420 lines
16 KiB
Python
420 lines
16 KiB
Python
#!/usr/bin/env python
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#
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# statefbk_test.py - test state feedback functions
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# RMM, 30 Mar 2011 (based on TestStatefbk from v0.4a)
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from __future__ import print_function
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import unittest
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import sys as pysys
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import numpy as np
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import warnings
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from control.statefbk import ctrb, obsv, place, place_varga, lqr, gram, acker
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from control.matlab import *
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from control.exception import slycot_check, ControlDimension
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from control.mateqn import care, dare
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from control.config import use_numpy_matrix, reset_defaults
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class TestStatefbk(unittest.TestCase):
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"""Test state feedback functions"""
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def setUp(self):
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# Use array instead of matrix (and save old value to restore at end)
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use_numpy_matrix(False)
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# Maximum number of states to test + 1
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self.maxStates = 5
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# Maximum number of inputs and outputs to test + 1
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self.maxTries = 4
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# Set to True to print systems to the output.
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self.debug = False
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# get consistent test results
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np.random.seed(0)
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def testCtrbSISO(self):
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A = np.array([[1., 2.], [3., 4.]])
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B = np.array([[5.], [7.]])
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Wctrue = np.array([[5., 19.], [7., 43.]])
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Wc = ctrb(A, B)
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np.testing.assert_array_almost_equal(Wc, Wctrue)
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self.assertTrue(isinstance(Wc, np.ndarray))
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self.assertFalse(isinstance(Wc, np.matrix))
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# This test only works in Python 3 due to a conflict with the same
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# warning type in other test modules (frd_test.py). See
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# https://bugs.python.org/issue4180 for more details
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@unittest.skipIf(pysys.version_info < (3, 0), "test requires Python 3+")
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def test_ctrb_siso_deprecated(self):
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A = np.array([[1., 2.], [3., 4.]])
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B = np.array([[5.], [7.]])
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# Check that default using np.matrix generates a warning
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# TODO: remove this check with matrix type is deprecated
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warnings.resetwarnings()
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with warnings.catch_warnings(record=True) as w:
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use_numpy_matrix(True)
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self.assertTrue(issubclass(w[-1].category, UserWarning))
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Wc = ctrb(A, B)
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self.assertTrue(isinstance(Wc, np.matrix))
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self.assertTrue(issubclass(w[-1].category,
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PendingDeprecationWarning))
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use_numpy_matrix(False)
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def testCtrbMIMO(self):
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A = np.array([[1., 2.], [3., 4.]])
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B = np.array([[5., 6.], [7., 8.]])
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Wctrue = np.array([[5., 6., 19., 22.], [7., 8., 43., 50.]])
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Wc = ctrb(A, B)
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np.testing.assert_array_almost_equal(Wc, Wctrue)
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# Make sure default type values are correct
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self.assertTrue(isinstance(Wc, np.ndarray))
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def testObsvSISO(self):
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A = np.array([[1., 2.], [3., 4.]])
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C = np.array([[5., 7.]])
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Wotrue = np.array([[5., 7.], [26., 38.]])
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Wo = obsv(A, C)
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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# Make sure default type values are correct
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self.assertTrue(isinstance(Wo, np.ndarray))
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# This test only works in Python 3 due to a conflict with the same
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# warning type in other test modules (frd_test.py). See
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# https://bugs.python.org/issue4180 for more details
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@unittest.skipIf(pysys.version_info < (3, 0), "test requires Python 3+")
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def test_obsv_siso_deprecated(self):
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A = np.array([[1., 2.], [3., 4.]])
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C = np.array([[5., 7.]])
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# Check that default type generates a warning
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# TODO: remove this check with matrix type is deprecated
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with warnings.catch_warnings(record=True) as w:
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use_numpy_matrix(True, warn=False) # warnings off
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self.assertEqual(len(w), 0)
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Wo = obsv(A, C)
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self.assertTrue(isinstance(Wo, np.matrix))
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use_numpy_matrix(False)
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def testObsvMIMO(self):
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A = np.array([[1., 2.], [3., 4.]])
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C = np.array([[5., 6.], [7., 8.]])
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Wotrue = np.array([[5., 6.], [7., 8.], [23., 34.], [31., 46.]])
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Wo = obsv(A, C)
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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def testCtrbObsvDuality(self):
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A = np.array([[1.2, -2.3], [3.4, -4.5]])
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B = np.array([[5.8, 6.9], [8., 9.1]])
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Wc = ctrb(A, B)
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A = np.transpose(A)
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C = np.transpose(B)
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Wo = np.transpose(obsv(A, C));
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np.testing.assert_array_almost_equal(Wc,Wo)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramWc(self):
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5., 6.], [7., 8.]])
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C = np.array([[4., 5.], [6., 7.]])
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D = np.array([[13., 14.], [15., 16.]])
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sys = ss(A, B, C, D)
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Wctrue = np.array([[18.5, 24.5], [24.5, 32.5]])
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Wc = gram(sys, 'c')
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np.testing.assert_array_almost_equal(Wc, Wctrue)
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# This test only works in Python 3 due to a conflict with the same
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# warning type in other test modules (frd_test.py). See
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# https://bugs.python.org/issue4180 for more details
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@unittest.skipIf(pysys.version_info < (3, 0) or not slycot_check(),
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"test requires Python 3+ and slycot")
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def test_gram_wc_deprecated(self):
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5., 6.], [7., 8.]])
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C = np.array([[4., 5.], [6., 7.]])
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D = np.array([[13., 14.], [15., 16.]])
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sys = ss(A, B, C, D)
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# Check that default type generates a warning
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# TODO: remove this check with matrix type is deprecated
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with warnings.catch_warnings(record=True) as w:
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use_numpy_matrix(True)
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self.assertTrue(issubclass(w[-1].category, UserWarning))
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Wc = gram(sys, 'c')
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self.assertTrue(isinstance(Wc, np.ndarray))
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use_numpy_matrix(False)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramRc(self):
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5., 6.], [7., 8.]])
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C = np.array([[4., 5.], [6., 7.]])
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D = np.array([[13., 14.], [15., 16.]])
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sys = ss(A, B, C, D)
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Rctrue = np.array([[4.30116263, 5.6961343], [0., 0.23249528]])
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Rc = gram(sys, 'cf')
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np.testing.assert_array_almost_equal(Rc, Rctrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramWo(self):
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5., 6.], [7., 8.]])
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C = np.array([[4., 5.], [6., 7.]])
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D = np.array([[13., 14.], [15., 16.]])
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sys = ss(A, B, C, D)
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Wotrue = np.array([[257.5, -94.5], [-94.5, 56.5]])
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Wo = gram(sys, 'o')
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramWo2(self):
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5.], [7.]])
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C = np.array([[6., 8.]])
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D = np.array([[9.]])
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sys = ss(A,B,C,D)
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Wotrue = np.array([[198., -72.], [-72., 44.]])
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Wo = gram(sys, 'o')
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramRo(self):
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5., 6.], [7., 8.]])
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C = np.array([[4., 5.], [6., 7.]])
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D = np.array([[13., 14.], [15., 16.]])
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sys = ss(A, B, C, D)
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Rotrue = np.array([[16.04680654, -5.8890222], [0., 4.67112593]])
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Ro = gram(sys, 'of')
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np.testing.assert_array_almost_equal(Ro, Rotrue)
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def testGramsys(self):
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num =[1.]
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den = [1., 1., 1.]
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sys = tf(num,den)
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self.assertRaises(ValueError, gram, sys, 'o')
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self.assertRaises(ValueError, gram, sys, 'c')
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def testAcker(self):
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for states in range(1, self.maxStates):
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for i in range(self.maxTries):
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# start with a random SS system and transform to TF then
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# back to SS, check that the matrices are the same.
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sys = rss(states, 1, 1)
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if (self.debug):
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print(sys)
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# Make sure the system is not degenerate
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Cmat = ctrb(sys.A, sys.B)
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if np.linalg.matrix_rank(Cmat) != states:
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if (self.debug):
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print(" skipping (not reachable or ill conditioned)")
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continue
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# Place the poles at random locations
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des = rss(states, 1, 1);
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poles = pole(des)
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# Now place the poles using acker
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K = acker(sys.A, sys.B, poles)
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new = ss(sys.A - sys.B * K, sys.B, sys.C, sys.D)
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placed = pole(new)
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# Debugging code
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# diff = np.sort(poles) - np.sort(placed)
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# if not all(diff < 0.001):
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# print("Found a problem:")
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# print(sys)
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# print("desired = ", poles)
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np.testing.assert_array_almost_equal(np.sort(poles),
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np.sort(placed), decimal=4)
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def testPlace(self):
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# Matrices shamelessly stolen from scipy example code.
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A = np.array([[1.380, -0.2077, 6.715, -5.676],
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[-0.5814, -4.290, 0, 0.6750],
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[1.067, 4.273, -6.654, 5.893],
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[0.0480, 4.273, 1.343, -2.104]])
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B = np.array([[0, 5.679],
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[1.136, 1.136],
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[0, 0,],
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[-3.146, 0]])
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P = np.array([-0.5+1j, -0.5-1j, -5.0566, -8.6659])
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K = place(A, B, P)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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# Test that the dimension checks work.
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np.testing.assert_raises(ControlDimension, place, A[1:, :], B, P)
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np.testing.assert_raises(ControlDimension, place, A, B[1:, :], P)
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# Check that we get an error if we ask for too many poles in the same
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# location. Here, rank(B) = 2, so lets place three at the same spot.
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P_repeated = np.array([-0.5, -0.5, -0.5, -8.6659])
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np.testing.assert_raises(ValueError, place, A, B, P_repeated)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_continuous(self):
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"""
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Check that we can place eigenvalues for dtime=False
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"""
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5.], [7.]])
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P = np.array([-2., -2.])
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K = place_varga(A, B, P)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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# Test that the dimension checks work.
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np.testing.assert_raises(ControlDimension, place, A[1:, :], B, P)
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np.testing.assert_raises(ControlDimension, place, A, B[1:, :], P)
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# Regression test against bug #177
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# https://github.com/python-control/python-control/issues/177
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A = np.array([[0, 1], [100, 0]])
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B = np.array([[0], [1]])
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P = np.array([-20 + 10*1j, -20 - 10*1j])
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K = place_varga(A, B, P)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_continuous_partial_eigs(self):
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"""
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Check that we are able to use the alpha parameter to only place
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a subset of the eigenvalues, for the continous time case.
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"""
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# A matrix has eigenvalues at s=-1, and s=-2. Choose alpha = -1.5
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# and check that eigenvalue at s=-2 stays put.
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5.], [7.]])
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P = np.array([-3.])
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P_expected = np.array([-2.0, -3.0])
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alpha = -1.5
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K = place_varga(A, B, P, alpha=alpha)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P_expected.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P_expected, P_placed)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_discrete(self):
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"""
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Check that we can place poles using dtime=True (discrete time)
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"""
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A = np.array([[1., 0], [0, 0.5]])
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B = np.array([[5.], [7.]])
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P = np.array([0.5, 0.5])
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K = place_varga(A, B, P, dtime=True)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_discrete_partial_eigs(self):
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""""
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Check that we can only assign a single eigenvalue in the discrete
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time case.
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"""
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# A matrix has eigenvalues at 1.0 and 0.5. Set alpha = 0.51, and
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# check that the eigenvalue at 0.5 is not moved.
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A = np.array([[1., 0], [0, 0.5]])
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B = np.array([[5.], [7.]])
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P = np.array([0.2, 0.6])
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P_expected = np.array([0.5, 0.6])
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alpha = 0.51
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K = place_varga(A, B, P, dtime=True, alpha=alpha)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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P_expected.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P_expected, P_placed)
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def check_LQR(self, K, S, poles, Q, R):
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S_expected = np.array(np.sqrt(Q * R))
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K_expected = S_expected / R
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poles_expected = np.array([-K_expected])
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np.testing.assert_array_almost_equal(S, S_expected)
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np.testing.assert_array_almost_equal(K, K_expected)
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np.testing.assert_array_almost_equal(poles, poles_expected)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_LQR_integrator(self):
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A, B, Q, R = 0., 1., 10., 2.
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K, S, poles = lqr(A, B, Q, R)
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self.check_LQR(K, S, poles, Q, R)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_LQR_3args(self):
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sys = ss(0., 1., 1., 0.)
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Q, R = 10., 2.
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K, S, poles = lqr(sys, Q, R)
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self.check_LQR(K, S, poles, Q, R)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_care(self):
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#unit test for stabilizing and anti-stabilizing feedbacks
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#continuous-time
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A = np.diag([1,-1])
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B = np.identity(2)
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Q = np.identity(2)
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R = np.identity(2)
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S = 0 * B
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E = np.identity(2)
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X, L , G = care(A, B, Q, R, S, E, stabilizing=True)
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assert np.all(np.real(L) < 0)
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X, L , G = care(A, B, Q, R, S, E, stabilizing=False)
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assert np.all(np.real(L) > 0)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_dare(self):
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#discrete-time
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A = np.diag([0.5,2])
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B = np.identity(2)
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Q = np.identity(2)
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R = np.identity(2)
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S = 0 * B
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E = np.identity(2)
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X, L , G = dare(A, B, Q, R, S, E, stabilizing=True)
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assert np.all(np.abs(L) < 1)
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X, L , G = dare(A, B, Q, R, S, E, stabilizing=False)
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assert np.all(np.abs(L) > 1)
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def tearDown(self):
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reset_defaults()
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def test_suite():
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status1 = unittest.TestLoader().loadTestsFromTestCase(TestStatefbk)
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status2 = unittest.TestLoader().loadTestsFromTestCase(TestStatefbk)
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return status1 and status2
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if __name__ == '__main__':
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unittest.main()
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