Kratos::PolynomialUtilities Namespace Reference

Typedefs
using	PolynomialType = std::vector< double >
using	IntervalType = std::array< double, 2 >

Functions
std::size_t	Degree (const PolynomialType &rPolynomial)
double	Evaluate (const PolynomialType &rPolynomial, double x)
PolynomialType	Differentiate (const PolynomialType &rPolynomial)
PolynomialType	Multiply (const PolynomialType &rA, const PolynomialType &rB)
void	Divide (PolynomialType &rQuotient, PolynomialType &rRemainder, const PolynomialType &rA, const PolynomialType &rB)
void	IsolateRoots (std::vector< IntervalType > &rRootIntervals, const PolynomialType &rPolynomial, const IntervalType &rRange)
	Define disjoint subintervals of rRange, each containing a single root of rPolynomial. More...
double	FindRoot (const PolynomialType &rPolynomial, const IntervalType &rRange)
	Find a root of rPolynomial within the interval defined by rRange. More...

Typedef Documentation

IntervalType

using Kratos::PolynomialUtilities::IntervalType = typedef std::array<double, 2>

PolynomialType

using Kratos::PolynomialUtilities::PolynomialType = typedef std::vector<double>

Function Documentation

Degree()

std::size_t Kratos::PolynomialUtilities::Degree

(

const PolynomialType &

rPolynomial

)

Degree of the polynomial

Differentiate()

PolynomialType Kratos::PolynomialUtilities::Differentiate

(

const PolynomialType &

rPolynomial

)

Derivative of the polynomial

Divide()

void Kratos::PolynomialUtilities::Divide	(	PolynomialType &	rQuotient,
		PolynomialType &	rRemainder,
		const PolynomialType &	rA,
		const PolynomialType &	rB
	)

Euclidian division of polynomials rA / rB = rQuotient*rB + rRemainder

Evaluate()

double Kratos::PolynomialUtilities::Evaluate	(	const PolynomialType &	rPolynomial,
		double	x
	)

Evaluate the polynomial at the given x value

FindRoot()

double Kratos::PolynomialUtilities::FindRoot	(	const PolynomialType &	rPolynomial,
		const IntervalType &	rRange
	)

Find a root of rPolynomial within the interval defined by rRange.

The implementation assumes that rRange contains exactly one root and that rRange[0]*rRange[1] < 0

Parameters

rPolynomial	the polynomial
rRange	interval containing the root

Returns

The root.

See also

IsolateRoots to identify suitable ranges.

IsolateRoots()

void Kratos::PolynomialUtilities::IsolateRoots	(	std::vector< IntervalType > &	rRootIntervals,
		const PolynomialType &	rPolynomial,
		const IntervalType &	rRange
	)

Define disjoint subintervals of rRange, each containing a single root of rPolynomial.

The function uses the signs of the Sturm sequence in order to isolate the roots.

Parameters

rRootIntervals	each term defines a subinterval of rRange containing a single root.
rPolynomial	the polynomial for which we want to find the roots.
rRange	the interval in which the roots are to be found.

Multiply()

PolynomialType Kratos::PolynomialUtilities::Multiply	(	const PolynomialType &	rA,
		const PolynomialType &	rB
	)

Product of two polynomials