#!/usr/bin/env python

import os

import numpy as np

import control.modelsimp as msimp

import control.matlab as mt

from control.statesp import StateSpace

import matplotlib.pyplot as plt

plt.close('all')

# controllable canonical realization computed in MATLAB for the

# transfer function: num = [1 11 45 32], den = [1 15 60 200 60]

A = np.array([

[-15., -7.5, -6.25, -1.875],

[8., 0., 0., 0.],

[0., 4., 0., 0.],

[0., 0., 1., 0.]

])

B = np.array([

[2.],

[0.],

[0.],

[0.]

])

C = np.array([[0.5, 0.6875, 0.7031, 0.5]])

D = np.array([[0.]])

# The full system

fsys = StateSpace(A, B, C, D)

# The reduced system, truncating the order by 1

n = 3

rsys = msimp.balred(fsys, n, method='truncate')

# Comparison of the step responses of the full and reduced systems

plt.figure(1)

y, t = mt.step(fsys)

yr, tr = mt.step(rsys)

plt.plot(t.T, y.T)

plt.plot(tr.T, yr.T)

# Repeat balanced reduction, now with 100-dimensional random state space

sysrand = mt.rss(100, 1, 1)

rsysrand = msimp.balred(sysrand, 10, method='truncate')

# Comparison of the impulse responses of the full and reduced random systems

plt.figure(2)

yrand, trand = mt.impulse(sysrand)

yrandr, trandr = mt.impulse(rsysrand)

plt.plot(trand.T, yrand.T, trandr.T, yrandr.T)

if 'PYCONTROL_TEST_EXAMPLES' not in os.environ:

plt.show()