def _make_sigma(self, r_bins, sigmaBinned):
"""
Generates the surface density as a function of r, a callable object
sigma(r) and assigns it to self.sigma
Generates a spline interpolation of sigma vs r from the file
defined by settings.filenames.sigmaFileName. Returns sigma vs r as
an cubic spline interpolation object
(see scipy.interpolation.InterpolatedUnivariateSpline)
sigma_input should be a pickled dictionary with the entries:
'sigma': <sigma evaluated at r>
'r': <r for the bins>
If the input sigma has units, sigma vs r will be returned in units
of Msol/au^2
"""
# Convert to default units of Msol/au^2. If no units, assign default
sigmaBinned = match_units(sigmaBinned, 'Msol au**-2')[0]
# Convert r_bins to default units of 'au'
r_bins = match_units(r_bins, 'au')[0]
# Calculate spline interpolation
sigspline = spline(r_bins, sigmaBinned, k=3, ext='zeros')
# print 'Calculating spline interpolation (slow for many data points)'
# sigspline = interp1d(r_bins,sigmaBinned,kind='cubic',fill_value=0.0,\
# bounds_error=False)
def sigout(r):
"""
Linear spline interpolation of sigma(r).
ARGUMENTS:
r - can be scalar, numpy array, or sim array
RETURNS:
sigma (surface density) evaluated at r
"""
# Try to convert r to the units used to make sigspline ('au')
r = match_units(r, 'au')[0]
return SimArray(sigspline(r), 'Msol au**-2')
self.sigma = sigout
self.r_bins = r_bins
def _make_pdf(self):
"""
Generates the probability density as a function of r (from the surface
density) and returns it as a callable function pdf(r) to self.pdf
pdf(r) = 2*pi*r*sigma(r), up to a normalization
Using sigma(r) calculated in _make_sigma and r_bins loaded from
settings.filenames.sigmaFileName, creates an interpolation over
r_bins, sigma(r_bins). The PDF will be approximately normalized
"""
# Calculate the binned PDF
pdfBinned = 2 * np.pi * self.r_bins * self.sigma(self.r_bins)
# Normalize
integral = simps(pdfBinned, self.r_bins)
pdfBinned /= integral
# Calculate a spline interpolation
pdfSpline = spline(self.r_bins, pdfBinned, k=3, ext='zeros')
# print 'Calculating spline interpolation (slow for many data points)'
# pdfSpline = interp1d(self.r_bins, pdfBinned, kind='cubic',\
# fill_value=0.0, bounds_error=False)
def pdf_fcn(r_in):
"""
Normalized cubic spline interpolation of the PDF(r) from sigma(r).
The PDF is just calculated as 2*pi*r*sigma(r).
ARGUMENTS:
r_in - radii at which to calculate the PDF
RETURNS:
probability density function from sigma(r) evaluated at r_in
"""
# Put r_in into the units used in generating the pdf
r_in = match_units(r_in, self.r_bins)[0]
# Evaluate the pdf at r_in
pdf_vals = pdfSpline(r_in)
# Put the pdf into units of r_in.units**-1
pdf_vals = match_units(pdf_vals, 1 / r_in)[0]
return pdf_vals
self.pdf = pdf_fcn
def _make_pdf(self):
"""
Generates the probability density as a function of r (from the surface
density) and returns it as a callable function pdf(r) to self.pdf
pdf(r) = 2*pi*r*sigma(r), up to a normalization
Using sigma(r) calculated in _make_sigma and r_bins loaded from
settings.filenames.sigmaFileName, creates an interpolation over
r_bins, sigma(r_bins). The PDF will be approximately normalized
"""
# Calculate the binned PDF
pdfBinned = 2*np.pi*self.r_bins * self.sigma(self.r_bins)
# Normalize
integral = simps(pdfBinned,self.r_bins)
pdfBinned /= integral
# Calculate a spline interpolation
pdfSpline = spline(self.r_bins, pdfBinned, k=3, ext='zeros')
# print 'Calculating spline interpolation (slow for many data points)'
# pdfSpline = interp1d(self.r_bins, pdfBinned, kind='cubic',\
# fill_value=0.0, bounds_error=False)
def pdf_fcn(r_in):
"""
Normalized cubic spline interpolation of the PDF(r) from sigma(r).
The PDF is just calculated as 2*pi*r*sigma(r).
ARGUMENTS:
r_in - radii at which to calculate the PDF
RETURNS:
probability density function from sigma(r) evaluated at r_in
"""
# Put r_in into the units used in generating the pdf
r_in = match_units(r_in, self.r_bins)[0]
# Evaluate the pdf at r_in
pdf_vals = pdfSpline(r_in)
# Put the pdf into units of r_in.units**-1
pdf_vals = match_units(pdf_vals, 1/r_in)[0]
return pdf_vals
self.pdf = pdf_fcn
def _make_sigma(self, r_bins, sigmaBinned):
"""
Generates the surface density as a function of r, a callable object
sigma(r) and assigns it to self.sigma
Generates a spline interpolation of sigma vs r from the file
defined by settings.filenames.sigmaFileName. Returns sigma vs r as
an cubic spline interpolation object
(see scipy.interpolation.InterpolatedUnivariateSpline)
sigma_input should be a pickled dictionary with the entries:
'sigma': <sigma evaluated at r>
'r': <r for the bins>
If the input sigma has units, sigma vs r will be returned in units
of Msol/au^2
"""
# Convert to default units of Msol/au^2. If no units, assign default
sigmaBinned = match_units(sigmaBinned, 'Msol au**-2')[0]
# Convert r_bins to default units of 'au'
r_bins = match_units(r_bins, 'au')[0]
# Calculate spline interpolation
sigspline = spline(r_bins, sigmaBinned, k=3, ext='zeros')
def sigout(r):
"""
Linear spline interpolation of sigma(r).
ARGUMENTS:
r - can be scalar, numpy array, or sim array
RETURNS:
sigma (surface density) evaluated at r
"""
# Try to convert r to the units used to make sigspline ('au')
r = match_units(r, 'au')[0]
return SimArray(sigspline(r), 'Msol au**-2')
self.sigma = sigout
self.r_bins = r_bins
