Modelica.Media.Incompressible.TableBased.Polynomials_Temp

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 © 2004-2013, Modelica Association and DLR.

This package is free software. It can be redistributed and/or modified under the terms of the Modelica license, see the license conditions and the accompanying disclaimer in the documentation of package Modelica in file "Modelica/package.mo".

Package Content

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

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.evaluate

Information

Inputs

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

Outputs

Name	Description
y	Value of polynomial at u

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.evaluateWithRange

Information

Inputs

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

Outputs

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

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.derivative

Information

Inputs

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

Outputs

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

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.derivativeValue

Information

Inputs

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

Outputs

Name	Description
y	Value of derivative of polynomial at u

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.secondDerivativeValue

Information

Inputs

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

Outputs

Name	Description
y	Value of 2nd derivative of polynomial at u

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.integral

Information

Inputs

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

Outputs

Name	Description
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)

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.integralValue

Information

Inputs

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

Outputs

Name	Description
integral	Integral of polynomial p from u_low to u_high

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.fitting

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];

Inputs

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

Outputs

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

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.evaluate_der

Information

Inputs

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

Outputs

Name	Description
dy	Value of derivative of polynomial at u

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.evaluateWithRange_der

Information

Inputs

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

Outputs

Name	Description
dy	Value of derivative of polynomial at u

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.integralValue_der

Information

Inputs

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

Outputs

Name	Description
dintegral	Integral of polynomial p from u_low to u_high

Modelica.Media.Incompressible.TableBased.Polynomials_Temp.derivativeValue_der

Information

Inputs

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

Outputs

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