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Complex.mo
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Complex.mo
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within ;
operator record Complex "Complex number with overloaded operators"
replaceable Real re "Real part of complex number" annotation(Dialog);
replaceable Real im "Imaginary part of complex number" annotation(Dialog);
encapsulated operator 'constructor' "Constructor"
function fromReal "Construct Complex from Real"
import Complex;
input Real re "Real part of complex number";
input Real im=0 "Imaginary part of complex number";
output Complex result(re=re, im=im) "Complex number";
algorithm
annotation(Inline=true, Documentation(info="<html>
<p>This function returns a Complex number defined by real part <em>re</em> and optional imaginary part <em>im</em> (default=0).</p>
</html>"));
end fromReal;
annotation (Documentation(info="<html>
<p>Here the constructor operator(s) is/are defined.</p>
</html>"), Icon(graphics={Rectangle(
lineColor={200,200,200},
fillColor={248,248,248},
fillPattern=FillPattern.HorizontalCylinder,
extent={{-100,-100},{100,100}},
radius=25.0), Rectangle(
lineColor={128,128,128},
extent={{-100,-100},{100,100}},
radius=25.0)}));
end 'constructor';
encapsulated operator function '0' "Zero-element of addition (= Complex(0))"
import Complex;
output Complex result "Complex(0)";
algorithm
result := Complex(0);
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the zero-element of Complex, that is, Complex(0) = 0 + j*0.</p>
</html>"));
end '0';
encapsulated operator '-' "Unary and binary minus"
function negate "Unary minus (multiply complex number by -1)"
import Complex;
input Complex c1 "Complex number";
output Complex c2 "= -c1";
algorithm
c2 := Complex(-c1.re, -c1.im);
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the binary minus of the given Complex number.</p>
</html>"));
end negate;
function subtract "Subtract two complex numbers"
import Complex;
input Complex c1 "Complex number 1";
input Complex c2 "Complex number 2";
output Complex c3 "= c1 - c2";
algorithm
c3 := Complex(c1.re - c2.re, c1.im - c2.im);
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the difference of two given Complex numbers.</p>
</html>"));
end subtract;
annotation (Documentation(info="<html>
<p>Here the unary and binary minus operator(s) is/are defined.</p>
</html>"), Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100},
{100,100}}), graphics={
Rectangle(
lineColor={200,200,200},
fillColor={248,248,248},
fillPattern=FillPattern.HorizontalCylinder,
extent={{-100,-100},{100,100}},
radius=25.0),
Rectangle(
lineColor={128,128,128},
extent={{-100,-100},{100,100}},
radius=25.0),
Line(
points={{-50,0},{50,0}})}));
end '-';
encapsulated operator '*' "Multiplication"
function multiply "Multiply two complex numbers"
import Complex;
input Complex c1 "Complex number 1";
input Complex c2 "Complex number 2";
output Complex c3 "= c1*c2";
algorithm
c3 := Complex(c1.re*c2.re - c1.im*c2.im, c1.re*c2.im + c1.im*c2.re);
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the product of two given Complex numbers.</p>
</html>"));
end multiply;
function scalarProduct "Scalar product c1*c2 of two complex vectors"
import Complex;
input Complex c1[:] "Vector of Complex numbers 1";
input Complex c2[size(c1,1)] "Vector of Complex numbers 2";
output Complex c3 "= c1*c2";
algorithm
c3 :=Complex(0);
for i in 1:size(c1,1) loop
c3 :=c3 + c1[i]*c2[i];
/*
c3 :=Complex(c3.re + c1[i].re*c2[i].re - c1[i].im*c2[i].im,
c3.im + c1[i].re*c2[i].im + c1[i].im*c2[i].re);
*/
end for;
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the scalar product of two given arrays of Complex numbers.</p>
</html>"));
end scalarProduct;
annotation (
Documentation(info="<html>
<p>Here the multiplication operator(s) is/are defined.</p>
</html>"),
Icon(coordinateSystem(
preserveAspectRatio=false,
extent={{-100,-100},{100,100}}),
graphics={
Rectangle(
lineColor={200,200,200},
fillColor={248,248,248},
fillPattern=FillPattern.HorizontalCylinder,
extent={{-100,-100},{100,100}},
radius=25.0),
Rectangle(
lineColor={128,128,128},
extent={{-100,-100},{100,100}},
radius=25.0),
Line(
points={{-42,36},{39,-34}}),
Line(
points={{-42,-35},{39,37}}),
Line(
points={{-55,1},{52,1}}),
Line(
points={{-1.5,55},{-2,-53}})}));
end '*';
encapsulated operator function '+' "Add two complex numbers"
import Complex;
input Complex c1 "Complex number 1";
input Complex c2 "Complex number 2";
output Complex c3 "= c1 + c2";
algorithm
c3 := Complex(c1.re + c2.re, c1.im + c2.im);
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the sum of two given Complex numbers.</p>
</html>"));
end '+';
encapsulated operator function '/' "Divide two complex numbers"
import Complex;
input Complex c1 "Complex number 1";
input Complex c2 "Complex number 2";
output Complex c3 "= c1/c2";
algorithm
c3 := Complex((+c1.re*c2.re + c1.im*c2.im)/(c2.re*c2.re + c2.im*c2.im),
(-c1.re*c2.im + c1.im*c2.re)/(c2.re*c2.re + c2.im*c2.im));
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the quotient of two given Complex numbers.</p>
</html>"));
end '/';
encapsulated operator function '^' "Complex power of complex number"
import Complex;
input Complex c1 "Complex number";
input Complex c2 "Complex exponent";
output Complex c3 "= c1^c2";
protected
Real lnz=0.5*log(c1.re*c1.re + c1.im*c1.im);
Real phi=atan2(c1.im, c1.re);
Real re=lnz*c2.re - phi*c2.im;
Real im=lnz*c2.im + phi*c2.re;
algorithm
c3 := Complex(exp(re)*cos(im), exp(re)*sin(im));
annotation(Inline=true, Documentation(info="<html>
<p>This function returns the given Complex numbers c1 to the power of the Complex number c2.</p>
</html>"));
end '^';
encapsulated operator function '=='
"Test whether two complex numbers are identical"
import Complex;
input Complex c1 "Complex number 1";
input Complex c2 "Complex number 2";
output Boolean result "c1 == c2";
algorithm
result := c1.re == c2.re and c1.im == c2.im;
annotation(Inline=true, Documentation(info="<html>
<p>This function tests whether two given Complex numbers are equal.</p>
</html>"));
end '==';
encapsulated operator function '<>'
"Test whether two complex numbers are not identical"
import Complex;
input Complex c1 "Complex number 1";
input Complex c2 "Complex number 2";
output Boolean result "c1 <> c2";
algorithm
result := c1.re <> c2.re or c1.im <> c2.im;
annotation(Inline=true, Documentation(info="<html>
<p>This function tests whether two given Complex numbers are not equal.</p>
</html>"));
end '<>';
encapsulated operator function 'String'
"Transform Complex number into a String representation"
import Complex;
input Complex c
"Complex number to be transformed in a String representation";
input String name="j"
"Name of variable representing sqrt(-1) in the string";
input Integer significantDigits=6
"Number of significant digits that are shown";
output String s="";
algorithm
s := String(c.re, significantDigits=significantDigits);
if c.im <> 0 then
if c.im > 0 then
s := s + " + ";
else
s := s + " - ";
end if;
s := s + String(abs(c.im), significantDigits=significantDigits) + "*" + name;
end if;
annotation(Inline=true, Documentation(info="<html>
<p>This function converts a given Complex number to String representation.</p>
</html>"));
end 'String';
annotation (
version="4.0.0",
versionDate="2020-03-11",
dateModified = "2020-03-11 19:00:00Z",
revisionId="$Format:%h %ci$",
conversion(
noneFromVersion="3.2.2",
noneFromVersion="3.2.1",
noneFromVersion="1.0",
noneFromVersion="1.1"),
Documentation(info="<html>
<p>Complex number defined as a record containing real and imaginary part, utilizing operator overloading.</p>
<p>
<strong>Licensed by the Modelica Association under the 3-Clause BSD License</strong><br>
Copyright © 2010-2020, Modelica Association and <a href=\"modelica://Modelica.UsersGuide.Contact\">contributors</a>
</p>
<p>
<em>This Modelica package is <u>free</u> software and the use is completely at <u>your own risk</u>; it can be redistributed and/or modified under the terms of the 3-Clause BSD license. For license conditions (including the disclaimer of warranty) visit <a href=\"https://modelica.org/licenses/modelica-3-clause-bsd\">https://modelica.org/licenses/modelica-3-clause-bsd</a>.</em>
</p></html>"),
Icon(graphics={Rectangle(
lineColor={160,160,164},
fillColor={160,160,164},
fillPattern=FillPattern.Solid,
extent={{-100,-100},{100,100}},
radius=25.0), Text(
textColor={255,255,255},
extent={{-90,-50},{90,50}},
textString="C")}));
end Complex;