Python Forum

I'm using the following code as part of a recursively called process.
It processes a proportional feedback loop provided by a polynom, that might use complex coefficients.

import numpy.polynomial.polynomial as poly
import math
import cmath

def coefficients(k, ts, t1):
    z1 = complex(1-k*t1,0)
    z2 = complex(k*(ts+2*t1)-1-math.exp(-ts/t1),0)
    z3 = complex(math.exp(-ts/t1)-k*(t1+ts*math.exp(-ts/t1)),0)
    coeff = (z1,z2,z3)
    return coeff

coeff = coefficients(0, 0.3, 0.4)
# coeff = ((1+0j), (-1.4723665527410148+0j), (0.47236655274101474+0j))
roots = poly.polyroots(coeff)
# roots = [ 1.00000000+0.j  2.11700002+0.j]
# ... 
# The first root is ok, the second is not a root:
>>> coeff[0]*roots[0]**2+coeff[1]*roots[0]+coeff[2]
-2.7755575615628914e-16
>>> coeff[0]*roots[1]**2+coeff[1]*roots[1]+coeff[2]
1.8370556064664063
# The correct value for the 2nd root would have been 0.4723665524
>>> coeff[0]*0.4723665524**2+coeff[1]*0.4723665524+coeff[2]
1.799307924876814e-10

What are I'm doing wrong? Or is there another method to calculate the root locus in NumPy?

By the way, I can't use the usual formula for quadratic equations because is swapped by an other function of higher degree for PI and PID-feedbacks. Thank you for any hints
Thomas

Check reverse coefficients order instead:

coeff[2]*roots[0]**2+coeff[1]*roots[0]+coeff[0]
coeff[2]*roots[1]**2+coeff[1]*roots[1]+coeff[0]

Note, that polyroot function uses np.linalg.eigs to get roots of a polynomial; In case of higher dimension precise computing eigenvalues
of a non-symmetric matrix might be problematic due to their high sensitivity to numerical errors, even to errors of representing floating point
numbers in a computer memory.

Thomas

scidam