DUNE::Math Namespace Reference

Detailed Description

Math routines and classes.

Namespaces
	Random

Classes
class	Angles
class	Derivative
struct	LinIntParam
struct	LineSegParam
class	Matrix
class	MovingAverage
class	MultiMovingAverage
struct	FuncWrapper
class	Optimization
class	tvector
class	QPSolver

Functions
uint32_t	computeNextPowerOfTwo (uint32_t val)
template<typename Type >
Type	average (Type *a, uint32_t size)
template<typename Type >
Type	norm (const Type &a, const Type &b)
template<typename Type >
void	insertionSort (Type *a, uint16_t size)
template<typename Type >
Type	medianOrdered (Type *a, uint16_t size)
template<typename Type >
Type	median (Type *a, uint16_t size)
template<typename Type >
Type	linearInterpolation (const LinIntParam< Type > &p)
template<typename Type >
Type	piecewiseLI (const std::vector< Type > &x_vec, const std::vector< Type > &t_vec, Type t)
template<typename Type >
bool	lineSegmentIntersect (const LineSegParam< Type > &p, Type *coord_x, Type *coord_y)
template<typename Ta , typename Tb , typename Tc >
Ta	trimValue (Ta v, Tb min, Tc max)
template<typename Ta , typename Tb , typename Tc >
bool	trimValueMod (Ta &value, Tb min, Tc max)
char	getSignalChar (fp64_t v)
int	getSignal (float v)
double	round (double value)
long int	roundToInteger (double value)
uint8_t	fromBCD (uint8_t value)
uint8_t	toBCD (uint8_t value)
template<typename T >
T	gcd (T a, T b)
template<typename T >
bool	isNaN (const T &var)
Matrix	operator+ (const Matrix &m1, const Matrix &m2)
Matrix	operator- (const Matrix &m1, const Matrix &m2)
Matrix	operator* (const Matrix &m1, const Matrix &m2)
Matrix	operator& (const Matrix &m1, const Matrix &m2)
Matrix	operator/ (const Matrix &a, const Matrix &b)
Matrix	operator* (double x, const Matrix &a)
Matrix	operator* (const Matrix &a, double x)
Matrix	operator/ (const Matrix &a, double x)
std::ostream &	operator<< (std::ostream &os, const Matrix &a)
std::istream &	operator>> (std::istream &is, Matrix &a)
Matrix	transpose (const Matrix &a)
Matrix	inverse_pp (const Matrix &a)
Matrix	inverse_pp (const Matrix &a, const Matrix &b)
Matrix	inverse (const Matrix &a)
Matrix	inverse (const Matrix &a, const Matrix &b)
Matrix	skew (double data[3])
Matrix	skew (const Matrix &a)
Matrix	inverse_lup (const Matrix &a)
Matrix	abs (const Matrix &a)
double	max (const Matrix &a)
double	min (const Matrix &a)
double	sum (const Matrix &a)
double	squaresum (const Matrix &a)

Variables
class DUNE_DLL_SYM	Angles
class DUNE_DLL_SYM	Matrix
class DUNE_DLL_SYM	Optimization
class DUNE_DLL_SYM	QPSolver

Function Documentation

Matrix DUNE::Math::abs

(

const Matrix &

a

)

Parameters

[in]

a

matrix

Returns

matrix with absolute values

References DUNE::Math::Matrix::isEmpty().

Referenced by Sensors::Imagenex881A::Task::setAbsorption().

template<typename Type >

Type DUNE::Math::average	(	Type *	a,
		uint32_t	size
	)

Computes the average value of a fixed size array.

Parameters

a	array with values.
size	size of the array.

Returns

average value of the array.

uint32_t DUNE::Math::computeNextPowerOfTwo ( uint32_t  val )

inline

Compute the next power of two of a value.

Parameters

val

value.

Returns

next power of two.

Referenced by DUNE::Math::Matrix::expmts(), DUNE::Utils::ByteBuffer::grow(), and DUNE::Utils::RawFifo::RawFifo().

uint8_t DUNE::Math::fromBCD ( uint8_t  value )

inline

Convert a number in Binary Coded Decimal (BCD) format to decimal.

Parameters

value

BCD encoded value.

Returns

decimal representation of value.

template<typename T >

T DUNE::Math::gcd	(	T	a,
		T	b
	)

int DUNE::Math::getSignal ( float  v )

inline

Computes the signal of a number.

Parameters

v

number.

Returns

1 or -1. If the number is 0.0 1 is returned.

char DUNE::Math::getSignalChar ( fp64_t  v )

inline

Computes the character representing the signal of a number.

Parameters

v

number.

Returns

ASCII character representing the number signal. Space ' ' is returned in the case of the number beeing 0.0.

template<typename Type >

void DUNE::Math::insertionSort	(	Type *	a,
		uint16_t	size
	)

Insertion Sort algorithm.

insertionSort algorithm implementation for zero based vectors better for lists with 8 to 20 elements This method sorts a vector in the ascending order using insertion sort algorithm

Referenced by median().

Matrix DUNE::Math::inverse

(

const Matrix &

a

)

The inverse is calculated using Gauss elimination with total pivoting.

If Matrix 'a' is singular (with current precision) a zero Matrix with the same dimension of 'a' is returned and the variable 'dMatrix::inversionerror' is set to 1. Otherwise it is set to 0.

Parameters

[in]

a

matrix to be inverted.

Returns

inverted matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::upper_triangular_tp().

Referenced by Control::AUV::Attitude::Task::onEstimatedState(), and DUNE::Control::AUVModel::stepInv().

Matrix DUNE::Math::inverse	(	const Matrix &	a,
		const Matrix &	b
	)

The system is solved using Gauss elimination with total pivoting.

If Matrix 'a' is singular (with current precision) a zero Matrix with the same dimension of 'b' is returned and the variable 'dMatrix::inversionerror' is set to 1. Otherwise it is set to 0.

Parameters

[in]	a	matrix
[in]	b	matrix

Returns

resultant matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::upper_triangular_tp().

Matrix DUNE::Math::inverse_lup

(

const Matrix &

a

)

Parameters

[in]

a

reference to matrix to be inverted

Returns

inverted matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::lup().

Matrix DUNE::Math::inverse_pp

(

const Matrix &

a

)

The inverse is calculated using Gauss elimination with partial pivoting.

If Matrix is singular (with current precision) a zero Matrix with the same dimension is returned and the variable. 'dMatrix::inversionerror' is set to 1. Otherwise is is set to 0.

Parameters

[in]

a

reference to matrix to be inverted

Returns

inverted matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::upper_triangular_pp().

Matrix DUNE::Math::inverse_pp	(	const Matrix &	a,
		const Matrix &	b
	)

The system is solved using Gauss elimination with partial pivoting.

If Matrix 'a' is singular (with current precision) a zero Matrix with the same dimension of 'b' is returned and the variable. 'dMatrix::inversionerror' is set to 1. Otherwise it is set to 0.

Parameters

[in]	a	matrix
[in]	b	matrix

Returns

resultant matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::upper_triangular_pp().

template<typename T >

bool DUNE::Math::isNaN

(

const T &

var

)

Test if a floating point variable holds a value that is not a number.

Returns

true if variable is not a number, false otherwise.

Referenced by DUNE::Simulation::UAVSimulation::commandAirspeed(), DUNE::Simulation::UAVSimulation::commandAlt(), DUNE::Simulation::UAVSimulation::commandBank(), DUNE::Simulation::UAVSimulation::commandFPA(), and DUNE::Simulation::UAVSimulation::commandPitch().

template<typename Type >

Type DUNE::Math::linearInterpolation

(

const LinIntParam< Type > &

p

)

References DUNE::Math::LinIntParam< Type >::t, DUNE::Math::LinIntParam< Type >::t0, DUNE::Math::LinIntParam< Type >::t1, DUNE::Math::LinIntParam< Type >::x0, and DUNE::Math::LinIntParam< Type >::x1.

Referenced by Maneuver::VehicleFormation::SMC::Task::findXY(), Maneuver::VehicleFormation::SMC::Task::onPathCompletion(), and piecewiseLI().

template<typename Type >

bool DUNE::Math::lineSegmentIntersect	(	const LineSegParam< Type > &	p,
		Type *	coord_x,
		Type *	coord_y
	)

References DUNE::Math::LineSegParam< Type >::line_a_x1, DUNE::Math::LineSegParam< Type >::line_a_x2, DUNE::Math::LineSegParam< Type >::line_a_y1, DUNE::Math::LineSegParam< Type >::line_a_y2, DUNE::Math::LineSegParam< Type >::line_b_x1, DUNE::Math::LineSegParam< Type >::line_b_x2, DUNE::Math::LineSegParam< Type >::line_b_y1, and DUNE::Math::LineSegParam< Type >::line_b_y2.

Referenced by Simulators::Environment::Task::bottomIntersection(), and Simulators::Environment::Task::forwardRange().

double DUNE::Math::max

(

const Matrix &

a

)

Parameters

[in]

a

matrix

Returns

maximum value of matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Referenced by Maneuver::CoverArea::Task::intersectSegmentPolygon(), Maneuver::CoverArea::Task::longRowsDirection(), Sensors::WifiRSSI::Task::poll(), trimValue(), and trimValueMod().

template<typename Type >

Type DUNE::Math::median	(	Type *	a,
		uint16_t	size
	)

Computes the median value of a fixed size UNORDERED array.

Parameters

a	array with values.
size	size of the array.

Returns

median value of the array.

References insertionSort(), and medianOrdered().

Referenced by Sensors::Imagenex852::Task::filterRange(), and DUNE::Math::Matrix::median().

template<typename Type >

Type DUNE::Math::medianOrdered	(	Type *	a,
		uint16_t	size
	)

Computes the median value of a fixed size ORDERED array.

Parameters

a	array with values.
size	size of the array.

Returns

median value of the array.

References round().

Referenced by median().

double DUNE::Math::min

(

const Matrix &

a

)

Parameters

[in]

a

matrix

Returns

minimum value of matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Referenced by Maneuver::CoverArea::Task::getRows(), Maneuver::CoverArea::Task::intersectSegmentPolygon(), Maneuver::CoverArea::Task::longRowsDirection(), Sensors::Imagenex837B::Frame::setGpsData(), Maneuver::VehicleFormation::Test::Task::Task(), Simulators::UAV::Task::Task(), Maneuver::VehicleFormation::Coordinator::Task::Task(), Maneuver::VehicleFormation::FormCollAvoid::Task::Task(), trimValue(), and trimValueMod().

template<typename Type >

Type DUNE::Math::norm	(	const Type &	a,
		const Type &	b
	)

Computes the norm between two points.

Parameters

a	first point.
b	second point.

Returns

norm between two points.

Referenced by DUNE::Navigation::BasicNavigation::consume(), Simulators::USBL::Task::getSensorData(), and DUNE::Maneuvers::StationKeep::updatePathControl().

Matrix DUNE::Math::operator&	(	const Matrix &	m1,
		const Matrix &	m2
	)

Parameters

[in]	m1	matrix to be multiplied (element-element).
[in]	m2	matrix to be multiplied (element-element).

Returns

resultant matrix.

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Matrix DUNE::Math::operator*	(	const Matrix &	m1,
		const Matrix &	m2
	)

Note on optimization by Eduardo Marques - Sep 8 2010

Applied loop interchange to achieve memory stride 1 (better data locality) in iterations of the innermost loop, This makes for better cache behavior (i.e. less cache misses), particularly as matrix dimensions increase. For those interested, see papers or books by M J Wolfe.

Parameters

[in]	m1	matrix to be summed.
[in]	m2	matrix to be summed.

Returns

resultant matrix.

References DUNE::Math::Matrix::isEmpty().

Matrix DUNE::Math::operator*	(	double	x,
		const Matrix &	a
	)

Parameters

[in]	x	real number.
[in]	a	matrix to be multiplied.

Returns

resultant matrix.

Matrix DUNE::Math::operator*	(	const Matrix &	a,
		double	x
	)

Parameters

[in]	a	matrix to be multiplied.
[in]	x	real number.

Returns

resultant matrix.

Matrix DUNE::Math::operator+	(	const Matrix &	m1,
		const Matrix &	m2
	)

Parameters

[in]	m1	matrix to be summed.
[in]	m2	matrix to be summed.

Returns

resultant matrix.

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Matrix DUNE::Math::operator-	(	const Matrix &	m1,
		const Matrix &	m2
	)

Parameters

[in]	m1	matrix to be subtracted.
[in]	m2	matrix to subtract.

Returns

resultant matrix.

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Matrix DUNE::Math::operator/	(	const Matrix &	a,
		const Matrix &	b
	)

Parameters

[in]	a	matrix for element-element quocient.
[in]	b	matrix for element-element quocient.

Returns

resultant matrix.

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Matrix DUNE::Math::operator/	(	const Matrix &	a,
		double	x
	)

Parameters

[in]	a	matrix to be divided.
[in]	x	real number.

Returns

resultant matrix.

std::ostream& DUNE::Math::operator<<	(	std::ostream &	os,
		const Matrix &	a
	)

Each row of the Matrix is put on a different line.

Parameters

[in]	os	output stream.
[in]	a	matrix to be outputted.

std::istream& DUNE::Math::operator>>	(	std::istream &	is,
		Matrix &	a
	)

The Matrix is filled row by row.

Parameters

[in]	is	input stream.
[in]	a	matrix to be filled.

Returns

resultant matrix.

References DUNE::Math::Matrix::Matrix(), and DUNE::Math::Matrix::vertCat().

template<typename Type >

Type DUNE::Math::piecewiseLI	(	const std::vector< Type > &	x_vec,
		const std::vector< Type > &	t_vec,
		Type	t
	)

Interpolates a point for a piecewise linear function If outside of the function's domain, returns the interpolation using closest points.

Parameters

x_vec	piecewise linear function value for the values of t_vec
t_vec	read line above. ASSUMED TO BE IN ASCENDING ORDER!
t	value for which the function is to be interpolated

Returns

resuling value of the interpolation

References linearInterpolation().

Referenced by DUNE::Power::Model::computeMotionEnergy().

double DUNE::Math::round ( double  value )

inline

Referenced by DUNE::Network::TDMA::check(), medianOrdered(), Maneuver::VehicleFormation::SMC::Task::onUpdate(), roundToInteger(), DUNE::IMC::DeviceUpdate::serialize(), and DUNE::IMC::ExtendedDeviceUpdate::serialize().

long int DUNE::Math::roundToInteger ( double  value )

inline

References round().

Matrix DUNE::Math::skew

(

double

data[3]

)

Parameters

[in]

data

array with 3 elements

Returns

skewed matrix

Matrix DUNE::Math::skew

(

const Matrix &

a

)

Parameters

[in]

a

row or column vector with 3 elements

Returns

skewed matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::skew.

double DUNE::Math::squaresum

(

const Matrix &

a

)

Parameters

[in]

a

matrix

Returns

squared sum of the elements of matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

double DUNE::Math::sum

(

const Matrix &

a

)

Parameters

[in]

a

matrix

Returns

sum of the elements of matrix

References DUNE::Math::Matrix::isEmpty(), and DUNE::Math::Matrix::size().

Referenced by Maneuver::VehicleFormation::FormCollAvoid::Task::formationControl(), Sensors::MTi::Task::sendMessage(), and DUNE::Math::QPSolver::solve().

uint8_t DUNE::Math::toBCD ( uint8_t  value )

inline

Convert a number in decimal format to Binary Coded Decimal (BCD) format.

Parameters

value

decimal value.

Returns

BCD encoded value.

Matrix DUNE::Math::transpose

(

const Matrix &

a

)

Parameters

[in]

a

to be transposed.

Returns

transposed matrix.

References DUNE::Math::Matrix::isEmpty().

Referenced by Navigation::General::LBL::Task::consume(), Sensors::LIMU::Task::decodeOutputData(), Maneuver::VehicleFormation::FormCollAvoid::Task::formationControl(), Maneuver::VehicleFormation::FormCollAvoid::Task::leaderOutput(), Sensors::MicrostrainMIP::Task::onUpdateParameters(), Sensors::LIMU::Task::onUpdateParameters(), Sensors::Microstrain3DMGX3::Task::onUpdateParameters(), Maneuver::VehicleFormation::Coordinator::Task::periodicUpdate(), Simulators::UAVAutopilot::Task::task(), Sensors::Microstrain3DMGX3::Task::task(), and Simulators::UAV::Task::task().

template<typename Ta , typename Tb , typename Tc >

Ta DUNE::Math::trimValue ( Ta  v, Tb  min, Tc  max  )

inline

References max(), and min().

Referenced by Control::ROV::RemoteOperation::Task::actuateThruster(), Control::AUV::Allocator::Task::allocate(), Control::AUV::Allocator::Task::brake(), DUNE::Plans::Progress::compute(), DUNE::Control::PathController::consume(), Simulators::Servos::Task::consume(), Control::Path::Height::Task::consume(), Simulators::Docking::Task::consume(), Maneuver::VehicleFormation::Coordinator::Task::consume(), Maneuver::VehicleFormation::FormCollAvoid::Task::consume(), Control::AUV::Speed::Task::dispatchThrust(), Control::ASV::HeadingAndSpeed::Task::dispatchThrust(), Maneuver::VehicleFormation::FormCollAvoid::Task::formationControl(), Control::ROV::RemoteOperation::Task::forwardControl(), Control::UAV::Ardupilot::Task::map2PWM(), Control::AUV::LMI::Task::onEstimatedState(), Control::AUV::Attitude::Task::onEstimatedState(), Maneuver::VehicleFormation::SMC::Task::onPathCompletion(), Maneuver::VehicleFormation::SMC::Task::onUpdate(), Actuators::FLIRPTU::Task::rad2pos(), Actuators::Broom::Task::sanitizeRef(), Maneuver::VehicleFormation::Coordinator::Task::setLeaderState(), Maneuver::VehicleFormation::FormCollAvoid::Task::setLeaderState(), Actuators::Broom::Task::setRefCurrent(), Actuators::Broom::Task::setRefDcycle(), Sensors::Imagenex837B::Frame837::setRepRate(), DUNE::Control::DiscretePID::step(), Control::UAV::LOS::Task::step(), Maneuver::FollowTrajectory::Task::step(), Control::Path::LOSnSMC::Task::step(), Control::ROV::HorizontalPlane::Task::tal(), Actuators::FLIRPTU::Task::task(), Navigation::AUV::Navigation::Task::task(), DUNE::Monitors::ServoPositionMonitor< T >::updateAndTest(), and Simulators::Environment::Task::updateForwardDistance().

template<typename Ta , typename Tb , typename Tc >

bool DUNE::Math::trimValueMod ( Ta &  value, Tb  min, Tc  max  )

inline

References max(), and min().

Referenced by Control::AUV::Allocator::Task::allocate(), DUNE::Maneuvers::Circular::Circular(), DUNE::Maneuvers::Elevate::Elevate(), DUNE::Maneuvers::FigureEight::FigureEight(), and DUNE::Maneuvers::StationKeep::StationKeep().

Variable Documentation

class DUNE_DLL_SYM DUNE::Math::Angles

class DUNE_DLL_SYM DUNE::Math::Matrix

Referenced by Maneuver::VehicleFormation::Coordinator::Task::onUpdateParameters(), Maneuver::VehicleFormation::FormCollAvoid::Task::onUpdateParameters(), DUNE::Tasks::BasicParameterParser< Math::Matrix >::read(), DUNE::Simulation::UAVSimulation::resetModel(), and DUNE::Coordinates::sphericalToCartesian().

class DUNE_DLL_SYM DUNE::Math::Optimization

class DUNE_DLL_SYM DUNE::Math::QPSolver