Gaussian PDF transformation functions

Detailed Description

Collaboration diagram for Gaussian PDF transformation functions:

Functions
template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void	mrpt::math::transform_gaussian_unscented (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const bool *elem_do_wrap2pi=nullptr, const double alpha=1e-3, const double K=0, const double beta=2.0)
	Scaled unscented transformation (SUT) for estimating the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user. More...
template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void	mrpt::math::transform_gaussian_montecarlo (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const size_t num_samples=1000, std::vector< VECTORLIKE3 > *out_samples_y=nullptr)
	Simple Montecarlo-base estimation of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user. More...
template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void	mrpt::math::transform_gaussian_linear (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const VECTORLIKE1 &x_increments)
	First order uncertainty propagation estimator of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user. More...

Function Documentation

transform_gaussian_linear()

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >

void mrpt::math::transform_gaussian_linear	(	const VECTORLIKE1 &	x_mean,
		const MATLIKE1 &	x_cov,
		void(*)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y)	functor,
		const USERPARAM &	fixed_param,
		VECTORLIKE2 &	y_mean,
		MATLIKE2 &	y_cov,
		const VECTORLIKE1 &	x_increments
	)

First order uncertainty propagation estimator of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.

The user must supply the function in "functor" which takes points in the X space and returns the mapped point in Y, optionally using an extra, constant parameter ("fixed_param") which remains constant. The Jacobians are estimated numerically using the vector of small increments "x_increments".

See also

The example in MRPT/samples/unscented_transform_test

transform_gaussian_unscented, transform_gaussian_montecarlo

Note

This function requires #include <Eigen/Dense>

Definition at line 152 of file transform_gaussian.h.

References mrpt::math::estimateJacobian(), MRPT_END, MRPT_START, and mrpt::math::multiply_HCHt().

Referenced by Pose3DQuatPDFGaussTests::testInverse(), Pose3DPDFGaussTests::testPoseComposition(), Pose3DQuatPDFGaussTests::testPoseComposition(), PosePDFGaussTests::testPoseInverse(), Pose3DPDFGaussTests::testPoseInverseComposition(), and Pose3DQuatPDFGaussTests::testPoseInverseComposition().

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transform_gaussian_montecarlo()

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >

void mrpt::math::transform_gaussian_montecarlo	(	const VECTORLIKE1 &	x_mean,
		const MATLIKE1 &	x_cov,
		void(*)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y)	functor,
		const USERPARAM &	fixed_param,
		VECTORLIKE2 &	y_mean,
		MATLIKE2 &	y_cov,
		const size_t	num_samples = 1000,
		std::vector< VECTORLIKE3 > *	out_samples_y = nullptr
	)

Simple Montecarlo-base estimation of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.

The user must supply the function in "functor" which takes points in the X space and returns the mapped point in Y, optionally using an extra, constant parameter ("fixed_param") which remains constant.

Parameters

out_samples_y

If !=nullptr, this vector will contain, upon return, the sequence of random samples generated and propagated through the functor().

See also

The example in MRPT/samples/unscented_transform_test

transform_gaussian_unscented, transform_gaussian_linear

Definition at line 114 of file transform_gaussian.h.

References mrpt::math::covariancesAndMean(), mrpt::random::CRandomGenerator::drawGaussianMultivariateMany(), mrpt::random::getRandomGenerator(), MRPT_END, and MRPT_START.

Referenced by mrpt::maps::COccupancyGridMap2D::laserScanSimulatorWithUncertainty().

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transform_gaussian_unscented()

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >

void mrpt::math::transform_gaussian_unscented	(	const VECTORLIKE1 &	x_mean,
		const MATLIKE1 &	x_cov,
		void(*)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y)	functor,
		const USERPARAM &	fixed_param,
		VECTORLIKE2 &	y_mean,
		MATLIKE2 &	y_cov,
		const bool *	elem_do_wrap2pi = nullptr,
		const double	alpha = 1e-3,
		const double	K = 0,
		const double	beta = 2.0
	)

Scaled unscented transformation (SUT) for estimating the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.

The user must supply the function in "functor" which takes points in the X space and returns the mapped point in Y, optionally using an extra, constant parameter ("fixed_param") which remains constant.

The parameters alpha, K and beta are the common names of the SUT method, and the default values are those recommended in most papers.

Parameters

elem_do_wrap2pi

If !=nullptr; it must point to an array of "bool" of size()==dimension of each element, stating if it's needed to do a wrap to [-pi,pi] to each dimension.

See also

The example in MRPT/samples/unscented_transform_test

transform_gaussian_montecarlo, transform_gaussian_linear

Definition at line 46 of file transform_gaussian.h.

References mrpt::math::covariancesAndMeanWeighted(), MRPT_END, and MRPT_START.

Referenced by mrpt::poses::CPose3DQuatPDFGaussian::copyFrom(), mrpt::poses::CPose3DPDFGaussian::copyFrom(), and mrpt::maps::COccupancyGridMap2D::laserScanSimulatorWithUncertainty().

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