ModelicaStandardLibrary/Complex.mo at master · modelscript/ModelicaStandardLibrary · GitHub

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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>

This function returns a Complex number defined by real part re and optional imaginary part im (default=0).

</html>"));

end fromReal;

annotation (Documentation(info="<html>

Here the constructor operator(s) is/are defined.

</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>

This function returns the zero-element of Complex, that is, Complex(0) = 0 + j*0.

</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, smoothOrder=100, Documentation(info="<html>

This function returns the binary minus of the given Complex number.

</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, smoothOrder=100, Documentation(info="<html>

This function returns the difference of two given Complex numbers.

</html>"));

end subtract;

annotation (Documentation(info="<html>

Here the unary and binary minus operator(s) is/are defined.

</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),

Text(

extent={{-200,-200},{200,250}},

textColor={128,128,128},

textString="-",

fontName="serif")}));

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, smoothOrder=100, Documentation(info="<html>

This function returns the product of two given Complex numbers.

</html>"));

end multiply;

function scalarProduct "Scalar product of two complex vectors c1 and c2"

import Complex;

input Complex c1[:] "Vector of Complex numbers 1";

input Complex c2[size(c1,1)] "Vector of Complex numbers 2";

output Complex c3 "Scalar product of c1 and c2";

algorithm

c3 := Complex(0);

for i in 1:size(c1,1) loop

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, smoothOrder=100, Documentation(info = "<html>This function returns the scalar product of two given vectors of Complex numbers of length <code>n</code>.

<blockquote><pre>c3 = sum(conj(c1[k]) * c2[k] for k in 1:n)

</pre></blockquote>

</html>",

revisions = "<html>Important bug fix note: The scalar product function was originally implemented without conjugating the argument <code>c1</code>. This issue is fixed based on <a href=\"https://github.com/modelica/ModelicaStandardLibrary/issues/1260\">#1260</a>.</html>"));

end scalarProduct;

annotation (

Documentation(info="<html>

Here the multiplication operator(s) is/are defined.

</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),

Text(

extent={{-200,-200},{200,100}},

textColor={128,128,128},

fontName="serif",

textString="*")}));

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, smoothOrder=100, Documentation(info="<html>

This function returns the sum of two given Complex numbers.

</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, smoothOrder=100, Documentation(info="<html>

This function returns the quotient of two given Complex numbers.

</html>"));

end '/';

encapsulated operator '^' "Power"

function complexPower "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, smoothOrder=100, Documentation(info="<html>

This function returns the given Complex number c1 to the power of the Complex number c2.

</html>"));

end complexPower;

function integerPower "Integer power of complex number"

import Complex;

input Complex c1 "Complex number";

input Integer c2 "Integer exponent";

output Complex c3 "= c1^c2";

algorithm

c3 := if c2==0 then Complex(1) else Complex.'^'.complexPower(c1,Complex(c2));

annotation(Inline=true, smoothOrder=100, Documentation(info="<html>

This function returns the given Complex number c1 to the power of the Integer number c2.

This also works for zero exponent.

</html>"));

end integerPower;

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>

This function tests whether two given Complex numbers are equal.

</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>

This function tests whether two given Complex numbers are not equal.

</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>

This function converts a given Complex number to String representation.

</html>"));

end 'String';

annotation (

version="4.2.0 dev",

versionDate="20xx-xx-xx",

dateModified = "2025-05-23 15:00:00Z",

revisionId="$Format:%h %ci$",

conversion(

noneFromVersion="4.1.0",

noneFromVersion="4.0.0",

noneFromVersion="3.2.3",

noneFromVersion="3.2.2",

noneFromVersion="3.2.1",

noneFromVersion="1.0",

noneFromVersion="1.1"),

Documentation(info="<html>

Complex number defined as a record containing real and imaginary part, utilizing operator overloading.

Licensed by the Modelica Association under the 3-Clause BSD License

This Modelica package is free software and the use is completely at your own risk; 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>.

</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;

ModelicaStandardLibrary/Complex.mo at master · modelscript/ModelicaStandardLibrary · GitHub

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