Find polynomial roots (`#include <mrpt/math/poly_roots.h>`)

Detailed Description

Collaboration diagram for Find polynomial roots (`#include <mrpt/math/poly_roots.h>`):

Functions
int BASE_IMPEXP	mrpt::math::solve_poly3 (double *x, double a, double b, double c) MRPT_NO_THROWS
	Solves cubic equation x^3 + a*x^2 + b*x + c = 0. More...
int BASE_IMPEXP	mrpt::math::solve_poly4 (double *x, double a, double b, double c, double d) MRPT_NO_THROWS
	Solves quartic equation x^4 + a*x^3 + b*x^2 + c*x + d = 0 by Dekart-Euler method. More...
int BASE_IMPEXP	mrpt::math::solve_poly5 (double *x, double a, double b, double c, double d, double e) MRPT_NO_THROWS
	Solves equation x^5 + a*x^4 + b*x^3 + c*x^2 + d*x + e = 0. More...
int BASE_IMPEXP	mrpt::math::solve_poly4Bi (double *x, double b, double d) MRPT_NO_THROWS
	Solve equation x^4 + b*x^2 + d = 0. More...
int BASE_IMPEXP	mrpt::math::solve_poly4De (double *x, double b, double c, double d) MRPT_NO_THROWS
	Solve equation x^4 + b*x^2 + c*x + d = 0. More...
int BASE_IMPEXP	mrpt::math::solve_poly2 (double a, double b, double c, double &r1, double &r2) MRPT_NO_THROWS
	Solves equation a*x^2 + b*x + c = 0. More...

Function Documentation

solve_poly2()

int mrpt::math::solve_poly2	(	double	a,
		double	b,
		double	c,
		double &	r1,
		double &	r2
	)

Solves equation a*x^2 + b*x + c = 0.

Returns the number of real roots: either 0 or 2; or 1 if a=0 (in this case the root is in r1). r1, r2 are the roots. (r1<=r2)

Note

Based on poly34.h, by Khashin S.I. http://math.ivanovo.ac.ru/dalgebra/Khashin/index.html - khash2 (at) gmail.com

Definition at line 302 of file poly_roots.cpp.

References eps, and SWAP.

Referenced by mrpt::nav::collision_free_dist_segment_circ_robot(), mrpt::nav::CPTG_Holo_Blend::getPathPose(), and TEST().

solve_poly3()

int mrpt::math::solve_poly3	(	double *	x,
		double	a,
		double	b,
		double	c
	)

Solves cubic equation x^3 + a*x^2 + b*x + c = 0.

Returns the number of real roots N<=3. The roots are returned in the first entries of x, i.e. x[0] if N=1, x[0] and x[1] if N=2, etc.

Parameters

x	array of size 3

Note

Based on poly34.h, by Khashin S.I. http://math.ivanovo.ac.ru/dalgebra/Khashin/index.html - khash2 (at) gmail.com

Definition at line 29 of file poly_roots.cpp.

References mrpt::obs::gnss::a2, eps, and TwoPi.

Referenced by SolveP4De(), TEST(), and mrpt::nav::CPTG_Holo_Blend::updateTPObstacleSingle().

solve_poly4()

int mrpt::math::solve_poly4	(	double *	x,
		double	a,
		double	b,
		double	c,
		double	d
	)

Solves quartic equation x^4 + a*x^3 + b*x^2 + c*x + d = 0 by Dekart-Euler method.

Returns the number of real roots N<=4:

• return 4: 4 real roots x[0], x[1], x[2], x[3], possible multiple roots
• return 2: 2 real roots x[0], x[1] and complex x[2]+-i*x[3],
• return 0: two pair of complex roots: x[0]+-i*x[1], x[2]+-i*x[3],

The roots are returned in the first entries of x, i.e. x[0] if N=1, x[0] and x[1] if N=2, etc.

Parameters

x	array of size 4

Note

Based on poly34.h, by Khashin S.I. http://math.ivanovo.ac.ru/dalgebra/Khashin/index.html - khash2 (at) gmail.com

Definition at line 215 of file poly_roots.cpp.

References mrpt::obs::gnss::b1, N4Step(), and SolveP4De().

Referenced by mrpt::math::solve_poly5(), TEST(), and mrpt::nav::CPTG_Holo_Blend::updateTPObstacleSingle().

solve_poly4Bi()

int BASE_IMPEXP mrpt::math::solve_poly4Bi	(	double *	x,
		double	b,
		double	d
	)

Solve equation x^4 + b*x^2 + d = 0.

solve_poly4De()

int BASE_IMPEXP mrpt::math::solve_poly4De	(	double *	x,
		double	b,
		double	c,
		double	d
	)

Solve equation x^4 + b*x^2 + c*x + d = 0.

solve_poly5()

int mrpt::math::solve_poly5	(	double *	x,
		double	a,
		double	b,
		double	c,
		double	d,
		double	e
	)

Solves equation x^5 + a*x^4 + b*x^3 + c*x^2 + d*x + e = 0.

Returns the number of real roots N<=5. The roots are returned in the first entries of x, i.e. x[0] if N=1, x[0] and x[1] if N=2, etc.

Parameters

x	array of size 5

Note

Based on poly34.h, by Khashin S.I. http://math.ivanovo.ac.ru/dalgebra/Khashin/index.html - khash2 (at) gmail.com

Definition at line 293 of file poly_roots.cpp.

References mrpt::obs::gnss::a1, mrpt::obs::gnss::b1, mrpt::math::solve_poly4(), and SolveP5_1().