#include <PolynomialRoots.hh>

Public Member Functions
	Cubic ()

	Cubic (real_type a, real_type b, real_type c, real_type d)

void	setup (real_type a, real_type b, real_type c, real_type d)

integer	num_roots () const

integer	numRoots () const
	alias of `num_roots`

bool	complex_root () const

bool	complexRoot () const
	alias of `complex_root`

bool	double_root () const

bool	doubleRoot () const
	alias of `double_root`

bool	triple_root () const

bool	tripleRoot () const
	alias of `triple_root`

integer	get_real_roots (real_type r[]) const

integer	getRealRoots (real_type r[]) const
	alias of `get_real_roots`

integer	get_positive_roots (real_type r[]) const

integer	getPositiveRoots (real_type r[]) const
	alias of `get_positive_roots`

integer	get_negative_roots (real_type r[]) const

integer	getNegativeRoots (real_type r[]) const
	alias of `get_negative_roots`

integer	get_roots_in_range (real_type a, real_type b, real_type r[]) const

integer	getRootsInRange (real_type a, real_type b, real_type r[]) const
	alias of `get_roots_in_range`

integer	get_roots_in_open_range (real_type a, real_type b, real_type r[]) const

integer	getRootsInOpenRange (real_type a, real_type b, real_type r[]) const
	alias of `get_roots_in_open_range`

real_type	real_root0 () const

real_type	real_root1 () const

real_type	real_root2 () const

complex_type	root0 () const

complex_type	root1 () const

complex_type	root2 () const

void	get_root0 (real_type &re, real_type &im) const

void	getRoot0 (real_type &re, real_type &im) const
	alias of `get_root0`

void	get_root0 (complex_type &r) const

void	getRoot0 (complex_type &r) const
	alias of `get_root0`

void	get_root1 (real_type &re, real_type &im) const

void	getRoot1 (real_type &re, real_type &im) const
	alias of `get_root1`

void	get_root1 (complex_type &r) const

void	getRoot1 (complex_type &r) const
	alias of `get_root1`

void	get_root2 (real_type &re, real_type &im) const

void	getRoot2 (real_type &re, real_type &im) const
	alias of `get_root2`

void	get_root2 (complex_type &r) const

void	getRoot2 (complex_type &r) const
	alias of `get_root2`

real_type	eval (real_type x) const

complex_type	eval (complex_type x) const

void	eval (real_type x, real_type &p, real_type &dp) const

void	info (ostream_type &s) const

bool	check (ostream_type &s) const

Detailed Description

Cubic polynomial class

Constructor

double a = 1;
double b = 2;
double c = 3;
double d = 3;
Cubic p(a,b,c,d); // build an solve a x^3 + b x^2 + c x + d = 0
 
Cubic p;
p.setup(a,b,c,d); // build an solve a x^3 + b x^2 + c x + d = 0

Get kind of solution

int  nroots = p.num_roots();
bool has_complex_root  = p.complex_root();
bool has_a_double_root = p.double_root();
bool has_a_triple_root = p.triple_root();

Get real roots

double r_min = 0;
double r_max = 2;
double r[3];
int nroots;
nroots = p.getRealRoots( r );
nroots = p.getPositiveRoots( r );
nroots = p.getNegativeRoots( r );
nroots = p.getRootsInRange( r_min, r_max, r );
nroots = p.getRootsInOpenRange( r_min, r_max, r );

Get roots

double r0 = p.real_root0();
double r1 = p.real_root1();
double r2 = p.real_root2();
complex_type r0 = p.root0();
complex_type r1 = p.root1();
complex_type r2 = p.root2();
 
complex_type r;
double re, im;
p.getRoot0( re, im );
p.getRoot0( r );
p.getRoot1( re, im );
p.getRoot1( r );
p.getRoot2( re, im );
p.getRoot2( r );

Evaluate polynomial

{double or complex} v, x;
v = p.eval( x );
 
p.eval( x, p, dp );

Information

p.info( cout );

bool ok = p.check( cout );

PolynomialRoots::Cubic::info

void info(ostream_type &s) const

PolynomialRoots::Cubic::check

bool check(ostream_type &s) const

Constructor & Destructor Documentation

◆ Cubic() [1/2]

PolynomialRoots::Cubic::Cubic ( )

inline

Build an empty instance of Cubic polynomial solver

◆ Cubic() [2/2]

PolynomialRoots::Cubic::Cubic	(	real_type	a,
		real_type	b,
		real_type	c,
		real_type	d )

inline

Build the instance of the calss and compute the roots of cubic polynomial \( a x^3 + b x^2 + c x + d \)

Parameters

[in]	a	coefficient of \( x^3 \)
[in]	b	coefficient of \( x^2 \)
[in]	c	coefficient of \( x \)
[in]	d	coefficient of \( x^0 \)

Member Function Documentation

◆ check()

bool PolynomialRoots::Cubic::check ( ostream_type & s ) const

Check tolerenace and quality of the computed roots.

◆ complex_root()

bool PolynomialRoots::Cubic::complex_root ( ) const

inline

Has complex roots?

◆ complexRoot()

bool PolynomialRoots::Cubic::complexRoot ( ) const

inline

alias of complex_root

◆ double_root()

bool PolynomialRoots::Cubic::double_root ( ) const

inline

Has a double root?

◆ doubleRoot()

bool PolynomialRoots::Cubic::doubleRoot ( ) const

inline

alias of double_root

◆ eval() [1/3]

complex_type PolynomialRoots::Cubic::eval ( complex_type x ) const

inline

Evalute the cubic polynomial.

Parameters

x	value where compute \( p(x) \), x complex

Returns: the value \( p(x) \)

◆ eval() [2/3]

real_type PolynomialRoots::Cubic::eval ( real_type x ) const

inline

Evalute the cubic polynomial.

Parameters

x	value where compute \( p(x) \)

Returns: the value \( p(x) \)

◆ eval() [3/3]

void PolynomialRoots::Cubic::eval	(	real_type	x,
		real_type &	p,
		real_type &	dp ) const

inline

Evalute the polynomial with its derivative.

Parameters

x	value where compute \( p(x) \)
p	value \( p(x) \)
dp	value \( p'(x) \)

◆ get_negative_roots()

integer PolynomialRoots::Cubic::get_negative_roots ( real_type r[] ) const

Get negative real roots.

Parameters

[out] r vector that will be filled with the real roots

Returns: the total number of negative real roots, 0, 1, 2 or 3

◆ get_positive_roots()

integer PolynomialRoots::Cubic::get_positive_roots ( real_type r[] ) const

Get positive real roots.

Parameters

[out] r vector that will be filled with the real roots

Returns: the total number of positive real roots, 0, 1, 2 or 3

◆ get_real_roots()

integer PolynomialRoots::Cubic::get_real_roots ( real_type r[] ) const

Get the real roots.

Parameters

[out] r vector that will be filled with the real roots

Returns: the total number of real roots, 0, 1, 2 or 3

◆ get_root0() [1/2]

void PolynomialRoots::Cubic::get_root0 ( complex_type & r ) const

inline

First complex or real root.

◆ get_root0() [2/2]

void PolynomialRoots::Cubic::get_root0	(	real_type &	re,
		real_type &	im ) const

inline

First complex or real root.

◆ get_root1() [1/2]

void PolynomialRoots::Cubic::get_root1 ( complex_type & r ) const

inline

Second complex or real root.

◆ get_root1() [2/2]

void PolynomialRoots::Cubic::get_root1	(	real_type &	re,
		real_type &	im ) const

inline

Second complex or real root.

◆ get_root2() [1/2]

void PolynomialRoots::Cubic::get_root2 ( complex_type & r ) const

inline

Third complex or real root.

◆ get_root2() [2/2]

void PolynomialRoots::Cubic::get_root2	(	real_type &	re,
		real_type &	im ) const

inline

Third complex or real root.

◆ get_roots_in_open_range()

integer PolynomialRoots::Cubic::get_roots_in_open_range	(	real_type	a,
		real_type	b,
		real_type	r[] ) const

Get real roots in an open range.

Parameters

[in]	a	left side of the range
[in]	b	right side of the range
[out]	r	vector that will be filled with the real roots

Returns: the total number of real roots in the open range (a,b)

◆ get_roots_in_range()

integer PolynomialRoots::Cubic::get_roots_in_range	(	real_type	a,
		real_type	b,
		real_type	r[] ) const

Get real roots in a closed range.

Parameters

[in]	a	left side of the range
[in]	b	right side of the range
[out]	r	vector that will be filled with the real roots

Returns: the total number of real roots in the range [a,b]

◆ getNegativeRoots()

integer PolynomialRoots::Cubic::getNegativeRoots ( real_type r[] ) const

inline

alias of get_negative_roots

◆ getPositiveRoots()

integer PolynomialRoots::Cubic::getPositiveRoots ( real_type r[] ) const

inline

alias of get_positive_roots

◆ getRealRoots()

integer PolynomialRoots::Cubic::getRealRoots ( real_type r[] ) const

inline

alias of get_real_roots

◆ getRoot0() [1/2]

void PolynomialRoots::Cubic::getRoot0 ( complex_type & r ) const

inline

alias of get_root0

◆ getRoot0() [2/2]

void PolynomialRoots::Cubic::getRoot0	(	real_type &	re,
		real_type &	im ) const

inline

alias of get_root0

◆ getRoot1() [1/2]

void PolynomialRoots::Cubic::getRoot1 ( complex_type & r ) const

inline

alias of get_root1

◆ getRoot1() [2/2]

void PolynomialRoots::Cubic::getRoot1	(	real_type &	re,
		real_type &	im ) const

inline

alias of get_root1

◆ getRoot2() [1/2]

void PolynomialRoots::Cubic::getRoot2 ( complex_type & r ) const

inline

alias of get_root2

◆ getRoot2() [2/2]

void PolynomialRoots::Cubic::getRoot2	(	real_type &	re,
		real_type &	im ) const

inline

alias of get_root2

◆ getRootsInOpenRange()

integer PolynomialRoots::Cubic::getRootsInOpenRange	(	real_type	a,
		real_type	b,
		real_type	r[] ) const

inline

alias of get_roots_in_open_range

◆ getRootsInRange()

integer PolynomialRoots::Cubic::getRootsInRange	(	real_type	a,
		real_type	b,
		real_type	r[] ) const

inline

alias of get_roots_in_range

◆ info()

void PolynomialRoots::Cubic::info ( ostream_type & s ) const

Print info of the roots of the polynomial.

◆ num_roots()

integer PolynomialRoots::Cubic::num_roots ( ) const

inline

Number of found roots.

◆ numRoots()

integer PolynomialRoots::Cubic::numRoots ( ) const

inline

alias of num_roots

◆ real_root0()

real_type PolynomialRoots::Cubic::real_root0 ( ) const

inline

First real root.

◆ real_root1()

real_type PolynomialRoots::Cubic::real_root1 ( ) const

inline

Second real root.

◆ real_root2()

real_type PolynomialRoots::Cubic::real_root2 ( ) const

inline

Third real root.

◆ root0()

complex_type PolynomialRoots::Cubic::root0 ( ) const

inline

First complex or real root.

◆ root1()

complex_type PolynomialRoots::Cubic::root1 ( ) const

inline

Second complex or real root.

◆ root2()

complex_type PolynomialRoots::Cubic::root2 ( ) const

inline

Third complex or real root.

◆ setup()

void PolynomialRoots::Cubic::setup	(	real_type	a,
		real_type	b,
		real_type	c,
		real_type	d )

inline

Compute the roots of cubic polynomial \( a x^3 + b x^2 + c x + d \)

Parameters

[in]	a	coefficient of \( x^3 \)
[in]	b	coefficient of \( x^2 \)
[in]	c	coefficient of \( x \)
[in]	d	coefficient of \( x^0 \)

◆ triple_root()

bool PolynomialRoots::Cubic::triple_root ( ) const

inline

Has a triple root?

◆ tripleRoot()

bool PolynomialRoots::Cubic::tripleRoot ( ) const

inline

alias of triple_root

The documentation for this class was generated from the following file:

/Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/quarticRootsFlocke/src/PolynomialRoots.hh

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Cubic() [1/2]

◆ Cubic() [2/2]

Member Function Documentation

◆ check()

◆ complex_root()

◆ complexRoot()

◆ double_root()

◆ doubleRoot()

◆ eval() [1/3]

◆ eval() [2/3]

◆ eval() [3/3]

◆ get_negative_roots()

◆ get_positive_roots()

◆ get_real_roots()

◆ get_root0() [1/2]

◆ get_root0() [2/2]

◆ get_root1() [1/2]

◆ get_root1() [2/2]

◆ get_root2() [1/2]

◆ get_root2() [2/2]

◆ get_roots_in_open_range()

◆ get_roots_in_range()

◆ getNegativeRoots()

◆ getPositiveRoots()

◆ getRealRoots()

◆ getRoot0() [1/2]

◆ getRoot0() [2/2]

◆ getRoot1() [1/2]

◆ getRoot1() [2/2]

◆ getRoot2() [1/2]

◆ getRoot2() [2/2]

◆ getRootsInOpenRange()

◆ getRootsInRange()

◆ info()

◆ num_roots()

◆ numRoots()

◆ real_root0()

◆ real_root1()

◆ real_root2()

◆ root0()

◆ root1()

◆ root2()

◆ setup()

◆ triple_root()

◆ tripleRoot()