Smooth approximation of ReLU function: softplus(x) = (1/beta) * log(1 + exp(beta * x)). More...

Classes
struct	BipartiteComponent
struct	is_tuple
	Helper to detect if a type is a std::tuple. More...
struct	is_tuple< std::tuple< Ts... > >
struct	SparseJacobianArtifacts
struct	SparseHessianArtifacts
struct	AliasCandidate
struct	TarjanState
struct	InterpnGridData
class	FunctionalPreconditioner
struct	EmbeddedQuadratureRule
struct	NumericState
struct	StageOutcome

Functions
std::vector< int >	sort_unique (std::vector< int > values)
std::vector< casadi_int >	to_casadi_int (const std::vector< int > &values)
std::string	join_labels (const std::vector< std::string > &labels)
std::string	property_name (StructuralProperty property)
std::string	property_subject_plural (StructuralProperty property)
std::string	property_subject_singular (StructuralProperty property)
std::string	property_fix_hint (StructuralProperty property)
std::string	input_label (const std::string &input_name, int local_index)
std::string	output_label (const std::string &output_name, int rows, int cols, int flat_index)
std::vector< int >	canonical_output_indices (const casadi::Function &cfn, const std::vector< int > &requested, const std::string &context)
void	validate_input_block (const casadi::Function &cfn, int input_idx, const std::string &context)
void	validate_output_blocks (const casadi::Function &cfn, const std::vector< int > &output_indices, const std::string &context)
casadi::MX	flatten_output (const casadi::MX &output)
std::vector< DiagnosticInputRef >	make_input_refs (const casadi::Function &cfn, int input_idx)
std::vector< DiagnosticOutputRef >	make_output_refs (const casadi::Function &cfn, const std::vector< int > &output_indices)
casadi::MX	collect_selected_outputs (const std::vector< casadi::MX > &outputs, const std::vector< int > &output_indices)
std::vector< BipartiteComponent >	connected_components (const casadi::Sparsity &sp)
int	structural_rank (const casadi::Sparsity &sp)
int	structural_rank_of_component (const casadi::Sparsity &sp, const BipartiteComponent &component)
std::vector< int >	zero_sensitivity_columns (const casadi::Sparsity &sp)
std::vector< std::string >	labels_for_inputs (const std::vector< DiagnosticInputRef > &inputs, const std::vector< int > &indices)
std::vector< std::string >	labels_for_outputs (const std::vector< DiagnosticOutputRef > &outputs, const std::vector< int > &rows)
std::vector< StructuralDiagnosticIssue >	build_issues (StructuralProperty property, const std::vector< DiagnosticInputRef > &inputs, const std::vector< DiagnosticOutputRef > &outputs, const std::vector< int > &zero_sensitivity_local_indices, const std::vector< StructuralDeficiencyGroup > &deficiency_groups)
StructuralSensitivityReport	analyze_property (const Function &fn, int input_idx, StructuralProperty property, const StructuralSensitivityOptions &opts)
std::string	to_casadi_parallelization (MapParallelization parallelization)
template<typename Tuple, std::size_t... Is>
std::vector< SymbolicArg >	tuple_to_outputs_impl (const Tuple &t, std::index_sequence< Is... >)
	Convert a tuple of symbolic scalars to a vector of SymbolicArg.
template<typename... Ts>
std::vector< SymbolicArg >	tuple_to_outputs (const std::tuple< Ts... > &t)
template<typename Func, std::size_t... Is>
auto	invoke_with_symbols_impl (Func &&fn, const std::vector< SymbolicScalar > &syms, std::index_sequence< Is... >)
	Invoke lambda with unpacked symbolic arguments.
template<int NInputs, typename Func>
auto	invoke_with_symbols (Func &&fn, const std::vector< SymbolicScalar > &syms)
std::string	escape_dot_label (const std::string &s)
	Escape special characters for DOT format.
std::string	get_op_name (const SymbolicScalar &mx)
	Get a short description of an MX operation type.
std::string	escape_for_js (const std::string &content)
	Escape a string for embedding in a JavaScript string literal.
std::string	escape_for_json (const std::string &s)
	Escape a string for embedding in JSON.
void	write_graph_html (std::ostream &out, const std::string &title, const std::string &escaped_dot, const std::string &node_data_json, const std::string &edges_json, const std::string &extra_header_js="")
	Write a complete interactive graph HTML page.
std::string	get_sx_operation (const casadi::SXElem &elem)
	Map CasADi SX operation codes to readable labels.
void	get_sx_node_style (const casadi::SXElem &elem, std::string &color, std::string &shape)
	Get node styling based on SX element type.
std::vector< SymbolicScalar >	to_mx_vector (const std::vector< SymbolicArg > &args)
std::vector< SymbolicArg >	to_symbolic_args (const std::vector< SymbolicScalar > &args)
SymbolicScalar	stack_nonzeros (const SymbolicScalar &expr)
void	validate_function_indices (const Function &fn, int output_idx, int input_idx, const char *where)
std::vector< SymbolicScalar >	symbolic_inputs_like (const Function &fn, const std::string &prefix)
GraphColoring	make_forward_coloring (const casadi::Sparsity &jac_sparsity)
GraphColoring	make_reverse_coloring (const casadi::Sparsity &jac_sparsity)
SparseJacobianArtifacts	make_sparse_jacobian_artifacts (const std::vector< SymbolicArg > &expressions, const std::vector< SymbolicArg > &variables, const std::string &name)
SparseJacobianArtifacts	make_sparse_jacobian_artifacts (const Function &fn, int output_idx, int input_idx, const std::string &name)
SparseHessianArtifacts	make_sparse_hessian_artifacts (const SymbolicArg &expression, const std::vector< SymbolicArg > &variables, const std::string &name)
SparseHessianArtifacts	make_sparse_hessian_artifacts (const Function &fn, int output_idx, int input_idx, const std::string &name)
SparsityPattern	function_jacobian_sparsity (const Function &fn, int output_idx, int input_idx)
void	validate_options (const StructuralTransformOptions &opts, const std::string &context)
void	validate_selected_block (const Function &fn, const StructuralTransformOptions &opts, const std::string &context)
std::vector< int >	make_index_vector (int n)
std::vector< casadi::MX >	mx_elements (const casadi::MX &v)
casadi::MX	vertcat_subset (const std::vector< casadi::MX > &elems, const std::vector< int > &indices)
std::vector< int >	find_row_nonzeros (const casadi::MX &A, int row)
bool	has_no_free_symbols (const casadi::MX &expr)
bool	coefficients_are_constant (const casadi::MX &A, int row, const std::vector< int > &nz_cols)
bool	try_make_alias_candidate (const casadi::MX &expr, const casadi::MX &state_symbol, const std::vector< int > &active_var_indices, const StructuralTransformOptions &opts, AliasCandidate &candidate)
std::vector< int >	erase_value (const std::vector< int > &values, int erased_index)
std::vector< int >	casadi_to_int (const std::vector< casadi_int > &values)
void	tarjan_visit (int node, TarjanState &state)
std::vector< std::vector< int > >	strongly_connected_components (const std::vector< std::vector< int > > &adjacency, const std::vector< bool > &removed)
std::vector< int >	tearing_recommendation (const casadi::Sparsity &incidence, const std::vector< int > &row_indices, const std::vector< int > &col_indices)
int	input_numel (const Function &fn, int input_idx)
int	output_numel (const Function &fn, int output_idx)
void	validate_scalar_output (const Function &fn, int output_idx, const std::string &context)
void	validate_same_shape (const casadi::MX &lhs, const casadi::MX &rhs, const std::string &context, const std::string &rhs_name)
std::vector< casadi::MX >	symbolic_inputs_like (const Function &fn)
casadi::MX	make_zero_seed (int rows, int cols, int directions)
casadi::MX	make_basis_seed (int rows, int cols)
casadi::MX	stacked_blocks_to_columns (const casadi::MX &stacked, int block_rows, int block_cols, int n_blocks)
std::string	sensitivity_function_name (const Function &fn, const std::string &suffix, int output_idx, int input_idx)
std::string	lagrangian_function_name (const Function &fn, const std::string &suffix, int objective_output_idx, int constraint_output_idx, int input_idx)
void	validate_scalar_expression (const casadi::MX &expr, const std::string &context, const std::string &name)
casadi::MX	lagrangian_scalar (const SymbolicArg &objective, const SymbolicArg &constraints, const SymbolicArg &multipliers, const std::string &context)
casadi::MX	forward_block_jacobian (const Function &fn, int output_idx, int input_idx)
casadi::MX	reverse_block_jacobian (const Function &fn, int output_idx, int input_idx)
NumericVector	to_numeric_vector (std::initializer_list< double > init)
const char *	method_name (SecondOrderIntegratorMethod method)
const char *	method_name (MassMatrixIntegratorMethod method)
void	validate_eval_count (const std::string &context, int n_eval)
void	validate_second_order_options (const SecondOrderIvpOptions &opts, const std::string &context)
void	validate_mass_matrix_options (const MassMatrixIvpOptions &opts, const std::string &context)
void	validate_second_order_initial_state (const NumericVector &q0, const NumericVector &v0)
double	inf_norm (const NumericVector &x)
bool	is_constant_zero (const SymbolicScalar &expr)
template<typename VectorFunc>
NumericMatrix	finite_difference_jacobian (VectorFunc &&func, const NumericVector &x, double epsilon)
template<typename MassFunc>
NumericMatrix	evaluate_mass_matrix (MassFunc &&mass_matrix, double t, const NumericVector &y, const std::string &context)
template<typename RhsFunc, typename MassFunc>
NumericVector	rosenbrock_euler_step (RhsFunc &&rhs, MassFunc &&mass_matrix, const NumericVector &y, double t, double dt, const MassMatrixIvpOptions &opts)
template<typename RhsFunc, typename MassFunc>
NumericVector	bdf1_step (RhsFunc &&rhs, MassFunc &&mass_matrix, const NumericVector &y, double t, double dt, const MassMatrixIvpOptions &opts)
template<typename DerivedX>
auto	compute_dx (const Eigen::MatrixBase< DerivedX > &x)
template<typename Derived>
auto	slice (const Eigen::MatrixBase< Derived > &m, Eigen::Index start, Eigen::Index end)
template<typename DerivedA, typename DerivedB>
auto	concatenate (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedB > &b)
template<typename DerivedF, typename DerivedX>
auto	integrate_forward_simpson (const Eigen::MatrixBase< DerivedF > &f, const Eigen::MatrixBase< DerivedX > &x)
template<typename DerivedF, typename DerivedX>
auto	integrate_backward_simpson (const Eigen::MatrixBase< DerivedF > &f, const Eigen::MatrixBase< DerivedX > &x)
template<typename DerivedF, typename DerivedX>
auto	integrate_cubic (const Eigen::MatrixBase< DerivedF > &f, const Eigen::MatrixBase< DerivedX > &x)
std::string	method_to_casadi_string (InterpolationMethod method)
	Convert InterpolationMethod enum to CasADi string.
const char *	hermite_symbolic_error_message ()
template<typename Derived>
JanusVector< typename Derived::Scalar >	flatten_fortran_order (const Eigen::MatrixBase< Derived > &values)
	Flatten N-D values array in Fortran order for CasADi.
std::string	symbolic_values_method_error_message (InterpolationMethod method)
InterpnGridData	build_interpn_grid (const std::vector< NumericVector > &points, const char *context)
void	validate_bspline_grid (const std::vector< std::vector< double > > &grid, const char *context)
template<JanusScalar Scalar>
JanusMatrix< Scalar >	normalize_query_matrix (const JanusMatrix< Scalar > &xi, int n_dims, const char *context)
template<JanusScalar Scalar>
SymbolicScalar	clamp_query_point (const JanusVector< Scalar > &point, const std::vector< std::vector< double > > &grid)
template<JanusScalar Scalar>
bool	point_out_of_bounds_numeric (const JanusVector< Scalar > &point, const std::vector< std::vector< double > > &grid)
SymbolicScalar	point_out_of_bounds_symbolic (const SymbolicVector &point, const std::vector< std::vector< double > > &grid)
casadi::Function	make_parametric_interpolant (const std::vector< std::vector< double > > &grid, InterpolationMethod method)
double	catmull_rom_slope (const std::vector< double > &x, const std::vector< double > &y, size_t i)
	Compute Catmull-Rom slope at a point using neighboring values.
double	hermite_interp_1d_numeric (const std::vector< double > &x, const std::vector< double > &y, double query)
	Evaluate 1D Catmull-Rom cubic Hermite spline (numeric only).
std::vector< int >	flat_to_multi_index (int flat_idx, const std::vector< int > &dims)
	Compute multi-dimensional index from flat index (Fortran order).
int	multi_to_flat_index (const std::vector< int > &multi, const std::vector< int > &dims)
	Compute flat index from multi-dimensional index (Fortran order).
double	hermite_interpn_numeric (const std::vector< std::vector< double > > &grid, const std::vector< double > &values, const std::vector< double > &query)
	N-dimensional Catmull-Rom interpolation via tensor product (numeric only).
void	validate_linear_solve_dims (Eigen::Index a_rows, Eigen::Index a_cols, Eigen::Index b_rows, const std::string &context)
void	validate_square_required (Eigen::Index rows, Eigen::Index cols, const std::string &context, const std::string &solver_name)
void	validate_iterative_policy (const LinearSolvePolicy &policy, const std::string &context)
std::function< NumericVector(const NumericVector &)>	make_preconditioner (const SparseMatrix &A, const LinearSolvePolicy &policy)
template<typename MatrixLike>
SparseMatrix	dense_to_sparse (const MatrixLike &A)
template<typename DerivedB>
auto	solve_sparse_direct_numeric (const SparseMatrix &A, const Eigen::MatrixBase< DerivedB > &b, const LinearSolvePolicy &policy)
template<typename Solver, typename DerivedB>
auto	solve_iterative_with_solver (Solver &solver, const Eigen::MatrixBase< DerivedB > &b)
template<typename DerivedB>
auto	solve_iterative_numeric (const SparseMatrix &A, const Eigen::MatrixBase< DerivedB > &b, const LinearSolvePolicy &policy)
template<typename DerivedA, typename DerivedB>
auto	solve_dense_numeric (const Eigen::MatrixBase< DerivedA > &A, const Eigen::MatrixBase< DerivedB > &b, const LinearSolvePolicy &policy)
template<typename Scalar>
JanusVector< Scalar >	normalize_vector (const JanusVector< Scalar > &v)
template<typename Scalar>
JanusVector< Scalar >	best_eigenvector_candidate (const std::array< JanusVector< Scalar >, 3 > &cands)
template<typename Scalar>
JanusVector< Scalar >	symmetric_eigenvector_2x2 (const JanusMatrix< Scalar > &A, const Scalar &lambda)
template<typename Scalar>
JanusVector< Scalar >	symmetric_eigenvector_3x3 (const JanusMatrix< Scalar > &A, const Scalar &lambda)
template<typename Scalar>
Scalar	determinant_3x3 (const JanusMatrix< Scalar > &A)
template<typename Scalar>
void	sort_eigenpairs (JanusVector< Scalar > &eigenvalues, JanusMatrix< Scalar > &eigenvectors)
template<typename Scalar>
EigenDecomposition< Scalar >	eig_symmetric_symbolic (const JanusMatrix< Scalar > &A)
template<typename Cond, typename DerivedTrue, typename DerivedFalse>
auto	select (const Cond &cond, const Eigen::MatrixBase< DerivedTrue > &if_true, const Eigen::MatrixBase< DerivedFalse > &if_false)
bool	is_symbolic_predicate (const SymbolicScalar &expr)
SymbolicScalar	as_symbolic_predicate (const SymbolicScalar &expr)
template<typename Derived>
SymbolicScalar	count_symbolic_truthy (const Eigen::MatrixBase< Derived > &a)
std::pair< NumericVector, NumericVector >	gauss_legendre_rule (int n)
void	validate_degree (int degree, const std::string &context)
void	validate_dimension (const PolynomialChaosDimension &dimension, const std::string &context)
template<JanusScalar Scalar>
Scalar	raw_hermite_polynomial (int degree, const Scalar &x)
template<JanusScalar Scalar>
Scalar	raw_legendre_polynomial (int degree, const Scalar &x)
template<JanusScalar Scalar>
Scalar	raw_jacobi_polynomial (int degree, const Scalar &x, double alpha, double beta)
template<JanusScalar Scalar>
Scalar	raw_laguerre_polynomial (int degree, const Scalar &x, double alpha)
double	squared_norm_raw (const PolynomialChaosDimension &dimension, int degree)
double	squared_norm_probability (const PolynomialChaosDimension &dimension, int degree)
bool	multi_index_less (const std::vector< int > &lhs, const std::vector< int > &rhs)
void	total_order_recursive (int dim, int order, int axis, std::vector< int > &current, std::vector< std::vector< int > > &indices)
void	tensor_product_recursive (int dim, int order, int axis, std::vector< int > &current, std::vector< std::vector< int > > &indices)
std::vector< std::vector< int > >	generate_multi_indices (int dim, int order, PolynomialChaosTruncation truncation)
template<JanusScalar Scalar>
JanusVector< Scalar >	apply_operator (const NumericMatrix &op, const JanusVector< Scalar > &values, const std::string &context)
template<JanusScalar Scalar>
JanusMatrix< Scalar >	apply_operator (const NumericMatrix &op, const JanusMatrix< Scalar > &values, const std::string &context)
void	validate_samples (const NumericMatrix &samples, int dimension, const std::string &context)
NumericMatrix	regression_operator (const NumericMatrix &design_matrix, double ridge, const std::string &context)
const EmbeddedQuadratureRule &	gauss_kronrod_15_rule ()
void	validate_order (int order, const std::string &context)
void	validate_level (int level, const std::string &context)
double	binomial (int n, int k)
int	clenshaw_curtis_order_from_level (int level)
int	gauss_order_from_level (int level)
bool	is_bounded_support (const PolynomialChaosDimension &dimension)
double	standard_normal_moment (int degree)
double	shifted_beta_moment (int degree, double alpha, double beta)
double	probability_moment (const PolynomialChaosDimension &dimension, int degree)
NumericVector	clenshaw_curtis_probability_weights (const PolynomialChaosDimension &dimension, const NumericVector &nodes)
UnivariateQuadratureRule	make_gauss_from_jacobi_matrix (const NumericVector &diag, const NumericVector &offdiag, int level)
UnivariateQuadratureRule	gauss_rule (const PolynomialChaosDimension &dimension, int order, int level)
UnivariateQuadratureRule	gauss_kronrod_rule (const PolynomialChaosDimension &dimension, int order, int level)
UnivariateQuadratureRule	clenshaw_curtis_rule (const PolynomialChaosDimension &dimension, int order, int level)
std::vector< std::vector< int > >	positive_compositions (int dim, int sum)
std::string	sample_key (const NumericVector &point, double tolerance)
std::string	method_name (RootSolveMethod method)
RootSolveMethod	strategy_to_method (RootSolveStrategy strategy)
std::string	unique_name (const std::string &prefix)
void	validate_root_options (const RootFinderOptions &opts, const std::string &context)
void	validate_root_problem (const casadi::Function &f_casadi, const std::string &context)
casadi::Dict	opts_to_dict (const RootFinderOptions &opts)
casadi::DM	vector_to_dm (const Eigen::VectorXd &x)
Eigen::VectorXd	dm_to_vector (const casadi::DM &x)
Eigen::MatrixXd	dm_to_matrix (const casadi::DM &x)
std::string	implicit_function_name (const casadi::Function &g_casadi)
void	validate_implicit_problem (const casadi::Function &g_casadi, const Eigen::VectorXd &x_guess, const ImplicitFunctionOptions &implicit_opts)
Eigen::VectorXd	solve_linear_system (const Eigen::MatrixXd &A, const Eigen::VectorXd &b)
bool	all_finite (const Eigen::VectorXd &x)
bool	all_finite (const Eigen::MatrixXd &x)
Eigen::VectorXd	evaluate_residual_only (const casadi::Function &residual_fn, const Eigen::VectorXd &x)
NumericState	evaluate_state (const casadi::Function &residual_fn, const casadi::Function &jacobian_fn, const Eigen::VectorXd &x, const std::string &context)
void	maybe_log (const RootFinderOptions &opts, const std::string &message)
bool	is_converged (const NumericState &state, const RootFinderOptions &opts)
StageOutcome	solve_trust_region (const casadi::Function &residual_fn, const casadi::Function &jacobian_fn, const NumericState &start, const RootFinderOptions &opts, int max_iterations)
StageOutcome	solve_line_search (const casadi::Function &residual_fn, const casadi::Function &jacobian_fn, const NumericState &start, const RootFinderOptions &opts, int max_iterations)
StageOutcome	solve_broyden (const casadi::Function &residual_fn, const casadi::Function &jacobian_fn, const NumericState &start, const RootFinderOptions &opts, int max_iterations)
StageOutcome	solve_pseudo_transient (const casadi::Function &residual_fn, const casadi::Function &jacobian_fn, const NumericState &start, const RootFinderOptions &opts, int max_iterations)
double	rbf_phi (double r, RBFKernel kernel, double epsilon=1.0)
	Evaluate RBF kernel φ(r) for a given distance.
double	euclidean_distance (const double p1, const double p2, int dims)
	Compute Euclidean distance between two points.
void	validate_hardness (double hardness, const char *function_name)
void	validate_rho (double rho)
template<std::floating_point T>
auto	softplus_scalar (const T &x, double beta)
auto	softplus_scalar (const SymbolicScalar &x, double beta)
double	validate_positive_scale (double scale, const std::string &context)
double	max_finite_abs (std::optional< double > lower_bound, std::optional< double > upper_bound)
double	suggest_scalar_scale (double init_guess, std::optional< double > lower_bound, std::optional< double > upper_bound)
double	suggest_vector_scale (const NumericVector &init_guess, std::optional< double > lower_bound, std::optional< double > upper_bound)
std::vector< double >	dm_to_std_vector (const casadi::DM &value)
double	dm_to_scalar (const casadi::DM &value)
std::vector< casadi::MX >	current_assignments (const casadi::Opti &opti)
double	normalized_magnitude (double magnitude, double scale)
bool	nearly_equal (double a, double b)
double	constraint_violation (double value, double lower_bound, bool has_lower_bound, double upper_bound, bool has_upper_bound)
double	constraint_magnitude (double value, double lower_bound, bool has_lower_bound, double upper_bound, bool has_upper_bound)
ScalingIssueLevel	issue_level (double normalized, const ScalingAnalysisOptions &opts)

Variables
template<typename T>
constexpr bool	is_tuple_v = is_tuple<T>::value
constexpr double	rms_fusion_epsilon = 1e-100
	Small epsilon to prevent division by zero in RMS fusion.
constexpr double	polynomial_root_tolerance = 1e-15
	Tolerance for zero-length integration intervals in Birkhoff matrix.
constexpr double	rbf_regularization = 1e-10
	Regularization term for RBF interpolation matrix to prevent singularity.
constexpr double	rbf_zero_threshold = 1e-15
	Threshold below which thin-plate spline uses linear fallback to avoid log(0).

Detailed Description

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

Parameters

x	Input value
beta	Sharpness parameter (default 1.0). Higher = closer to ReLU.
threshold	Retained for backwards compatibility. Unused by the smooth implementation.

Returns: Softplus value

Function Documentation

◆ all_finite() [1/2]

bool janus::detail::all_finite ( const Eigen::MatrixXd & x )

inline

◆ all_finite() [2/2]

bool janus::detail::all_finite ( const Eigen::VectorXd & x )

inline

◆ analyze_property()

StructuralSensitivityReport janus::detail::analyze_property	(	const Function &	fn,
		int	input_idx,
		StructuralProperty	property,
		const StructuralSensitivityOptions &	opts )

inline

◆ apply_operator() [1/2]

template<JanusScalar Scalar>

JanusMatrix< Scalar > janus::detail::apply_operator	(	const NumericMatrix &	op,
		const JanusMatrix< Scalar > &	values,
		const std::string &	context )

◆ apply_operator() [2/2]

template<JanusScalar Scalar>

JanusVector< Scalar > janus::detail::apply_operator	(	const NumericMatrix &	op,
		const JanusVector< Scalar > &	values,
		const std::string &	context )

◆ as_symbolic_predicate()

SymbolicScalar janus::detail::as_symbolic_predicate ( const SymbolicScalar & expr )

inline

◆ bdf1_step()

template<typename RhsFunc, typename MassFunc>

NumericVector janus::detail::bdf1_step	(	RhsFunc &&	rhs,
		MassFunc &&	mass_matrix,
		const NumericVector &	y,
		double	t,
		double	dt,
		const MassMatrixIvpOptions &	opts )

◆ best_eigenvector_candidate()

template<typename Scalar>

JanusVector< Scalar > janus::detail::best_eigenvector_candidate ( const std::array< JanusVector< Scalar >, 3 > & cands )

◆ binomial()

double janus::detail::binomial	(	int	n,
		int	k )

inline

◆ build_interpn_grid()

InterpnGridData janus::detail::build_interpn_grid	(	const std::vector< NumericVector > &	points,
		const char *	context )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ build_issues()

std::vector< StructuralDiagnosticIssue > janus::detail::build_issues	(	StructuralProperty	property,
		const std::vector< DiagnosticInputRef > &	inputs,
		const std::vector< DiagnosticOutputRef > &	outputs,
		const std::vector< int > &	zero_sensitivity_local_indices,
		const std::vector< StructuralDeficiencyGroup > &	deficiency_groups )

inline

◆ canonical_output_indices()

std::vector< int > janus::detail::canonical_output_indices	(	const casadi::Function &	cfn,
		const std::vector< int > &	requested,
		const std::string &	context )

inline

◆ casadi_to_int()

std::vector< int > janus::detail::casadi_to_int ( const std::vector< casadi_int > & values )

inline

◆ catmull_rom_slope()

double janus::detail::catmull_rom_slope	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		size_t	i )

inline

Compute Catmull-Rom slope at a point using neighboring values.

For interior points: m = (y[i+1] - y[i-1]) / (x[i+1] - x[i-1]) For endpoints: use one-sided differences

Parameters

x	Grid x-coordinates
y	Grid y-values
i	Index of point

Returns: Slope at point i

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ clamp_query_point()

template<JanusScalar Scalar>

SymbolicScalar janus::detail::clamp_query_point	(	const JanusVector< Scalar > &	point,
		const std::vector< std::vector< double > > &	grid )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ clenshaw_curtis_order_from_level()

int janus::detail::clenshaw_curtis_order_from_level ( int level )

inline

◆ clenshaw_curtis_probability_weights()

NumericVector janus::detail::clenshaw_curtis_probability_weights	(	const PolynomialChaosDimension &	dimension,
		const NumericVector &	nodes )

inline

◆ clenshaw_curtis_rule()

UnivariateQuadratureRule janus::detail::clenshaw_curtis_rule	(	const PolynomialChaosDimension &	dimension,
		int	order,
		int	level )

inline

◆ coefficients_are_constant()

bool janus::detail::coefficients_are_constant	(	const casadi::MX &	A,
		int	row,
		const std::vector< int > &	nz_cols )

inline

◆ collect_selected_outputs()

casadi::MX janus::detail::collect_selected_outputs	(	const std::vector< casadi::MX > &	outputs,
		const std::vector< int > &	output_indices )

inline

◆ compute_dx()

template<typename DerivedX>

auto janus::detail::compute_dx ( const Eigen::MatrixBase< DerivedX > & x )

◆ concatenate()

template<typename DerivedA, typename DerivedB>

auto janus::detail::concatenate	(	const Eigen::MatrixBase< DerivedA > &	a,
		const Eigen::MatrixBase< DerivedB > &	b )

◆ connected_components()

std::vector< BipartiteComponent > janus::detail::connected_components ( const casadi::Sparsity & sp )

inline

◆ constraint_magnitude()

double janus::detail::constraint_magnitude	(	double	value,
		double	lower_bound,
		bool	has_lower_bound,
		double	upper_bound,
		bool	has_upper_bound )

inline

◆ constraint_violation()

double janus::detail::constraint_violation	(	double	value,
		double	lower_bound,
		bool	has_lower_bound,
		double	upper_bound,
		bool	has_upper_bound )

inline

◆ count_symbolic_truthy()

template<typename Derived>

SymbolicScalar janus::detail::count_symbolic_truthy ( const Eigen::MatrixBase< Derived > & a )

◆ current_assignments()

std::vector< casadi::MX > janus::detail::current_assignments ( const casadi::Opti & opti )

inline

◆ dense_to_sparse()

template<typename MatrixLike>

SparseMatrix janus::detail::dense_to_sparse ( const MatrixLike & A )

◆ determinant_3x3()

template<typename Scalar>

Scalar janus::detail::determinant_3x3 ( const JanusMatrix< Scalar > & A )

◆ dm_to_matrix()

Eigen::MatrixXd janus::detail::dm_to_matrix ( const casadi::DM & x )

inline

◆ dm_to_scalar()

double janus::detail::dm_to_scalar ( const casadi::DM & value )

inline

◆ dm_to_std_vector()

std::vector< double > janus::detail::dm_to_std_vector ( const casadi::DM & value )

inline

◆ dm_to_vector()

Eigen::VectorXd janus::detail::dm_to_vector ( const casadi::DM & x )

inline

◆ eig_symmetric_symbolic()

template<typename Scalar>

EigenDecomposition< Scalar > janus::detail::eig_symmetric_symbolic ( const JanusMatrix< Scalar > & A )

◆ erase_value()

std::vector< int > janus::detail::erase_value	(	const std::vector< int > &	values,
		int	erased_index )

inline

◆ escape_dot_label()

std::string janus::detail::escape_dot_label ( const std::string & s )

inline

Escape special characters for DOT format.

◆ escape_for_js()

std::string janus::detail::escape_for_js ( const std::string & content )

inline

Escape a string for embedding in a JavaScript string literal.

Parameters

content Raw string

Returns: Escaped string safe for use inside a <script> tag

◆ escape_for_json()

std::string janus::detail::escape_for_json ( const std::string & s )

inline

Escape a string for embedding in JSON.

Parameters

s	Raw string

Returns: Escaped string safe for use inside a <script> tag

◆ euclidean_distance()

double janus::detail::euclidean_distance	(	const double *	p1,
		const double *	p2,
		int	dims )

inline

Compute Euclidean distance between two points.

◆ evaluate_mass_matrix()

template<typename MassFunc>

NumericMatrix janus::detail::evaluate_mass_matrix	(	MassFunc &&	mass_matrix,
		double	t,
		const NumericVector &	y,
		const std::string &	context )

◆ evaluate_residual_only()

Eigen::VectorXd janus::detail::evaluate_residual_only	(	const casadi::Function &	residual_fn,
		const Eigen::VectorXd &	x )

inline

◆ evaluate_state()

NumericState janus::detail::evaluate_state	(	const casadi::Function &	residual_fn,
		const casadi::Function &	jacobian_fn,
		const Eigen::VectorXd &	x,
		const std::string &	context )

inline

◆ find_row_nonzeros()

std::vector< int > janus::detail::find_row_nonzeros	(	const casadi::MX &	A,
		int	row )

inline

◆ finite_difference_jacobian()

template<typename VectorFunc>

NumericMatrix janus::detail::finite_difference_jacobian	(	VectorFunc &&	func,
		const NumericVector &	x,
		double	epsilon )

◆ flat_to_multi_index()

std::vector< int > janus::detail::flat_to_multi_index	(	int	flat_idx,
		const std::vector< int > &	dims )

inline

Compute multi-dimensional index from flat index (Fortran order).

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ flatten_fortran_order()

template<typename Derived>

JanusVector< typename Derived::Scalar > janus::detail::flatten_fortran_order ( const Eigen::MatrixBase< Derived > & values )

inline

Flatten N-D values array in Fortran order for CasADi.

CasADi expects values flattened in column-major (Fortran) order. For a 2D array with shape (m, n), this means iterating over the first dimension fastest.

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ flatten_output()

casadi::MX janus::detail::flatten_output ( const casadi::MX & output )

inline

◆ forward_block_jacobian()

casadi::MX janus::detail::forward_block_jacobian	(	const Function &	fn,
		int	output_idx,
		int	input_idx )

inline

◆ function_jacobian_sparsity()

SparsityPattern janus::detail::function_jacobian_sparsity	(	const Function &	fn,
		int	output_idx,
		int	input_idx )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ gauss_kronrod_15_rule()

const EmbeddedQuadratureRule & janus::detail::gauss_kronrod_15_rule ( )

inline

◆ gauss_kronrod_rule()

UnivariateQuadratureRule janus::detail::gauss_kronrod_rule	(	const PolynomialChaosDimension &	dimension,
		int	order,
		int	level )

inline

◆ gauss_legendre_rule()

std::pair< NumericVector, NumericVector > janus::detail::gauss_legendre_rule ( int n )

inline

◆ gauss_order_from_level()

int janus::detail::gauss_order_from_level ( int level )

inline

◆ gauss_rule()

UnivariateQuadratureRule janus::detail::gauss_rule	(	const PolynomialChaosDimension &	dimension,
		int	order,
		int	level )

inline

◆ generate_multi_indices()

std::vector< std::vector< int > > janus::detail::generate_multi_indices	(	int	dim,
		int	order,
		PolynomialChaosTruncation	truncation )

inline

◆ get_op_name()

std::string janus::detail::get_op_name ( const SymbolicScalar & mx )

inline

Get a short description of an MX operation type.

◆ get_sx_node_style()

void janus::detail::get_sx_node_style	(	const casadi::SXElem &	elem,
		std::string &	color,
		std::string &	shape )

inline

Get node styling based on SX element type.

◆ get_sx_operation()

std::string janus::detail::get_sx_operation ( const casadi::SXElem & elem )

inline

Map CasADi SX operation codes to readable labels.

Uses casadi_math.hpp operation codes. Returns a short human-readable string for each operation type.

◆ has_no_free_symbols()

bool janus::detail::has_no_free_symbols ( const casadi::MX & expr )

inline

◆ hermite_interp_1d_numeric()

double janus::detail::hermite_interp_1d_numeric	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		double	query )

inline

Evaluate 1D Catmull-Rom cubic Hermite spline (numeric only).

Uses cubic Hermite basis functions: h00(t) = 2t³ - 3t² + 1 h10(t) = t³ - 2t² + t h01(t) = -2t³ + 3t² h11(t) = t³ - t²

p(t) = h00(t)*p0 + h10(t)*m0*h + h01(t)*p1 + h11(t)*m1*h where h = x1 - x0, t = (x - x0) / h

Parameters

x	Grid x-coordinates (sorted)
y	Grid y-values
query	Query point (must be numeric)

Returns: Interpolated value

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ hermite_interpn_numeric()

double janus::detail::hermite_interpn_numeric	(	const std::vector< std::vector< double > > &	grid,
		const std::vector< double > &	values,
		const std::vector< double > &	query )

inline

N-dimensional Catmull-Rom interpolation via tensor product (numeric only).

Interpolates in each dimension sequentially using 1D Hermite splines. This function is numeric-only because interval finding requires comparisons.

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ hermite_symbolic_error_message()

const char * janus::detail::hermite_symbolic_error_message ( )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ implicit_function_name()

std::string janus::detail::implicit_function_name ( const casadi::Function & g_casadi )

inline

◆ inf_norm()

double janus::detail::inf_norm ( const NumericVector & x )

inline

◆ input_label()

std::string janus::detail::input_label	(	const std::string &	input_name,
		int	local_index )

inline

◆ input_numel()

int janus::detail::input_numel	(	const Function &	fn,
		int	input_idx )

inline

◆ integrate_backward_simpson()

template<typename DerivedF, typename DerivedX>

auto janus::detail::integrate_backward_simpson	(	const Eigen::MatrixBase< DerivedF > &	f,
		const Eigen::MatrixBase< DerivedX > &	x )

◆ integrate_cubic()

template<typename DerivedF, typename DerivedX>

auto janus::detail::integrate_cubic	(	const Eigen::MatrixBase< DerivedF > &	f,
		const Eigen::MatrixBase< DerivedX > &	x )

◆ integrate_forward_simpson()

template<typename DerivedF, typename DerivedX>

auto janus::detail::integrate_forward_simpson	(	const Eigen::MatrixBase< DerivedF > &	f,
		const Eigen::MatrixBase< DerivedX > &	x )

◆ invoke_with_symbols()

template<int NInputs, typename Func>

auto janus::detail::invoke_with_symbols	(	Func &&	fn,
		const std::vector< SymbolicScalar > &	syms )

◆ invoke_with_symbols_impl()

template<typename Func, std::size_t... Is>

auto janus::detail::invoke_with_symbols_impl	(	Func &&	fn,
		const std::vector< SymbolicScalar > &	syms,
		std::index_sequence< Is... >	)

Invoke lambda with unpacked symbolic arguments.

◆ is_bounded_support()

bool janus::detail::is_bounded_support ( const PolynomialChaosDimension & dimension )

inline

◆ is_constant_zero()

bool janus::detail::is_constant_zero ( const SymbolicScalar & expr )

inline

◆ is_converged()

bool janus::detail::is_converged	(	const NumericState &	state,
		const RootFinderOptions &	opts )

inline

◆ is_symbolic_predicate()

bool janus::detail::is_symbolic_predicate ( const SymbolicScalar & expr )

inline

◆ issue_level()

ScalingIssueLevel janus::detail::issue_level	(	double	normalized,
		const ScalingAnalysisOptions &	opts )

inline

◆ join_labels()

std::string janus::detail::join_labels ( const std::vector< std::string > & labels )

inline

◆ labels_for_inputs()

std::vector< std::string > janus::detail::labels_for_inputs	(	const std::vector< DiagnosticInputRef > &	inputs,
		const std::vector< int > &	indices )

inline

◆ labels_for_outputs()

std::vector< std::string > janus::detail::labels_for_outputs	(	const std::vector< DiagnosticOutputRef > &	outputs,
		const std::vector< int > &	rows )

inline

◆ lagrangian_function_name()

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 )

inline

◆ lagrangian_scalar()

casadi::MX janus::detail::lagrangian_scalar	(	const SymbolicArg &	objective,
		const SymbolicArg &	constraints,
		const SymbolicArg &	multipliers,
		const std::string &	context )

inline

◆ make_basis_seed()

casadi::MX janus::detail::make_basis_seed	(	int	rows,
		int	cols )

inline

◆ make_forward_coloring()

GraphColoring janus::detail::make_forward_coloring ( const casadi::Sparsity & jac_sparsity )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ make_gauss_from_jacobi_matrix()

UnivariateQuadratureRule janus::detail::make_gauss_from_jacobi_matrix	(	const NumericVector &	diag,
		const NumericVector &	offdiag,
		int	level )

inline

◆ make_index_vector()

std::vector< int > janus::detail::make_index_vector ( int n )

inline

◆ make_input_refs()

std::vector< DiagnosticInputRef > janus::detail::make_input_refs	(	const casadi::Function &	cfn,
		int	input_idx )

inline

◆ make_output_refs()

std::vector< DiagnosticOutputRef > janus::detail::make_output_refs	(	const casadi::Function &	cfn,
		const std::vector< int > &	output_indices )

inline

◆ make_parametric_interpolant()

casadi::Function janus::detail::make_parametric_interpolant	(	const std::vector< std::vector< double > > &	grid,
		InterpolationMethod	method )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ make_preconditioner()

std::function< NumericVector(const NumericVector &)> janus::detail::make_preconditioner	(	const SparseMatrix &	A,
		const LinearSolvePolicy &	policy )

inline

◆ make_reverse_coloring()

GraphColoring janus::detail::make_reverse_coloring ( const casadi::Sparsity & jac_sparsity )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ make_sparse_hessian_artifacts() [1/2]

SparseHessianArtifacts janus::detail::make_sparse_hessian_artifacts	(	const Function &	fn,
		int	output_idx,
		int	input_idx,
		const std::string &	name )

inline

◆ make_sparse_hessian_artifacts() [2/2]

SparseHessianArtifacts janus::detail::make_sparse_hessian_artifacts	(	const SymbolicArg &	expression,
		const std::vector< SymbolicArg > &	variables,
		const std::string &	name )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ make_sparse_jacobian_artifacts() [1/2]

SparseJacobianArtifacts janus::detail::make_sparse_jacobian_artifacts	(	const Function &	fn,
		int	output_idx,
		int	input_idx,
		const std::string &	name )

inline

◆ make_sparse_jacobian_artifacts() [2/2]

SparseJacobianArtifacts janus::detail::make_sparse_jacobian_artifacts	(	const std::vector< SymbolicArg > &	expressions,
		const std::vector< SymbolicArg > &	variables,
		const std::string &	name )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ make_zero_seed()

casadi::MX janus::detail::make_zero_seed	(	int	rows,
		int	cols,
		int	directions )

inline

◆ max_finite_abs()

double janus::detail::max_finite_abs	(	std::optional< double >	lower_bound,
		std::optional< double >	upper_bound )

inline

◆ maybe_log()

void janus::detail::maybe_log	(	const RootFinderOptions &	opts,
		const std::string &	message )

inline

◆ method_name() [1/3]

const char * janus::detail::method_name ( MassMatrixIntegratorMethod method )

inline

◆ method_name() [2/3]

std::string janus::detail::method_name ( RootSolveMethod method )

inline

◆ method_name() [3/3]

const char * janus::detail::method_name ( SecondOrderIntegratorMethod method )

inline

◆ method_to_casadi_string()

std::string janus::detail::method_to_casadi_string ( InterpolationMethod method )

inline

Convert InterpolationMethod enum to CasADi string.

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ multi_index_less()

bool janus::detail::multi_index_less	(	const std::vector< int > &	lhs,
		const std::vector< int > &	rhs )

inline

◆ multi_to_flat_index()

int janus::detail::multi_to_flat_index	(	const std::vector< int > &	multi,
		const std::vector< int > &	dims )

inline

Compute flat index from multi-dimensional index (Fortran order).

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ mx_elements()

std::vector< casadi::MX > janus::detail::mx_elements ( const casadi::MX & v )

inline

◆ nearly_equal()

bool janus::detail::nearly_equal	(	double	a,
		double	b )

inline

◆ normalize_query_matrix()

template<JanusScalar Scalar>

JanusMatrix< Scalar > janus::detail::normalize_query_matrix	(	const JanusMatrix< Scalar > &	xi,
		int	n_dims,
		const char *	context )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ normalize_vector()

template<typename Scalar>

JanusVector< Scalar > janus::detail::normalize_vector ( const JanusVector< Scalar > & v )

◆ normalized_magnitude()

double janus::detail::normalized_magnitude	(	double	magnitude,
		double	scale )

inline

◆ opts_to_dict()

casadi::Dict janus::detail::opts_to_dict ( const RootFinderOptions & opts )

inline

◆ output_label()

std::string janus::detail::output_label	(	const std::string &	output_name,
		int	rows,
		int	cols,
		int	flat_index )

inline

◆ output_numel()

int janus::detail::output_numel	(	const Function &	fn,
		int	output_idx )

inline

◆ point_out_of_bounds_numeric()

template<JanusScalar Scalar>

bool janus::detail::point_out_of_bounds_numeric	(	const JanusVector< Scalar > &	point,
		const std::vector< std::vector< double > > &	grid )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ point_out_of_bounds_symbolic()

SymbolicScalar janus::detail::point_out_of_bounds_symbolic	(	const SymbolicVector &	point,
		const std::vector< std::vector< double > > &	grid )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ positive_compositions()

std::vector< std::vector< int > > janus::detail::positive_compositions	(	int	dim,
		int	sum )

inline

◆ probability_moment()

double janus::detail::probability_moment	(	const PolynomialChaosDimension &	dimension,
		int	degree )

inline

◆ property_fix_hint()

std::string janus::detail::property_fix_hint ( StructuralProperty property )

inline

◆ property_name()

std::string janus::detail::property_name ( StructuralProperty property )

inline

◆ property_subject_plural()

std::string janus::detail::property_subject_plural ( StructuralProperty property )

inline

◆ property_subject_singular()

std::string janus::detail::property_subject_singular ( StructuralProperty property )

inline

◆ raw_hermite_polynomial()

template<JanusScalar Scalar>

Scalar janus::detail::raw_hermite_polynomial	(	int	degree,
		const Scalar &	x )

◆ raw_jacobi_polynomial()

template<JanusScalar Scalar>

Scalar janus::detail::raw_jacobi_polynomial	(	int	degree,
		const Scalar &	x,
		double	alpha,
		double	beta )

◆ raw_laguerre_polynomial()

template<JanusScalar Scalar>

Scalar janus::detail::raw_laguerre_polynomial	(	int	degree,
		const Scalar &	x,
		double	alpha )

◆ raw_legendre_polynomial()

template<JanusScalar Scalar>

Scalar janus::detail::raw_legendre_polynomial	(	int	degree,
		const Scalar &	x )

◆ rbf_phi()

double janus::detail::rbf_phi	(	double	r,
		RBFKernel	kernel,
		double	epsilon = 1.0 )

inline

Evaluate RBF kernel φ(r) for a given distance.

Parameters

r	Distance between points (non-negative)
kernel	Kernel type
epsilon	Shape parameter (for Multiquadric/Gaussian)

Returns: Kernel value φ(r)

◆ regression_operator()

NumericMatrix janus::detail::regression_operator	(	const NumericMatrix &	design_matrix,
		double	ridge,
		const std::string &	context )

inline

◆ reverse_block_jacobian()

casadi::MX janus::detail::reverse_block_jacobian	(	const Function &	fn,
		int	output_idx,
		int	input_idx )

inline

◆ rosenbrock_euler_step()

template<typename RhsFunc, typename MassFunc>

NumericVector janus::detail::rosenbrock_euler_step	(	RhsFunc &&	rhs,
		MassFunc &&	mass_matrix,
		const NumericVector &	y,
		double	t,
		double	dt,
		const MassMatrixIvpOptions &	opts )

◆ sample_key()

std::string janus::detail::sample_key	(	const NumericVector &	point,
		double	tolerance )

inline

◆ select()

template<typename Cond, typename DerivedTrue, typename DerivedFalse>

auto janus::detail::select	(	const Cond &	cond,
		const Eigen::MatrixBase< DerivedTrue > &	if_true,
		const Eigen::MatrixBase< DerivedFalse > &	if_false )

◆ sensitivity_function_name()

std::string janus::detail::sensitivity_function_name	(	const Function &	fn,
		const std::string &	suffix,
		int	output_idx,
		int	input_idx )

inline

◆ shifted_beta_moment()

double janus::detail::shifted_beta_moment	(	int	degree,
		double	alpha,
		double	beta )

inline

◆ slice()

template<typename Derived>

auto janus::detail::slice	(	const Eigen::MatrixBase< Derived > &	m,
		Eigen::Index	start,
		Eigen::Index	end )

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ softplus_scalar() [1/2]

auto janus::detail::softplus_scalar	(	const SymbolicScalar &	x,
		double	beta )

inline

◆ softplus_scalar() [2/2]

template<std::floating_point T>

auto janus::detail::softplus_scalar	(	const T &	x,
		double	beta )

◆ solve_broyden()

StageOutcome janus::detail::solve_broyden	(	const casadi::Function &	residual_fn,
		const casadi::Function &	jacobian_fn,
		const NumericState &	start,
		const RootFinderOptions &	opts,
		int	max_iterations )

inline

◆ solve_dense_numeric()

template<typename DerivedA, typename DerivedB>

auto janus::detail::solve_dense_numeric	(	const Eigen::MatrixBase< DerivedA > &	A,
		const Eigen::MatrixBase< DerivedB > &	b,
		const LinearSolvePolicy &	policy )

◆ solve_iterative_numeric()

template<typename DerivedB>

auto janus::detail::solve_iterative_numeric	(	const SparseMatrix &	A,
		const Eigen::MatrixBase< DerivedB > &	b,
		const LinearSolvePolicy &	policy )

◆ solve_iterative_with_solver()

template<typename Solver, typename DerivedB>

auto janus::detail::solve_iterative_with_solver	(	Solver &	solver,
		const Eigen::MatrixBase< DerivedB > &	b )

◆ solve_line_search()

StageOutcome janus::detail::solve_line_search	(	const casadi::Function &	residual_fn,
		const casadi::Function &	jacobian_fn,
		const NumericState &	start,
		const RootFinderOptions &	opts,
		int	max_iterations )

inline

◆ solve_linear_system()

Eigen::VectorXd janus::detail::solve_linear_system	(	const Eigen::MatrixXd &	A,
		const Eigen::VectorXd &	b )

inline

◆ solve_pseudo_transient()

StageOutcome janus::detail::solve_pseudo_transient	(	const casadi::Function &	residual_fn,
		const casadi::Function &	jacobian_fn,
		const NumericState &	start,
		const RootFinderOptions &	opts,
		int	max_iterations )

inline

◆ solve_sparse_direct_numeric()

template<typename DerivedB>

auto janus::detail::solve_sparse_direct_numeric	(	const SparseMatrix &	A,
		const Eigen::MatrixBase< DerivedB > &	b,
		const LinearSolvePolicy &	policy )

◆ solve_trust_region()

StageOutcome janus::detail::solve_trust_region	(	const casadi::Function &	residual_fn,
		const casadi::Function &	jacobian_fn,
		const NumericState &	start,
		const RootFinderOptions &	opts,
		int	max_iterations )

inline

◆ sort_eigenpairs()

template<typename Scalar>

void janus::detail::sort_eigenpairs	(	JanusVector< Scalar > &	eigenvalues,
		JanusMatrix< Scalar > &	eigenvectors )

◆ sort_unique()

std::vector< int > janus::detail::sort_unique ( std::vector< int > values )

inline

◆ squared_norm_probability()

double janus::detail::squared_norm_probability	(	const PolynomialChaosDimension &	dimension,
		int	degree )

inline

◆ squared_norm_raw()

double janus::detail::squared_norm_raw	(	const PolynomialChaosDimension &	dimension,
		int	degree )

inline

◆ stack_nonzeros()

SymbolicScalar janus::detail::stack_nonzeros ( const SymbolicScalar & expr )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ stacked_blocks_to_columns()

casadi::MX janus::detail::stacked_blocks_to_columns	(	const casadi::MX &	stacked,
		int	block_rows,
		int	block_cols,
		int	n_blocks )

inline

◆ standard_normal_moment()

double janus::detail::standard_normal_moment ( int degree )

inline

◆ strategy_to_method()

RootSolveMethod janus::detail::strategy_to_method ( RootSolveStrategy strategy )

inline

◆ strongly_connected_components()

std::vector< std::vector< int > > janus::detail::strongly_connected_components	(	const std::vector< std::vector< int > > &	adjacency,
		const std::vector< bool > &	removed )

inline

◆ structural_rank()

int janus::detail::structural_rank ( const casadi::Sparsity & sp )

inline

◆ structural_rank_of_component()

int janus::detail::structural_rank_of_component	(	const casadi::Sparsity &	sp,
		const BipartiteComponent &	component )

inline

◆ suggest_scalar_scale()

double janus::detail::suggest_scalar_scale	(	double	init_guess,
		std::optional< double >	lower_bound,
		std::optional< double >	upper_bound )

inline

◆ suggest_vector_scale()

double janus::detail::suggest_vector_scale	(	const NumericVector &	init_guess,
		std::optional< double >	lower_bound,
		std::optional< double >	upper_bound )

inline

◆ symbolic_inputs_like() [1/2]

std::vector< casadi::MX > janus::detail::symbolic_inputs_like ( const Function & fn )

inline

◆ symbolic_inputs_like() [2/2]

std::vector< SymbolicScalar > janus::detail::symbolic_inputs_like	(	const Function &	fn,
		const std::string &	prefix )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ symbolic_values_method_error_message()

std::string janus::detail::symbolic_values_method_error_message ( InterpolationMethod method )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ symmetric_eigenvector_2x2()

template<typename Scalar>

JanusVector< Scalar > janus::detail::symmetric_eigenvector_2x2	(	const JanusMatrix< Scalar > &	A,
		const Scalar &	lambda )

◆ symmetric_eigenvector_3x3()

template<typename Scalar>

JanusVector< Scalar > janus::detail::symmetric_eigenvector_3x3	(	const JanusMatrix< Scalar > &	A,
		const Scalar &	lambda )

◆ tarjan_visit()

void janus::detail::tarjan_visit	(	int	node,
		TarjanState &	state )

inline

◆ tearing_recommendation()

std::vector< int > janus::detail::tearing_recommendation	(	const casadi::Sparsity &	incidence,
		const std::vector< int > &	row_indices,
		const std::vector< int > &	col_indices )

inline

◆ tensor_product_recursive()

void janus::detail::tensor_product_recursive	(	int	dim,
		int	order,
		int	axis,
		std::vector< int > &	current,
		std::vector< std::vector< int > > &	indices )

inline

◆ to_casadi_int()

std::vector< casadi_int > janus::detail::to_casadi_int ( const std::vector< int > & values )

inline

◆ to_casadi_parallelization()

std::string janus::detail::to_casadi_parallelization ( MapParallelization parallelization )

inline

◆ to_mx_vector()

std::vector< SymbolicScalar > janus::detail::to_mx_vector ( const std::vector< SymbolicArg > & args )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ to_numeric_vector()

NumericVector janus::detail::to_numeric_vector ( std::initializer_list< double > init )

inline

◆ to_symbolic_args()

std::vector< SymbolicArg > janus::detail::to_symbolic_args ( const std::vector< SymbolicScalar > & args )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ total_order_recursive()

void janus::detail::total_order_recursive	(	int	dim,
		int	order,
		int	axis,
		std::vector< int > &	current,
		std::vector< std::vector< int > > &	indices )

inline

◆ try_make_alias_candidate()

bool janus::detail::try_make_alias_candidate	(	const casadi::MX &	expr,
		const casadi::MX &	state_symbol,
		const std::vector< int > &	active_var_indices,
		const StructuralTransformOptions &	opts,
		AliasCandidate &	candidate )

inline

◆ tuple_to_outputs()

template<typename... Ts>

std::vector< SymbolicArg > janus::detail::tuple_to_outputs ( const std::tuple< Ts... > & t )

◆ tuple_to_outputs_impl()

template<typename Tuple, std::size_t... Is>

std::vector< SymbolicArg > janus::detail::tuple_to_outputs_impl	(	const Tuple &	t,
		std::index_sequence< Is... >	)

Convert a tuple of symbolic scalars to a vector of SymbolicArg.

◆ unique_name()

std::string janus::detail::unique_name ( const std::string & prefix )

inline

◆ validate_bspline_grid()

void janus::detail::validate_bspline_grid	(	const std::vector< std::vector< double > > &	grid,
		const char *	context )

inline

Examples: /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ validate_degree()

void janus::detail::validate_degree	(	int	degree,
		const std::string &	context )

inline

◆ validate_dimension()

void janus::detail::validate_dimension	(	const PolynomialChaosDimension &	dimension,
		const std::string &	context )

inline

◆ validate_eval_count()

void janus::detail::validate_eval_count	(	const std::string &	context,
		int	n_eval )

inline

◆ validate_function_indices()

void janus::detail::validate_function_indices	(	const Function &	fn,
		int	output_idx,
		int	input_idx,
		const char *	where )

inline

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp.

◆ validate_hardness()

void janus::detail::validate_hardness	(	double	hardness,
		const char *	function_name )

inline

◆ validate_implicit_problem()

void janus::detail::validate_implicit_problem	(	const casadi::Function &	g_casadi,
		const Eigen::VectorXd &	x_guess,
		const ImplicitFunctionOptions &	implicit_opts )

inline

◆ validate_input_block()

void janus::detail::validate_input_block	(	const casadi::Function &	cfn,
		int	input_idx,
		const std::string &	context )

inline

◆ validate_iterative_policy()

void janus::detail::validate_iterative_policy	(	const LinearSolvePolicy &	policy,
		const std::string &	context )

inline

◆ validate_level()

void janus::detail::validate_level	(	int	level,
		const std::string &	context )

inline

◆ validate_linear_solve_dims()

void janus::detail::validate_linear_solve_dims	(	Eigen::Index	a_rows,
		Eigen::Index	a_cols,
		Eigen::Index	b_rows,
		const std::string &	context )

inline

◆ validate_mass_matrix_options()

void janus::detail::validate_mass_matrix_options	(	const MassMatrixIvpOptions &	opts,
		const std::string &	context )

inline

◆ validate_options()

void janus::detail::validate_options	(	const StructuralTransformOptions &	opts,
		const std::string &	context )

inline

◆ validate_order()

void janus::detail::validate_order	(	int	order,
		const std::string &	context )

inline

◆ validate_output_blocks()

void janus::detail::validate_output_blocks	(	const casadi::Function &	cfn,
		const std::vector< int > &	output_indices,
		const std::string &	context )

inline

◆ validate_positive_scale()

double janus::detail::validate_positive_scale	(	double	scale,
		const std::string &	context )

inline

◆ validate_rho()

void janus::detail::validate_rho ( double rho )

inline

◆ validate_root_options()

void janus::detail::validate_root_options	(	const RootFinderOptions &	opts,
		const std::string &	context )

inline

◆ validate_root_problem()

void janus::detail::validate_root_problem	(	const casadi::Function &	f_casadi,
		const std::string &	context )

inline

◆ validate_same_shape()

void janus::detail::validate_same_shape	(	const casadi::MX &	lhs,
		const casadi::MX &	rhs,
		const std::string &	context,
		const std::string &	rhs_name )

inline

◆ validate_samples()

void janus::detail::validate_samples	(	const NumericMatrix &	samples,
		int	dimension,
		const std::string &	context )

inline

◆ validate_scalar_expression()

void janus::detail::validate_scalar_expression	(	const casadi::MX &	expr,
		const std::string &	context,
		const std::string &	name )

inline

◆ validate_scalar_output()

void janus::detail::validate_scalar_output	(	const Function &	fn,
		int	output_idx,
		const std::string &	context )

inline

◆ validate_second_order_initial_state()

void janus::detail::validate_second_order_initial_state	(	const NumericVector &	q0,
		const NumericVector &	v0 )

inline

◆ validate_second_order_options()

void janus::detail::validate_second_order_options	(	const SecondOrderIvpOptions &	opts,
		const std::string &	context )

inline

◆ validate_selected_block()

void janus::detail::validate_selected_block	(	const Function &	fn,
		const StructuralTransformOptions &	opts,
		const std::string &	context )

inline

◆ validate_square_required()

void janus::detail::validate_square_required	(	Eigen::Index	rows,
		Eigen::Index	cols,
		const std::string &	context,
		const std::string &	solver_name )

inline

◆ vector_to_dm()

casadi::DM janus::detail::vector_to_dm ( const Eigen::VectorXd & x )

inline

◆ vertcat_subset()

casadi::MX janus::detail::vertcat_subset	(	const std::vector< casadi::MX > &	elems,
		const std::vector< int > &	indices )

inline

◆ write_graph_html()

void janus::detail::write_graph_html	(	std::ostream &	out,
		const std::string &	title,
		const std::string &	escaped_dot,
		const std::string &	node_data_json,
		const std::string &	edges_json,
		const std::string &	extra_header_js = "" )

inline

Write a complete interactive graph HTML page.

Parameters

out	Output stream
title	Page title
escaped_dot	DOT source (JS-escaped)
node_data_json	Node metadata as JSON
edges_json	Edge list as JSON
extra_header_js	Optional JS inserted after data declarations

◆ zero_sensitivity_columns()

std::vector< int > janus::detail::zero_sensitivity_columns ( const casadi::Sparsity & sp )

inline

Variable Documentation

◆ is_tuple_v

template<typename T>

bool janus::detail::is_tuple_v = is_tuple<T>::value

inlineconstexpr

◆ polynomial_root_tolerance

double janus::detail::polynomial_root_tolerance = 1e-15

constexpr

Tolerance for zero-length integration intervals in Birkhoff matrix.

◆ rbf_regularization

double janus::detail::rbf_regularization = 1e-10

constexpr

Regularization term for RBF interpolation matrix to prevent singularity.

◆ rbf_zero_threshold

double janus::detail::rbf_zero_threshold = 1e-15

constexpr

Threshold below which thin-plate spline uses linear fallback to avoid log(0).

◆ rms_fusion_epsilon

double janus::detail::rms_fusion_epsilon = 1e-100

constexpr

Small epsilon to prevent division by zero in RMS fusion.

Classes

Functions

Variables

Detailed Description

Function Documentation

◆ all_finite() [1/2]

◆ all_finite() [2/2]

◆ analyze_property()

◆ apply_operator() [1/2]

◆ apply_operator() [2/2]

◆ as_symbolic_predicate()

◆ bdf1_step()

◆ best_eigenvector_candidate()

◆ binomial()

◆ build_interpn_grid()

◆ build_issues()

◆ canonical_output_indices()

◆ casadi_to_int()

◆ catmull_rom_slope()

◆ clamp_query_point()

◆ clenshaw_curtis_order_from_level()

◆ clenshaw_curtis_probability_weights()

◆ clenshaw_curtis_rule()

◆ coefficients_are_constant()

◆ collect_selected_outputs()

◆ compute_dx()

◆ concatenate()

◆ connected_components()

◆ constraint_magnitude()

◆ constraint_violation()

◆ count_symbolic_truthy()

◆ current_assignments()

◆ dense_to_sparse()

◆ determinant_3x3()

◆ dm_to_matrix()

◆ dm_to_scalar()

◆ dm_to_std_vector()

◆ dm_to_vector()

◆ eig_symmetric_symbolic()

◆ erase_value()

◆ escape_dot_label()

◆ escape_for_js()

◆ escape_for_json()

◆ euclidean_distance()

◆ evaluate_mass_matrix()

◆ evaluate_residual_only()

◆ evaluate_state()

◆ find_row_nonzeros()

◆ finite_difference_jacobian()

◆ flat_to_multi_index()

◆ flatten_fortran_order()

◆ flatten_output()

◆ forward_block_jacobian()

◆ function_jacobian_sparsity()

◆ gauss_kronrod_15_rule()

◆ gauss_kronrod_rule()

◆ gauss_legendre_rule()

◆ gauss_order_from_level()

◆ gauss_rule()

◆ generate_multi_indices()

◆ get_op_name()

◆ get_sx_node_style()

◆ get_sx_operation()

◆ has_no_free_symbols()

◆ hermite_interp_1d_numeric()

◆ hermite_interpn_numeric()

◆ hermite_symbolic_error_message()

◆ implicit_function_name()

◆ inf_norm()

◆ input_label()

◆ input_numel()

◆ integrate_backward_simpson()

◆ integrate_cubic()

◆ integrate_forward_simpson()

◆ invoke_with_symbols()

◆ invoke_with_symbols_impl()

◆ is_bounded_support()

◆ is_constant_zero()

◆ is_converged()

◆ is_symbolic_predicate()