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# LSST Data Management System 

# Copyright 2008-2019 AURA/LSST. 

# 

# This product includes software developed by the 

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

# 

# This program is free software: you can redistribute it and/or modify 

# it under the terms of the GNU General Public License as published by 

# the Free Software Foundation, either version 3 of the License, or 

# (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/>. 

 

import astropy.units as u 

import math 

import numpy as np 

import random 

from scipy.stats import norm 

 

import lsst.pipe.base as pipeBase 

from lsst.verify import Measurement, Datum 

 

thousandDivSqrtTwo = 1000/math.sqrt(2) 

 

 

def measurePhotRepeat(metric, filterName, *args, **kwargs): 

"""Measurement of a photometric repeatability metric across a set of 

observations. 

 

Parameters 

---------- 

metric : `lsst.verify.Metric` 

A Metric to construct a Measurement for. 

filterName : `str` 

Name of filter used for all observations. 

*args 

Additional arguments to pass to `calcPhotRepeat`. 

**kwargs 

Additional keyword arguments to pass to `calcPhotRepeat`. 

 

Returns 

------- 

measurement : `lsst.verify.Measurement` 

Measurement of the repeatability and its associated metadata. 

 

See also 

-------- 

calcPhotRepeat: Computes statistics of magnitudes differences of sources across 

multiple visits. This is the main computation function behind 

repeatability measurement. 

""" 

results = calcPhotRepeat(*args, **kwargs) 

datums = {} 

datums['filter_name'] = Datum(filterName, label='filter', 

description='Name of filter for this measurement') 

datums['rms'] = Datum(results['rms'], label='RMS', 

description='Photometric repeatability RMS of stellar pairs for ' 

'each random sampling') 

datums['iqr'] = Datum(results['iqr'], label='IQR', 

description='Photometric repeatability IQR of stellar pairs for ' 

'each random sample') 

datums['magDiff'] = Datum(results['magDiff'], label='Delta mag', 

description='Photometric repeatability differences magnitudes for ' 

'stellar pairs for each random sample') 

datums['magMean'] = Datum(results['magMean'], label='mag', 

description='Mean magnitude of pairs of stellar sources matched ' 

'across visits, for each random sample.') 

return Measurement(metric, results['repeatability'], extras=datums) 

 

 

def calcPhotRepeat(matches, magKey, numRandomShuffles=50): 

"""Calculate the photometric repeatability of measurements across a set 

of randomly selected pairs of visits. 

 

Parameters 

---------- 

matches : `lsst.afw.table.GroupView` 

`~lsst.afw.table.GroupView` of sources matched between visits, 

from MultiMatch, provided by 

`lsst.validate.drp.matchreduce.build_matched_dataset`. 

magKey : `lsst.afw.table` schema key 

Magnitude column key in the ``groupView``. 

E.g., ``magKey = allMatches.schema.find("slot_ModelFlux_mag").key`` 

where ``allMatches`` is the result of 

`lsst.afw.table.MultiMatch.finish()`. 

numRandomShuffles : int 

Number of times to draw random pairs from the different observations. 

 

Returns 

------- 

statistics : `dict` 

Statistics to compute model_phot_rep. Fields are: 

 

- ``model_phot_rep``: scalar `~astropy.unit.Quantity` of mean ``iqr``. 

This is formally the model_phot_rep metric measurement. 

- ``rms``: `~astropy.unit.Quantity` array in mmag of photometric 

repeatability RMS across ``numRandomShuffles``. 

Shape: ``(nRandomSamples,)``. 

- ``iqr``: `~astropy.unit.Quantity` array in mmag of inter-quartile 

range of photometric repeatability distribution. 

Shape: ``(nRandomSamples,)``. 

- ``magDiff``: `~astropy.unit.Quantity` array of magnitude differences 

between pairs of sources. Shape: ``(nRandomSamples, nMatches)``. 

- ``magMean``: `~astropy.unit.Quantity` array of mean magnitudes of 

each pair of sources. Shape: ``(nRandomSamples, nMatches)``. 

 

Notes 

----- 

We calculate differences for ``numRandomShuffles`` different random 

realizations of the measurement pairs, to provide some estimate of the 

uncertainty on our RMS estimates due to the random shuffling. This 

estimate could be stated and calculated from a more formally derived 

motivation but in practice 50 should be sufficient. 

 

The LSST Science Requirements Document (LPM-17), or SRD, characterizes the 

photometric repeatability by putting a requirement on the median RMS of 

measurements of non-variable bright stars. This quantity is PA1, with a 

design, minimum, and stretch goals of (5, 8, 3) millimag following LPM-17 

as of 2011-07-06, available at http://ls.st/LPM-17. model_phot_rep is a 

similar quantity measured for extended sources (almost entirely galaxies), 

for which no requirement currently exists in the SRD. 

 

This present routine calculates this quantity in two different ways: 

 

1. RMS 

2. interquartile range (IQR) 

 

**The repeatability scalar measurement is the median of the IQR.** 

 

This function also returns additional quantities of interest: 

 

- the pair differences of observations of sources, 

- the mean magnitude of each source 

 

Examples 

-------- 

Normally ``calcPhotRepeat`` is called by `measurePhotRepeat`, using 

data from `lsst.validate.drp.matchreduce.build_matched_dataset`. Here's an 

example of how to call ``calcPhotRepeat`` directly given the Butler output 

repository generated by examples/runHscQuickTest.sh: 

 

>>> import lsst.daf.persistence as dafPersist 

>>> from lsst.afw.table import SourceCatalog, SchemaMapper, Field 

>>> from lsst.afw.table import MultiMatch, SourceRecord, GroupView 

>>> from lsst.validate.drp.repeatability import calcPhotRepeat 

>>> from lsst.validate.drp.util import discoverDataIds 

>>> import numpy as np 

>>> repo = 'HscQuick/output' 

>>> butler = dafPersist.Butler(repo) 

>>> dataset = 'src' 

>>> schema = butler.get(dataset + '_schema', immediate=True).schema 

>>> visitDataIds = discoverDataIds(repo) 

>>> mmatch = None 

>>> for vId in visitDataIds: 

... cat = butler.get('src', vId) 

... calib = butler.get('calexp_photoCalib', vId) 

... cat = calib.calibrateCatalog(cat, ['modelfit_CModel']) 

... if mmatch is None: 

... mmatch = MultiMatch(cat.schema, 

... dataIdFormat={'visit': np.int32, 'ccd': np.int32}, 

... RecordClass=SourceRecord) 

... mmatch.add(catalog=cat, dataId=vId) 

... 

>>> matchCat = mmatch.finish() 

>>> allMatches = GroupView.build(matchCat) 

>>> magKey = allMatches.schema.find('slot_ModelFlux_mag').key 

>>> def matchFilter(cat): 

>>> if len(cat) < 2: 

>>> return False 

>>> return np.isfinite(cat.get(magKey)).all() 

>>> repeat = calcPhotRepeat(allMatches.where(matchFilter), magKey) 

 

""" 

mprSamples = [calcPhotRepeatSample(matches, magKey) 

for _ in range(numRandomShuffles)] 

 

rms = np.array([mpr.rms for mpr in mprSamples]) * u.mmag 

iqr = np.array([mpr.iqr for mpr in mprSamples]) * u.mmag 

magDiff = np.array([mpr.magDiffs for mpr in mprSamples]) * u.mmag 

magMean = np.array([mpr.magMean for mpr in mprSamples]) * u.mag 

repeat = np.mean(iqr) 

return {'rms': rms, 'iqr': iqr, 'magDiff': magDiff, 'magMean': magMean, 'repeatability': repeat} 

 

 

def calcPhotRepeatSample(matches, magKey): 

"""Compute one realization of repeatability by randomly sampling pairs of 

visits. 

 

Parameters 

---------- 

matches : `lsst.afw.table.GroupView` 

`~lsst.afw.table.GroupView` of sources matched between visits, 

from MultiMatch, provided by 

`lsst.validate.drp.matchreduce.build_matched_dataset`. 

magKey : `lsst.afw.table` schema key 

Magnitude column key in the ``groupView``. 

E.g., ``magKey = allMatches.schema.find("base_PsfFlux_mag").key`` 

where ``allMatches`` is the result of 

`lsst.afw.table.MultiMatch.finish()`. 

 

Returns 

------- 

metrics : `lsst.pipe.base.Struct` 

Metrics of pairs of sources matched between two visits. Fields are: 

 

- ``rms``: scalar RMS of differences of sources observed in this 

randomly sampled pair of visits. 

- ``iqr``: scalar inter-quartile range (IQR) of differences of sources 

observed in a randomly sampled pair of visits. 

- ``magDiffs`: array, shape ``(nMatches,)``, of magnitude differences 

(mmag) for observed sources across a randomly sampled pair of visits. 

- ``magMean``: array, shape ``(nMatches,)``, of mean magnitudes 

of sources observed across a randomly sampled pair of visits. 

 

See also 

-------- 

calcPhotRepeat : A wrapper that repeatedly calls this function to build 

the repeatability measurement. 

""" 

magDiffs = matches.aggregate(getRandomDiffRmsInMmags, field=magKey) 

magMean = matches.aggregate(np.mean, field=magKey) 

rms, iqr = computeWidths(magDiffs) 

return pipeBase.Struct(rms=rms, iqr=iqr, magDiffs=magDiffs, magMean=magMean,) 

 

 

def getRandomDiffRmsInMmags(array): 

"""Calculate the RMS difference in mmag between a random pairing of 

visits of a source. 

 

Parameters 

---------- 

array : `list` or `numpy.ndarray` 

Magnitudes from which to select the pair [mag]. 

 

Returns 

------- 

rmsMmags : `float` 

RMS difference in mmag from a random pair of visits. 

 

Notes 

----- 

The LSST SRD recommends computing repeatability from a histogram of 

magnitude differences for the same source measured on two visits 

(using a median over the magDiffs to reject outliers). 

Because we have N>=2 measurements for each source, we select a random 

pair of visits for each source. We divide each difference by sqrt(2) 

to obtain the RMS about the (unknown) mean magnitude, 

instead of obtaining just the RMS difference. 

 

See Also 

-------- 

getRandomDiff : Get the difference between two randomly selected elements of an array. 

 

Examples 

-------- 

>>> mag = [24.2, 25.5] 

>>> rms = getRandomDiffRmsInMmags(mag) 

>>> print(rms) 

212.132034 

""" 

return thousandDivSqrtTwo * getRandomDiff(array) 

 

 

def getRandomDiff(array): 

"""Get the difference between two randomly selected elements of an array. 

 

Parameters 

---------- 

array : `list` or `numpy.ndarray` 

Input array. 

 

Returns 

------- 

float or int 

Difference between two random elements of the array. 

""" 

a, b = random.sample(range(len(array)), 2) 

return array[a] - array[b] 

 

 

def computeWidths(array): 

"""Compute the RMS and the scaled inter-quartile range of an array. 

 

Parameters 

---------- 

array : `list` or `numpy.ndarray` 

Array. 

 

Returns 

------- 

rms : `float` 

RMS 

iqr : `float` 

Scaled inter-quartile range (IQR, see *Notes*). 

 

Notes 

----- 

We estimate the width of the histogram in two ways: 

 

- using a simple RMS, 

- using the interquartile range (IQR) 

 

The IQR is scaled by the IQR/RMS ratio for a Gaussian such that it 

if the array is Gaussian distributed, then the scaled IQR = RMS. 

""" 

# For scalars, math.sqrt is several times faster than numpy.sqrt. 

rmsSigma = math.sqrt(np.mean(array**2)) 

iqrSigma = np.subtract.reduce(np.percentile(array, [75, 25])) / (norm.ppf(0.75)*2) 

return rmsSigma, iqrSigma