Classes
class	AABox2d
	Implements a class of (undirected) axes-aligned bounding boxes in 2-D. This class is referential-agnostic. More...

class	AABoxKDTree2d
	The class of KD-tree of Aligned Axis Bounding Box(AABox). More...

class	AABoxKDTree2dNode
	The class of KD-tree node of axis-aligned bounding box. More...

class	AABoxKDTreeParams
	Contains parameters of axis-aligned bounding box. More...

class	Angle
	The Angle class uses an integer to represent an angle, and supports commonly-used operations such as addition and subtraction, as well as the use of trigonometric functions. More...

class	Box2d
	Rectangular (undirected) bounding box in 2-D. More...

class	CartesianFrenetConverter

class	EulerAnglesZXY
	Implements a class of Euler angles (actually, Tait-Bryan angles), with intrinsic sequence ZXY. More...

struct	Factorial

struct	Factorial< 0 >

class	HermiteSpline

class	KalmanFilter
	Implements a discrete-time Kalman filter. More...

class	LineSegment2d
	Line segment in 2-D. More...

class	MpcOsqp

class	PathMatcher

class	Polygon2d
	The class of polygon in 2-D. More...

class	QpSolver

class	Vec2d
	Implements a class of 2-dimensional vectors. More...

Typedefs
using	Angle8 = Angle< int8_t >

using	Angle16 = Angle< int16_t >

using	Angle32 = Angle< int32_t >

using	Angle64 = Angle< int64_t >

using	EulerAnglesZXYf = EulerAnglesZXY< float >

using	EulerAnglesZXYd = EulerAnglesZXY< double >

Functions
template<typename T >
Angle< T >	operator+ (Angle< T > lhs, Angle< T > rhs)
	Sums two angles. More...

template<typename T >
Angle< T >	operator- (Angle< T > lhs, Angle< T > rhs)
	Subtracts two angles. More...

template<typename T , typename Scalar >
Angle< T >	operator* (Angle< T > lhs, Scalar rhs)
	Multiplies an Angle by a scalar. More...

template<typename T , typename Scalar >
Angle< T >	operator* (Scalar lhs, Angle< T > rhs)
	Multiplies an Angle by a scalar. More...

template<typename T , typename Scalar >
Angle< T >	operator/ (Angle< T > lhs, Scalar rhs)
	Divides an Angle by a scalar. More...

template<typename T >
double	operator/ (Angle< T > lhs, Angle< T > rhs)
	Divides an Angle by a scalar. More...

template<typename T >
bool	operator== (Angle< T > lhs, Angle< T > rhs)
	Tests two Angle objects for equality. More...

template<typename T >
bool	operator!= (Angle< T > lhs, Angle< T > rhs)
	Tests two Angle objects for inequality. More...

float	sin (Angle16 a)

float	cos (Angle16 a)

float	tan (Angle16 a)

float	sin (Angle8 a)

float	cos (Angle8 a)

float	tan (Angle8 a)

template<std::size_t N>
double	EvaluatePolynomial (const std::array< double, N+1 > &coef, const double p)

template<std::size_t N, std::size_t M>
std::array< double, N+1 >	FitPolynomial (const std::array< Eigen::Vector2d, M > &points, double *ptr_error_square=nullptr)

double	IntegrateBySimpson (const std::vector< double > &funv_vec, const double dx, const std::size_t nsteps)

double	IntegrateByTrapezoidal (const std::vector< double > &funv_vec, const double dx, const std::size_t nsteps)

template<std::size_t N>
std::pair< std::array< double, N >, std::array< double, N > >	GetGaussLegendrePoints ()
	Get the points and weights for different ordered Gauss-Legendre integration. Currently support order 2 - 10. Other input order will trigger compiling error. More...

template<>
std::pair< std::array< double, 2 >, std::array< double, 2 > >	GetGaussLegendrePoints< 2 > ()

template<>
std::pair< std::array< double, 3 >, std::array< double, 3 > >	GetGaussLegendrePoints< 3 > ()

template<>
std::pair< std::array< double, 4 >, std::array< double, 4 > >	GetGaussLegendrePoints< 4 > ()

template<>
std::pair< std::array< double, 5 >, std::array< double, 5 > >	GetGaussLegendrePoints< 5 > ()

template<>
std::pair< std::array< double, 6 >, std::array< double, 6 > >	GetGaussLegendrePoints< 6 > ()

template<>
std::pair< std::array< double, 7 >, std::array< double, 7 > >	GetGaussLegendrePoints< 7 > ()

template<>
std::pair< std::array< double, 8 >, std::array< double, 8 > >	GetGaussLegendrePoints< 8 > ()

template<>
std::pair< std::array< double, 9 >, std::array< double, 9 > >	GetGaussLegendrePoints< 9 > ()

template<>
std::pair< std::array< double, 10 >, std::array< double, 10 > >	GetGaussLegendrePoints< 10 > ()

template<std::size_t N>
double	IntegrateByGaussLegendre (const std::function< double(double)> &func, const double lower_bound, const double upper_bound)
	Compute the integral of a target single-variable function from a lower bound to an upper bound, by 5-th Gauss-Legendre method Given a target function and integral lower and upper bound, compute the integral approximation using 5th order Gauss-Legendre integration. The target function must be a smooth function. Example: target function: auto func = [](const double x) {return x * x;}; double integral = gauss_legendre(func, -2, 3); This gives you the approximated integral of function x^2 in bound [-2, 3]. More...

template<typename T >
T	lerp (const T &x0, const double t0, const T &x1, const double t1, const double t)
	Linear interpolation between two points of type T. More...

double	slerp (const double a0, const double t0, const double a1, const double t1, const double t)
	Spherical linear interpolation between two angles. The two angles are within range [-M_PI, M_PI). More...

SLPoint	InterpolateUsingLinearApproximation (const SLPoint &p0, const SLPoint &p1, const double w)

PathPoint	InterpolateUsingLinearApproximation (const PathPoint &p0, const PathPoint &p1, const double s)

TrajectoryPoint	InterpolateUsingLinearApproximation (const TrajectoryPoint &tp0, const TrajectoryPoint &tp1, const double t)

void	SolveLQRProblem (const Eigen::MatrixXd &A, const Eigen::MatrixXd &B, const Eigen::MatrixXd &Q, const Eigen::MatrixXd &R, const Eigen::MatrixXd &M, const double tolerance, const uint max_num_iteration, Eigen::MatrixXd *ptr_K)
	Solver for discrete-time linear quadratic problem. More...

void	SolveLQRProblem (const Eigen::MatrixXd &A, const Eigen::MatrixXd &B, const Eigen::MatrixXd &Q, const Eigen::MatrixXd &R, const double tolerance, const uint max_num_iteration, Eigen::MatrixXd *ptr_K)
	Solver for discrete-time linear quadratic problem. More...

double	Sqr (const double x)

double	CrossProd (const Vec2d &start_point, const Vec2d &end_point_1, const Vec2d &end_point_2)
	Cross product between two 2-D vectors from the common start point, and end at two other points. More...

double	InnerProd (const Vec2d &start_point, const Vec2d &end_point_1, const Vec2d &end_point_2)
	Inner product between two 2-D vectors from the common start point, and end at two other points. More...

double	CrossProd (const double x0, const double y0, const double x1, const double y1)
	Cross product between two vectors. One vector is formed by 1st and 2nd parameters of the function. The other vector is formed by 3rd and 4th parameters of the function. More...

double	InnerProd (const double x0, const double y0, const double x1, const double y1)
	Inner product between two vectors. One vector is formed by 1st and 2nd parameters of the function. The other vector is formed by 3rd and 4th parameters of the function. More...

double	WrapAngle (const double angle)
	Wrap angle to [0, 2 * PI). More...

double	NormalizeAngle (const double angle)
	Normalize angle to [-PI, PI). More...

double	AngleDiff (const double from, const double to)
	Calculate the difference between angle from and to. More...

int	RandomInt (const int s, const int t, unsigned int rand_seed=1)
	Get a random integer between two integer values by a random seed. More...

double	RandomDouble (const double s, const double t, unsigned int rand_seed=1)
	Get a random double between two integer values by a random seed. More...

template<typename T >
T	Square (const T value)
	Compute squared value. More...

template<typename T >
T	Clamp (const T value, T bound1, T bound2)
	Clamp a value between two bounds. If the value goes beyond the bounds, return one of the bounds, otherwise, return the original value. More...

double	Gaussian (const double u, const double std, const double x)

double	Sigmoid (const double x)

Eigen::Vector2d	RotateVector2d (const Eigen::Vector2d &v_in, const double theta)

std::pair< double, double >	RFUToFLU (const double x, const double y)

std::pair< double, double >	FLUToRFU (const double x, const double y)

void	L2Norm (int feat_dim, float *feat_data)

std::pair< double, double >	Cartesian2Polar (double x, double y)

template<class T >
std::enable_if<!std::numeric_limits< T >::is_integer, bool >::type	almost_equal (T x, T y, int ulp)

template<typename T , unsigned int N>
Eigen::Matrix< T, N, N >	PseudoInverse (const Eigen::Matrix< T, N, N > &m, const double epsilon=1.0e-6)
	Computes the Moore-Penrose pseudo-inverse of a given square matrix, rounding all eigenvalues with absolute value bounded by epsilon to zero. More...

template<typename T , unsigned int M, unsigned int N>
Eigen::Matrix< T, N, M >	PseudoInverse (const Eigen::Matrix< T, M, N > &m, const double epsilon=1.0e-6)
	Computes the Moore-Penrose pseudo-inverse of a given matrix, rounding all eigenvalues with absolute value bounded by epsilon to zero. More...

template<typename T , unsigned int L, unsigned int N, unsigned int O>
bool	ContinuousToDiscrete (const Eigen::Matrix< T, L, L > &m_a, const Eigen::Matrix< T, L, N > &m_b, const Eigen::Matrix< T, O, L > &m_c, const Eigen::Matrix< T, O, N > &m_d, const double ts, Eigen::Matrix< T, L, L > ptr_a_d, Eigen::Matrix< T, L, N > ptr_b_d, Eigen::Matrix< T, O, L > ptr_c_d, Eigen::Matrix< T, O, N > ptr_d_d)
	Computes bilinear transformation of the continuous to discrete form for state space representation This assumes equation format of. More...

bool	ContinuousToDiscrete (const Eigen::MatrixXd &m_a, const Eigen::MatrixXd &m_b, const Eigen::MatrixXd &m_c, const Eigen::MatrixXd &m_d, const double ts, Eigen::MatrixXd ptr_a_d, Eigen::MatrixXd ptr_b_d, Eigen::MatrixXd ptr_c_d, Eigen::MatrixXd ptr_d_d)

template<typename T , int M, int N, typename D >
void	DenseToCSCMatrix (const Eigen::Matrix< T, M, N > &dense_matrix, std::vector< T > data, std::vector< D > indices, std::vector< D > *indptr)

double	QuaternionToHeading (const double qw, const double qx, const double qy, const double qz)

template<typename T >
T	QuaternionToHeading (const Eigen::Quaternion< T > &q)

template<typename T >
Eigen::Quaternion< T >	HeadingToQuaternion (T heading)

Eigen::Vector3d	QuaternionRotate (const Quaternion &orientation, const Eigen::Vector3d &original)

Eigen::Vector3d	InverseQuaternionRotate (const Quaternion &orientation, const Eigen::Vector3d &rotated)

double	GoldenSectionSearch (const std::function< double(double)> &func, const double lower_bound, const double upper_bound, const double tol=1e-6)
	Given a unimodal function defined on the interval, find a value on the interval to minimize the function. Reference: https://en.wikipedia.org/wiki/Golden-section_search. More...

Vec2d	operator* (const double ratio, const Vec2d &vec)
	Multiplies the given Vec2d by a given scalar. More...

Variables
const float	SIN_TABLE [SIN_TABLE_SIZE]

constexpr double	kMathEpsilon = 1e-10

Detailed Description

apollo::common::math

The math namespace deals with a number of useful mathematical objects.

Typedef Documentation

◆ Angle16

using apollo::common::math::Angle16 = typedef Angle<int16_t>

◆ Angle32

using apollo::common::math::Angle32 = typedef Angle<int32_t>

◆ Angle64

using apollo::common::math::Angle64 = typedef Angle<int64_t>

◆ Angle8

using apollo::common::math::Angle8 = typedef Angle<int8_t>

◆ EulerAnglesZXYd

using apollo::common::math::EulerAnglesZXYd = typedef EulerAnglesZXY<double>

◆ EulerAnglesZXYf

using apollo::common::math::EulerAnglesZXYf = typedef EulerAnglesZXY<float>

Function Documentation

◆ almost_equal()

template<class T >

std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type apollo::common::math::almost_equal	(	T	x,
		T	y,
		int	ulp
	)

◆ AngleDiff()

double apollo::common::math::AngleDiff	(	const double	from,
		const double	to
	)

Calculate the difference between angle from and to.

Parameters

from	the start angle
from	the end angle

Returns: The difference between from and to. The range is between [-PI, PI).

◆ Cartesian2Polar()

std::pair<double, double> apollo::common::math::Cartesian2Polar	(	double	x,
		double	y
	)

◆ Clamp()

template<typename T >

T apollo::common::math::Clamp	(	const T	value,
		T	bound1,
		T	bound2
	)

Clamp a value between two bounds. If the value goes beyond the bounds, return one of the bounds, otherwise, return the original value.

Parameters

value	The original value to be clamped.
bound1	One bound to clamp the value.
bound2	The other bound to clamp the value.

Returns: The clamped value.

◆ ContinuousToDiscrete() [1/2]

template<typename T , unsigned int L, unsigned int N, unsigned int O>

bool apollo::common::math::ContinuousToDiscrete	(	const Eigen::Matrix< T, L, L > &	m_a,
		const Eigen::Matrix< T, L, N > &	m_b,
		const Eigen::Matrix< T, O, L > &	m_c,
		const Eigen::Matrix< T, O, N > &	m_d,
		const double	ts,
		Eigen::Matrix< T, L, L > *	ptr_a_d,
		Eigen::Matrix< T, L, N > *	ptr_b_d,
		Eigen::Matrix< T, O, L > *	ptr_c_d,
		Eigen::Matrix< T, O, N > *	ptr_d_d
	)

Computes bilinear transformation of the continuous to discrete form for state space representation This assumes equation format of.

dot_x = Ax + Bu y = Cx + Du

Parameters

m_a,m_b,m_c,m_d are the state space matrix control matrix

Returns: true or false.

◆ ContinuousToDiscrete() [2/2]

bool apollo::common::math::ContinuousToDiscrete	(	const Eigen::MatrixXd &	m_a,
		const Eigen::MatrixXd &	m_b,
		const Eigen::MatrixXd &	m_c,
		const Eigen::MatrixXd &	m_d,
		const double	ts,
		Eigen::MatrixXd *	ptr_a_d,
		Eigen::MatrixXd *	ptr_b_d,
		Eigen::MatrixXd *	ptr_c_d,
		Eigen::MatrixXd *	ptr_d_d
	)

◆ cos() [1/2]

float apollo::common::math::cos ( Angle16 a )

◆ cos() [2/2]

float apollo::common::math::cos ( Angle8 a )

◆ CrossProd() [1/2]

double apollo::common::math::CrossProd	(	const Vec2d &	start_point,
		const Vec2d &	end_point_1,
		const Vec2d &	end_point_2
	)

Cross product between two 2-D vectors from the common start point, and end at two other points.

Parameters

start_point	The common start point of two vectors in 2-D.
end_point_1	The end point of the first vector.
end_point_2	The end point of the second vector.

Returns: The cross product result.

◆ CrossProd() [2/2]

double apollo::common::math::CrossProd	(	const double	x0,
		const double	y0,
		const double	x1,
		const double	y1
	)

Cross product between two vectors. One vector is formed by 1st and 2nd parameters of the function. The other vector is formed by 3rd and 4th parameters of the function.

Parameters

x0	The x coordinate of the first vector.
y0	The y coordinate of the first vector.
x1	The x coordinate of the second vector.
y1	The y coordinate of the second vector.

Returns: The cross product result.

◆ DenseToCSCMatrix()

template<typename T , int M, int N, typename D >

void apollo::common::math::DenseToCSCMatrix	(	const Eigen::Matrix< T, M, N > &	dense_matrix,
		std::vector< T > *	data,
		std::vector< D > *	indices,
		std::vector< D > *	indptr
	)

◆ EvaluatePolynomial()

template<std::size_t N>

double apollo::common::math::EvaluatePolynomial	(	const std::array< double, N+1 > &	coef,
		const double	p
	)

◆ FitPolynomial()

template<std::size_t N, std::size_t M>

std::array<double, N + 1> apollo::common::math::FitPolynomial	(	const std::array< Eigen::Vector2d, M > &	points,
		double *	ptr_error_square = `nullptr`
	)

◆ FLUToRFU()

std::pair<double, double> apollo::common::math::FLUToRFU	(	const double	x,
		const double	y
	)

inline

◆ Gaussian()

double apollo::common::math::Gaussian	(	const double	u,
		const double	std,
		const double	x
	)

◆ GetGaussLegendrePoints()

template<std::size_t N>

std::pair<std::array<double, N>, std::array<double, N> > apollo::common::math::GetGaussLegendrePoints ( )

Get the points and weights for different ordered Gauss-Legendre integration. Currently support order 2 - 10. Other input order will trigger compiling error.

◆ GetGaussLegendrePoints< 10 >()

template<>

std::pair<std::array<double, 10>, std::array<double, 10> > apollo::common::math::GetGaussLegendrePoints< 10 > ( )

inline

◆ GetGaussLegendrePoints< 2 >()

template<>

std::pair<std::array<double, 2>, std::array<double, 2> > apollo::common::math::GetGaussLegendrePoints< 2 > ( )

inline

◆ GetGaussLegendrePoints< 3 >()

template<>

std::pair<std::array<double, 3>, std::array<double, 3> > apollo::common::math::GetGaussLegendrePoints< 3 > ( )

inline

◆ GetGaussLegendrePoints< 4 >()

template<>

std::pair<std::array<double, 4>, std::array<double, 4> > apollo::common::math::GetGaussLegendrePoints< 4 > ( )

inline

◆ GetGaussLegendrePoints< 5 >()

template<>

std::pair<std::array<double, 5>, std::array<double, 5> > apollo::common::math::GetGaussLegendrePoints< 5 > ( )

inline

◆ GetGaussLegendrePoints< 6 >()

template<>

std::pair<std::array<double, 6>, std::array<double, 6> > apollo::common::math::GetGaussLegendrePoints< 6 > ( )

inline

◆ GetGaussLegendrePoints< 7 >()

template<>

std::pair<std::array<double, 7>, std::array<double, 7> > apollo::common::math::GetGaussLegendrePoints< 7 > ( )

inline

◆ GetGaussLegendrePoints< 8 >()

template<>

std::pair<std::array<double, 8>, std::array<double, 8> > apollo::common::math::GetGaussLegendrePoints< 8 > ( )

inline

◆ GetGaussLegendrePoints< 9 >()

template<>

std::pair<std::array<double, 9>, std::array<double, 9> > apollo::common::math::GetGaussLegendrePoints< 9 > ( )

inline

◆ GoldenSectionSearch()

double apollo::common::math::GoldenSectionSearch	(	const std::function< double(double)> &	func,
		const double	lower_bound,
		const double	upper_bound,
		const double	tol = `1e-6`
	)

Given a unimodal function defined on the interval, find a value on the interval to minimize the function. Reference: https://en.wikipedia.org/wiki/Golden-section_search.

Parameters

func	The target single-variable function to minimize.
lower_bound	The lower bound of the interval.
upper_bound	The upper bound of the interval.
tol	The tolerance of error.

Returns: The value that minimize the function fun.

◆ HeadingToQuaternion()

template<typename T >

Eigen::Quaternion<T> apollo::common::math::HeadingToQuaternion ( T heading )

inline

◆ InnerProd() [1/2]

double apollo::common::math::InnerProd	(	const Vec2d &	start_point,
		const Vec2d &	end_point_1,
		const Vec2d &	end_point_2
	)

Inner product between two 2-D vectors from the common start point, and end at two other points.

Parameters

start_point	The common start point of two vectors in 2-D.
end_point_1	The end point of the first vector.
end_point_2	The end point of the second vector.

Returns: The inner product result.

◆ InnerProd() [2/2]

double apollo::common::math::InnerProd	(	const double	x0,
		const double	y0,
		const double	x1,
		const double	y1
	)

Inner product between two vectors. One vector is formed by 1st and 2nd parameters of the function. The other vector is formed by 3rd and 4th parameters of the function.

Parameters

x0	The x coordinate of the first vector.
y0	The y coordinate of the first vector.
x1	The x coordinate of the second vector.
y1	The y coordinate of the second vector.

Returns: The inner product result.

◆ IntegrateByGaussLegendre()

template<std::size_t N>

double apollo::common::math::IntegrateByGaussLegendre	(	const std::function< double(double)> &	func,
		const double	lower_bound,
		const double	upper_bound
	)

Compute the integral of a target single-variable function from a lower bound to an upper bound, by 5-th Gauss-Legendre method Given a target function and integral lower and upper bound, compute the integral approximation using 5th order Gauss-Legendre integration. The target function must be a smooth function. Example: target function: auto func = [](const double x) {return x * x;}; double integral = gauss_legendre(func, -2, 3); This gives you the approximated integral of function x^2 in bound [-2, 3].

reference: https://en.wikipedia.org/wiki/Gaussian_quadrature http://www.mymathlib.com/quadrature/gauss_legendre.html

Parameters

func	The target single-variable function
lower_bound	The lower bound of the integral
upper_bound	The upper bound of the integral

Returns: The integral result

◆ IntegrateBySimpson()

double apollo::common::math::IntegrateBySimpson	(	const std::vector< double > &	funv_vec,
		const double	dx,
		const std::size_t	nsteps
	)

◆ IntegrateByTrapezoidal()

double apollo::common::math::IntegrateByTrapezoidal	(	const std::vector< double > &	funv_vec,
		const double	dx,
		const std::size_t	nsteps
	)

◆ InterpolateUsingLinearApproximation() [1/3]

SLPoint apollo::common::math::InterpolateUsingLinearApproximation	(	const SLPoint &	p0,
		const SLPoint &	p1,
		const double	w
	)

◆ InterpolateUsingLinearApproximation() [2/3]

PathPoint apollo::common::math::InterpolateUsingLinearApproximation	(	const PathPoint &	p0,
		const PathPoint &	p1,
		const double	s
	)

◆ InterpolateUsingLinearApproximation() [3/3]

TrajectoryPoint apollo::common::math::InterpolateUsingLinearApproximation	(	const TrajectoryPoint &	tp0,
		const TrajectoryPoint &	tp1,
		const double	t
	)

◆ InverseQuaternionRotate()

Eigen::Vector3d apollo::common::math::InverseQuaternionRotate	(	const Quaternion &	orientation,
		const Eigen::Vector3d &	rotated
	)

inline

◆ L2Norm()

void apollo::common::math::L2Norm	(	int	feat_dim,
		float *	feat_data
	)

inline

◆ lerp()

template<typename T >

T apollo::common::math::lerp	(	const T &	x0,
		const double	t0,
		const T &	x1,
		const double	t1,
		const double	t
	)

Linear interpolation between two points of type T.

Parameters

x0	The coordinate of the first point.
t0	The interpolation parameter of the first point.
x1	The coordinate of the second point.
t1	The interpolation parameter of the second point.
t	The interpolation parameter for interpolation.
x	The coordinate of the interpolated point.

Returns: Interpolated point.

◆ NormalizeAngle()

double apollo::common::math::NormalizeAngle ( const double angle )

Normalize angle to [-PI, PI).

Parameters

angle the original value of the angle.

Returns: The normalized value of the angle.

◆ operator!=()

template<typename T >

bool apollo::common::math::operator!=	(	Angle< T >	lhs,
		Angle< T >	rhs
	)

Tests two Angle objects for inequality.

Parameters

lhs	An Angle object
rhs	An Angle object

Returns: lhs != rhs

◆ operator*() [1/3]

Vec2d apollo::common::math::operator*	(	const double	ratio,
		const Vec2d &	vec
	)

Multiplies the given Vec2d by a given scalar.

◆ operator*() [2/3]

template<typename T , typename Scalar >

Angle<T> apollo::common::math::operator*	(	Angle< T >	lhs,
		Scalar	rhs
	)

Multiplies an Angle by a scalar.

Parameters

lhs	An Angle object
rhs	A scalar

Returns: Result of multiplication

◆ operator*() [3/3]

template<typename T , typename Scalar >

Angle<T> apollo::common::math::operator*	(	Scalar	lhs,
		Angle< T >	rhs
	)

Multiplies an Angle by a scalar.

Parameters

lhs	An Angle object
rhs	A scalar

Returns: Result of multiplication

◆ operator+()

template<typename T >

Angle<T> apollo::common::math::operator+	(	Angle< T >	lhs,
		Angle< T >	rhs
	)

Sums two angles.

Parameters

lhs	An Angle object
rhs	An Angle object

Returns: Result of addition

◆ operator-()

template<typename T >

Angle<T> apollo::common::math::operator-	(	Angle< T >	lhs,
		Angle< T >	rhs
	)

Subtracts two angles.

Parameters

lhs	An Angle object
rhs	An Angle object

Returns: Result of subtraction

◆ operator/() [1/2]

template<typename T , typename Scalar >

Angle<T> apollo::common::math::operator/	(	Angle< T >	lhs,
		Scalar	rhs
	)

Divides an Angle by a scalar.

Parameters

lhs	An Angle object
rhs	A scalar

Returns: Result of division

◆ operator/() [2/2]

template<typename T >

double apollo::common::math::operator/	(	Angle< T >	lhs,
		Angle< T >	rhs
	)

Divides an Angle by a scalar.

Parameters

lhs	An Angle object
rhs	A scalar

Returns: Result of division

◆ operator==()

template<typename T >

bool apollo::common::math::operator==	(	Angle< T >	lhs,
		Angle< T >	rhs
	)

Tests two Angle objects for equality.

Parameters

lhs	An Angle object
rhs	An Angle object

Returns: lhs == rhs

◆ PseudoInverse() [1/2]

template<typename T , unsigned int N>

Eigen::Matrix<T, N, N> apollo::common::math::PseudoInverse	(	const Eigen::Matrix< T, N, N > &	m,
		const double	epsilon = `1.0e-6`
	)

Computes the Moore-Penrose pseudo-inverse of a given square matrix, rounding all eigenvalues with absolute value bounded by epsilon to zero.

Parameters

m	The square matrix to be pseudo-inverted
epsilon	A small positive real number (optional; default is 1.0e-6).

Returns: Moore-Penrose pseudo-inverse of the given matrix.

◆ PseudoInverse() [2/2]

template<typename T , unsigned int M, unsigned int N>

Eigen::Matrix<T, N, M> apollo::common::math::PseudoInverse	(	const Eigen::Matrix< T, M, N > &	m,
		const double	epsilon = `1.0e-6`
	)

Computes the Moore-Penrose pseudo-inverse of a given matrix, rounding all eigenvalues with absolute value bounded by epsilon to zero.

Parameters

m	The matrix to be pseudo-inverted
epsilon	A small positive real number (optional; default is 1.0e-6).

Returns: Moore-Penrose pseudo-inverse of the given matrix.

◆ QuaternionRotate()

Eigen::Vector3d apollo::common::math::QuaternionRotate	(	const Quaternion &	orientation,
		const Eigen::Vector3d &	original
	)

inline

◆ QuaternionToHeading() [1/2]

double apollo::common::math::QuaternionToHeading	(	const double	qw,
		const double	qx,
		const double	qy,
		const double	qz
	)

inline

◆ QuaternionToHeading() [2/2]

template<typename T >

T apollo::common::math::QuaternionToHeading ( const Eigen::Quaternion< T > & q )

inline

◆ RandomDouble()

double apollo::common::math::RandomDouble	(	const double	s,
		const double	t,
		unsigned int	rand_seed = `1`
	)

Get a random double between two integer values by a random seed.

Parameters

s	The lower bound of the random double.
t	The upper bound of the random double.
random_seed	The random seed.

Returns: A random double between s and t based on the input random_seed.

◆ RandomInt()

int apollo::common::math::RandomInt	(	const int	s,
		const int	t,
		unsigned int	rand_seed = `1`
	)

Get a random integer between two integer values by a random seed.

Parameters

s	The lower bound of the random integer.
t	The upper bound of the random integer.
random_seed	The random seed.

Returns: A random integer between s and t based on the input random_seed.

◆ RFUToFLU()

std::pair<double, double> apollo::common::math::RFUToFLU	(	const double	x,
		const double	y
	)

inline

◆ RotateVector2d()

Eigen::Vector2d apollo::common::math::RotateVector2d	(	const Eigen::Vector2d &	v_in,
		const double	theta
	)

◆ Sigmoid()

double apollo::common::math::Sigmoid ( const double x )

inline

◆ sin() [1/2]

float apollo::common::math::sin ( Angle16 a )

◆ sin() [2/2]

float apollo::common::math::sin ( Angle8 a )

◆ slerp()

double apollo::common::math::slerp	(	const double	a0,
		const double	t0,
		const double	a1,
		const double	t1,
		const double	t
	)

Spherical linear interpolation between two angles. The two angles are within range [-M_PI, M_PI).

Parameters

a0	The value of the first angle.
t0	The interpolation parameter of the first angle.
a1	The value of the second angle.
t1	The interpolation parameter of the second angle.
t	The interpolation parameter for interpolation.
a	The value of the spherically interpolated angle.

Returns: Interpolated angle.

◆ SolveLQRProblem() [1/2]

void apollo::common::math::SolveLQRProblem	(	const Eigen::MatrixXd &	A,
		const Eigen::MatrixXd &	B,
		const Eigen::MatrixXd &	Q,
		const Eigen::MatrixXd &	R,
		const Eigen::MatrixXd &	M,
		const double	tolerance,
		const uint	max_num_iteration,
		Eigen::MatrixXd *	ptr_K
	)

Solver for discrete-time linear quadratic problem.

Parameters

A	The system dynamic matrix
B	The control matrix
Q	The cost matrix for system state
R	The cost matrix for control output
M	is the cross term between x and u, i.e. x'Qx + u'Ru + 2x'Mu
tolerance	The numerical tolerance for solving Discrete Algebraic Riccati equation (DARE)
max_num_iteration	The maximum iterations for solving ARE
ptr_K	The feedback control matrix (pointer)

◆ SolveLQRProblem() [2/2]

void apollo::common::math::SolveLQRProblem	(	const Eigen::MatrixXd &	A,
		const Eigen::MatrixXd &	B,
		const Eigen::MatrixXd &	Q,
		const Eigen::MatrixXd &	R,
		const double	tolerance,
		const uint	max_num_iteration,
		Eigen::MatrixXd *	ptr_K
	)

Solver for discrete-time linear quadratic problem.

Parameters

A	The system dynamic matrix
B	The control matrix
Q	The cost matrix for system state
R	The cost matrix for control output
tolerance	The numerical tolerance for solving Discrete Algebraic Riccati equation (DARE)
max_num_iteration	The maximum iterations for solving ARE
ptr_K	The feedback control matrix (pointer)

◆ Sqr()

double apollo::common::math::Sqr ( const double x )

◆ Square()

template<typename T >

T apollo::common::math::Square ( const T value )

inline

Compute squared value.

Parameters

value The target value to get its squared value.

Returns: Squared value of the input value.

◆ tan() [1/2]

float apollo::common::math::tan ( Angle16 a )

◆ tan() [2/2]

float apollo::common::math::tan ( Angle8 a )

◆ WrapAngle()

double apollo::common::math::WrapAngle ( const double angle )

Wrap angle to [0, 2 * PI).

Parameters

angle the original value of the angle.

Returns: The wrapped value of the angle.

Variable Documentation

◆ kMathEpsilon

constexpr double apollo::common::math::kMathEpsilon = 1e-10

◆ SIN_TABLE

const float apollo::common::math::SIN_TABLE[SIN_TABLE_SIZE]

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ Angle16

◆ Angle32

◆ Angle64

◆ Angle8

◆ EulerAnglesZXYd

◆ EulerAnglesZXYf

Function Documentation

◆ almost_equal()

◆ AngleDiff()

◆ Cartesian2Polar()

◆ Clamp()

◆ ContinuousToDiscrete() [1/2]

◆ ContinuousToDiscrete() [2/2]

◆ cos() [1/2]

◆ cos() [2/2]

◆ CrossProd() [1/2]

◆ CrossProd() [2/2]

◆ DenseToCSCMatrix()

◆ EvaluatePolynomial()

◆ FitPolynomial()

◆ FLUToRFU()

◆ Gaussian()

◆ GetGaussLegendrePoints()

◆ GetGaussLegendrePoints< 10 >()

◆ GetGaussLegendrePoints< 2 >()

◆ GetGaussLegendrePoints< 3 >()

◆ GetGaussLegendrePoints< 4 >()

◆ GetGaussLegendrePoints< 5 >()

◆ GetGaussLegendrePoints< 6 >()

◆ GetGaussLegendrePoints< 7 >()

◆ GetGaussLegendrePoints< 8 >()

◆ GetGaussLegendrePoints< 9 >()

◆ GoldenSectionSearch()

◆ HeadingToQuaternion()

◆ InnerProd() [1/2]

◆ InnerProd() [2/2]

◆ IntegrateByGaussLegendre()

◆ IntegrateBySimpson()

◆ IntegrateByTrapezoidal()

◆ InterpolateUsingLinearApproximation() [1/3]

◆ InterpolateUsingLinearApproximation() [2/3]

◆ InterpolateUsingLinearApproximation() [3/3]

◆ InverseQuaternionRotate()

◆ L2Norm()

◆ lerp()

◆ NormalizeAngle()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator==()

◆ PseudoInverse() [1/2]

◆ PseudoInverse() [2/2]

◆ QuaternionRotate()

◆ QuaternionToHeading() [1/2]

◆ QuaternionToHeading() [2/2]

◆ RandomDouble()

◆ RandomInt()

◆ RFUToFLU()

◆ RotateVector2d()

◆ Sigmoid()

◆ sin() [1/2]

◆ sin() [2/2]

◆ slerp()

◆ SolveLQRProblem() [1/2]

◆ SolveLQRProblem() [2/2]

◆ Sqr()

◆ Square()

◆ tan() [1/2]

◆ tan() [2/2]