```#!/usr/bin/env python
#
# minreal_test.py - test state space class
# Rvp, 13 Jun 2013

import unittest
import numpy as np
from scipy.linalg import eigvals
from control import matlab
from control.statesp import StateSpace
from control.xferfcn import TransferFunction
from itertools import permutations
from control.exception import slycot_check

@unittest.skipIf(not slycot_check(), "slycot not installed")
class TestMinreal(unittest.TestCase):
"""Tests for the StateSpace class."""

def setUp(self):
np.random.seed(5)
# depending on the seed and minreal performance, a number of
# reductions is produced. If random gen or minreal change, this
# will be likely to fail
self.nreductions = 0

def assert_numden_almost_equal(self, n1, n2, d1, d2):
n1[np.abs(n1) < 1e-10] = 0.
n1 = np.trim_zeros(n1)
d1[np.abs(d1) < 1e-10] = 0.
d1 = np.trim_zeros(d1)
n2[np.abs(n2) < 1e-10] = 0.
n2 = np.trim_zeros(n2)
d2[np.abs(d2) < 1e-10] = 0.
d2 = np.trim_zeros(d2)
np.testing.assert_array_almost_equal(n1, n2)
np.testing.assert_array_almost_equal(d2, d2)

def testMinrealBrute(self):
for n, m, p in permutations(range(1,6), 3):
sr = s.minreal()
if s.states > sr.states:
self.nreductions += 1
else:
# Check to make sure that poles and zeros match

# For poles, just look at eigenvalues of A
np.testing.assert_array_almost_equal(
np.sort(eigvals(s.A)), np.sort(eigvals(sr.A)))

# For zeros, need to extract SISO systems
for i in range(m):
for j in range(p):
# Extract SISO dynamixs from input i to output j
s1 = matlab.ss(s.A, s.B[:,i], s.C[j,:], s.D[j,i])
s2 = matlab.ss(sr.A, sr.B[:,i], sr.C[j,:], sr.D[j,i])

# Check that the zeros match
# Note: sorting doesn't work => have to do the hard way
z1 = matlab.zero(s1)
z2 = matlab.zero(s2)

# Start by making sure we have the same # of zeros
self.assertEqual(len(z1), len(z2))

# Make sure all zeros in s1 are in s2
for zero in z1:
# Find the closest zero
self.assertAlmostEqual(min(abs(z2 - zero)), 0.)

# Make sure all zeros in s2 are in s1
for zero in z2:
# Find the closest zero
self.assertAlmostEqual(min(abs(z1 - zero)), 0.)

# Make sure that the number of systems reduced is as expected
# (Need to update this number if you change the seed at top of file)
self.assertEqual(self.nreductions, 2)

def testMinrealSS(self):
"""Test a minreal model reduction"""
#A = [-2, 0.5, 0; 0.5, -0.3, 0; 0, 0, -0.1]
A = [[-2, 0.5, 0], [0.5, -0.3, 0], [0, 0, -0.1]]
#B = [0.3, -1.3; 0.1, 0; 1, 0]
B = [[0.3, -1.3], [0.1, 0.], [1.0, 0.0]]
#C = [0, 0.1, 0; -0.3, -0.2, 0]
C = [[0., 0.1, 0.0], [-0.3, -0.2, 0.0]]
#D = [0 -0.8; -0.3 0]
D = [[0., -0.8], [-0.3, 0.]]
# sys = ss(A, B, C, D)

sys = StateSpace(A, B, C, D)
sysr = sys.minreal()
self.assertEqual(sysr.states, 2)
self.assertEqual(sysr.inputs, sys.inputs)
self.assertEqual(sysr.outputs, sys.outputs)
np.testing.assert_array_almost_equal(
eigvals(sysr.A), [-2.136154, -0.1638459])

def testMinrealtf(self):
"""Try the minreal function, and also test easy entry by creation
of a Laplace variable s"""
s = TransferFunction([1, 0], )
h = (s+1)*(s+2.00000000001)/(s+2)/(s**2+s+1)
hm = h.minreal()
hr = (s+1)/(s**2+s+1)
np.testing.assert_array_almost_equal(hm.num, hr.num)
np.testing.assert_array_almost_equal(hm.den, hr.den)

if __name__ == "__main__":
unittest.main()
```