tjpcov.wigner_transform ======================= .. py:module:: tjpcov.wigner_transform Classes ------- .. autoapisummary:: tjpcov.wigner_transform.WignerTransform Functions --------- .. autoapisummary:: tjpcov.wigner_transform.wigner_d tjpcov.wigner_transform.wigner_d_parallel tjpcov.wigner_transform.bin_cov Module Contents --------------- .. py:class:: WignerTransform(theta, ell, s1_s2, ncpu=None) Class to compute curved sky Hankel transforms with wigner-d matrices. Initialize the class for the given angles, scales and spins. :param theta: Values of angular separation, theta, at which the Hankel transform is done. Should be in radians. :param ell: ell values at which the Hankel transform is done. Should be integers :param s1_s2: List of spin pairs of the tracers. Each spin pair should be a tuple. e.g. for 3X2 analysis, pass [(0,0),(0,2),(2,2),(2,-2)]. (0,0): (galaxy,galaxy) (0,2): (galaxy,shear). (2,0) is equivalent. (2,2): (shear,shear), xi+ (2,-2): (shear,shear), xi- :param ncpu: Number of python processes to use when computing wigner-d matrices. .. py:attribute:: name :value: 'Wigner' .. py:attribute:: ell .. py:attribute:: grad_ell .. py:attribute:: norm .. py:attribute:: grad_theta .. py:attribute:: inv_norm .. py:attribute:: inv_wig_norm .. py:attribute:: wig_d .. py:attribute:: wig_3j .. py:attribute:: s1_s2s .. py:attribute:: theta .. py:attribute:: taper_f :value: None .. py:attribute:: taper_f2 :value: None .. py:method:: cl_grid(ell_cl, cl, taper=False, **taper_kwargs) Interpolate the input C_ell. This is done in case the ell values of C_ell are different from the grid on which wigner-d matrices were computed during intialization. :param ell_cl: ell at which the input C_ell is computed. :type ell_cl: array :param cl: input C_ell :type cl: array :param taper: if True apply the tapering to the input C_ell. Tapering can help in reducing ringing. :type taper: bool :returns: C_ell evaluated at the initialization ells. :rtype: array .. py:method:: cl_cov_grid(ell_cl, cl_cov, taper=False, **taper_kwargs) Interpolate the input 2D covariances. This is done in case in case the ell values are different from the grid on which wigner-d matrices were computed during intialization. :param ell_cl: ell at which the input covariance was computed. :type ell_cl: array :param cl: input covariance :type cl: array :param taper: if True apply the tapering to the input C_ell. Tapering can help in reducing ringing. :type taper: bool :param \*\*taper_kwargs: Arguments to pass to the tapering method :returns: covariance evaluated at the initialization ells. :rtype: array .. py:method:: projected_covariance(ell_cl, cl_cov, s1_s2, s1_s2_cross=None, taper=False, **kwargs) Convert C_ell covariance to correlation function. This function assumes that cl_cov is 2D matrix. :param cl_cov: C_ell covariance matrix. :param ell_cl: ell values at which input C_ell is computed. :param s1_s2: Tuple of the spin factors of the first set of tracers. Used to identify the correct wigner-d matrix to use. :param s1_s2_cross: Tuple of the spin factors of the second set of tracers, if different from s1_s2. Used to identify the correct wigner-d matrix to use. :param taper: if True apply the tapering to the input C_ell. Tapering can help in reducing ringing. :type taper: bool :param \*\*kwargs: Arguments to pass to the tapering method :returns: - theta (array): angles given at initialization - cov (array): real space covariance at the given angles :rtype: tuple .. py:method:: taper(ell, large_k_lower=10, large_k_upper=100, low_k_lower=0, low_k_upper=1e-05) :abstractmethod: Apply tapering to input C_ell. Tapering is useful to reduce the ringing. This function uses the cosine function to apply the tapering. See eq. 71 in https://arxiv.org/pdf/2105.04548.pdf for the function and meaning of input parameters. :param ell: ell values at which input C_ell is computed. :param large_k_lower: :param large_k_upper: :param low_k_lower: :param low_k_upper: .. py:method:: diagonal_err(cov) Returns the diagonal error from the covariance. Useful for errorbar plots. :param cov: Covariance :type cov: array :returns: Diagonal errors (i.e. sqrt(diag(cov))) :rtype: array .. py:function:: wigner_d(s1, s2, theta, ell, l_use_bessel=10000.0) Function to compute the wigner-d matrices. :param s1: Spin factors for the wigner-d matrix. :param s2: Spin factors for the wigner-d matrix. :param theta: Angular separation for which to compute the wigner-d matrix. The matrix depends on cos(theta). :param ell: The spherical harmonics mode ell for which to compute the matrix. :param l_use_bessel: Due to numerical issues, we need to switch from wigner-d matrix to bessel functions at high ell (see the note below). This defines the scale at which the switch happens. :returns: Wigner-d matrix :rtype: array .. py:function:: wigner_d_parallel(s1, s2, theta, ell, ncpu=None, l_use_bessel=10000.0) Compute the wigner-d matrix in parallel using multiprocessing Pool. This function calls the wigner-d function defined above. :param s1: Spin factors for the wigner-d matrix. :param s2: Spin factors for the wigner-d matrix. :param theta: Angular separation for which to compute the wigner-d matrix. The matrix depends on cos(theta). :param ell: The spherical harmonics mode ell for which to compute the matrix. :param ncpu: number of processes to use for computing the matrix. :param l_use_bessel: Due to numerical issues, we need to switch from wigner-d matrix to bessel functions at high ell (see the note below). This defines the scale at which the switch happens. :returns: Wigner-d matrix :rtype: array .. py:function:: bin_cov(r, cov, r_bins) Function to apply the binning operator. This function works on both one dimensional vectors and two dimensional covariance covrices. :param r: theta or ell values at which the un-binned vector is computed. :param cov: Unbinned covariance. It also works for a vector of C_ell or xi :param r_bins: theta or ell bins to which the values should be binned. :returns: Binned covariance or vector of C_ell or xi :rtype: array_like