def test_ode_system(tb_args):
fvarspecs = {
"w": "k*w + a*itable + sin(t) + myauxfn1(t)*myauxfn2(w)",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)'
}
fnspecs = {'myauxfn1': (['t'], '2.5*cos(3*t)'), 'myauxfn2': (['w'], 'w/2')}
DSargs = {
'tdomain': [0.1, 2.1],
'pars': {
'k': 2,
'a': -0.5
},
'inputs': {
'itable': InterpolateTable(tb_args).variables['x1']
},
'auxvars': ['aux_wdouble', 'aux_other'],
'algparams': {
'init_step': 0.01,
'strict': False
},
'checklevel': 2,
'name': 'ODEtest',
'fnspecs': fnspecs,
'varspecs': fvarspecs
}
testODE = Vode_ODEsystem(DSargs)
assert testODE.pars == DSargs['pars']
assert (not testODE.defined)
testODE.set(ics={'w': 3.0}, tdata=[0.11, 2.1])
testtraj = testODE.compute('test1')
assert testODE.defined
assert_almost_equal(testtraj(0.5, 'w'), 6.05867901304, 3)
assert_almost_equal(testtraj(0.2, 'aux_other'), 3.90581993688, 3)
assert testODE.indepvariable.depdomain == Interval('t', float64,
[0.11, 2.1])
assert testODE.diagnostics.hasWarnings()
assert testODE.diagnostics.findWarnings(21) != []
# Now adding a terminating co-ordinate threshold event...
ev_args = {
'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True, # = default
'term': True,
'precise': True # = default
}
thresh_ev = Events.makePythonStateZeroCrossEvent('w', 20, 1, ev_args)
testODE.eventstruct.add(thresh_ev)
traj2 = testODE.compute('test2')
assert testODE.diagnostics.hasWarnings()
assert testODE.diagnostics.findWarnings(10) != []
print(testODE.diagnostics.showWarnings())
assert_almost_equal(traj2.getEventTimes()['threshold'][0], 1.51449456, 3)
assert testODE.indepvariable.depdomain == Interval('t', float64,
[0.11, 2.1])
def test_ode_system(tb_args):
fvarspecs = {
"w": "k*w + a*itable + sin(t) + myauxfn1(t)*myauxfn2(w)",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)'
}
fnspecs = {
'myauxfn1': (['t'], '2.5*cos(3*t)'),
'myauxfn2': (['w'], 'w/2')
}
DSargs = {
'tdomain': [0.1, 2.1],
'pars': {'k': 2, 'a': -0.5},
'inputs': {'itable': InterpolateTable(tb_args).variables['x1']},
'auxvars': ['aux_wdouble', 'aux_other'],
'algparams': {'init_step': 0.01, 'strict': False},
'checklevel': 2,
'name': 'ODEtest',
'fnspecs': fnspecs,
'varspecs': fvarspecs
}
testODE = Vode_ODEsystem(DSargs)
assert testODE.pars == DSargs['pars']
assert (not testODE.defined)
testODE.set(
ics={'w': 3.0},
tdata=[0.11, 2.1]
)
testtraj = testODE.compute('test1')
assert testODE.defined
assert_almost_equal(testtraj(0.5, 'w'), 6.05867901304, 3)
assert_almost_equal(testtraj(0.2, 'aux_other'), 3.90581993688, 3)
assert testODE.indepvariable.depdomain == Interval(
't', float64, [0.11, 2.1])
assert testODE.diagnostics.hasWarnings()
assert testODE.diagnostics.findWarnings(21) != []
# Now adding a terminating co-ordinate threshold event...
ev_args = {
'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True, # = default
'term': True,
'precise': True # = default
}
thresh_ev = Events.makePythonStateZeroCrossEvent('w', 20, 1, ev_args)
testODE.eventstruct.add(thresh_ev)
traj2 = testODE.compute('test2')
assert testODE.diagnostics.hasWarnings()
assert testODE.diagnostics.findWarnings(10) != []
print(testODE.diagnostics.showWarnings())
assert_almost_equal(traj2.getEventTimes()['threshold'][0], 1.51449456, 3)
assert testODE.indepvariable.depdomain == Interval(
't', float64, [0.11, 2.1])
def test_saveload_vode_odesystem(interptable):
"""Test pickling for saving and loading 'Vode_ODEsystem' Generator"""
# Vode object with event and external input trajectory (defined earlier)
fvarspecs = {
"w": "k*w + a*itable + sin(t) + myauxfn1(t)*myauxfn2(w)",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)'
}
fnspecs = {'myauxfn1': (['t'], '2.5*cos(3*t)'), 'myauxfn2': (['w'], 'w/2')}
ev_args = {
'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'term': True,
}
thresh_ev = Events.makePythonStateZeroCrossEvent('w', 20, 1, ev_args)
DSargs = {
'tdomain': [0.1, 2.1],
'tdata': [0.11, 2.1],
'ics': {
'w': 3.0
},
'pars': {
'k': 2,
'a': -0.5
},
'inputs': {
'itable': interptable.variables['x1']
},
'auxvars': ['aux_wdouble', 'aux_other'],
'algparams': {
'init_step': 0.01,
'strict': False
},
'events': thresh_ev,
'checklevel': 2,
'name': 'ODEtest',
'fnspecs': fnspecs,
'varspecs': fvarspecs
}
testODE = Vode_ODEsystem(DSargs)
odetraj = testODE.compute('testode')
saveObjects([odetraj, testODE], 'temp_objects.pkl', True)
objs_ode = loadObjects('temp_objects.pkl')
objs_ode[1].diagnostics.clearWarnings()
assert len(objs_ode[1].diagnostics.warnings) == 0
odetraj2 = objs_ode[1].compute('testode2')
assert odetraj2(0.6) == odetraj(0.6)
assert len(objs_ode[1].diagnostics.warnings) == 1
os.remove('temp_objects.pkl')
def test_saveload_vode_odesystem(interptable):
"""Test pickling for saving and loading 'Vode_ODEsystem' Generator"""
# Vode object with event and external input trajectory (defined earlier)
fvarspecs = {
"w": "k*w + a*itable + sin(t) + myauxfn1(t)*myauxfn2(w)",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)'
}
fnspecs = {
'myauxfn1': (['t'], '2.5*cos(3*t)'),
'myauxfn2': (['w'], 'w/2')
}
ev_args = {
'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'term': True,
}
thresh_ev = Events.makePythonStateZeroCrossEvent('w', 20, 1, ev_args)
DSargs = {
'tdomain': [0.1, 2.1],
'tdata': [0.11, 2.1],
'ics': {'w': 3.0},
'pars': {'k': 2, 'a': -0.5},
'inputs': {'itable': interptable.variables['x1']},
'auxvars': ['aux_wdouble', 'aux_other'],
'algparams': {'init_step': 0.01, 'strict': False},
'events': thresh_ev,
'checklevel': 2,
'name': 'ODEtest',
'fnspecs': fnspecs,
'varspecs': fvarspecs
}
testODE = Vode_ODEsystem(DSargs)
odetraj = testODE.compute('testode')
saveObjects([odetraj, testODE], 'temp_objects.pkl', True)
objs_ode = loadObjects('temp_objects.pkl')
objs_ode[1].diagnostics.clearWarnings()
assert len(objs_ode[1].diagnostics.warnings) == 0
odetraj2 = objs_ode[1].compute('testode2')
assert odetraj2(0.6) == odetraj(0.6)
assert len(objs_ode[1].diagnostics.warnings) == 1
os.remove('temp_objects.pkl')
def test_vode_events_compare_with_euler():
"""
Test terminal and non-terminal event testing with VODE integrator,
including some comparisons and tests of Euler integrator too.
"""
DSargs = args(varspecs={'w': 'k*sin(2*t) - w'}, name='ODEtest')
DSargs.tdomain = [0, 10]
DSargs.pars = {'k': 1, 'p_thresh': -0.25}
DSargs.algparams = {'init_step': 0.001, 'atol': 1e-12, 'rtol': 1e-13}
DSargs.checklevel = 2
DSargs.ics = {'w': -1.0}
DSargs.tdata = [0, 10]
ev_args_nonterm = {'name': 'monitor',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': False,
'precise': True}
thresh_ev_nonterm = Events.makeZeroCrossEvent('w', 0,
ev_args_nonterm, varnames=['w'])
ev_args_term = {'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': True,
'precise': True}
thresh_ev_term = Events.makeZeroCrossEvent('w-p_thresh',
-1, ev_args_term, varnames=['w'], parnames=['p_thresh'])
DSargs.events = [thresh_ev_nonterm, thresh_ev_term]
testODE = Vode_ODEsystem(DSargs)
# diagnostics and other possible user-defined python functions
# for python solvers only (currently only Euler)
# def before_func(euler):
# print(euler.algparams['init_step'])
#
# def after_func(euler):
# print(euler._solver.y)
#
##DSargs.user_func_beforestep = before_func
##DSargs.user_func_afterstep = after_func
testODE_Euler = Euler_ODEsystem(DSargs)
traj = testODE.compute('traj')
traj2 = testODE_Euler.compute('traj')
pts = traj.sample()
testODE.diagnostics.showWarnings()
mon_evs_found = testODE.getEvents('monitor')
term_evs_found = testODE.getEvents('threshold')
# test Euler
assert allclose(array(testODE.getEventTimes('monitor')),
array(traj2.getEventTimes('monitor')), atol=1e-3)
assert all(traj.getEvents('monitor') == mon_evs_found)
assert all(traj.getEventTimes('threshold')
== testODE.getEventTimes('threshold'))
term_evs_found.info()
# Alternative way to extract events: they are labelled in the
# pointset! These return dictionaries indexing into the pointset.
mon_evs_dict = pts.labels.by_label['Event:monitor']
mon_ev_points = pts[sort(list(mon_evs_dict.keys()))]
assert len(mon_evs_found) == len(mon_ev_points) == 2
assert all(mon_evs_found == mon_ev_points)
def test_vode_events_with_external_input(my_input):
"""
Test Vode_ODEsystem with events involving external inputs.
Robert Clewley, September 2006.
"""
xs = ['x1', 'x2', 'x3']
ys = [0, 0.5, 1]
fvarspecs = {"w": "k*w + pcwfn(sin(t)) + myauxfn1(t)*myauxfn2(w)",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)'}
fnspecs = {'myauxfn1': (['t'], '2.5*cos(3*t)'),
'myauxfn2': (['w'], 'w/2'),
'pcwfn': makeMultilinearRegrFn('x', xs, ys)}
# targetlang is optional if the default python target is desired
DSargs = args(fnspecs=fnspecs, name='ODEtest')
DSargs.varspecs = fvarspecs
DSargs.tdomain = [0.1, 2.1]
DSargs.pars = {'k': 2, 'a': -0.5, 'x1': -3, 'x2': 0.5, 'x3': 1.5}
DSargs.vars = 'w'
DSargs.inputs = {'in': my_input.variables['example_input']}
DSargs.algparams = {'init_step': 0.01}
DSargs.checklevel = 2
testODE = Vode_ODEsystem(DSargs)
assert not testODE.defined
testODE.set(ics={'w': 3.0},
tdata=[0.11, 2.1])
traj1 = testODE.compute('traj1')
assert testODE.defined
assert_almost_equal(traj1(0.5, 'w'), 8.9771499, 5)
assert not testODE.diagnostics.hasWarnings()
assert_almost_equal(traj1(0.2, ['aux_other']), 3.905819936, 5)
print("\nNow adding a terminating co-ordinate threshold event")
print(" and non-terminating timer event")
# Show off the general-purpose, language-independent event creator:
# 'makeZeroCrossEvent'
ev_args_nonterm = {'name': 'monitor',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': False,
'precise': True}
thresh_ev_nonterm = Events.makeZeroCrossEvent('in', 0,
ev_args_nonterm, inputnames=['in'])
# Now show use of the python-target specific creator:
# 'makePythonStateZeroCrossEvent', which is also only
# able to make events for state variable threshold crossings
ev_args_term = {'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': True,
'precise': True}
thresh_ev_term = Events.makePythonStateZeroCrossEvent('w',
20, 1, ev_args_term)
testODE.eventstruct.add([thresh_ev_nonterm, thresh_ev_term])
print("Recomputing trajectory:")
print("traj2 = testODE.compute('traj2')")
traj2 = testODE.compute('traj2')
print("\ntestODE.diagnostics.showWarnings() => ")
testODE.diagnostics.showWarnings()
print("\ntraj2.indepdomain.get() => ", traj2.indepdomain.get())
indep1 = traj2.indepdomain[1]
assert indep1 < 1.17 and indep1 > 1.16
mon_evs_found = testODE.getEvents('monitor')
assert len(mon_evs_found) == 1
def test_vode_events_compare_with_euler():
"""
Test terminal and non-terminal event testing with VODE integrator,
including some comparisons and tests of Euler integrator too.
"""
DSargs = args(varspecs={'w': 'k*sin(2*t) - w'}, name='ODEtest')
DSargs.tdomain = [0, 10]
DSargs.pars = {'k': 1, 'p_thresh': -0.25}
DSargs.algparams = {'init_step': 0.001, 'atol': 1e-12, 'rtol': 1e-13}
DSargs.checklevel = 2
DSargs.ics = {'w': -1.0}
DSargs.tdata = [0, 10]
ev_args_nonterm = {'name': 'monitor',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': False,
'precise': True}
thresh_ev_nonterm = Events.makeZeroCrossEvent('w', 0,
ev_args_nonterm, varnames=['w'])
ev_args_term = {'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': True,
'precise': True}
thresh_ev_term = Events.makeZeroCrossEvent('w-p_thresh',
-1, ev_args_term, varnames=['w'], parnames=['p_thresh'])
DSargs.events = [thresh_ev_nonterm, thresh_ev_term]
testODE = Vode_ODEsystem(DSargs)
# diagnostics and other possible user-defined python functions
# for python solvers only (currently only Euler)
# def before_func(euler):
# print(euler.algparams['init_step'])
#
# def after_func(euler):
# print(euler._solver.y)
#
##DSargs.user_func_beforestep = before_func
##DSargs.user_func_afterstep = after_func
testODE_Euler = Euler_ODEsystem(DSargs)
traj = testODE.compute('traj')
traj2 = testODE_Euler.compute('traj')
pts = traj.sample()
testODE.diagnostics.showWarnings()
mon_evs_found = testODE.getEvents('monitor')
term_evs_found = testODE.getEvents('threshold')
# test Euler
assert allclose(array(testODE.getEventTimes('monitor')),
array(traj2.getEventTimes('monitor')), atol=1e-3)
assert all(traj.getEvents('monitor') == mon_evs_found)
assert all(traj.getEventTimes('threshold')
== testODE.getEventTimes('threshold'))
term_evs_found.info()
# Alternative way to extract events: they are labelled in the
# pointset! These return dictionaries indexing into the pointset.
mon_evs_dict = pts.labels.by_label['Event:monitor']
mon_ev_points = pts[sort(mon_evs_dict.keys())]
assert len(mon_evs_found) == len(mon_ev_points) == 2
assert all(mon_evs_found == mon_ev_points)
def test_vode_events_with_external_input(my_input):
"""
Test Vode_ODEsystem with events involving external inputs.
Robert Clewley, September 2006.
"""
xs = ['x1', 'x2', 'x3']
ys = [0, 0.5, 1]
fvarspecs = {"w": "k*w + pcwfn(sin(t)) + myauxfn1(t)*myauxfn2(w)",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)'}
fnspecs = {'myauxfn1': (['t'], '2.5*cos(3*t)'),
'myauxfn2': (['w'], 'w/2'),
'pcwfn': makeMultilinearRegrFn('x', xs, ys)}
# targetlang is optional if the default python target is desired
DSargs = args(fnspecs=fnspecs, name='ODEtest')
DSargs.varspecs = fvarspecs
DSargs.tdomain = [0.1, 2.1]
DSargs.pars = {'k': 2, 'a': -0.5, 'x1': -3, 'x2': 0.5, 'x3': 1.5}
DSargs.vars = 'w'
DSargs.inputs = {'in': my_input.variables['example_input']}
DSargs.algparams = {'init_step': 0.01}
DSargs.checklevel = 2
testODE = Vode_ODEsystem(DSargs)
assert not testODE.defined
testODE.set(ics={'w': 3.0},
tdata=[0.11, 2.1])
traj1 = testODE.compute('traj1')
assert testODE.defined
assert_almost_equal(traj1(0.5, 'w'), 8.9771499, 5)
assert not testODE.diagnostics.hasWarnings()
assert_almost_equal(traj1(0.2, ['aux_other']), 3.905819936, 5)
print("\nNow adding a terminating co-ordinate threshold event")
print(" and non-terminating timer event")
# Show off the general-purpose, language-independent event creator:
# 'makeZeroCrossEvent'
ev_args_nonterm = {'name': 'monitor',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': False,
'precise': True}
thresh_ev_nonterm = Events.makeZeroCrossEvent('in', 0,
ev_args_nonterm, inputnames=['in'])
# Now show use of the python-target specific creator:
# 'makePythonStateZeroCrossEvent', which is also only
# able to make events for state variable threshold crossings
ev_args_term = {'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': True,
'precise': True}
thresh_ev_term = Events.makePythonStateZeroCrossEvent('w',
20, 1, ev_args_term)
testODE.eventstruct.add([thresh_ev_nonterm, thresh_ev_term])
print("Recomputing trajectory:")
print("traj2 = testODE.compute('traj2')")
traj2 = testODE.compute('traj2')
print("\ntestODE.diagnostics.showWarnings() => ")
testODE.diagnostics.showWarnings()
print("\ntraj2.indepdomain.get() => ", traj2.indepdomain.get())
indep1 = traj2.indepdomain[1]
assert indep1 < 1.17 and indep1 > 1.16
mon_evs_found = testODE.getEvents('monitor')
assert len(mon_evs_found) == 1