def __call__(self, calc_context, fignum, xstr, ystr, style):
self.sim = calc_context.sim
self.calc_context = calc_context
fig = plt.figure(fignum)
new_track = args(xstr=xstr, ystr=ystr, style=style)
if fignum in self.figs:
self.figs[fignum].tracked.append(new_track)
else:
self.figs[fignum] = args(figure=fig, tracked=[new_track])
self.sim.tracked_objects.append(self)
def __call__(self, calc_context, fignum, xstr, ystr, style):
self.sim = calc_context.sim
self.calc_context = calc_context
fig = plt.figure(fignum)
new_track = args(xstr=xstr, ystr=ystr, style=style)
if fignum in self.figs:
self.figs[fignum].tracked.append(new_track)
else:
self.figs[fignum] = args(figure=fig, tracked=[new_track])
self.sim.tracked_objects.append(self)
def _run_check_macros_2(ode, fnspecs):
DSargs2 = args(
name='test2',
pars={
'p0': 0,
'p1': 1,
'p2': 2
},
varspecs={
'y[i]':
'for(i, 0, 1, y[i]+if(y[i+1]<2, 2+p[i]+getbound(%s,0), indexfunc([i])+y[i+1]) - 3)'
% ('y2' if ode in [Vode_ODEsystem, Euler_ODEsystem] else '"y2"'),
'y2':
'0'
},
xdomain={'y2': [-10, 10]},
fnspecs=fnspecs,
ics={
'y0': 0,
'y1': 0,
'y2': 0.1
})
tm2 = ode(DSargs2)
tm2.set(tdata=[0, 10])
tm2.compute('test')
assert allclose(tm2.Rhs(0, {
'y0': 0,
'y1': 0.3,
'y2': 5
}), array([-11., 2.3 + pi, 0.]))
def compute_HO(self, initpoint='', name='HO1', ax=None, p1='a1', p2='a2'):
PCargs = args()
PCargs.name = name
PCargs.type = 'H-C2'
PCargs.initpoint = initpoint
PCargs.freepars = [p1, p2]
PCargs.MaxNumPoints = 800
PCargs.MinStepSize = 1e-5
PCargs.MaxStepSize = 1e-2
PCargs.StepSize = 1e-3
PCargs.LocBifPoints = 'all'
PCargs.SaveEigen = True
self.pc.newCurve(PCargs)
print('Computing Hopf curve...')
start = perf_counter()
# PyCont[name].forward()
self.pc[name].backward()
print('done in %.3f seconds!' % (perf_counter() - start))
#PCargs.MaxNumPoints = 2000
# PyCont[name].forward()
self.pc[name].display([p1, p2], figure=3)
sol = self.pc[name].sol
a1 = sol.coordarray[sol.coordnames.index(p1)]
b1 = sol.coordarray[sol.coordnames.index(p2)]
if not ax:
fig, ax = plt.subplots(figsize=(4, 4))
fig.subplots_adjust(left=.2, bottom=0.17, right=0.98)
ax.plot(a1, b1, label=name)
return ax
def test_1D_example():
"""
1D example: a half-circle using newton's method (secant method for estimating derivative)
Change sign of 'y' initial condition to solve for other half-circle
"""
fvarspecs = {"y": "t*t+y*y-r*r", "x": "t"}
##fnspecs = {'myauxfn': (['t'], '.5*cos(3*t)')}
dsargs = args()
##dsargs.fnspecs = fnspecs
dsargs.varspecs = fvarspecs
dsargs.algparams = {'solvemethod': 'newton', 'atol': 1e-4}
dsargs.xdomain = {'y': [-2, 2]}
dsargs.ics = {'y': 0.75}
dsargs.tdomain = [0, 2]
dsargs.pars = {'r': 2}
dsargs.vars = ['y']
dsargs.checklevel = 1
dsargs.name = 'imptest'
ex1d = ImplicitFnGen(dsargs)
assert not ex1d.defined
traj1 = ex1d.compute('traj1')
assert ex1d.defined
assert allclose(traj1(1.5)['y'], 1.3228755105)
assert traj1.dimension == 2
def compute_limit_cycle(self):
PCargs = args()
PCargs.name = 'LC1'
PCargs.type = 'LC-C'
PCargs.MaxNumPoints = 2500 # // 10
PCargs.NumIntervals = 30
PCargs.NumCollocation = 6
PCargs.initpoint = 'EQ1:H1'
PCargs.SolutionMeasures = 'all'
PCargs.NumSPOut = 200
PCargs.FuncTol = 1e-4
PCargs.VarTol = 1e-4
PCargs.TestTol = 1e-3
PCargs.SaveEigen = True
self.pc.newCurve(PCargs)
print('Computing limit-cycle curve...')
start = perf_counter()
self.pc['LC1'].forward()
# PyCont['LC1'].backward()
print('done in %.3f seconds!' % (perf_counter() - start))
# Get the lower branch of the cycle.
self.pc['LC1'].display(('mu', 'R_min'), stability=True, figure=1)
self.pc['LC1'].display(('mu', 'R'), stability=True, figure=1)
self.pc['LC1'].display(stability=True, figure='new', axes=(1, 2, 1))
self.pc['LC1'].plot_cycles(coords=('R', 'r'),
linewidth=1,
axes=(1, 2, 2),
figure='fig2')
def addFig(self, label, title="", xlabel="", ylabel="", tdom=None, display=True):
"""
User can add figures to plotter for data shown in different windows
label String to specify name of figure
title String to specify title to display on figure
xlabel String to specify label on x-axis
ylabel String to specify label on y-axis
tdom time domain (if applicable, and optional)
display Setting to determine whether or not figure is plotted when
plotter is built (defaults to True)
"""
# Check to see if label already exists
if self.figs.has_key(label):
raise KeyError("Figure label already exists!")
self.currFig = label
figAttr = args()
figAttr.title = title
figAttr.xlabel = xlabel
figAttr.ylabel = ylabel
figAttr.display = display
self._max_fig_num += 1
figAttr.fignum = self._max_fig_num
figAttr.layers = {}
figAttr.shape = [1,1]
figAttr.arrange = []
figAttr.window = None
figAttr.autoscaling = True
figAttr.tdom = tdom
self.figs.update({label: figAttr})
def copyFig(self, newFig, oldFig):
"""
Duplicates all figure, layer, and data information without arrangement
information.
"""
# Check to see if label already exists #
if self.figs.has_key(newFig):
raise KeyError("New figure label already exists!")
self.currFig = newFig
old = self.figs[oldFig]
figAttr = args()
figAttr.title = old.title
figAttr.xlabel = old.xlabel
figAttr.ylabel = old.ylabel
figAttr.display = old.display
self._max_fig_num += 1
figAttr.fignum = self._max_fig_num
figAttr.shape = [1,1]
figAttr.arrange = []
figAttr.window = None
figAttr.autoscaling = True
figAttr.layers = {}
self.figs.update({newFig: figAttr})
for layer in old.layers:
oldLay = self.figs[oldFig].layers[layer]
self.addLayer(layer, display=oldLay.display, zindex=oldLay.zindex, style=oldLay.style)
def _run_check_macros_1(ode, fnspecs):
DSargs = args(
name='test',
pars={
'p0': 0,
'p1': 1,
'p2': 2
},
# 'special_erfc' is not available for non-Python generators
varspecs={
'z[j]':
'for(j, 0, 1, 2*z[j+1] + p[j])',
'z2':
'-z0 + p2 + special_erfc(2.0)'
if ode is Vode_ODEsystem else '-z0 + p2 + 1',
},
fnspecs=fnspecs)
tmm = ode(DSargs)
# test user interface to aux functions and different combinations of embedded
# macros
assert tmm.auxfns.testif(1.0) == 1.0
assert tmm.auxfns.testmin(1.0, 2.0) == 1.0
assert tmm.auxfns.testmax(1.0, 2.0) == 2.0
assert tmm.auxfns.testmin2(1.0, 2.0) == 2.25
assert tmm.Rhs(0, {'z0': 0.5, 'z1': 0.2, 'z2': 2.1})[1] == 5.2
def test_1D_example():
"""
1D example: a half-circle using newton's method (secant method for estimating derivative)
Change sign of 'y' initial condition to solve for other half-circle
"""
fvarspecs = {
"y": "t*t+y*y-r*r",
"x": "t"
}
##fnspecs = {'myauxfn': (['t'], '.5*cos(3*t)')}
dsargs = args()
##dsargs.fnspecs = fnspecs
dsargs.varspecs = fvarspecs
dsargs.algparams = {'solvemethod': 'newton', 'atol': 1e-4}
dsargs.xdomain = {'y': [-2, 2]}
dsargs.ics = {'y': 0.75}
dsargs.tdomain = [0, 2]
dsargs.pars = {'r': 2}
dsargs.vars = ['y']
dsargs.checklevel = 1
dsargs.name = 'imptest'
ex1d = ImplicitFnGen(dsargs)
assert not ex1d.defined
traj1 = ex1d.compute('traj1')
assert ex1d.defined
assert allclose(traj1(1.5)['y'], 1.3228755105)
assert traj1.dimension == 2
def _limit_cycle_curve(self, pars, index=-1):
(name, PyCont) = self.cont_classes[index]
# Limit cycle curve
PCargs = args(freepars=PyCont[name].freepars)
PCargs.name = 'LC1'
PCargs.type = 'LC-C'
PCargs.MaxNumPoints = 2500 # // 10
PCargs.NumIntervals = 20
PCargs.NumCollocation = 6
PCargs.initpoint = name + ':H1'
PCargs.SolutionMeasures = 'all'
PCargs.NumSPOut = 50
PCargs.FuncTol = 1e-10
PCargs.VarTol = 1e-10
PCargs.TestTol = 1e-8
PyCont.newCurve(PCargs)
print('Computing limit-cycle curve...')
start = perf_counter()
PyCont['LC1'].backward()
PyCont['LC1'].forward()
print('done in %.3f seconds!' % (perf_counter() - start))
PyCont['LC1'].display(pars, stability=True)
PyCont['LC1'].display((pars[0], pars[1] + '_min'), stability=True)
# TODO(matthew-c21): Keep track of associated figures.
PyCont['LC1'].display(stability=True, figure='new', axes=(1, 2, 1))
PyCont['LC1'].plot_cycles(coords=('R', 'r'),
linewidth=1,
axes=(1, 2, 2),
figure='fig2')
pass
def test_discrete_domain():
disc_dom = domain_test('disc_dom_test',
pars=args(coordname='x',
derivname='dxdt',
interval=1,
verbose_level=3))
ic_disc = numeric_to_traj([[1], [0]], 'test', ['x', 'dxdt'], 0.)
assert disc_dom(ic_disc)
def fsargs():
fvarspecs = {
'z[i]': 'for(i, 0, 1, 2*a+myauxfn1(2+t) - ' +
'w*exp(-t)+ 3*z[i]**2 + z[i+1])',
'z2': '2*a+myauxfn1(2+t) - w*exp(-t) + 3*z2**2 + z0',
'w': 'k* w + a*sin(t)*itable + myauxfn1(t)*myauxfn2(w)/(a*sin(t))',
'aux_wdouble': 'w*2 + globalindepvar(t)-0.5*sin(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)',
'aux_iftest': '1+if(z1>0,(1e-2+w), k+0.4)'
}
fnspecs = {
'simpfn': ([''], '1+a'),
'myauxfn1': (['t'], '2.5*cos(3*t)*simpfn()+sin(t)*2.e-3'),
'myauxfn2': (['z0', 'w'], 'if(-z0<0,w/2+exp(-w),0)'),
'myauxfn3': (['w'], 'k*w/2+ pow(w,-3.0+k)'),
# not supposed to be the actual Jacobian!
'Jacobian': (['t', 'z0', 'z1', 'z2', 'w'],
"""[[2e5*z0+.1, -w/2, 0, 1.],
[-3.e-2 - a*w+z1, 1., z0+1, z0+sin(t)],
[k, w*z1+exp(-t), 0., z2/3+w],
[0, z1+a, 1., z0-w/3]]"""),
# not supposed to be the actual Jacobian_pars!
'Jacobian_pars': (['t', 'k', 'a'],
"""[[0., 2.],
[z0, 1],
[3*w, 0.],
[2-z1, sin(t)*z2]]""")
}
return {
'name': 'xfn',
# vars is always unrolled by Gen base class if there are FOR loop macros
'vars': ['w', 'z0', 'z1', 'z2'],
'auxvars': ['aux_wdouble', 'aux_other', 'aux_iftest'],
'pars': ['k', 'a'],
'inputs': 'itable',
'varspecs': fvarspecs,
'fnspecs': fnspecs,
# In practice, _for_macro_info created automatically by Generator base class
'_for_macro_info': args(
numfors=1,
totforvars=2,
varsbyforspec={
'z[i]': ['z0', 'z1'],
'w': ['w'],
'z2': ['z2'],
'aux_wdouble': ['aux_wdouble'],
'aux_other': ['aux_other'],
'aux_iftest': ['aux_iftest']
}
),
'reuseterms': {'a*sin_t': 'ast',
'exp(-t)': 'expmt',
'sin(t)': 'sin_t',
'myauxfn1(2+t)': 'afn1call'},
'codeinsert_end': """ print('code inserted at end')""",
'codeinsert_start': """ print('code inserted at start')""",
'targetlang': 'python'
}
def fsargs():
fvarspecs = {
'z[i]': 'for(i, 0, 1, 2*a+myauxfn1(2+t) - ' +
'w*exp(-t)+ 3*z[i]**2 + z[i+1])',
'z2': '2*a+myauxfn1(2+t) - w*exp(-t) + 3*z2**2 + z0',
'w': 'k* w + a*sin(t)*itable + myauxfn1(t)*myauxfn2(w)/(a*sin(t))',
'aux_wdouble': 'w*2 + globalindepvar(t)-0.5*sin(t)',
'aux_other': 'myauxfn1(2*t) + initcond(w)',
'aux_iftest': '1+if(z1>0,(1e-2+w), k+0.4)'
}
fnspecs = {
'simpfn': ([''], '1+a'),
'myauxfn1': (['t'], '2.5*cos(3*t)*simpfn()+sin(t)*2.e-3'),
'myauxfn2': (['z0', 'w'], 'if(-z0<0,w/2+exp(-w),0)'),
'myauxfn3': (['w'], 'k*w/2+ pow(w,-3.0+k)'),
# not supposed to be the actual Jacobian!
'Jacobian': (['t', 'z0', 'z1', 'z2', 'w'],
"""[[2e5*z0+.1, -w/2, 0, 1.],
[-3.e-2 - a*w+z1, 1., z0+1, z0+sin(t)],
[k, w*z1+exp(-t), 0., z2/3+w],
[0, z1+a, 1., z0-w/3]]"""),
# not supposed to be the actual Jacobian_pars!
'Jacobian_pars': (['t', 'k', 'a'],
"""[[0., 2.],
[z0, 1],
[3*w, 0.],
[2-z1, sin(t)*z2]]""")
}
return {
'name': 'xfn',
# vars is always unrolled by Gen base class if there are FOR loop macros
'vars': ['w', 'z0', 'z1', 'z2'],
'auxvars': ['aux_wdouble', 'aux_other', 'aux_iftest'],
'pars': ['k', 'a'],
'inputs': 'itable',
'varspecs': fvarspecs,
'fnspecs': fnspecs,
# In practice, _for_macro_info created automatically by Generator base class
'_for_macro_info': args(
numfors=1,
totforvars=2,
varsbyforspec={
'z[i]': ['z0', 'z1'],
'w': ['w'],
'z2': ['z2'],
'aux_wdouble': ['aux_wdouble'],
'aux_other': ['aux_other'],
'aux_iftest': ['aux_iftest']
}
),
'reuseterms': {'a*sin_t': 'ast',
'exp(-t)': 'expmt',
'sin(t)': 'sin_t',
'myauxfn1(2+t)': 'afn1call'},
'codeinsert_end': """ print('code inserted at end')""",
'codeinsert_start': """ print('code inserted at start')""",
'targetlang': 'python'
}
def __init__(self, name, model, ics):
self.cont_classes = []
self.name = name
self.model = model
self.ics = [ics]
self.DSargs = args(name=self.name)
self.TestDS = None
self._revise_dsargs()
def __call__(self, calc_context, fignum, attribute_name):
self.sim = calc_context.sim
self.calc_context = calc_context
old_toolbar = plt.rcParams['toolbar']
plt.rcParams['toolbar'] = 'None'
fig = plt.figure(fignum, figsize=(2, 6)) #, frameon=False)
plt.rcParams['toolbar'] = old_toolbar
if fignum in self.figs:
self.figs[fignum].tracked.append(attribute_name)
else:
self.figs[fignum] = args(figure=fig, tracked=[attribute_name])
self.sim.tracked_objects.append(self)
def __call__(self, calc_context, fignum, attribute_name):
self.sim = calc_context.sim
self.calc_context = calc_context
old_toolbar = plt.rcParams['toolbar']
plt.rcParams['toolbar'] = 'None'
fig = plt.figure(fignum, figsize=(2,6)) #, frameon=False)
plt.rcParams['toolbar'] = old_toolbar
if fignum in self.figs:
self.figs[fignum].tracked.append(attribute_name)
else:
self.figs[fignum] = args(figure=fig, tracked=[attribute_name])
self.sim.tracked_objects.append(self)
def _run_check_macros_3(ode, fnspecs):
# show example of summing where i != p defines the sum range, and p is a
# special value (here, 2)
DSargs3 = args(name='test3',
pars={'p0': 0, 'p1': 1, 'p2': 2},
varspecs={
'x': 'sum(i, 0, 4, sum(j, 0, 1, if([i]==2, 0, indexfunc([j] + p[j]))))'},
fnspecs=fnspecs
)
tm3 = ode(DSargs3)
tm3.set(tdata=[0, 10], ics={'x': 1})
tm3.compute('test')
assert allclose(tm3.Rhs(0, {'x': 0}), 8 * pi)
def _run_check_macros_3(ode, fnspecs):
# show example of summing where i != p defines the sum range, and p is a
# special value (here, 2)
DSargs3 = args(
name="test3",
pars={"p0": 0, "p1": 1, "p2": 2},
varspecs={"x": "sum(i, 0, 4, sum(j, 0, 1, if([i]==2, 0, indexfunc([j] + p[j]))))"},
fnspecs=fnspecs,
)
tm3 = ode(DSargs3)
tm3.set(tdata=[0, 10], ics={"x": 1})
tm3.compute("test")
assert allclose(tm3.Rhs(0, {"x": 0}), 8 * pi)
def test_get_spike_data():
"""Test Context class and example of qualitative fitting of spikes"""
sigma = 0.05
# import doesn't actually create a Pointset (it's slightly misnamed for this
# purpose but it can do other things...)
data = importPointset(path.join(path.dirname(__file__), 'test_spikes.dat'),
t=0,
sep='\t')
vs = data['vararray'][0] # pick one of the signals
ts = data['t']
traj = numeric_to_traj([vs], 'test_traj', ['x'], ts, discrete=False)
# ---------------------------------------------------------------------
# set debug = True and verbose_level = 2 for plot of fit
is_spike = get_spike_data('one_spike',
pars=args(height_tol=2000.,
thresh_pc=0.15,
fit_width_max=20,
weight=0,
noise_tol=300,
tlo=260,
width_tol=ts[-1],
coord='x',
eventtol=1e-2,
verbose_level=0,
debug=False))
# compare
# plot(ts, vs)
# assert ensures that is_spike returns True when passed the particular
# set of data
assert is_spike(traj)
# given that it returned true, try another time for next spike
is_spike.pars.tlo = 268
assert is_spike(traj)
# introspect the is_spike object with info(is_spike)
# .results values now guaranteed to exist
assert_allclose(is_spike.results.tlo, 269.98922, rtol=1e-5)
assert_allclose(is_spike.results.thi, 272.0108, rtol=1e-5)
assert_allclose(is_spike.results.spike_time, 270.5574, rtol=1e-5)
assert_allclose(is_spike.results.spike_val, 5117.07697, rtol=1e-4)
def dual_bifurcation(self, name, initpoint, p1, p2):
# TODO(matthew-c21): Fancy graph stuff. Possibly use smaller aggregate objects to keep track of that by itself.
pcargs = args()
pcargs.name = name
pcargs.type = 'H-C2'
pcargs.initpoint = initpoint
pcargs.freepars = [p1, p2]
pcargs.MaxNumPoints = 800
pcargs.MinStepSize = 1e-5
pcargs.MaxStepSize = 1e-2
pcargs.StepSize = 1e-3
pcargs.LocBifPoints = 'all'
pcargs.SaveEigen = True
self.compute(pcargs, 'Computing 2-parameter bifurcation analysis...')
def _find_steady_state(self, tdata):
ssargs = args(name='steadyState')
ssargs.tdata = tdata
# Test code.
ssargs.ics = ics
ssargs.pars = self.model_params.pars
ssargs.varspecs = self.model_params.varspecs
ssargs.fnspecs = self.model_params.fnspecs
ssargs.algparams = {'refine': True}
ssDS = Generator.Radau_ODEsystem(ssargs)
trajectory = ssDS.compute('steady state')
pts = trajectory.sample()
return pts
def limit_cycle(self, name, initpoint, freepars):
# TODO(matthew-c21): See below comment.
pcargs = args(name=name, type='LC-C')
pcargs.MaxNumPoints = 2500 # // 10
pcargs.NumIntervals = 30
pcargs.NumCollocation = 6
pcargs.initpoint = initpoint
pcargs.SolutionMeasures = 'all'
pcargs.NumSPOut = 200
pcargs.FuncTol = 1e-4
pcargs.VarTol = 1e-4
pcargs.TestTol = 1e-3
pcargs.SaveEigen = True
pcargs.freepars = freepars
self.compute(pcargs, 'Computing limit cycle...')
def ode():
"""Dummy system with all functions set"""
DSargs = args(
name='test_interfaces',
fnspecs={
'Jacobian': (['t', 'y0', 'y1',
'y2'], """[[-0.04, 1e4*y2 , 1e4*y1 ],
[ 0.04, -1e4*y2-6e7*y1, -1e4*y1 ],
[ 0.0 , 6e7*y1 , 0.0 ]]"""),
'Jacobian_pars': (['t', 'p1', 'p2',
'p3'], "[[1, 0, p1], [-1, 0, p2], [0, 0, p3]]"),
'ydot0': (['y0', 'y1', 'y2'], "-0.04*y0 + 1e4*y1*y2"),
'ydot2': (['y0', 'y1', 'y2'], "3e7*y1*y1"),
'massMatrix': (['t', 'y0', 'y1',
'y2'], """[[-0.04, 1e4*y2 , 1e4*y1 ],
[ 0.04, -1e4*y2-6e7*y1, -1e4*y1 ],
[ 0.0 , 6e7*y1 , 0.0 ]]"""),
},
varspecs={
"y0": "ydot0(y0,y1,y2)",
"y2": "ydot2(y0,y1,y2)",
"y1": "-ydot0(y0,y1,y2)-ydot2(y0,y1,y2)",
'aux0': 'y0 + 2 * y1 - t',
'aux1': 'y2 - y1 - 2 * y0',
},
auxvars=['aux0', 'aux1'],
pars={
'p1': 0.01,
'p2': 0.02,
'p3': 0.03
},
tdomain=[0., 1e20],
ics={
'y0': 1.0,
'y1': 0.,
'y2': 0.
},
algparams={
'init_step': 0.4,
'rtol': 1e-4,
'atol': [1e-8, 1e-14, 1e-6]
},
checklevel=2,
)
return Radau_ODEsystem(DSargs)
def create_pcargs(name,
freepars,
StepSize,
MaxNumPoints,
LocBifPoints='all',
alg_type='EP-C'):
PCargs = args(name=name, type=alg_type)
PCargs.freepars = freepars
PCargs.StepSize = StepSize
PCargs.MaxNumPoints = MaxNumPoints
PCargs.LocBifPoints = LocBifPoints
PCargs.verbosity = 2
PCargs.SaveJacobian = True
PCargs.SaveEigen = True
return PCargs
def test_event1a(self):
pardict = {'Tmelt': self.params.Tmelt}
icdict = {'Tp': 44.1}
ode = {'Tp': '0'}
DSargs = args(name='Event1aTest')
DSargs.events = [event.event1(self.params)]
DSargs.pars = pardict
DSargs.tdata =[0, self.params.tfinal]
DSargs.algparams = {'init_step': self.params.tstep, 'rtol':self.params.RelTol, 'atol': self.params.AbsTol}
DSargs.varspecs = ode
DSargs.ics = icdict
event1aTest = PyDSTool.Generator.Vode_ODEsystem(DSargs)
traj = event1aTest.compute('event1aTest')
evs = traj.getEvents('event_melt_begin')
assert evs is None
def test_event1b(self):
pardict = {'Tmelt': self.params.Tmelt}
icdict = {'Tp': 44.1}
ode = {'Tp': '0.1'}
DSargs = args(name='Event1bTest')
DSargs.events = [event.event1(self.params)]
DSargs.pars = pardict
DSargs.tdata = [0, self.params.tfinal]
DSargs.algparams = {'init_step': 0.5, 'rtol': self.params.RelTol, 'atol': self.params.AbsTol}
DSargs.varspecs = ode
DSargs.ics = icdict
event1bTest = PyDSTool.Generator.Vode_ODEsystem(DSargs)
traj = event1bTest.compute('event1bTest')
evs = traj.getEvents('event_melt_begin')
self.assertAlmostEqual(evs['t'][-1], 1, places=None, msg='event1b', delta=1e-10)
def _run_check_macros_2(ode, fnspecs):
DSargs2 = args(
name="test2",
pars={"p0": 0, "p1": 1, "p2": 2},
varspecs={
"y[i]": "for(i, 0, 1, y[i]+if(y[i+1]<2, 2+p[i]+getbound(%s,0), indexfunc([i])+y[i+1]) - 3)"
% ("y2" if ode in [Vode_ODEsystem, Euler_ODEsystem] else '"y2"'),
"y2": "0",
},
xdomain={"y2": [-10, 10]},
fnspecs=fnspecs,
ics={"y0": 0, "y1": 0, "y2": 0.1},
)
tm2 = ode(DSargs2)
tm2.set(tdata=[0, 10])
tm2.compute("test")
assert allclose(tm2.Rhs(0, {"y0": 0, "y1": 0.3, "y2": 5}), array([-11.0, 2.3 + pi, 0.0]))
def test_event2b(self):
pardict = {'Hf': self.params.Hf,
'Mp': self.params.Mp}
icdict = {'Qp': 600000}
ode = {'Qp': '0'}
DSargs = args(name='Event2bTest')
DSargs.events = [event.event2(self.params)]
DSargs.pars = pardict
DSargs.tdata = [0, self.params.tfinal]
DSargs.algparams = {'init_step': self.params.tstep, 'rtol': self.params.RelTol, 'atol': self.params.AbsTol}
DSargs.varspecs = ode
DSargs.ics = icdict
event2bTest = PyDSTool.Generator.Vode_ODEsystem(DSargs)
traj = event2bTest.compute('event2bTest')
evs = traj.getEvents('event_melt_end')
assert evs is None
def test_event2c(self):
pardict = {'Hf': self.params.Hf,
'Mp': self.params.Mp}
icdict = {'Qp': 10654059.9}
ode = {'Qp': '0.1'}
DSargs = args(name='Event2cTest')
DSargs.events = [event.event2(self.params)]
DSargs.pars = pardict
DSargs.tdata = [0, self.params.tfinal]
DSargs.algparams = {'init_step': 0.5, 'rtol': self.params.RelTol, 'atol': self.params.AbsTol}
DSargs.varspecs = ode
DSargs.ics = icdict
event2cTest = PyDSTool.Generator.Vode_ODEsystem(DSargs)
traj = event2cTest.compute('event2cTest')
evs = traj.getEvents('event_melt_end')
self.assertAlmostEqual(evs['t'][-1], 1, places=None, msg='event2c', delta=1e-4)
def addLayer(self, layer_name, figure=None, **kwargs):
"""
User method to add data sets to a layer in a figure
figure name
layer name
display toggle Boolean
kind a user-defined kind, e.g. 'data', 'vline', 'hline', 'epoch', etc.
scale a pair of axes scale pairs or None
zindex (currently unused)
"""
fig_struct, figure = self._resolveFig(figure)
# Check to see layer does not already exist #
if fig_struct.layers.has_key(layer_name):
raise KeyError("Layer name already exists in figure!")
# default plot style generated from list of colors
color = self.colors[len(fig_struct.layers)%len(self.colors)]
line = '-'
style = color+line
layAttrs = args()
layAttrs.data = {}
layAttrs.display = True
# default zindex based on order of layer declaration
layAttrs.zindex = len(fig_struct.layers)+1
layAttrs.style = style
#layAttrs.axes = None
layAttrs.scale = None
layAttrs.kind = 'data'
layAttrs.dynamic = False
layAttrs.trajs = {}
layAttrs.axes_vars = []
for kw in kwargs:
# Check to see that parameter exists in layers #
## Possibly change to account for different properties of specific artist objects?
if not layAttrs.has_key(kw):
raise KeyError("Parameter is not a property of the layer.")
layAttrs[kw] = kwargs[kw]
fig_struct.layers[layer_name] = layAttrs
def test_get_spike_data():
"""Test Context class and example of qualitative fitting of spikes"""
sigma = 0.05
# import doesn't actually create a Pointset (it's slightly misnamed for this
# purpose but it can do other things...)
data = importPointset(path.join(path.dirname(__file__), 'test_spikes.dat'),t=0,sep='\t')
vs = data['vararray'][0] # pick one of the signals
ts = data['t']
traj = numeric_to_traj([vs], 'test_traj', ['x'], ts, discrete=False)
# ---------------------------------------------------------------------
# set debug = True and verbose_level = 2 for plot of fit
is_spike = get_spike_data('one_spike', pars=args(
height_tol=2000., thresh_pc=0.15,
fit_width_max=20, weight=0, noise_tol=300,
tlo=260, width_tol=ts[-1], coord='x', eventtol=1e-2,
verbose_level=0, debug=False))
# compare
# plot(ts, vs)
# assert ensures that is_spike returns True when passed the particular
# set of data
assert is_spike(traj)
# given that it returned true, try another time for next spike
is_spike.pars.tlo = 268
assert is_spike(traj)
# introspect the is_spike object with info(is_spike)
# .results values now guaranteed to exist
assert_allclose(is_spike.results.tlo, 269.98922, rtol=1e-5)
assert_allclose(is_spike.results.thi, 272.0108, rtol=1e-5)
assert_allclose(is_spike.results.spike_time, 270.5574, rtol=1e-5)
assert_allclose(is_spike.results.spike_val, 5117.07697, rtol=1e-4)
def _run_check_macros_1(ode, fnspecs):
DSargs = args(
name="test",
pars={"p0": 0, "p1": 1, "p2": 2},
# 'special_erfc' is not available for non-Python generators
varspecs={
"z[j]": "for(j, 0, 1, 2*z[j+1] + p[j])",
"z2": "-z0 + p2 + special_erfc(2.0)" if ode is Vode_ODEsystem else "-z0 + p2 + 1",
},
fnspecs=fnspecs,
)
tmm = ode(DSargs)
# test user interface to aux functions and different combinations of embedded
# macros
assert tmm.auxfns.testif(1.0) == 1.0
assert tmm.auxfns.testmin(1.0, 2.0) == 1.0
assert tmm.auxfns.testmax(1.0, 2.0) == 2.0
assert tmm.auxfns.testmin2(1.0, 2.0) == 2.25
assert tmm.Rhs(0, {"z0": 0.5, "z1": 0.2, "z2": 2.1})[1] == 5.2
def ode():
"""Dummy system with all functions set"""
DSargs = args(
name='test_interfaces',
fnspecs={
'Jacobian': (['t', 'y0', 'y1', 'y2'],
"""[[-0.04, 1e4*y2 , 1e4*y1 ],
[ 0.04, -1e4*y2-6e7*y1, -1e4*y1 ],
[ 0.0 , 6e7*y1 , 0.0 ]]"""),
'Jacobian_pars': (['t', 'p1', 'p2', 'p3'],
"[[1, 0, p1], [-1, 0, p2], [0, 0, p3]]"),
'ydot0': (['y0', 'y1', 'y2'], "-0.04*y0 + 1e4*y1*y2"),
'ydot2': (['y0', 'y1', 'y2'], "3e7*y1*y1"),
'massMatrix': (['t', 'y0', 'y1', 'y2'],
"""[[-0.04, 1e4*y2 , 1e4*y1 ],
[ 0.04, -1e4*y2-6e7*y1, -1e4*y1 ],
[ 0.0 , 6e7*y1 , 0.0 ]]"""),
},
varspecs={"y0": "ydot0(y0,y1,y2)",
"y2": "ydot2(y0,y1,y2)",
"y1": "-ydot0(y0,y1,y2)-ydot2(y0,y1,y2)",
'aux0': 'y0 + 2 * y1 - t',
'aux1': 'y2 - y1 - 2 * y0',
},
auxvars=['aux0', 'aux1'],
pars={'p1': 0.01, 'p2': 0.02, 'p3': 0.03},
tdomain=[0., 1e20],
ics={'y0': 1.0, 'y1': 0., 'y2': 0.},
algparams={
'init_step': 0.4,
'rtol': 1e-4, 'atol': [1e-8, 1e-14, 1e-6]},
checklevel=2,
)
return Radau_ODEsystem(DSargs)
import fovea.diagnostics as dgn
from PyDSTool import args
from pprint import pprint
dm = dgn.diagnostic_manager('test')
log = dm.log
log = log.bind(user='******', val=3.1416)
log.msg('begin', status='sofarsogood')
log.user_error('user.forgot_towel')
log.msg('done', status='nope')
test_obj = args(name='test_obj', contents='stuff')
dm.attach_obj(test_obj, 'dummy_objname')
log = log.bind(user='******', val=-1.01)
log.msg('begin', status='yarp')
log.user_action('user.remembered_towel')
log.msg('done')
print("\n")
pprint(log.dump_events())
pprint(dm.log_items_digest[dm.name_to_digest['dummy_objname']])
print("\n")
print(dm.db.all())
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_bd_containment():
"""Basic tests for boundary containment features."""
vals1 = linspace(-3, 3, 20)
test_traj1 = numeric_to_traj([vals1],
'test', 'x', arange(len(vals1), dtype='d'))
vals2 = array(
[1., 1., 1.00000000001, 1.0000001, 1., 0.9999999999, 0.99999])
test_traj2 = numeric_to_traj([vals2],
'test', 'x', arange(len(vals2), dtype='d'))
bc = boundary_containment_by_postproc('bc_test', description='Test BCs',
pars=args(thresh=1, interior_dirn=-1, abseps=1e-4))
# Test whether test trajectory 1 remains below x_ref=1
# up to rounding error tolerance of 1e-4...
assert not bc(test_traj1)
# print "... failed at index", bc._find_idx()
# print "\nbc.results -->\n"
# print bc.results
# Test whether test trajectory 2 remains below x_ref=1
# up to rounding error tolerance of 1e-4...
assert bc(test_traj2)
# Test whether initial condition lies within a domain
# (includes transversality condition: derivative must point into interior
# of domain):
ic_inside = numeric_to_traj([[0.3], [-10.5]], 'test', ['x', 'dxdt'], 0.)
ic_crit_ok = numeric_to_traj([[1], [-1.]], 'test', ['x', 'dxdt'], 0.)
ic_crit_not_ok = numeric_to_traj([[1], [1.]], 'test', ['x', 'dxdt'], 0.)
ic_outside = numeric_to_traj([[1.01], [-1.]], 'test', ['x', 'dxdt'], 0.)
in_domain = domain_test('domain_test', pars=args(coordname='x',
derivname='dxdt', interval=[-1, 1], verbose_level=3))
assert in_domain(ic_inside)
assert in_domain(ic_crit_ok)
assert not in_domain(ic_crit_not_ok)
assert not in_domain(ic_outside)
# Check that exterior IC failed at trajectory point index '0' with
# in_domain._find_idx()==0
# ------------------------------------------------------------------
# Test for domain with rounding-error tolerated boundaries:
in_domain_loose = domain_test('domain_test', pars=args(coordname='x',
derivname='dxdt', interval=Interval('x', float, [-1, 1], abseps=1e-4),
verbose_level=0))
ic_crit_round_ok = numeric_to_traj(
[[1.000001], [-1.]], 'test', ['x', 'dxdt'], 0.)
ic_crit_round_not_ok = numeric_to_traj(
[[1.000001], [1.]], 'test', ['x', 'dxdt'], 0.)
assert in_domain_loose(ic_inside)
assert in_domain_loose(ic_crit_ok)
assert not in_domain_loose(ic_crit_not_ok)
assert not in_domain_loose(ic_outside)
assert in_domain_loose(ic_crit_round_ok)
assert not in_domain_loose(ic_crit_round_not_ok)
zbd1 = domain_test(
'z', pars=args(coordname='z', derivname='D_z', interval=[0.0, 1.0], verbose_level=0))
zbd2 = domain_test(
'z', pars=args(coordname='z', derivname='D_z', interval=1.0, verbose_level=0))
ztraj = {}
ztraj[0] = numeric_to_traj([[1], [0.437]], 'test', ['z', 'D_z'], 0)
ztraj[1] = numeric_to_traj([[1], [1]], 'test', ['z', 'D_z'], 0)
ztraj[2] = numeric_to_traj([[1.0], [1]], 'test', ['z', 'D_z'], 0)
ztraj[3] = numeric_to_traj([[1], [1.0]], 'test', ['z', 'D_z'], 0)
ztraj[4] = numeric_to_traj([[1], [1.0]], 'test', ['z', 'D_z'], 0)
ztraj[5] = numeric_to_traj([[1.0], [5.0]], 'test', ['z', 'D_z'], 0)
assert not zbd1(ztraj[0])
for i in range(1, 6):
assert zbd2(ztraj[i])
import numpy as np
from matplotlib import pyplot as plt
# The approximate map for the triple-zero unfolding of the Lorenz ODEs
# see http://www.math.pitt.edu/~bard/bardware/tut/newstyle.html#triple
# Map given by:
# z(n+1) = a+b*(z-c)^2
# with z(0)=2
# For Lyapunov exponent:
# zp(n+1) = zp+log(abs(2*b*(z-c)))
# with zp(0) = 0, so that Lyapunov Exponent L will be zp/(t+1)
# (because t starts at 0)
DSargs = args(name='Lorenz map')
DSargs.varspecs = {'z': 'a+b*(z-c)**2', # note syntax for power
'zp': 'zp+log(abs(2*b*(z-c)))',
'L': 'zp/(t+1)'} # L is an auxiliary variable
DSargs.tdomain = [0, 200]
DSargs.pars = args(a=2.93, b=-1.44, c=1.85)
DSargs.vars = ['z', 'zp'] # Implicitly, then, L must be an auxiliary variable
DSargs.ics = {'z': 2, 'zp': 0}
DSargs.ttype = int # force independent variable type to be integer (discrete time)
lmap = dst.MapSystem(DSargs)
traj = lmap.compute('test')
pts = traj.sample()
plt.figure(1)
plt.plot(pts['t'], pts['z'], 'ko-')
pardict = {'Ap': params.Ap,
'Tmelt': params.Tmelt,
'Hf': params.Hf,
'Tc': params.Tc,
'hp': params.hp,
'Tinit': params.Tinit,
'tau_w': params.tau_w,
'eta': params.eta,
'Mp': params.Mp,
'tau_ps': params.tau_ps,
'tau_pl': params.tau_pl}
icdict1 = {'Tw': pardict['Tinit'],
'Tp': pardict['Tinit']}
DSargs1 = args(name='PreMelt')
DSargs1.events = [event.event1(params)]
DSargs1.pars = pardict
DSargs1.tdata = [0, params.tfinal]
DSargs1.algparams = {'init_step': params.tstep, 'rtol': params.RelTol, 'atol': params.AbsTol}
DSargs1.varspecs = temperature.temperature1()
DSargs1.ics = icdict1
preMelt = PyDSTool.Generator.Vode_ODEsystem(DSargs1)
traj1 = preMelt.compute('preMelt')
pts1 = traj1.sample()
evs1 = traj1.getEvents('event_melt_begin')
eWat = energy.energy1Wat(pts1['Tw'], params)
ePCM = energy.energy1PCM(pts1['Tp'], params)
time = []
for element in pts1['t']:
time = time + [element]
from PyDSTool import args, Generator, perf_counter, ContClass, show
import matplotlib.pyplot as plt
from model import model_mmi2 as m, ics_1 as ics
DSargs = args(name='bifurcation')
DSargs.ics = ics
DSargs.pars = m['pars']
DSargs.varspecs = m['vars']
DSargs.fnspecs = m['fns']
DSargs.algparams = {'refine': True, 'init_step': 1e-3}
output_file = 'output.bin'
class Continuation:
def __init__(self, dsargs):
self.ics = dsargs.ics
self.model_params = dsargs
self._init_ODESystem()
def _init_ODESystem(self):
self.model_params.ics = self.ics
self.testDS = Generator.Radau_ODEsystem(self.model_params)
self.pc = ContClass(self.testDS)
def _find_steady_state(self, tdata):
ssargs = args(name='steadyState')
ssargs.tdata = tdata
# Test code.
- b1 * 1 * 2 * kr * c1 \
- b2 * 2 * 1 * kr * c2)',
'R': \
'g*(sR - kR * (R - 2 * c1 - 1 * c2) \
- 2 * kR * c1 * a1 - 1 * kR * c2 * a2)',
'c1':\
'Ts * (K1 * (R - 2 * c1 - c2) * (r - 2 * c1 - 2 * c2) - c1)',
'c2':\
'Ts * (K2 * c1 * (r - 2 * c1 - 2 * c2) - c2)',
},
'fns': {}, 'aux': [], 'name': 'mmi2'}
ics_1 = {'r': 0.8, 'R': 0.1, 'c1': 0.0, 'c2': 0.0}
DSargs = args(name='mmi2')
DSargs.pars = model_mmi2['pars']
DSargs.varspecs = model_mmi2['vars']
DSargs.fnspecs = {}
DSargs.ics = ics_1
DSargs.algparams = {'refine': True,
}
testDS = Generator.Radau_ODEsystem(DSargs)
# Set up continuation class
PyCont = ContClass(testDS)
PCargs = args(name='EQ1', type='EP-C')
PCargs.freepars = ['mu']
#PCargs.StepSize = 3e-6
#PCargs.MaxStepSize = 3e-5
def dsargs():
timeData = linspace(0, 10, 20)
sindata = sin(20 * timeData)
xData = {'in': sindata}
my_input = InterpolateTable({
'tdata': timeData,
'ics': xData,
'name': 'interp1d',
'method': 'linear',
'checklevel': 1,
'abseps': 1e-5
}).compute('interp')
fvarspecs = {
"w": "k*w + 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')
}
# targetlang is optional if the default python target is desired
DSargs = args(fnspecs=fnspecs, name='event_test')
DSargs.varspecs = fvarspecs
DSargs.tdomain = [0.1, 2.1]
DSargs.pars = {'k': 2, 'a': -0.5}
DSargs.vars = 'w'
DSargs.ics = {'w': 3}
DSargs.inputs = {'in': my_input.variables['in']}
DSargs.algparams = {'init_step': 0.01}
DSargs.checklevel = 2
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'],
targetlang='c'
)
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-20',
1,
ev_args_term,
['w'],
targetlang='c'
)
DSargs.events = [thresh_ev_nonterm, thresh_ev_term]
return DSargs
def test_symbolic():
assert doneg('-x-y') == 'x+y'
assert doneg('(-x-y)') == '(x+y)'
assert doneg('-(-x-y)') == '(-x-y)'
assert dosub('1', '-x-y') == '(1+x+y)'
g2 = expr2fun('1-max([0., -a+b*x])', **{'a': 3, 'b': 1.5})
assert g2._args == ['x']
assert g2(1) == 1.0
assert g2(10) == -11.0
ds = {'a': 3, 'bbb': 1}
f = expr2fun('1+ds["a"]')
assert f._args == ['ds']
assert f(ds) == 4
f2 = expr2fun('1+ds["a"]')
assert f2(**{'ds': ds}) == 4
assert f2._args == ['ds']
g = expr2fun('1+ds["bbb"]', ds=ds)
assert g() == 2
# g must be dynamic and not based on static eval of ds on initialization
ds['bbb'] = 2
assert g._args == []
assert g() == 3
m = args(pars=copy(ds))
h = expr2fun('m.pars["a"]+c', m=m, c=1)
assert h() == 4
assert h._args == []
h2 = expr2fun('1 + m.pars["a"]/2.', m=m)
assert h2() == 2.5
assert h2._args == []
def func(x, y):
return x * (y + 1)
m.func = func
i = expr2fun('1+func(x,y)+b', func=m.func, b=0.5)
assert 1 + func(2, 3) + 0.5 == i(2, 3)
j = expr2fun('i(x,func(2,y))*2', i=i, func=m.func)
assert j(1, 0) == 9
fnspec = {'f': (['x', 'y'], 'x+1+2*y-a')}
# a is expected to be in scope like a FuncSpec parameter
# so can't use the above method of providing explicit functions
k = expr2fun('-f(c,d)+b', f=fnspec['f'], b=0.5, a=1)
assert k(1, 2) == -4.5
s = '1+a/(f(x,y)-3)+h(2)'
t = s.replace('y', 'g(x,z)')
u = t.replace('z', 'f(z)')
r1, d1 = replaceCallsWithDummies(s, ['f', 'g', 'h'])
r2, d2 = replaceCallsWithDummies(t, ['f', 'g', 'h'])
r3, d3 = replaceCallsWithDummies(u, ['f', 'g', 'h'])
assert r1 == '1+a/(__dummy1__-3)+__dummy2__'
assert len(d1) == 2
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d2) == 3
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d3) == 4
ps = 'abs((HB9_fs_Vq-HB9_fs_V)*(-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C)+(HB9_fs_Knq-HB9_fs_K_n)*(((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))))/(sqrt(HB9_fs_Vq*HB9_fs_Vq+HB9_fs_Knq*HB9_fs_Knq)+sqrt(pow((-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C),2)+pow((((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))),2)))'
parnames = [
'HB9_fs_Vq', 'HB9_fs_Lk_g', 'HB9_fs_Lk_vrev', 'HB9_fs_Iapp_Ibias',
'HB9_fs_Na_g', 'HB9_fs_Na_theta_m', 'HB9_fs_Na_k_m', 'HB9_fs_Na_vrev',
'HB9_fs_K_g', 'HB9_fs_K_vrev', 'HB9_fs_isyn_g', 'HB9_fs_isyn_vrev',
'HB9_fs_esyn_g', 'HB9_fs_esyn_vrev', 'HB9_fs_C', 'HB9_fs_Knq',
'HB9_fs_K_theta_n', 'HB9_fs_K_k_n', 'HB9_fs_K_taun_bar'
]
varnames = ['HB9_fs_V', 'HB9_fs_K_n']
ps2 = convertPowers(ps, 'pow')
for n in parnames + varnames:
v = rand(1)[0] + 1e-5
ps2 = ps2.replace(n, str(v))
ps = ps.replace(n, str(v))
eps = eval(ps)
eps2 = eval(ps2)
assert eps == eps2
a = Par('3.5', 'a')
qa = Var(['a*3', 'b'], 'array_test')
assert str(qa.eval(a=1)) == '[3,b]'
# explicit exporting 'a' to globals to make this work as expected
globals()['a'] = a
assert str(qa.eval()) == '[10.5,b]'
testq = QuantSpec('d', 'a')
testq.simplify()
assert testq() == 'a'
assert str(testq.eval(a=3)) == '3'
q = QuantSpec('q', 'zeta(yrel(y,initcond(y)),z)-1')
print(q.eval({}))
assert 'initcond' in str(q.eval({}))
q2 = QuantSpec('q', 'Exp(-spikeTable+b)/k')
assert 'spikeTable' in q2.freeSymbols
# x = Var('x')
# print x.isDefined()
# xs = QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec')
# x.bindSpec(xs)
# print x.isDefined(),"\n"
x = Var(QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec'))
p = Par('p')
az = Var(QuantSpec('z', 'myfunc(0,z)+abs(x+1)', 'RHSfuncSpec'))
w = Var('x-1/w[i]', 'w[i,0,1]', specType='RHSfuncSpec')
myLeaf1.compatibleContainers = (myNode, )
myLeaf2.compatibleContainers = (myNode, )
myNode.compatibleSubcomponents = (myLeaf1, myLeaf2)
c = myLeaf1('leaf1')
assert c.isDefined() == False
c.add(x)
print(c.freeSymbols, c.isDefined())
c.add(az)
print(c.freeSymbols, c.isDefined())
c.add(w)
print(c.freeSymbols, c.isDefined())
c.compileFuncSpec()
print(c.funcSpecDict)
empty_fn = Fun('1+exp(1)', [], 'dumb_fn')
print(empty_fn())
q = Par('qpar')
y = Var(QuantSpec('rel', 'v+p'), domain=[0, 1])
g = Fun(QuantSpec('qfunc', '-1.e-05+sin(qpar)*(10.e-5-xtol)'), ['xtol'])
d = myLeaf2('leaf2')
## d.add(y)
q_dummy = Var(QuantSpec('q_notpar', '-2+sin(30)'))
g_dummy = Fun(QuantSpec('qfunc_dummy', 'sin(q_notpar)*(10.e-5-xtol)'),
['xtol'])
d.add([q_dummy, g_dummy]) # will delete these later
d.add([q, g])
d2 = myLeaf2('leaf3')
d2.add([q, g])
v = Var(QuantSpec('v', 'v * myfunc(rel,v) - sin(p)*t', 'RHSfuncSpec'))
# p is a global parameter so this is ok in v
f = Fun(QuantSpec('myfunc', '2.0+s-t+exp(p)'), ['s', 't'])
# t is just a local argument here, so it won't clash with its
# occurrence in v (which we'll see is declared as a global
# when we call flattenSpec()).
ipar = Par('ipar')
z = Var('z[i]+v/(i*ipar)', 'z[i,0,5]', specType='RHSfuncSpec')
a = myNode('sys1')
a.add([f, p, y])
print(a.isDefined(True))
a.add(c)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add(d)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add(d2)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add(v)
print("Added v")
print(a.freeSymbols, a.isDefined(), a.isComplete())
print("Removed v")
a.remove(v)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add([z, ipar])
print(a.freeSymbols, a.isDefined(), a.isComplete())
print("\na._registry --> ")
print(a._registry)
print("Re-added v")
a.add(v)
print(a.freeSymbols, a.isDefined(), a.isComplete())
print("\nv in a -->", v in a)
print("\n")
with pytest.raises(TypeError):
a.compileFuncSpec()
a.remove(['leaf2.qfunc_dummy', 'leaf2.q_notpar'])
print("--------- sys1: funcSpecDict ---------------------")
a.compileFuncSpec()
info(a.funcSpecDict)
print("\n\n------------- Flatten spec with unravelling\n")
print("\n\ninfo(a.flattenSpec()) --> \n")
info(a.flattenSpec(globalRefs=['t']), "Model specification")
print("\n\n------------- Flatten spec with no unravelling\n")
print("\n\ninfo(a.flattenSpec(False, globalRefs=['t'])) --> \n")
info(a.flattenSpec(False, globalRefs=['t']), "Model specification")
print("\n\nDemos for functions (results are strings):\n")
h = f(p, -x)
z = QuantSpec('zero', '0')
print("h = f(p, -x) --> ", h)
print("z = QuantSpec('zero','0') --> ", z)
print("f(g(3)*1,h) --> ", f(g(3) * 1, h))
print("f(g(p),h) --> ", f(g(p), h))
print("f(g(p),0*h) --> ", f(g(p), 0 * h))
print("f(g(x),h+z) --> ", f(g(x), h + z))
# e is the math constant, but it doesn't evaluate to a float!
print("f(g(x()),(e+h)/2) --> ", f(g(x()), (e + h) / 2))
print("f(g(x()),-h) --> ", f(g(x()), -h))
print("f(g(x()),.5-h+0) --> ", f(g(x()), .5 - h + 0))
print("Sin(pi+q) --> ", Sin(pi + q))
qsin = QuantSpec('qsin', 'zv-sin(beta)')
assert str(qsin.eval()) == 'zv-sin(beta)'
print("\n\nDemos for local scope evaluation and **:\n")
print("q=Var('xv+1','qv')")
print("x=Var('3','xv')")
q = Var('xv+1', 'qv')
x = Var('3', 'xv')
globals()['x'] = x
globals()['q'] = q
sc1 = str(q.eval()) == '4'
print("q.eval() == 4? ", sc1)
assert sc1
print("a=x/q")
a = x / q
sc2 = str(a) == 'xv/qv'
print("a == xv/qv? ", sc2)
assert sc2
sc3 = str(a.eval()) == '0.75'
print("a.eval() == 0.75? ", sc3)
assert sc3
sc4 = str(a.eval(xv=5)) == '5/qv'
print("a.eval(xv=5) == 5/q? ", sc4)
assert sc4
sc5 = (str(a.eval(xv=5, qv=q())), '0.83333333333333337')
assert_approx_equal(*sc5)
print("assert_approx_equal(%s,%s)" % sc5)
sc6 = (str(a.eval({'xv': 10, 'qv': q()})), '0.90909090909090906')
print("assert_approx_equal(%s,%s)" % sc6)
assert_approx_equal(*sc6)
print("qs=QuantSpec('qsv','xsv+1')")
print("xs=QuantSpec('xsv','3')")
qs = QuantSpec('qsv', 'xsv+1')
xs = QuantSpec('xsv', '3')
globals()['qs'] = qs
globals()['xs'] = xs
qse = qs.eval()
qt1 = str(qse) == '4'
print("qs.eval() == 4? ", qt1)
assert qt1
assert qse.tonumeric() == 4
print("asq = xs/qs")
asq = xs / qs
qt2 = str(asq) == '3/(xsv+1)'
print("asq == 3/(xsv+1)? ", qt2)
assert qt2
qt3 = str(asq.eval()) == '0.75'
print("as.eval() == 0.75? ", qt3)
assert qt3
ps = asq**xs
print("ps = as**xs")
qt4 = str(ps) == 'Pow(3/(xsv+1),3)'
print("ps == Pow(3/(xsv+1),3)? ", qt4)
assert qt4
qt5 = str(ps.eval()) == str(0.75**3)
print("ps.eval() == 0.421875? ", qt5)
assert qt5
print("sq=QuantSpec('sv','sin(xsv)')")
print("s2q=QuantSpec('s2v','Sin(xv)')")
sq = QuantSpec('sv', 'sin(xsv)')
s2q = QuantSpec('s2v', 'Sin(xv)')
print("sq.eval() --> ", sq.eval())
print("s2q.eval() --> ", s2q.eval())
assert sq.eval().tonumeric() == s2q.eval().tonumeric()
assert sq[:] == ['sin', '(', 'xsv', ')']
print("\n\nDemos for multiple quantity definitions:\n")
mp = QuantSpec('p', 'a + 3*z[4*i-2]')
m = Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')
v = Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')
print("mp=QuantSpec('p','a + 3*z[4*i-2]')")
print("m=Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')")
print("v=Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')")
print("v[3] -->", v[3])
assert str(v[3]) == 'z3'
print("v.freeSymbols -->", v.freeSymbols)
assert v.freeSymbols == ['z0']
print("\nModelSpec a already contains 'z0', which was defined as part of")
print("a multiple quantity definition, so check that attempting to add")
print("v to a results in an error ...")
with pytest.raises(AttributeError):
a.add(v)
print("\nTest of eval method, e.g. on a function f(s,t)...")
print("f.eval(s='1', t='t_val') -->", f.eval(s='1', t='t_val'))
print("f.eval(s=1, t='t_val', p=0.5) -->", f.eval(s=1, t='t_val', p=0.5))
print("\nTesting convertPowers():")
cp_tests = [
"phi1dot^m3", "1+phi1dot^m3*s", "phi1dot**m3", "1+phi1dot**m3*s",
"sin(x^3)**4", "(2/3)^2.5", "3^cos(x)-pi", "3^(cos(x)-pi)",
"2^(sin(y**p))"
]
for spec in cp_tests:
print(spec, " --> ", convertPowers(spec))
globals().pop('a')
qc = QuantSpec('t', "a+coot+b/'coot'")
assert str(qc.eval()) == 'a+coot+b/"coot"'
coot = QuantSpec('coot', "1.05")
globals()['coot'] = coot
assert str(qc.eval()) == 'a+1.05+b/"coot"'
print("\nTest of function calling with argument names that clash with")
print("bound names inside the function.")
x0 = Var('x0')
x1 = Var('x1')
x2 = Var('x2')
F = Fun([x0 * x2, x0 * 5, x2**0.5], [x0, x1, x2], 'F')
print("F=Fun([x0*x2,x0*5,x2**0.5], [x0,x1,x2], 'F')")
print("F(3,2,Sin(x0))) = [3*Sin(x0),15,Pow(Sin(x0),0.5)] ...")
print(" ... even though x0 is a bound name inside definition of F")
assert str(F(3, 2, Sin(x0))) == '[3*Sin(x0),15,Pow(Sin(x0),0.5)]'
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_mapsystem():
# datafn provides an external input to the map system -- this could have
# been from an experimentally measured signal
datafn = Generator.InterpolateTable(
{'name': 'datafunction',
'tdata': [-30., 0., 5., 10., 30., 100., 180., 400.],
'ics': {'x': [4., 1., 0., 1., 2., 3., 4., 8.]}
}
)
fvarspecs = {
"w": "15-a*w + 2*x",
"v": "1+k*w/10",
'aux_wdouble': 'w*2 + globalindepvar(t)',
'aux_other': 'myauxfn(2*t) + initcond(w)'
}
fnspecs = {
'myauxfn': (['t'], '.5*cos(3*t)'),
}
# targetlang is optional if default=python is OK
DSargs = args(name='maptest', fnspecs=fnspecs)
DSargs.varspecs = fvarspecs
DSargs.tdomain = [0, 400]
DSargs.pars = {'k': 2.1, 'a': -0.5}
DSargs.vars = ['w', 'v']
DSargs.ttype = int # force independent variable type to be integer
DSargs.checklevel = 2
DSargs.inputs = datafn.variables
testmap = MapSystem(DSargs)
assert testmap.pars == DSargs.pars
assert not testmap.defined
assert_array_almost_equal([0, 400], testmap.tdata)
testmap.set(
ics={'w': 3.0, 'v': 2.},
tdata=[10, 400])
assert_array_almost_equal([10, 400], testmap.tdata)
assert_almost_equal(3.0, testmap.initialconditions['w'])
assert_almost_equal(2.0, testmap.initialconditions['v'])
traj1 = testmap.compute('traj1')
assert testmap.defined
p = Point({'coorddict': {
'aux_other': 3.34962540324,
'aux_wdouble': 98.1981323242,
'v': 8.64360778809,
'w': 36.5990661621,
}})
assert_almost_equal(p.toarray(), traj1(25).toarray())
assert testmap.diagnostics.hasWarnings()
assert_array_almost_equal(testmap.tdata, traj1.indepdomain.get())
assert_almost_equal(2.70076996547, traj1(30, 'aux_other'))
ps = traj1(range(10, 40))
assert isinstance(ps, Pointset)
assert ps._parameterized
ev_args = {'name': 'threshold',
'eventtol': 1e-4,
'eventdelay': 1e-5,
'starttime': 0,
'active': True,
'term': True,
'precise': False}
thresh_ev = Events.makePythonStateZeroCrossEvent('w', 58, 1, ev_args)
testmap.eventstruct.add(thresh_ev)
traj2 = testmap.compute('traj2')
assert testmap.getEventTimes()['threshold'] == [347.]
assert_array_almost_equal([10, 347], traj2.indepdomain.get())
assert testmap.diagnostics.hasWarnings()
assert testmap.diagnostics.findWarnings(10) != []
assert_almost_equal(58.0, traj2(traj2.indepdomain[1], 'w'))
def test_bd_containment():
"""Basic tests for boundary containment features."""
vals1 = linspace(-3, 3, 20)
test_traj1 = numeric_to_traj([vals1], 'test', 'x',
arange(len(vals1), dtype='d'))
vals2 = array(
[1., 1., 1.00000000001, 1.0000001, 1., 0.9999999999, 0.99999])
test_traj2 = numeric_to_traj([vals2], 'test', 'x',
arange(len(vals2), dtype='d'))
bc = boundary_containment_by_postproc('bc_test',
description='Test BCs',
pars=args(thresh=1,
interior_dirn=-1,
abseps=1e-4))
# Test whether test trajectory 1 remains below x_ref=1
# up to rounding error tolerance of 1e-4...
assert not bc(test_traj1)
# print "... failed at index", bc._find_idx()
# print "\nbc.results -->\n"
# print bc.results
# Test whether test trajectory 2 remains below x_ref=1
# up to rounding error tolerance of 1e-4...
assert bc(test_traj2)
# Test whether initial condition lies within a domain
# (includes transversality condition: derivative must point into interior
# of domain):
ic_inside = numeric_to_traj([[0.3], [-10.5]], 'test', ['x', 'dxdt'], 0.)
ic_crit_ok = numeric_to_traj([[1], [-1.]], 'test', ['x', 'dxdt'], 0.)
ic_crit_not_ok = numeric_to_traj([[1], [1.]], 'test', ['x', 'dxdt'], 0.)
ic_outside = numeric_to_traj([[1.01], [-1.]], 'test', ['x', 'dxdt'], 0.)
in_domain = domain_test('domain_test',
pars=args(coordname='x',
derivname='dxdt',
interval=[-1, 1],
verbose_level=3))
assert in_domain(ic_inside)
assert in_domain(ic_crit_ok)
assert not in_domain(ic_crit_not_ok)
assert not in_domain(ic_outside)
# Check that exterior IC failed at trajectory point index '0' with
# in_domain._find_idx()==0
# ------------------------------------------------------------------
# Test for domain with rounding-error tolerated boundaries:
in_domain_loose = domain_test('domain_test',
pars=args(coordname='x',
derivname='dxdt',
interval=Interval('x',
float, [-1, 1],
abseps=1e-4),
verbose_level=0))
ic_crit_round_ok = numeric_to_traj([[1.000001], [-1.]], 'test',
['x', 'dxdt'], 0.)
ic_crit_round_not_ok = numeric_to_traj([[1.000001], [1.]], 'test',
['x', 'dxdt'], 0.)
assert in_domain_loose(ic_inside)
assert in_domain_loose(ic_crit_ok)
assert not in_domain_loose(ic_crit_not_ok)
assert not in_domain_loose(ic_outside)
assert in_domain_loose(ic_crit_round_ok)
assert not in_domain_loose(ic_crit_round_not_ok)
zbd1 = domain_test('z',
pars=args(coordname='z',
derivname='D_z',
interval=[0.0, 1.0],
verbose_level=0))
zbd2 = domain_test('z',
pars=args(coordname='z',
derivname='D_z',
interval=1.0,
verbose_level=0))
ztraj = {}
ztraj[0] = numeric_to_traj([[1], [0.437]], 'test', ['z', 'D_z'], 0)
ztraj[1] = numeric_to_traj([[1], [1]], 'test', ['z', 'D_z'], 0)
ztraj[2] = numeric_to_traj([[1.0], [1]], 'test', ['z', 'D_z'], 0)
ztraj[3] = numeric_to_traj([[1], [1.0]], 'test', ['z', 'D_z'], 0)
ztraj[4] = numeric_to_traj([[1], [1.0]], 'test', ['z', 'D_z'], 0)
ztraj[5] = numeric_to_traj([[1.0], [5.0]], 'test', ['z', 'D_z'], 0)
assert not zbd1(ztraj[0])
for i in range(1, 6):
assert zbd2(ztraj[i])
"""
Cross-channel coupling for a biophysical neural network.
Example courtesy of Mark Olenik (Bristol University).
"""
from PyDSTool import Var, Exp, Par, Pow, args
from PyDSTool.Toolbox.neuralcomp import voltage, \
ModelConstructor, makeSoma, channel
from matplotlib import pyplot as plt
v = Var(voltage)
# Create placeholder structs to collect together related symbols
# (not used internally by PyDSTool)
NMDA = args()
KCa = args()
# Calcium concentration through nmda channels
# Ca_nmda won't create a current but will be used for KCa.I
Ca_nmda = args()
Iapp = args()
NMDA.g = Par(0.75, 'g')
NMDA.erev = Par(0., 'erev')
KCa.g = Par(0.0072, 'g')
KCa.erev = Par(-80., 'erev')
Ca_nmda.erev = Par(20., 'Ca_erev')
Ca_nmda.rho = Par(0.0004, 'rho')
Ca_nmda.delta = Par(0.002, 'delta')
Iapp.amp = Par(0.0, 'amp')
NMDA.p = Var('p') # nmda gating variable
Ca_nmda.c = Var('c') # concentration
def dsargs():
timeData = linspace(0, 10, 20)
sindata = sin(20 * timeData)
xData = {'in': sindata}
my_input = InterpolateTable({
'tdata': timeData,
'ics': xData,
'name': 'interp1d',
'method': 'linear',
'checklevel': 1,
'abseps': 1e-5
}).compute('interp')
fvarspecs = {
"w": "k*w + 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')}
# targetlang is optional if the default python target is desired
DSargs = args(fnspecs=fnspecs, name='event_test')
DSargs.varspecs = fvarspecs
DSargs.tdomain = [0.1, 2.1]
DSargs.pars = {'k': 2, 'a': -0.5}
DSargs.vars = 'w'
DSargs.ics = {'w': 3}
DSargs.inputs = {'in': my_input.variables['in']}
DSargs.algparams = {'init_step': 0.01}
DSargs.checklevel = 2
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'],
targetlang='c')
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-20',
1,
ev_args_term, ['w'],
targetlang='c')
DSargs.events = [thresh_ev_nonterm, thresh_ev_term]
return DSargs
pars = {"eps": 1e-2, "a": 0.5}
icdict = {"x": pars["a"], "y": pars["a"] - pars["a"] ** 3 / 3}
xstr = "(y - (x*x*x/3 - x))/eps"
ystr = "a - x"
event_x_a = dst.makeZeroCrossEvent(
"x-a",
0,
{"name": "event_x_a", "eventtol": 1e-6, "term": False, "active": True},
varnames=["x"],
parnames=["a"],
targetlang="python",
) # targetlang is redundant (defaults to python)
DSargs = args(name="vanderpol") # struct-like data
DSargs.events = [event_x_a]
DSargs.pars = pars
DSargs.tdata = [0, 3]
DSargs.algparams = {"max_pts": 3000, "init_step": 0.02, "stiff": True}
DSargs.varspecs = {"x": xstr, "y": ystr}
DSargs.xdomain = {"x": [-2.2, 2.5], "y": [-2, 2]}
DSargs.fnspecs = {
"Jacobian": (
["t", "x", "y"],
"""[[(1-x*x)/eps, 1/eps ],
[ -1, 0 ]]""",
)
}
DSargs.ics = icdict
vdp = dst.Vode_ODEsystem(DSargs)
def prep_boxplots(data, xlabel_str, figname='', fignum=1, do_legend=1,
means=1, xlegoff=0, ylegstep=1, ylegoff=0, spacing=None):
spacing_actual = {
'width': 0.1,
'wgapfac': 0.75,
'markersize': 12,
'off_fac': 0.7,
'x_step': 0.9, # 9 * width
'x_off': 0,
'box_to_marker': 1.1,
'notch_size': 0.2}
if spacing is not None:
spacing_actual.update(spacing)
width = spacing_actual['width']
wgapfac = spacing_actual['wgapfac']
markersize = spacing_actual['markersize']
off_fac = spacing_actual['off_fac']
x_step = spacing_actual['x_step']
x_off = spacing_actual['x_off']
box_to_marker = spacing_actual['box_to_marker']
notch_size = spacing_actual['notch_size']
n = len(data)
x_min = -width*3.8 #3.75
x_max = (n-1)*x_step+width*4.5 #3.75
if n > 1:
halfticks = arange(1,n)*x_step-x_step/2
figure(fignum)
# work out ordering of data from 'pos' key
order = {}
# `pos` position runs from 1 to n, `ns` runs from 0 to n-1
ns = []
for k, v in data.iteritems():
order[v['pos']] = k
ns.append(v['pos']-1)
ns.sort()
assert ns == range(n)
maxD = 0
max_dimval_markers = 0
labels = []
for pos in range(n):
name = order[pos+1]
pde_name = 'PD_E-'+name
if 'known_dim' in data[name]:
if n == 1:
kdx1 = x_min
kdx2 = x_max
else:
if pos == 0:
kdx1 = x_min
kdx2 = halfticks[0]
elif pos == n-1:
kdx1 = halfticks[n-2]
kdx2 = x_max
else:
kdx1 = halfticks[pos-1]
kdx2 = halfticks[pos]
plot([[kdx1], [kdx2]],
[data[name]['known_dim'],data[name]['known_dim']],
'k', linewidth=1, zorder=0)
slope_data = loadObjects(pde_name)[2]
ds_mins = array(slope_data[:,0])#,shape=(len(slope_data),1))
ds_mins.shape=(len(slope_data),1)
ds_maxs = array(slope_data[:,1])#,shape=(len(slope_data),1))
ds_maxs.shape=(len(slope_data),1)
max_ds = max([max(ds_mins[:,0]),max(ds_maxs[:,0])])
if max_ds > maxD:
maxD = max_ds
# limits args are ineffective here
boxplot(ds_mins,positions=[pos*x_step-width*wgapfac+x_off],whis=100,
means=means,monochrome=True,notch=2,notchsize=notch_size,
limits=(),widths=width,fill=1)
boxplot(ds_maxs,positions=[pos*x_step+width*wgapfac+x_off],whis=100,
means=means,monochrome=True,notch=2,notchsize=notch_size,
limits=(),widths=width,fill=1)
if pos == 0:
fa = figure(fignum).axes[0]
fa.hold(True)
if means:
ds_all_mean = (mean(ds_mins[:,0])+mean(ds_maxs[:,0]))/2
plot([pos*x_step+x_off], [ds_all_mean], 'k^',
markersize=markersize-2)
pca_x = pos*x_step-width*(wgapfac+box_to_marker)+x_off
isomap_x = pos*x_step+width*(wgapfac+box_to_marker)+x_off
pca_ds = {}
isomap_ds = {}
try:
pca_data = data[name]['pca']
except KeyError:
pca_data = []
pca_ds, max_dimval_pca, pca_used = plot_markers(pca_data,
pca_x, 'PCA',
symbol_map['pca'], -1,
width, off_fac, markersize)
if max_dimval_pca > maxD:
maxD = max_dimval_pca
if max_dimval_pca > max_dimval_markers:
max_dimval_markers = max_dimval_pca
try:
isomap_data = data[name]['isomap']
except KeyError:
isomap_data = []
isomap_ds, max_dimval_iso, isomap_used = plot_markers(isomap_data,
isomap_x, 'Isomap',
symbol_map['isomap'], 1,
width, off_fac, markersize)
if max_dimval_iso > maxD:
maxD = max_dimval_iso
if max_dimval_iso > max_dimval_markers:
max_dimval_markers = max_dimval_iso
labels.append(data[name]['label'])
## legend
if do_legend:
font = FontProperties()
font.set_family('sans-serif')
font.set_size(11)
x_legend = x_min + 3*width/4 + xlegoff
y_legend = maxD+ylegoff
# pca legend
for k, s in pca_used:
plot_markers([(k,s,y_legend)], x_legend, 'Legend', symbol_map['pca'],
1, width, off_fac, markersize)
if k == 'var':
legstr = "%s=%d%%"%(k,s)
else:
legstr = "%s=%d"%(k,s)
text(x_legend+3*width/4, y_legend-width*2., legstr,
fontproperties=font)
y_legend -= ylegstep
# isomap legend
isomap_leg_data = []
for k, s in isomap_used:
if y_legend-width*2. <= max_dimval_markers + 2:
y_legend = maxD+ylegoff
x_legend += x_step #-width*.75
plot_markers([(k,s,y_legend)], x_legend, 'Legend', symbol_map['isomap'],
1, width, off_fac, markersize)
## if k == 'eps':
## kstr = '\\epsilon'
## else:
## kstr = k
text(x_legend+3*width/4, y_legend-width*2., "%s=%d"%(k,s),
fontproperties=font)
y_legend -= ylegstep
## tidy up axes, etc.
fa.set_xticks(arange(n)*x_step)
if n>1:
for h in range(n-1):
plot([halfticks[h], halfticks[h]], [0,maxD+1+ylegoff], 'k:')
fa.set_xticklabels(labels)
fa.set_position([0.07, 0.11, 0.9, 0.85])
fa.set_xlim(x_min,x_max)
fa.set_ylim(0,maxD+1+ylegoff)
if xlabel_str != '':
xlabel(r'$\rm{'+xlabel_str+r'}$',args(fontsize=20,fontname='Times'))
ylabel(r'$\rm{Dimension}$',args(fontsize=20,fontname='Times'))
draw()
if figname != '':
save_fig(fignum, figname)
# coding=utf-8
import PyDSTool as dst
from PyDSTool import args
import numpy as np
from matplotlib import pyplot as plt
DSargs = args(name='Lorenz map')
DSargs.varspecs = {
'z': 'a+b*(z-c)**2', # note syntax for power
'zp': 'zp+log(abs(2*b*(z-c)))',
'L': 'zp/(t+1)'
} # L is an auxiliary variable
DSargs.tdomain = [0, 200] # Default range of independent variable 't'
DSargs.pars = args(
a=2.93, b=-1.44, c=1.85
) # Using args() class to specify parameters with less syntax than a dictionary
DSargs.vars = ['z', 'zp'] # Implicitly, then, L will be an auxiliary variable
DSargs.ics = {'z': 2, 'zp': 0} # Initial conditions
DSargs.ttype = int # force independent variable type to be integer (discrete time)
lmap = dst.Generator.MapSystem(
DSargs) # an instance of the 'Generator' class for maps.
traj = lmap.compute('test') # compute a trajectory named 'test'
pts = traj.sample() # sample the points from the trajectory
# PyPlot commands
plt.figure(1)
plt.plot(pts['t'], pts['z'], 'ko-')
plt.title(lmap.name)
"""
Cross-channel coupling for a biophysical neural network.
Example courtesy of Mark Olenik (Bristol University).
"""
from PyDSTool import Var, Exp, Par, Pow, args
from PyDSTool.Toolbox.neuralcomp import voltage, \
ModelConstructor, makeSoma, channel
from matplotlib import pyplot as plt
v = Var(voltage)
# Create placeholder structs to collect together related symbols
# (not used internally by PyDSTool)
NMDA = args()
KCa = args()
# Calcium concentration through nmda channels
# Ca_nmda won't create a current but will be used for KCa.I
Ca_nmda = args()
Iapp = args()
NMDA.g = Par(0.75, 'g')
NMDA.erev = Par(0., 'erev')
KCa.g = Par(0.0072, 'g')
KCa.erev = Par(-80., 'erev')
Ca_nmda.erev = Par(20., 'Ca_erev')
Ca_nmda.rho = Par(0.0004, 'rho')
Ca_nmda.delta = Par(0.002, 'delta')
Iapp.amp = Par(0.0, 'amp')
NMDA.p = Var('p') # nmda gating variable
Ca_nmda.c = Var('c') # concentration
def test_symbolic():
assert doneg('-x-y') == 'x+y'
assert doneg('(-x-y)') == '(x+y)'
assert doneg('-(-x-y)') == '(-x-y)'
assert dosub('1', '-x-y') == '(1+x+y)'
g2 = expr2fun('1-max([0., -a+b*x])', **{'a': 3, 'b': 1.5})
assert g2._args == ['x']
assert g2(1) == 1.0
assert g2(10) == -11.0
ds = {'a': 3, 'bbb': 1}
f=expr2fun('1+ds["a"]')
assert f._args == ['ds']
assert f(ds) == 4
f2=expr2fun('1+ds["a"]')
assert f2(**{'ds':ds}) == 4
assert f2._args == ['ds']
g=expr2fun('1+ds["bbb"]', ds=ds)
assert g() == 2
# g must be dynamic and not based on static eval of ds on initialization
ds['bbb'] = 2
assert g._args == []
assert g() == 3
m = args(pars=copy(ds))
h = expr2fun('m.pars["a"]+c', m=m, c=1)
assert h() == 4
assert h._args == []
h2 = expr2fun('1 + m.pars["a"]/2.', m=m)
assert h2() == 2.5
assert h2._args == []
def func(x, y):
return x * (y+1)
m.func = func
i = expr2fun('1+func(x,y)+b', func=m.func, b=0.5)
assert 1+func(2,3)+0.5 == i(2,3)
j = expr2fun('i(x,func(2,y))*2', i=i, func=m.func)
assert j(1,0) == 9
fnspec = {'f': (['x','y'], 'x+1+2*y-a')}
# a is expected to be in scope like a FuncSpec parameter
# so can't use the above method of providing explicit functions
k = expr2fun('-f(c,d)+b', f=fnspec['f'], b=0.5, a=1)
assert k(1,2) == -4.5
s='1+a/(f(x,y)-3)+h(2)'
t=s.replace('y','g(x,z)')
u=t.replace('z','f(z)')
r1, d1 = replaceCallsWithDummies(s, ['f','g','h'])
r2, d2 = replaceCallsWithDummies(t, ['f','g','h'])
r3, d3 = replaceCallsWithDummies(u, ['f','g','h'])
assert r1 == '1+a/(__dummy1__-3)+__dummy2__'
assert len(d1) == 2
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d2) == 3
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d3) == 4
ps = 'abs((HB9_fs_Vq-HB9_fs_V)*(-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C)+(HB9_fs_Knq-HB9_fs_K_n)*(((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))))/(sqrt(HB9_fs_Vq*HB9_fs_Vq+HB9_fs_Knq*HB9_fs_Knq)+sqrt(pow((-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C),2)+pow((((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))),2)))'
parnames = ['HB9_fs_Vq', 'HB9_fs_Lk_g', 'HB9_fs_Lk_vrev', 'HB9_fs_Iapp_Ibias', 'HB9_fs_Na_g', 'HB9_fs_Na_theta_m', 'HB9_fs_Na_k_m', 'HB9_fs_Na_vrev', 'HB9_fs_K_g', 'HB9_fs_K_vrev', 'HB9_fs_isyn_g', 'HB9_fs_isyn_vrev', 'HB9_fs_esyn_g', 'HB9_fs_esyn_vrev', 'HB9_fs_C', 'HB9_fs_Knq', 'HB9_fs_K_theta_n', 'HB9_fs_K_k_n', 'HB9_fs_K_taun_bar']
varnames = ['HB9_fs_V', 'HB9_fs_K_n']
ps2 = convertPowers(ps, 'pow')
for n in parnames+varnames:
v=rand(1)[0]+1e-5
ps2=ps2.replace(n,str(v))
ps=ps.replace(n,str(v))
eps=eval(ps)
eps2=eval(ps2)
assert eps==eps2
a = Par('3.5', 'a')
qa = Var(['a*3', 'b'], 'array_test')
assert str(qa.eval(a=1)) == '[3,b]'
# explicit exporting 'a' to globals to make this work as expected
globals()['a'] = a
assert str(qa.eval()) == '[10.5,b]'
testq = QuantSpec('d', 'a')
testq.simplify()
assert testq() == 'a'
assert str(testq.eval(a=3)) == '3'
q = QuantSpec('q', 'zeta(yrel(y,initcond(y)),z)-1')
print q.eval({})
assert 'initcond' in str(q.eval({}))
q2=QuantSpec('q','Exp(-spikeTable+b)/k')
assert 'spikeTable' in q2.freeSymbols
# x = Var('x')
# print x.isDefined()
# xs = QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec')
# x.bindSpec(xs)
# print x.isDefined(),"\n"
x = Var(QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec'))
p = Par('p')
az = Var(QuantSpec('z', 'myfunc(0,z)+abs(x+1)', 'RHSfuncSpec'))
w = Var('x-1/w[i]', 'w[i,0,1]', specType='RHSfuncSpec')
myLeaf1.compatibleContainers=(myNode,)
myLeaf2.compatibleContainers=(myNode,)
myNode.compatibleSubcomponents=(myLeaf1,myLeaf2)
c = myLeaf1('leaf1')
assert c.isDefined() == False
c.add(x)
print c.freeSymbols, c.isDefined()
c.add(az)
print c.freeSymbols, c.isDefined()
c.add(w)
print c.freeSymbols, c.isDefined()
c.compileFuncSpec()
print c.funcSpecDict
empty_fn = Fun('1+exp(1)', [], 'dumb_fn')
print empty_fn()
q = Par('qpar')
y = Var(QuantSpec('rel', 'v+p'), domain=[0,1])
g = Fun(QuantSpec('qfunc', '-1.e-05+sin(qpar)*(10.e-5-xtol)'), ['xtol'])
d = myLeaf2('leaf2')
## d.add(y)
q_dummy = Var(QuantSpec('q_notpar', '-2+sin(30)'))
g_dummy = Fun(QuantSpec('qfunc_dummy', 'sin(q_notpar)*(10.e-5-xtol)'), ['xtol'])
d.add([q_dummy, g_dummy]) # will delete these later
d.add([q,g])
d2 = myLeaf2('leaf3')
d2.add([q,g])
v = Var(QuantSpec('v', 'v * myfunc(rel,v) - sin(p)*t', 'RHSfuncSpec'))
# p is a global parameter so this is ok in v
f = Fun(QuantSpec('myfunc', '2.0+s-t+exp(p)'), ['s','t'])
# t is just a local argument here, so it won't clash with its
# occurrence in v (which we'll see is declared as a global
# when we call flattenSpec()).
ipar = Par('ipar')
z = Var('z[i]+v/(i*ipar)', 'z[i,0,5]', specType='RHSfuncSpec')
a = myNode('sys1')
a.add([f,p,y])
print a.isDefined(True)
a.add(c)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add(d)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add(d2)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add(v)
print "Added v"
print a.freeSymbols, a.isDefined(), a.isComplete()
print "Removed v"
a.remove(v)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add([z,ipar])
print a.freeSymbols, a.isDefined(), a.isComplete()
print "\na._registry --> "
print a._registry
print "Re-added v"
a.add(v)
print a.freeSymbols, a.isDefined(), a.isComplete()
print "\nv in a -->", v in a
print "\n"
with pytest.raises(TypeError):
a.compileFuncSpec()
a.remove(['leaf2.qfunc_dummy', 'leaf2.q_notpar'])
print "--------- sys1: funcSpecDict ---------------------"
a.compileFuncSpec()
info(a.funcSpecDict)
print "\n\n------------- Flatten spec with unravelling\n"
print "\n\ninfo(a.flattenSpec()) --> \n"
info(a.flattenSpec(globalRefs=['t']), "Model specification")
print "\n\n------------- Flatten spec with no unravelling\n"
print "\n\ninfo(a.flattenSpec(False, globalRefs=['t'])) --> \n"
info(a.flattenSpec(False, globalRefs=['t']), "Model specification")
print "\n\nDemos for functions (results are strings):\n"
h = f(p, -x)
z = QuantSpec('zero','0')
print "h = f(p, -x) --> ", h
print "z = QuantSpec('zero','0') --> ", z
print "f(g(3)*1,h) --> ", f(g(3)*1,h)
print "f(g(p),h) --> ", f(g(p),h)
print "f(g(p),0*h) --> ", f(g(p),0*h)
print "f(g(x),h+z) --> ", f(g(x),h+z)
# e is the math constant, but it doesn't evaluate to a float!
print "f(g(x()),(e+h)/2) --> ", f(g(x()),(e+h)/2)
print "f(g(x()),-h) --> ", f(g(x()),-h)
print "f(g(x()),.5-h+0) --> ", f(g(x()),.5-h+0)
print "Sin(pi+q) --> ", Sin(pi+q)
qsin=QuantSpec('qsin','zv-sin(beta)')
assert str(qsin.eval()) == 'zv-sin(beta)'
print "\n\nDemos for local scope evaluation and **:\n"
print "q=Var('xv+1','qv')"
print "x=Var('3','xv')"
q=Var('xv+1','qv')
x=Var('3','xv')
globals()['x'] = x
globals()['q'] = q
sc1 = str(q.eval()) == '4'
print "q.eval() == 4? ", sc1
assert sc1
print "a=x/q"
a=x/q
sc2 = str(a) == 'xv/qv'
print "a == xv/qv? ", sc2
assert sc2
sc3 = str(a.eval())=='0.75'
print "a.eval() == 0.75? ", sc3
assert sc3
sc4 = str(a.eval(xv=5))=='5/qv'
print "a.eval(xv=5) == 5/q? ", sc4
assert sc4
sc5 = (str(a.eval(xv=5,qv=q())),'0.83333333333333337')
assert_approx_equal(*sc5)
print "assert_approx_equal(%s,%s)" % sc5
sc6 = (str(a.eval({'xv': 10, 'qv': q()})),'0.90909090909090906')
print "assert_approx_equal(%s,%s)" % sc6
assert_approx_equal(*sc6)
print "qs=QuantSpec('qsv','xsv+1')"
print "xs=QuantSpec('xsv','3')"
qs=QuantSpec('qsv','xsv+1')
xs=QuantSpec('xsv','3')
globals()['qs'] = qs
globals()['xs'] = xs
qse = qs.eval()
qt1 = str(qse) == '4'
print "qs.eval() == 4? ", qt1
assert qt1
assert qse.tonumeric() == 4
print "asq = xs/qs"
asq=xs/qs
qt2 = str(asq) == '3/(xsv+1)'
print "asq == 3/(xsv+1)? ", qt2
assert qt2
qt3 = str(asq.eval()) == '0.75'
print "as.eval() == 0.75? ", qt3
assert qt3
ps = asq**xs
print "ps = as**xs"
qt4 = str(ps) == 'Pow(3/(xsv+1),3)'
print "ps == Pow(3/(xsv+1),3)? ", qt4
assert qt4
qt5 = str(ps.eval()) == str(0.75**3)
print "ps.eval() == 0.421875? ", qt5
assert qt5
print "sq=QuantSpec('sv','sin(xsv)')"
print "s2q=QuantSpec('s2v','Sin(xv)')"
sq=QuantSpec('sv','sin(xsv)')
s2q=QuantSpec('s2v','Sin(xv)')
print "sq.eval() --> ", sq.eval()
print "s2q.eval() --> ", s2q.eval()
assert sq.eval().tonumeric() == s2q.eval().tonumeric()
assert sq[:] == ['sin','(','xsv',')']
print "\n\nDemos for multiple quantity definitions:\n"
mp=QuantSpec('p','a + 3*z[4*i-2]')
m=Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')
v=Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')
print "mp=QuantSpec('p','a + 3*z[4*i-2]')"
print "m=Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')"
print "v=Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')"
print "v[3] -->", v[3]
assert str(v[3])=='z3'
print "v.freeSymbols -->", v.freeSymbols
assert v.freeSymbols == ['z0']
print "\nModelSpec a already contains 'z0', which was defined as part of"
print "a multiple quantity definition, so check that attempting to add"
print "v to a results in an error ..."
with pytest.raises(AttributeError):
a.add(v)
print "\nTest of eval method, e.g. on a function f(s,t)..."
print "f.eval(s='1', t='t_val') -->", f.eval(s='1', t='t_val')
print "f.eval(s=1, t='t_val', p=0.5) -->", f.eval(s=1, t='t_val', p=0.5)
print "\nTesting convertPowers():"
cp_tests = ["phi1dot^m3", "1+phi1dot^m3*s",
"phi1dot**m3", "1+phi1dot**m3*s",
"sin(x^3)**4", "(2/3)^2.5", "3^cos(x)-pi",
"3^(cos(x)-pi)", "2^(sin(y**p))"]
for spec in cp_tests:
print spec, " --> ", convertPowers(spec)
globals().pop('a')
qc=QuantSpec('t', "a+coot+b/'coot'")
assert str(qc.eval()) == 'a+coot+b/"coot"'
coot=QuantSpec('coot', "1.05")
globals()['coot'] = coot
assert str(qc.eval()) == 'a+1.05+b/"coot"'
print "\nTest of function calling with argument names that clash with"
print "bound names inside the function."
x0=Var('x0')
x1=Var('x1')
x2=Var('x2')
F=Fun([x0*x2,x0*5,x2**0.5], [x0,x1,x2], 'F')
print "F=Fun([x0*x2,x0*5,x2**0.5], [x0,x1,x2], 'F')"
print "F(3,2,Sin(x0))) = [3*Sin(x0),15,Pow(Sin(x0),0.5)] ..."
print " ... even though x0 is a bound name inside definition of F"
assert str(F(3,2,Sin(x0)))=='[3*Sin(x0),15,Pow(Sin(x0),0.5)]'
def test_discrete_domain():
disc_dom = domain_test('disc_dom_test', pars=args(
coordname='x', derivname='dxdt', interval=1, verbose_level=3))
ic_disc = numeric_to_traj([[1], [0]], 'test', ['x', 'dxdt'], 0.)
assert disc_dom(ic_disc)
pars = {'eps': 1e-2, 'a': 0.5}
icdict = {'x': pars['a'],
'y': pars['a'] - pars['a']**3/3}
xstr = '(y - (x*x*x/3 - x))/eps'
ystr = 'a - x'
event_x_a = dst.makeZeroCrossEvent('x-a', 0,
{'name': 'event_x_a',
'eventtol': 1e-6,
'term': False,
'active': True},
varnames=['x'], parnames=['a'],
targetlang='python') # targetlang is redundant (defaults to python)
DSargs = args(name='vanderpol') # struct-like data
DSargs.events = [event_x_a]
DSargs.pars = pars
DSargs.tdata = [0, 3]
DSargs.algparams = {'max_pts': 3000, 'init_step': 0.02, 'stiff': True}
DSargs.varspecs = {'x': xstr, 'y': ystr}
DSargs.xdomain = {'x': [-2.2, 2.5], 'y': [-2, 2]}
DSargs.fnspecs = {'Jacobian': (['t','x','y'],
"""[[(1-x*x)/eps, 1/eps ],
[ -1, 0 ]]""")}
DSargs.ics = icdict
vdp = dst.Vode_ODEsystem(DSargs)
traj = vdp.compute('test_traj')
pts = traj.sample()
evs = traj.getEvents('event_x_a')
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