PolynomialRoots::CubicT< T_real, T_complex > Class Template Reference

#include <PolynomialRoots.hh>

Public Types
using	value_type = T_real
using	complex_type = T_complex

Public Member Functions
	CubicT ()=default
	CubicT (T_real const &a, T_real const &b, T_real const &c, T_real const &d)
void	setup (T_real const &a, T_real const &b, T_real const &c, T_real const &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 (T_real r[]) const
integer	getRealRoots (T_real r[]) const
	Alias of get_real_roots().
integer	get_positive_roots (T_real r[]) const
integer	getPositiveRoots (T_real r[]) const
	Alias of get_positive_roots().
integer	get_negative_roots (T_real r[]) const
integer	getNegativeRoots (T_real r[]) const
	Alias of get_negative_roots().
integer	get_roots_in_range (T_real const &a, T_real const &b, T_real r[]) const
integer	getRootsInRange (T_real const &a, T_real const &b, T_real r[]) const
	Alias of get_roots_in_range().
integer	get_roots_in_open_range (T_real const &a, T_real const &b, T_real r[]) const
integer	getRootsInOpenRange (T_real const &a, T_real const &b, T_real r[]) const
	Alias of get_roots_in_open_range().
T_real	real_root0 () const
T_real	real_root1 () const
T_real	real_root2 () const
	Return the third stored real root.
T_complex	root0 () const
T_complex	root1 () const
T_complex	root2 () const
void	get_root0 (T_real &re, T_real &im) const
void	getRoot0 (T_real &re, T_real &im) const
	Alias of get_root0().
void	get_root0 (T_complex &r) const
void	getRoot0 (T_complex &r) const
	Alias of get_root0().
void	get_root1 (T_real &re, T_real &im) const
void	getRoot1 (T_real &re, T_real &im) const
	Alias of get_root1().
void	get_root1 (T_complex &r) const
void	getRoot1 (T_complex &r) const
	Alias of get_root1().
void	get_root2 (T_real &re, T_real &im) const
void	getRoot2 (T_real &re, T_real &im) const
	Alias of get_root2().
void	get_root2 (T_complex &r) const
void	getRoot2 (T_complex &r) const
	Alias of get_root2().
T_complex	root (integer const i) const
void	get_root (integer const i, T_real &re, T_real &im) const
T_real	eval (T_real const &x) const
T_complex	eval (T_complex const &x) const
void	eval (T_real const &x, T_real &p, T_real &dp) const
void	info (ostream_type &s) const
bool	check (ostream_type &s) const

Detailed Description

template<typename T_real, typename T_complex>
class PolynomialRoots::CubicT< T_real, T_complex >

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

real_type    r0 = p.real_root0();
real_type    r1 = p.real_root1();
real_type    r2 = p.real_root2();
real_complex r0 = p.root0();
real_complex r1 = p.root1();
real_complex r2 = p.root2();
 
real_complex r;
real_type    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 );

Member Typedef Documentation

complex_type

template<typename T_real, typename T_complex>

using PolynomialRoots::CubicT< T_real, T_complex >::complex_type = T_complex

value_type

template<typename T_real, typename T_complex>

using PolynomialRoots::CubicT< T_real, T_complex >::value_type = T_real

Constructor & Destructor Documentation

CubicT() [1/2]

template<typename T_real, typename T_complex>

PolynomialRoots::CubicT< T_real, T_complex >::CubicT ( )

default

Build an empty instance of Cubic polynomial solver

Build an empty cubic solver instance.

CubicT() [2/2]

template<typename T_real, typename T_complex>

PolynomialRoots::CubicT< T_real, T_complex >::CubicT ( T_real const & a, T_real const & b, T_real const & c, T_real const & 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()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::check ( ostream_type & s ) const

nodiscard

Check tolerance and quality of the computed roots.

complex_root()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::complex_root ( ) const

inline

Has complex roots?

complexRoot()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::complexRoot ( ) const

inline

Alias of complex_root().

double_root()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::double_root ( ) const

inline

Has a double root?

doubleRoot()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::doubleRoot ( ) const

inline

Alias of double_root().

eval() [1/3]

template<typename T_real, typename T_complex>

T_complex PolynomialRoots::CubicT< T_real, T_complex >::eval ( T_complex const & x ) const

inline

Evaluate the cubic polynomial at a complex point.

Parameters

[in]

x

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

Returns

the value \( p(x) \)

eval() [2/3]

template<typename T_real, typename T_complex>

T_real PolynomialRoots::CubicT< T_real, T_complex >::eval ( T_real const & x ) const

inline

Evaluate the cubic polynomial at a real point.

Parameters

[in]

x

value where compute \( p(x) \)

Returns

the value \( p(x) \)

eval() [3/3]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::eval ( T_real const & x, T_real & p, T_real & dp ) const

inline

Evaluate the cubic polynomial and its derivative at a real point.

Parameters

[in]	x	value where compute \( p(x) \)
[out]	p	value \( p(x) \)
[out]	dp	value \( p'(x) \)

get_negative_roots()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::get_negative_roots

(

T_real

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()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::get_positive_roots

(

T_real

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()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::get_real_roots

(

T_real

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_root()

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root ( integer const i, T_real & re, T_real & im ) const

inline

Store the i-th root in split real/imaginary form.

Parameters

[in]	i	root index in [0,2]
[out]	re	real part of the selected root
[out]	im	imaginary part of the selected root

get_root0() [1/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root0 ( T_complex & r ) const

inline

First complex or real root.

get_root0() [2/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root0 ( T_real & re, T_real & im ) const

inline

First complex or real root.

get_root1() [1/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root1 ( T_complex & r ) const

inline

Second complex or real root.

get_root1() [2/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root1 ( T_real & re, T_real & im ) const

inline

Second complex or real root.

get_root2() [1/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root2 ( T_complex & r ) const

inline

Third complex or real root.

get_root2() [2/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::get_root2 ( T_real & re, T_real & im ) const

inline

Third complex or real root.

get_roots_in_open_range()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::get_roots_in_open_range	(	T_real const &	a,
		T_real const &	b,
		T_real	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()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::get_roots_in_range	(	T_real const &	a,
		T_real const &	b,
		T_real	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()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::getNegativeRoots ( T_real r[] ) const

inline

Alias of get_negative_roots().

getPositiveRoots()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::getPositiveRoots ( T_real r[] ) const

inline

Alias of get_positive_roots().

getRealRoots()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::getRealRoots ( T_real r[] ) const

inline

Alias of get_real_roots().

getRoot0() [1/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::getRoot0 ( T_complex & r ) const

inline

Alias of get_root0().

getRoot0() [2/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::getRoot0 ( T_real & re, T_real & im ) const

inline

Alias of get_root0().

getRoot1() [1/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::getRoot1 ( T_complex & r ) const

inline

Alias of get_root1().

getRoot1() [2/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::getRoot1 ( T_real & re, T_real & im ) const

inline

Alias of get_root1().

getRoot2() [1/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::getRoot2 ( T_complex & r ) const

inline

Alias of get_root2().

getRoot2() [2/2]

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::getRoot2 ( T_real & re, T_real & im ) const

inline

Alias of get_root2().

getRootsInOpenRange()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::getRootsInOpenRange ( T_real const & a, T_real const & b, T_real r[] ) const

inline

Alias of get_roots_in_open_range().

getRootsInRange()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::getRootsInRange ( T_real const & a, T_real const & b, T_real r[] ) const

inline

Alias of get_roots_in_range().

info()

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::info

(

ostream_type &

s

)

const

Print info of the roots of the polynomial.

num_roots()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::num_roots ( ) const

inline

Number of found roots.

numRoots()

template<typename T_real, typename T_complex>

integer PolynomialRoots::CubicT< T_real, T_complex >::numRoots ( ) const

inline

Alias of num_roots().

real_root0()

template<typename T_real, typename T_complex>

T_real PolynomialRoots::CubicT< T_real, T_complex >::real_root0 ( ) const

inline

Return the first stored real component.

When complex_root() is true, this is the common real part of the conjugate pair returned by root0() and root1().

real_root1()

template<typename T_real, typename T_complex>

T_real PolynomialRoots::CubicT< T_real, T_complex >::real_root1 ( ) const

inline

Return the second stored real component.

When complex_root() is true, this is the positive imaginary part of the conjugate pair. Otherwise it is the second real root.

real_root2()

template<typename T_real, typename T_complex>

T_real PolynomialRoots::CubicT< T_real, T_complex >::real_root2 ( ) const

inline

Return the third stored real root.

root()

template<typename T_real, typename T_complex>

T_complex PolynomialRoots::CubicT< T_real, T_complex >::root ( integer const i ) const

inline

Return the i-th root as a complex value.

Parameters

[in]

i

root index in [0,2]

Returns

requested root, or zero for an invalid index

root0()

template<typename T_real, typename T_complex>

T_complex PolynomialRoots::CubicT< T_real, T_complex >::root0 ( ) const

inline

First complex or real root.

root1()

template<typename T_real, typename T_complex>

T_complex PolynomialRoots::CubicT< T_real, T_complex >::root1 ( ) const

inline

Second complex or real root.

root2()

template<typename T_real, typename T_complex>

T_complex PolynomialRoots::CubicT< T_real, T_complex >::root2 ( ) const

inline

Third complex or real root.

setup()

template<typename T_real, typename T_complex>

void PolynomialRoots::CubicT< T_real, T_complex >::setup ( T_real const & a, T_real const & b, T_real const & c, T_real const & 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()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::triple_root ( ) const

inline

Has a triple root?

tripleRoot()

template<typename T_real, typename T_complex>

bool PolynomialRoots::CubicT< T_real, T_complex >::tripleRoot ( ) const

inline

Alias of triple_root().

---

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

• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/quarticRootsFlocke/src/PolynomialRoots.hh
• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/quarticRootsFlocke/src/PolynomialRoots-2-Cubic.cc