def test_gaussian1d_fit():
"""Test histogram fitting function"""
mean_value = 0.5
sigma_value = 0.05
image = np.random.normal(loc=mean_value, scale=sigma_value, size=(100, 100))
hist, bin_edges = np.histogram(image, bins='auto')
bin_centers = (bin_edges[1:] + bin_edges[0: -1]) / 2.
initial_params = [np.max(hist), 0.55, 0.1]
amplitude, peak, width = calculations.gaussian1d_fit(bin_centers, hist, initial_params)
assert np.isclose(peak[0], mean_value, atol=0.0015, rtol=0.)
assert np.isclose(width[0], sigma_value, atol=0.0015, rtol=0.)
assert ((mean_value <= peak[0]+3*peak[1]) & (mean_value >= peak[0]-3*peak[1]))
assert ((sigma_value <= width[0]+3*width[1]) & (sigma_value >= width[0]-3*width[1]))
def stats_by_amp(self, image, amps):
"""Calculate statistics in the input image for each amplifier as
well as the full image
Parameters
----------
image : numpy.ndarray
2D array on which to calculate statistics
amps : dict
Dictionary containing amp boundary coordinates (output from
``amplifier_info`` function)
``amps[key] = [(xmin, xmax, xstep), (ymin, ymax, ystep)]``
Returns
-------
amp_means : dict
Sigma-clipped mean value for each amp. Keys are amp numbers
as strings (e.g. ``'1'``)
amp_stdevs : dict
Sigma-clipped standard deviation for each amp. Keys are amp
numbers as strings (e.g. ``'1'``)
gaussian_params : dict
Best-fit Gaussian parameters to the dark current histogram.
Keys are amp numbers as strings. Values are three-element
lists ``[amplitude, peak, width]``. Each element in the list
is a tuple of the best-fit value and the associated
uncertainty.
gaussian_chi_squared : dict
Reduced chi-squared for the best-fit parameters. Keys are
amp numbers as strings
double_gaussian_params : dict
Best-fit double Gaussian parameters to the dark current
histogram. Keys are amp numbers as strings. Values are six-
element lists. (3-elements * 2 Gaussians).
``[amplitude1, peak1, stdev1, amplitude2, peak2, stdev2]``
Each element of the list is a tuple containing the best-fit
value and associated uncertainty.
double_gaussian_chi_squared : dict
Reduced chi-squared for the best-fit parameters. Keys are
amp numbers as strings
hist : numpy.ndarray
1D array of histogram values
bin_centers : numpy.ndarray
1D array of bin centers that match the ``hist`` values.
"""
amp_means = {}
amp_stdevs = {}
gaussian_params = {}
gaussian_chi_squared = {}
double_gaussian_params = {}
double_gaussian_chi_squared = {}
# Add full image coords to the list of amp_boundaries, so that full
# frame stats are also calculated.
if 'FULL' in self.aperture:
maxx = 0
maxy = 0
for amp in amps:
mxx = amps[amp][0][1]
mxy = amps[amp][1][1]
if mxx > maxx:
maxx = copy(mxx)
if mxy > maxy:
maxy = copy(mxy)
amps['5'] = [(0, maxx, 1), (0, maxy, 1)]
logging.info((
'\tFull frame exposure detected. Adding the full frame to the list '
'of amplifiers upon which to calculate statistics.'))
for key in amps:
x_start, x_end, x_step = amps[key][0]
y_start, y_end, y_step = amps[key][1]
indexes = np.mgrid[y_start:y_end:y_step, x_start:x_end:x_step]
# Basic statistics, sigma clipped areal mean and stdev
amp_mean, amp_stdev = calculations.mean_stdev(image[indexes[0],
indexes[1]])
amp_means[key] = amp_mean
amp_stdevs[key] = amp_stdev
# Create a histogram
lower_bound = (amp_mean - 7 * amp_stdev)
upper_bound = (amp_mean + 7 * amp_stdev)
hist, bin_edges = np.histogram(image[indexes[0], indexes[1]],
bins='auto',
range=(lower_bound, upper_bound))
bin_centers = (bin_edges[1:] + bin_edges[0:-1]) / 2.
initial_params = [np.max(hist), amp_mean, amp_stdev]
# Fit a Gaussian to the histogram. Save best-fit params and
# uncertainties, as well as reduced chi squared
amplitude, peak, width = calculations.gaussian1d_fit(
bin_centers, hist, initial_params)
gaussian_params[key] = [amplitude, peak, width]
gauss_fit_model = models.Gaussian1D(amplitude=amplitude[0],
mean=peak[0],
stddev=width[0])
gauss_fit = gauss_fit_model(bin_centers)
positive = hist > 0
degrees_of_freedom = len(hist) - 3.
total_pix = np.sum(hist[positive])
p_i = gauss_fit[positive] / total_pix
gaussian_chi_squared[key] = (np.sum(
(hist[positive] - (total_pix * p_i)**2) / (total_pix * p_i)) /
degrees_of_freedom)
# Double Gaussian fit only for full frame data (and only for
# NIRISS, NIRCam at the moment.)
if key == '5':
if self.instrument.upper() in ['NIRISS', 'NIRCAM']:
initial_params = (np.max(hist), amp_mean, amp_stdev * 0.8,
np.max(hist) / 7., amp_mean / 2.,
amp_stdev * 0.9)
double_gauss_params, double_gauss_sigma = calculations.double_gaussian_fit(
bin_centers, hist, initial_params)
double_gaussian_params[key] = [
[param, sig] for param, sig in zip(
double_gauss_params, double_gauss_sigma)
]
double_gauss_fit = calculations.double_gaussian(
bin_centers, *double_gauss_params)
degrees_of_freedom = len(bin_centers) - 6.
dp_i = double_gauss_fit[positive] / total_pix
double_gaussian_chi_squared[key] = np.sum(
(hist[positive] - (total_pix * dp_i)**2) /
(total_pix * dp_i)) / degrees_of_freedom
else:
double_gaussian_params[key] = [[0., 0.] for i in range(6)]
double_gaussian_chi_squared[key] = 0.
else:
double_gaussian_params[key] = [[0., 0.] for i in range(6)]
double_gaussian_chi_squared[key] = 0.
logging.info('\tMean dark rate by amplifier: {}'.format(amp_means))
logging.info(
'\tStandard deviation of dark rate by amplifier: {}'.format(
amp_means))
logging.info(
'\tBest-fit Gaussian parameters [amplitude, peak, width]'.format(
gaussian_params))
logging.info(
'\tReduced chi-squared associated with Gaussian fit: {}'.format(
gaussian_chi_squared))
logging.info(
'\tBest-fit double Gaussian parameters [amplitude1, peak1, width1, amplitude2, peak2, '
'width2]'.format(double_gaussian_params))
logging.info(
'\tReduced chi-squared associated with double Gaussian fit: {}'.
format(double_gaussian_chi_squared))
return (amp_means, amp_stdevs, gaussian_params, gaussian_chi_squared,
double_gaussian_params, double_gaussian_chi_squared,
hist.astype(np.float), bin_centers)