425 lines
20 KiB
Python
425 lines
20 KiB
Python
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from __future__ import division
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import sys
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import numpy as np
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import numpy.testing as tst
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import networkx
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import nose
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import skfuzzy as fuzz
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import skfuzzy.control as ctrl
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def test_tipping_problem():
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# The full tipping problem uses many of these methods
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food = ctrl.Antecedent(np.linspace(0, 10, 11), 'quality')
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service = ctrl.Antecedent(np.linspace(0, 10, 11), 'service')
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tip = ctrl.Consequent(np.linspace(0, 25, 26), 'tip')
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food.automf(3)
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service.automf(3)
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# Manual membership function definition
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tip['bad'] = fuzz.trimf(tip.universe, [0, 0, 13])
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tip['middling'] = fuzz.trimf(tip.universe, [0, 13, 25])
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tip['lots'] = fuzz.trimf(tip.universe, [13, 25, 25])
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# Define fuzzy rules
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rule1 = ctrl.Rule(food['poor'] | service['poor'], tip['bad'])
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rule2 = ctrl.Rule(service['average'], tip['middling'])
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rule3 = ctrl.Rule(service['good'] | food['good'], tip['lots'])
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# The control system - defined both possible ways
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tipping = ctrl.ControlSystem([rule1, rule2, rule3])
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tipping2 = ctrl.ControlSystem(rule1)
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tipping2.addrule(rule2)
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tipping2.addrule(rule3)
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tip_sim = ctrl.ControlSystemSimulation(tipping)
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tip_sim2 = ctrl.ControlSystemSimulation(tipping2)
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# Inputs added both possible ways
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inputs = {'quality': 6.5, 'service': 9.8}
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for key, value in inputs.items():
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tip_sim.input[key] = value
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tip_sim2.inputs(inputs)
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# Compute the system
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tip_sim.compute()
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tip_sim2.compute()
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# Ensure both methods of defining rules yield the same results
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for val0, val1 in zip(tip_sim.output.values(),
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tip_sim2.output.values()):
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tst.assert_allclose(val0, val1)
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# Verify against manual computation
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tst.assert_allclose(tip_sim.output['tip'], 19.8578, atol=1e-2, rtol=1e-2)
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def setup_rule_order():
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global a, b, c, d
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a = ctrl.Antecedent(np.linspace(0, 10, 11), 'a')
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b = ctrl.Antecedent(np.linspace(0, 10, 11), 'b')
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c = ctrl.Antecedent(np.linspace(0, 10, 11), 'c')
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d = ctrl.Antecedent(np.linspace(0, 10, 11), 'd')
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for v in (a, b, c, d):
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v.automf(3)
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@tst.decorators.skipif(float(networkx.__version__) >= 2.0)
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@nose.with_setup(setup_rule_order)
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def test_rule_order():
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# Make sure rules are exposed in the order needed to solve them
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# correctly
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global a, b, c, d
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r1 = ctrl.Rule(a['average'] | a['poor'], c['poor'], label='r1')
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r2 = ctrl.Rule(c['poor'] | b['poor'], c['good'], label='r2')
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r3 = ctrl.Rule(c['good'] | a['good'], d['good'], label='r3')
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ctrl_sys = ctrl.ControlSystem([r1, r2, r3])
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resolved = [r for r in ctrl_sys.rules]
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assert resolved == [r1, r2, r3], "Order given was: {0}, expected {1}".format(
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resolved, [r1.label, r2.label, r3.label])
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# The assert_raises decorator does not work in Python 2.6
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@tst.decorators.skipif(
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(sys.version_info < (2, 7)) or (float(networkx.__version__) >= 2.0))
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@nose.with_setup(setup_rule_order)
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def test_unresolvable_rule_order():
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# Make sure we don't get suck in an infinite loop when the user
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# gives an unresolvable rule order
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global a, b, c, d
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r1 = ctrl.Rule(a['average'] | a['poor'], c['poor'], label='r1')
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r2 = ctrl.Rule(c['poor'] | b['poor'], c['poor'], label='r2')
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r3 = ctrl.Rule(c['good'] | a['good'], d['good'], label='r3')
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ex_msg = "Unable to resolve rule execution order"
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with tst.assert_raises(RuntimeError, expected_regexp=ex_msg):
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ctrl_sys = ctrl.ControlSystem([r1, r2, r3])
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list(ctrl_sys.rules)
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@nose.with_setup(setup_rule_order)
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def test_bad_rules():
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not_rules = ['me', 192238, 42, dict()]
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tst.assert_raises(ValueError, ctrl.ControlSystem, not_rules)
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testsystem = ctrl.ControlSystem()
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tst.assert_raises(ValueError, testsystem.addrule, a)
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def test_multiple_rules_same_consequent_term():
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# 2 input variables, 1 output variable and 7 instances.
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x1_inputs = [0.6, 0.2, 0.4, 0.7, 1, 1.2, 1.8]
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x2_inputs = [0.9, 1, 0.8, 0, 1.2, 0.6, 1.8]
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dom = np.arange(0, 2.1, 0.01)
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x1 = ctrl.Antecedent(dom, "x1")
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x1['label0'] = fuzz.trimf(x1.universe, (0.2, 0.2, 0.6))
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x1['label1'] = fuzz.trimf(x1.universe, (0.2, 0.6, 1.0))
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x1['label2'] = fuzz.trimf(x1.universe, (0.6, 1.0, 1.4))
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x1['label3'] = fuzz.trimf(x1.universe, (1.0, 1.4, 1.8))
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x1['label4'] = fuzz.trimf(x1.universe, (1.4, 1.8, 1.8))
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x2 = ctrl.Antecedent(dom, "x2")
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x2['label0'] = fuzz.trimf(x2.universe, (0.0, 0.0, 0.45))
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x2['label1'] = fuzz.trimf(x2.universe, (0.0, 0.45, 0.9))
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x2['label2'] = fuzz.trimf(x2.universe, (0.45, 0.9, 1.35))
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x2['label3'] = fuzz.trimf(x2.universe, (0.9, 1.35, 1.8))
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x2['label4'] = fuzz.trimf(x2.universe, (1.35, 1.8, 1.8))
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y = ctrl.Consequent(dom, "y")
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y['label0'] = fuzz.trimf(y.universe, (0.3, 0.3, 0.725))
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y['label1'] = fuzz.trimf(y.universe, (0.3, 0.725, 1.15))
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y['label2'] = fuzz.trimf(y.universe, (0.725, 1.15, 1.575))
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y['label3'] = fuzz.trimf(y.universe, (1.15, 1.575, 2.0))
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y['label4'] = fuzz.trimf(y.universe, (1.575, 2.0, 2.0))
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r1 = ctrl.Rule(x1['label0'] & x2['label2'], y['label0'])
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r2 = ctrl.Rule(x1['label1'] & x2['label0'], y['label0'])
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r3 = ctrl.Rule(x1['label1'] & x2['label2'], y['label0'])
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# Equivalent to above 3 rules
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r123 = ctrl.Rule((x1['label0'] & x2['label2']) |
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(x1['label1'] & x2['label0']) |
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(x1['label1'] & x2['label2']), y['label0'])
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r4 = ctrl.Rule(x1['label2'] & x2['label1'], y['label2'])
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r5 = ctrl.Rule(x1['label2'] & x2['label3'], y['label3'])
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r6 = ctrl.Rule(x1['label4'] & x2['label4'], y['label4'])
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# Build a system with three rules targeting the same Consequent Term,
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# and then an equivalent system with those three rules combined into one.
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cs0 = ctrl.ControlSystem([r1, r2, r3, r4, r5, r6])
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cs1 = ctrl.ControlSystem([r123, r4, r5, r6])
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expected_results = [0.438372093023,
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0.443962536855,
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0.461436409933,
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0.445290345769,
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1.575,
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1.15,
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1.86162790698]
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# Ensure the results are equivalent within error
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for inst, expected in zip(range(7), expected_results):
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sim0 = ctrl.ControlSystemSimulation(cs0)
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sim1 = ctrl.ControlSystemSimulation(cs1)
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sim0.input["x1"] = x1_inputs[inst]
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sim0.input["x2"] = x2_inputs[inst]
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sim1.input["x1"] = x1_inputs[inst]
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sim1.input["x2"] = x2_inputs[inst]
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sim0.compute()
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sim1.compute()
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tst.assert_allclose(sim0.output['y'], sim1.output['y'])
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tst.assert_allclose(expected, sim0.output['y'], atol=1e-4, rtol=1e-4)
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def test_complex_system():
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# A much more complex system, run multiple times & with array inputs
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universe = np.linspace(-2, 2, 5)
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error = ctrl.Antecedent(universe, 'error')
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delta = ctrl.Antecedent(universe, 'delta')
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output = ctrl.Consequent(universe, 'output')
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names = ['nb', 'ns', 'ze', 'ps', 'pb']
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error.automf(names=names)
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delta.automf(names=names)
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output.automf(names=names)
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# The rulebase:
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# rule 1: IF e = ZE AND delta = ZE THEN output = ZE
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# rule 2: IF e = ZE AND delta = SP THEN output = SN
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# rule 3: IF e = SN AND delta = SN THEN output = LP
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# rule 4: IF e = LP OR delta = LP THEN output = LN
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rule0 = ctrl.Rule(antecedent=((error['nb'] & delta['nb']) | # This combination, or...
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(error['ns'] & delta['nb']) |
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(error['nb'] & delta['ns'])),
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consequent=output['nb'], label='rule nb')
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rule1 = ctrl.Rule(antecedent=((error['nb'] & delta['ze']) |
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(error['nb'] & delta['ps']) |
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(error['ns'] & delta['ns']) |
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(error['ns'] & delta['ze']) |
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(error['ze'] & delta['ns']) |
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(error['ze'] & delta['nb']) |
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(error['ps'] & delta['nb'])),
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consequent=output['ns'], label='rule ns')
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rule2 = ctrl.Rule(antecedent=((error['nb'] & delta['pb']) |
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(error['ns'] & delta['ps']) |
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(error['ze'] & delta['ze']) |
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(error['ps'] & delta['ns']) |
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(error['pb'] & delta['nb'])),
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consequent=output['ze'], label='rule ze')
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rule3 = ctrl.Rule(antecedent=((error['ns'] & delta['pb']) |
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(error['ze'] & delta['pb']) |
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(error['ze'] & delta['ps']) |
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(error['ps'] & delta['ps']) |
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(error['ps'] & delta['ze']) |
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(error['pb'] & delta['ze']) |
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(error['pb'] & delta['ns'])),
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consequent=output['ps'], label='rule ps')
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rule4 = ctrl.Rule(antecedent=((error['ps'] & delta['pb']) |
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(error['pb'] & delta['pb']) |
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(error['pb'] & delta['ps'])),
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consequent=output['pb'], label='rule pb')
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system = ctrl.ControlSystem(rules=[rule0, rule1, rule2, rule3, rule4])
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sim = ctrl.ControlSystemSimulation(system, cache=False)
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x, y = np.meshgrid(np.linspace(-2, 2, 21), np.linspace(-2, 2, 21))
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z0 = np.zeros_like(x)
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z1 = np.zeros_like(x)
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# The original, slow way - one set of values at a time
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for i in range(21):
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for j in range(21):
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sim.input['error'] = x[i, j]
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sim.input['delta'] = y[i, j]
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sim.compute()
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z0[i, j] = sim.output['output']
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sim.reset()
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# The new way - array inputs
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sim.input['error'] = x
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sim.input['delta'] = y
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sim.compute()
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z1 = sim.output['output']
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# Ensure results align
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np.testing.assert_allclose(z0, z1)
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# Big expected array
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expected = \
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np.array([[ -1.66666667e+00, -1.65555556e+00, -1.62857143e+00,
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-1.62857143e+00, -1.65555556e+00, -1.66666667e+00,
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-1.34414414e+00, -1.18294574e+00, -1.10000000e+00,
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-1.05641026e+00, -1.00000000e+00, -1.00000000e+00,
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-1.00000000e+00, -1.00000000e+00, -1.00000000e+00,
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-1.00000000e+00, -7.37704918e-01, -5.72916667e-01,
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-4.27083333e-01, -2.62295082e-01, -2.77555756e-17],
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[ -1.65555556e+00, -1.34414414e+00, -1.29494949e+00,
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-1.29494949e+00, -1.34414414e+00, -1.34414414e+00,
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-1.34414414e+00, -1.18294574e+00, -1.10000000e+00,
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-1.05641026e+00, -1.00000000e+00, -7.37704918e-01,
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-7.13580247e-01, -7.13580247e-01, -7.37704918e-01,
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-7.37704918e-01, -4.36619718e-01, -2.91555556e-01,
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-1.56140351e-01, 1.96914557e-16, 2.62295082e-01],
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[ -1.62857143e+00, -1.29494949e+00, -1.18294574e+00,
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-1.18294574e+00, -1.18294574e+00, -1.18294574e+00,
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-1.18294574e+00, -1.18294574e+00, -1.10000000e+00,
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-1.05333333e+00, -1.00000000e+00, -7.13580247e-01,
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-5.72916667e-01, -5.72916667e-01, -5.72916667e-01,
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-5.72916667e-01, -2.91555556e-01, -1.26984127e-01,
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6.45478503e-17, 1.56140351e-01, 4.27083333e-01],
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[ -1.62857143e+00, -1.29494949e+00, -1.18294574e+00,
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-1.10000000e+00, -1.10000000e+00, -1.10000000e+00,
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-1.10000000e+00, -1.10000000e+00, -1.10000000e+00,
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-1.05333333e+00, -1.00000000e+00, -7.13580247e-01,
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-5.72916667e-01, -4.27083333e-01, -4.27083333e-01,
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-4.27083333e-01, -1.56140351e-01, 2.42054439e-16,
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1.26984127e-01, 2.91555556e-01, 5.72916667e-01],
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[ -1.65555556e+00, -1.34414414e+00, -1.18294574e+00,
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-1.10000000e+00, -1.05641026e+00, -1.05641026e+00,
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-1.05641026e+00, -1.05333333e+00, -1.05333333e+00,
|
||
|
|
-1.05641026e+00, -1.00000000e+00, -7.37704918e-01,
|
||
|
|
-5.72916667e-01, -4.27083333e-01, -2.62295082e-01,
|
||
|
|
-2.62295082e-01, 2.29733650e-16, 1.56140351e-01,
|
||
|
|
2.91555556e-01, 4.36619718e-01, 7.37704918e-01],
|
||
|
|
[ -1.66666667e+00, -1.34414414e+00, -1.18294574e+00,
|
||
|
|
-1.10000000e+00, -1.05641026e+00, -1.00000000e+00,
|
||
|
|
-1.00000000e+00, -1.00000000e+00, -1.00000000e+00,
|
||
|
|
-1.00000000e+00, -1.00000000e+00, -7.37704918e-01,
|
||
|
|
-5.72916667e-01, -4.27083333e-01, -2.62295082e-01,
|
||
|
|
-2.77555756e-17, 2.62295082e-01, 4.27083333e-01,
|
||
|
|
5.72916667e-01, 7.37704918e-01, 1.00000000e+00],
|
||
|
|
[ -1.34414414e+00, -1.34414414e+00, -1.18294574e+00,
|
||
|
|
-1.10000000e+00, -1.05641026e+00, -1.00000000e+00,
|
||
|
|
-7.37704918e-01, -7.13580247e-01, -7.13580247e-01,
|
||
|
|
-7.37704918e-01, -7.37704918e-01, -4.36619718e-01,
|
||
|
|
-2.91555556e-01, -1.56140351e-01, 4.17271323e-16,
|
||
|
|
2.62295082e-01, 2.62295082e-01, 4.27083333e-01,
|
||
|
|
5.72916667e-01, 7.37704918e-01, 1.00000000e+00],
|
||
|
|
[ -1.18294574e+00, -1.18294574e+00, -1.18294574e+00,
|
||
|
|
-1.10000000e+00, -1.05333333e+00, -1.00000000e+00,
|
||
|
|
-7.13580247e-01, -5.72916667e-01, -5.72916667e-01,
|
||
|
|
-5.72916667e-01, -5.72916667e-01, -2.91555556e-01,
|
||
|
|
-1.26984127e-01, 2.09780513e-16, 1.56140351e-01,
|
||
|
|
4.27083333e-01, 4.27083333e-01, 4.27083333e-01,
|
||
|
|
5.72916667e-01, 7.13580247e-01, 1.00000000e+00],
|
||
|
|
[ -1.10000000e+00, -1.10000000e+00, -1.10000000e+00,
|
||
|
|
-1.10000000e+00, -1.05333333e+00, -1.00000000e+00,
|
||
|
|
-7.13580247e-01, -5.72916667e-01, -4.27083333e-01,
|
||
|
|
-4.27083333e-01, -4.27083333e-01, -1.56140351e-01,
|
||
|
|
2.42054439e-16, 1.26984127e-01, 2.91555556e-01,
|
||
|
|
5.72916667e-01, 5.72916667e-01, 5.72916667e-01,
|
||
|
|
5.72916667e-01, 7.13580247e-01, 1.00000000e+00],
|
||
|
|
[ -1.05641026e+00, -1.05641026e+00, -1.05333333e+00,
|
||
|
|
-1.05333333e+00, -1.05641026e+00, -1.00000000e+00,
|
||
|
|
-7.37704918e-01, -5.72916667e-01, -4.27083333e-01,
|
||
|
|
-2.62295082e-01, -2.62295082e-01, 2.29733650e-16,
|
||
|
|
1.56140351e-01, 2.91555556e-01, 4.36619718e-01,
|
||
|
|
7.37704918e-01, 7.37704918e-01, 7.13580247e-01,
|
||
|
|
7.13580247e-01, 7.37704918e-01, 1.00000000e+00],
|
||
|
|
[ -1.00000000e+00, -1.00000000e+00, -1.00000000e+00,
|
||
|
|
-1.00000000e+00, -1.00000000e+00, -1.00000000e+00,
|
||
|
|
-7.37704918e-01, -5.72916667e-01, -4.27083333e-01,
|
||
|
|
-2.62295082e-01, -2.77555756e-17, 2.62295082e-01,
|
||
|
|
4.27083333e-01, 5.72916667e-01, 7.37704918e-01,
|
||
|
|
1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
|
||
|
|
1.00000000e+00, 1.00000000e+00, 1.00000000e+00],
|
||
|
|
[ -1.00000000e+00, -7.37704918e-01, -7.13580247e-01,
|
||
|
|
-7.13580247e-01, -7.37704918e-01, -7.37704918e-01,
|
||
|
|
-4.36619718e-01, -2.91555556e-01, -1.56140351e-01,
|
||
|
|
2.29733650e-16, 2.62295082e-01, 2.62295082e-01,
|
||
|
|
4.27083333e-01, 5.72916667e-01, 7.37704918e-01,
|
||
|
|
1.00000000e+00, 1.05641026e+00, 1.05333333e+00,
|
||
|
|
1.05333333e+00, 1.05641026e+00, 1.05641026e+00],
|
||
|
|
[ -1.00000000e+00, -7.13580247e-01, -5.72916667e-01,
|
||
|
|
-5.72916667e-01, -5.72916667e-01, -5.72916667e-01,
|
||
|
|
-2.91555556e-01, -1.26984127e-01, 2.42054439e-16,
|
||
|
|
1.56140351e-01, 4.27083333e-01, 4.27083333e-01,
|
||
|
|
4.27083333e-01, 5.72916667e-01, 7.13580247e-01,
|
||
|
|
1.00000000e+00, 1.05333333e+00, 1.10000000e+00,
|
||
|
|
1.10000000e+00, 1.10000000e+00, 1.10000000e+00],
|
||
|
|
[ -1.00000000e+00, -7.13580247e-01, -5.72916667e-01,
|
||
|
|
-4.27083333e-01, -4.27083333e-01, -4.27083333e-01,
|
||
|
|
-1.56140351e-01, 2.09780513e-16, 1.26984127e-01,
|
||
|
|
2.91555556e-01, 5.72916667e-01, 5.72916667e-01,
|
||
|
|
5.72916667e-01, 5.72916667e-01, 7.13580247e-01,
|
||
|
|
1.00000000e+00, 1.05333333e+00, 1.10000000e+00,
|
||
|
|
1.18294574e+00, 1.18294574e+00, 1.18294574e+00],
|
||
|
|
[ -1.00000000e+00, -7.37704918e-01, -5.72916667e-01,
|
||
|
|
-4.27083333e-01, -2.62295082e-01, -2.62295082e-01,
|
||
|
|
4.17271323e-16, 1.56140351e-01, 2.91555556e-01,
|
||
|
|
4.36619718e-01, 7.37704918e-01, 7.37704918e-01,
|
||
|
|
7.13580247e-01, 7.13580247e-01, 7.37704918e-01,
|
||
|
|
1.00000000e+00, 1.05641026e+00, 1.10000000e+00,
|
||
|
|
1.18294574e+00, 1.34414414e+00, 1.34414414e+00],
|
||
|
|
[ -1.00000000e+00, -7.37704918e-01, -5.72916667e-01,
|
||
|
|
-4.27083333e-01, -2.62295082e-01, -2.77555756e-17,
|
||
|
|
2.62295082e-01, 4.27083333e-01, 5.72916667e-01,
|
||
|
|
7.37704918e-01, 1.00000000e+00, 1.00000000e+00,
|
||
|
|
1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
|
||
|
|
1.00000000e+00, 1.05641026e+00, 1.10000000e+00,
|
||
|
|
1.18294574e+00, 1.34414414e+00, 1.66666667e+00],
|
||
|
|
[ -7.37704918e-01, -4.36619718e-01, -2.91555556e-01,
|
||
|
|
-1.56140351e-01, 2.29733650e-16, 2.62295082e-01,
|
||
|
|
2.62295082e-01, 4.27083333e-01, 5.72916667e-01,
|
||
|
|
7.37704918e-01, 1.00000000e+00, 1.05641026e+00,
|
||
|
|
1.05333333e+00, 1.05333333e+00, 1.05641026e+00,
|
||
|
|
1.05641026e+00, 1.05641026e+00, 1.10000000e+00,
|
||
|
|
1.18294574e+00, 1.34414414e+00, 1.65555556e+00],
|
||
|
|
[ -5.72916667e-01, -2.91555556e-01, -1.26984127e-01,
|
||
|
|
2.42054439e-16, 1.56140351e-01, 4.27083333e-01,
|
||
|
|
4.27083333e-01, 4.27083333e-01, 5.72916667e-01,
|
||
|
|
7.13580247e-01, 1.00000000e+00, 1.05333333e+00,
|
||
|
|
1.10000000e+00, 1.10000000e+00, 1.10000000e+00,
|
||
|
|
1.10000000e+00, 1.10000000e+00, 1.10000000e+00,
|
||
|
|
1.18294574e+00, 1.29494949e+00, 1.62857143e+00],
|
||
|
|
[ -4.27083333e-01, -1.56140351e-01, 6.45478503e-17,
|
||
|
|
1.26984127e-01, 2.91555556e-01, 5.72916667e-01,
|
||
|
|
5.72916667e-01, 5.72916667e-01, 5.72916667e-01,
|
||
|
|
7.13580247e-01, 1.00000000e+00, 1.05333333e+00,
|
||
|
|
1.10000000e+00, 1.18294574e+00, 1.18294574e+00,
|
||
|
|
1.18294574e+00, 1.18294574e+00, 1.18294574e+00,
|
||
|
|
1.18294574e+00, 1.29494949e+00, 1.62857143e+00],
|
||
|
|
[ -2.62295082e-01, 1.96914557e-16, 1.56140351e-01,
|
||
|
|
2.91555556e-01, 4.36619718e-01, 7.37704918e-01,
|
||
|
|
7.37704918e-01, 7.13580247e-01, 7.13580247e-01,
|
||
|
|
7.37704918e-01, 1.00000000e+00, 1.05641026e+00,
|
||
|
|
1.10000000e+00, 1.18294574e+00, 1.34414414e+00,
|
||
|
|
1.34414414e+00, 1.34414414e+00, 1.29494949e+00,
|
||
|
|
1.29494949e+00, 1.34414414e+00, 1.65555556e+00],
|
||
|
|
[ -2.77555756e-17, 2.62295082e-01, 4.27083333e-01,
|
||
|
|
5.72916667e-01, 7.37704918e-01, 1.00000000e+00,
|
||
|
|
1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
|
||
|
|
1.00000000e+00, 1.00000000e+00, 1.05641026e+00,
|
||
|
|
1.10000000e+00, 1.18294574e+00, 1.34414414e+00,
|
||
|
|
1.66666667e+00, 1.65555556e+00, 1.62857143e+00,
|
||
|
|
1.62857143e+00, 1.65555556e+00, 1.66666667e+00]])
|
||
|
|
|
||
|
|
# Ensure results are within expected limits
|
||
|
|
np.testing.assert_allclose(z1, expected)
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
tst.run_module_suite()
|