# Copyright (c) 2003-2024 by Mike Jarvis
#
# TreeCorr is free software: redistribution and use in source and binary forms,
# with or without modification, are permitted provided that the following
# conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions, and the disclaimer given in the accompanying LICENSE
# file.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions, and the disclaimer given in the documentation
# and/or other materials provided with the distribution.
"""
.. module:: nnncorrelation
"""
import numpy as np
from . import _treecorr
from .catalog import calculateVarG
from .corr3base import Corr3
from .util import make_writer, make_reader
[docs]class GGGCorrelation(Corr3):
r"""This class handles the calculation and storage of a 3-point shear-shear-shear correlation
function.
We use the "natural components" of the shear 3-point function described by Schneider &
Lombardi (2003) [Astron.Astrophys. 397 (2003) 809-818]. In this paradigm, the shears
are projected relative to some point defined by the geometry of the triangle. They
give several reasonable choices for this point. We choose the triangle's centroid as the
"most natural" point, as many simple shear fields have purely real :math:`\Gamma_0` using
this definition. It is also a fairly simple point to calculate in the code compared to
some of the other options they offer, so projections relative to it are fairly efficient.
There are 4 complex-valued 3-point shear corrletion functions defined for triples of shear
values projected relative to the line joining the location of the shear to the cenroid of
the triangle:
.. math::
\Gamma_0 &= \langle \gamma(\mathbf{x1}) \gamma(\mathbf{x2}) \gamma(\mathbf{x3}) \rangle \\
\Gamma_1 &= \langle \gamma(\mathbf{x1})^* \gamma(\mathbf{x2}) \gamma(\mathbf{x3}) \rangle \\
\Gamma_2 &= \langle \gamma(\mathbf{x1}) \gamma(\mathbf{x2})^* \gamma(\mathbf{x3}) \rangle \\
\Gamma_3 &= \langle \gamma(\mathbf{x1}) \gamma(\mathbf{x2}) \gamma(\mathbf{x3})^* \rangle \\
where :math:`\mathbf{x1}, \mathbf{x2}, \mathbf{x3}` are the corners of the triange opposite
sides d1, d2, d3 respectively, where d1 > d2 > d3, and :math:`{}^*` indicates complex
conjugation.
See the doc string of `Corr3` for a description of how the triangles are binned along
with the attributes related to the different binning options.
In addition to the attributes common to all `Corr3` subclasses, objects of this class
hold the following attributes:
Attributes:
gam0: The 0th "natural" correlation function, :math:`\Gamma_0`.
gam1: The 1st "natural" correlation function, :math:`\Gamma_1`.
gam2: The 2nd "natural" correlation function, :math:`\Gamma_2`.
gam3: The 3rd "natural" correlation function, :math:`\Gamma_3`.
vargam0: The variance of :math:`\Gamma_0`, only including the shot noise
propagated into the final correlation. This (and the related values for
1,2,3) does not include sample variance, so it is always an underestimate
of the actual variance.
vargam1: The variance of :math:`\Gamma_1`.
vargam2: The variance of :math:`\Gamma_2`.
vargam3: The variance of :math:`\Gamma_3`.
The typical usage pattern is as follows::
>>> ggg = treecorr.GGGCorrelation(config)
>>> ggg.process(cat) # Compute auto-correlation.
>>> ggg.process(cat1, cat2, cat3) # Compute cross-correlation.
>>> ggg.write(file_name) # Write out to a file.
>>> gam0 = ggg.gam0, etc. # Access gamma values directly.
>>> gam0r = ggg.gam0r # Or access real and imag parts separately.
>>> gam0i = ggg.gam0i
Parameters:
config (dict): A configuration dict that can be used to pass in kwargs if desired.
This dict is allowed to have addition entries besides those listed
in `Corr3`, which are ignored here. (default: None)
logger: If desired, a logger object for logging. (default: None, in which case
one will be built according to the config dict's verbose level.)
Keyword Arguments:
**kwargs: See the documentation for `Corr3` for the list of allowed keyword
arguments, which may be passed either directly or in the config dict.
"""
_cls = 'GGGCorrelation'
_letter1 = 'G'
_letter2 = 'G'
_letter3 = 'G'
_letters = 'GGG'
_builder = _treecorr.GGGCorr
_calculateVar1 = staticmethod(calculateVarG)
_calculateVar2 = staticmethod(calculateVarG)
_calculateVar3 = staticmethod(calculateVarG)
_sig1 = 'sig_sn (per component)'
_sig2 = 'sig_sn (per component)'
_sig3 = 'sig_sn (per component)'
[docs] def __init__(self, config=None, *, logger=None, **kwargs):
super().__init__(config, logger=logger, **kwargs)
shape = self.data_shape
self._z = [np.zeros(shape, dtype=float) for _ in range(8)]
self.logger.debug('Finished building GGGCorr')
@property
def gam0(self):
return self._z[0] + 1j * self._z[1]
@property
def gam1(self):
return self._z[2] + 1j * self._z[3]
@property
def gam2(self):
return self._z[4] + 1j * self._z[5]
@property
def gam3(self):
return self._z[6] + 1j * self._z[7]
@property
def gam0r(self):
return self._z[0]
@property
def gam0i(self):
return self._z[1]
@property
def gam1r(self):
return self._z[2]
@property
def gam1i(self):
return self._z[3]
@property
def gam2r(self):
return self._z[4]
@property
def gam2i(self):
return self._z[5]
@property
def gam3r(self):
return self._z[6]
@property
def gam3i(self):
return self._z[7]
[docs] def finalize(self, varg1, varg2, varg3):
"""Finalize the calculation of the correlation function.
Parameters:
varg1 (float): The variance per component of the first shear field.
varg2 (float): The variance per component of the second shear field.
varg3 (float): The variance per component of the third shear field.
"""
self._finalize()
self._var_num = 4 * varg1 * varg2 * varg3
# I don't really understand why the variance is coming out 2x larger than the normal
# formula for LogSAS. But with just Gaussian noise, I need to multiply the numerator
# by two to get the variance estimates to come out right.
if self.bin_type in ['LogSAS', 'LogMultipole']:
self._var_num *= 2
@property
def vargam0(self):
if self._varzeta is None:
self._calculate_varzeta(4)
return self._varzeta[0]
@property
def vargam1(self):
if self._varzeta is None:
self._calculate_varzeta(4)
return self._varzeta[1]
@property
def vargam2(self):
if self._varzeta is None:
self._calculate_varzeta(4)
return self._varzeta[2]
@property
def vargam3(self):
if self._varzeta is None:
self._calculate_varzeta(4)
return self._varzeta[3]
[docs] def getStat(self):
"""The standard statistic for the current correlation object as a 1-d array.
In this case, the concatenation of gam0.ravel(), gam1.ravel(), gam2.ravel(), gam3.ravel().
.. note::
This is a complex array, unlike most other statistics.
The computed covariance matrix will be complex, although since it is Hermitian the
diagonal is real, so the resulting vargam0, etc. will all be real arrays.
"""
return np.concatenate([self.gam0.ravel(), self.gam1.ravel(),
self.gam2.ravel(), self.gam3.ravel()])
[docs] def getWeight(self):
"""The weight array for the current correlation object as a 1-d array.
In this case, 4 copies of self.weight.ravel().
"""
return np.concatenate([np.abs(self.weight.ravel())] * 4)
[docs] def write(self, file_name, *, file_type=None, precision=None, write_patch_results=False,
write_cov=False):
super().write(file_name, file_type=file_type, precision=precision,
write_patch_results=write_patch_results, write_cov=write_cov)
write.__doc__ = Corr3.write.__doc__.format(
r"""
gam0r The real part of the estimator of :math:`\Gamma_0`
gam0i The imag part of the estimator of :math:`\Gamma_0`
gam1r The real part of the estimator of :math:`\Gamma_1`
gam1i The imag part of the estimator of :math:`\Gamma_1`
gam2r The real part of the estimator of :math:`\Gamma_2`
gam2i The imag part of the estimator of :math:`\Gamma_2`
gam3r The real part of the estimator of :math:`\Gamma_3`
gam3i The imag part of the estimator of :math:`\Gamma_3`
sigma_gam0 The sqrt of the variance estimate of :math:`\Gamma_0`
sigma_gam1 The sqrt of the variance estimate of :math:`\Gamma_1`
sigma_gam2 The sqrt of the variance estimate of :math:`\Gamma_2`
sigma_gam3 The sqrt of the variance estimate of :math:`\Gamma_3`
""")
# These properties just include the class-specific info.
@property
def _write_class_col_names(self):
return ['gam0r', 'gam0i', 'gam1r', 'gam1i',
'gam2r', 'gam2i', 'gam3r', 'gam3i',
'sigma_gam0', 'sigma_gam1', 'sigma_gam2', 'sigma_gam3']
@property
def _write_class_data(self):
return [self.gam0r, self.gam0i, self.gam1r, self.gam1i,
self.gam2r, self.gam2i, self.gam3r, self.gam3i,
np.sqrt(self.vargam0), np.sqrt(self.vargam1),
np.sqrt(self.vargam2), np.sqrt(self.vargam3) ]
def _read_from_data(self, data, params):
super()._read_from_data(data, params)
s = self.data_shape
self._z[0] = data['gam0r'].reshape(s)
self._z[1] = data['gam0i'].reshape(s)
self._z[2] = data['gam1r'].reshape(s)
self._z[3] = data['gam1i'].reshape(s)
self._z[4] = data['gam2r'].reshape(s)
self._z[5] = data['gam2i'].reshape(s)
self._z[6] = data['gam3r'].reshape(s)
self._z[7] = data['gam3i'].reshape(s)
vargam0 = data['sigma_gam0'].reshape(s)**2
vargam1 = data['sigma_gam1'].reshape(s)**2
vargam2 = data['sigma_gam2'].reshape(s)**2
vargam3 = data['sigma_gam3'].reshape(s)**2
self._varzeta = [vargam0, vargam1, vargam2, vargam3]
@classmethod
def _calculateT(cls, s, t, k1, k2, k3):
# First calculate q values:
q1 = (s+t)/3.
q2 = q1-t
q3 = q1-s
# |qi|^2 shows up a lot, so save these.
# The a stands for "absolute", and the ^2 part is implicit.
a1 = np.abs(q1)**2
a2 = np.abs(q2)**2
a3 = np.abs(q3)**2
a123 = a1*a2*a3
# These combinations also appear multiple times.
# The b doesn't stand for anything. It's just the next letter after a.
b1 = np.conjugate(q1)**2*q2*q3
b2 = np.conjugate(q2)**2*q1*q3
b3 = np.conjugate(q3)**2*q1*q2
if k1==1 and k2==1 and k3==1:
# Some factors we use multiple times
expfactor = -np.exp(-(a1 + a2 + a3)/2)
# JBJ Equation 51
# Note that we actually accumulate the Gammas with a different choice for
# alpha_i. We accumulate the shears relative to the q vectors, not relative to s.
# cf. JBJ Equation 41 and footnote 3. The upshot is that we multiply JBJ's formulae
# by (q1q2q3)^2 / |q1q2q3|^2 for T0 and (q1*q2q3)^2/|q1q2q3|^2 for T1.
# Then T0 becomes
# T0 = -(|q1 q2 q3|^2)/24 exp(-(|q1|^2+|q2|^2+|q3|^2)/2)
T0 = expfactor * a123 / 24
# JBJ Equation 52
# After the phase adjustment, T1 becomes:
# T1 = -[(|q1 q2 q3|^2)/24
# - (q1*^2 q2 q3)/9
# + (q1*^4 q2^2 q3^2 + 2 |q2 q3|^2 q1*^2 q2 q3)/(|q1 q2 q3|^2)/27
# ] exp(-(|q1|^2+|q2|^2+|q3|^2)/2)
T1 = expfactor * (a123 / 24 - b1 / 9 + (b1**2 + 2*a2*a3*b1) / (a123 * 27))
T2 = expfactor * (a123 / 24 - b2 / 9 + (b2**2 + 2*a1*a3*b2) / (a123 * 27))
T3 = expfactor * (a123 / 24 - b3 / 9 + (b3**2 + 2*a1*a2*b3) / (a123 * 27))
else:
# SKL Equation 63:
k1sq = k1*k1
k2sq = k2*k2
k3sq = k3*k3
Theta2 = ((k1sq*k2sq + k1sq*k3sq + k2sq*k3sq)/3.)**0.5
k1sq /= Theta2 # These are now what SKL calls theta_i^2 / Theta^2
k2sq /= Theta2
k3sq /= Theta2
Theta4 = Theta2*Theta2
Theta6 = Theta4*Theta2
S = k1sq * k2sq * k3sq
# SKL Equation 64:
Z = ((2*k2sq + 2*k3sq - k1sq) * a1 +
(2*k3sq + 2*k1sq - k2sq) * a2 +
(2*k1sq + 2*k2sq - k3sq) * a3) / (6*Theta2)
expfactor = -S * np.exp(-Z) / Theta4
# SKL Equation 65:
f1 = (k2sq+k3sq)/2 + (k2sq-k3sq)*(q2-q3)/(6*q1)
f2 = (k3sq+k1sq)/2 + (k3sq-k1sq)*(q3-q1)/(6*q2)
f3 = (k1sq+k2sq)/2 + (k1sq-k2sq)*(q1-q2)/(6*q3)
f1c = np.conjugate(f1)
f2c = np.conjugate(f2)
f3c = np.conjugate(f3)
# SKL Equation 69:
g1 = k2sq*k3sq + (k3sq-k2sq)*k1sq*(q2-q3)/(3*q1)
g2 = k3sq*k1sq + (k1sq-k3sq)*k2sq*(q3-q1)/(3*q2)
g3 = k1sq*k2sq + (k2sq-k1sq)*k3sq*(q1-q2)/(3*q3)
g1c = np.conjugate(g1)
g2c = np.conjugate(g2)
g3c = np.conjugate(g3)
# SKL Equation 62:
T0 = expfactor * a123 * f1c**2 * f2c**2 * f3c**2 / (24.*Theta6)
# SKL Equation 68:
T1 = expfactor * (
a123 * f1**2 * f2c**2 * f3c**2 / (24*Theta6) -
b1 * f1*f2c*f3c*g1c / (9*Theta4) +
(b1**2 * g1c**2 + 2*k2sq*k3sq*a2*a3*b1 * f2c * f3c) / (a123 * 27*Theta2))
T2 = expfactor * (
a123 * f1c**2 * f2**2 * f3c**2 / (24*Theta6) -
b2 * f1c*f2*f3c*g2c / (9*Theta4) +
(b2**2 * g2c**2 + 2*k1sq*k3sq*a1*a3*b2 * f1c * f3c) / (a123 * 27*Theta2))
T3 = expfactor * (
a123 * f1c**2 * f2c**2 * f3**2 / (24*Theta6) -
b3 * f1c*f2c*f3*g3c / (9*Theta4) +
(b3**2 * g3c**2 + 2*k1sq*k2sq*a1*a2*b3 * f1c * f2c) / (a123 * 27*Theta2))
return T0, T1, T2, T3
[docs] def calculateMap3(self, *, R=None, k2=1, k3=1):
r"""Calculate the skewness of the aperture mass from the correlation function.
The equations for this come from Jarvis, Bernstein & Jain (2004, MNRAS, 352).
See their section 3, especially equations 51 and 52 for the :math:`T_i` functions,
equations 60 and 61 for the calculation of :math:`\langle \cal M^3 \rangle` and
:math:`\langle \cal M^2 M^* \rangle`, and equations 55-58 for how to convert
these to the return values.
If k2 or k3 != 1, then this routine calculates the generalization of the skewness
proposed by Schneider, Kilbinger & Lombardi (2005, A&A, 431):
:math:`\langle M_{ap}^3(R, k_2 R, k_3 R)\rangle` and related values.
If k2 = k3 = 1 (the default), then there are only 4 combinations of Map and Mx
that are relevant:
- map3 = :math:`\langle M_{ap}^3(R)\rangle`
- map2mx = :math:`\langle M_{ap}^2(R) M_\times(R)\rangle`,
- mapmx2 = :math:`\langle M_{ap}(R) M_\times(R)\rangle`
- mx3 = :math:`\langle M_{\rm \times}^3(R)\rangle`
However, if k2 or k3 != 1, then there are 8 combinations:
- map3 = :math:`\langle M_{ap}(R) M_{ap}(k_2 R) M_{ap}(k_3 R)\rangle`
- mapmapmx = :math:`\langle M_{ap}(R) M_{ap}(k_2 R) M_\times(k_3 R)\rangle`
- mapmxmap = :math:`\langle M_{ap}(R) M_\times(k_2 R) M_{ap}(k_3 R)\rangle`
- mxmapmap = :math:`\langle M_\times(R) M_{ap}(k_2 R) M_{ap}(k_3 R)\rangle`
- mxmxmap = :math:`\langle M_\times(R) M_\times(k_2 R) M_{ap}(k_3 R)\rangle`
- mxmapmx = :math:`\langle M_\times(R) M_{ap}(k_2 R) M_\times(k_3 R)\rangle`
- mapmxmx = :math:`\langle M_{ap}(R) M_\times(k_2 R) M_\times(k_3 R)\rangle`
- mx3 = :math:`\langle M_\times(R) M_\times(k_2 R) M_\times(k_3 R)\rangle`
To accommodate this full generality, we always return all 8 values, along with the
estimated variance (which is equal for each), even when k2 = k3 = 1.
.. note::
The formulae for the ``m2_uform`` = 'Schneider' definition of the aperture mass,
described in the documentation of `calculateMapSq`, are not known, so that is not an
option here. The calculations here use the definition that corresponds to
``m2_uform`` = 'Crittenden'.
Parameters:
R (array): The R values at which to calculate the aperture mass statistics.
(default: None, which means use self.rnom1d)
k2 (float): If given, the ratio R2/R1 in the SKL formulae. (default: 1)
k3 (float): If given, the ratio R3/R1 in the SKL formulae. (default: 1)
Returns:
Tuple containing:
- map3 = array of :math:`\langle M_{ap}(R) M_{ap}(k_2 R) M_{ap}(k_3 R)\rangle`
- mapmapmx = array of :math:`\langle M_{ap}(R) M_{ap}(k_2 R) M_\times(k_3 R)\rangle`
- mapmxmap = array of :math:`\langle M_{ap}(R) M_\times(k_2 R) M_{ap}(k_3 R)\rangle`
- mxmapmap = array of :math:`\langle M_\times(R) M_{ap}(k_2 R) M_{ap}(k_3 R)\rangle`
- mxmxmap = array of :math:`\langle M_\times(R) M_\times(k_2 R) M_{ap}(k_3 R)\rangle`
- mxmapmx = array of :math:`\langle M_\times(R) M_{ap}(k_2 R) M_\times(k_3 R)\rangle`
- mapmxmx = array of :math:`\langle M_{ap}(R) M_\times(k_2 R) M_\times(k_3 R)\rangle`
- mx3 = array of :math:`\langle M_\times(R) M_\times(k_2 R) M_\times(k_3 R)\rangle`
- varmap3 = array of variance estimates of the above values
"""
# As in the calculateMapSq function, we Make s and t matrices, so we can eventually do the
# integral by doing a matrix product.
if R is None:
R = self.rnom1d
else:
R = np.asarray(R)
# Pick s = d2, so dlogs is bin_size
s = d2 = np.outer(1./R, self.meand2.ravel())
if self.bin_type == 'LogRUV':
# We take t = d3, but we need the x and y components. (relative to s along x axis)
# cf. Figure 1 in JBJ.
# d1^2 = d2^2 + d3^2 - 2 d2 d3 cos(theta1)
# tx = d3 cos(theta1) = (d2^2 + d3^2 - d1^2)/2d2
# Simplify this using u=d3/d2 and v=(d1-d2)/d3
# = (d3^2 - (d1+d2)(d1-d2)) / 2d2
# = d3 (d3 - (d1+d2)v) / 2d2
# = d3 (u - (2+uv)v)/2
# = d3 (u - 2v - uv^2)/2
# = d3 (u(1-v^2)/2 - v)
# Note that v here is really |v|. We'll account for the sign of v in ty.
d3 = np.outer(1./R, self.meand3.ravel())
d1 = np.outer(1./R, self.meand1.ravel())
u = self.meanu.ravel()
v = self.meanv.ravel()
tx = d3*(0.5*u*(1-v**2) - np.abs(v))
# This form tends to be more stable near potentially degenerate triangles
# than tx = (d2*d2 + d3*d3 - d1*d1) / (2*d2)
# However, add a check to make sure.
bad = (tx <= -d3) | (tx >= d3)
if np.any(bad): # pragma: no cover
self.logger.warning("Warning: Detected some invalid triangles when computing Map^3")
self.logger.warning("Excluding these triangles from the integral.")
self.logger.debug("N bad points = %s",np.sum(bad))
self.logger.debug("d1[bad] = %s",d1[bad])
self.logger.debug("d2[bad] = %s",d2[bad])
self.logger.debug("d3[bad] = %s",d3[bad])
self.logger.debug("tx[bad] = %s",tx[bad])
bad = np.where(bad)
tx[bad] = 0 # for now to avoid nans
ty = np.sqrt(d3**2 - tx**2)
ty[:,self.meanv.ravel() > 0] *= -1.
t = tx + 1j * ty
else:
d3 = np.outer(1./R, self.meand3.ravel())
t = d3 * np.exp(1j * self.meanphi.ravel() * self._phi_units)
# Next we need to construct the T values.
T0, T1, T2, T3 = self._calculateT(s,t,1.,k2,k3)
if self.bin_type == 'LogRUV':
# Finally, account for the Jacobian in d^2t: jac = |J(tx, ty; u, v)|,
# since our Gammas are accumulated in s, u, v, not s, tx, ty.
# u = d3/d2, v = (d1-d2)/d3
# tx = d3 (u - 2v - uv^2)/2
# = s/2 (u^2 - 2uv - u^2v^2)
# dtx/du = s (u - v - uv^2)
# dtx/dv = -us (1 + uv)
# ty = sqrt(d3^2 - tx^2) = sqrt(u^2 s^2 - tx^2)
# dty/du = s^2 u/2ty (1-v^2) (2 + 3uv - u^2 + u^2v^2)
# dty/dv = s^2 u^2/2ty (1 + uv) (u - uv^2 - 2uv)
#
# After some algebra...
#
# J = s^3 u^2 (1+uv) / ty
# = d3^2 d1 / ty
#
jac = np.abs(d3*d3*d1/ty)
jac[bad] = 0. # Exclude any bad triangles from the integral.
d2t = jac * self.ubin_size * self.vbin_size / (2.*np.pi)
else:
# In SAS binning, d2t is easier.
# We bin directly in ln(d3) and phi, so
# tx = d3 cos(phi)
# ty = d3 sin(phi)
# dtx/dlnd3 = d3 dtx/dd3 = d3 cos(phi)
# dty/dlnd3 = d3 dty/dd3 = d3 sin(phi)
# dtx/dphi = -d3 sin(phi)
# dty/dphi = d3 cos(phi)
# J(tx,ty; lnd3, phi) = d3^2
d2t = d3**2 * self.bin_size * self.phi_bin_size / (2*np.pi)
sds = s * s * self.bin_size # Remember bin_size is dln(s)
# Note: these are really d2t/2piR^2 and sds/R^2, which are what actually show up
# in JBJ equations 45 and 50.
T0 *= sds * d2t
T1 *= sds * d2t
T2 *= sds * d2t
T3 *= sds * d2t
# Now do the integral by taking the matrix products.
gam0 = self.gam0.ravel()
gam1 = self.gam1.ravel()
gam2 = self.gam2.ravel()
gam3 = self.gam3.ravel()
vargam0 = self.vargam0.ravel()
vargam1 = self.vargam1.ravel()
vargam2 = self.vargam2.ravel()
vargam3 = self.vargam3.ravel()
mmm = T0.dot(gam0)
mcmm = T1.dot(gam1)
mmcm = T2.dot(gam2)
mmmc = T3.dot(gam3)
# These accumulate the coefficients that are being dotted to gam0,1,2,3 respectively.
# Below, we will take the abs^2 and dot it to gam0,1,2,3 in each case to compute the
# total variance.
# Note: This assumes that gam0, gam1, gam2, gam3 have no covariance.
# This is not technically true, but I think it's approximately ok.
var0 = T0.copy()
var1 = T1.copy()
var2 = T2.copy()
var3 = T3.copy()
if self.bin_type == 'LogRUV':
if k2 == 1 and k3 == 1:
mmm *= 6
mcmm += mmcm
mcmm += mmmc
mcmm *= 2
mmcm = mmmc = mcmm
var0 *= 6
var1 *= 6
var2 *= 6
var3 *= 6
else:
# Repeat the above for the other permutations
for (_k1, _k2, _k3, _mcmm, _mmcm, _mmmc) in [
(1,k3,k2,mcmm,mmmc,mmcm),
(k2,1,k3,mmcm,mcmm,mmmc),
(k2,k3,1,mmcm,mmmc,mcmm),
(k3,1,k2,mmmc,mcmm,mmcm),
(k3,k2,1,mmmc,mmcm,mcmm) ]:
T0, T1, T2, T3 = self._calculateT(s,t,_k1,_k2,_k3)
T0 *= sds * d2t
T1 *= sds * d2t
T2 *= sds * d2t
T3 *= sds * d2t
# Relies on numpy array overloading += to actually update in place.
mmm += T0.dot(gam0)
_mcmm += T1.dot(gam1)
_mmcm += T2.dot(gam2)
_mmmc += T3.dot(gam3)
var0 += T0
var1 += T1
var2 += T2
var3 += T3
else:
# SAS binning counts each triangle with each vertex in the c1 position.
# Just need to account for the cases where 1-2-3 are clockwise, rather than CCW.
if k2 == 1 and k3 == 1:
mmm *= 2
mcmm *= 2
mmcm += mmmc
mmmc = mmcm
var0 *= 2
var1 *= 2
var2 *= 2
var3 *= 2
else:
# Repeat the above with 2,3 swapped.
T0, T1, T2, T3 = self._calculateT(s,t,1,k3,k2)
T0 *= sds * d2t
T1 *= sds * d2t
T2 *= sds * d2t
T3 *= sds * d2t
mmm += T0.dot(gam0)
mcmm += T1.dot(gam1)
mmmc += T2.dot(gam2)
mmcm += T3.dot(gam3)
var0 += T0
var1 += T1
var2 += T2
var3 += T3
map3 = 0.25 * np.real(mcmm + mmcm + mmmc + mmm)
mapmapmx = 0.25 * np.imag(mcmm + mmcm - mmmc + mmm)
mapmxmap = 0.25 * np.imag(mcmm - mmcm + mmmc + mmm)
mxmapmap = 0.25 * np.imag(-mcmm + mmcm + mmmc + mmm)
mxmxmap = 0.25 * np.real(mcmm + mmcm - mmmc - mmm)
mxmapmx = 0.25 * np.real(mcmm - mmcm + mmmc - mmm)
mapmxmx = 0.25 * np.real(-mcmm + mmcm + mmmc - mmm)
mx3 = 0.25 * np.imag(mcmm + mmcm + mmmc - mmm)
var0 /= 4
var1 /= 4
var2 /= 4
var3 /= 4
# Now finally add up the coefficient squared times each vargam element.
var = np.abs(var0**2).dot(vargam0)
var += np.abs(var1**2).dot(vargam1)
var += np.abs(var2**2).dot(vargam2)
var += np.abs(var3**2).dot(vargam3)
return map3, mapmapmx, mapmxmap, mxmapmap, mxmxmap, mxmapmx, mapmxmx, mx3, var
[docs] def writeMap3(self, file_name, *, R=None, file_type=None, precision=None):
r"""Write the aperture mass skewness based on the correlation function to the
file, file_name.
The output file will include the following columns:
========== ==========================================================
Column Description
========== ==========================================================
R The aperture radius
Map3 An estimate of :math:`\langle M_{ap}^3\rangle(R)`
(cf. `calculateMap3`)
Map2Mx An estimate of :math:`\langle M_{ap}^2 M_\times\rangle(R)`
MapMx2 An estimate of :math:`\langle M_{ap} M_\times^2\rangle(R)`
Mx3 An estimate of :math:`\langle M_\times^3\rangle(R)`
sig_map The sqrt of the variance estimate of each of these
========== ==========================================================
Parameters:
file_name (str): The name of the file to write to.
R (array): The R values at which to calculate the statistics.
(default: None, which means use self.rnom)
file_type (str): The type of file to write ('ASCII' or 'FITS'). (default: determine
the type automatically from the extension of file_name.)
precision (int): For ASCII output catalogs, the desired precision. (default: 4;
this value can also be given in the constructor in the config dict.)
"""
self.logger.info('Writing Map^3 from GGG correlations to %s',file_name)
if R is None:
R = self.rnom1d
stats = self.calculateMap3(R=R)
if precision is None:
precision = self.config.get('precision', 4)
col_names = ['R','Map3','Map2Mx', 'MapMx2', 'Mx3','sig_map']
columns = [ R, stats[0], stats[1], stats[4], stats[7], np.sqrt(stats[8]) ]
with make_writer(file_name, precision, file_type, logger=self.logger) as writer:
writer.write(col_names, columns)