def _root_amplitude_brentq(counts, background, model, rtol=RTOL):
"""Fit amplitude by finding roots using Brent algorithm.
See Appendix A Stewart (2009).
Parameters
----------
counts : `~numpy.ndarray`
Slice of count image
background : `~numpy.ndarray`
Slice of background image
model : `~numpy.ndarray`
Model template to fit.
Returns
-------
amplitude : float
Fitted flux amplitude.
niter : int
Number of function evaluations needed for the fit.
"""
# Compute amplitude bounds and assert counts > 0
bounds = amplitude_bounds_cython(counts, background, model)
amplitude_min, amplitude_max, amplitude_min_total = bounds
if not counts.sum() > 0:
return amplitude_min_total, 0
args = (counts, background, model)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
try:
result = scipy.optimize.brentq(
f_cash_root_cython,
amplitude_min,
amplitude_max,
args=args,
maxiter=MAX_NITER,
full_output=True,
rtol=rtol,
)
return max(result[0], amplitude_min_total), result[1].iterations
except (RuntimeError, ValueError):
# Where the root finding fails NaN is set as amplitude
return np.nan, MAX_NITER
def _leastsq_iter_amplitude(counts,
background,
model,
maxiter=MAX_NITER,
rtol=RTOL):
"""Fit amplitude using an iterative least squares algorithm.
Parameters
----------
counts : `~numpy.ndarray`
Slice of counts image
background : `~numpy.ndarray`
Slice of background image
model : `~numpy.ndarray`
Model template to fit.
maxiter : int
Maximum number of iterations.
rtol : float
Relative flux error.
Returns
-------
amplitude : float
Fitted flux amplitude.
niter : int
Number of function evaluations needed for the fit.
"""
bounds = amplitude_bounds_cython(counts, background, model)
amplitude_min, amplitude_max, amplitude_min_total = bounds
if not counts.sum() > 0:
return amplitude_min_total, 0
weights = np.ones(model.shape)
x_old = 0
for i in range(maxiter):
x = x_best_leastsq(counts, background, model, weights)
if abs((x - x_old) / x) < rtol:
return max(x / FLUX_FACTOR, amplitude_min_total), i + 1
else:
weights = x * model + background
x_old = x
return max(x / FLUX_FACTOR, amplitude_min_total), MAX_NITER