Detailed Description

The base class for all Polynomials.

A clear and straight forward implementation of polynomial operations. Still very basic, but serves its purpose.

Definition at line 27 of file PolyMath.h.

#include <PolyMath.h>

Inheritance diagram for CoolProp::Polynomial2D:

Public Member Functions
	Polynomial2D ()=default
	Constructors. More...

virtual	~Polynomial2D ()=default
	Destructor. No implementation. More...

Eigen::MatrixXd	convertCoefficients (const std::vector< double > &coefficients)

Eigen::MatrixXd	convertCoefficients (const std::vector< std::vector< double > > &coefficients)

bool	checkCoefficients (const Eigen::MatrixXd &coefficients, const unsigned int rows, const unsigned int columns)
	Basic checks for coefficient vectors. More...

Eigen::MatrixXd	integrateCoeffs (const Eigen::MatrixXd &coefficients, const int &axis, const int &times)
	Integration functions. More...

Eigen::MatrixXd	deriveCoeffs (const Eigen::MatrixXd &coefficients, const int &axis=-1, const int &times=1)
	Derivative coefficients calculation. More...

double	evaluate (const Eigen::MatrixXd &coefficients, const double &x_in)
	The core functions to evaluate the polynomial. More...

double	evaluate (const Eigen::MatrixXd &coefficients, const double &x_in, const double &y_in)

double	derivative (const Eigen::MatrixXd &coefficients, const double &x_in, const double &y_in, const int &axis)

double	integral (const Eigen::MatrixXd &coefficients, const double &x_in, const double &y_in, const int &axis)

Eigen::VectorXd	solve (const Eigen::MatrixXd &coefficients, const double &in, const double &z_in, const int &axis)

double	solve_limits (const Eigen::MatrixXd &coefficients, const double &in, const double &z_in, const double &min, const double &max, const int &axis)

double	solve_guess (const Eigen::MatrixXd &coefficients, const double &in, const double &z_in, const double &guess, const int &axis)

Protected Member Functions
double	solve_limits (Poly2DResidual *res, const double &min, const double &max)

double	solve_guess (Poly2DResidual *res, const double &guess)

double	simplePolynomial (const std::vector< double > &coefficients, double x)
	Simple polynomial function generator. <- Deprecated due to poor performance, use Horner-scheme instead. More...

double	simplePolynomial (const std::vector< std::vector< double > > &coefficients, double x, double y)

double	baseHorner (const std::vector< double > &coefficients, double x)
	Horner function generator implementations. More...

double	baseHorner (const std::vector< std::vector< double > > &coefficients, double x, double y)

bool	do_debug ()

Constructor & Destructor Documentation

◆ Polynomial2D()

CoolProp::Polynomial2D::Polynomial2D ( )

default

Constructors.

◆ ~Polynomial2D()

virtual CoolProp::Polynomial2D::~Polynomial2D ( )

virtualdefault

Destructor. No implementation.

Member Function Documentation

◆ baseHorner() [1/2]

double CoolProp::Polynomial2D::baseHorner	(	const std::vector< double > &	coefficients,
		double	x
	)

protected

Horner function generator implementations.

Represent polynomials according to Horner's scheme. This avoids unnecessary multiplication and thus speeds up calculation. Deprecated since we moved everything to the Eigen framework.

Represent polynomials according to Horner's scheme. This avoids unnecessary multiplication and thus speeds up calculation.

Definition at line 283 of file PolyMath.cpp.

◆ baseHorner() [2/2]

double CoolProp::Polynomial2D::baseHorner	(	const std::vector< std::vector< double > > &	coefficients,
		double	x,
		double	y
	)

protected

Definition at line 294 of file PolyMath.cpp.

◆ checkCoefficients()

bool CoolProp::Polynomial2D::checkCoefficients	(	const Eigen::MatrixXd &	coefficients,
		const unsigned int	rows,
		const unsigned int	columns
	)

Basic checks for coefficient vectors.

Starts with only the first coefficient dimension and checks the matrix size against the parameters rows and columns.

Parameters

coefficients	matrix containing the ordered coefficients
rows	unsigned integer value that represents the desired degree of the polynomial in the 1st dimension
columns	unsigned integer value that represents the desired degree of the polynomial in the 2nd dimension

Definition at line 30 of file PolyMath.cpp.

◆ convertCoefficients() [1/2]

Eigen::MatrixXd CoolProp::Polynomial2D::convertCoefficients ( const std::vector< double > & coefficients )

inline

Convert the coefficient vector.

Parameters

coefficients vector containing the ordered coefficients

Definition at line 40 of file PolyMath.h.

◆ convertCoefficients() [2/2]

Eigen::MatrixXd CoolProp::Polynomial2D::convertCoefficients ( const std::vector< std::vector< double > > & coefficients )

inline

Convert the coefficient matrix.

Parameters

coefficients matrix containing the ordered coefficients

Definition at line 45 of file PolyMath.h.

◆ derivative()

double CoolProp::Polynomial2D::derivative	(	const Eigen::MatrixXd &	coefficients,
		const double &	x_in,
		const double &	y_in,
		const int &	axis = `-1`
	)

Parameters

coefficients	vector containing the ordered coefficients
x_in	double value that represents the current input in the 1st dimension
y_in	double value that represents the current input in the 2nd dimension
axis	unsigned integer value that represents the axis to derive for (0=x, 1=y)

Definition at line 178 of file PolyMath.cpp.

◆ deriveCoeffs()

Eigen::MatrixXd CoolProp::Polynomial2D::deriveCoeffs	(	const Eigen::MatrixXd &	coefficients,
		const int &	axis = `-1`,
		const int &	times = `1`
	)

Derivative coefficients calculation.

Deriving coefficients for polynomials is done by multiplying the original coefficients with i and lowering the order by 1.

Parameters

coefficients	matrix containing the ordered coefficients
axis	unsigned integer value that represents the desired direction of derivation
times	integer value that represents the desired order of derivation

Deriving coefficients for polynomials is done by multiplying the original coefficients with i and lowering the order by 1.

Definition at line 103 of file PolyMath.cpp.

◆ do_debug()

bool CoolProp::Polynomial2D::do_debug ( )

inlineprotected

Definition at line 172 of file PolyMath.h.

◆ evaluate() [1/2]

double CoolProp::Polynomial2D::evaluate	(	const Eigen::MatrixXd &	coefficients,
		const double &	x_in
	)

The core functions to evaluate the polynomial.

It is here we implement the different special functions that allow us to specify certain types of polynomials.

Try to avoid many calls to the derivative and integral functions. Both of them have to calculate the new coefficients internally, which slows things down. Instead, you should use the deriveCoeffs and integrateCoeffs functions and store the coefficient matrix you need for future calls to evaluate derivative and integral.

Parameters

coefficients	vector containing the ordered coefficients
x_in	double value that represents the current input in the 1st dimension

It is here we implement the different special functions that allow us to specify certain types of polynomials. The derivative might bee needed during the solution process of the solver. It could also be a protected function...

Definition at line 159 of file PolyMath.cpp.

◆ evaluate() [2/2]

double CoolProp::Polynomial2D::evaluate	(	const Eigen::MatrixXd &	coefficients,
		const double &	x_in,
		const double &	y_in
	)

Parameters

coefficients	vector containing the ordered coefficients
x_in	double value that represents the current input in the 1st dimension
y_in	double value that represents the current input in the 2nd dimension

Definition at line 165 of file PolyMath.cpp.

◆ integral()

double CoolProp::Polynomial2D::integral	(	const Eigen::MatrixXd &	coefficients,
		const double &	x_in,
		const double &	y_in,
		const int &	axis = `-1`
	)

Parameters

coefficients	vector containing the ordered coefficients
x_in	double value that represents the current input in the 1st dimension
y_in	double value that represents the current input in the 2nd dimension
axis	unsigned integer value that represents the axis to integrate for (0=x, 1=y)

Definition at line 182 of file PolyMath.cpp.

◆ integrateCoeffs()

Eigen::MatrixXd CoolProp::Polynomial2D::integrateCoeffs	(	const Eigen::MatrixXd &	coefficients,
		const int &	axis = `-1`,
		const int &	times = `1`
	)

Integration functions.

Integrating coefficients for polynomials is done by dividing the original coefficients by (i+1) and elevating the order by 1 through adding a zero as first coefficient. Some reslicing needs to be applied to integrate along the x-axis. In the brine/solution equations, reordering of the parameters avoids this expensive operation. However, it is included for the sake of completeness.

Parameters

coefficients	matrix containing the ordered coefficients
axis	unsigned integer value that represents the desired direction of integration
times	integer value that represents the desired order of integration

Integrating coefficients for polynomials is done by dividing the original coefficients by (i+1) and elevating the order by 1 through adding a zero as first coefficient. Some reslicing needs to be applied to integrate along the x-axis. In the brine/solution equations, reordering of the parameters avoids this expensive operation. However, it is included for the sake of completeness.

Definition at line 52 of file PolyMath.cpp.

◆ simplePolynomial() [1/2]

double CoolProp::Polynomial2D::simplePolynomial	(	const std::vector< double > &	coefficients,
		double	x
	)

protected

Simple polynomial function generator. <- Deprecated due to poor performance, use Horner-scheme instead.

Base function to produce n-th order polynomials based on the length of the coefficient vector. Starts with only the first coefficient at x^0.

Definition at line 258 of file PolyMath.cpp.

◆ simplePolynomial() [2/2]

double CoolProp::Polynomial2D::simplePolynomial	(	const std::vector< std::vector< double > > &	coefficients,
		double	x,
		double	y
	)

protected

Definition at line 267 of file PolyMath.cpp.

◆ solve()

Eigen::VectorXd CoolProp::Polynomial2D::solve	(	const Eigen::MatrixXd &	coefficients,
		const double &	in,
		const double &	z_in,
		const int &	axis = `-1`
	)

Returns a vector with ALL the real roots of p(x_in,y_in)-z_in

Parameters

coefficients	vector containing the ordered coefficients
in	double value that represents the current input in x (1st dimension) or y (2nd dimension)
z_in	double value that represents the current output in the 3rd dimension
axis	unsigned integer value that represents the axis to solve for (0=x, 1=y)

Definition at line 213 of file PolyMath.cpp.

◆ solve_guess() [1/2]

double CoolProp::Polynomial2D::solve_guess	(	const Eigen::MatrixXd &	coefficients,
		const double &	in,
		const double &	z_in,
		const double &	guess,
		const int &	axis
	)

Uses the Newton solver to find the roots of p(x_in,y_in)-z_in

Parameters

coefficients	vector containing the ordered coefficients
in	double value that represents the current input in x (1st dimension) or y (2nd dimension)
z_in	double value that represents the current output in the 3rd dimension
guess	double value that represents the start value
axis	unsigned integer value that represents the axis to solve for (0=x, 1=y)

Definition at line 249 of file PolyMath.cpp.

◆ solve_guess() [2/2]

double CoolProp::Polynomial2D::solve_guess	(	Poly2DResidual *	res,
		const double &	guess
	)

protected

Uses the Newton solver to find the roots of p(x_in,y_in)-z_in

Parameters

res	Poly2DResidual object to calculate residuals and derivatives
guess	double value that represents the start value

Definition at line 203 of file PolyMath.cpp.

◆ solve_limits() [1/2]

double CoolProp::Polynomial2D::solve_limits	(	const Eigen::MatrixXd &	coefficients,
		const double &	in,
		const double &	z_in,
		const double &	min,
		const double &	max,
		const int &	axis
	)

Uses the Brent solver to find the roots of p(x_in,y_in)-z_in

Parameters

coefficients	vector containing the ordered coefficients
in	double value that represents the current input in x (1st dimension) or y (2nd dimension)
z_in	double value that represents the current output in the 3rd dimension
min	double value that represents the minimum value
max	double value that represents the maximum value
axis	unsigned integer value that represents the axis to solve for (0=x, 1=y)

Definition at line 243 of file PolyMath.cpp.

◆ solve_limits() [2/2]

double CoolProp::Polynomial2D::solve_limits	(	Poly2DResidual *	res,
		const double &	min,
		const double &	max
	)

protected

Uses the Brent solver to find the roots of p(x_in,y_in)-z_in

Parameters

res	Poly2DResidual object to calculate residuals and derivatives
min	double value that represents the minimum value
max	double value that represents the maximum value

Definition at line 190 of file PolyMath.cpp.

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

include/CoolProp/numerics/PolyMath.h
src/PolyMath.cpp

Detailed Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ Polynomial2D()

◆ ~Polynomial2D()

Member Function Documentation

◆ baseHorner() [1/2]

◆ baseHorner() [2/2]

◆ checkCoefficients()

◆ convertCoefficients() [1/2]

◆ convertCoefficients() [2/2]

◆ derivative()

◆ deriveCoeffs()

◆ do_debug()

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ integral()

◆ integrateCoeffs()

◆ simplePolynomial() [1/2]

◆ simplePolynomial() [2/2]

◆ solve()

◆ solve_guess() [1/2]

◆ solve_guess() [2/2]

◆ solve_limits() [1/2]

◆ solve_limits() [2/2]