307 lines
11 KiB
Python
307 lines
11 KiB
Python
#!/usr/bin/env python
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from __future__ import print_function
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#
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# mateqn_test.py - test wuit for matrix equation solvers
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#
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#! Currently uses numpy.testing framework; will dump you out of unittest
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#! if an error occurs. Should figure out the right way to fix this.
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""" Test cases for lyap, dlyap, care and dare functions in the file
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pyctrl_lin_alg.py. """
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"""Copyright (c) 2011, All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. Neither the name of the project author nor the names of its
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contributors may be used to endorse or promote products derived
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from this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CALTECH
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OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
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USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
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OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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SUCH DAMAGE.
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Author: Bjorn Olofsson
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"""
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import unittest
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from numpy import array
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from numpy.testing import assert_array_almost_equal, assert_array_less, \
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assert_raises
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# need scipy version of eigvals for generalized eigenvalue problem
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from scipy.linalg import eigvals, solve
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from scipy import zeros,dot
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from control.mateqn import lyap,dlyap,care,dare
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from control.exception import slycot_check, ControlArgument
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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class TestMatrixEquations(unittest.TestCase):
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"""These are tests for the matrix equation solvers in mateqn.py"""
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def test_lyap(self):
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A = array([[-1, 1],[-1, 0]])
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Q = array([[1,0],[0,1]])
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X = lyap(A,Q)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X) + X.dot(A.T) + Q, zeros((2,2)))
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A = array([[1, 2],[-3, -4]])
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Q = array([[3, 1],[1, 1]])
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X = lyap(A,Q)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X) + X.dot(A.T) + Q, zeros((2,2)))
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def test_lyap_sylvester(self):
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A = 5
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B = array([[4, 3], [4, 3]])
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C = array([2, 1])
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X = lyap(A,B,C)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A * X + X.dot(B) + C, zeros((1,2)))
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A = array([[2,1],[1,2]])
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B = array([[1,2],[0.5,0.1]])
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C = array([[1,0],[0,1]])
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X = lyap(A,B,C)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X) + X.dot(B) + C, zeros((2,2)))
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def test_lyap_g(self):
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A = array([[-1, 2],[-3, -4]])
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Q = array([[3, 1],[1, 1]])
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E = array([[1,2],[2,1]])
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X = lyap(A,Q,None,E)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X).dot(E.T) + E.dot(X).dot(A.T) + Q, zeros((2,2)))
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def test_dlyap(self):
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A = array([[-0.6, 0],[-0.1, -0.4]])
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Q = array([[1,0],[0,1]])
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X = dlyap(A,Q)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X).dot(A.T) - X + Q, zeros((2,2)))
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A = array([[-0.6, 0],[-0.1, -0.4]])
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Q = array([[3, 1],[1, 1]])
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X = dlyap(A,Q)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X).dot(A.T) - X + Q, zeros((2,2)))
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def test_dlyap_g(self):
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A = array([[-0.6, 0],[-0.1, -0.4]])
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Q = array([[3, 1],[1, 1]])
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E = array([[1, 1],[2, 1]])
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X = dlyap(A,Q,None,E)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X).dot(A.T) - E.dot(X).dot(E.T) + Q, zeros((2,2)))
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def test_dlyap_sylvester(self):
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A = 5
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B = array([[4, 3], [4, 3]])
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C = array([2, 1])
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X = dlyap(A,B,C)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A * X.dot(B.T) - X + C, zeros((1,2)))
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A = array([[2,1],[1,2]])
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B = array([[1,2],[0.5,0.1]])
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C = array([[1,0],[0,1]])
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X = dlyap(A,B,C)
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# print("The solution obtained is ", X)
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assert_array_almost_equal(A.dot(X).dot(B.T) - X + C, zeros((2,2)))
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def test_care(self):
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A = array([[-2, -1],[-1, -1]])
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Q = array([[0, 0],[0, 1]])
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B = array([[1, 0],[0, 4]])
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X,L,G = care(A,B,Q)
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# print("The solution obtained is", X)
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assert_array_almost_equal(A.T.dot(X) + X.dot(A) - X.dot(B).dot(B.T).dot(X) + Q,
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zeros((2,2)))
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assert_array_almost_equal(B.T.dot(X), G)
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def test_care_g(self):
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A = array([[-2, -1],[-1, -1]])
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Q = array([[0, 0],[0, 1]])
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B = array([[1, 0],[0, 4]])
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R = array([[2, 0],[0, 1]])
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S = array([[0, 0],[0, 0]])
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E = array([[2, 1],[1, 2]])
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X,L,G = care(A,B,Q,R,S,E)
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# print("The solution obtained is", X)
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Gref = solve(R, B.T.dot(X).dot(E) + S.T)
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assert_array_almost_equal(Gref, G)
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assert_array_almost_equal(
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A.T.dot(X).dot(E) + E.T.dot(X).dot(A)
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- (E.T.dot(X).dot(B) + S).dot(Gref) + Q,
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zeros((2,2)))
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A = array([[-2, -1],[-1, -1]])
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Q = array([[0, 0],[0, 1]])
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B = array([[1],[0]])
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R = 1
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S = array([[1],[0]])
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E = array([[2, 1],[1, 2]])
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X,L,G = care(A,B,Q,R,S,E)
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# print("The solution obtained is", X)
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Gref = 1/R * (B.T.dot(X).dot(E) + S.T)
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assert_array_almost_equal(
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A.T.dot(X).dot(E) + E.T.dot(X).dot(A)
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- (E.T.dot(X).dot(B) + S).dot(Gref) + Q ,
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zeros((2,2)))
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assert_array_almost_equal(Gref , G)
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def test_dare(self):
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A = array([[-0.6, 0],[-0.1, -0.4]])
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Q = array([[2, 1],[1, 0]])
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B = array([[2, 1],[0, 1]])
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R = array([[1, 0],[0, 1]])
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X,L,G = dare(A,B,Q,R)
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# print("The solution obtained is", X)
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Gref = solve(B.T.dot(X).dot(B) + R, B.T.dot(X).dot(A))
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assert_array_almost_equal(Gref, G)
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assert_array_almost_equal(
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A.T.dot(X).dot(A) - X -
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A.T.dot(X).dot(B).dot(Gref) + Q,
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zeros((2,2)))
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# check for stable closed loop
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lam = eigvals(A - B.dot(G))
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assert_array_less(abs(lam), 1.0)
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A = array([[1, 0],[-1, 1]])
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Q = array([[0, 1],[1, 1]])
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B = array([[1],[0]])
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R = 2
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X,L,G = dare(A,B,Q,R)
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# print("The solution obtained is", X)
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assert_array_almost_equal(
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A.T.dot(X).dot(A) - X -
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A.T.dot(X).dot(B) * solve(B.T.dot(X).dot(B) + R, B.T.dot(X).dot(A)) + Q, zeros((2,2)))
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assert_array_almost_equal(B.T.dot(X).dot(A) / (B.T.dot(X).dot(B) + R), G)
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# check for stable closed loop
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lam = eigvals(A - B.dot(G))
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assert_array_less(abs(lam), 1.0)
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def test_dare_g(self):
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A = array([[-0.6, 0],[-0.1, -0.4]])
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Q = array([[2, 1],[1, 3]])
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B = array([[1, 5],[2, 4]])
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R = array([[1, 0],[0, 1]])
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S = array([[1, 0],[2, 0]])
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E = array([[2, 1],[1, 2]])
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X,L,G = dare(A,B,Q,R,S,E)
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# print("The solution obtained is", X)
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Gref = solve(B.T.dot(X).dot(B) + R, B.T.dot(X).dot(A) + S.T)
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assert_array_almost_equal(Gref,G)
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assert_array_almost_equal(
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A.T.dot(X).dot(A) - E.T.dot(X).dot(E)
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- (A.T.dot(X).dot(B) + S).dot(Gref) + Q,
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zeros((2,2)) )
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# check for stable closed loop
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lam = eigvals(A - B.dot(G), E)
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assert_array_less(abs(lam), 1.0)
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A = array([[-0.6, 0],[-0.1, -0.4]])
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Q = array([[2, 1],[1, 3]])
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B = array([[1],[2]])
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R = 1
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S = array([[1],[2]])
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E = array([[2, 1],[1, 2]])
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X,L,G = dare(A,B,Q,R,S,E)
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# print("The solution obtained is", X)
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assert_array_almost_equal(
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A.T.dot(X).dot(A) - E.T.dot(X).dot(E) -
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(A.T.dot(X).dot(B) + S).dot(solve(B.T.dot(X).dot(B) + R, B.T.dot(X).dot(A) + S.T)) + Q,
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zeros((2,2)) )
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assert_array_almost_equal((B.T.dot(X).dot(A) + S.T) / (B.T.dot(X).dot(B) + R), G)
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# check for stable closed loop
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lam = eigvals(A - B.dot(G), E)
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assert_array_less(abs(lam), 1.0)
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def test_raise(self):
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""" Test exception raise for invalid inputs """
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# correct shapes and forms
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A = array([[1, 0], [-1, -1]])
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Q = array([[2, 1], [1, 2]])
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C = array([[1, 0], [0, 1]])
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E = array([[2, 1], [1, 2]])
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# these fail
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Afq = array([[1, 0, 0], [-1, -1, 0]])
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Qfq = array([[2, 1, 0], [1, 2, 0]])
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Qfs = array([[2, 1], [-1, 2]])
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Cfd = array([[1, 0, 0], [0, 1, 0]])
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Efq = array([[2, 1, 0], [1, 2, 0]])
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for cdlyap in [lyap, dlyap]:
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assert_raises(ControlArgument, cdlyap, Afq, Q)
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assert_raises(ControlArgument, cdlyap, A, Qfq)
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assert_raises(ControlArgument, cdlyap, A, Qfs)
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assert_raises(ControlArgument, cdlyap, Afq, Q, C)
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assert_raises(ControlArgument, cdlyap, A, Qfq, C)
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assert_raises(ControlArgument, cdlyap, A, Q, Cfd)
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assert_raises(ControlArgument, cdlyap, A, Qfq, None, E)
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assert_raises(ControlArgument, cdlyap, A, Q, None, Efq)
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assert_raises(ControlArgument, cdlyap, A, Qfs, None, E)
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assert_raises(ControlArgument, cdlyap, A, Q, C, E)
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B = array([[1, 0], [0, 1]])
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Bf = array([[1, 0], [0, 1], [1, 1]])
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R = Q
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Rfs = Qfs
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Rfq = Qfq
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S = array([[0, 0], [0, 0]])
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Sf = array([[0, 0, 0], [0, 0, 0]])
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E = array([[2, 1], [1, 2]])
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Ef = array([[2, 1], [1, 2], [1, 2]])
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assert_raises(ControlArgument, care, Afq, B, Q)
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assert_raises(ControlArgument, care, A, B, Qfq)
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assert_raises(ControlArgument, care, A, Bf, Q)
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assert_raises(ControlArgument, care, 1, B, 1)
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assert_raises(ControlArgument, care, A, B, Qfs)
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assert_raises(ValueError, dare, A, B, Q, Rfs)
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for cdare in [care, dare]:
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assert_raises(ControlArgument, cdare, Afq, B, Q, R, S, E)
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assert_raises(ControlArgument, cdare, A, B, Qfq, R, S, E)
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assert_raises(ControlArgument, cdare, A, Bf, Q, R, S, E)
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assert_raises(ControlArgument, cdare, A, B, Q, R, S, Ef)
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assert_raises(ControlArgument, cdare, A, B, Q, Rfq, S, E)
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assert_raises(ControlArgument, cdare, A, B, Q, R, Sf, E)
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assert_raises(ControlArgument, cdare, A, B, Qfs, R, S, E)
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assert_raises(ControlArgument, cdare, A, B, Q, Rfs, S, E)
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assert_raises(ControlArgument, cdare, A, B, Q, R, S)
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def suite():
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return unittest.TestLoader().loadTestsFromTestCase(TestMatrixEquations)
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if __name__ == "__main__":
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unittest.main()
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