Modelica.Math

Information

This package contains the following basic mathematical functions:

   sin(u)        sine
   cos(u)        cosine
   tan(u)        tangent     (u shall not be -pi/2, pi/2, 3*pi/2, ...)
   asin(u)       inverse sine    (-1 <= u <= 1)
   acos(u)       inverse cosine  (-1 <= u <= 1)
   atan(u)       inverse tangent
   atan2(u1,u2)  four quadrant inverse tangent
   sinh(u)       hyperbolic sine
   cosh(u)       hyperbolic cosine
   tanh(u)       hyperbolic tangent
   exp(u)        exponential, base e
   log(u)        natural (base e) logarithm (u > 0)
   log10(u)      base 10 logarithm (u > 0)

These functions are used by calling them directly with a full name (e.g. y = Modelica.Math.asin(0.5)).

Main Author:

Martin Otter
Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
Institut für Robotik und Mechatronik
Postfach 1116
D-82230 Wessling
Germany
email: Martin.Otter@dlr.de

Release Notes:

• October 21, 2002 by Martin Otter and Christian Schweiger:
  Function tempInterpol2 added.
• Oct. 24, 1999 by Martin Otter:
  Icons for icon and diagram level introduced.
• June 30, 1999 by Martin Otter:
  Realized.

Copyright © 1999-2002, Modelica Association and DLR.

The Modelica 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".

Name	Description
baseIcon1	Basic icon for mathematical function with y-axis on left side
baseIcon2	Basic icon for mathematical function with y-axis in middle
sin	sine
cos	cosine
tan	tangent (u shall not be -pi/2, pi/2, 3*pi/2, ...)
asin	inverse sine (-1 <= u <= 1)
acos	inverse cosine (-1 <= u <= 1)
atan	inverse tangent
atan2	four quadrant inverse tangent
sinh	hyperbolic sine
cosh	hyperbolic cosine
tanh	hyperbolic tangent
exp	exponential, base e
log	natural (base e) logarithm (u shall be > 0)
log10	base 10 logarithm (u shall be > 0)
tempInterpol1	temporary routine for linear interpolation (will be removed)
tempInterpol2	temporary routine for vectorized linear interpolation (will be removed)

Modelica.Math.baseIcon1

Modelica definition

partial function baseIcon1 
  "Basic icon for mathematical function with y-axis on left side" 
end baseIcon1;

Modelica.Math.baseIcon2

Modelica definition

partial function baseIcon2 
  "Basic icon for mathematical function with y-axis in middle" 
end baseIcon2;

Modelica.Math.sin

Inputs

Name	Default	Description
u		[rad]

Outputs

Name	Default	Description
y

Modelica definition

function sin "sine" 
  extends baseIcon1;
  input SI.Angle u;
  output Real y;
external "C" y = sin(u);
end sin;

Modelica.Math.cos

Inputs

Name	Default	Description
u		[rad]

Outputs

Name	Default	Description
y

Modelica definition

function cos "cosine" 
  extends baseIcon1;
  input SI.Angle u;
  output Real y;
external "C" y = cos(u);
end cos;

Modelica.Math.tan

Inputs

Name	Default	Description
u		[rad]

Outputs

Name	Default	Description
y

Modelica definition

function tan "tangent (u shall not be -pi/2, pi/2, 3*pi/2, ...)" 
  extends baseIcon2;
  input SI.Angle u;
  output Real y;
external "C" y = tan(u);
end tan;

Modelica.Math.asin

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y		[rad]

Modelica definition

function asin "inverse sine (-1 <= u <= 1)" 
  extends baseIcon2;
  input Real u;
  output SI.Angle y;
external "C" y = asin(u);
end asin;

Modelica.Math.acos

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y		[rad]

Modelica definition

function acos "inverse cosine (-1 <= u <= 1)" 
  extends baseIcon2;
  input Real u;
  output SI.Angle y;
external "C" y = acos(u);
end acos;

Modelica.Math.atan

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y		[rad]

Modelica definition

function atan "inverse tangent" 
  extends baseIcon2;
  input Real u;
  output SI.Angle y;
external "C" y = atan(u);
end atan;

Modelica.Math.atan2

Information

Inputs

Name	Default	Description
u1
u2

Outputs

Name	Default	Description
y		[rad]

Modelica definition

function atan2 "four quadrant inverse tangent" 
  extends baseIcon2;
  input Real u1;
  input Real u2;
  output SI.Angle y;
external "C" y = atan2(u1, u2);
end atan2;

Modelica.Math.sinh

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y

Modelica definition

function sinh "hyperbolic sine" 
  extends baseIcon2;
  input Real u;
  output Real y;
external "C" y = sinh(u);
end sinh;

Modelica.Math.cosh

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y

Modelica definition

function cosh "hyperbolic cosine" 
  extends baseIcon2;
  input Real u;
  output Real y;
external "C" y = cosh(u);
end cosh;

Modelica.Math.tanh

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y

Modelica definition

function tanh "hyperbolic tangent" 
  extends baseIcon2;
  input Real u;
  output Real y;
external "C" y = tanh(u);
end tanh;

Modelica.Math.exp

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y

Modelica definition

function exp "exponential, base e" 
  extends baseIcon2;
  input Real u;
  output Real y;
external "C" y = exp(u);
end exp;

Modelica.Math.log

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y

Modelica definition

function log "natural (base e) logarithm (u shall be > 0)" 
  extends baseIcon1;
  input Real u;
  output Real y;
external "C" y = log(u);
end log;

Modelica.Math.log10

Inputs

Name	Default	Description
u

Outputs

Name	Default	Description
y

Modelica definition

function log10 "base 10 logarithm (u shall be > 0)" 
  extends baseIcon1;
  input Real u;
  output Real y;
external "C" y = log10(u);
end log10;

Modelica.Math.tempInterpol1

Inputs

Name	Default	Description
u		input value (first column of table)
table[:, :]		table to be interpolated
icol		column of table to be interpolated

Outputs

Name	Default	Description
y		interpolated input value (icol column of table)

Modelica definition

function tempInterpol1 
  "temporary routine for linear interpolation (will be removed)" 
  input Real u "input value (first column of table)";
  input Real table[:, :] "table to be interpolated";
  input Integer icol "column of table to be interpolated";
  output Real y "interpolated input value (icol column of table)";
protected 
  Integer i;
  Integer n "number of rows of table";
  Real u1;
  Real u2;
  Real y1;
  Real y2;
algorithm 
  n := size(table, 1);
  if n <= 1 then
    y := table[1, icol];
  else
    // Search interval
    if u <= table[1, 1] then
      i := 1;
    else
      i := 2;
      // Supports duplicate table[i, 1] values
      // in the interior to allow discontinuities.
      // Interior means that
      // if table[i, 1] = table[i+1, 1] we require i>1 and i+1<n
      while i < n and u >= table[i, 1] loop
        i := i + 1;
      end while;
      i := i - 1;
    end if;
    
    // Get interpolation data
    u1 := table[i, 1];
    u2 := table[i + 1, 1];
    y1 := table[i, icol];
    y2 := table[i + 1, icol];
    
    assert(u2 > u1, "Table index must be increasing");
    // Interpolate
    y := y1 + (y2 - y1)*(u - u1)/(u2 - u1);
  end if;
end tempInterpol1;

Modelica.Math.tempInterpol2

Inputs

Name	Default	Description
u		input value (first column of table)
table[:, :]		table to be interpolated
icol[:]		column(s) of table to be interpolated

Outputs

Name	Default	Description
y[1, size(icol, 1)]		interpolated input value(s) (column(s) icol of table)

Modelica definition

function tempInterpol2 
  "temporary routine for vectorized linear interpolation (will be removed)" 
  input Real u "input value (first column of table)";
  input Real table[:, :] "table to be interpolated";
  input Integer icol[:] "column(s) of table to be interpolated";
  output Real y[1, size(icol, 1)] 
    "interpolated input value(s) (column(s) icol of table)";
protected 
  Integer i;
  Integer n "number of rows of table";
  Real u1;
  Real u2;
  Real y1[1, size(icol, 1)];
  Real y2[1, size(icol, 1)];
algorithm 
  n := size(table, 1);
  if n <= 1 then
    y := transpose([table[1, icol]]);
  else
    // Search interval
    if u <= table[1, 1] then
      i := 1;
    else
      i := 2;
      // Supports duplicate table[i, 1] values
      // in the interior to allow discontinuities.
      // Interior means that
      // if table[i, 1] = table[i+1, 1] we require i>1 and i+1<n
      while i < n and u >= table[i, 1] loop
        i := i + 1;
      end while;
      i := i - 1;
    end if;
    
    // Get interpolation data
    u1 := table[i, 1];
    u2 := table[i + 1, 1];
    y1 := transpose([table[i, icol]]);
    y2 := transpose([table[i + 1, icol]]);
    
    assert(u2 > u1, "Table index must be increasing");
    // Interpolate
    y := y1 + (y2 - y1)*(u - u1)/(u2 - u1);
  end if;
end tempInterpol2;