mirror of
https://github.com/CoolProp/CoolProp.git
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639 lines
33 KiB
C++
639 lines
33 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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protected:
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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<long double> &coefficients, const unsigned int n);
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bool checkCoefficients(const std::vector< std::vector<long 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<long double> integrateCoeffs(const std::vector<long double> &coefficients);
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std::vector< std::vector<long double> > integrateCoeffs(const std::vector< std::vector<long 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<long double> deriveCoeffs(const std::vector<long double> &coefficients);
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std::vector< std::vector<long double> > deriveCoeffs(const std::vector< std::vector<long 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 T^0. */
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DEPRECATED(long double simplePolynomial(const std::vector<long double> &coefficients, long double T));
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DEPRECATED(long double simplePolynomial(const std::vector<std::vector<long double> > &coefficients, long double x, long double T));
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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 T^0 */
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///Indefinite integral in T-direction
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long double simplePolynomialInt(const std::vector<long double> &coefficients, long double T);
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///Indefinite integral in T-direction only
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long double simplePolynomialInt(const std::vector<std::vector<long double> > &coefficients, long double x, long double T);
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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 T^0 */
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///Indefinite integral of a polynomial divided by its independent variable
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long double simpleFracInt(const std::vector<long double> &coefficients, long double T);
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///Indefinite integral of a polynomial divided by its 2nd independent variable
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long double simpleFracInt(const std::vector<std::vector<long double> > &coefficients, long double x, long double T);
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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 Tbase
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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 T^0 */
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///Helper function to calculate the D vector:
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long double factorial(long double nValue);
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long double binom(long double nValue, long double nValue2);
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std::vector<long double> fracIntCentralDvector(int m, long double T, long double Tbase);
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///Indefinite integral of a centred polynomial divided by its independent variable
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long double fracIntCentral(const std::vector<long double> &coefficients, long double T, long double Tbase);
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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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long double baseHorner(const std::vector<long double> &coefficients, long double T);
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long double baseHorner(const std::vector< std::vector<long double> > &coefficients, long double x, long double T);
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///Indefinite integral in T-direction
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long double baseHornerInt(const std::vector<long double> &coefficients, long double T);
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///Indefinite integral in T-direction only
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long double baseHornerInt(const std::vector<std::vector<long double> > &coefficients, long double x, long double T);
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///Indefinite integral of a polynomial divided by its independent variable
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long double baseHornerFracInt(const std::vector<long double> &coefficients, long double T);
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///Indefinite integral of a polynomial divided by its 2nd independent variable
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long double baseHornerFracInt(const std::vector<std::vector<long double> > &coefficients, long double x, long double T);
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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 T-direction
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long double deriveIn2Steps(const std::vector<long double> &coefficients, long double T);
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///Derivative in terms of x(axis=true) or T(axis=false).
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long double deriveIn2Steps(const std::vector< std::vector<long double> > &coefficients, long double x, long double T, bool axis);
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///Indefinite integral in T-direction
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long double integrateIn2Steps(const std::vector<long double> &coefficients, long double T);
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///Indefinite integral in terms of x(axis=true) or T(axis=false).
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long double integrateIn2Steps(const std::vector< std::vector<long double> > &coefficients, long double x, long double T, bool axis);
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///Indefinite integral in T-direction of a polynomial divided by its independent variable
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long double fracIntIn2Steps(const std::vector<long double> &coefficients, long double T);
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///Indefinite integral in T-direction of a polynomial divided by its 2nd independent variable
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long double fracIntIn2Steps(const std::vector<std::vector<long double> > &coefficients, long double x, long double T);
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///Indefinite integral of a centred polynomial divided by its 2nd independent variable
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long double fracIntCentral2Steps(const std::vector<std::vector<long double> > &coefficients, long double x, long double T, long double Tbase);
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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 functions for both evaluation and solving
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* of 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 long double value that represents the current input
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inline long double polyval(const std::vector<long double> &coefficients, long 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 long double value that represents the current input in the 1st dimension
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/// @param y long double value that represents the current input in the 2nd dimension
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inline long double polyval(const std::vector< std::vector<long double> > &coefficients, long double x, long 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 functions for both evaluation and solving
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* of 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 T long double value that represents the current input
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inline long double polyint(const std::vector<long double> &coefficients, long double T){
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return baseHornerInt(coefficients,T);
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}
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/// Evaluates the indefinite integral of a two-dimensional polynomial along the 2nd axis (T)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param T long double value that represents the current input in the 2nd dimension
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inline long double polyint(const std::vector< std::vector<long double> > &coefficients, long double x, long double T){
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return baseHornerInt(coefficients,x,T);
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}
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/** Everything related to the derived polynomials goes in this
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* section, holds functions for both evaluation and solving
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* of 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 T long double value that represents the current input
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inline long double polyder(const std::vector<long double> &coefficients, long double T){
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return deriveIn2Steps(coefficients,T);
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}
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/// Evaluates the derivative of a two-dimensional polynomial along the 2nd axis (T)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param T long double value that represents the current input in the 2nd dimension
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inline long double polyder(const std::vector< std::vector<long double> > &coefficients, long double x, long double T){
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return deriveIn2Steps(coefficients,x,T,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 functions for both evaluation and solving
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* of 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 T long double value that represents the current position
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inline long double polyfracval(const std::vector<long double> &coefficients, long double T){
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return baseHornerFracInt(coefficients,T);
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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 long double value that represents the current input in the 1st dimension
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/// @param T long double value that represents the current input in the 2nd dimension
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inline long double polyfracval(const std::vector< std::vector<long double> > &coefficients, long double x, long double T){
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return baseHornerFracInt(coefficients,x,T);
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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 T long double value that represents the current position
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inline long double polyfracint(const std::vector<long double> &coefficients, long double T){
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return baseHornerFracInt(coefficients,T);
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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 long double value that represents the current input in the 1st dimension
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/// @param T long double value that represents the current input in the 2nd dimension
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inline long double polyfracint(const std::vector< std::vector<long double> > &coefficients, long double x, long double T){
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return baseHornerFracInt(coefficients,x,T);
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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 T long double value that represents the current position
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/// @param Tbase central temperature for fitted function
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inline long double polyfracintcentral(const std::vector<long double> &coefficients, long double T, long double Tbase){
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return fracIntCentral(coefficients,T,Tbase);
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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 long double value that represents the current input in the 1st dimension
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/// @param T long double value that represents the current input in the 2nd dimension
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/// @param Tbase central temperature for fitted function
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inline long double polyfracintcentral(const std::vector< std::vector<long double> > &coefficients, long double x, long double T, long double Tbase){
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return fracIntCentral2Steps(coefficients,x,T,Tbase);
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}
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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 T long 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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long double expval(const std::vector<long double> &coefficients, long double T, 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 long double value that represents the current input in the 1st dimension
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/// @param T long 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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long double expval(const std::vector< std::vector<long double> > &coefficients, long double x, long double T, int n);
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};
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/// The classes for Polynomials
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class PolynomialImpl1D : public BasePolynomial{
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protected:
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std::vector<long double> coefficients;
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/// A nested class that is used by the solvers to calculate
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/// residuals and derivatives during the solution process.
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class Residual : public FuncWrapper1D {
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private:
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PolynomialImpl1D *poly;
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long double y;
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Residual();
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public:
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Residual(PolynomialImpl1D *poly, long double y);
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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 ResidualInt : public Residual {
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public:
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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 ResidualDer : public Residual {
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public:
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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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private:
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PolynomialImpl1D();
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public:
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PolynomialImpl1D(const std::vector<long double> &coefficients);
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virtual ~PolynomialImpl1D(){};
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/// Evaluates a one-dimensional polynomial for the given coefficients
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/// @param x long double value that represents the current input
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virtual long double eval(long double x);
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/// Evaluates the indefinite integral of a one-dimensional polynomial
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/// @param x long double value that represents the current input
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virtual long double integ(long double x);
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/// Evaluates the derivative of a one-dimensional polynomial
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/// @param x long double value that represents the current input
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virtual long double deriv(long double x);
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/// Solves a one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param x0 long double value that represents the first guess for x
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virtual long double solve(long double y, long double x0);
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/// Solves a one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param xmin long double value that represents the lower limit for x
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/// @param xmax long double value that represents the upper limit for x
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virtual long double solve(long double y, long double xmin, long double xmax);
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/// Solves an integrated one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param x0 long double value that represents the first guess for x
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virtual long double solveInt(long double y, long double x0);
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/// Solves an integrated one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param xmin long double value that represents the lower limit for x
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/// @param xmax long double value that represents the upper limit for x
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virtual long double solveInt(long double y, long double xmin, long double xmax);
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/// Solves the derivative of a one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param x0 long double value that represents the first guess for x
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virtual long double solveDer(long double y, long double x0);
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/// Solves the derivative of a one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param xmin long double value that represents the lower limit for x
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/// @param xmax long double value that represents the upper limit for x
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virtual long double solveDer(long double y, long double xmin, long double xmax);
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};
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class PolynomialImpl2D : public BasePolynomial{
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protected:
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std::vector< std::vector<long double> > coefficients;
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/// A nested class that is used by the solvers to calculate
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/// residuals and derivatives during the solution process.
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class Residual : public FuncWrapper1D {
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private:
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PolynomialImpl2D *poly;
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long double x, y;
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Residual();
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public:
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Residual(PolynomialImpl2D *poly, long double y, long double x);
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virtual double call(double z);
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virtual double deriv(double z);
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};
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class ResidualInt : public Residual {
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public:
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virtual double call(double z);
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virtual double deriv(double z);
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};
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class ResidualDer : public Residual {
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public:
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virtual double call(double z);
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virtual double deriv(double z);
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};
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private:
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PolynomialImpl2D();
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public:
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PolynomialImpl2D(const std::vector< std::vector<long double> > &coefficients);
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virtual ~PolynomialImpl2D(){};
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/// Evaluates a two-dimensional polynomial for the given coefficients
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param z long double value that represents the current input in the 2nd dimension
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virtual long double eval(long double x, long double z);
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/// Evaluates the indefinite integral of a two-dimensional polynomial along the 2nd axis (z)
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param z long double value that represents the current input in the 2nd dimension
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virtual long double integ(long double x, long double z);
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/// Evaluates the derivative of a two-dimensional polynomial along the 2nd axis (z)
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/// @param coefficients vector containing the ordered coefficients
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param z long double value that represents the current input in the 2nd dimension
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virtual long double deriv(long double x, long double z);
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/// Solves a two-dimensional polynomial for the 2nd input (z)
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/// @param y long double value that represents the current function output
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param z0 long double value that represents the first guess for z
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virtual long double solve(long double y, long double x, long double z0);
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/// Solves a two-dimensional polynomial for the 2nd input (z)
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/// @param y long double value that represents the current function output
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param zmin long double value that represents the lower limit for z
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/// @param zmax long double value that represents the upper limit for z
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virtual long double solve(long double y, long double x, long double zmin, long double zmax);
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/// Solves an integrated two-dimensional polynomial for the 2nd input (z)
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/// @param y long double value that represents the current function output
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param z0 long double value that represents the first guess for z
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virtual long double solveInt(long double y, long double x, long double z0);
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/// Solves an integrated two-dimensional polynomial for the 2nd input (z)
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/// @param y long double value that represents the current function output
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param zmin long double value that represents the lower limit for z
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/// @param zmax long double value that represents the upper limit for z
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virtual long double solveInt(long double y, long double x, long double zmin, long double zmax);
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/// Solves the derivative of a two-dimensional polynomial for the 2nd input (z)
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/// @param y long double value that represents the current function output
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param z0 long double value that represents the first guess for z
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virtual long double solveDer(long double y, long double x, long double z0);
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/// Solves the derivative of a two-dimensional polynomial for the 2nd input (z)
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/// @param y long double value that represents the current function output
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/// @param x long double value that represents the current input in the 1st dimension
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/// @param zmin long double value that represents the lower limit for z
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/// @param zmax long double value that represents the upper limit for z
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virtual long double solveDer(long double y, long double x, long double zmin, long double zmax);
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};
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class PolynomialFrac1D : public PolynomialImpl1D{
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private:
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PolynomialFrac1D();
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public:
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PolynomialFrac1D(const std::vector<long double> &coefficients);
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virtual ~PolynomialFrac1D(){};
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/// Evaluates a one-dimensional polynomial for the given coefficients
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/// @param x long double value that represents the current input
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virtual long double eval(long double x);
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/// Evaluates the indefinite integral of a one-dimensional polynomial
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/// @param x long double value that represents the current input
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|
virtual long double integ(long double x);
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/// Evaluates the derivative of a one-dimensional polynomial
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/// @param x long double value that represents the current input
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virtual long double deriv(long double x);
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/// Solves a one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param x0 long double value that represents the first guess for x
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virtual long double solve(long double y, long double x0);
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/// Solves a one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param xmin long double value that represents the lower limit for x
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/// @param xmax long double value that represents the upper limit for x
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virtual long double solve(long double y, long double xmin, long double xmax);
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/// Solves an integrated one-dimensional polynomial for the given coefficients
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/// @param y long double value that represents the current function output
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/// @param x0 long double value that represents the first guess for x
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virtual long double solveInt(long double y, long double x0);
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/// Solves an integrated one-dimensional polynomial for the given coefficients
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|
/// @param y long double value that represents the current function output
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|
/// @param xmin long double value that represents the lower limit for x
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/// @param xmax long double value that represents the upper limit for x
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virtual long double solveInt(long double y, long double xmin, long double xmax);
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// virtual long double solveIntCentral(long double y, long double xBase, long double x0); // TODO: implement solveIntCentral with x0
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/// Solves an integrated one-dimensional polynomial
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|
/// @param y long double value that represents the current function output
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|
/// @param xBase long double value that represents the central value for x
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|
/// @param xmin long double value that represents the lower limit for x
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/// @param xmax long double value that represents the upper limit for x
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|
virtual long double solveIntCentral(long double y, long double xBase, long double xmin, long double xmax);
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/// Solves the derivative of a one-dimensional polynomial for the given coefficients
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|
/// @param y long double value that represents the current function output
|
|
/// @param x0 long double value that represents the first guess for x
|
|
virtual long double solveDer(long double y, long double x0);
|
|
/// Solves the derivative of a one-dimensional polynomial for the given coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param xmin long double value that represents the lower limit for x
|
|
/// @param xmax long double value that represents the upper limit for x
|
|
virtual long double solveDer(long double y, long double xmin, long double xmax);
|
|
// virtual long double solveDerCentral(long double y, long double xBase, long double x0); // TODO: implement solveDerCentral with x0
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|
// virtual long double solveDerCentral(long double y, long double xBase, long double xmin, long double xmax); // TODO: implement solveDerCentral with xmin, xmax
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/// Solves a one-dimensional polynomial for the given coefficients
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x0 long double value that represents the first guess for x
|
|
virtual long double solve(const std::vector<long double> &coefficients, long double y, long double x0);
|
|
/// Solves a two-dimensional polynomial for the 2nd input (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z0 long double value that represents the first guess for z
|
|
virtual long double solve(const std::vector< std::vector<long double> > &coefficients, long double y, long double x, long double z0);
|
|
/// Solves a one-dimensional polynomial for the given coefficients
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param xmin long double value that represents the lower limit for x
|
|
/// @param xmax long double value that represents the upper limit for x
|
|
virtual long double solve(const std::vector<long double> &coefficients, long double y, long double xmin, long double xmax);
|
|
/// Solves a two-dimensional polynomial for the 2nd input (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param zmin long double value that represents the lower limit for z
|
|
/// @param zmax long double value that represents the upper limit for z
|
|
virtual long double solve(const std::vector< std::vector<long double> > &coefficients, long double y, long double x, long double zmin, long double zmax);
|
|
/// Solves an integrated one-dimensional polynomial for the given coefficients
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x0 long double value that represents the first guess for x
|
|
virtual long double solveInt(const std::vector<long double> &coefficients, long double y, long double x0);
|
|
/// Solves an integrated two-dimensional polynomial for the 2nd input (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z0 long double value that represents the first guess for z
|
|
virtual long double solveInt(const std::vector< std::vector<long double> > &coefficients, long double y, long double x, long double z0);
|
|
/// Solves an integrated one-dimensional polynomial for the given coefficients
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param xmin long double value that represents the lower limit for x
|
|
/// @param xmax long double value that represents the upper limit for x
|
|
virtual long double solveInt(const std::vector<long double> &coefficients, long double y, long double xmin, long double xmax);
|
|
/// Solves an integrated two-dimensional polynomial for the 2nd input (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param zmin long double value that represents the lower limit for z
|
|
/// @param zmax long double value that represents the upper limit for z
|
|
virtual long double solveInt(const std::vector< std::vector<long double> > &coefficients, long double y, long double x, long double zmin, long double zmax);
|
|
/// Solves the derivative of a one-dimensional polynomial for the given coefficients
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x0 long double value that represents the first guess for x
|
|
virtual long double solveDer(const std::vector<long double> &coefficients, long double y, long double x0);
|
|
/// Solves the derivative of a one-dimensional polynomial for the given coefficients
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param xmin long double value that represents the lower limit for x
|
|
/// @param xmax long double value that represents the upper limit for x
|
|
virtual long double solveDer(const std::vector<long double> &coefficients, long double y, long double xmin, long double xmax);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/// Solves the derivative of a two-dimensional polynomial for the 2nd input (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z0 long double value that represents the first guess for z
|
|
virtual long double solveDer(const std::vector< std::vector<long double> > &coefficients, long double y, long double x, long double z0);
|
|
/// Solves the derivative of a two-dimensional polynomial for the 2nd input (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param y long double value that represents the current function output
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param zmin long double value that represents the lower limit for z
|
|
/// @param zmax long double value that represents the upper limit for z
|
|
virtual long double solveDer(const std::vector< std::vector<long double> > &coefficients, long double y, long double x, long double zmin, long double zmax);
|
|
// virtual long double solveDerCentral(long double y, long double x, long double zBase, long double z0); // TODO: implement solveDerCentral with z0
|
|
// virtual long double solveDerCentral(long double y, long double x, long double zBase, long double zmin, long double zmax); // TODO: implement solveDerCentral with zmin, zmax
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
};
|
|
|
|
class PolynomialFrac2D : public PolynomialImpl2D{
|
|
private:
|
|
PolynomialFrac2D();
|
|
public:
|
|
PolynomialFrac2D(const std::vector< std::vector<long double> > &coefficients);
|
|
virtual ~PolynomialFrac2D(){};
|
|
/// Evaluates a two-dimensional polynomial for the given coefficients
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z long double value that represents the current input in the 2nd dimension
|
|
virtual long double eval(long double x, long double z);
|
|
/// Evaluates the indefinite integral of a two-dimensional polynomial along the 2nd axis (z)
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z long double value that represents the current input in the 2nd dimension
|
|
virtual long double integ(long double x, long double z);
|
|
/// Evaluates the indefinite integral of a two-dimensional polynomial along the 2nd axis (z)
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z long double value that represents the current input in the 2nd dimension
|
|
/// @param zBase long double value that represents the central value for z
|
|
virtual long double integCentral(long double x, long double z, long double zBase);
|
|
/// Evaluates the derivative of a two-dimensional polynomial along the 2nd axis (z)
|
|
/// @param coefficients vector containing the ordered coefficients
|
|
/// @param x long double value that represents the current input in the 1st dimension
|
|
/// @param z long double value that represents the current input in the 2nd dimension
|
|
virtual long double deriv(long double x, long double z);
|
|
|
|
|
|
};
|
|
|
|
|
|
}; /* namespace CoolProp */
|
|
#endif
|