Package Modelica.​Media.​Incompressible.​TableBased.​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.

Copyright © 2004-2018, Modelica Association and contributors

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

Package Contents

NameDescription
derivativeDerivative of polynomial
derivativeValueValue of derivative of polynomial at abscissa value u
derivativeValue_derTime derivative of derivative of polynomial
evaluateEvaluate polynomial at a given abscissa value
evaluate_derEvaluate derivative of polynomial at a given abscissa value
evaluateWithRangeEvaluate polynomial at a given abscissa value with linear extrapolation outside of the defined range
evaluateWithRange_derEvaluate derivative of polynomial at a given abscissa value with extrapolation outside of the defined range
fittingComputes the coefficients of a polynomial that fits a set of data points in a least-squares sense
integralIndefinite integral of polynomial p(u)
integralValueIntegral of polynomial p(u) from u_low to u_high
integralValue_derTime derivative of integral of polynomial p(u) from u_low to u_high, assuming only u_high as time-dependent (Leibniz rule)
secondDerivativeValueValue of 2nd derivative of polynomial at abscissa value u

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuAbscissa value

Outputs

TypeNameDescription
RealyValue of polynomial at u

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuMinPolynomial valid in the range uMin .. uMax
RealuMaxPolynomial valid in the range uMin .. uMax
RealuAbscissa value

Outputs

TypeNameDescription
RealyValue of polynomial at u. Outside of uMin,uMax, linear extrapolation is used

Function Modelica.​Media.​Incompressible.​TableBased.​Polynomials_Temp.​derivative
Derivative of polynomial

Information

This icon indicates Modelica functions.

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

Inputs

TypeNameDescription
Realp1[:]Polynomial coefficients (p1[1] is coefficient of highest power)

Outputs

TypeNameDescription
Realp2[size(p1, 1) - 1]Derivative of polynomial p1

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuAbscissa value

Outputs

TypeNameDescription
RealyValue of derivative of polynomial at u

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuAbscissa value

Outputs

TypeNameDescription
RealyValue of 2nd derivative of polynomial at u

Function Modelica.​Media.​Incompressible.​TableBased.​Polynomials_Temp.​integral
Indefinite integral of polynomial p(u)

Information

This icon indicates Modelica functions.

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

Inputs

TypeNameDescription
Realp1[:]Polynomial coefficients (p1[1] is coefficient of highest power)

Outputs

TypeNameDescription
Realp2[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.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients
Realu_highHigh integrand value
Realu_lowLow integrand value, default 0

Outputs

TypeNameDescription
RealintegralIntegral of polynomial p from u_low to u_high

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realu[:]Abscissa data values
Realy[size(u, 1)]Ordinate data values
IntegernOrder of desired polynomial that fits the data points (u,y)

Outputs

TypeNameDescription
Realp[n + 1]Polynomial coefficients of polynomial that fits the date points

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuAbscissa value
RealduDelta of abscissa value

Outputs

TypeNameDescription
RealdyValue of derivative of polynomial at u

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuMinPolynomial valid in the range uMin .. uMax
RealuMaxPolynomial valid in the range uMin .. uMax
RealuAbscissa value
RealduDelta of abscissa value

Outputs

TypeNameDescription
RealdyValue of derivative of polynomial at u

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients
Realu_highHigh integrand value
Realu_lowLow integrand value, default 0
Realdu_highHigh integrand value
Realdu_lowLow integrand value, default 0

Outputs

TypeNameDescription
RealdintegralIntegral of polynomial p from u_low to u_high

Function Modelica.​Media.​Incompressible.​TableBased.​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

TypeNameDescription
Realp[:]Polynomial coefficients (p[1] is coefficient of highest power)
RealuAbscissa value
RealduDelta of abscissa value

Outputs

TypeNameDescription
RealdyTime-derivative of derivative of polynomial w.r.t. input variable at u

Generated 2018-12-12 12:14:18 EST by MapleSim.