def integrate_to_bins(self, new_bin_edges, theta_unit='a'):
"""
Uses integrate_gp to rebin the existing G_p. Note that the new G_p
does not have the new bin widths divided out so it follows
Sum{G_p,i} = 1, not integral(G_p(theta) d theta) = 1
Parameters
----------
new_bin_edges: array
The values of theta defining the bin edges that you want to
integrate to. The theta values are in units theta_unit
theta_unit : string (optional)
The unit in which new_bin_edges are given. The options are
'a', 'arcsec', 'arcseconds'; 'd', 'deg', 'degrees'; 'r',
'rad', 'radians'. Default is 'arcseconds'
Returns
-------
new_gp : array
Gp integrated over the new bins
"""
#Convert the thetas to degrees
new_bin_edges = misc.put_thetas_in_degrees(new_bin_edges, theta_unit)
#Integrate Gp over each bin
n_new_bins = len(new_bin_edges)-1
binned = np.zeros(n_new_bins)
for i in range(n_new_bins):
binned[i] = self.integrate_gp(new_bin_edges[i], new_bin_edges[i+1])
return binned
def integrate_powerlaw(self, A, beta, lowlim, highlim, param_unit='d',
theta_unit='d'):
"""
A funtion that integrates the power law A * theta^-beta over a
range of thetas
Parameters
----------
A : float
The amplitude of the power law for theta in units param_unit
beta : float
The power in the power law
lowlim : float
The lower limit of the theta range to integrate over
highlim : float
The upper limit of the theta range to integrate over
param_unit : string (optional)
The units of theta for which A was calculated. The options
are 'a', 'arcsec', 'arcseconds'; 'd', 'deg', 'degrees'; 'r',
'rad', 'radians'. Default is 'd'
theta_unit : string (optional)
The units of lowlim and highlim. The options are 'a',
'arcsec', 'arcseconds'; 'd', 'deg', 'degrees'; 'r',
'rad', 'radians'. Default is 'd'
Returns
-------
integral : float
The integral of the power law over the specified range
"""
#Do the integral of a power law A*theta^-beta from lowlim to highlim
A = np.float(A)
beta=np.float(beta)
#Make sure the A is for theta in degrees
A = self.convert_A_to_degrees(A, beta, param_unit)
#Convert the limits to degrees
lowlim, highlim = misc.put_thetas_in_degrees([lowlim, highlim],
unit=theta_unit)
#First define the function to be integrated
def powerlaw(theta):
return A * theta ** (-beta)
#Do the integral
pl_int, pl_int_err= intg.quad(powerlaw, lowlim, highlim)
return pl_int
def _make_theta_bins(self, min_theta, max_theta, nbins,
unit='arcseconds'):
"""
Internally sets the edges and centers of the angular bins
Parameters
----------
min_theta : float
The minimum of the theta bin edges
max_theta : float
The maximum of the theta bin edges
nbins : float
The number of theta bins
unit : string (optional)
The unit that min and max theta are in. Default is 'arcseconds'
"""
#Make sure the min and max are in degrees
min_theta, max_theta = misc.put_thetas_in_degrees([min_theta, max_theta],
unit)
#Record things in degrees
self._min_theta = min_theta
self._max_theta = max_theta
self._nbins = nbins
#Make the bins
if self._logbins:
if min_theta<=0:
print ("make_theta_bins says: you've asked for log theta bins "
"and a min of theta<=0 which makes logs unhappy. "
"Changed to 1e-4")
min_theta=0.0001
edges = np.logspace(np.log10(min_theta), np.log10(max_theta), nbins+1)
lcenters=misc.centers(np.log10(edges))
centers=10.**lcenters
else:
edges=np.linspace(min_theta, max_theta, nbins+1)
centers=misc.centers(edges)
#Record the bins and return
self._theta_bins=edges
self._thetas=centers
return
def set_new_bins(self, min_theta, max_theta, nbins, unit='a'):
"""
Redo the range and number of bins.
Parameters
----------
min_theta : float
The minimum of the theta bin edges
max_theta : float
The maximum of the theta bin edges
nbins : float
The number of theta bins
unit : string (optional)
The unit that min and max theta are in. Default is 'arcseconds'
"""
#Set new params and rerun if different
#First, convert to degrees if we need to
min_theta, max_theta = misc.put_thetas_in_degrees([min_theta, max_theta],
unit)
#Are they different?
min_different = self._min_theta != min_theta
max_different = self._max_theta != max_theta
n_different = self._nbins != nbins
#If so, record and rerun bins
if min_different or max_different or n_different:
self._min_theta = min_theta
self._max_theta = max_theta
self._nbins = nbins
self._make_theta_bins(min_theta, max_theta, nbins, unit='d')
return
def integrate_gp_times_powerlaw(self, A, beta, lowlim, highlim,
theta_unit='d', param_unit='d'):
"""
Integrates G_p * A * theta^-beta over a range in thetas. Useful
for calculating the integral constraint.
Parameters
----------
A : float
The amplitude of the power law for theta in units param_unit
beta : float
The power in the power law
lowlim : float
The lower limit of the theta range to integrate over
highlim : float
The upper limit of the theta range to integrate over
param_unit : string (optional)
The units of theta for which A was calculated. The options
are 'a', 'arcsec', 'arcseconds'; 'd', 'deg', 'degrees'; 'r',
'rad', 'radians'. Default is 'd'
theta_unit : string (optional)
The units of lowlim and highlim. The options are 'a',
'arcsec', 'arcseconds'; 'd', 'deg', 'degrees'; 'r', 'rad',
'radians'. Default is 'd'
Returns
-------
integral : float
The integral of G_p * A * theta^-beta
"""
#Compute the integral of G_p * A * theta^-beta from lowlim to
#highlim. A and beta are for the unit specified
#Pull the theta properties
centers, edges = self._theta_bins.get_bins(unit='d')
#Get basic info and convert everything for theta in degrees
nbins_gp = len(self._Gp)
lowlim, highlim = misc.put_thetas_in_degrees([lowlim, highlim],
unit=theta_unit)
A = self.convert_A_to_degrees(A, beta, param_unit)
#If it's completely outside the G_p range, we assume that G_p is 0
#and return 0
if (lowlim >= edges[-1]) or (highlim <= edges[0]):
return 0
#Figure out which bins are all the way inside [lowlim, highlim]
above_lowlim = edges >= lowlim
min_edge_inside_val = edges[above_lowlim][0]
min_edge_inside_index = np.arange(nbins_gp+1)[above_lowlim][0]
below_highlim = edges <= highlim
max_edge_inside_val = edges[below_highlim][-1]
max_edge_inside_index = np.arange(nbins_gp+1)[below_highlim][-1]
#Make sure that the limits aren't above or below the limits where G_p is defined
if lowlim < edges[0]:
min_edge_inside_val = edges[0]
lowlim = edges[0]
min_edge_inside_index = 0
if highlim > edges[-1]:
max_edge_inside_val = edges[-1]
highlim = edges[-1]
max_edge_inside_index = nbins_gp
#Initialize the holder for the result
result=0
#Start by integrating the two partial bins if we didn't happen upon
#an integration limit that corresponds exactly to an edge
if min_edge_inside_val != lowlim:
this_gp_val = self._Gp[min_edge_inside_index-1]
w_int = self.integrate_powerlaw(A, beta, lowlim, min_edge_inside_val)
result += this_gp_val * w_int
if max_edge_inside_val != highlim:
this_gp_val = self._Gp[max_edge_inside_index]
w_int = self.integrate_powerlaw(A, beta, max_edge_inside_val, highlim)
result += this_gp_val * w_int
#Now loop through the bins that are inside
nbins_inside = max_edge_inside_index - min_edge_inside_index
for i in np.arange(nbins_inside):
this_index = min_edge_inside_index + i
this_gp_val = self._Gp[this_index]
w_int = self.integrate_powerlaw(A, beta, edges[this_index], edges[this_index+1])
result += this_gp_val * w_int
return result
