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253 lines
9.1 KiB
253 lines
9.1 KiB
import os
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import stormpy
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from configurations import gspn, xml
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@gspn
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class TestGSPNBuilder:
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def test_layout_info(self):
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layout = stormpy.gspn.LayoutInfo()
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assert layout.x == 0
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assert layout.y == 0
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assert layout.rotation == 0
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layout.x = 1
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assert layout.x == 1
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layout_xy = stormpy.gspn.LayoutInfo(2, 3)
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assert layout_xy.x == 2
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assert layout_xy.rotation == 0
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layout_xyr = stormpy.gspn.LayoutInfo(2, 3, 4)
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assert layout_xyr.rotation == 4
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def test_place(self):
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p_id = 4
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place = stormpy.gspn.Place(id=p_id)
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assert p_id == place.get_id()
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assert not place.has_restricted_capacity()
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place.set_capacity(cap=5)
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assert place.has_restricted_capacity()
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assert place.get_capacity() == 5
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p_name = "P_0"
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place.set_name(name=p_name)
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assert place.get_name() == p_name
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p_tokens = 2
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place.set_number_of_initial_tokens(p_tokens)
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assert place.get_number_of_initial_tokens() == p_tokens
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def test_transition(self):
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# test TimedTransition
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tt = stormpy.gspn.TimedTransition()
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tt_name = " tt"
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tt.set_name(tt_name)
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assert tt_name == tt.get_name()
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tt_rate = 0.2
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tt.set_rate(tt_rate)
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assert tt_rate == tt.get_rate()
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# connect a place to this transition and test arcs
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place = stormpy.gspn.Place(0)
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# test input arcs
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assert not tt.exists_input_arc(place)
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tt.set_input_arc_multiplicity(place, 2)
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assert tt.exists_input_arc(place)
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assert tt.get_input_arc_multiplicity(place) == 2
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tt.remove_input_arc(place)
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assert not tt.exists_input_arc(place)
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# test output arcs
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assert not tt.exists_output_arc(place)
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tt.set_output_arc_multiplicity(place, 3)
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assert tt.exists_output_arc(place)
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assert tt.get_output_arc_multiplicity(place) == 3
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tt.remove_output_arc(place)
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assert not tt.exists_output_arc(place)
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# test inhibition arcs
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assert not tt.exists_inhibition_arc(place)
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tt.set_inhibition_arc_multiplicity(place, 5)
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assert tt.exists_inhibition_arc(place)
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assert tt.get_inhibition_arc_multiplicity(place) == 5
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tt.remove_inhibition_arc(place)
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assert not tt.exists_inhibition_arc(place)
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# test ImmediateTransition
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ti = stormpy.gspn.ImmediateTransition()
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ti_name = " ti"
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ti.set_name(ti_name)
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assert ti_name == ti.get_name()
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assert ti.no_weight_attached()
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ti_weight = 0.2
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ti.set_weight(ti_weight)
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assert ti_weight == ti.get_weight()
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assert not ti.no_weight_attached()
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def test_build_gspn(self):
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gspn_name = "gspn_test"
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builder = stormpy.gspn.GSPNBuilder()
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id_p_0 = builder.add_place()
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id_p_1 = builder.add_place(initial_tokens=1)
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id_p_2 = builder.add_place(initial_tokens=0, name="place_2")
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id_p_3 = builder.add_place(capacity=2, initial_tokens=3, name="place_3")
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p_layout = stormpy.gspn.LayoutInfo(1, 2)
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builder.set_place_layout_info(id_p_0, p_layout)
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id_ti_0 = builder.add_immediate_transition(priority=1, weight=0.5, name="ti_0")
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id_ti_1 = builder.add_immediate_transition()
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id_tt_0 = builder.add_timed_transition(priority=2, rate=0.4, name="tt_0")
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id_tt_1 = builder.add_timed_transition(priority=0, rate=0.5, num_servers=2, name="tt_1")
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t_layout = stormpy.gspn.LayoutInfo(1, 2)
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builder.set_transition_layout_info(id_ti_0, t_layout)
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# add arcs
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builder.add_input_arc(id_p_0, id_ti_1, multiplicity=2)
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builder.add_input_arc("place_2", "ti_0", multiplicity=2)
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builder.add_output_arc(id_ti_1, id_p_2, multiplicity=2)
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builder.add_output_arc("tt_0", "place_3", multiplicity=2)
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builder.add_inhibition_arc(id_p_2, id_tt_0, multiplicity=2)
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builder.add_inhibition_arc("place_3", "tt_0", multiplicity=2)
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builder.add_normal_arc("place_3", "tt_0", multiplicity=2)
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builder.add_normal_arc("tt_0", "place_3", multiplicity=2)
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# test gspn composition
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builder.set_name(gspn_name)
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gspn = builder.build_gspn()
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assert gspn.get_name() == gspn_name
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assert gspn.is_valid()
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assert gspn.get_number_of_immediate_transitions() == 2
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assert gspn.get_number_of_timed_transitions() == 2
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assert gspn.get_number_of_places() == 4
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assert len(gspn.get_places()) == 4
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assert len(gspn.get_immediate_transitions()) == 2
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assert len(gspn.get_timed_transitions()) == 2
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# test places
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p_0 = gspn.get_place(id_p_0)
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assert p_0.get_id() == id_p_0
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p_1 = gspn.get_place(id_p_1)
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assert p_1.get_id() == id_p_1
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assert p_1.get_number_of_initial_tokens() == 1
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p_2 = gspn.get_place(id_p_2)
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assert p_2.get_id() == id_p_2
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assert p_2.get_name() == "place_2"
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p_3 = gspn.get_place(id_p_3)
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assert p_3.get_name() == "place_3"
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assert p_3.get_capacity() == 2
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assert p_3.get_number_of_initial_tokens() == 3
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assert p_3.has_restricted_capacity()
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# test transitions
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ti_0 = gspn.get_immediate_transition("ti_0")
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assert ti_0.get_id() == id_ti_0
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assert ti_0.get_weight() == 0.5
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assert ti_0.get_priority() == 1
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tt_0 = gspn.get_timed_transition("tt_0")
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assert tt_0.get_id() == id_tt_0
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assert tt_0.get_rate() == 0.4
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assert tt_0.get_priority() == 2
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tt_1 = gspn.get_timed_transition("tt_1")
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assert tt_1.get_id() == id_tt_1
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assert tt_1.get_number_of_servers() == 2
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# test new name
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gspn_new_name = "new_name"
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gspn.set_name(gspn_new_name)
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assert gspn.get_name() == gspn_new_name
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def test_export_to_pnpro(self, tmpdir):
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builder = stormpy.gspn.GSPNBuilder()
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builder.set_name("gspn_test")
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# add places and transitions
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id_p_0 = builder.add_place()
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id_p_1 = builder.add_place(initial_tokens=3, name="place_1", capacity=2)
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id_ti_0 = builder.add_immediate_transition(priority=0, weight=0.5, name="ti_0")
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id_tt_0 = builder.add_timed_transition(priority=0, rate=0.5, num_servers=2, name="tt_0")
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gspn = builder.build_gspn()
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export_file = os.path.join(str(tmpdir), "gspn.pnpro")
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# export gspn to pnml
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gspn.export_gspn_pnpro_file(export_file)
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# import gspn
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gspn_parser = stormpy.gspn.GSPNParser()
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gspn_import = gspn_parser.parse(export_file)
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# test imported gspn
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assert gspn_import.get_name() == gspn.get_name()
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assert gspn_import.get_number_of_timed_transitions() == gspn.get_number_of_timed_transitions()
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assert gspn_import.get_number_of_immediate_transitions() == gspn.get_number_of_immediate_transitions()
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assert gspn_import.get_number_of_places() == gspn.get_number_of_places()
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p_0 = gspn_import.get_place(id_p_0)
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assert p_0.get_id() == id_p_0
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p_1 = gspn_import.get_place(id_p_1)
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assert p_1.get_name() == "place_1"
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# todo capacity info lost
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# assert p_1.get_capacity() == 2
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# assert p_1.has_restricted_capacity() == True
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assert p_1.get_number_of_initial_tokens() == 3
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ti_0 = gspn_import.get_immediate_transition("ti_0")
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assert ti_0.get_id() == id_ti_0
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tt_0 = gspn_import.get_timed_transition("tt_0")
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assert tt_0.get_id() == id_tt_0
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@xml
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def test_export_to_pnml(self, tmpdir):
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builder = stormpy.gspn.GSPNBuilder()
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builder.set_name("gspn_test")
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# add places and transitions
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id_p_0 = builder.add_place()
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id_p_1 = builder.add_place(initial_tokens=3, name="place_1", capacity=2)
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id_ti_0 = builder.add_immediate_transition(priority=0, weight=0.5, name="ti_0")
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id_tt_0 = builder.add_timed_transition(priority=0, rate=0.5, num_servers=2, name="tt_0")
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gspn = builder.build_gspn()
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export_file = os.path.join(str(tmpdir), "gspn.pnml")
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# export gspn to pnml
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gspn.export_gspn_pnml_file(export_file)
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# import gspn
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gspn_parser = stormpy.gspn.GSPNParser()
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gspn_import = gspn_parser.parse(export_file)
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# test imported gspn
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assert gspn_import.get_name() == gspn.get_name()
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assert gspn_import.get_number_of_timed_transitions() == gspn.get_number_of_timed_transitions()
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assert gspn_import.get_number_of_immediate_transitions() == gspn.get_number_of_immediate_transitions()
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assert gspn_import.get_number_of_places() == gspn.get_number_of_places()
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p_0 = gspn_import.get_place(id_p_0)
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assert p_0.get_id() == id_p_0
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p_1 = gspn_import.get_place(id_p_1)
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assert p_1.get_name() == "place_1"
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assert p_1.get_capacity() == 2
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assert p_1.get_number_of_initial_tokens() == 3
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assert p_1.has_restricted_capacity()
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ti_0 = gspn_import.get_immediate_transition("ti_0")
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assert ti_0.get_id() == id_ti_0
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tt_0 = gspn_import.get_timed_transition("tt_0")
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#This file was created by <bruno> Sun Feb 16 14:19:06 1997
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#LyX 0.10 (C) 1995 1996 Matthias Ettrich and the LyX Team
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\lyxformat 2.10
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\textclass article
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\begin_preamble
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\catcode`@=11 % @ ist ab jetzt ein gewoehnlicher Buchstabe
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\def\Res{\mathop{\operator@font Res}}
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\def\ll{\langle\!\langle}
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\def\gg{\rangle\!\rangle}
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\catcode`@=12 % @ ist ab jetzt wieder ein Sonderzeichen
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\end_preamble
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\language default
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\inputencoding latin1
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\fontscheme default
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\epsfig dvips
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\papersize a4paper
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\paperfontsize 12
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\baselinestretch 1.00
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\secnumdepth 3
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\tocdepth 3
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\paragraph_separation indent
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\quotes_language english
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\quotes_times 2
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\paperorientation portrait
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\papercolumns 0
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\papersides 1
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\paperpagestyle plain
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\layout LaTeX Title
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The diagonal of a rational function
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\layout Description
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Theorem:
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\layout Standard
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Let
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\begin_inset Formula \( M \)
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\end_inset
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be a torsion-free
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\begin_inset Formula \( R \)
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\end_inset
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-module, and
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\begin_inset Formula \( d>0 \)
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\end_inset
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.
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Let
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\begin_inset Formula
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\[
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f=\sum _{n_{1},...,n_{d}}a_{n_{1},...,n_{d}}\, x_{1}^{n_{1}}\cdots x_{d}^{n_{d}}\in M[[x_{1},\ldots x_{d}]]\]
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\end_inset
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be a rational function, i.
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e.
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there are
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\begin_inset Formula \( P\in M[x_{1},\ldots ,x_{d}] \)
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\end_inset
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and
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\begin_inset Formula \( Q\in R[x_{1},\ldots ,x_{d}] \)
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\end_inset
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with
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\begin_inset Formula \( Q(0,\ldots ,0)=1 \)
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\end_inset
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and
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\begin_inset Formula \( Q\cdot f=P \)
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\end_inset
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.
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Then the full diagonal of
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\begin_inset Formula \( f \)
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\end_inset
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\begin_inset Formula
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\[
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g=\sum ^{\infty }_{n=0}a_{n,\ldots ,n}\, x_{1}^{n}\]
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\end_inset
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is a D-finite element of
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\begin_inset Formula \( M[[x_{1}]] \)
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\end_inset
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, w.
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r.
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t.
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\begin_inset Formula \( R[x_{1}] \)
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\end_inset
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and
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\begin_inset Formula \( \{\partial _{x_{1}}\} \)
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\end_inset
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.
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\layout Description
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Proof:
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\layout Standard
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From the hypotheses,
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\begin_inset Formula \( M[[x_{1},\ldots ,x_{d}]] \)
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\end_inset
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is a torsion-free differential module over
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\begin_inset Formula \( R[x_{1},\ldots ,x_{d}] \)
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\end_inset
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w.
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r.
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t.
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the derivatives
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\begin_inset Formula \( \{\partial _{x_{1}},\ldots ,\partial _{x_{d}}\} \)
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\end_inset
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, and
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\begin_inset Formula \( f \)
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\end_inset
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is a D-finite element of
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\begin_inset Formula \( M[[x_{1},\ldots ,x_{d}]] \)
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\end_inset
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over
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\begin_inset Formula \( R[x_{1},\ldots ,x_{d}] \)
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\end_inset
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w.
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r.
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t.
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\begin_inset Formula \( \{\partial _{x_{1}},\ldots ,\partial _{x_{d}}\} \)
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\end_inset
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.
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Now apply the general diagonal theorem ([1], section 2.
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18)
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\begin_inset Formula \( d-1 \)
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\end_inset
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times.
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\layout Description
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Theorem:
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\layout Standard
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Let
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\begin_inset Formula \( R \)
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\end_inset
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be an integral domain of characteristic 0 and
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\begin_inset Formula \( M \)
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\end_inset
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simultaneously a torsion-free
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\begin_inset Formula \( R \)
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\end_inset
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-module and a commutative
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\begin_inset Formula \( R \)
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\end_inset
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-algebra without zero divisors.
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Let
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\begin_inset Formula
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\[
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f=\sum _{m,n\geq 0}a_{m,n}x^{m}y^{n}\in M[[x,y]]\]
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\end_inset
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be a rational function.
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Then the diagonal of
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\begin_inset Formula \( f \)
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\end_inset
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\begin_inset Formula
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\[
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g=\sum ^{\infty }_{n=0}a_{n,n}\, x^{n}\]
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\end_inset
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is algebraic over
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\begin_inset Formula \( R[x] \)
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\end_inset
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.
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\layout Description
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Motivation
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\protected_separator
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of
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\protected_separator
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proof:
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\layout Standard
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The usual proof ([2]) uses complex analysis and works only for
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\begin_inset Formula \( R=M=C \)
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\end_inset
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.
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The idea is to compute
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\begin_inset Formula
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\[
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g(x^{2})=\frac{1}{2\pi i}\oint _{|z|=1}f(xz,\frac{x}{z})\frac{dz}{z}\]
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\end_inset
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This integral, whose integrand is a rational function in
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\begin_inset Formula \( x \)
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\end_inset
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and
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\begin_inset Formula \( z \)
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\end_inset
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, is calculated using the residue theorem.
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Since
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\begin_inset Formula \( f(x,y) \)
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\end_inset
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is continuous at
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\begin_inset Formula \( (0,0) \)
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\end_inset
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, there is a
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\begin_inset Formula \( \delta >0 \)
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\end_inset
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such that
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\begin_inset Formula \( f(x,y)\neq \infty \)
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\end_inset
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for
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\begin_inset Formula \( |x|<\delta \)
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\end_inset
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| </ |