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"""modelsimp_array_test.py - test model reduction functions
RMM, 30 Mar 2011 (based on TestModelSimp from v0.4a)
"""
import numpy as np
import pytest
from control import StateSpace, forced_response, tf, rss, c2d
from control.exception import ControlMIMONotImplemented
from control.tests.conftest import slycotonly, matarrayin
from control.modelsimp import balred, hsvd, markov, modred
class TestModelsimp:
"""Test model reduction functions"""
@slycotonly
def testHSVD(self, matarrayout, matarrayin):
A = matarrayin([[1., -2.], [3., -4.]])
B = matarrayin([[5.], [7.]])
C = matarrayin([[6., 8.]])
D = matarrayin([[9.]])
sys = StateSpace(A, B, C, D)
hsv = hsvd(sys)
hsvtrue = np.array([24.42686, 0.5731395]) # from MATLAB
np.testing.assert_array_almost_equal(hsv, hsvtrue)
# test for correct return type: ALWAYS return ndarray, even when
# use_numpy_matrix(True) was used
assert isinstance(hsv, np.ndarray)
assert not isinstance(hsv, np.matrix)
def testMarkovSignature(self, matarrayout, matarrayin):
U = matarrayin([[1., 1., 1., 1., 1.]])
Y = U
m = 3
H = markov(Y, U, m, transpose=False)
Htrue = np.array([[1., 0., 0.]])
np.testing.assert_array_almost_equal(H, Htrue)
# Make sure that transposed data also works
H = markov(np.transpose(Y), np.transpose(U), m, transpose=True)
np.testing.assert_array_almost_equal(H, np.transpose(Htrue))
# Generate Markov parameters without any arguments
H = markov(Y, U, m)
np.testing.assert_array_almost_equal(H, Htrue)
# Test example from docstring
T = np.linspace(0, 10, 100)
U = np.ones((1, 100))
T, Y = forced_response(tf([1], [1, 0.5], True), T, U)
H = markov(Y, U, 3, transpose=False)
# Test example from issue #395
inp = np.array([1, 2])
outp = np.array([2, 4])
mrk = markov(outp, inp, 1, transpose=False)
# Make sure MIMO generates an error
U = np.ones((2, 100)) # 2 inputs (Y unchanged, with 1 output)
with pytest.raises(ControlMIMONotImplemented):
markov(Y, U, m)
# Make sure markov() returns the right answer
@pytest.mark.parametrize("k, m, n",
[(2, 2, 2),
(2, 5, 5),
(5, 2, 2),
(5, 5, 5),
(5, 10, 10)])
def testMarkovResults(self, k, m, n):
#
# Test over a range of parameters
#
# k = order of the system
# m = number of Markov parameters
# n = size of the data vector
#
# Values *should* match exactly for n = m, otherewise you get a
# close match but errors due to the assumption that C A^k B =
# 0 for k > m-2 (see modelsimp.py).
#
# Generate stable continuous time system
Hc = rss(k, 1, 1)
# Choose sampling time based on fastest time constant / 10
w, _ = np.linalg.eig(Hc.A)
Ts = np.min(-np.real(w)) / 10.
# Convert to a discrete time system via sampling
Hd = c2d(Hc, Ts, 'zoh')
# Compute the Markov parameters from state space
Mtrue = np.hstack([Hd.D] + [
Hd.C @ np.linalg.matrix_power(Hd.A, i) @ Hd.B
for i in range(m-1)])
# Generate input/output data
T = np.array(range(n)) * Ts
U = np.cos(T) + np.sin(T/np.pi)
_, Y = forced_response(Hd, T, U, squeeze=True)
Mcomp = markov(Y, U, m)
# Compare to results from markov()
# experimentally determined probability to get non matching results
# with rtot=1e-6 and atol=1e-8 due to numerical errors
# for k=5, m=n=10: 0.015 %
np.testing.assert_allclose(Mtrue, Mcomp, rtol=1e-6, atol=1e-8)
def testModredMatchDC(self, matarrayin):
#balanced realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin(
[[-1.958, -1.194, 1.824, -1.464],
[-1.194, -0.8344, 2.563, -1.351],
[-1.824, -2.563, -1.124, 2.704],
[-1.464, -1.351, -2.704, -11.08]])
B = matarrayin([[-0.9057], [-0.4068], [-0.3263], [-0.3474]])
C = matarrayin([[-0.9057, -0.4068, 0.3263, -0.3474]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
rsys = modred(sys,[2, 3],'matchdc')
Artrue = np.array([[-4.431, -4.552], [-4.552, -5.361]])
Brtrue = np.array([[-1.362], [-1.031]])
Crtrue = np.array([[-1.362, -1.031]])
Drtrue = np.array([[-0.08384]])
np.testing.assert_array_almost_equal(rsys.A, Artrue, decimal=3)
np.testing.assert_array_almost_equal(rsys.B, Brtrue, decimal=3)
np.testing.assert_array_almost_equal(rsys.C, Crtrue, decimal=3)
np.testing.assert_array_almost_equal(rsys.D, Drtrue, decimal=2)
def testModredUnstable(self, matarrayin):
"""Check if an error is thrown when an unstable system is given"""
A = matarrayin(
[[4.5418, 3.3999, 5.0342, 4.3808],
[0.3890, 0.3599, 0.4195, 0.1760],
[-4.2117, -3.2395, -4.6760, -4.2180],
[0.0052, 0.0429, 0.0155, 0.2743]])
B = matarrayin([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
C = matarrayin([[1.0, 2.0, 3.0, 4.0], [1.0, 2.0, 3.0, 4.0]])
D = matarrayin([[0.0, 0.0], [0.0, 0.0]])
sys = StateSpace(A, B, C, D)
np.testing.assert_raises(ValueError, modred, sys, [2, 3])
def testModredTruncate(self, matarrayin):
#balanced realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin(
[[-1.958, -1.194, 1.824, -1.464],
[-1.194, -0.8344, 2.563, -1.351],
[-1.824, -2.563, -1.124, 2.704],
[-1.464, -1.351, -2.704, -11.08]])
B = matarrayin([[-0.9057], [-0.4068], [-0.3263], [-0.3474]])
C = matarrayin([[-0.9057, -0.4068, 0.3263, -0.3474]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
rsys = modred(sys,[2, 3],'truncate')
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[-0.9057], [-0.4068]])
Crtrue = np.array([[-0.9057, -0.4068]])
Drtrue = np.array([[0.]])
np.testing.assert_array_almost_equal(rsys.A, Artrue)
np.testing.assert_array_almost_equal(rsys.B, Brtrue)
np.testing.assert_array_almost_equal(rsys.C, Crtrue)
np.testing.assert_array_almost_equal(rsys.D, Drtrue)
@slycotonly
def testBalredTruncate(self, matarrayin):
# controlable canonical realization computed in matlab for the transfer
# function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin(
[[-15., -7.5, -6.25, -1.875],
[8., 0., 0., 0.],
[0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = matarrayin([[2.], [0.], [0.], [0.]])
C = matarrayin([[0.5, 0.6875, 0.7031, 0.5]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
orders = 2
rsys = balred(sys, orders, method='truncate')
Ar, Br, Cr, Dr = rsys.A, rsys.B, rsys.C, rsys.D
# Result from MATLAB
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[0.9057], [0.4068]])
Crtrue = np.array([[0.9057, 0.4068]])
Drtrue = np.array([[0.]])
# Look for possible changes in state in slycot
T1 = np.array([[1, 0], [0, -1]])
T2 = np.array([[-1, 0], [0, 1]])
T3 = np.array([[0, 1], [1, 0]])
for T in (T1, T2, T3):
if np.allclose(T @ Ar @ T, Artrue, atol=1e-2, rtol=1e-2):
# Apply a similarity transformation
Ar, Br, Cr = T @ Ar @ T, T @ Br, Cr @ T
break
# Make sure we got the correct answer
np.testing.assert_array_almost_equal(Ar, Artrue, decimal=2)
np.testing.assert_array_almost_equal(Br, Brtrue, decimal=4)
np.testing.assert_array_almost_equal(Cr, Crtrue, decimal=4)
np.testing.assert_array_almost_equal(Dr, Drtrue, decimal=4)
@slycotonly
def testBalredMatchDC(self, matarrayin):
# controlable canonical realization computed in matlab for the transfer
# function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin(
[[-15., -7.5, -6.25, -1.875],
[8., 0., 0., 0.],
[0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = matarrayin([[2.], [0.], [0.], [0.]])
C = matarrayin([[0.5, 0.6875, 0.7031, 0.5]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
orders = 2
rsys = balred(sys,orders,method='matchdc')
Ar, Br, Cr, Dr = rsys.A, rsys.B, rsys.C, rsys.D
# Result from MATLAB
Artrue = np.array(
[[-4.43094773, -4.55232904],
[-4.55232904, -5.36195206]])
Brtrue = np.array([[1.36235673], [1.03114388]])
Crtrue = np.array([[1.36235673, 1.03114388]])
Drtrue = np.array([[-0.08383902]])
# Look for possible changes in state in slycot
T1 = np.array([[1, 0], [0, -1]])
T2 = np.array([[-1, 0], [0, 1]])
T3 = np.array([[0, 1], [1, 0]])
for T in (T1, T2, T3):
if np.allclose(T @ Ar @ T, Artrue, atol=1e-2, rtol=1e-2):
# Apply a similarity transformation
Ar, Br, Cr = T @ Ar @ T, T @ Br, Cr @ T
break
# Make sure we got the correct answer
np.testing.assert_array_almost_equal(Ar, Artrue, decimal=2)
np.testing.assert_array_almost_equal(Br, Brtrue, decimal=4)
np.testing.assert_array_almost_equal(Cr, Crtrue, decimal=4)
np.testing.assert_array_almost_equal(Dr, Drtrue, decimal=4)