clmm.utils.ellipticity module

General utility functions that are used in multiple modules

clmm.utils.ellipticity.build_ellipticities(q11, q22, q12)[source]

Build ellipticties from second moments. See, e.g., Schneider et al. (2006)

Parameters:

  • q11 (float, numpy.ndarray) -- Second brightness moment tensor, component (1,1)

  • q22 (float, numpy.ndarray) -- Second brightness moment tensor, component (2,2)

  • q12 (float, numpy.ndarray) -- Second brightness moment tensor, component (1,2)

Returns:

  • chi1, chi2 (float, numpy.ndarray) -- Ellipticities using the "chi definition"

  • epsilon1, epsilon2 (float, numpy.ndarray) -- Ellipticities using the "epsilon definition"

clmm.utils.ellipticity.compute_lensed_ellipticity(ellipticity1_true, ellipticity2_true, shear1, shear2, convergence)[source]

Compute lensed ellipticities from the intrinsic ellipticities, shear and convergence. Following Schneider et al. (2006)

\[\epsilon^{\text{lensed}}=\epsilon^{\text{lensed}}_1+i\epsilon^{\text{lensed}}_2= \frac{\epsilon^{\text{true}}+g}{1+g^\ast\epsilon^{\text{true}}},\]

where, the complex reduced shear \(g\) is obtained from the shear \(\gamma=\gamma_1+i\gamma_2\) and convergence \(\kappa\) as \(g = \gamma/(1-\kappa)\), and the complex intrinsic ellipticity is \(\epsilon^{\text{ true}}=\epsilon^{\text{true}}_1+i\epsilon^{\text{true}}_2\)

Parameters:

  • ellipticity1_true (float, numpy.ndarray) -- Intrinsic ellipticity of the sources along the principal axis

  • ellipticity2_true (float, numpy.ndarray) -- Intrinsic ellipticity of the sources along the second axis

  • shear1 (float, numpy.ndarray) -- Shear component (not reduced shear) along the principal axis at the source location

  • shear2 (float, numpy.ndarray) -- Shear component (not reduced shear) along the 45-degree axis at the source location

  • convergence (float, numpy.ndarray) -- Convergence at the source location

Returns:

e1, e2 -- Lensed ellipicity along both reference axes.

Return type:

float, numpy.ndarray

clmm.utils.ellipticity.convert_shapes_to_epsilon(shape_1, shape_2, shape_definition='epsilon', kappa=0)[source]

Convert shape components 1 and 2 appropriately to make them estimators of the reduced shear once averaged. The shape 1 and 2 components may correspond to ellipticities according the \(\epsilon\)- or \(\chi\)-definition, but also to the 1 and 2 components of the shear. See Bartelmann & Schneider 2001 for details (https://arxiv.org/pdf/astro-ph/9912508.pdf).

The \(\epsilon\)-ellipticity is a direct estimator of the reduced shear. The shear \(\gamma\) may be converted to reduced shear \(g\) if the convergence \(\kappa\) is known. The conversions are given below.

\[\epsilon = \frac{\chi}{1+(1-|\chi|^2)^{1/2}}\]
\[g=\frac{\gamma}{1-\kappa}\]

  • If shape_definition = 'chi', this function returns the corresponding epsilon ellipticities

  • If shape_definition = 'shear', it returns the corresponding reduced shear, given the convergence kappa

  • If shape_definition = 'epsilon' or 'reduced_shear', it returns them as is as no conversion is needed.

Parameters:

  • shape_1 (float, numpy.ndarray) -- Input shapes or shears along principal axis (g1 or e1)

  • shape_2 (float, numpy.ndarray) -- Input shapes or shears along secondary axis (g2 or e2)

  • shape_definition (str, optional) -- Definition of the input shapes, can be ellipticities 'epsilon' or 'chi' or shears 'shear' or 'reduced_shear'. Defaut: 'epsilon'

  • kappa (float, numpy.ndarray, optional) -- Convergence for transforming to a reduced shear. Default is 0

Returns:

  • epsilon_1 (float, numpy.ndarray) -- Epsilon ellipticity (or reduced shear) along principal axis (epsilon1)

  • epsilon_2 (float, numpy.ndarray) -- Epsilon ellipticity (or reduced shear) along secondary axis (epsilon2)