AutoDiff.hpp File Reference

Symbolic automatic differentiation (Jacobian, gradient, Hessian, sensitivity analysis). More...

#include "janus/core/Function.hpp"
#include "janus/core/JanusConcepts.hpp"
#include "janus/core/JanusTypes.hpp"
#include "janus/core/Sparsity.hpp"
#include <string>
#include <vector>

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Classes
struct	janus::SensitivitySwitchOptions
	Heuristics controlling automatic forward-vs-adjoint selection. More...
struct	janus::SensitivityRecommendation
	Result of Janus sensitivity regime selection. More...

Namespaces
namespace	janus
namespace	janus::detail
	Smooth approximation of ReLU function: softplus(x) = (1/beta) * log(1 + exp(beta * x)).

Enumerations
enum class	janus::SensitivityRegime { janus::Forward , janus::Adjoint , janus::CheckpointedAdjoint }
	Sensitivity regime selected for a Jacobian-like derivative workload. More...
enum class	janus::CheckpointInterpolation { janus::None , janus::Hermite , janus::Polynomial }
	Checkpoint interpolation recommendation for long-horizon adjoints. More...

Functions
template<typename Expr, typename... Vars>
auto	janus::jacobian (const Expr &expression, const Vars &...variables)
	Computes Jacobian of an expression with respect to variables.
int	janus::detail::input_numel (const Function &fn, int input_idx)
int	janus::detail::output_numel (const Function &fn, int output_idx)
void	janus::detail::validate_scalar_output (const Function &fn, int output_idx, const std::string &context)
void	janus::detail::validate_same_shape (const casadi::MX &lhs, const casadi::MX &rhs, const std::string &context, const std::string &rhs_name)
std::vector< casadi::MX >	janus::detail::symbolic_inputs_like (const Function &fn)
casadi::MX	janus::detail::make_zero_seed (int rows, int cols, int directions)
casadi::MX	janus::detail::make_basis_seed (int rows, int cols)
casadi::MX	janus::detail::stacked_blocks_to_columns (const casadi::MX &stacked, int block_rows, int block_cols, int n_blocks)
std::string	janus::detail::sensitivity_function_name (const Function &fn, const std::string &suffix, int output_idx, int input_idx)
std::string	janus::detail::lagrangian_function_name (const Function &fn, const std::string &suffix, int objective_output_idx, int constraint_output_idx, int input_idx)
void	janus::detail::validate_scalar_expression (const casadi::MX &expr, const std::string &context, const std::string &name)
casadi::MX	janus::detail::lagrangian_scalar (const SymbolicArg &objective, const SymbolicArg &constraints, const SymbolicArg &multipliers, const std::string &context)
casadi::MX	janus::detail::forward_block_jacobian (const Function &fn, int output_idx, int input_idx)
casadi::MX	janus::detail::reverse_block_jacobian (const Function &fn, int output_idx, int input_idx)
SensitivityRecommendation	janus::select_sensitivity_regime (int parameter_count, int output_count, int horizon_length=1, bool stiff=false, const SensitivitySwitchOptions &opts=SensitivitySwitchOptions())
	Recommend a sensitivity regime from parameter/output counts.
SensitivityRecommendation	janus::select_sensitivity_regime (const Function &fn, int output_idx=0, int input_idx=0, int horizon_length=1, bool stiff=false, const SensitivitySwitchOptions &opts=SensitivitySwitchOptions())
	Recommend a sensitivity regime for a selected janus::Function block.
Function	janus::sensitivity_jacobian (const Function &fn, int output_idx=0, int input_idx=0, int horizon_length=1, bool stiff=false, const SensitivitySwitchOptions &opts=SensitivitySwitchOptions())
	Build a Jacobian function for one output/input block using the recommended regime.
auto	janus::jacobian (const std::vector< SymbolicArg > &expressions, const std::vector< SymbolicArg > &variables)
	Computes Jacobian with vector arguments (expressions and variables).
SymbolicVector	janus::sym_gradient (const SymbolicArg &expr, const SymbolicArg &vars)
	Symbolic gradient (for scalar-output functions).
SymbolicMatrix	janus::hessian (const SymbolicArg &expr, const SymbolicArg &vars)
	Hessian matrix (second-order derivatives).
SymbolicMatrix	janus::hessian_lagrangian (const SymbolicArg &objective, const SymbolicArg &constraints, const SymbolicArg &vars, const SymbolicArg &multipliers)
	Hessian of Lagrangian for constrained optimization.
SymbolicMatrix	janus::hessian_vector_product (const SymbolicArg &expr, const SymbolicArg &vars, const SymbolicArg &direction)
	Hessian-vector product for a scalar expression without forming the dense Hessian.
SymbolicMatrix	janus::lagrangian_hessian_vector_product (const SymbolicArg &objective, const SymbolicArg &constraints, const SymbolicArg &vars, const SymbolicArg &multipliers, const SymbolicArg &direction)
	Hessian-vector product of a Lagrangian, i.e. a second-order adjoint action.
Function	janus::hessian_vector_product (const Function &fn, int output_idx=0, int input_idx=0)
	Build a matrix-free Hessian-vector product function for one scalar output/input block.
Function	janus::lagrangian_hessian_vector_product (const Function &fn, int objective_output_idx, int constraint_output_idx, int input_idx=0)
	Build a Lagrangian Hessian-vector product function for optimization workflows.
SymbolicVector	janus::sym_gradient (const SymbolicArg &expr, const std::vector< SymbolicArg > &vars)
	Symbolic gradient with vector of variables.
SymbolicMatrix	janus::hessian (const SymbolicArg &expr, const std::vector< SymbolicArg > &vars)
	Hessian with vector of variables.
SymbolicMatrix	janus::hessian_lagrangian (const SymbolicArg &objective, const SymbolicArg &constraints, const std::vector< SymbolicArg > &vars, const SymbolicArg &multipliers)
	Hessian of Lagrangian with vector inputs.
SymbolicMatrix	janus::hessian_vector_product (const SymbolicArg &expr, const std::vector< SymbolicArg > &vars, const SymbolicArg &direction)
	Hessian-vector product with vector of variables.
SymbolicMatrix	janus::lagrangian_hessian_vector_product (const SymbolicArg &objective, const SymbolicArg &constraints, const std::vector< SymbolicArg > &vars, const SymbolicArg &multipliers, const SymbolicArg &direction)
	Lagrangian Hessian-vector product with vector of variables.

Detailed Description

Symbolic automatic differentiation (Jacobian, gradient, Hessian, sensitivity analysis).

See also

Calculus.hpp, FiniteDifference.hpp