Interpolation, least-squares fit, splines

Detailed Description

Collaboration diagram for Interpolation, least-squares fit, splines:

Classes
class	mrpt::math::CSplineInterpolator1D
	A (persistent) sequence of (x,y) coordinates, allowing queries of intermediate points through spline interpolation, where possible. More...
class	mrpt::poses::CPose2DInterpolator
	This class stores a time-stamped trajectory in SE(2) (mrpt::math::TPose2D poses). More...
class	mrpt::poses::CPose3DInterpolator
	This class stores a time-stamped trajectory in SE(3) (CPose3D poses). More...
class	mrpt::poses::CPoseInterpolatorBase< DIM >
	Base class for SE(2)/SE(3) interpolators. More...

Functions
template<class T , class VECTOR >
T	mrpt::math::interpolate (const T &x, const VECTOR &ys, const T &x0, const T &x1)
	Interpolate a data sequence "ys" ranging from "x0" to "x1" (equally spaced), to obtain the approximation of the sequence at the point "x". More...
double	mrpt::math::interpolate2points (const double x, const double x0, const double y0, const double x1, const double y1, bool wrap2pi=false)
	Linear interpolation/extrapolation: evaluates at "x" the line (x0,y0)-(x1,y1). More...
template<typename NUMTYPE , class VECTORLIKE >
NUMTYPE	mrpt::math::spline (const NUMTYPE t, const VECTORLIKE &x, const VECTORLIKE &y, bool wrap2pi=false)
	Interpolates the value of a function in a point "t" given 4 SORTED points where "t" is between the two middle points If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range). More...
template<typename NUMTYPE , class VECTORLIKE , int NUM_POINTS = -1>
NUMTYPE	mrpt::math::leastSquareLinearFit (const NUMTYPE t, const VECTORLIKE &x, const VECTORLIKE &y, bool wrap2pi=false)
	Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a single point "t". More...
template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 , int NUM_POINTS = -1>
void	mrpt::math::leastSquareLinearFit (const VECTORLIKE1 &ts, VECTORLIKE2 &outs, const VECTORLIKE3 &x, const VECTORLIKE3 &y, bool wrap2pi=false)
	Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a sequence of points "ts" and returned at "outs". More...

Function Documentation

interpolate()

template<class T , class VECTOR >

T mrpt::math::interpolate	(	const T &	x,
		const VECTOR &	ys,
		const T &	x0,
		const T &	x1
	)

Interpolate a data sequence "ys" ranging from "x0" to "x1" (equally spaced), to obtain the approximation of the sequence at the point "x".

If the point "x" is out of the range [x0,x1], the closest extreme "ys" value is returned.

Note

Implementation in #include <mrpt/math/interp_fit.hpp>

See also

spline, interpolate2points

Definition at line 17 of file interp_fit.hpp.

References ASSERT_, MRPT_END, and MRPT_START.

Referenced by mrpt::img::hot2rgb(), mrpt::poses::CPoseInterpolatorBase< 3 >::interpolate(), mrpt::img::jet2rgb(), and mrpt::poses::CPoseInterpolatorBase< 3 >::saveInterpolatedToTextFile().

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interpolate2points()

double mrpt::math::interpolate2points	(	const double	x,
		const double	x0,
		const double	y0,
		const double	x1,
		const double	y1,
		bool	wrap2pi = false
	)

Linear interpolation/extrapolation: evaluates at "x" the line (x0,y0)-(x1,y1).

If wrap2pi is true, output is wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also

spline, interpolate, leastSquareLinearFit

Definition at line 438 of file math.cpp.

References MRPT_END, MRPT_START, THROW_EXCEPTION_FMT, and mrpt::math::wrapToPi().

Referenced by mrpt::poses::CPoseInterpolatorBase< 3 >::impl_interpolation().

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leastSquareLinearFit() [1/2]

template<typename NUMTYPE , class VECTORLIKE , int NUM_POINTS = -1>

NUMTYPE mrpt::math::leastSquareLinearFit	(	const NUMTYPE	t,
		const VECTORLIKE &	x,
		const VECTORLIKE &	y,
		bool	wrap2pi = false
	)

Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a single point "t".

The vectors x and y must have size >=2, and all values of "x" must be different. If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also

spline

getRegressionLine, getRegressionPlane

Note

Implementation in #include <mrpt/math/interp_fit.hpp>

Definition at line 119 of file interp_fit.hpp.

References ASSERT_, MRPT_END, MRPT_START, and mrpt::math::wrapToPi().

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leastSquareLinearFit() [2/2]

template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 , int NUM_POINTS = -1>

void mrpt::math::leastSquareLinearFit	(	const VECTORLIKE1 &	ts,
		VECTORLIKE2 &	outs,
		const VECTORLIKE3 &	x,
		const VECTORLIKE3 &	y,
		bool	wrap2pi = false
	)

Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a sequence of points "ts" and returned at "outs".

If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also

spline, getRegressionLine, getRegressionPlane

Note

Implementation in #include <mrpt/math/interp_fit.hpp>

Requires #include <Eigen/Dense>

Definition at line 157 of file interp_fit.hpp.

References ASSERT_, mrpt::math::MatrixBase< T, CMatrixDynamic< T > >::inverse_LLt(), mrpt::math::MatrixBase< T, CMatrixDynamic< T > >::matProductOf_AAt(), mrpt::math::MatrixVectorBase< T, CMatrixDynamic< T > >::matProductOf_Ab(), MRPT_END, MRPT_START, mrpt::math::CMatrixDynamic< T >::resize(), mrpt::math::CMatrixDynamic< T >::size(), and mrpt::math::wrapToPi().

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spline()

template<typename NUMTYPE , class VECTORLIKE >

NUMTYPE mrpt::math::spline	(	const NUMTYPE	t,
		const VECTORLIKE &	x,
		const VECTORLIKE &	y,
		bool	wrap2pi = false
	)

Interpolates the value of a function in a point "t" given 4 SORTED points where "t" is between the two middle points If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also

leastSquareLinearFit

Note

Implementation in #include <mrpt/math/interp_fit.hpp>

Definition at line 34 of file interp_fit.hpp.

References ASSERT_, mrpt::obs::gnss::b1, mrpt::obs::gnss::b2, M_2PI, M_PI, and mrpt::math::wrapToPi().

Referenced by mrpt::poses::CPoseInterpolatorBase< 3 >::impl_interpolation(), and mrpt::math::CSplineInterpolator1D::query().

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