Skip to content

polymv Usage Guide

This guide demonstrates how to use the main features of the polymv package for working with multipole vectors.

Setup

Import the necessary libraries:

import numpy as np
import healpy as hp

from polymv import polymv
from polymv import utils

Generating Test Data

Let's create a test set of \(a_{\ell m}\)s:

lmax = 1500
np.random.seed(1)
alm = hp.synalm(np.ones(2000), lmax=lmax)
alm = np.column_stack([alm.real, alm.imag])
alm.shape

Output: 

(1127251, 2)

Multipole Vectors (mvs)

To obtain multipole vectors from \(\ell=2\) to \(\ell=1500\):

mvs_1500 = polymv.mvs(alm[:, 0], alm[:, 1], lmax)
np.vstack(mvs_1500).shape

Output: 

(2, 2251498)

You can view a sample of the multipole vectors:

np.vstack(mvs_1500)[:, :5]

Output: 

array([[ 1.83441666,  1.37302603,  1.30717599,  1.52087956,  1.62071309],
       [ 0.12767786,  1.33828394, -3.01391479,  0.19300013, -2.94859252]])

Utility Functions

Extracting Specific Multipole Vectors

Get multipole vectors for \(\ell=3\):

utils.get_mvs_from_many(np.vstack(mvs_1500).T, 2, lmax, 3)

Output: 

array([[ 2.73836992,  2.08191869],
       [ 1.52087956,  0.19300013],
       [ 1.62071309, -2.94859252],
       [ 2.34022757,  0.13144151],
       [ 0.40322273, -1.05967396],
       [ 0.80136509, -3.01015115]])

Convert to Cartesian Coordinates

Convert the multipole vectors to Cartesian coordinates:

cart_coords = utils.to_cart(np.vstack(mvs_1500).T)
cart_coords[:3]

Output: 

array([[ 0.95759438,  0.12293233, -0.26057752],
       [ 0.22593142,  0.95412221,  0.19648358],
       [-0.95759438, -0.12293233,  0.26057752]])

Filter for North Hemisphere

Get only vectors in the north hemisphere:

north_mvs = utils.mvs_north(np.vstack(mvs_1500).T)
north_mvs.shape

Output: 

(1125749, 2)

Fréchet Mean Vectors (fvs)

Compute Fréchet mean vectors for all multipoles:

fvs = polymv.fvs(mvs_1500[0], mvs_1500[1], lmax)
np.vstack(fvs).shape

Output: 

(2, 1498)

Show a sample:

np.vstack(fvs)[:, :5]

Output: 

array([[0.39372199, 1.30678037, 1.41442982, 1.18631234, 1.2620573 ],
       [5.54727987, 1.64990686, 0.53026658, 2.88028155, 0.76763323]])