PolynomialRoots::Quadratic Class Reference

#include <PolynomialRoots.hh>

Public Member Functions
	Quadratic ()
	Quadratic (real_type a, real_type b, real_type c)
void	setup (real_type a, real_type b, real_type c)
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
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
complex_type	root0 () const
complex_type	root1 () 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
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

Quadratic polynomial class

Constructor

double a = 1;
double b = 2;
double c = 3;
Quadratic q(a,b,c); // build an solve `a x^2 + b x + c = 0`
 
Quadratic q;
q.setup(a,b,c); // build an solve `a x^2 + b x + c = 0`

Get kind of solution

int  nroots            = q.num_roots();
bool has_complex_root  = q.complex_root();
bool has_a_double_root = q.double_root();

Get real roots

double r_min = 0;
double r_max = 2;
double r[2];
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();
complex_type r0 = p.root0();
complex_type r1 = p.root1();
 
complex_type r;
double re, im;
p.getRoot0( re, im );
p.getRoot0( r );
p.getRoot1( re, im );
p.getRoot1( 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 );

Constructor & Destructor Documentation

Quadratic() [1/2]

PolynomialRoots::Quadratic::Quadratic ( )

inline

Quadratic() [2/2]

PolynomialRoots::Quadratic::Quadratic ( real_type a, real_type b, real_type c )

inline

Build the object that store the roots of the quadratic polynomial

\[ q(x) = a x^2 + b x + c \]

Parameters

[in]	a	leading coefficient of \( q(x) \)
[in]	b	coefficient of \( x \)
[in]	c	coefficient of \( x^0 \)

Member Function Documentation

check()

bool PolynomialRoots::Quadratic::check

(

ostream_type &

s

)

const

Check tolerance and quality of the computed roots

complex_root()

bool PolynomialRoots::Quadratic::complex_root ( ) const

inline

true if roots are complex conjugated

complexRoot()

bool PolynomialRoots::Quadratic::complexRoot ( ) const

inline

alias of complex_root

double_root()

bool PolynomialRoots::Quadratic::double_root ( ) const

inline

true if \( p(x) = a x^2 + b x + c = (x-r)^2 \)

doubleRoot()

bool PolynomialRoots::Quadratic::doubleRoot ( ) const

inline

alias of double_root

eval() [1/3]

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

inline

Evalute the quadratic polynomial

Parameters

[in]

x

value where compute \( p(x)=ax^2+bx+c \)

Returns

the value \( p(x) \)

eval() [2/3]

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

inline

Evaluate the quadratic polynomial

Parameters

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

Returns

the value \( p(x) \)

eval() [3/3]

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

inline

Evaluate the polynomial with its derivative

Parameters

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

get_negative_roots()

integer PolynomialRoots::Quadratic::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 or 2

get_positive_roots()

integer PolynomialRoots::Quadratic::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 or 2

get_real_roots()

integer PolynomialRoots::Quadratic::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 or 2

get_root0() [1/2]

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

inline

Get the first root (complex or real)

Parameters

[out]

r

the first complex root

get_root0() [2/2]

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

inline

Get the first root (complex or real)

Parameters

[out]	re	the first complex root, real part
[out]	im	the first complex root, imaginary part

get_root1() [1/2]

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

inline

Get the second root (complex or real)

Parameters

[out]

r

the second complex root

get_root1() [2/2]

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

inline

Get the second root (complex or real)

Parameters

[out]	re	the second complex root, real part
[out]	im	the second complex root, imaginary part

get_roots_in_open_range()

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

inline

alias of get_negative_roots

getPositiveRoots()

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

inline

alias of get_positive_roots

getRealRoots()

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

inline

alias of get_real_roots

getRoot0() [1/2]

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

inline

alias of get_root0

getRoot0() [2/2]

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

inline

alias of get_root0

getRoot1() [1/2]

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

inline

alias of get_root1

getRoot1() [2/2]

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

inline

alias of get_root1

getRootsInOpenRange()

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

inline

alias of get_roots_in_open_range

getRootsInRange()

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

inline

alias of get_roots_in_range

info()

void PolynomialRoots::Quadratic::info

(

ostream_type &

s

)

const

Print info of the roots of the polynomial.

num_roots()

integer PolynomialRoots::Quadratic::num_roots ( ) const

inline

Return the number of computed roots of

\[ q(x) = a x^2 + b x + c \]

Normally return 2 but if e.g. \( a = 0 \) return 1 or less depending on the values of \( a, b, c \)

Returns

number of computed roots

numRoots()

integer PolynomialRoots::Quadratic::numRoots ( ) const

inline

alias of num_roots

real_root0()

real_type PolynomialRoots::Quadratic::real_root0 ( ) const

inline

The first real root

real_root1()

real_type PolynomialRoots::Quadratic::real_root1 ( ) const

inline

The second real root

root0()

complex_type PolynomialRoots::Quadratic::root0 ( ) const

inline

The first complex root

root1()

complex_type PolynomialRoots::Quadratic::root1 ( ) const

inline

The second complex root

setup()

void PolynomialRoots::Quadratic::setup ( real_type a, real_type b, real_type c )

inline

Setup the object that store the roots of the quadratic polynomial

\[ q(x) = a x^2 + b x + c \]

Parameters

[in]	a	leading coefficient of \( q(x) \)
[in]	b	coefficient of \( x \)
[in]	c	coefficient of \( x^0 \)

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

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