def decayfit(t, y, p=(0.05, 0.9), prepend_zero=False, rse=False, lm=False):
"""
Fit exponential decay, y(t) = w exp(-t/tau), to latter part of trajectory.
:param t: time
:param y: variable, e.g. an ion current
:param p: proportion of return to initial value,
as for action potential duration
:param bool prepend_zero: add a 0 at the start of y (hack for use with
ion currents)
:param bool rse: return relative standard error of slope (not of *tau*!).
:param bool lm: Return R object for fitted linear model.
:return tau: -1/slope for estimated slope of log(y) vs t
tau has dimension 'time' and is analogous to half-life: '1/e'-life = 0.37-life.
For use with results from :meth:`Clampable.vecvclamp`, see :func:`decayfits`.
Trivial example.
>>> t = np.arange(10)
>>> y = np.exp(-t)
>>> y[0] = 0
>>> decayfit(t, y)
1.0
Relative standard error when adding noise.
>>> np.random.seed(0)
>>> noisy = y + 0.05 * np.random.random(size=y.shape)
>>> decayfit(t, noisy, rse=True, p=[0.5, 0.99])
(1.292..., 0.045...)
"""
assert len(p) == 2
if prepend_zero:
t = np.r_[0, t]
y = np.r_[0, y]
stats = apd(t, y, p)
_ip, i0, i1 = stats["i"]
# Avoid "Warning message: In is.na(rows) :
# is.na() applied to non-(list or vector) of type 'NULL'"
if i1 <= i0:
tau = rse_slope = np.nan
rlm = None
else:
with roptions(show_error_messages=False, deparse_max_lines=0):
try:
rlm = r.lm("log(y)~t", data=dict(t=t[i0:i1],
y=y[i0:i1].squeeze()))
coef = r2rec(r.as_data_frame(r.coef(r.summary(rlm))))
_intercept, slope = coef.Estimate
_rse_intercept, rse_slope = (coef["Std. Error"] /
abs(coef.Estimate))
tau = - 1.0 / slope
except RRuntimeError:
tau = rse_slope = np.nan
rlm = None
result = (tau,)
if rse:
result += (rse_slope,)
if lm:
result += (rlm,)
return result if len(result) > 1 else result[0]
>>> mmfit(x, -y)
(nan, nan)
"""
with roptions(show_error_messages=False, deparse_max_lines=0):
kwargs = dict(formula="y~ymax*x/(x+xhalf)", data=dict(x=x, y=y),
start=dict(ymax=max(y), xhalf=np.mean(x)))
try:
fit = r.nls(**kwargs)
except RRuntimeError, exc:
s = str(exc.exc).split("\n")[1].strip()
errmsg = "Michaelis-Menten fit failed with message '%s'. " % s
errmsg += "Arguments to r.nls() were: %s"
logger.debug(errmsg, kwargs)
ymax = xhalf = rse_ymax = rse_xhalf = np.nan
else:
coef = r2rec(r.as_data_frame(r.coef(r.summary(fit))))
ymax, xhalf = coef.Estimate
rse_ymax, rse_xhalf = coef["Std. Error"] / coef.Estimate
if (ymax < 0) or (xhalf < 0):
errmsg = ("Michalis-Menten fit gave negative estimate(s): "
"ymax=%s, xhalf=%s. Arguments to r.nls() were: %s")
logger.debug(errmsg, ymax, xhalf, kwargs)
ymax = xhalf = rse_ymax = rse_xhalf = np.nan
return (ymax, xhalf, rse_ymax, rse_xhalf) if rse else (ymax, xhalf)
def decayfits(L, i, k, abs_=True):
"""
Convenience wrapper for applying decayfit() to list returned by vecvclamp().
:param L: list of (proto, traj), where *proto* is a list of
(duration, voltage) for each pulse, and *traj* is a list of