issue/591/triaxiality: Build scripts in examples/triaxiality

README.md

@@ -1,4 +1,3 @@
-
 # CLMM
 [![Build and Check](https://github.com/LSSTDESC/CLMM/workflows/Build%20and%20Check/badge.svg)](https://github.com/LSSTDESC/CLMM/actions?query=workflow%3A%22Build+and+Check%22)
 [![Coverage Status](https://coveralls.io/repos/github/LSSTDESC/CLMM/badge.svg?branch=main)](https://coveralls.io/github/LSSTDESC/CLMM?branch=main)
@@ -110,6 +109,7 @@ the `CCL` publication be cited.  See details
 The `Cluster Toolkit` documentation can be found
 [here](https://cluster-toolkit.readthedocs.io/en/latest/#).
 
+The data for the notebook test_coordinate.ipynb is available at https://www.dropbox.com/scl/fo/dwsccslr5iwb7lnkf8jvx/AJkjgFeemUEHpHaZaHHqpAg?rlkey=efbtsr15mdrs3y6xsm7l48o0r&st=xb58ap0g&dl=0
 
 # Contributing to CLMM <a name="contributing"></a>
 

clmm/__init__.py

@@ -24,6 +24,12 @@
     Modeling,
     Cosmology,
 )
+from .theory.func_layer import (
+    compute_delta_sigma_4theta_triaxiality,
+    compute_delta_sigma_const_triaxiality,
+    compute_delta_sigma_excess_triaxiality,
+)
+
 from . import support
 
 __version__ = "1.12.5"

clmm/dataops/__init__.py

@@ -3,6 +3,7 @@
 import warnings
 import numpy as np
 import scipy
+from scipy.stats import binned_statistic
 from astropy.coordinates import SkyCoord
 from astropy import units as u
 from ..gcdata import GCData
@@ -15,6 +16,7 @@
     _validate_ra,
     _validate_dec,
     _validate_is_deltasigma_sigma_c,
+    _validate_include_quadrupole_phi_major,
     _validate_coordinate_system,
 )
 from ..redshift import (
@@ -35,6 +37,9 @@ def compute_tangential_and_cross_components(
     geometry="curve",
     is_deltasigma=False,
     sigma_c=None,
+    include_quadrupole=False,
+    phi_major=None,
+    info_mem=None,
     validate_input=True,
 ):
     r"""Computes tangential- and cross- components for shear or ellipticity
@@ -74,6 +79,14 @@ def compute_tangential_and_cross_components(
         g_t =& -\left( g_1\cos\left(2\phi\right)+g_2\sin\left(2\phi\right)\right)\\
         g_x =& g_1 \sin\left(2\phi\right)-g_2\cos\left(2\phi\right)
 
+    The quadrupole ellipticity/shear components, :math:`g_4theta' and :math:`g_const', 
+    are also calculated using the two ellipticity/shear components :math:`g_1' and :math:`g_2' 
+    of the source galaxies, following Eq.31 and Eq.34 in Shin et al. (2018), arXiv:1705.11167. 
+
+    .. math::
+        g_4theta =& \left( g_1\cos\left(4\phi\right)+g_2\sin\left(4\phi\right)\right)\\
+        g_const =& g_1
+
     Finally, if  the critical surface density (:math:`\Sigma_\text{crit}`) is provided, an estimate
     of the excess surface density :math:`\widehat{\Delta\Sigma}` is obtained from
 
@@ -111,6 +124,20 @@ def compute_tangential_and_cross_components(
     sigma_c : None, array_like
         Critical (effective) surface density in units of :math:`M_\odot\ Mpc^{-2}`.
         Used only when is_deltasigma=True.
+    include_quadrupole: bool
+        If `True`, the quadrupole shear components (g_4theta, g_const; Shin+2018) are calculated
+        instead of g_t and g_x
+    phi_major : float, optional
+        the direction of the major axis of the input cluster in the unit of radian. 
+        only needed when `include_quadrupole` is `True`.
+        Users could choose to provide ra_mem, dec_mem and weight_mem instead of this quantity.
+    info_mem : list of array, optional
+        RAs, DECs and weights of the member galaxies of the input cluster,
+        to calcualte the direction of the major axis of the cluster.
+        Only needed when `include_quadrupole` is `True` and `phi_major` is not provided.
+        The shape must be in `[ra_mem,dec_mem,weight_mem]`, where each element is an array.
+        The weights could be `1` (no weights) or 
+        `membership probability (p_mem)` or any user choice. 
     validate_input: bool
         Validade each input argument
 
@@ -122,6 +149,11 @@ def compute_tangential_and_cross_components(
         Tangential shear (or assimilated quantity) for each source galaxy
     cross_component: array_like
         Cross shear (or assimilated quantity) for each source galaxy
+    IF include_quadrupole:
+        4theta_component: array_like
+            4theta shear component (or assimilated quantity) for each source galaxy
+        const_component: array_like
+            constant shear component (or assimilated quantity) for each source galaxy
     """
     # pylint: disable-msg=too-many-locals
     # Note: we make these quantities to be np.array so that a name is not passed from astropy
@@ -134,6 +166,8 @@ def compute_tangential_and_cross_components(
         validate_argument(locals(), "shear1", "float_array")
         validate_argument(locals(), "shear2", "float_array")
         validate_argument(locals(), "geometry", str)
+        validate_argument(locals(), "is_deltasigma", bool)
+        validate_argument(locals(), "include_quadrupole", bool)
         validate_argument(locals(), "sigma_c", "float_array", none_ok=True)
         _validate_coordinate_system(locals(), "coordinate_system", str)
         ra_source_, dec_source_, shear1_, shear2_ = arguments_consistency(
@@ -142,6 +176,9 @@ def compute_tangential_and_cross_components(
             prefix="Tangential- and Cross- shape components sources",
         )
         _validate_is_deltasigma_sigma_c(is_deltasigma, sigma_c)
+        _validate_include_quadrupole_phi_major(include_quadrupole, phi_major, info_mem)
+        validate_argument(locals(), "phi_major", float, none_ok=True)
+        validate_argument(locals(), "info_mem", list, none_ok=True)
     elif np.iterable(ra_source):
         ra_source_, dec_source_, shear1_, shear2_ = (
             np.array(col) for col in [ra_source, dec_source, shear1, shear2]
@@ -167,12 +204,32 @@ def compute_tangential_and_cross_components(
     # Compute the tangential and cross shears
     tangential_comp = _compute_tangential_shear(shear1_, shear2_, phi)
     cross_comp = _compute_cross_shear(shear1_, shear2_, phi)
-
+    # If the is_deltasigma flag is True, multiply the results by Sigma_crit.
     if sigma_c is not None:
         _sigma_c_arr = np.array(sigma_c)
         tangential_comp *= _sigma_c_arr
         cross_comp *= _sigma_c_arr
 
+    if include_quadrupole:
+        if (phi_major is None) and (info_mem is None):
+            raise ValueError("Either phi_major or (ra_mem, dec_mem, weight_mem) should be provided")
+        phi_major_ = phi_major
+        if phi_major_ is None:
+            # info_mem=[ra_mem,dec_mem,weight_mem]
+            phi_major_ = _calculate_major_axis(
+                ra_lens, dec_lens, info_mem[0], info_mem[1], info_mem[2]
+            )
+        rotated_phi = phi - phi_major_
+        rotated_shear1, rotated_shear2 = _rotate_shear(shear1_, shear2_, phi_major_)
+        # Compute the quadrupole shear components
+        four_theta_comp = _compute_4theta_shear(rotated_shear1, rotated_shear2, rotated_phi)
+        const_comp = rotated_shear1
+        # If the is_deltasigma flag is True, multiply the results by Sigma_crit.
+        if sigma_c is not None:
+            four_theta_comp *= _sigma_c_arr
+            const_comp *= _sigma_c_arr
+    if include_quadrupole:
+        return angsep, tangential_comp, cross_comp, four_theta_comp, const_comp
     return angsep, tangential_comp, cross_comp
 
 
@@ -445,6 +502,51 @@ def _compute_lensing_angles_astropy(
     return angsep, phi
 
 
+def _calculate_major_axis(ra_lens_, dec_lens_, ra_mem_, dec_mem_, weight_mem_):
+    r"""Compute the major axis of a given cluster from the distribution of
+    its member galaxies using the position second moments.
+
+    The computation is done according to Eq. 5-10 of Shin et al. 2018, arXiv:1705.11167
+
+    Current implementation assumes the +RA direction is aligned with +x direction.
+
+    For extended descriptions of parameters, see `compute_shear()` documentation.
+    """
+    ind_bcg = (np.array(ra_mem_) == ra_lens_) * (np.array(dec_mem_) == dec_lens_)
+    sk_lens = SkyCoord(ra_lens_ * u.deg, dec_lens_ * u.deg, frame="icrs")
+    sk_mem = SkyCoord(
+        np.array(ra_mem_)[~ind_bcg] * u.deg, np.array(dec_mem_)[~ind_bcg] * u.deg, frame="icrs"
+    )
+    position_angle_mem = np.array(sk_lens.position_angle(sk_mem).radian + np.pi / 2.0)
+    separation_mem = np.array(sk_lens.separation(sk_mem).degree)
+    x_mem = separation_mem * np.cos(position_angle_mem)
+    y_mem = separation_mem * np.sin(position_angle_mem)
+    distance_weight_mem = 1.0 / (separation_mem**2)
+    weight_total_mem = np.array(weight_mem_) * distance_weight_mem
+    sum_weight_total_mem = np.sum(weight_total_mem)
+    # Calcualte second moments of the member galaxies
+    ixx = np.sum(x_mem**2 * weight_total_mem) / sum_weight_total_mem
+    iyy = np.sum(y_mem**2 * weight_total_mem) / sum_weight_total_mem
+    ixy = np.sum(x_mem * y_mem * weight_total_mem) / sum_weight_total_mem
+    # Transformation of the second moments to the direction of the major axis
+    phi_major = np.arctan2(2.0 * ixy, ixx - iyy) / 2.0
+    return phi_major
+
+
+def _rotate_shear(shear1, shear2, phi_major):
+    r"""Rotate shear components into the coordinate where +x axis is aligned with
+    the cluster major axis.
+
+    .. math::
+        g_rotated = g * \exp\left(-2i\phi\right)
+
+    For extended descriptions of parameters, see `compute_shear()` documentation.
+    """
+    shear_vec = shear1 + shear2 * 1.0j
+    rotated_shear_vec = shear_vec * np.exp(-2.0j * phi_major)
+    return np.real(rotated_shear_vec), np.imag(rotated_shear_vec)
+
+
 def _compute_tangential_shear(shear1, shear2, phi):
     r"""Compute the tangential shear given the two shears and azimuthal positions for
     a single source or list of sources.
@@ -474,6 +576,25 @@ def _compute_cross_shear(shear1, shear2, phi):
     return shear1 * np.sin(2.0 * phi) - shear2 * np.cos(2.0 * phi)
 
 
+def _compute_4theta_shear(shear1, shear2, phi):
+    r"""Compute the 4theta component of the quadrupole shear given the two shear components and
+    azimuthal positions for a single source or list of sources.
+
+    We compute the tangential shear following Eq. 31 of Shin et al. 2018, arXiv:1705.11167
+
+    .. math::
+        g_4theta = g_1\cos\left(4\phi\right)+g_2\sin\left(4\phi\right)
+
+    Note that here `\phi` is the position angle of the source galaxies
+    with respect to the major axis of the cluster.
+    Also, `shear1` and `shear2` are measured in the coordinate where
+    the +x axis is aligned with the major axis of the cluster.
+
+    For extended descriptions of parameters, see `compute_shear()' documentation.
+    """
+    return shear1 * np.cos(4.0 * phi) + shear2 * np.sin(4.0 * phi)
+
+
 def make_radial_profile(
     components,
     angsep,
@@ -613,7 +734,7 @@ def make_stacked_radial_profile(angsep, weights, components):
     Parameters
     ----------
     angsep: 2d array
-        Transvesal distances corresponding to each object with shape `n_obj, n_rad_bins`.
+        Transversal distances corresponding to each object with shape `n_obj, n_rad_bins`.
     weights: 2d array
         Weights corresponding to each objects with shape `n_obj, n_rad_bins`.
     components: list of 2d arrays