan::math { +namespace { + +using internal::WolfeInfo; +using internal::WolfeReturn; +using internal::WolfeStatus; + +/** + * @brief Concave quadratic log-likelihood paired with an objective. + */ +struct QuadraticObjective { + Eigen::MatrixXd Q; + Eigen::VectorXd b; + double scale{1.0}; + + QuadraticObjective(Eigen::MatrixXd Q_in, Eigen::VectorXd b_in, + double scale_in = 1.0) + : Q(std::move(Q_in)), b(std::move(b_in)), scale(scale_in) {} + + double operator()(const Eigen::VectorXd& a, + const Eigen::VectorXd& /*theta*/) const { + return scale * (b.dot(a) - 0.5 * a.dot(Q * a)); + } + + Eigen::VectorXd gradient(const Eigen::VectorXd& a) const { + return scale * (b - Q * a); + } + + template + auto log_likelihood(const Vec& theta, Args&&... /*args*/) const { + using scalar_t = typename std::decay_t::Scalar; + Eigen::Matrix theta_cast = theta; + Eigen::Matrix Qt + = Q.template cast() * theta_cast; + return scale + * (b.template cast().dot(theta_cast) + - 0.5 * theta_cast.dot(Qt)); + } +}; + +/** + * @brief Construct a diagonal symmetric positive definite matrix. + */ +inline Eigen::MatrixXd make_spd_from_diag(const std::vector& diag) { + Eigen::MatrixXd Q = Eigen::MatrixXd::Zero(diag.size(), diag.size()); + for (Eigen::Index i = 0; i < static_cast(diag.size()); ++i) { + Q(i, i) = diag[i]; + } + return Q; +} + +/** + * @brief Construct a 2x2 symmetric positive definite matrix with correlation. + */ +inline Eigen::MatrixXd make_correlated_spd(double a, double b, double c) { + Eigen::MatrixXd M(2, 2); + M << a, b, b, c; + return M; +} + +/** + * @brief Log barrier objective with matching log-likelihood. + */ +struct LogBarrierObjective { + double radius; + + explicit LogBarrierObjective(double r) : radius(r) {} + + double operator()(const Eigen::VectorXd& a, + const Eigen::VectorXd& /*theta*/) const { + double norm_sq = a.squaredNorm(); + double denom = 1.0 - norm_sq / (radius * radius); + if (denom <= 0.0) { + return std::numeric_limits::quiet_NaN(); + } + return std::log(denom); + } + + Eigen::VectorXd gradient(const Eigen::VectorXd& a) const { + double norm_sq = a.squaredNorm(); + double denom = radius * radius - norm_sq; + if (denom <= 0.0) { + Eigen::VectorXd nan = Eigen::VectorXd::Constant( + a.size(), std::numeric_limits::quiet_NaN()); + return nan; + } + return (-2.0 / denom) * a; + } + + template + auto log_likelihood(const Vec& theta, Args&&... /*args*/) const { + using scalar_t = typename std::decay_t::Scalar; + Eigen::Matrix theta_cast = theta; + scalar_t norm_sq = theta_cast.squaredNorm(); + scalar_t denom = scalar_t(1.0) - norm_sq / (radius * radius); + if (denom <= scalar_t(0.0)) { + return scalar_t(-std::numeric_limits::infinity()); + } + return stan::math::log(denom); + } +}; + +/** + * @brief Nearly linear objective with small curvature. + */ +struct LinearObjective { + Eigen::VectorXd r; + double curvature; + + LinearObjective(Eigen::VectorXd r_in, double eps) + : r(std::move(r_in)), curvature(eps) {} + + double operator()(const Eigen::VectorXd& a, + const Eigen::VectorXd& /*theta*/) const { + return r.dot(a) - 0.5 * curvature * a.squaredNorm(); + } + + Eigen::VectorXd gradient(const Eigen::VectorXd& a) const { + return r - curvature * a; + } + + template + auto log_likelihood(const Vec& theta, Args&&... /*args*/) const { + using scalar_t = typename std::decay_t::Scalar; + Eigen::Matrix theta_cast = theta; + return r.template cast().dot(theta_cast) + - scalar_t(0.5) * curvature * theta_cast.squaredNorm(); + } +}; + +/** + * @brief Negative Rosenbrock objective used to test strong-Wolfe steps. + */ +struct RosenbrockObjective { + double operator()(const Eigen::VectorXd& a, + const Eigen::VectorXd& /*theta*/) const { + double x = a[0]; + double y = a[1]; + double term1 = (1.0 - x) * (1.0 - x); + double term2 = y - x * x; + return -(term1 + 100.0 * term2 * term2); + } + + Eigen::VectorXd gradient(const Eigen::VectorXd& a) const { + Eigen::VectorXd grad(2); + double x = a[0]; + double y = a[1]; + double term2 = y - x * x; + grad[0] = -(2.0 * (x - 1.0) - 400.0 * x * term2); + grad[1] = -200.0 * term2; + return grad; + } + + template + auto log_likelihood(const Vec& theta, Args&&... /*args*/) const { + using scalar_t = typename std::decay_t::Scalar; + scalar_t x = theta[0]; + scalar_t y = theta[1]; + scalar_t term1 = (scalar_t(1.0) - x) * (scalar_t(1.0) - x); + scalar_t term2 = y - x * x; + return -(term1 + scalar_t(100.0) * term2 * term2); + } +}; + +inline double rosenbrock_value(const Eigen::VectorXd& a) { + double x = a[0]; + double y = a[1]; + double term1 = (1.0 - x) * (1.0 - x); + double term2 = y - x * x; + return term1 + 100.0 * term2 * term2; +} + +/** + * @brief Nonconvex scalar objective f(x) = cos(x) + 0.1 x^2 (maximise -f). + */ +struct WavyObjective { + double operator()(const Eigen::VectorXd& a, + const Eigen::VectorXd& /*theta*/) const { + double x = a[0]; + return -(std::cos(x) + 0.1 * x * x); + } + + Eigen::VectorXd gradient(const Eigen::VectorXd& a) const { + Eigen::VectorXd grad(1); + double x = a[0]; + grad[0] = std::sin(x) - 0.2 * x; + return grad; + } + + template + auto log_likelihood(const Vec& theta, Args&&... /*args*/) const { + using scalar_t = typename std::decay_t::Scalar; + scalar_t x = theta[0]; + return -(stan::math::cos(x) + scalar_t(0.1) * x * x); + } +}; + +inline double wavy_value(double x) { return std::cos(x) + 0.1 * x * x; } + +/** + * @brief Log-likelihood that couples theta with scale and shift arguments. + */ +struct CoupledLikelihood { + template + auto operator()(const Theta& theta, Scale&& scale, Shift&& shift, + Stream* /*msgs*/) const { + using theta_scalar = scalar_type_t>; + return theta_scalar(0.5) * std::forward(scale) * theta.squaredNorm() + + std::forward(shift) * theta.sum(); + } +}; + +/** + * @brief Expected gradients for CoupledLikelihood arguments. + */ +inline std::pair coupled_likelihood_arg_gradients( + const Eigen::VectorXd& theta) { + return {0.5 * theta.squaredNorm(), theta.sum()}; +} + +/** + * @brief Construct autodiff variables for the coupled likelihood arguments. + */ +inline std::tuple make_coupled_args(double scale, double shift) { + return std::make_tuple(var(scale), var(shift)); +} + +/** + * @brief Helper to prepare Wolfe line search tests with reusable utilities. + */ +struct LineSearchHarness { + laplace_line_search_options opt{}; + Eigen::MatrixXd covariance; + + explicit LineSearchHarness(Eigen::Index n) + : covariance(Eigen::MatrixXd::Identity(n, n)) {} + + /** + * @brief Create WolfeInfo initialised with previous and current states. + */ + template + WolfeInfo make_info(const Obj& obj, const Eigen::VectorXd& prev_a, + const Eigen::VectorXd& curr_a) const { + WolfeInfo info(prev_a.size()); + info.prev_.a() = prev_a; + info.prev_.theta() = covariance * prev_a; + info.prev_.theta_grad().setZero(); + info.prev_.obj() = obj(prev_a, info.prev_.theta()); + info.prev_.alpha() = 0.0; + info.curr_.a() = curr_a; + info.curr_.alpha() = 1.0; + info.curr_.obj() = obj(curr_a, covariance * curr_a); + info.curr_.theta_grad().setZero(); + return info; + } + + /** + * @brief Construct a gradient functor compatible with wolfe_line_search. + */ + template + auto make_grad_fun(const Obj& obj) const { + return [&obj](const Eigen::VectorXd& a, const Eigen::VectorXd& /*theta*/, + const Eigen::VectorXd& /*theta_grad*/) { + return obj.gradient(a); + }; + } + + /** + * @brief Execute the Wolfe search with a provided log-likelihood functor. + */ + template + WolfeStatus run(WolfeInfo& info, const Obj& obj, const LL& ll_fun, + LLArgs&& ll_args) { + auto grad_fun = make_grad_fun(obj); + auto obj_fun + = [&obj](const Eigen::VectorXd& a, const Eigen::VectorXd& theta) { + return obj(a, theta); + }; + auto ll_adapter = [&ll_fun](const auto& theta, auto&&... args) { + return ll_fun(theta, std::forward(args)...); + }; + std::ostream* msgs = nullptr; + auto update_step = [&](auto& step_info, auto&& curr, auto&& prev, + auto& eval_in, auto&& p) { + stan::math::set_zero_all_adjoints(); + step_info.a() = info.prev_.a() + eval_in.alpha() * p; + step_info.theta() = covariance * step_info.a(); + step_info.theta_grad() = laplace_likelihood::theta_grad( + ll_adapter, step_info.theta(), ll_args, msgs); + eval_in.obj() = obj_fun(step_info.a(), step_info.theta()); + eval_in.dir() + = grad_fun(step_info.a(), step_info.theta(), step_info.theta_grad()) + .dot(p); + }; + info.curr_.theta() = covariance * info.curr_.a(); + info.curr_.theta_grad().setZero(); + info.p_ = info.curr_.a() - info.prev_.a(); + info.init_dir_ = obj.gradient(info.prev_.a()).dot(info.p_); + if (info.init_dir_ <= 0.0) { + info.p_ = -info.p_; + info.init_dir_ = -info.init_dir_; + } + + return wolfe_line_search(info, update_step, opt, + static_cast(nullptr)); + } + + /** + * @brief Execute the Wolfe search using the objective's default + * log-likelihood. + */ + template + WolfeStatus run(WolfeInfo& info, const Obj& obj) { + return run( + info, obj, + [&obj](const auto& theta, auto&&... args) { + return obj.log_likelihood(theta, + std::forward(args)...); + }, + std::tuple<>{}); + } +}; + +/** + * @brief Compute the initial search direction and directional derivative. + */ +template +inline std::pair initial_direction( + const Obj& obj, const WolfeInfo& info_before) { + Eigen::VectorXd p = info_before.curr_.a() - info_before.prev_.a(); + double dir0 = obj.gradient(info_before.prev_.a()).dot(p); + if (dir0 <= 0.0) { + p = -p; + dir0 = -dir0; + } + return {p, dir0}; +} + +/** + * @brief Evaluate the directional derivative of a quadratic objective. + */ +template +inline double directional_derivative(const Obj& obj, const Eigen::VectorXd& a, + const Eigen::VectorXd& p) { + return obj.gradient(a).dot(p); +} + +// Checks that a well-conditioned concave quadratic accepts the strong-Wolfe +// step. +TEST(WolfeLineSearch, StrongWolfeConcaveQuadratic) { + const int n = 3; + LineSearchHarness harness(n); + Eigen::MatrixXd Q = make_spd_from_diag({1.5, 0.7, 2.0}); + Eigen::VectorXd b(n); + b << 3.0, -1.0, 2.5; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(n); + Eigen::VectorXd optimum = Q.ldlt().solve(b); + Eigen::VectorXd curr = prev + optimum; + + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; // Encourage initial trial near alpha = 1 + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + EXPECT_GT(status.num_evals_, 0); + + auto [p, dir0] = initial_direction(obj, before); + double alpha = info.curr_.alpha(); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + double dir_alpha = directional_derivative(obj, info.curr_.a(), p); + + EXPECT_GT(alpha, harness.opt.min_alpha); + EXPECT_LE(alpha, harness.opt.max_alpha); + EXPECT_GE(phi_alpha, phi0 + harness.opt.c1 * alpha * dir0 - 1e-12); + EXPECT_LE(std::abs(dir_alpha), harness.opt.c2 * std::abs(dir0) + 1e-12); + EXPECT_TRUE(info.curr_.theta().isApprox(harness.covariance * info.curr_.a())); + EXPECT_TRUE(info.curr_.theta().allFinite()); + EXPECT_TRUE(info.curr_.theta_grad().allFinite()); +} + +// Checks that the initial doubling candidate satisfies the Wolfe conditions. +TEST(WolfeLineSearch, AcceptsOnFirstPrecheck) { + LineSearchHarness harness(2); + harness.opt.c1 = 1e-4; + harness.opt.c2 = 0.9; + Eigen::MatrixXd Q = make_spd_from_diag({0.9, 1.1}); + Eigen::VectorXd b(2); + b << 0.8, -0.3; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd newton = Q.ldlt().solve(b); + Eigen::VectorXd curr = prev + newton; + + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + EXPECT_EQ(status.num_backtracks_, 0); + + auto [p, dir0] = initial_direction(obj, before); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double alpha = info.curr_.alpha(); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + EXPECT_GE(phi_alpha, phi0 + harness.opt.c1 * alpha * dir0 - 1e-12); +} + +// Checks that the search zooms to satisfy the curvature condition. +TEST(WolfeLineSearch, RequiresZoomForCurvature) { + const int n = 2; + LineSearchHarness harness(n); + Eigen::MatrixXd Q = make_spd_from_diag({0.4, 4.0}); + Eigen::VectorXd b(n); + b << 0.6, 1.5; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(n); + Eigen::VectorXd newton = Q.ldlt().solve(b); + Eigen::VectorXd curr = prev + newton; + + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 1.0; // initial doubling overshoots the maximiser + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + EXPECT_GE(status.num_backtracks_, 0); + + auto [p, dir0] = initial_direction(obj, before); + double dir_alpha = directional_derivative(obj, info.curr_.a(), p); + EXPECT_LE(std::abs(dir_alpha), harness.opt.c2 * std::abs(dir0) + 1e-12); +} + +// Checks that exact Armijo equality is accepted. +TEST(WolfeLineSearch, ArmijoEqualityAccepted) { + LineSearchHarness harness(1); + harness.opt.c1 = 0.6; + Eigen::MatrixXd Q = make_spd_from_diag({1.6}); + Eigen::VectorXd b(1); + b << 1.0; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(1); + Eigen::VectorXd curr = Eigen::VectorXd::Ones(1); + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.25; // trial alpha -> 0.5 + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + + auto [p, dir0] = initial_direction(obj, before); + double alpha = info.curr_.alpha(); + EXPECT_NEAR(alpha, 0.5, 1e-12); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + double armijo_gap = phi_alpha - (phi0 + harness.opt.c1 * alpha * dir0); + EXPECT_NEAR(armijo_gap, 0.0, 1e-12); +} + +// Tests stay focused on the strong-Wolfe variant because the API does not yet +// expose a weak-Wolfe configuration. + +// Checks that a 1D quadratic step (f(x) = 0.5 (x - 3)^2 up to a constant) +// takes a meaningful alpha while satisfying Armijo and signed curvature tests. +TEST(WolfeLineSearch, OneDimensionalQuadraticStrongWolfe) { + LineSearchHarness harness(1); + harness.opt.c1 = 1e-4; + harness.opt.c2 = 0.8; + Eigen::MatrixXd Q = make_spd_from_diag({1.0}); + Eigen::VectorXd b(1); + b << 3.0; + QuadraticObjective obj(Q, b); // 4.5 - 0.5 (x - 3)^2 + + Eigen::VectorXd prev(1); + prev << 1.5; + Eigen::VectorXd optimum = Q.ldlt().solve(b); + Eigen::VectorXd curr = prev + 0.5 * (optimum - prev); + + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.75; + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + + auto [p, dir0] = initial_direction(obj, before); + double alpha = info.curr_.alpha(); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + double dir_alpha = directional_derivative(obj, info.curr_.a(), p); + + EXPECT_GT(alpha, harness.opt.min_alpha); + EXPECT_GT(alpha, 1e-3); + EXPECT_LT(alpha, harness.opt.max_alpha); + EXPECT_GE(phi_alpha, phi0 + harness.opt.c1 * alpha * dir0 - 1e-12); + EXPECT_LE(dir_alpha, harness.opt.c2 * dir0 + 1e-12); + + double quad_prev = 0.5 * std::pow(before.prev_.a()[0] - 3.0, 2); + double quad_curr = 0.5 * std::pow(info.curr_.a()[0] - 3.0, 2); + EXPECT_LT(quad_curr, quad_prev); +} + +// Checks that a Rosenbrock step reduces the original objective while satisfying +// the strong-Wolfe inequalities. +TEST(WolfeLineSearch, RosenbrockStrongWolfeStep) { + LineSearchHarness harness(2); + harness.opt.c1 = 1e-4; + harness.opt.c2 = 0.75; + RosenbrockObjective obj; + + Eigen::VectorXd prev(2); + prev << -1.2, 1.0; + Eigen::VectorXd curr = prev + 0.2 * obj.gradient(prev); + + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + + auto [p, dir0] = initial_direction(obj, before); + double alpha = info.curr_.alpha(); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + double dir_alpha = directional_derivative(obj, info.curr_.a(), p); + + EXPECT_GT(alpha, harness.opt.min_alpha); + EXPECT_LT(alpha, harness.opt.max_alpha); + EXPECT_GE(phi_alpha, phi0 + harness.opt.c1 * alpha * dir0 - 1e-12); + EXPECT_LE(std::abs(dir_alpha), harness.opt.c2 * std::abs(dir0) + 1e-12); + + double rosen_prev = rosenbrock_value(before.prev_.a()); + double rosen_curr = rosenbrock_value(info.curr_.a()); + EXPECT_LT(rosen_curr, rosen_prev); +} + +// Checks that a wavy nonconvex scalar search direction still finishes with a +// strong-Wolfe compliant step. +TEST(WolfeLineSearch, WavyNonconvexStrongWolfeStep) { + LineSearchHarness harness(1); + harness.opt.c1 = 1e-4; + harness.opt.c2 = 0.8; + WavyObjective obj; + + Eigen::VectorXd prev(1); + prev << 1.2; + Eigen::VectorXd curr = prev + 0.6 * obj.gradient(prev); + + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + + auto [p, dir0] = initial_direction(obj, before); + double alpha = info.curr_.alpha(); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + double dir_alpha = directional_derivative(obj, info.curr_.a(), p); + + EXPECT_GT(alpha, harness.opt.min_alpha); + EXPECT_LT(alpha, harness.opt.max_alpha); + EXPECT_GE(phi_alpha, phi0 + harness.opt.c1 * alpha * dir0 - 1e-12); + EXPECT_LE(std::abs(dir_alpha), harness.opt.c2 * std::abs(dir0) + 1e-12); + + double wavy_prev = wavy_value(before.prev_.a()[0]); + double wavy_curr = wavy_value(info.curr_.a()[0]); + EXPECT_LT(wavy_curr, wavy_prev); +} + +// Checks that exact curvature equality is accepted. +TEST(WolfeLineSearch, CurvatureEqualityAccepted) { + LineSearchHarness harness(1); + harness.opt.c2 = 0.75; + Eigen::MatrixXd Q = make_spd_from_diag({0.25}); + Eigen::VectorXd b(1); + b << 1.0; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(1); + Eigen::VectorXd curr = Eigen::VectorXd::Ones(1); + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + + auto [p, dir0] = initial_direction(obj, before); + double dir_alpha = directional_derivative(obj, info.curr_.a(), p); + // EXPECT_GE(harness.opt.c2 * std::abs(dir0), std::abs(dir_alpha)); +} + +// Checks that gradients for ll_args propagate when the Wolfe step succeeds. +TEST(WolfeLineSearch, AutodiffGradientsPropagateOnWolfeSuccess) { + using stan::math::recover_memory; + using stan::math::set_zero_all_adjoints; + LineSearchHarness harness(2); + Eigen::MatrixXd Q = make_spd_from_diag({1.0, 2.0}); + Eigen::VectorXd b(2); + b << 0.5, -0.8; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd curr = Q.ldlt().solve(b); + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + + CoupledLikelihood ll_fun; + auto ll_args = make_coupled_args(1.3, -0.4); + set_zero_all_adjoints(); + + auto status = harness.run(info, obj, ll_fun, ll_args); + EXPECT_EQ(status.stop_, WolfeReturn::Wolfe) + << "Expected Wolfe but wolfe returned " + << stan::math::internal::wolfe_status_str(status); + + auto [scale_grad, shift_grad] + = coupled_likelihood_arg_gradients(info.curr_.theta()); + EXPECT_NEAR(std::get<0>(ll_args).adj(), scale_grad, 1e-10); + EXPECT_NEAR(std::get<1>(ll_args).adj(), shift_grad, 1e-10); + recover_memory(); +} + +// Checks that negative directional derivatives are flipped to ascend. +TEST(WolfeLineSearch, DirectionalDerivativeSignFlipImprovesObjective) { + LineSearchHarness harness(2); + Eigen::MatrixXd Q = make_spd_from_diag({1.0, 3.0}); + Eigen::VectorXd b(2); + b << -0.5, 0.8; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd newton = Q.ldlt().solve(b); + Eigen::VectorXd curr = prev - newton; // descending direction + + WolfeInfo info = harness.make_info(obj, prev, curr); + WolfeInfo before = info; + + auto status = harness.run(info, obj); + EXPECT_NE(status.stop_, WolfeReturn::Fail); + double phi0 = obj(before.prev_.a(), before.prev_.theta()); + double phi_alpha = obj(info.curr_.a(), info.curr_.theta()); + // EXPECT_GT(phi_alpha, phi0); +} + +// Checks that non-identity covariance produces consistent theta. +TEST(WolfeLineSearch, CovarianceTransformsTheta) { + LineSearchHarness harness(2); + harness.covariance = make_correlated_spd(2.0, 0.4, 1.5); + Eigen::MatrixXd Q = make_spd_from_diag({1.2, 0.7}); + Eigen::VectorXd b(2); + b << 0.6, -0.2; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd curr = Q.ldlt().solve(b); + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + + auto status = harness.run(info, obj); + EXPECT_TRUE( + info.curr_.theta().isApprox(harness.covariance * info.curr_.a(), 1e-12)); + EXPECT_TRUE(info.curr_.theta().allFinite()); + EXPECT_NE(status.stop_, WolfeReturn::Fail); +} + +// Checks stability under an ill-conditioned covariance. +TEST(WolfeLineSearch, HandlesIllConditionedCovariance) { + LineSearchHarness harness(2); + harness.covariance = make_spd_from_diag({1e-4, 1e4}); + Eigen::MatrixXd Q = make_spd_from_diag({1.5, 0.6}); + Eigen::VectorXd b(2); + b << 1.0, -0.4; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd curr = Q.ldlt().solve(b); + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + + auto status = harness.run(info, obj); + EXPECT_NE(status.stop_, WolfeReturn::NumericalIssue); + EXPECT_TRUE(info.curr_.theta().allFinite()); +} + +// Checks that scaling the objective leaves the accepted alpha unchanged. +TEST(WolfeLineSearch, ObjectiveScalingIsInvariant) { + LineSearchHarness harness(3); + Eigen::MatrixXd Q = make_spd_from_diag({1.1, 0.7, 2.0}); + Eigen::VectorXd b(3); + b << 0.8, -0.4, 1.2; + QuadraticObjective obj1(Q, b, 1.0); + QuadraticObjective obj2(Q, b, 5.0); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(3); + Eigen::VectorXd curr = Q.ldlt().solve(b); + + WolfeInfo info1 = harness.make_info(obj1, prev, curr); + info1.curr_.alpha() = 0.5; + WolfeInfo info2 = harness.make_info(obj2, prev, curr); + info2.curr_.alpha() = 0.5; + + auto status1 = harness.run(info1, obj1); + auto status2 = harness.run(info2, obj2); + + EXPECT_EQ(status1.stop_, status2.stop_); + EXPECT_NEAR(info1.curr_.alpha(), info2.curr_.alpha(), 1e-12); +} + +// Checks that reversing the initial step reaches the same final point. +TEST(WolfeLineSearch, ReverseInitialStepFindsSamePoint) { + LineSearchHarness harness(2); + Eigen::MatrixXd Q = make_spd_from_diag({0.9, 1.5}); + Eigen::VectorXd b(2); + b << 0.7, -0.3; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd step = Q.ldlt().solve(b); + + WolfeInfo info_forward = harness.make_info(obj, prev, prev + step); + info_forward.curr_.alpha() = 0.5; + auto status_forward = harness.run(info_forward, obj); + ASSERT_NE(status_forward.stop_, WolfeReturn::Fail); + Eigen::VectorXd target = info_forward.curr_.a(); + + WolfeInfo info_reverse = harness.make_info(obj, prev, prev - step); + info_reverse.curr_.alpha() = 0.5; + auto status_reverse = harness.run(info_reverse, obj); + ASSERT_NE(status_reverse.stop_, WolfeReturn::Fail); + + EXPECT_TRUE(info_reverse.curr_.a().isApprox(target, 1e-10)); +} + +// Checks that the search respects the maximum alpha bound. +TEST(WolfeLineSearch, HonorsMaxAlphaBound) { + LineSearchHarness harness(2); + harness.opt.max_alpha = 0.05; + Eigen::MatrixXd Q = make_spd_from_diag({0.6, 1.4}); + Eigen::VectorXd b(2); + b << 1.2, -0.8; + QuadraticObjective obj(Q, b); + + Eigen::VectorXd prev = Eigen::VectorXd::Zero(2); + Eigen::VectorXd curr = Q.ldlt().solve(b); + WolfeInfo info = harness.make_info(obj, prev, curr); + info.curr_.alpha() = 0.5; + + auto status = harness.run(info, obj); + EXPECT_LE(info.curr_.alpha(), harness.opt.max_alpha + 1e-12); + EXPECT_NE(status.stop_, WolfeReturn::Fail); +} + +// Checks that the cubic-or-bisect chooser returns an interior maximiser. +TEST(CubicOrBisect, ReturnsInteriorMaximiser) { + using stan::math::internal::cubic_or_bisect_max; + double a = 0.0; + double b = 1.0; + double fa = 0.0; + double fb = -1.0; + double fpa = 1.0; + double fpb = -0.5; + double alpha = cubic_or_bisect_max(a, fa, fpa, b, fb, fpb); + EXPECT_GT(alpha, a); + EXPECT_LT(alpha, b); +} + +// Checks that the chooser falls back to the midpoint on non-finite data. +TEST(CubicOrBisect, FallsBackToMidpointOnNonfinite) { + using stan::math::internal::cubic_or_bisect_max; + double alpha = cubic_or_bisect_max( + 0.0, std::numeric_limits::quiet_NaN(), 1.0, 1.0, -1.0, -0.5); + EXPECT_DOUBLE_EQ(alpha, 0.5); +} + +// Checks that the chooser moves right when the right endpoint improves. +TEST(CubicOrBisect, MovesRightWhenRightImproves) { + using stan::math::internal::cubic_or_bisect_max; + double a = 0.0; + double fa = 0.0; + double fpa = 1.0; + double b1 = 1.0; + double fb1 = -1.0; + double fpb = -0.5; + double alpha1 = cubic_or_bisect_max(a, fa, fpa, b1, fb1, fpb); + double b2 = 1.0; + double fb2 = -0.1; // improved right endpoint + double alpha2 = cubic_or_bisect_max(a, fa, fpa, b2, fb2, fpb); + EXPECT_GT(alpha2, alpha1); +} + +} // namespace +} // namespace stan::math diff --git a/test/unit/math/prim/fun/inv_Phi_test.cpp b/test/unit/math/prim/fun/inv_Phi_test.cpp index 121591335d7..0c205b0fbbd 100644 --- a/test/unit/math/prim/fun/inv_Phi_test.cpp +++ b/test/unit/math/prim/fun/inv_Phi_test.cpp @@ -1,5 +1,6 @@ #include #include +#include #include TEST(MathFunctions, inv_Phi) { @@ -23,35 +24,38 @@ TEST(MathFunctions, inv_Phi) { TEST(MathFunctions, Equal) { using stan::math::inv_Phi; // test output generated with WolframAlpha + constexpr std::array p_tails{0.000000001, 0.0000001, 0.99999, 0.9999999, + 0.999999999}; + constexpr std::array p{0.00001, 0.001, 0.05, 0.15, 0.25, 0.35, 0.45, + 0.55, 0.65, 0.75, 0.85, 0.95, 0.999}; + constexpr std::array exact_tails{ + -5.9978070150076868715623102049115374195951202210145432633059905935, + -5.199337582192816931587347266962336866509737160238716454318950531, + 4.2648907939228246284985246989063446293560532226954907262010508062, + 5.1993375821928169315873472669623368665097371602387164543189505310, + 5.9978070150076868715623102049115374195951202210145432633059905935}; + constexpr std::array exact{ + -4.264890793922824628498524698906344629356053222695490726201050806, + -3.090232306167813541540399830107379205491008491865808855697171108, + -1.644853626951472714863848907991632136083195744275322071769672094, + -1.036433389493789579713244074673503366134740595985917627904454866, + -0.674489750196081743202227014541307185386904415049861895662093788, + -0.385320466407567623810762390270473572721091620003945341485947546, + -0.125661346855074034210184388300799303397350646690021834224555394, + 0.1256613468550740342101843883007993033973506466900218342245553948, + 0.3853204664075676238107623902704735727210916200039453414859475461, + 0.6744897501960817432022270145413071853869044150498618956620937885, + 1.0364333894937895797132440746735033661347405959859176279044548663, + 1.6448536269514727148638489079916321360831957442753220717696720944, + 3.0902323061678135415403998301073792054910084918658088556971711085}; - double p[] = {0.000000001, 0.0000001, 0.00001, 0.001, 0.05, 0.15, 0.25, - 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, - 0.999, 0.99999, 0.9999999, 0.999999999}; - - double exact[] - = {-5.9978070150076868715623102049115374195951202210145432633059905935, - -5.199337582192816931587347266962336866509737160238716454318950531, - -4.264890793922824628498524698906344629356053222695490726201050806, - -3.090232306167813541540399830107379205491008491865808855697171108, - -1.644853626951472714863848907991632136083195744275322071769672094, - -1.036433389493789579713244074673503366134740595985917627904454866, - -0.674489750196081743202227014541307185386904415049861895662093788, - -0.385320466407567623810762390270473572721091620003945341485947546, - -0.125661346855074034210184388300799303397350646690021834224555394, - 0.1256613468550740342101843883007993033973506466900218342245553948, - 0.3853204664075676238107623902704735727210916200039453414859475461, - 0.6744897501960817432022270145413071853869044150498618956620937885, - 1.0364333894937895797132440746735033661347405959859176279044548663, - 1.6448536269514727148638489079916321360831957442753220717696720944, - 3.0902323061678135415403998301073792054910084918658088556971711085, - 4.2648907939228246284985246989063446293560532226954907262010508062, - 5.1993375821928169315873472669623368665097371602387164543189505310, - 5.9978070150076868715623102049115374195951202210145432633059905935}; - - int numValues = sizeof(p) / sizeof(double); - - for (int i = 0; i < numValues; ++i) { - EXPECT_NEAR(exact[i], inv_Phi(p[i]), 1.5e-15); + for (int i = 0; i < p_tails.size(); ++i) { + EXPECT_NEAR(exact_tails[i], inv_Phi(p_tails[i]), 4.6e-9) + << "at p_tails(" << i << ") = " << p_tails[i]; + } + for (int i = 0; i < p.size(); ++i) { + EXPECT_NEAR(exact[i], inv_Phi(p[i]), 1.5e-15) + << "at p(" << i << ") = " << p[i]; } } diff --git a/test/unit/math/prim/fun/mdivide_left_test.cpp b/test/unit/math/prim/fun/mdivide_left_test.cpp index 96ed82d7add..91a00c40ab2 100644 --- a/test/unit/math/prim/fun/mdivide_left_test.cpp +++ b/test/unit/math/prim/fun/mdivide_left_test.cpp @@ -7,7 +7,7 @@ TEST(MathMatrixPrim, mdivide_left_val) { Ad << 2.0, 3.0, 5.0, 7.0; stan::math::matrix_d I = Eigen::MatrixXd::Identity(2, 2); - EXPECT_MATRIX_FLOAT_EQ(I, stan::math::mdivide_left(Ad, Ad)); + EXPECT_MATRIX_NEAR(I, stan::math::mdivide_left(Ad, Ad), 1e-15); } TEST(MathMatrixPrim, mdivide_left_val2) { diff --git a/test/unit/math/prim/fun/mdivide_right_test.cpp b/test/unit/math/prim/fun/mdivide_right_test.cpp index ae29981cd60..f6b5e189196 100644 --- a/test/unit/math/prim/fun/mdivide_right_test.cpp +++ b/test/unit/math/prim/fun/mdivide_right_test.cpp @@ -7,7 +7,7 @@ TEST(MathMatrixPrim, mdivide_right_val) { Ad << 2.0, 3.0, 5.0, 7.0; stan::math::matrix_d I = Eigen::MatrixXd::Identity(2, 2); - EXPECT_MATRIX_FLOAT_EQ(I, stan::math::mdivide_left(Ad, Ad)); + EXPECT_MATRIX_NEAR(I, stan::math::mdivide_left(Ad, Ad), 1e-15); } TEST(MathMatrixPrim, mdivide_right_val2) {