operator record Complex "Complex number with overloaded operators" //record Complex "Complex number with overloaded operators" replaceable Real re "Real part of complex number"; replaceable Real im "Imaginary part of complex number"; 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 end fromReal; end 'constructor'; encapsulated operator function '0' "Zero-element of addition (= Complex(0))" import Complex; output Complex result "Complex(0)"; algorithm result := Complex(0); 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); 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); end subtract; 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); 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; end scalarProduct; 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); 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)); 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)); 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; 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; 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; end 'String'; end Complex;