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Modelica.Math.Special.{der(erf), der(erfc)} #4753

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26 changes: 22 additions & 4 deletions Modelica/Math/Special.mo
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Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,8 @@ package Special "Library of special mathematical functions"
y :=-y;
end if;

annotation (Documentation(info="<html>
annotation (derivative=erfDer,
Documentation(info="<html>
<h4>Syntax</h4>
<blockquote><pre>
Special.<strong>erf</strong>(u);
Expand Down Expand Up @@ -137,7 +138,8 @@ erf(0.5) // = 0.520499877813047
else
y := 0;
end if;
annotation (Documentation(info="<html>
annotation (derivative=erfcDer,
Documentation(info="<html>
<h4>Syntax</h4>
<blockquote><pre>
Special.<strong>erfc</strong>(u);
Expand Down Expand Up @@ -214,7 +216,8 @@ erfc(0.5) // = 0.4795001221869534
y :=Internal.erfInvUtil(u, 1 - u);
end if;

annotation (smoothOrder=1, Documentation(info="<html>
annotation (smoothOrder=1,
Documentation(info="<html>
<h4>Syntax</h4>
<blockquote><pre>
Special.<strong>erfInv</strong>(u);
Expand Down Expand Up @@ -304,7 +307,8 @@ erfInv(0.9999999999) // = 4.572824958544925
y :=Internal.erfInvUtil(1-u, u);
end if;

annotation (Documentation(info="<html>
annotation (
Documentation(info="<html>
<h4>Syntax</h4>
<blockquote><pre>
Special.<strong>erfInv</strong>(u);
Expand Down Expand Up @@ -372,6 +376,20 @@ erfInv(1.999999) // = -3.4589107372909473
</html>"));
end erfcInv;

function erfDer "Derivative of erf-function"
extends Modelica.Icons.Function;
input Real u "Input argument";
input Real der_u "Derivative of input";
output Real y= 2/sqrt(Modelica.Constants.pi)*exp(-u^2)*der_u "Derivative of erf(u)";
end erfDer;

function erfcDer "Derivative of erfc-function"
extends Modelica.Icons.Function;
input Real u "Input argument";
input Real der_u "Derivative of input";
output Real y=-2/sqrt(Modelica.Constants.pi)*exp(-u^2)*der_u "Derivative of erfc(u)";
end erfcDer;

function sinc "Unnormalized sinc function: sinc(u) = sin(u)/u"
extends Modelica.Icons.Function;
input Real u "Input argument";
Expand Down
23 changes: 23 additions & 0 deletions ModelicaTest/Math.mo
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Expand Up @@ -838,6 +838,29 @@ extends Modelica.Icons.ExamplesPackage;
annotation (experiment(StopTime=5));
end TestInterpolateTimeVarying;

model TestErf "Test error function"
extends Modelica.Icons.Example;
import Modelica.Math.Special;
Real x=time;
Real y1=Special.erf(x);
Real dy1=der(y1) "der(erf)";
Real y1i "integral(dy1) == erf ?";
Real y2=Special.erfc(x) "erfc == 1 - erf ?";
Real dy2=der(y2) "der(erfc)";
Real y2i "integral(dy2) == erfc ?";
initial equation
y1i=Special.erf(x);
y2i=Special.erfc(x);
equation
der(y1i)=dy1;
der(y2i)=dy2;
annotation (experiment(
StartTime=-10,
StopTime=10,
Interval=0.0001,
Tolerance=1e-06));
end TestErf;

package Random
function randomNumbers
"Demonstrate the generation of uniform random numbers in the range 0..1"
Expand Down
7 changes: 7 additions & 0 deletions ModelicaTest/Resources/Reference/ModelicaTest/Math/TestErf/comparisonSignals.txt
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@@ -0,0 +1,7 @@
time
y1
dy1
y1i
y2
dy2
y2i