def _sensitivity(exposure, workspace, protocol, statistic, par=None, seed=None):
"""
Sensitivity analysis.
>>> _sensitivity("11df840d0150d34c9716cd4cbdd164c8", "bondarenko_szigeti_bett_kim_rasmusson_2004_apical", "protocol", "apd90", ("g_Na", "Nao"), seed=1)
TODO: Make optional arguments of exposure, lower, upper, etc.
TODO: Accept json dict of model_kwargs, morris_kwargs
"""
m = Model(exposure + "/" + workspace, maxsteps=1e6, chunksize=1e5, reltol=1e-8)
phenotypes(m, m.name) # initialize and cache default
par = [str(i) for i in par] # Numpy cannot handle Unicode names
if not par:
# Default: sample within plus/minus 50% of all nonzero parameters
par = [k for k in m.dtype.p.names if m.pr[k] != 0]
baseline = unstruct(m.pr[par]).squeeze()
lower = 0.5 * baseline
upper = 1.5 * baseline
if seed is not None:
r.set_seed(seed)
r("fun <- function(func, x) func(x)")
raise Exception(str(r.fun(r.sum, baseline)))
fun = scalar_pheno(m, statistic)
r.as_vector(baseline)
return r.morris(fun, factors=par, r=2, design={"type": "oat", "levels": 10, "grid.jump": 5}, binf=lower, bsup=upper)
def cycle(self, index=0, tmax=None, tol=1e-4, n=None):
"""
Find limit cycle (integrate until successive extrema are almost equal).
:param str_or_int index: Index of state variable to base search on.
:param float tmax: Time limit for aborting search for limit cycle.
:param float tol: Tolerance for weighted root-mean-square norm of
change in state vector between successive extrema.
:param int n: Keep history of up to n extrema while searching for
limit cycle.
.. plot::
:include-source:
>>> from matplotlib import pyplot as plt
>>> from cgp.cvodeint.namedcvodeint import Namedcvodeint
>>> from cgp.utils.unstruct import unstruct
>>> from cgp.phenotyping.attractor import AttractorMixin
>>> class Test(Namedcvodeint, AttractorMixin):
... '''Inherits van der Pol equations as default example.'''
... pass
>>> test = Test(t=[0, 10000])
>>> t, y, period = test.cycle()
>>> period
6.663...
>>> h = plt.plot(t, unstruct(y), '-')
"""
if tmax is None:
tmax = self.t[-1]
extrema = deque([self.next_extremum(tmax, index)], maxlen=n)
while True:
t, y, (te, ye) = tup = self.next_extremum(tmax, index)
extrema.appendleft(tup)
# pylint:disable=W0612,C0301
for lag, (t_, y_, (te_, ye_)) in enumerate(extrema): #@UnusedVariable
if lag == 0:
continue
diff = unstruct(ye_) - unstruct(ye)
if self.weighted_rms(diff) < tol:
L = reversed(list(extrema)[:lag])
t, y, _ = catrec(*L, globalize_time=False)
period = te - te_
return t, y.squeeze(), period
def test_dimensions():
"""Check relationship between dimensions of x and unstruct(x)."""
# x has 2 fields and dimensions (3, 4)
x = np.arange(24).view(dtype=[(i, int) for i in "ab"]).reshape(3, 4)
# u has dimensions (3, 4, 2)
u = unstruct(x)
# change to u affects x
u[:] += 10
# Last dimension of u corresponds to fields of x
np.testing.assert_equal(x["a"], u[..., 0])
# First dimensions of u corresponds to first dimensions of x
np.testing.assert_equal(x[0][0].item(), u[0][0])
def test_zero_rank():
"""
Handle intricacies of zero-rank arrays.
`Zero-rank arrays
<http://projects.scipy.org/numpy/wiki/ZeroRankArray>`_
are tricky; they can be structured, yet be of type numpy.void.
Here, x0 and x1 are almost, but not completely, the same:
>>> fieldtype = np.int32 # ensure same result on 32- and 64-bit platforms
>>> dtype = [("a", fieldtype), ("b", fieldtype)]
>>> x0 = np.array([(0, 1)], dtype=dtype)[0]
>>> x1 = np.array((0, 1), dtype=dtype)
Despite a lot of equalities below, x0 and x1 are of different type.
>>> (x0 == x1) and (x0.shape == x1.shape) and (x0.dtype == x1.dtype)
True
>>> x0
(0, 1)
>>> x1
array((0, 1), dtype=[('a', '<i4'), ('b', '<i4')])
>>> type(x0), type(x1)
(<type 'numpy.void'>, <type 'numpy.ndarray'>)
Unstructuring them was tricky, but finally works.
>>> unstruct(x0)
array([0, 1])
>>> unstruct(x1)
array([0, 1])
"""
fieldtype = np.int32 # ensure same result on 32- and 64-bit platforms
dtype = [("a", fieldtype), ("b", fieldtype)]
x0 = np.array([(0, 1)], dtype=dtype)[0]
x1 = np.array((0, 1), dtype=dtype)
np.testing.assert_equal(unstruct(x0), unstruct(x1))
def do_sensitivity(exposure, workspace, protocol, statistic, par=None,
seed=None, model=None, changeset=None, variant=None):
"""
Sensitivity analysis.
Callback from R.
>>> r("fun <- function(func, x) func(x)")
RClosure with name <return value from eval>:
<R function>
>>> r.fun(r.sum, range(5))
array([10])
(R-style, sealed)
>>> m = Model(workspace="beeler_reuter_1977", rename=dict(
... p=dict(IstimPeriod="stim_period", IstimAmplitude="stim_amplitude",
... IstimPulseDuration="stim_duration", IstimStart="stim_start")),
... reltol=1e-10, maxsteps=1e6, chunksize=100000)
>>> m.pr.IstimStart = 0
>>> print "Result:", do_sensitivity("", "", "protocol", "apbase", ("C", "g_Na"), seed=1, model=m)
Result:...
Model runs: 6
mu mu.star sigma
C 0.03672701 0.03672701 0.05130616
g_Na -0.41200934 0.41200934 0.04219007
TODO: Make optional arguments of exposure, lower, upper, etc.
TODO: Accept json dict of model_kwargs, morris_kwargs
"""
if model is None:
m = Model(workspace, exposure, changeset, variant,
maxsteps=1e6, chunksize=1e5, reltol=1e-8)
m.pr.stim_start = 0
else:
m = model
phenotypes(m) # initialize and cache default
factors = [str(i) for i in par] # Numpy cannot handle Unicode names
if not factors:
# Default: sample within plus/minus 50% of all nonzero parameters
factors = [k for k in m.dtype.p.names if m.pr[k] != 0]
baseline = unstruct(m.pr[factors]).squeeze()
lower = 0.5 * baseline
upper = 1.5 * baseline
if seed is not None:
r.set_seed(seed)
fun = scalar_pheno(statistic, m, factors)
design = {"type": "oat", "levels": 10, "grid.jump": 5}
return r.morris(fun, factors=factors, r=2, design=design,
binf=lower, bsup=upper)
def shoehorn_recarray(x, ndim=1):
"""
Shoehorn multi-dimensional record array into HDF-compatible form.
Pytables does not allow table rows to be arrays. Thus, a record array with
dimension > 1 cannot be converted to an HDF table. However, it will accept
a 1-D record array whose *fields* are arrays. This function rearranges the
dimensions of the entire array and its fields, retaining *ndim* dimensions
and pushing the rest into the fields.
One dimension is suitable for creating a table, whereas zero dimensions
is suitable for a table row.
>>> x = np.arange(24.0).view([("a", float), ("b", float)]).reshape(4, 3)
>>> y = shoehorn_recarray(x)
>>> np.testing.assert_equal(x["a"], y["a"])
>>> x.shape
(4, 3)
>>> x.dtype
dtype([('a', '<f8'), ('b', '<f8')])
>>> y.shape
(4,)
>>> y.dtype
dtype([('a', '<f8', (3,)), ('b', '<f8', (3,))])
>>> z = shoehorn_recarray(x, ndim=0)
>>> np.testing.assert_equal(x["a"], z["a"])
>>> z.shape
()
>>> z.dtype
dtype([('a', '<f8', (4, 3)), ('b', '<f8', (4, 3))])
"""
u = unstruct(x)
# The shape of u is x.shape + (#fields,) + fieldshape
# Roll the #fields dimension to position ndim (note zero-based indexing)
r = np.rollaxis(u, len(x.shape), ndim)
dtype = [i[:2] + (r.shape[1 + ndim:],)
for i in ast.literal_eval(str(x.dtype))]
return r.flatten().view(dtype).squeeze()
def restruct(a, axes=0):
"""
Convert shape dimensions to field dimensions.
Converting a record array of shape (3,) with two scalar fields
to one of size () whose fields are shape (3,).
>>> restruct(np.array([(0, 1), (2, 3), (4, 5)],
... dtype=[("a", "|i1"), ("b", "|i1")]))
array(([0, 2, 4], [1, 3, 5]), dtype=[('a', '|i1', (3,)), ('b', '|i1', (3,))])
This is an array of shape (2, 3) with two scalar fields.
>>> a = np.array([[(0, 1), (2, 3), (4, 5)],
... [(6, 7), (8, 9), (10, 11)]],
... dtype=[('a', '|i1'), ('b', '|i1')])
Folding the first dimension into each field gives an array of shape (3,)
whose fields have shape (2,).
>>> restruct(a)
array([([0, 6], [1, 7]),
([2, 8], [3, 9]),
([4, 10], [5, 11])], dtype=[('a', '|i1', (2,)), ('b', '|i1', (2,))])
"""
axes = np.atleast_1d(axes)
u = unstruct(a)
ax = range(u.ndim)
# Move the given axes to the end
for i in axes:
ax.remove(i)
ax.append(i)
ut = u.transpose(ax).ravel()
dtype = [(k, u.dtype, a.shape[axes]) for k in a.dtype.names]
result = ut.view(dtype)
result.shape = result.shape[:a.ndim - len(axes)]
return result
ph = np.concatenate([phenotypes(i) for i in mat2par(mat)])
result = ph["apd90"]
result[np.isnan(result)] = 0
return py2ri(result)
@ri.rternalize
def appeak(mat):
ph = np.concatenate([phenotypes(i) for i in mat2par(mat)])
result = ph["appeak"]
result[np.isnan(result)] = 0
return py2ri(result)
# mu mu.star sigma
#Cm -0.4348831 0.6603604 0.9338907
#Vmyo 0.1264869 0.1264869 0.1657938
# mu mu.star sigma
#Cm 0.6716927 0.6716927 0.3328038
#Vmyo -0.3135712 0.3135712 0.3033346
if __name__ == "__main__":
binf = 0.5 * unstruct(m.pr[factors])
bsup = 1.5 * unstruct(m.pr[factors])
r.pdf("morrisplot.pdf")
r.plot(r.morris(apd90, factors=factors, r=2, design={"type": "oat", "levels": 10, "grid.jump": 5}, binf=binf, bsup=bsup))
r.dev_off()
# saved = np.load("/tmp/saveme.npy")
# ph = [phenotypes(i) for i in saved]
# fail = [np.isnan(i).all() for i in ph]
# result = np.logical_not(fail).astype(float)
return par
def scalar_pheno(field):
"""Make a function to return a named field of the phenotype array."""
@ri.rternalize
def fun(rmatrix):
"""Scalar function for use with R's sensitivity::morris()."""
ph = np.concatenate([phenotypes(i) for i in mat2par(rmatrix)])
return py2ri(ph[field])
return fun
if __name__ == "__main__":
# Sensitivity analysis
baseline = unstruct(m.pr[factors])
lower = 0.5 * baseline
upper = 1.5 * baseline
result = dict()
for field in "appeak", "apd90", "ctpeak", "ctbase", "ctd90":
r.set_seed(20120221) # repeatable random sampling
result[field] = r.morris(scalar_pheno(field), factors=factors, r=2,
design={"type": "oat", "levels": 10, "grid.jump": 5},
binf=lower, bsup=upper)
# Print and visualize results
r.png("sensitivity.png", width=1024, height=768, pointsize=24)
r.par(mfrow=(2, 3)) # multiple figures in two rows, three columns
for k, v in result.items():
print "===================================================="
print k
print v
def test_dtypes():
"""Verify that unstruct() handles different dtypes correctly."""
for fieldtype in np.int8, np.int32, float:
dtype = [(i, fieldtype) for i in "ab"]
x = np.arange(4, dtype=fieldtype).view(dtype)
yield np.testing.assert_equal, unstruct(x), [[0, 1], [2, 3]]