Coverage for python/lsst/validate/drp/photerrmodel.py : 16%

# LSST Data Management System 

# Copyright 2016 AURA/LSST. 

# 

# This product includes software developed by the 

# LSST Project (http://www.lsst.org/). 

# 

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# (at your option) any later version. 

# 

# This program is distributed in the hope that it will be useful, 

# but WITHOUT ANY WARRANTY; without even the implied warranty of 

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

# GNU General Public License for more details. 

# 

# You should have received a copy of the LSST License Statement and 

# the GNU General Public License along with this program. If not, 

# see <https://www.lsstcorp.org/LegalNotices/>. 

"""Analytic single-visit photometric error model. 

""" 

__all__ = ['photErrModel', 'fitPhotErrModel', 'build_photometric_error_model'] 

import astropy.units as u 

import numpy as np 

from scipy.optimize import curve_fit 

from lsst.verify import Blob, Datum 

def photErrModel(mag, sigmaSys, gamma, m5, **kwargs): 

r"""Model of photometric error for a single visit. 

The model is described in the LSST Overview paper: 

http://arxiv.org/abs/0805.2366v4. 

Photometric error of a single visit (Eq. 4): 

.. math: 

\sigma_1^2 = \sigma_\mathrm{sys}^2 + \sigma_\mathrm{rand}^2 

Where random uncertainty is (Eq. 5): 

.. math:: 

\sigma_\mathrm{rand}^2 = (0.04 - \gamma) * x + \gamma * x^2~[\mathrm{mag}^2] 

and $x = 10^(0.4*(m-m_5))$. 

Parameters 

---------- 

mag : `astropy.unit.Quantity` 

Source magnitude. 

sigmaSq : `astropy.unit.Quantity` 

Systematic photometric error (magnitude). 

gamma : `astropy.unit.Quantity` 

Proxy for sky brightness and readout noise (dimensionless). 

m5 : `astropy.unit.Quantity` 

5-sigma depth (magnitude). 

Returns 

------- 

sigma : `astropy.units.Quantity` 

Photometric error for a single visit. 

""" 

x = 10**(0.4*(mag - m5)) 

sigmaRandSq = (0.04 - gamma) * x + gamma * x**2 

sigmaSq = sigmaSys**2 + sigmaRandSq 

return np.sqrt(sigmaSq) 

def fitPhotErrModel(mag, mag_err): 

"""Fit photometric error model from the LSST Overview paper: 

http://arxiv.org/abs/0805.2366v4 

The fit is performed with `scipy.optimize.curvefit`. 

Parameters 

---------- 

mag : `astropy.units.Quantity` 

Magnitude. 

mag_err : `astropy.units.Quantity` 

Magnitude uncertainty or variation. 

Returns 

------- 

params : `dict` 

Fitted model. Fields are: 

- `sigmaSys`: systematic error (magnitude, `astropy.units.Quantity`). 

- `gamma`: Proxy for sky brightness and readout noise (dimensionless, 

`astropy.units.Quantity`). 

- `m5`: 5-sigma limiting depth (magnitude, `astropy.units.Quantity`). 

See also 

-------- 

photErrModel 

""" 

# if not isinstance(mag, u.Quantity): 

# mag = mag * u.mag 

# if not isinstance(mag_err, u.Quantity): 

# mag_err = mag_err * u.mag 

# p0 = [0.01 * u.mag, # sigmaSys 

# 0.039 * u.Unit(''), # gamma 

# 24.35 * u.mag] # m5 

# fit_params, fit_param_covariance = curve_fit( 

# photErrModel, mag, mag_err, p0=p0) 

# params = { 

# 'sigmaSys': fit_params[0], 

# 'gamma': fit_params[1], 

# 'm5': fit_params[2], 

# } 

if isinstance(mag, u.Quantity): 

mag = mag.to(u.mag).value 

if isinstance(mag_err, u.Quantity): 

mag_err = mag_err.to(u.mag).value 

p0 = [0.01, # sigmaSys (mag) 

0.039, # gamma ('') 

24.35] # m5 (mag) 

try: 

fit_params, fit_param_covariance = curve_fit( 

photErrModel, mag, mag_err, p0=p0) 

sigmaSys, gamma, m5 = fit_params 

except (RuntimeError, ValueError) as e: 

print("fitPhotErrorModel fitting failed with") 

print(e) 

print("sigmaSys, gamma, m5 are being set to NaN.") 

sigmaSys, gamma, m5 = np.nan, np.nan, np.nan 

params = { 

'sigmaSys': sigmaSys * u.mag, 

'gamma': gamma * u.Unit(''), 

'm5': m5 * u.mag, 

} 

return params 

def build_photometric_error_model(matchedMultiVisitDataset, brightSnr=100, medianRef=100, 

matchRef=500): 

r"""Returns a serializable analytic photometry error model for a single visit. 

This model is originally presented in http://arxiv.org/abs/0805.2366v4 

(Eq 4, 5): 

.. math:: 

\sigma_1^2 &= \sigma_\mathrm{sys}^2 + \sigma_\mathrm{rand}^2 \\ 

x &= 10^{0.4(m-m_5)} \\ 

\sigma_\mathrm{rand}^2 &= (0.04 - \gamma) x + \gamma x^2~[\mathrm{mag}^2] 

Parameters 

---------- 

matchedMultiVisitDataset : `lsst.valididate.drp.matchreduce.MatchedMultiVisitDataset` 

A dataset containing matched statistics for stars across multiple 

visits. 

brightSnr : `float` or `astropy.unit.Quantity`, optional 

Minimum SNR for a star to be considered "bright." 

medianRef : `float` or `astropy.unit.Quantity`, optional 

Median reference astrometric scatter (millimagnitudes by default). 

matchRef : `int` or `astropy.unit.Quantity`, optional 

Should match at least matchRef stars. 

Returns 

---------- 

blob : `lsst.verify.Blob` 

Blob with datums: 

- ``brightSnr``: Threshold in SNR for bright sources used in this model. 

- ``sigmaSys``: Systematic error floor. 

- ``gamma``: Proxy for sky brightness and read noise. 

- ``m5``: 5-sigma photometric depth (magnitudes). 

- ``photRms``: RMS photometric scatter for 'good' stars (millimagnitudes). 

Notes 

----- 

The scatter and match defaults are appropriate to SDSS are stored here. 

For SDSS, stars with mag < 19.5 should be completely well measured. 

This limit is a band-dependent statement most appropriate to r. 

""" 

blob = Blob('PhotometricErrorModel') 

# FIXME add a description field to blobs? 

# _doc['doc'] \ 

# = "Photometric uncertainty model from " \ 

# "http://arxiv.org/abs/0805.2366v4 (Eq 4, 5): " \ 

# "sigma_1^2 = sigma_sys^2 + sigma_rand^2, " \ 

# "sigma_rand^2 = (0.04 - gamma) * x + gamma * x^2 [mag^2] " \ 

# "where x = 10**(0.4*(m-m_5))" 

if not isinstance(medianRef, u.Quantity): 

medianRef = medianRef * u.mmag 

if not isinstance(brightSnr, u.Quantity): 

brightSnr = brightSnr * u.Unit('') 

_compute(blob, 

matchedMultiVisitDataset['snr'].quantity, 

matchedMultiVisitDataset['mag'].quantity, 

matchedMultiVisitDataset['magerr'].quantity, 

matchedMultiVisitDataset['magrms'].quantity, 

matchedMultiVisitDataset['dist'].quantity, 

len(matchedMultiVisitDataset.goodMatches), 

brightSnr, 

medianRef, 

matchRef) 

return blob 

def _compute(blob, snr, mag, magErr, magRms, dist, nMatch, 

brightSnr, medianRef, matchRef): 

blob['brightSnr'] = Datum(quantity=brightSnr, 

label='Bright SNR', 

description='Threshold in SNR for bright sources used in this ' 

'model') 

bright = np.where(snr > blob['brightSnr'].quantity) 

blob['photScatter'] = Datum(quantity=np.median(magRms[bright]), 

label='RMS', 

description='RMS photometric scatter for good stars') 

print('Photometric scatter (median) - SNR > {0:.1f} : {1:.1f}'.format( 

blob['brightSnr'].quantity, blob['photScatter'].quantity.to(u.mmag))) 

fit_params = fitPhotErrModel(mag[bright], magErr[bright]) 

blob['sigmaSys'] = Datum(quantity=fit_params['sigmaSys'], 

label='sigma(sys)', 

description='Systematic error floor') 

blob['gamma'] = Datum(quantity=fit_params['gamma'], 

label='gamma', 

description='Proxy for sky brightness and read noise') 

blob['m5'] = Datum(quantity=fit_params['m5'], 

label='m5', 

description='5-sigma depth') 

if blob['photScatter'].quantity > medianRef: 

msg = 'Median photometric scatter {0:.3f} is larger than ' \ 

'reference : {1:.3f}' 

print(msg.format(blob['photScatter'].quantity.value, medianRef)) 

if nMatch < matchRef: 

msg = 'Number of matched sources {0:d} is too small ' \ 

'(should be > %d)' 

print(msg.format(nMatch, matchRef))