Buildings.Utilities.Math.Functions.BaseClasses

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Buildings.Utilities.Math.Functions.BaseClasses

Package with base classes for Buildings.Utilities.Math.Functions

Information

This package contains base classes that are used to construct the models in Buildings.Utilities.Math.Functions.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

Name	Description
$Buildings.Utilities.Math.Functions.BaseClasses.der_2_regNonZeroPower$ der_2_regNonZeroPower	Power function, regularized near zero, but nonzero value for x=0
$Buildings.Utilities.Math.Functions.BaseClasses.der_polynomial$ der_polynomial	Derivative for polynomial function
$Buildings.Utilities.Math.Functions.BaseClasses.der_regNonZeroPower$ der_regNonZeroPower	Power function, regularized near zero, but nonzero value for x=0
$Buildings.Utilities.Math.Functions.BaseClasses.der_spliceFunction$ der_spliceFunction	Derivative of splice function

Buildings.Utilities.Math.Functions.BaseClasses.der_2_regNonZeroPower

Power function, regularized near zero, but nonzero value for x=0

Information

Implementation of the second derivative of the function Buildings.Utilities.Math.Functions.regNonZeroPower.

Inputs

Type	Name	Default	Description
Real	x		Abscissa value
Real	n		Exponent
Real	delta	0.01	Abscissa value where transition occurs
Real	der_x
Real	der_2_x

Outputs

Type	Name	Description
Real	der_2_y	Function value

Modelica definition

function der_2_regNonZeroPower "Power function, regularized near zero, but nonzero value for x=0" input Real x "Abscissa value"; input Real n "Exponent"; input Real delta = 0.01 "Abscissa value where transition occurs"; input Real der_x; input Real der_2_x; output Real der_2_y "Function value"; protected Real a1; Real a3; Real delta2; Real x2; Real y_d "=y(delta)"; Real yP_d "=dy(delta)/dx"; Real yPP_d "=d^2y(delta)/dx^2"; algorithm if abs(x) > delta then der_2_y := n*(n-1)*abs(x)^(n-2); else delta2 :=delta*delta; x2 :=x*x; y_d :=delta^n; yP_d :=n*delta^(n - 1); yPP_d :=n*(n - 1)*delta^(n - 2); a1 := -(yP_d/delta - yPP_d)/delta2/8; a3 := (yPP_d - 12 * a1 * delta2)/2; der_2_y := 12*a1*x2+2*a3; end if; end der_2_regNonZeroPower;

Buildings.Utilities.Math.Functions.BaseClasses.der_polynomial

Derivative for polynomial function

Information

This function computes the first derivative of a polynomial of arbitrary order. The original polynomial has the form

y = a₁ + a₂ x + a₃ x² + ...

This function computes new coefficients

b₁ = a₂, b₂ = 2 a₃, ...

and then calls recursively Buildings.Utilities.Math.polynomial

Inputs

Type	Name	Default	Description
Real	x
Real	a[:]
Real	dx

Outputs

Type	Name	Description
Real	y

Modelica definition

function der_polynomial "Derivative for polynomial function" input Real x; input Real a[:]; input Real dx; output Real y; protected parameter Integer n = size(a, 1)-1; Real b[n] "Coefficients of derivative polynomial"; algorithm for i in 1:n loop b[i] :=a[i+1]*i; end for; y := Buildings.Utilities.Math.Functions.polynomial( a=b, x=x); end der_polynomial;

Buildings.Utilities.Math.Functions.BaseClasses.der_regNonZeroPower

Power function, regularized near zero, but nonzero value for x=0

Information

Implementation of the first derivative of the function Buildings.Utilities.Math.Functions.regNonZeroPower.

Inputs

Type	Name	Default	Description
Real	x		Abscissa value
Real	n		Exponent
Real	delta	0.01	Abscissa value where transition occurs
Real	der_x

Outputs

Type	Name	Description
Real	der_y	Function value

Modelica definition

function der_regNonZeroPower "Power function, regularized near zero, but nonzero value for x=0" annotation(derivative=der_2_regNonZeroPower); input Real x "Abscissa value"; input Real n "Exponent"; input Real delta = 0.01 "Abscissa value where transition occurs"; input Real der_x; output Real der_y "Function value"; protected Real a1; Real a3; Real delta2; Real x2; Real y_d "=y(delta)"; Real yP_d "=dy(delta)/dx"; Real yPP_d "=d^2y(delta)/dx^2"; algorithm if abs(x) > delta then der_y := sign(x)*n*abs(x)^(n-1); else delta2 :=delta*delta; x2 :=x*x; y_d :=delta^n; yP_d :=n*delta^(n - 1); yPP_d :=n*(n - 1)*delta^(n - 2); a1 := -(yP_d/delta - yPP_d)/delta2/8; a3 := (yPP_d - 12 * a1 * delta2)/2; der_y := x * ( 4 * a1 * x * x + 2 * a3); end if; end der_regNonZeroPower;

Buildings.Utilities.Math.Functions.BaseClasses.der_spliceFunction

Derivative of splice function

Information

Implementation of the first derivative of the function Buildings.Utilities.Math.Functions.spliceFunction.

Inputs

Type	Name	Default
Real	pos
Real	neg
Real	x
Real	deltax	1
Real	dpos
Real	dneg
Real	dx
Real	ddeltax	0

Outputs

Type	Name	Description
Real	out

Modelica definition

function der_spliceFunction "Derivative of splice function" input Real pos; input Real neg; input Real x; input Real deltax=1; input Real dpos; input Real dneg; input Real dx; input Real ddeltax=0; output Real out; protected Real scaledX; Real scaledX1; Real dscaledX1; Real y; constant Real asin1 = Modelica.Math.asin(1); algorithm scaledX1 := x/deltax; if scaledX1 <= -0.99999999999 then out := dneg; elseif scaledX1 >= 0.9999999999 then out := dpos; else scaledX := scaledX1*asin1; dscaledX1 := (dx - scaledX1*ddeltax)/deltax; y := (Modelica.Math.tanh(Modelica.Math.tan(scaledX)) + 1)/2; out := dpos*y + (1 - y)*dneg; out := out + (pos - neg)*dscaledX1*asin1/2/( Modelica.Math.cosh(Modelica.Math.tan(scaledX))*Modelica.Math.cos( scaledX))^2; end if; end der_spliceFunction;

Automatically generated Thu Jun 19 11:01:08 2014.