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https://github.com/CoolProp/CoolProp.git
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536 lines
26 KiB
C++
536 lines
26 KiB
C++
#ifndef POLYMATH_H
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#define POLYMATH_H
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#include "CoolPropTools.h"
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#include "Exceptions.h"
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#include <vector>
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#include <string>
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#include "Solvers.h"
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//#include <numeric> // inner_product
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//#include <sstream>
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//#include "float.h"
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namespace CoolProp{
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/// The base class for Polynomials
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class BasePolynomial{
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protected:
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bool DEBUG;
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public:
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// Constructor
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BasePolynomial();
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// Destructor. No implementation
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virtual ~BasePolynomial(){};
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public:
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/// Basic checks for coefficient vectors.
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/** Starts with only the first coefficient dimension
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* and checks the vector length against parameter n. */
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bool checkCoefficients(const std::vector<double> &coefficients, const unsigned int n);
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bool checkCoefficients(const std::vector< std::vector<double> > &coefficients, const unsigned int rows, const unsigned int columns);
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/** Integrating coefficients for polynomials is done by dividing the
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* original coefficients by (i+1) and elevating the order by 1
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* through adding a zero as first coefficient.
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* Some reslicing needs to be applied to integrate along the x-axis.
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* In the brine/solution equations, reordering of the parameters
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* avoids this expensive operation. However, it is included for the
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* sake of completeness.
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*/
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std::vector<double> integrateCoeffs(const std::vector<double> &coefficients);
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std::vector< std::vector<double> > integrateCoeffs(const std::vector< std::vector<double> > &coefficients, bool axis);
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/** Deriving coefficients for polynomials is done by multiplying the
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* original coefficients with i and lowering the order by 1.
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*
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* It is not really deprecated, but untested and therefore a warning
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* is issued. Please check this method before you use it.
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*/
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std::vector<double> deriveCoeffs(const std::vector<double> &coefficients);
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std::vector< std::vector<double> > deriveCoeffs(const std::vector< std::vector<double> > &coefficients, unsigned int axis);
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private:
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/** The core of the polynomial wrappers are the different
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* implementations that follow below. In case there are
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* new calculation schemes available, please do not delete
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* the implementations, but mark them as deprecated.
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* The old functions are good for debugging since the
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* structure is easier to read than the backward Horner-scheme
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* or the recursive Horner-scheme.
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*/
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/// Simple polynomial function generator. <- Deprecated due to poor performance, use Horner-scheme instead
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/** Base function to produce n-th order polynomials
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* based on the length of the coefficient vector.
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* Starts with only the first coefficient at x^0. */
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DEPRECATED(double simplePolynomial(const std::vector<double> &coefficients, double x));
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DEPRECATED(double simplePolynomial(const std::vector<std::vector<double> > &coefficients, double x, double y));
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/// Simple integrated polynomial function generator.
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/** Base function to produce integrals of n-th order polynomials based on
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* the length of the coefficient vector.
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* Starts with only the first coefficient at x^0 */
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///Indefinite integral in x-direction
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double simplePolynomialInt(const std::vector<double> &coefficients, double x);
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///Indefinite integral in y-direction only
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double simplePolynomialInt(const std::vector<std::vector<double> > &coefficients, double x, double y);
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/// Simple integrated polynomial function generator divided by independent variable.
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/** Base function to produce integrals of n-th order
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* polynomials based on the length of the coefficient
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* vector. Starts with only the first coefficient at x^0 */
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///Indefinite integral of a polynomial divided by its independent variable
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double simpleFracInt(const std::vector<double> &coefficients, double x);
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///Indefinite integral of a polynomial divided by its 2nd independent variable
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double simpleFracInt(const std::vector<std::vector<double> > &coefficients, double x, double y);
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/** Simple integrated centred(!) polynomial function generator divided by independent variable.
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* We need to rewrite some of the functions in order to
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* use central fit. Having a central temperature xbase
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* allows for a better fit, but requires a different
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* formulation of the fracInt function group. Other
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* functions are not affected.
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* Starts with only the first coefficient at x^0 */
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///Helper function to calculate the D vector:
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double factorial(double nValue);
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double binom(double nValue, double nValue2);
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std::vector<double> fracIntCentralDvector(int m, double x, double xbase);
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///Indefinite integral of a centred polynomial divided by its independent variable
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double fracIntCentral(const std::vector<double> &coefficients, double x, double xbase);
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/// Horner function generator implementations
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/** Represent polynomials according to Horner's scheme.
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* This avoids unnecessary multiplication and thus
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* speeds up calculation.
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*/
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double baseHorner(const std::vector<double> &coefficients, double x);
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double baseHorner(const std::vector< std::vector<double> > &coefficients, double x, double y);
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///Indefinite integral in x-direction
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double baseHornerInt(const std::vector<double> &coefficients, double x);
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///Indefinite integral in y-direction only
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double baseHornerInt(const std::vector<std::vector<double> > &coefficients, double x, double y);
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///Indefinite integral of a polynomial divided by its independent variable
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double baseHornerFracInt(const std::vector<double> &coefficients, double x);
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///Indefinite integral of a polynomial divided by its 2nd independent variable
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double baseHornerFracInt(const std::vector<std::vector<double> > &coefficients, double x, double y);
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/** Alternatives
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* Simple functions that heavily rely on other parts of this file.
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* We still need to check which combinations yield the best
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* performance.
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*/
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///Derivative in x-direction
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double deriveIn2Steps(const std::vector<double> &coefficients, double x); // TODO: Check results!
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///Derivative in terms of x(axis=true) or y(axis=false).
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double deriveIn2Steps(const std::vector< std::vector<double> > &coefficients, double x, double y, bool axis); // TODO: Check results!
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///Indefinite integral in x-direction
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double integrateIn2Steps(const std::vector<double> &coefficients, double x);
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///Indefinite integral in terms of x(axis=true) or y(axis=false).
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double integrateIn2Steps(const std::vector< std::vector<double> > &coefficients, double x, double y, bool axis);
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///Indefinite integral in x-direction of a polynomial divided by its independent variable
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double fracIntIn2Steps(const std::vector<double> &coefficients, double x);
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///Indefinite integral in y-direction of a polynomial divided by its 2nd independent variable
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double fracIntIn2Steps(const std::vector<std::vector<double> > &coefficients, double x, double y);
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///Indefinite integral of a centred polynomial divided by its 2nd independent variable
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double fracIntCentral2Steps(const std::vector<std::vector<double> > &coefficients, double x, double y, double ybase);
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public:
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/** Here we define the functions that should be used by the
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* respective implementations. Please do no use any other
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* method since this would break the purpose of this interface.
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* Note that the functions below are supposed to be aliases
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* to implementations declared elsewhere in this file.
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*/
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/** Everything related to the normal polynomials goes in this
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* section, holds all the functions for evaluating polynomials.
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*/
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/// Evaluates a one-dimensional polynomial for the given coefficients
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input
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virtual inline double polyval(const std::vector<double> &coefficients, double x){
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return baseHorner(coefficients,x);
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}
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/// Evaluates a two-dimensional polynomial for the given coefficients
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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virtual inline double polyval(const std::vector< std::vector<double> > &coefficients, double x, double y){
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return baseHorner(coefficients,x,y);
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}
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/** Everything related to the integrated polynomials goes in this
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* section, holds all the functions for evaluating polynomials.
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*/
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/// Evaluates the indefinite integral of a one-dimensional polynomial
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input
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virtual inline double polyint(const std::vector<double> &coefficients, double x){
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return baseHornerInt(coefficients,x);
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}
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/// Evaluates the indefinite integral of a two-dimensional polynomial along the 2nd axis (y)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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virtual inline double polyint(const std::vector< std::vector<double> > &coefficients, double x, double y){
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return baseHornerInt(coefficients,x,y);
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}
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/** Everything related to the derived polynomials goes in this
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* section, holds all the functions for evaluating polynomials.
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*/
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/// Evaluates the derivative of a one-dimensional polynomial
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input
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virtual inline double polyder(const std::vector<double> &coefficients, double x){
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return deriveIn2Steps(coefficients,x);
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}
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/// Evaluates the derivative of a two-dimensional polynomial along the 2nd axis (y)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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virtual inline double polyder(const std::vector< std::vector<double> > &coefficients, double x, double y){
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return deriveIn2Steps(coefficients,x,y,false);
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}
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/** Everything related to the polynomials divided by one variable goes in this
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* section, holds all the functions for evaluating polynomials.
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*/
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/// Evaluates the indefinite integral of a one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current position
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virtual inline double polyfracval(const std::vector<double> &coefficients, double x){
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return baseHornerFracInt(coefficients,x);
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}
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/// Evaluates the indefinite integral of a two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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virtual inline double polyfracval(const std::vector< std::vector<double> > &coefficients, double x, double y){
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return baseHornerFracInt(coefficients,x,y);
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}
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/** Everything related to the integrated polynomials divided by one variable goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Evaluates the indefinite integral of a one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current position
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virtual inline double polyfracint(const std::vector<double> &coefficients, double x){
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return baseHornerFracInt(coefficients,x);
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}
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/// Evaluates the indefinite integral of a two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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virtual inline double polyfracint(const std::vector< std::vector<double> > &coefficients, double x, double y){
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return baseHornerFracInt(coefficients,x,y);
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}
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/// Evaluates the indefinite integral of a centred one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current position
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/// @param xbase central temperature for fitted function
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virtual inline double polyfracintcentral(const std::vector<double> &coefficients, double x, double xbase){
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return fracIntCentral(coefficients,x,xbase);
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}
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/// Evaluates the indefinite integral of a centred two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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/// @param ybase central temperature for fitted function
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virtual inline double polyfracintcentral(const std::vector< std::vector<double> > &coefficients, double x, double y, double ybase){
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return fracIntCentral2Steps(coefficients,x,y,ybase);
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}
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/** Everything related to the derived polynomials divided by one variable goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Evaluates the derivative of a one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current position
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virtual inline double polyfracder(const std::vector<double> &coefficients, double x){
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throw CoolProp::NotImplementedError("Derivatives of polynomials divided by their independent variable have not been implemented."); // TODO: Implement polyfracder1D
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}
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/// Evaluates the derivative of a two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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virtual inline double polyfracder(const std::vector< std::vector<double> > &coefficients, double x, double y){
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throw CoolProp::NotImplementedError("Derivatives of polynomials divided by their independent variable have not been implemented."); // TODO: Implement polyfracder2D
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}
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/// Evaluates the derivative of a centred one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current position
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/// @param xbase central temperature for fitted function
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virtual inline double polyfracdercentral(const std::vector<double> &coefficients, double x, double xbase){
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throw CoolProp::NotImplementedError("Derivatives of polynomials divided by their independent variable have not been implemented."); // TODO: Implement polyfracdercentral1D
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}
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/// Evaluates the derivative of a centred two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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/// @param ybase central temperature for fitted function
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virtual inline double polyfracdercentral(const std::vector< std::vector<double> > &coefficients, double x, double y, double ybase){
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throw CoolProp::NotImplementedError("Derivatives of polynomials divided by their independent variable have not been implemented."); // TODO: Implement polyfracdercentral2D
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}
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};
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/** Implements the function wrapper interface and can be
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* used by the solvers.
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* TODO: Make multidimensional
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*/
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class PolyResidual : public FuncWrapper1D {
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protected:
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enum dims {i1D, i2D};
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/// Object that evaluates the equation
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BasePolynomial poly;
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/// Current output value
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double output, firstDim;
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int dim;
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std::vector< std::vector<double> > coefficients;
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private:
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PolyResidual();
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public:
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PolyResidual(const std::vector<double> &coefficients, double y);
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PolyResidual(const std::vector< std::vector<double> > &coefficients, double x, double z);
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virtual ~PolyResidual(){};
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bool is2D(){return (this->dim==i2D);};
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virtual double call(double x);
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virtual double deriv(double x);
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};
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class PolyIntResidual : public PolyResidual {
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public:
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PolyIntResidual(const std::vector<double> &coefficients, double y):PolyResidual(coefficients, y){};
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PolyIntResidual(const std::vector< std::vector<double> > &coefficients, double x, double z):PolyResidual(coefficients, x, z){};
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virtual double call(double x);
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virtual double deriv(double x);
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};
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class PolyFracIntResidual : public PolyResidual {
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public:
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PolyFracIntResidual(const std::vector<double> &coefficients, double y):PolyResidual(coefficients, y){};
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PolyFracIntResidual(const std::vector< std::vector<double> > &coefficients, double x, double z):PolyResidual(coefficients, x, z){};
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virtual double call(double x);
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virtual double deriv(double x);
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};
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class PolyDerResidual : public PolyResidual {
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public:
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PolyDerResidual(const std::vector<double> &coefficients, double y):PolyResidual(coefficients, y){};
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PolyDerResidual(const std::vector< std::vector<double> > &coefficients, double x, double z):PolyResidual(coefficients, x, z){};
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virtual double call(double x);
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virtual double deriv(double x);
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};
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/** Implements the same public functions as the
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* but solves the polynomial for the given value
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* instead of evaluating it.
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* TODO: This class does not check for bijective
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* polynomials and is therefore a little
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* fragile.
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*/
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class PolynomialSolver : public BasePolynomial{
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private:
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enum solvers {iNewton, iBrent};
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int uses;
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double guess, min, max;
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double macheps, tol;
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int maxiter;
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public:
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// Constructor
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PolynomialSolver();
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// Destructor. No implementation
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virtual ~PolynomialSolver(){};
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public:
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/** Here we redefine the functions that solve the polynomials.
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* These implementations all use the base class to evaluate
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* the polynomial during the solution process.
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*/
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/** Everything related to the normal polynomials goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Solves a one-dimensional polynomial for the given coefficients
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current input
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virtual double polyval(const std::vector<double> &coefficients, double y);
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/// Solves a two-dimensional polynomial for the given coefficients
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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virtual double polyval(const std::vector< std::vector<double> > &coefficients, double x, double z);
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/** Everything related to the integrated polynomials goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Solves the indefinite integral of a one-dimensional polynomial
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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virtual double polyint(const std::vector<double> &coefficients, double y);
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/// Solves the indefinite integral of a two-dimensional polynomial along the 2nd axis (y)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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virtual double polyint(const std::vector< std::vector<double> > &coefficients, double x, double z);
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/** Everything related to the derived polynomials goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Solves the derivative of a one-dimensional polynomial
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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virtual double polyder(const std::vector<double> &coefficients, double y);
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/// Solves the derivative of a two-dimensional polynomial along the 2nd axis (y)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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virtual double polyder(const std::vector< std::vector<double> > &coefficients, double x, double z);
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/** Everything related to the polynomials divided by one variable goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Solves the indefinite integral of a one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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virtual double polyfracval(const std::vector<double> &coefficients, double y);
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/// Solves the indefinite integral of a two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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virtual double polyfracval(const std::vector< std::vector<double> > &coefficients, double x, double z);
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/** Everything related to the integrated polynomials divided by one variable goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Solves the indefinite integral of a one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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virtual double polyfracint(const std::vector<double> &coefficients, double y);
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/// Solves the indefinite integral of a two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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virtual double polyfracint(const std::vector< std::vector<double> > &coefficients, double x, double z);
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/// Solves the indefinite integral of a centred one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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/// @param xbase central x-value for fitted function
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virtual double polyfracintcentral(const std::vector<double> &coefficients, double y, double xbase);
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/// Solves the indefinite integral of a centred two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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/// @param ybase central y-value for fitted function
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virtual double polyfracintcentral(const std::vector< std::vector<double> > &coefficients, double x, double z, double ybase);
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/** Everything related to the derived polynomials divided by one variable goes in this
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* section, holds all the functions for solving polynomials.
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*/
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/// Solves the derivative of a one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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virtual double polyfracder(const std::vector<double> &coefficients, double y);
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/// Solves the derivative of a two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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virtual double polyfracder(const std::vector< std::vector<double> > &coefficients, double x, double z);
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/// Solves the derivative of a centred one-dimensional polynomial divided by its independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param y double value that represents the current output
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/// @param xbase central x-value for fitted function
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virtual double polyfracdercentral(const std::vector<double> &coefficients, double y, double xbase);
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/// Solves the derivative of a centred two-dimensional polynomial divided by its 2nd independent variable
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param z double value that represents the current output
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/// @param ybase central y-value for fitted function
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virtual double polyfracdercentral(const std::vector< std::vector<double> > &coefficients, double x, double z, double ybase);
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/** Set the solvers and updates either the guess values or the
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* boundaries for the variable to solve for.
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*/
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/// Sets the guess value for the Newton solver and enables it.
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/// @param guess double value that represents the guess value
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virtual void setGuess(double guess);
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/// Sets the limits for the Brent solver and enables it.
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/// @param min double value that represents the lower boundary
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/// @param max double value that represents the upper boundary
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virtual void setLimits(double min, double max);
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/// Solves the equations based on previously defined parameters.
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/// @param min double value that represents the lower boundary
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/// @param max double value that represents the upper boundary
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virtual double solve(PolyResidual &res);
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};
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/// The base class for exponential functions
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class BaseExponential{
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protected:
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BasePolynomial poly;
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bool DEBUG;
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public:
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BaseExponential();
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virtual ~BaseExponential(){};
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public:
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/// Evaluates an exponential function for the given coefficients
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input
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/// @param n int value that determines the kind of exponential function
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double expval(const std::vector<double> &coefficients, double x, int n);
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/// Evaluates an exponential function for the given coefficients
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/// @param coefficients vector containing the ordered coefficients
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/// @param x double value that represents the current input in the 1st dimension
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/// @param y double value that represents the current input in the 2nd dimension
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/// @param n int value that determines the kind of exponential function
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double expval(const std::vector< std::vector<double> > &coefficients, double x, double y, int n);
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};
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}; /* namespace CoolProp */
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#endif
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