Convenience header bringing common Janus symbols into scope. More...

#include "janus.hpp"

Include dependency graph for using.hpp:

Classes
struct	LinearSolvePolicy
	Configuration for linear system solve backend and algorithm. More...
class	PolynomialChaosBasis
	Multidimensional polynomial chaos basis with fixed truncation/order. More...
struct	PolynomialChaosBasisOptions
	Basis construction controls for multidimensional PCE. More...
struct	PolynomialChaosDimension
	One stochastic dimension in a polynomial chaos basis. More...
struct	PolynomialChaosTerm
	One multidimensional chaos basis term. More...
struct	SmolyakQuadratureOptions
	Options for Smolyak sparse-grid construction. More...
struct	StochasticQuadratureGrid
	Multidimensional stochastic quadrature grid with row-major sample layout. More...
struct	StructuralDiagnosticsOptions
	Combined observability and identifiability analysis options. More...
struct	StructuralDiagnosticsReport
	Combined structural diagnostics report. More...
struct	StructuralSensitivityOptions
	Output-selection options shared by the structural diagnostics helpers. More...
struct	StructuralSensitivityReport
	Structural rank analysis of selected outputs with respect to one input block. More...
struct	UnivariateQuadratureRule
	One-dimensional stochastic quadrature rule on a probability measure. More...

Typedefs
using	NumericMatrix
	Eigen::MatrixXd equivalent.
using	NumericScalar
	Numeric scalar type.
using	NumericVector
	Eigen::VectorXd equivalent.
using	SymbolicMatrix
	Eigen matrix of MX elements.
using	SymbolicScalar
	CasADi MX symbolic scalar.
using	SymbolicVector
	Eigen vector of MX elements.

Enumerations
enum class	DenseLinearSolver
	Dense linear solver algorithm. More...
enum class	IterativeKrylovSolver
	Iterative Krylov solver algorithm. More...
enum class	IterativePreconditioner
	Preconditioner for iterative solvers. More...
enum class	LinearSolveBackend
	Backend selection for linear system solves. More...
enum class	PolynomialChaosFamily
	Univariate Askey-scheme family used for a PCE input dimension. More...
enum class	PolynomialChaosTruncation
	Multi-index truncation strategy for a multidimensional basis. More...
enum class	SparseDirectLinearSolver
	Sparse direct solver algorithm. More...
enum class	StochasticQuadratureRule
	One-dimensional rule family used to generate stochastic quadrature nodes. More...

Functions
SymbolicScalar	sym (const std::string &name)
	Create a named symbolic scalar variable.
SymbolicVector	sym_vec (const std::string &name, int size)
	Create a symbolic vector preserving the CasADi primitive connection.
std::pair< SymbolicVector, SymbolicScalar >	sym_vec_pair (const std::string &name, int size)
	Create symbolic vector and return both SymbolicVector and underlying MX.
SymbolicVector	sym_vector (const std::string &name, int size)
	Create a named symbolic vector (returns SymbolicVector).
SymbolicScalar	as_mx (const SymbolicVector &v)
	Get the underlying MX representation of a SymbolicVector.
SymbolicVector	as_vector (const casadi::MX &m)
	Convert CasADi MX vector to SymbolicVector (Eigen container of MX).
Eigen::Matrix< casadi::MX, Eigen::Dynamic, Eigen::Dynamic >	to_eigen (const casadi::MX &m)
	Convert CasADi MX to Eigen matrix of MX.
template<typename Derived>
casadi::MX	to_mx (const Eigen::MatrixBase< Derived > &e)
	Convert Eigen matrix of MX (or numeric) to CasADi MX.
StructuralDiagnosticsReport	analyze_structural_diagnostics (const Function &fn, const StructuralDiagnosticsOptions &opts)
	Run structural observability and identifiability checks together.
StructuralSensitivityReport	analyze_structural_identifiability (const Function &fn, int parameter_input_idx, const StructuralSensitivityOptions &opts={})
	Analyze which parameters are structurally identifiable from selected outputs.
StructuralSensitivityReport	analyze_structural_observability (const Function &fn, int state_input_idx=0, const StructuralSensitivityOptions &opts={})
	Analyze which states are structurally observable from selected outputs.
template<JanusScalar T>
T	abs (const T &x)
	Computes the absolute value of a scalar.
template<JanusScalar T>
T	acos (const T &x)
	Computes arc cosine of x.
template<JanusScalar T>
T	asin (const T &x)
	Computes arc sine of x.
template<JanusScalar T>
T	atan (const T &x)
	Computes arc tangent of x.
template<JanusScalar T>
T	atan2 (const T &y, const T &x)
	Computes arc tangent of y/x using signs of both arguments.
template<JanusScalar T>
T	ceil (const T &x)
	Computes ceiling of x.
template<JanusScalar T>
T	cos (const T &x)
	Computes cosine of x.
template<JanusScalar T>
T	cosh (const T &x)
	Computes hyperbolic cosine of x.
template<JanusScalar T>
T	exp (const T &x)
	Computes the exponential function e^x.
template<JanusScalar T>
T	floor (const T &x)
	Computes floor of x.
template<JanusScalar T>
T	log (const T &x)
	Computes the natural logarithm of x.
template<JanusScalar T>
T	log10 (const T &x)
	Computes the base-10 logarithm of x.
template<JanusScalar T>
T	pow (const T &base, const T &exponent)
	Computes the power function: base^exponent.
template<JanusScalar T>
T	sin (const T &x)
	Computes sine of x.
template<JanusScalar T>
T	sinh (const T &x)
	Computes hyperbolic sine.
template<JanusScalar T>
T	sqrt (const T &x)
	Computes the square root of a scalar.
template<JanusScalar T>
T	tan (const T &x)
	Computes tangent of x.
template<JanusScalar T>
T	tanh (const T &x)
	Computes hyperbolic tangent of x.
template<typename Cond, JanusScalar T1, JanusScalar T2>
auto	where (const Cond &cond, const T1 &if_true, const T2 &if_false)
	Select values based on condition (ternary operator) Returns: cond ? if_true : if_false Supports mixed types.
template<typename DerivedF, typename Spacing = double>
auto	gradient (const Eigen::MatrixBase< DerivedF > &f, const Spacing &dx=1.0, int edge_order=1, int n=1)
	Computes gradient using second-order accurate central differences.
PolynomialChaosDimension	hermite_dimension ()
	Create a standard normal (Hermite) dimension.
SymbolicMatrix	hessian (const SymbolicArg &expr, const SymbolicArg &vars)
	Hessian matrix (second-order derivatives).
SymbolicMatrix	hessian_vector_product (const SymbolicArg &expr, const SymbolicArg &vars, const SymbolicArg &direction)
	Hessian-vector product for a scalar expression without forming the dense Hessian.
PolynomialChaosDimension	jacobi_dimension (double alpha, double beta)
	Create a Beta-family (Jacobi) dimension on [-1, 1].
template<typename Expr, typename... Vars>
auto	jacobian (const Expr &expression, const Vars &...variables)
	Computes Jacobian of an expression with respect to variables.
SymbolicMatrix	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.
PolynomialChaosDimension	laguerre_dimension (double alpha=0.0)
	Create a Gamma-family (Laguerre) dimension on [0, inf).
PolynomialChaosDimension	legendre_dimension ()
	Create a uniform (Legendre) dimension on [-1, 1].
template<JanusScalar Scalar>
Scalar	pce_mean (const JanusVector< Scalar > &coefficients)
	Extract PCE mean (zeroth coefficient).
template<JanusScalar Scalar>
Scalar	pce_polynomial (const PolynomialChaosDimension &dimension, int degree, const Scalar &x, bool normalized=true)
	Evaluate a univariate chaos basis polynomial.
template<JanusScalar Scalar>
JanusVector< Scalar >	pce_projection_coefficients (const PolynomialChaosBasis &basis, const NumericMatrix &samples, const NumericVector &weights, const JanusVector< Scalar > &sample_values)
	Compute PCE projection coefficients from weighted samples (vector).
template<JanusScalar Scalar>
JanusVector< Scalar >	pce_regression_coefficients (const PolynomialChaosBasis &basis, const NumericMatrix &samples, const JanusVector< Scalar > &sample_values, double ridge=1e-12)
	Compute PCE coefficients via least-squares regression (vector).
double	pce_squared_norm (const PolynomialChaosDimension &dimension, int degree, bool normalized=true)
	Return the probability-measure squared norm of a univariate basis term.
template<JanusScalar Scalar>
Scalar	pce_variance (const PolynomialChaosBasis &basis, const JanusVector< Scalar > &coefficients)
	Compute PCE variance from coefficients.
StochasticQuadratureGrid	smolyak_sparse_grid (const std::vector< PolynomialChaosDimension > &dimensions, int level, SmolyakQuadratureOptions options={})
	Build a Smolyak sparse grid on probability measures.
UnivariateQuadratureRule	stochastic_quadrature_level (const PolynomialChaosDimension &dimension, int level, StochasticQuadratureRule rule=StochasticQuadratureRule::AutoNested)
	Build a one-dimensional stochastic quadrature rule from a refinement level.
UnivariateQuadratureRule	stochastic_quadrature_rule (const PolynomialChaosDimension &dimension, int order, StochasticQuadratureRule rule=StochasticQuadratureRule::Gauss)
	Build a one-dimensional stochastic quadrature rule with a fixed order.
StochasticQuadratureGrid	tensor_product_quadrature (const std::vector< UnivariateQuadratureRule > &rules)
	Build the tensor-product grid from a list of one-dimensional rules.
template<typename T>
JanusVector< T >	linspace (const T &start, const T &end, int n)
	Generates linearly spaced vector.

Detailed Description

Convenience header bringing common Janus symbols into scope.

Include this header for cleaner code without explicit janus:: prefixes.

#include <janus/using.hpp>
 
auto x = sym("x");
auto y = sin(x) + pow(x, 2);
auto z = where(x > 0, x, -x);

Warning: This header pollutes the global namespace. Use with care in library code - prefer explicit janus:: prefixes there.

Typedef Documentation

◆ NumericMatrix

using janus::NumericMatrix

Eigen::MatrixXd equivalent.

Examples: Basic.

◆ NumericScalar

using janus::NumericScalar

Numeric scalar type.

◆ NumericVector

using janus::NumericVector

Eigen::VectorXd equivalent.

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp, /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp, 1D, Basic, and N-D.

◆ SymbolicMatrix

using janus::SymbolicMatrix

Eigen matrix of MX elements.

◆ SymbolicScalar

using janus::SymbolicScalar

CasADi MX symbolic scalar.

Examples: /home/runner/work/janus/janus/include/janus/core/Sparsity.hpp, and /home/runner/work/janus/janus/include/janus/math/Interpolate.hpp.

◆ SymbolicVector

using janus::SymbolicVector

Eigen vector of MX elements.

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

Enumeration Type Documentation

◆ DenseLinearSolver

enum class janus::DenseLinearSolver

strong

Dense linear solver algorithm.

◆ IterativeKrylovSolver

enum class janus::IterativeKrylovSolver

strong

Iterative Krylov solver algorithm.

◆ IterativePreconditioner

enum class janus::IterativePreconditioner

strong

Preconditioner for iterative solvers.

◆ LinearSolveBackend

enum class janus::LinearSolveBackend

strong

Backend selection for linear system solves.

◆ PolynomialChaosFamily

enum class janus::PolynomialChaosFamily

strong

Univariate Askey-scheme family used for a PCE input dimension.

◆ PolynomialChaosTruncation

enum class janus::PolynomialChaosTruncation

strong

Multi-index truncation strategy for a multidimensional basis.

◆ SparseDirectLinearSolver

enum class janus::SparseDirectLinearSolver

strong

Sparse direct solver algorithm.

◆ StochasticQuadratureRule

enum class janus::StochasticQuadratureRule

strong

One-dimensional rule family used to generate stochastic quadrature nodes.

Function Documentation

◆ abs()

template<JanusScalar T>

T janus::abs ( const T & x )

Computes the absolute value of a scalar.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Absolute value of x

◆ acos()

template<JanusScalar T>

T janus::acos ( const T & x )

Computes arc cosine of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Arc cosine of x (radians)

◆ analyze_structural_diagnostics()

StructuralDiagnosticsReport janus::analyze_structural_diagnostics	(	const Function &	fn,
		const StructuralDiagnosticsOptions &	opts )

inline

Run structural observability and identifiability checks together.

Parameters

fn	Function to analyze
opts	Combined analysis options (at least one input index must be non-negative)

Returns: Combined diagnostics report

See also: analyze_structural_observability, analyze_structural_identifiability

◆ analyze_structural_identifiability()

StructuralSensitivityReport janus::analyze_structural_identifiability	(	const Function &	fn,
		int	parameter_input_idx,
		const StructuralSensitivityOptions &	opts = {} )

inline

Analyze which parameters are structurally identifiable from selected outputs.

Parameters

fn	Function whose Jacobian sparsity is analyzed
parameter_input_idx	Index of the parameter input block
opts	Output selection options

Returns: Structural sensitivity report

See also: analyze_structural_observability

◆ analyze_structural_observability()

StructuralSensitivityReport janus::analyze_structural_observability	(	const Function &	fn,
		int	state_input_idx = 0,
		const StructuralSensitivityOptions &	opts = {} )

inline

Analyze which states are structurally observable from selected outputs.

Parameters

fn	Function whose Jacobian sparsity is analyzed
state_input_idx	Index of the state input block
opts	Output selection options

Returns: Structural sensitivity report

See also: analyze_structural_identifiability, analyze_structural_diagnostics

◆ as_mx()

SymbolicScalar janus::as_mx ( const SymbolicVector & v )

inline

Get the underlying MX representation of a SymbolicVector.

This packs an Eigen container of MX elements back into a single CasADi MX for use with janus::Function or janus::jacobian.

Parameters

v	SymbolicVector to convert

Returns: Single casadi::MX representing the vector

◆ as_vector()

SymbolicVector janus::as_vector ( const casadi::MX & m )

inline

Convert CasADi MX vector to SymbolicVector (Eigen container of MX).

Parameters

m	Input CasADi MX (column vector)

Returns: SymbolicVector (Eigen::Matrix<casadi::MX, Dynamic, 1>)

◆ asin()

template<JanusScalar T>

T janus::asin ( const T & x )

Computes arc sine of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Arc sine of x (radians)

◆ atan()

template<JanusScalar T>

T janus::atan ( const T & x )

Computes arc tangent of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Arc tangent of x (radians)

◆ atan2()

template<JanusScalar T>

T janus::atan2	(	const T &	y,
		const T &	x )

Computes arc tangent of y/x using signs of both arguments.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

y	Numerator
x	Denominator

Returns: Arc tangent of y/x (radians, included in [-pi, pi])

◆ ceil()

template<JanusScalar T>

T janus::ceil ( const T & x )

Computes ceiling of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Ceiling of x

◆ cos()

template<JanusScalar T>

T janus::cos ( const T & x )

Computes cosine of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value (radians)

Returns: Cosine of x

◆ cosh()

template<JanusScalar T>

T janus::cosh ( const T & x )

Computes hyperbolic cosine of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Hyperbolic cosine of x

◆ exp()

template<JanusScalar T>

T janus::exp ( const T & x )

Computes the exponential function e^x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: e raised to the power of x

◆ floor()

template<JanusScalar T>

T janus::floor ( const T & x )

Computes floor of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Floor of x

◆ gradient()

template<typename DerivedF, typename Spacing = double>

auto janus::gradient	(	const Eigen::MatrixBase< DerivedF > &	f,
		const Spacing &	dx = 1.0,
		int	edge_order = 1,
		int	n = 1 )

Computes gradient using second-order accurate central differences.

Returns the gradient of a 1D array using second-order accurate central differences in the interior and first or second-order accurate one-sided differences at boundaries.

Template Parameters

Derived Eigen vector type

Parameters

f	Function values (vector)
dx	Spacing (scalar or vector). If scalar, uniform spacing is assumed.
edge_order	Order of accuracy at boundaries (1 or 2)
n	Derivative order (1 for first derivative, 2 for second derivative)

Returns: Gradient vector (same size as f)

◆ hermite_dimension()

PolynomialChaosDimension janus::hermite_dimension ( )

inline

Create a standard normal (Hermite) dimension.

Returns: Hermite dimension descriptor

◆ hessian()

SymbolicMatrix janus::hessian	(	const SymbolicArg &	expr,
		const SymbolicArg &	vars )

inline

Hessian matrix (second-order derivatives).

Computes the matrix of second derivatives: H_ij = d²f / (dx_i dx_j)

Parameters

expr	Scalar expression
vars	Variables

Returns: Symmetric Hessian matrix (SymbolicMatrix)

◆ hessian_vector_product()

SymbolicMatrix janus::hessian_vector_product	(	const SymbolicArg &	expr,
		const SymbolicArg &	vars,
		const SymbolicArg &	direction )

inline

Hessian-vector product for a scalar expression without forming the dense Hessian.

This uses CasADi's directional derivative of the reverse-mode gradient, i.e. forward-over-reverse AD.

Parameters

expr	Scalar expression f(x)
vars	Differentiation variables x
direction	Direction vector/matrix v with the same shape as x

Returns: Matrix/vector with the same shape as x containing ∇²f(x) v

◆ jacobi_dimension()

PolynomialChaosDimension janus::jacobi_dimension	(	double	alpha,
		double	beta )

inline

Create a Beta-family (Jacobi) dimension on [-1, 1].

Parameters

alpha	Jacobi alpha parameter (> -1)
beta	Jacobi beta parameter (> -1)

Returns: Jacobi dimension descriptor

◆ jacobian()

template<typename Expr, typename... Vars>

auto janus::jacobian	(	const Expr &	expression,
		const Vars &...	variables )

Computes Jacobian of an expression with respect to variables.

Wraps CasADi's jacobian function. Automatic Jacobian only supported for Symbolic types currently.

Template Parameters

Expr	Expression type (must be convertible to MX)
Vars	Variable types (must be convertible to MX)

Parameters

expression	Expression to differentiate
variables	Variables to differentiate with respect to

Returns: Jacobian matrix (symbolic)

◆ lagrangian_hessian_vector_product()

SymbolicMatrix janus::lagrangian_hessian_vector_product	(	const SymbolicArg &	objective,
		const SymbolicArg &	constraints,
		const SymbolicArg &	vars,
		const SymbolicArg &	multipliers,
		const SymbolicArg &	direction )

inline

Hessian-vector product of a Lagrangian, i.e. a second-order adjoint action.

Computes ∇²L(x, λ) v for L(x, λ) = f(x) + λᵀ g(x) without forming the dense Hessian.

Parameters

objective	Objective function f(x) (scalar)
constraints	Constraint function g(x)
vars	Decision variables x
multipliers	Lagrange multipliers λ (same number of entries as g)
direction	Direction vector/matrix v with the same shape as x

Returns: Matrix/vector with the same shape as x containing ∇²L(x, λ) v

◆ laguerre_dimension()

PolynomialChaosDimension janus::laguerre_dimension ( double alpha = 0.0 )

inline

Create a Gamma-family (Laguerre) dimension on [0, inf).

Parameters

alpha Laguerre alpha parameter (> -1)

Returns: Laguerre dimension descriptor

◆ legendre_dimension()

PolynomialChaosDimension janus::legendre_dimension ( )

inline

Create a uniform (Legendre) dimension on [-1, 1].

Returns: Legendre dimension descriptor

◆ linspace()

template<typename T>

JanusVector< T > janus::linspace	(	const T &	start,
		const T &	end,
		int	n )

Generates linearly spaced vector.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

start	Start value
end	End value
n	Number of points

Returns: Vector of n linearly spaced points

◆ log()

template<JanusScalar T>

T janus::log ( const T & x )

Computes the natural logarithm of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Natural logarithm of x

◆ log10()

template<JanusScalar T>

T janus::log10 ( const T & x )

Computes the base-10 logarithm of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Base-10 logarithm of x

◆ pce_mean()

template<JanusScalar Scalar>

Scalar janus::pce_mean ( const JanusVector< Scalar > & coefficients )

Extract PCE mean (zeroth coefficient).

Template Parameters

Scalar Scalar type (NumericScalar or SymbolicScalar)

Parameters

coefficients PCE coefficient vector

Returns: Mean value

◆ pce_polynomial()

template<JanusScalar Scalar>

Scalar janus::pce_polynomial	(	const PolynomialChaosDimension &	dimension,
		int	degree,
		const Scalar &	x,
		bool	normalized = true )

Evaluate a univariate chaos basis polynomial.

The input x is assumed to already be expressed on the natural support of the chosen family:

Hermite: standard normal variable
Legendre/Jacobi: support [-1, 1]
Laguerre: support [0, inf)

◆ pce_projection_coefficients()

template<JanusScalar Scalar>

JanusVector< Scalar > janus::pce_projection_coefficients	(	const PolynomialChaosBasis &	basis,
		const NumericMatrix &	samples,
		const NumericVector &	weights,
		const JanusVector< Scalar > &	sample_values )

Compute PCE projection coefficients from weighted samples (vector).

Template Parameters

Scalar Scalar type (NumericScalar or SymbolicScalar)

Parameters

basis	Polynomial chaos basis
samples	Sample matrix (rows = samples, cols = dimensions)
weights	Quadrature weights
sample_values	Function values at sample points

Returns: PCE coefficient vector

◆ pce_regression_coefficients()

template<JanusScalar Scalar>

JanusVector< Scalar > janus::pce_regression_coefficients	(	const PolynomialChaosBasis &	basis,
		const NumericMatrix &	samples,
		const JanusVector< Scalar > &	sample_values,
		double	ridge = 1e-12 )

Compute PCE coefficients via least-squares regression (vector).

Template Parameters

Scalar Scalar type (NumericScalar or SymbolicScalar)

Parameters

basis	Polynomial chaos basis
samples	Sample matrix
sample_values	Function values at sample points
ridge	Ridge regularization parameter

Returns: PCE coefficient vector

◆ pce_squared_norm()

double janus::pce_squared_norm	(	const PolynomialChaosDimension &	dimension,
		int	degree,
		bool	normalized = true )

inline

Return the probability-measure squared norm of a univariate basis term.

◆ pce_variance()

template<JanusScalar Scalar>

Scalar janus::pce_variance	(	const PolynomialChaosBasis &	basis,
		const JanusVector< Scalar > &	coefficients )

Compute PCE variance from coefficients.

Template Parameters

Scalar Scalar type (NumericScalar or SymbolicScalar)

Parameters

basis	Polynomial chaos basis
coefficients	PCE coefficient vector

Returns: Variance

◆ pow()

template<JanusScalar T>

T janus::pow	(	const T &	base,
		const T &	exponent )

Computes the power function: base^exponent.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

base	Base value
exponent	Exponent value

Returns: base raised to the power of exponent

◆ sin()

template<JanusScalar T>

T janus::sin ( const T & x )

Computes sine of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value (radians)

Returns: Sine of x

◆ sinh()

template<JanusScalar T>

T janus::sinh ( const T & x )

Computes hyperbolic sine.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Hyperbolic sine of x

◆ smolyak_sparse_grid()

StochasticQuadratureGrid janus::smolyak_sparse_grid	(	const std::vector< PolynomialChaosDimension > &	dimensions,
		int	level,
		SmolyakQuadratureOptions	options = {} )

inline

Build a Smolyak sparse grid on probability measures.

The level follows the standard convention with one-dimensional indices i_j >= 1 and total-index band level <= |i| <= level + d - 1.

Parameters

dimensions	Stochastic dimension descriptors
level	Sparse grid level (>= 1)
options	Smolyak construction options

Returns: Sparse quadrature grid

◆ sqrt()

template<JanusScalar T>

T janus::sqrt ( const T & x )

Computes the square root of a scalar.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Square root of x

◆ stochastic_quadrature_level()

UnivariateQuadratureRule janus::stochastic_quadrature_level	(	const PolynomialChaosDimension &	dimension,
		int	level,
		StochasticQuadratureRule	rule = StochasticQuadratureRule::AutoNested )

inline

Build a one-dimensional stochastic quadrature rule from a refinement level.

Parameters

dimension	Stochastic dimension descriptor
level	Refinement level (>= 1)
rule	Quadrature rule family

Returns: Univariate quadrature rule

◆ stochastic_quadrature_rule()

UnivariateQuadratureRule janus::stochastic_quadrature_rule	(	const PolynomialChaosDimension &	dimension,
		int	order,
		StochasticQuadratureRule	rule = StochasticQuadratureRule::Gauss )

inline

Build a one-dimensional stochastic quadrature rule with a fixed order.

Parameters

dimension	Stochastic dimension descriptor
order	Number of quadrature points
rule	Quadrature rule family

Returns: Univariate quadrature rule

◆ sym()

SymbolicScalar janus::sym ( const std::string & name )

inline

Create a named symbolic scalar variable.

Parameters

name	Name of the variable

Returns: SymbolicScalar (casadi::MX)

◆ sym_vec()

SymbolicVector janus::sym_vec	(	const std::string &	name,
		int	size )

inline

Create a symbolic vector preserving the CasADi primitive connection.

auto state = janus::sym_vec("state", 3);

auto jac = janus::jacobian({janus::to_mx(dydt)}, {janus::to_mx(state)});

janus::sym_vec

SymbolicVector sym_vec(const std::string &name, int size)

Create a symbolic vector preserving the CasADi primitive connection.

Definition JanusTypes.hpp:137

janus::to_mx

casadi::MX to_mx(const Eigen::MatrixBase< Derived > &e)

Convert Eigen matrix of MX (or numeric) to CasADi MX.

Definition JanusTypes.hpp:189

janus::jacobian

auto jacobian(const Expr &expression, const Vars &...variables)

Computes Jacobian of an expression with respect to variables.

Definition AutoDiff.hpp:109

Parameters

name	Name of the variable
size	Number of elements

Returns: SymbolicVector with MX elements from single underlying vector

See also: sym_vector, sym_vec_pair

◆ sym_vec_pair()

std::pair< SymbolicVector, SymbolicScalar > janus::sym_vec_pair	(	const std::string &	name,
		int	size )

inline

Create symbolic vector and return both SymbolicVector and underlying MX.

auto [state_vec, state_mx] = janus::sym_vec_pair("state", 3);

auto jac = janus::jacobian({janus::to_mx(dydt)}, {state_mx, theta});

janus::sym_vec_pair

std::pair< SymbolicVector, SymbolicScalar > sym_vec_pair(const std::string &name, int size)

Create symbolic vector and return both SymbolicVector and underlying MX.

Definition JanusTypes.hpp:155

Parameters

name	Name of the variable
size	Number of elements

Returns: Pair of (SymbolicVector, underlying MX)

See also: sym_vec

◆ sym_vector()

SymbolicVector janus::sym_vector	(	const std::string &	name,
		int	size )

inline

Create a named symbolic vector (returns SymbolicVector).

auto x = janus::sym_vector("x", 3); // Returns SymbolicVector

janus::sym_vector

SymbolicVector sym_vector(const std::string &name, int size)

Create a named symbolic vector (returns SymbolicVector).

Definition JanusTypes.hpp:115

Parameters

name	Name of the variable
size	Number of elements

Returns: SymbolicVector with MX elements

See also: sym_vec, sym_vec_pair

◆ tan()

template<JanusScalar T>

T janus::tan ( const T & x )

Computes tangent of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value (radians)

Returns: Tangent of x

◆ tanh()

template<JanusScalar T>

T janus::tanh ( const T & x )

Computes hyperbolic tangent of x.

Template Parameters

T	Scalar type (NumericScalar or SymbolicScalar)

Parameters

x	Input value

Returns: Hyperbolic tangent of x

◆ tensor_product_quadrature()

StochasticQuadratureGrid janus::tensor_product_quadrature ( const std::vector< UnivariateQuadratureRule > & rules )

inline

Build the tensor-product grid from a list of one-dimensional rules.

Parameters

rules Vector of univariate quadrature rules

Returns: Tensor-product grid

◆ to_eigen()

Eigen::Matrix< casadi::MX, Eigen::Dynamic, Eigen::Dynamic > janus::to_eigen ( const casadi::MX & m )

inline

Convert CasADi MX to Eigen matrix of MX.

Parameters

m	Input CasADi MX

Returns: Eigen matrix (dynamic size)

◆ to_mx()

template<typename Derived>

casadi::MX janus::to_mx ( const Eigen::MatrixBase< Derived > & e )

Convert Eigen matrix of MX (or numeric) to CasADi MX.

Template Parameters

Derived Eigen matrix type

Parameters

e	Input Eigen matrix

Returns: CasADi MX (dense)

◆ where()

template<typename Cond, JanusScalar T1, JanusScalar T2>

auto janus::where	(	const Cond &	cond,
		const T1 &	if_true,
		const T2 &	if_false )

Select values based on condition (ternary operator) Returns: cond ? if_true : if_false Supports mixed types.

Parameters

cond	Condition
if_true	Value if true
if_false	Value if false

Returns: Selected value

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

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ NumericMatrix

◆ NumericScalar

◆ NumericVector

◆ SymbolicMatrix

◆ SymbolicScalar

◆ SymbolicVector

Enumeration Type Documentation

◆ DenseLinearSolver

◆ IterativeKrylovSolver

◆ IterativePreconditioner

◆ LinearSolveBackend

◆ PolynomialChaosFamily

◆ PolynomialChaosTruncation

◆ SparseDirectLinearSolver

◆ StochasticQuadratureRule

Function Documentation

◆ abs()

◆ acos()

◆ analyze_structural_diagnostics()

◆ analyze_structural_identifiability()

◆ analyze_structural_observability()

◆ as_mx()

◆ as_vector()

◆ asin()

◆ atan()

◆ atan2()

◆ ceil()

◆ cos()

◆ cosh()

◆ exp()

◆ floor()

◆ gradient()

◆ hermite_dimension()

◆ hessian()

◆ hessian_vector_product()

◆ jacobi_dimension()

◆ jacobian()

◆ lagrangian_hessian_vector_product()

◆ laguerre_dimension()

◆ legendre_dimension()

◆ linspace()

◆ log()

◆ log10()

◆ pce_mean()

◆ pce_polynomial()

◆ pce_projection_coefficients()

◆ pce_regression_coefficients()

◆ pce_squared_norm()

◆ pce_variance()

◆ pow()

◆ sin()

◆ sinh()

◆ smolyak_sparse_grid()

◆ sqrt()

◆ stochastic_quadrature_level()

◆ stochastic_quadrature_rule()

◆ sym()

◆ sym_vec()

◆ sym_vec_pair()

◆ sym_vector()

◆ tan()

◆ tanh()

◆ tensor_product_quadrature()

◆ to_eigen()

◆ to_mx()

◆ where()