operator recordComplex

Information

This record defines a complex number consisting of a real and an imaginary part. Additionally, various utility functions are provided in the record to operate on instances of this record. Example (note: "j" in the comments is defined as j=sqrt(-1)):

   import Modelica.Utilities.Streams;
   import Modelica_LinearSystems2.Math.Complex;
   Complex c1=Complex(re=2, im=3) "= 2 + 3j";
   Complex c2=Complex(3,4) "= 3 + 4j";
 algorithm
   c3 := Complex.'+'(c1, c2) "= c1 + c2";
   Streams.print("c3 = " + Complex.'String'(c3));
   Streams.print("c3 = " + Complex.'String'(c3,"i"));
   // This gives the following print-out:
   c3 = 5 + 7j
   c3 = 5 + 7i

The utility functions are written in such a way that it is convenient to work with them, once operator overloading is provided in Modelica and Modelica tools. Example:

   // Assume operator overloading is available (this is not yet the case):
   Complex j  = Complex.j();
   Complex c4 = -2 + 5*j;
   // A Modelica tool will transform the statement of c4 into
   Complex c4 = Complex.'+'( Complex.(-2,0), Complex.'*'(Complex(5,0),j)));

The utility functions are implemented so that they can be easily inlined by a tool. In such a case, the above statement will not lead to any overhead.

Components

Contents

Name	Description
Examples	Package of examples to demonstrate the usage of complex numbers
Vectors	Package of functions operating on vectors of complex numbers
Matrices	Package of functions operating on matrices of complex numbers
'constructor'	Collection of operators to construct a Complex number data record
'-'	Collection of operators for subtraction of complex numbers
'+'	Add two complex numbers
'*'	Multiply two complex numbers
'/'	Divide two complex numbers (c1 / c2)
'=='	Test whether two complex numbers are identical
'String'	Transform Complex number into a String representation
j	Returns sqrt(-1)
'abs'	Absolute value of complex number
'sqrt'	Square root of complex number
'max'	Return maximum element of complex vector
exp	Exponential of complex number
log	Logarithm of complex number
sin	Sine of complex number
cos	Cosine of complex number
arg	Phase angle of complex number
conj	Conjugate of complex number
real	Real part of complex number
imag	Imaginary part of complex number
eigenValues	Compute eingenvalues of a matrix A, using lapack routine dgeevx
eigenVectors	Calculate the rigth eigenvectors of a linear state space system and write them columnwise in a matrix.
frequency	Frequency and damping of conjugated complex pole pair
Internal	Package of internal functions operating on complex number (for advanced users only)