functionextractRealZeros

Extract real and conjugate complex elements from a complex vector

Information

Syntax

                realZeros = Matrices.extractRealZeros(complexVector, numberOfRealRoots);
(realZeros, complexZeros) = Matrices.extractRealZeros(
                              complexVector,
                              numberOfRealRoots,
                              name="complexVector");

Description

This function extracts the real zeros from the Complex vector "complexVector". It is required that all elements of complexVector define either a real zero (complexVector[i].im=0) or a conjugate complex zero pair (complexVector[i].re == complexVector[i+1].re and complexVector[i].im == -complexVector[i+1].im). The second argument "numberOfRealZeros" is determined by a function call of Internal.numberOfRealZeros(). The optional input argument "name" is used as name of "complexVector" in error messages.

The function returns the real elements of complexVector in vector "realZeros" and the real and imaginary part of a conjugate complex zero pair in matrix "complexZeros[:]".

Example

  // c = {0; 1+2j; 1-2j; 2; -3; -1-j; -1+j};
  Integer n = numberOfRealZeros(c);
  Real realZeros[n];
  Real complexZeros[:] = fill(Complex(0), integer((size(c,1)-n)/2));
algorithm
  (realZeros, complexZeros) := extractRealZeros(c, n);
           -> realZeros    = {0, 2, (-3)};
              complexZeros = { 1+2j,
                              -1+j}

Inputs

Type	Name	Default	Description
Complex[:]	complexVector		Zeros of a polynomial with real coefficients, e.g., eigen values of a real matrix
Integer	numberOfRealZeros		Number of real zeros of ComplexVector determined with function numberOfRealZeros
String	name	"complexVector"	Name of complexVector to be used in error message

Outputs

Type	Name	Default	Description
Real[numberOfRealZeros]	realZeros		Real zeros of complexVector
Complex[:]	complexZeros	fill(Complex(0), integer((size(complexVector, 1) - numberOfRealZeros)/2))	Complex zeros without the corresponding conjugate complex pair element