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Merge pull request #10 from rabraker/master
Added wrapper for TB05AD, which finds the frequency response of a state-space system.
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,165 @@ | ||
| # =================================================== | ||
| # tb05ad tests | ||
| import unittest | ||
| from slycot import transform | ||
| import numpy as np | ||
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| from numpy.testing import assert_raises, assert_almost_equal | ||
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| # set the random seed so we can get consistent results. | ||
| np.random.seed(40) | ||
| CASES = {} | ||
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| # This is a known failure for tb05ad when running job 'AG' | ||
| CASES['fail1'] = {'A': np.array([[-0.5, 0., 0., 0. ], | ||
| [ 0., -1., 0. , 0. ], | ||
| [ 1., 0., -0.5, 0. ], | ||
| [ 0., 1., 0., -1. ]]), | ||
| 'B': np.array([[ 1., 0.], | ||
| [ 0., 1.], | ||
| [ 0., 0.], | ||
| [ 0., 0.]]), | ||
| 'C': np.array([[ 0., 1., 1., 0.], | ||
| [ 0., 1., 0., 1.], | ||
| [ 0., 1., 1., 1.]])} | ||
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| n = 20 | ||
| p = 10 | ||
| m = 14 | ||
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| CASES['pass1'] = {'A': np.random.randn(n, n), | ||
| 'B': np.random.randn(n, m), | ||
| 'C': np.random.randn(p, n)} | ||
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| class test_tb05ad(unittest.TestCase): | ||
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| def test_tb05ad_ng(self): | ||
| """ | ||
| Test that tb05ad with job 'NG' computes the correct | ||
| frequency response. | ||
| """ | ||
| for key in CASES: | ||
| sys = CASES[key] | ||
| self.check_tb05ad_AG_NG(sys, 10*1j, 'NG') | ||
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| @unittest.expectedFailure | ||
| def test_tb05ad_ag_failure(self): | ||
| """ Test tb05ad and job 'AG' (i.e., balancing enabled) fails | ||
| on certain A matrices. | ||
| """ | ||
| self.check_tb05ad_AG_NG(CASES['fail1'], 10*1j, 'AG') | ||
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| def test_tb05ad_nh(self): | ||
| """Test that tb05ad with job = 'NH' computes the correct | ||
| frequency response after conversion to Hessenberg form. | ||
| First call tb05ad with job='NH' to transform to upper Hessenberg | ||
| form which outputs the transformed system. | ||
| Subsequently, call tb05ad with job='NH' using this transformed system. | ||
| """ | ||
| jomega = 10*1j | ||
| for key in CASES: | ||
| sys = CASES[key] | ||
| sys_transformed = self.check_tb05ad_AG_NG(sys, jomega, 'NG') | ||
| self.check_tb05ad_NH(sys_transformed, sys, jomega) | ||
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| def test_tb05ad_errors(self): | ||
| """ | ||
| Test tb05ad error handling. We give wrong inputs and | ||
| and check that this raises an error. | ||
| """ | ||
| self.check_tb05ad_errors(CASES['pass1']) | ||
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| def check_tb05ad_AG_NG(self, sys, jomega, job): | ||
| """ | ||
| Check that tb05ad computes the correct frequency response when | ||
| running jobs 'AG' and/or 'NG'. | ||
| Inputs | ||
| ------ | ||
| sys: A a dict of system matrices with keys 'A', 'B', and 'C'. | ||
| jomega: A complex scalar, which is the frequency we are | ||
| evaluating the system at. | ||
| job: A string, either 'AG' or 'NH' | ||
| Returns | ||
| ------- | ||
| sys_transformed: A dict of the system matrices which have been | ||
| transformed according the job. | ||
| """ | ||
| n, m = sys['B'].shape | ||
| p = sys['C'].shape[0] | ||
| result = transform.tb05ad(n, m, p, jomega, | ||
| sys['A'], sys['B'], sys['C'], job=job) | ||
| g_i = result[3] | ||
| hinvb = np.linalg.solve(np.eye(n) * jomega - sys['A'], sys['B']) | ||
| g_i_solve = sys['C'].dot(hinvb) | ||
| assert_almost_equal(g_i_solve, g_i) | ||
| sys_transformed = {'A': result[0], 'B': result[1], 'C': result[2]} | ||
| return sys_transformed | ||
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| def check_tb05ad_NH(self, sys_transformed, sys, jomega): | ||
| """ | ||
| Check tb05ad, computes the correct frequency response when | ||
| job='NH' and we supply system matrices 'A', 'B', and 'C' | ||
| which have been transformed by a previous call to tb05ad. | ||
| We check we get the same result as computing C(sI - A)^-1B | ||
| with the original system. | ||
| Inputs | ||
| ------ | ||
| sys_transformed: A a dict of the transformed (A in upper | ||
| hessenberg form) system matrices with keys | ||
| 'A', 'B', and 'C'. | ||
| sys: A dict of the original un-transformed system matrices. | ||
| jomega: A complex scalar, which is the frequency to evaluate at. | ||
| """ | ||
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| n, m = sys_transformed['B'].shape | ||
| p = sys_transformed['C'].shape[0] | ||
| result = transform.tb05ad(n, m, p, jomega, sys_transformed['A'], | ||
| sys_transformed['B'], sys_transformed['C'], | ||
| job='NH') | ||
| g_i = result[0] | ||
| hinvb = np.linalg.solve(np.eye(n) * jomega - sys['A'], sys['B']) | ||
| g_i_solve = sys['C'].dot(hinvb) | ||
| assert_almost_equal(g_i_solve, g_i) | ||
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| def check_tb05ad_errors(self, sys): | ||
| """ | ||
| Check the error handling of tb05ad. We give wrong inputs and | ||
| and check that this raises an error. | ||
| """ | ||
| n, m = sys['B'].shape | ||
| p = sys['C'].shape[0] | ||
| jomega = 10*1j | ||
| # test error handling | ||
| # wrong size A | ||
| assert_raises(ValueError, transform.tb05ad, n+1, m, p, | ||
| jomega, sys['A'], sys['B'], sys['C'], job='NH') | ||
| # wrong size B | ||
| assert_raises(ValueError, transform.tb05ad, n, m+1, p, | ||
| jomega, sys['A'], sys['B'], sys['C'], job='NH') | ||
| # wrong size C | ||
| assert_raises(ValueError, transform.tb05ad, n, m, p+1, | ||
| jomega, sys['A'], sys['B'], sys['C'], job='NH') | ||
| # unrecognized job | ||
| assert_raises(ValueError, transform.tb05ad, n, m, p, jomega, | ||
| sys['A'], sys['B'], sys['C'], job='a') | ||
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| def suite(): | ||
| return unittest.TestLoader().loadTestsFromTestCase(TestConvert) | ||
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| if __name__ == "__main__": | ||
| unittest.main() |
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