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FeatureExtractor.py
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FeatureExtractor.py
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"""
**************************************************************************
| FeatureExtractor.py |
**************************************************************************
| Description: |
| |
| Contains feature extraction methods shared by both PHCX and PFD files. |
| This code runs on python 2.4 or later. |
**************************************************************************
| Author: Rob Lyon |
| Email : [email protected] |
| web : www.scienceguyrob.com |
**************************************************************************
"""
# Numpy Imports:
from numpy import array
from numpy import ceil
from numpy import argmax
from numpy import delete
from numpy import sin
from numpy import pi
from numpy import exp
from numpy import sqrt
from numpy import log
from numpy import mean
from numpy import histogram
from numpy import corrcoef
from numpy import append
from numpy import sum
from scipy.optimize import leastsq
from scipy import std
from scipy import stats
import matplotlib.pyplot as plt
# Custom file Imports:
import Utilities
# ****************************************************************************************************
#
# CLASS DEFINITION
#
# ****************************************************************************************************
class FeatureExtractor(Utilities.Utilities):
"""
Contains the functions used to generate the features that describe the key features of
a pulsar candidate.
"""
# ****************************************************************************************************
#
# Constructor.
#
# ****************************************************************************************************
def __init__(self,debugFlag):
Utilities.Utilities.__init__(self,debugFlag)
# Set default bin width, won't be used since it is now dynamically recomputed.
self.histogramBins = 60
# ****************************************************************************************************
#
# Feature Extraction functions --> Eatough et al., MNRAS 407, 4, 2010.
# | | | | | | |
# v v v v v v v
# ****************************************************************************************************
# Please add PHCX and PFD compatible feature extraction code for this work as appropriate.
# ****************************************************************************************************
#
# Feature Extraction functions --> Bates et al., MNRAS 427, 2, 2012.
# | | | | | | |
# v v v v v v v
# ****************************************************************************************************
# Please add PHCX and PFD compatible feature extraction code for this work as appropriate.
# ****************************************************************************************************
#
# Feature Extraction functions --> Thornton., PhD Thesis, Univ. Manchester, 2013.
# | | | | | | |
# v v v v v v v
# ****************************************************************************************************
def getSinusoidFittings(self,profile):
"""
Features 1-4 of those described in Thornton., PhD Thesis, Univ. Manchester, 2013.
Computes the sinusoid fitting features for the profile data. There are four computed:
Feature 1. Chi-Squared value for sine fit to raw profile. This attempts to fit a sine curve
to the pulse profile. The reason for doing this is that many forms of RFI are sinusoidal.
Thus the chi-squared value for such a fit should be low for RFI (indicating
a close fit) and high for a signal of interest (indicating a poor fit).
Feature 2. Chi-Squared value for sine-squared fit to amended profile. This attempts to fit a sine
squared curve to the pulse profile, on the understanding that a sine-squared curve is similar
to legitimate pulsar emission. Thus the chi-squared value for such a fit should be low for
RFI (indicating a close fit) and high for a signal of interest (indicating a poor fit).
Feature 3. Difference between maxima. This is the number of peaks the program identifies in the pulse
profile - 1. Too high a value may indicate that a candidate is caused by RFI. If there is only
one pulse in the profile this value should be zero.
Feature 4. Sum over residuals. Given a pulse profile represented by an array of profile intensities P,
the sum over residuals subtracts ( (max-min) /2) from each value in P. A larger sum generally
means a higher SNR and hence other features will also be stronger, such as correlation between
sub-bands. Example,
P = [ 10 , 13 , 17 , 50 , 20 , 10 , 5 ]
max = 50
min = 5
(abs(max-min))/2 = 22.5
so the sum over residuals is:
= (22.5 - 10) + (22.5 - 13) + (22.5 - 17) + (22.5 - 50) + (22.5 - 20) + (22.5 - 10) + (22.5 - 5)
= 12.5 + 9.5 + 5.5 + (-27.5) + 2.5 + 12.5 + 17.5
= 32.5
Parameters:
profile - a numpy.ndarray containing profile data.
Returns:
the chi squared value of the sine fit.
the chi squared value of the sine fit.
the difference between maxima.
the sum over the residuals.
"""
profile_mean = profile.mean()
profile_std = profile.std() # Note this is over n, not n-1.
profile_max = profile.max()
profile_min = profile.min()
sumOverResiduals = 0
# Calculate sum over residuals.
for i in range( len(profile) ):
sumOverResiduals += (abs( profile_max - profile_min ) / 2.)-profile[i]
#print "Sum Over Residuals:\t",sumOverResiduals
# Subtract background from profile. This is a type of feature scaling or
# normalization of the data. I'm not sure why the standard score isn't calculated
# here, i.e. (x-mean) / standard deviation , but there must be a good reason. If
# you would like to use the standard score, just uncomment/comment as needed.
#p = (profile - profile_mean) / profile_std
normalisedProfile = profile - profile_mean - profile_std
normalisedProfileLength = len(normalisedProfile)
for i in range( normalisedProfileLength ):
if normalisedProfile[i] < 0:
normalisedProfile[i] = 0
#print "Profile after normalization:\n",normalisedProfile
# Find peaks in the normalized profile.
# This code works by looking at small blocks of the normalized profile
# for maximum values. The array indexes of the maximum values in the
# normalized profile are then stored in 'peakIndexes'. The 'newProfile'
# variable contains only those blocks from the normalized profile that
# contain peaks. For example, a profile as follows:
#
# index: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
#
# profile = [ 0 , 0 , 5 , 10 , 5 , 0 , 0 , 0 , 0 , 0 , 0 , 15 , 0 , 0 , 0 , 0]
#
# would give:
#
# peakIndexes = [3 , 11]
# newProfile = [0 , 0 , 5 , 10 , 5 , 0 , 0 , 15 , 0 , 0 , 0 , 0]
# | | | |
# ------------------------- -----------------
# | |
# v v
# Block 1 Block 2
#
# Each block contains four zeros. So in this code a peak appears to be defined
# as the maximum value occurring in a block of the normalized profile separated
# by 4 bins with a normalized intensity of zero. Note that a block containing
# intensities of only zero will be ignored. In this example the data in indexes
# 7-10 was ignored.
#
# Note: I'm not sure why four zeroes was chosen, but I certainly won't change it!
# Changing it would give very different results.
tempBinIndexes, tempBinValues, peakIndexes, newProfile = [],[],[],[] # 4 new array variables.
zeroCounter = 0
for i in range( normalisedProfileLength ):
# If intensity at index i is not equal to zero, there is some signal.
# This is not necessarily a peak.
if normalisedProfile[i] != 0:
tempBinValues.append(normalisedProfile[i])
tempBinIndexes.append(i)
# If four zeroes encountered, increment the counter.
# This will cause the final else statement to be executed
# if the next data item is another zero.
elif zeroCounter < 4:
tempBinValues.append(normalisedProfile[i])
tempBinIndexes.append(i)
zeroCounter += 1
else:
if max(tempBinValues) != 0:# If there is a peak...
peakIndexes.append(tempBinIndexes[argmax(tempBinValues)])
newProfile += list(tempBinValues)
# Reset for next iteration.
tempBinIndexes,tempBinValues = [],[]
zeroCounter = 0
# If there are leftover bins not processed in the loop above...
if (tempBinValues != []):
if (max(tempBinValues) != 0):# If there is a peak...
peakIndexes.append(tempBinIndexes[argmax(tempBinValues)])
newProfile += list(tempBinValues)# Add to the new profile.
# The newProfile array will contain zero's at the start and end. This is
# because if 4 zeros haven't been seen, then they will be added
# to the newProfile array. Just in case you wonder where the zeroes are coming
# from. I did not design this :)
# Locate and count maxima.
maxima = len(peakIndexes)
# Calculate difference between maxima. This code simply subtracts
# the peaks in the peakIndexes array at the indexes between 1 to n, from
# the peak values in the same array at indexes at 0 to (n-1).
#
# i.e. if peakIndexes = [ 1 , 2 , 3 , 4 , 5 , 6] , then:
#
# peakIndexs from 1 to n are [ 2 , 3 , 4 , 5 , 6]
# peakIndexs from 0 to n-1 are [ 1 , 2 , 3 , 4 , 5]
#
# So diff is given by,
# diff = [ (2-1) , (3-2) , (4-3) , (5-4) , (6-5) ]
# = [ 1 , 1 , 1 , 1 , 1 ]
if maxima > 0:
diff = delete(peakIndexes,0) - delete(peakIndexes,maxima-1)
else:
diff = []
# Delete zeros in newProfile array. Does not delete all zero's however.
# It leaves a single zero in between each block with data.
finalProfile = []
zeroCounter , i = 0,0
while i < len(newProfile):
if newProfile[i] != 0:
finalProfile.append(newProfile[i])
zeroCounter = 0
elif zeroCounter < 1:
finalProfile.append(newProfile[i])
zeroCounter += 1
i += 1 # Increment loop variable.
#print "Final Profile for Sine fitting:\n",finalProfile
# Perform fits to profile.
# Divide chi-squared by maxima to reduce feature values of data with many peaks.
chisq_profile_sine_fit = self.fitSine(profile,maxima)/maxima # Fit sine curve to raw profile.
chisq_finalProfile_sine_sqr_fit = self.fitSineSqr(profile,maxima)/maxima # Fit sine-squared curve to amended profile.
return chisq_profile_sine_fit , chisq_finalProfile_sine_sqr_fit , float(len (diff)) , sumOverResiduals
# ******************************************************************************************
def fitSine(self,yData,maxima):
"""
Fits a sine curve to data and returns the chi-squared value of the fit. Here
the amplitude is fixed to max(yData) - min(yData) ) / 2 and the background term
is fixed to the same value.
Parameters:
yData - a numpy.ndarray containing the data to fit the curve to (y-axis data).
maxima - the number of maxima in the data.
Returns:
The chi-squared value of the fit.
"""
# Obtain parameters for fitting.
xData = array(range(len(yData)))
amplitude = abs( max(yData) - min(yData) ) / 2.
frequency = float( maxima / (len(yData) - 1.) )
# The background terms decides where the middle of the sine curve will be,
# i.e. smaller moves the curve down the y-axis, higher moves the curve up the
# y-axis.
background = abs( max(yData) - min(yData) ) / 2.
# Calculates the residuals.
def __residuals(paras, x, y,amp,bg):
# amp = the amplitude
# f = the frequency
# pi = Good old pi or 3.14159... mmmm pi.
# phi = the phase.
# bg = the mean of the data, centre amplitude.
# err = error.
# Remember that here x and y are the data, such that,
# x = bin number
# y = intensity in bin number x
f, phi = paras
err = y - (abs(amp) * sin( 2 * pi * f * x + phi) + abs(bg))
return err
# Evaluates the function.
def __evaluate(x, paras,amp,bg):
# Same variables as above.
f, phi = paras
return abs(amp) * sin( 2 * pi * f * x + phi) + abs(bg)
if yData[0] == background:
phi0 = 0
elif yData[0] < background:
try:
phi0 = -1 / (4 * frequency)
except ZeroDivisionError:
phi0 = -1.0 / (4.0 * 0.00000000001)
elif yData[0] > background:
try:
phi0 = +1 / (4 * frequency)
except ZeroDivisionError:
phi0 = +1.0 / (4.0 * 0.00000000001)
# Perform sine fit.
parameters = (frequency,phi0)
# This call to leastsq() uses the full-output=True flag so that we can compute the
# R2 and other stats. This makes it easier to validate and debug the resulting fit
# in other tools like Matlab. The original code is left below, just uncomment and
# remove new code if necessary (1).
#leastSquaresParameters = leastsq(__residuals, parameters, args=(xData,yData,amplitude),full_output=True)
#fit = __evaluate(xData, leastSquaresParameters[0],amplitude)
leastSquaresParameters,cov,infodict,mesg,ier = leastsq(__residuals, parameters, args=(xData,yData,amplitude,background),full_output=True) # @UnusedVariable
fit = __evaluate(xData, leastSquaresParameters,amplitude,background)
# Chi-squared fit.
chisq = 0
for i in range(len(yData)):
#if yData[i] >= 5.: # Not sure why this restriction is here.
chisq += (yData[i]-fit[i])**2
chisq /= len(yData)
# Note leastSquaresParameters[0] contains the parameters of the fit obtained
# by the least squares optimize call, [frequency,phi0,background].
#print "Least squares parameters:\n", leastSquaresParameters[0]# This is used if the area below (1) above is uncommented.
#print "Least squares parameters Full:\n", leastSquaresParameters
#print "Chi Squared:\n", chisq*pow(float(maxima),4)/100000000.
#print "fit:\n", fit
# This section should be commented out when testing is completed.
if(self.debug):
ssErr = (infodict['fvec']**2).sum() # 'fvec' is an array of residuals.
yData = array(yData)
ssTot = ((yData-yData.mean())**2).sum()
rsquared = 1-(ssErr/ssTot )
print("\n\tSine fit to Pulse profile statistics:")
print("\tStandard Error: ", ssErr)
print("\tTotal Error: ", ssTot)
print("\tR-Squared: ", rsquared)
print("\tAmplitude: ",amplitude)
print("\tFrequency: ",str(leastSquaresParameters[0]))
print("\tPhi: ",str(leastSquaresParameters[1]))
print("\tBackground: ",background)
plt.plot(xData,yData,'o', xData, __evaluate(xData, leastSquaresParameters,amplitude,background))
plt.title("Sine fit to Profile")
plt.show()
#return leastSquaresParameters[0], chisq*pow(maxima,4)/100000000., fit, xData, yData
# I've commented out the return statement above, as only the chi-squared value is used.
# By not returning the extra items, the memory they use will be freed up when this
# function terminates, reducing memory overhead.
#return chisq*pow(float(maxima),4)/100000000.
return chisq
# ******************************************************************************************
def fitSineSqr(self,yData,maxima):
"""
Fits a sine-squared curve to data and returns the chi-squared value of the fit.
Parameters:
yData - a numpy.ndarray containing the data to fit the curve to (y-axis data).
maxima - the number of maxima in the data.
Returns:
The chi-squared value of the fit.
"""
# Calculates the residuals.
def __residuals(paras, x, y,amp,bg):
# a = the amplitude
# f = the frequency
# pi = Good old pi or 3.14159... mmmm pi.
# phi = the phase.
# err = error.
# bg = background term
# Remembmer that here x and y are the data, such that,
# x = bin number.
# y = intensity in bin number x.
f, phi = paras
err = y - (abs(amp) * pow ( sin ( 2 * pi * f * x + phi),2)) + abs(bg)
return err
# Evaluates the function.
def __evaluate(x, paras,amp,bg):
# Same variables as above.
f, phi = paras
return abs(amp) * pow ( sin ( 2 * pi * f * x + phi),2) + abs(bg)
# Obtain parameters for fitting.
xData = array(range(len(yData)))
#amplitude = max(yData)
amplitude = abs( max(yData) - min(yData) ) / 2.
frequency = float( maxima / (len(yData) - 1.) / 2. )
background = abs( max(yData) - min(yData) ) / 2.
if yData[0] == 0:
phi0 = 0
else:
try:
phi0 = -1 / (4 * frequency)
except ZeroDivisionError:
phi0 = -1.0 / (4.0 * 0.00000000001)
# Perform sine fit.
parameters = (frequency,phi0)
leastSquaresParameters,cov,infodict,mesg,ier = leastsq(__residuals, parameters, args=(xData,yData,amplitude,background),full_output=True)#@UnusedVariable
fit = __evaluate(xData, leastSquaresParameters,amplitude,background)
# Chi-squared fit.
chisq = 0
for i in range(len(yData)):
chisq += (yData[i]-fit[i])**2
chisq /= len(yData)
#print "Least squares parameters:\n", leastSquaresParameters[0]
#print "Chi Squared:\n", chisq / pow(float(maxima),4)
#print "fit:\n", fit
if(self.debug):
ssErr = (infodict['fvec']**2).sum() # 'fvec' is an array of residuals.
ssTot = ((yData-mean(yData))**2).sum()
rsquared = 1-(ssErr/ssTot )
print("\n\tSine Squared fit to Pulse profile statistics:")
print("\tStandard Error: ", ssErr)
print("\tTotal Error: ", ssTot)
print("\tR-Squared: ", rsquared)
print("\tAmplitude: ",amplitude)
print("\tFrequency: ",str(leastSquaresParameters[0]))
print("\tPhi: ",str(leastSquaresParameters[1]))
plt.plot(xData,yData,'o', xData, __evaluate(xData, leastSquaresParameters,amplitude,background))
plt.title("Sine Squared fit to Profile")
plt.show()
#return leastSquaresParameters[0], chisq / pow(float(maxima),4), fit, xData, yData
# I've commented out return statement above, as only the chi-squared value is used.
# By not returning the extra items, the memory they use will be freed up when this
# function terminates, reducing memory overhead.
return chisq
# ****************************************************************************************************
#
# Gaussian Fittings
#
# ****************************************************************************************************
def getGaussianFittings(self,profile):
"""
Features 5-11 of those described in Thornton., PhD Thesis, Univ. Manchester, 2013.
Computes the Gaussian fitting features for the profile data. There are seven computed:
Feature 5. Distance between expectation values of Gaussian and fixed Gaussian fits to profile histogram.
This fits a two Gaussian curves to a histogram of the profile data. One of these
Gaussian fits has its mean value set to the value in the centre bin of the histogram,
the other is not constrained. Thus it is expected that for a candidate arising from noise,
these two fits will be very similar - the distance between them will be zero. However a
legitimate signal should be different giving rise to a higher feature value.
Feature 6. Ratio of the maximum values of Gaussian and fixed Gaussian fits to profile histogram.
This computes the maximum height of the fixed Gaussian curve (mean fixed to the centre
bin) to the profile histogram, and the maximum height of the non-fixed Gaussian curve
to the profile histogram. This ratio will be equal to 1 for perfect noise, or close to zero
for legitimate pulsar emission.
Feature 7. Distance between expectation values of derivative histogram and profile histogram. A histogram
of profile derivatives is computed. This finds the absolute value of the mean of the
derivative histogram, minus the mean of the profile histogram. A value close to zero indicates
a candidate arising from noise, a value greater than zero some form of legitimate signal.
Feature 8. Full-width-half-maximum (FWHM) of Gaussian fit to pulse profile. Describes the width of the
pulse, i.e. the width of the Gaussian fit of the pulse profile. Equal to 2*sqrt( 2 ln(2) )*sigma.
Not clear whether a higher or lower value is desirable.
Feature 9. Chi squared value from Gaussian fit to pulse profile. Lower values are indicators of a close fit,
and a possible profile source.
Feature 10. Smallest FWHM of double-Gaussian fit to pulse profile. Some pulsars have a doubly peaked
profile. This fits two Gaussians to the pulse profile, then computes the FWHM of this
double Gaussian fit. Not clear if higher or lower values are desired.
Feature 11. Chi squared value from double Gaussian fit to pulse profile. Smaller values are indicators
of a close fit and possible pulsar source.
Parameters:
profile - a numpy.ndarray containing profile data.
Returns:
the chi squared value of the sine fit.
the chi squared value of the sine fit.
the difference between maxima.
the sum over the residuals.
"""
# Stores the features obtained just by this function.
guassian_features=[]
self.histogramBins = self.freedmanDiaconisRule(profile)
dy = self.getDerivative(profile)
self.dy_histogramBins = self.freedmanDiaconisRule(dy)
histogram_dy = histogram(dy,self.dy_histogramBins) # Calculates a histogram of the derivative dy.
# Performs a gaussian fit on the derivative histogram.
gaussianFitToDerivativeHistogram = self.fitGaussian(histogram_dy[1],histogram_dy[0])
derivativeHistogram_sigma, derivativeHistogram_expect, derivativeHistogram_maximum = gaussianFitToDerivativeHistogram[0]
if(self.debug==True):
print("\n\tGaussian fit to Derivative Histogram details: ")
print("\tSigma of derivative histogram = " , derivativeHistogram_sigma)
print("\tMu of derivative histogram = " , derivativeHistogram_expect)
print("\tMax of derivative histogram = " , derivativeHistogram_maximum)
# View histogram - for debugging only... uncomment matlibplot import at top if needed.
hist, bins = histogram(dy,self.dy_histogramBins) # Calculates a histogram of the derivative.
center = (bins[:-1] + bins[1:]) / 2
plt.bar(center, hist, align='center')
plt.title("Histogram of derivative dy")
plt.show()
histogram_profile = histogram(profile,self.histogramBins) # Calculates a histogram of the profile data.
# Performs a gaussian fit on the profile histogram.
gaussianFitToProfileHistogram = self.fitGaussian(histogram_profile[1],histogram_profile[0])
profileHistogram_sigma, profileHistogram_expect, profileHistogram_maximum = gaussianFitToProfileHistogram[0]
if(self.debug==True):
print("\n\tGaussian fit to Profile Histogram details: ")
print("\tSigma of profile histogram = " , profileHistogram_sigma)
print("\tMu of profile histogram = " , profileHistogram_expect)
print("\tMax of profile histogram = " , profileHistogram_maximum)
# View histogram - for debugging only... uncomment matlibplot import at top if needed.
hist, bins = histogram(profile,self.histogramBins) # Calculates a histogram of the profile.
center = (bins[:-1] + bins[1:]) / 2
plt.bar(center, hist, align='center')
plt.title("Histogram of profile")
plt.show()
# Here gf refers to Gaussian fit.
# Performs a gaussian fit with fixed expectation value on the profile histogram.
gf_ProfileHistogram_fixed_Expect = self.fitGaussianFixedWidthBins(histogram_profile[1],histogram_profile[0],self.histogramBins)
gf_ProfileHistogram_fixed_sigma, gf_ProfileHistogram_fixed_maximum = gf_ProfileHistogram_fixed_Expect[0]
gf_ProfileHistogram_fixed_fwhm = gf_ProfileHistogram_fixed_Expect[1]
gf_ProfileHistogram_fixed_chi = gf_ProfileHistogram_fixed_Expect[2]
gf_ProfileHistogram_fixed_xmax = gf_ProfileHistogram_fixed_Expect[4]
if(self.debug==True):
print("\n\tGaussian fits to Profile Historgram with fixed Mu details:")
print("\tSigma of Gaussian fit to Profile Historgram = " , gf_ProfileHistogram_fixed_sigma)
print("\tMax of Gaussian fit to Profile Historgram = " , gf_ProfileHistogram_fixed_maximum)
print("\tFWHM of Gaussian fit to Profile Historgram = " , gf_ProfileHistogram_fixed_fwhm)
print("\tChi-squared of Gaussian fit to Profile Historgram = " , gf_ProfileHistogram_fixed_chi)
print("\txmax of Gaussian fit to Profile Historgram = ")
dexp_fix = abs(gf_ProfileHistogram_fixed_xmax - profileHistogram_expect) # Feature 5.
amp_fix = abs( gf_ProfileHistogram_fixed_maximum / profileHistogram_maximum) # Feature 6.
dexp = abs(derivativeHistogram_expect - profileHistogram_expect) # Feature 7.
# Add features.
guassian_features.append(float(dexp_fix)) # Feature 5. Distance between expectation values of Gaussian and fixed Gaussian fits to profile histogram.
guassian_features.append(float(amp_fix)) # Feature 6. Ratio of the maximum values of Gaussian and fixed Gaussian fits to profile histogram.
guassian_features.append(float(dexp)) # Feature 7. Distance between expectation values of derivative histogram and profile histogram.
minbg = min(profileHistogram_expect,profile.mean()) # Estimate background.
tempProfile = []
if minbg > 0.:
for i in range(len(profile)):
newy = profile[i] - minbg + profile.std() # Substract background from profile
if newy < 0.: # and store the new profile in list temp
newy = 0.
tempProfile.append(newy)
else:
tempProfile = profile
# Here gf refers to Gaussian fit
gf_profile_result = self.fitGaussianT1(tempProfile)
gf_profile_fwhm, gf_profile_chi = gf_profile_result[1], gf_profile_result[2]
# Add featuress.
guassian_features.append(float(gf_profile_fwhm)) # Feature 8. Full-width-half-maximum (FWHM) of Gaussian fit to pulse profile.
guassian_features.append(float(gf_profile_chi)) # Feature 9. Chi squared value from Gaussian fit to pulse profile.
# dgf means double Gaussian fit
try:
dgf_profile_result = self.fitDoubleGaussianT2(profile) # Double gaussian fit around the maximum of the profile.
dgf_profile_fwhm1 = dgf_profile_result[1]
dgf_profile_chi = dgf_profile_result[2]
dgf_profile_fwhm2 = dgf_profile_result[6]
# Here profile.std() is the standard deviation of the profile.
# gf is Gaussian fit, dgf is double Gaussian fit.
gf_dgf_diff = dgf_profile_result[3] - (gf_profile_result[3] + minbg - profile.std()) # Differences of gaussian fits t1 and t2.
gf_dgf_std = float(abs(gf_dgf_diff.std())) # Standard deviation of differences.
if gf_dgf_std < 3.:
dgf_fwhm = gf_profile_fwhm
else:
dgf_fwhm = float(min(dgf_profile_fwhm1 , dgf_profile_fwhm2))
except IndexError:
dgf_fwhm = 1000000
dgf_profile_chi = 1000000
# Add features.
guassian_features.append(float(dgf_fwhm)) # Feature 10. Smallest FWHM of double-Gaussian fit to pulse profile.
guassian_features.append(float(dgf_profile_chi)) # Feature 11. Chi squared value from double Gaussian fit to pulse profile.
return guassian_features
# ******************************************************************************************
def fitGaussian(self,xData,yData):
"""
Fits a Gaussian to the supplied data. This should be histrogram data,
that is the details of the bins (xData) and the frequencies (yData).
Parameters:
xData - a numpy.ndarray containing data (x-axis data).
yData - a numpy.ndarray containing data (y-axis data).
Returns:
The parameters of the fit, one array and three other variables.
leastSquaresParameters - array containing optimum three values for:
* sigma
* expect
* maximum
fwhm - the full width half maximum of the Gaussian.
chisq - the chi-squared value of the fit.
fit - the fit.
"""
#print "xData (LENGTH=",len(xData),"):\n", xData
#print "yData (LENGTH=",len(yData),"):\n", yData
# Calculates the residuals.
def __residuals(paras, x, y):
# sigma = the standard deviation.
# mu = the mean aka the expectation of the distribution.
# maximum = .
# Remembmer that here x and y are the data, such that,
# x = bin number.
# y = intensity in bin number x.
sigma, mu, maximum = paras
err = y - ( abs(maximum) * exp( (-((x - mu) / sigma )**2) / 2))
return err
# Evaluates the function.
def __evaluate(x, paras):
# Same variables as above.
sigma, mu, maximum = paras
return ( abs(maximum) * exp( (-((x - mu) / sigma )**2) / 2))
# Reverses the order of the list entries.
def __mirror(_list):
reversedList = []
listLength = len(_list)
for i in range( listLength ):
reversedList.append(_list[abs(i - listLength + 1)])
return reversedList
if xData == []:
xData = range(len(yData))
# Set up variables required to perfrom fit.
_exit,counter = 0,0
indexOfLargestValue_xAxis = argmax(yData) # First index of largest value along x-axis (highest frequency).
expect = xData[indexOfLargestValue_xAxis]
sigma = std(yData)
maximum = max(yData)
meansq = mean(yData)**2
temp = yData
#print "Index of largest value on x-axis:\t", indexOfLargestValue_xAxis
#print "expect:\t", expect
#print "sigma:\t", sigma
#print "maximum:\t", maximum
#print "meansq:\t", meansq
# We are chopping off some the x-axis data here. This is because this function
# is running on histogram data, i.e bin positions and frequncies. The xData array
# holds details of the bins, yData the frequencies. So if the length of xData is n,
# than the length of yData must be n-1.
#
# For example, if the yData has been split across 6 bins then if we had:
#
# xData = [ 0 , 10 , 20 , 30 , 40 , 50 ] # Bins
# yData = [ 1 , 2 , 5 , 1 , 0] # Frequencies
#
# So here the last data point in xData is removed.
if len(xData) == len(yData)+1:
xData = xData[0:-1] # Chopping off last data point.
xDatalength = len(xData)
# Here check if maximum frequency is on the border. If it is then the data
# is reversed. This code appears to throw data away, since when reversing
# the data, the part not being reversed is discarded. Is this acceptable?
#
# For example, if we have data as follows:
#
# yData = [10 , 0 , 3 , 1 , 1 , 1 , 0 , 1 , 3 , 0]
#
# then,
#
# indexOfLargestValue_xAxis = 0
#
# So,
#
# cut = ceil( len(yData) / 2) = 5
# part1 = [10 , 0 , 3 , 1 , 1]
# part2 = [1 , 1 , 3 , 0 , 10]
#
# then yData is set to:
#
# yData = part2+ part1 = [1 , 1 , 3 , 0 , 10 , 10 , 0 , 3 , 1 , 1]
#
# Obviously this isn't the data we started with, so is this a bug?
#
# BUG: If there are two bins with an equal MAXIMUM frequency, one of those *Could* be discarded here.
# This is because the indexOfLargestValue_xAxis variable from above, is obtained from
# the first bin with the maximum frequency, but there could be multiple bins with the
# maximum frequency in the histogram. So if,
#
# a) there is a max value in the first or last bin which we label b;
# b) 1 or more bins have the same frequency as bin b;
# c) those 1 or more bins which share the same frequency as b are not in the same half of the data;
#
# Then the other bins with the the shared max frequency will be discarded.
# Perform the gaussian fit.
while _exit == 0:
parameters = [sigma, expect, maximum]
# Hackey solution to prevent situations where
# there are more parameters than data points!
# This causes the scipy least squares call to
# fail.
if(len(parameters)> len(xData)):
lengthDifference = len(parameters)-len(xData)
for i in range(0,lengthDifference):
xData=append(xData,0)
yData=append(yData,0)
leastSquaresParameters = leastsq(__residuals, parameters, args=(xData,yData))
fwhm = abs(2 * sqrt(2 * log(2)) * leastSquaresParameters[0][0])
fit = __evaluate(xData, leastSquaresParameters[0])
# Compute Chi-squared value for fit.
chisq = 0
for i in range(xDatalength):
chisq += (yData[i] - fit[i])**2
chisq /= len(yData)
if (chisq > meansq * xDatalength) & (leastSquaresParameters[0][0] < 0.2 * xDatalength):
counter += 1
temp = delete(temp,indexOfLargestValue_xAxis)
pos = argmax(temp)
expect = xData[pos+counter]
if counter > 5:
_exit += 1
else:
_exit += 1
# I've commented this return statement out to avoid returning all the data (xData and yData),
# since this data was passed in to the method in the first place.
#return leastSquaresParameters[0], fwhm, chisq, fit, xData, yData
return leastSquaresParameters[0], fwhm, chisq, fit
# ******************************************************************************************
def fitGaussianFixedWidthBins(self,xData,yData,bins):
"""
Fits a Gaussian to the supplied data under the constraint
that the expectation value is fixed.
Parameters:
xData - a numpy.ndarray containing data (x-axis data).
yData - a numpy.ndarray containing data (y-axis data).
bins - the number of bins in the profile histogram.
Returns:
The parameters of the fit, one array and four other variables.
leastSquaresParameters - array containing optimum three values for:
* sigma
* expect
* maximum
fwhm - the full width half maximum of the Gaussian.
chisq - the chi-squared value of the fit.
fit - the fit.
xmax - the max expectation value.
"""
#print "xData (LENGTH=",len(xData),"):\n", xData
#print "yData (LENGTH=",len(yData),"):\n", yData
# Calculates the residuals.
def __residuals(paras, x, y, xmax):
# sigma = the standard deviation.
# Remembmer that here x and y are the data, such that,
# x = bin number.
# y = intensity in bin number x.
sigma, maximum = paras
err = y - ( abs(maximum) * exp( (-((x - xmax) / sigma )**2) / 2))
return err
# Evaluates the function.
def __evaluate(x, paras, xmax):
# Same variables as above.
sigma, maximum = paras
return ( abs(maximum) * exp( (-((x - xmax) / sigma )**2) / 2))
if xData == []:
xData = range(len(yData))
if len(xData) == len(yData)+1:
xData = xData[0:-1]
# Set up variables required to perfrom fit.
sigma = std(yData)
maximum = max(yData)
xmax = xData[int(bins/2)-1] # Made change here to ensure we start with centre bin.
# perform fit ######
parameters = [sigma, maximum]
leastSquaresParameters = leastsq(__residuals, parameters, args=(xData,yData,xmax))
fwhm = abs(2 * sqrt( 2 * log(2) ) * leastSquaresParameters[0][0])
fit = __evaluate(xData, leastSquaresParameters[0],xmax)
# Chi-squared fit.
chisq = 0
for i in range(len(yData)):
chisq += (yData[i]-fit[i])**2
chisq /= len(yData)
return leastSquaresParameters[0], fwhm, chisq, fit, xmax
# ******************************************************************************************
def fitGaussianT1(self,yData):
"""
Fits a Gaussian to the supplied data.
Parameters:
yData - a numpy.ndarray containing data (y-axis data).
Returns:
An object containing:
the parameters of the fit, one array and three other variables.
leastSquaresParameters - array containing optimum three values for:
* sigma
* expect
* maximum
fwhm - the full width half maximum of the Gaussian.
chisq - the chi-squared value of the fit.
fit - the fit.
params - the parmeters of the fit.
"""
xData =[] # @UnusedVariable
part1,part2 = [],[]
yDataLength = len(yData)
xData = range(yDataLength)
xmax = argmax(yData) # Finds index of max value in yData.
# Check if maximum is near borders of the interval.
# The original script was hardcoded to look for peaks in bins 0-15
# and 112-128 - if the peak was here the data would be processed further.
# Since the length of the profile data may vary, we can't just hard code
# literal values any more. So as a hack what we do is rescale the value
# and check if it is less that 15 or greater than 112 and proceed as before.
min_ = 0
max_ = yDataLength
newMin = 0
newMax = 128
tempXmax = self.scale(xmax, min_, max_, newMin, newMax)
nearBorder = False
if (tempXmax < 15) or (tempXmax >= 112): # If index of max value is near begining or end.
cut = int(ceil(yDataLength/2)) # Obtain midpoint.
part1 = yData[:cut] # Part 1 contains 1st half of data.
part2 = yData[cut:] # Part 2 contains 2nd half of data.
yData = list(part2)+list(part1)# Swap the parts around. This is done differently in the function fit_gaussian(self,xData,yData) in this file.
nearBorder = True
# Perform gaussian fit.
result = self.fitGaussianWithBackground(xData,yData)
# This bit increases the mu value for some reason. So if the peak
# is near the border, then this code below will add the centre bin
# number to the mean!?
if nearBorder == True:
result[0][1] = result[0][1]+cut
return result
# ******************************************************************************************
def fitDoubleGaussianT2(self,yData):
"""
Fits a double Gaussian to the supplied data.
Parameters:
yData - a numpy.ndarray containing data (y-axis data).
Returns:
An object containing the parameters of the fit.
"""
part1,part2 = [],[]
yDataLength = len(yData)
xmax = argmax(yData) # Finds index of max value in yData.
# The original script was hardcoded to look for peaks in bins 0-15
# and 112-128 - if the peak was here the data would be processed further.
# Since the length of the profile data may vary, we can't just hard code
# literal values any more. So as a hack what we do is rescale the value
# and check if it is less that 15 or greater than 112 and proceed as before.
min_ = 0
max_ = yDataLength
newMin = 0
newMax = 128
tempXmax = self.scale(xmax, min_, max_, newMin, newMax)
nearBorder = False
if (tempXmax < 15) or (tempXmax >= 112): # If index of max value is near begining or end.
cut = int(ceil(yDataLength/2)) # Obtain midpoint.
part1 = yData[:cut] # Part 1 contains 1st half of data.
part2 = yData[cut:] # Part 2 contains 2nd half of data.
yData = list(part2)+list(part1)# Swap the parts around. This is done differently in the function fit_gaussian(self,xData,yData) in this file.
nearBorder = True