Class Quartic

Class Documentation

class PolynomialRoots::Quartic

Quartic polynomial class

Constructor

double a = 1;
double b = 2;
double c = 3;
double d = 3;
double e = 3;
Quartic p(a,b,c,d,e); // build an solve ``a x^4 + b x^3 + c x^2 + d x + e = 0``


Quartic p;
p.setup(a,b,c,d,e); // build an solve ``a x^4 + b x^3 + c x^2 + d x + e = 0``

Get kind of solution

int nroots = p.numRoots(); 
int nroots = p.numRealRoots();
int nroots = p.numComplexRoots();

Get real roots

double r_min = 0;
double r_max = 2;
double r[4];
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();
double r3 = p.real_root3();
complexType r0 = p.root0();
complexType r1 = p.root1();
complexType r2 = p.root2();
complexType r3 = p.root3();

complexType 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 );
p.getRoot3( re, im );
p.getRoot3( 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 );

Public Functions

inline Quartic()
inline Quartic(valueType _a, valueType _b, valueType _c, valueType _d, valueType _e)
inline void setup(valueType a, valueType b, valueType c, valueType d, valueType e)

Compute the roots of quartic polynomial \( a x^4 + b x^3 + c x^2 + d x + e \)

Parameters

  • a – [in] coefficient of \( x^4 \)

  • b – [in] coefficient of \( x^3 \)

  • c – [in] coefficient of \( x^2 \)

  • d – [in] coefficient of \( x \)

  • e – [in] coefficient of \( x^0 \)

inline indexType numRoots() const

Number of roots found.

inline indexType numRealRoots() const

Number of real roots.

inline indexType numComplexRoots() const

Number of complex roots

indexType getRealRoots(valueType r[]) const

Get the real roots.

Parameters

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

Returns

the total number of real roots, 0, 1, 2, 3 or 4

indexType getPositiveRoots(valueType r[]) const

Get positive real roots

Parameters

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

Returns

the total number of positive real roots, 0, 1, 2, 3 or 4

indexType getNegativeRoots(valueType r[]) const

Get negative real roots.

Parameters

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

Returns

the total number of negative real roots, 0, 1, 2, 3 or 4

indexType getRootsInRange(valueType a, valueType b, valueType r[]) const

Get real roots in a closed range.

Parameters

  • a – [in] left side of the range

  • b – [in] right side of the range

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

Returns

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

indexType getRootsInOpenRange(valueType a, valueType b, valueType r[]) const

Get real roots in an open range.

Parameters

  • a – [in] left side of the range

  • b – [in] right side of the range

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

Returns

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

inline valueType real_root0() const

First real root.

inline valueType real_root1() const

Second real root.

inline valueType real_root2() const

Third real root.

inline valueType real_root3() const

Fourth real root.

inline complexType root0() const

First real or complex root.

inline complexType root1() const

Second real or complex root.

inline complexType root2() const

Third real or complex root.

inline complexType root3() const

4th real or complex root.

inline void getRoot0(valueType &re, valueType &im) const

First real or complex root.

inline void getRoot0(complexType &r) const

First real or complex root.

inline void getRoot1(valueType &re, valueType &im) const

Second real or complex root.

inline void getRoot1(complexType &r) const

Second real or complex root.

inline void getRoot2(valueType &re, valueType &im) const

Third real or complex root.

inline void getRoot2(complexType &r) const

Third real or complex root.

inline void getRoot3(valueType &re, valueType &im) const

4th real or complex root.

inline void getRoot3(complexType &r) const

4th real or complex root.

inline valueType eval(valueType x) const

Evalute the quartic polynomial.

Parameters

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

Returns

the value \( p(x) \)

inline complexType eval(complexType const &x) const

Evalute the quartic polynomial.

Parameters

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

Returns

the value \( p(x) \)

void info(std::ostream &s) const

Print info of the roots of the polynomial.

bool check(std::ostream &s) const

Check tolerenace and quality of the computed roots.