Is there an R function for finding complex numbers and counting them?

Question

I generated 1000 2x2 matrices whose elements are random numbers that range between -10 and 10.

I provided the codes I have so far.

But I'm not sure if this is the right code to find whether my list of eigenvalues are complex or not. Then for each matrix, I have to determine if the system is a stable node (both eigenvalues are real and negative); an unstable node (both eigenvalues are real and positive); a saddle (both eigenvalues are real one is positive the other negative); a stable focus (complex eigenvalues with a negative real part); an unstable focus (complex eigenvalues with a positive real part); or a center (imaginary eigenvalues, real part is zero).

I also have counters set up but not sure how to incorporate them. When I enter in the code, nothing shows up.

M=lapply(1:1000, function(z) matrix(runif(1000,min=-10,max=10), ncol = 2, nrow = 2))

eig=lapply(M, eigen)

V=sapply(eig, `[[`, "values")

SFcounter=0

if (is.complex(V)==T)
Re(V)>0

SFcounter=SFcounter+1

Answer 1

For each node you have create a column in V. you can use the Im function to extract the imaginary part (whether its equal to zero or otherwise) of any complex number. You can extract the real component with Re. Further, if you're interested in classifying real numbers, it is all those which satisfy Im(V) == 0 [the imaginary component is equal to zero].

If you use apply you can assess each eigenvalue pair in V, which are grouped together at each column. Based on your different classification criteria, you can identify these points using if statements:

node.classification <- function(x) {
  if ( (Im(x) == 0) && (Re(x) < 0) ) { #both eigenvalues are real and negative
    return("stable")
  } else {
    if ( (Im(x) == 0) && (Re(x) > 0) ) { #both eigenvalues are real and positive
      return("unstable")
    } else {
      if ( (Im(x) == 0) && sum((Re(x) > 0) == 1) ){ #both real one pos./one neg.
        return("saddle")
      } else {
        if ( (Im(x) != 0) && (Re(x) < 0) ) { #each complex, real part negative
          return("stable focus")
        } else {
          if ( (Im(x) != 0) && (Re(x) > 0) ) { #each complex, real part positive
            return("unstable focus")
          } else {
            return(NA)
          }
        }
      }
    }
  }
}

head(apply(V, 2, node.classification))
[1] "unstable"       "stable focus"   "stable"        
[4] "unstable"       "unstable"       "unstable focus"