Package Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp
Temporary Functions operating on polynomials (including polynomial fitting); only to be used in Modelica.Media.Incompressible.TableBased

Information

This package contains functions to operate on polynomials, in particular to determine the derivative and the integral of a polynomial and to use a polynomial to fit a given set of data points.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Contents

Name	Description
`derivative`	Derivative of polynomial
`derivativeValue`	Value of derivative of polynomial at abscissa value u
`derivativeValue_der`	Time derivative of derivative of polynomial
`evaluate`	Evaluate polynomial at a given abscissa value
`evaluate_der`	Evaluate derivative of polynomial at a given abscissa value
`evaluateWithRange`	Evaluate polynomial at a given abscissa value with linear extrapolation outside of the defined range
`evaluateWithRange_der`	Evaluate derivative of polynomial at a given abscissa value with extrapolation outside of the defined range
`fitting`	Computes the coefficients of a polynomial that fits a set of data points in a least-squares sense
`integral`	Indefinite integral of polynomial p(u)
`integralValue`	Integral of polynomial p(u) from u_low to u_high
`integralValue_der`	Time derivative of integral of polynomial p(u) from u_low to u_high, assuming only u_high as time-dependent (Leibniz rule)
`secondDerivativeValue`	Value of 2nd derivative of polynomial at abscissa value u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluate
Evaluate polynomial at a given abscissa value

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`u`	Abscissa value

Outputs

Type	Name	Description
`Real`	`y`	Value of polynomial at u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluateWithRange
Evaluate polynomial at a given abscissa value with linear extrapolation outside of the defined range

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`uMin`	Polynomial valid in the range uMin .. uMax
`Real`	`uMax`	Polynomial valid in the range uMin .. uMax
`Real`	`u`	Abscissa value

Outputs

Type	Name	Description
`Real`	`y`	Value of polynomial at u. Outside of uMin,uMax, linear extrapolation is used

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.derivative
Derivative of polynomial

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p1[:]`	Polynomial coefficients (p1[1] is coefficient of highest power)

Outputs

Type	Name	Description
`Real`	`p2[size(p1, 1) - 1]`	Derivative of polynomial p1

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.derivativeValue
Value of derivative of polynomial at abscissa value u

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`u`	Abscissa value

Outputs

Type	Name	Description
`Real`	`y`	Value of derivative of polynomial at u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.secondDerivativeValue
Value of 2nd derivative of polynomial at abscissa value u

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`u`	Abscissa value

Outputs

Type	Name	Description
`Real`	`y`	Value of 2nd derivative of polynomial at u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.integral
Indefinite integral of polynomial p(u)

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p1[:]`	Polynomial coefficients (p1[1] is coefficient of highest power)

Outputs

Type	Name	Description
`Real`	`p2[size(p1, 1) + 1]`	Polynomial coefficients of indefinite integral of polynomial p1 (polynomial p2 + C is the indefinite integral of p1, where C is an arbitrary constant)

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.integralValue
Integral of polynomial p(u) from u_low to u_high

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients
`Real`	`u_high`	High integrand value
`Real`	`u_low`	Low integrand value, default 0

Outputs

Type	Name	Description
`Real`	`integral`	Integral of polynomial p from u_low to u_high

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.fitting
Computes the coefficients of a polynomial that fits a set of data points in a least-squares sense

Information

Polynomials.fitting(u,y,n) computes the coefficients of a polynomial p(u) of degree "n" that fits the data "p(u[i]) - y[i]" in a least squares sense. The polynomial is returned as a vector p[n+1] that has the following definition:

  p(u) = p[1]*u^n + p[2]*u^(n-1) + ... + p[n]*u + p[n+1];

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`u[:]`	Abscissa data values
`Real`	`y[size(u, 1)]`	Ordinate data values
`Integer`	`n`	Order of desired polynomial that fits the data points (u,y)

Outputs

Type	Name	Description
`Real`	`p[n + 1]`	Polynomial coefficients of polynomial that fits the date points

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluate_der
Evaluate derivative of polynomial at a given abscissa value

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`u`	Abscissa value
`Real`	`du`	Delta of abscissa value

Outputs

Type	Name	Description
`Real`	`dy`	Value of derivative of polynomial at u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluateWithRange_der
Evaluate derivative of polynomial at a given abscissa value with extrapolation outside of the defined range

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`uMin`	Polynomial valid in the range uMin .. uMax
`Real`	`uMax`	Polynomial valid in the range uMin .. uMax
`Real`	`u`	Abscissa value
`Real`	`du`	Delta of abscissa value

Outputs

Type	Name	Description
`Real`	`dy`	Value of derivative of polynomial at u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.integralValue_der
Time derivative of integral of polynomial p(u) from u_low to u_high, assuming only u_high as time-dependent (Leibniz rule)

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients
`Real`	`u_high`	High integrand value
`Real`	`u_low`	Low integrand value, default 0
`Real`	`du_high`	High integrand value
`Real`	`du_low`	Low integrand value, default 0

Outputs

Type	Name	Description
`Real`	`dintegral`	Integral of polynomial p from u_low to u_high

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.derivativeValue_der
Time derivative of derivative of polynomial

Information

This icon indicates Modelica functions.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Description
`Real`	`p[:]`	Polynomial coefficients (p[1] is coefficient of highest power)
`Real`	`u`	Abscissa value
`Real`	`du`	Delta of abscissa value

Outputs

Type	Name	Description
`Real`	`dy`	Time-derivative of derivative of polynomial w.r.t. input variable at u

Package Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_TempTemporary Functions operating on polynomials (including polynomial fitting); only to be used in Modelica.Media.Incompressible.TableBased

Information

Package Contents

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​evaluateEvaluate polynomial at a given abscissa value

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​evaluateWithRangeEvaluate polynomial at a given abscissa value with linear extrapolation outside of the defined range

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​derivativeDerivative of polynomial

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​derivativeValueValue of derivative of polynomial at abscissa value u

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​secondDerivativeValueValue of 2nd derivative of polynomial at abscissa value u

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​integralIndefinite integral of polynomial p(u)

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​integralValueIntegral of polynomial p(u) from u_low to u_high

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​fittingComputes the coefficients of a polynomial that fits a set of data points in a least-squares sense

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​evaluate_derEvaluate derivative of polynomial at a given abscissa value

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​evaluateWithRange_derEvaluate derivative of polynomial at a given abscissa value with extrapolation outside of the defined range

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​integralValue_derTime derivative of integral of polynomial p(u) from u_low to u_high, assuming only u_high as time-dependent (Leibniz rule)

Information

Inputs

Outputs

Function Modelica.​Media.​Incompressible.​Examples.​Essotherm650.​Polynomials_Temp.​derivativeValue_derTime derivative of derivative of polynomial

Information

Inputs

Outputs

Package Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp
Temporary Functions operating on polynomials (including polynomial fitting); only to be used in Modelica.Media.Incompressible.TableBased

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluate
Evaluate polynomial at a given abscissa value

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluateWithRange
Evaluate polynomial at a given abscissa value with linear extrapolation outside of the defined range

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.derivative
Derivative of polynomial

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.derivativeValue
Value of derivative of polynomial at abscissa value u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.secondDerivativeValue
Value of 2nd derivative of polynomial at abscissa value u

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.integral
Indefinite integral of polynomial p(u)

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.integralValue
Integral of polynomial p(u) from u_low to u_high

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.fitting
Computes the coefficients of a polynomial that fits a set of data points in a least-squares sense

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluate_der
Evaluate derivative of polynomial at a given abscissa value

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.evaluateWithRange_der
Evaluate derivative of polynomial at a given abscissa value with extrapolation outside of the defined range

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.integralValue_der
Time derivative of integral of polynomial p(u) from u_low to u_high, assuming only u_high as time-dependent (Leibniz rule)

Function Modelica.Media.Incompressible.Examples.Essotherm650.Polynomials_Temp.derivativeValue_der
Time derivative of derivative of polynomial