Utils

This module contains a bunch of utility functions that may or may not be useful.

utils.flatten_mlm(wav_lm, scal_lm)

Takes a set of wavelet and scaling coefficients and flattens them into a single vector

Parameters

  • wav_lm – array of wavelet coefficients. Gets flattened if has multiple dimensions

  • scal_lm – array of wavelet coefficients

Returns

1D array of coefficients, with the scaling coefficients first

utils.expand_mlm(mlm, nscales=None, nscalcoefs=None, flatten_wavs=False)

Sepatates scaling and wavelet coefficients from a single vector to separate arrays.

Parameters

  • mlm – 1D array containing scaling and wavelet coefficients. Assumes the scaling coefficients come first followed by the wavelet coefficients at increasingly smaller scales.

  • nscales (int) – number of wavlet scales + 1 scaling function. Use only if coefficients do not follow the multiresolution algorithm, otherwise leave as None

  • nscalcoefs (int) – number of scaling function coefficients. Use only if coefficients follow the multiresolution algorithm, otherwise leave as None

  • flatten_wavs (bool) – flattens the wavelet coefficients into a 1D array, otherwise 2D. Ignored if nscalcoefs is not None.

Returns

tuple (wavelet coefficients, scaling coefficients)

utils.soft(X, T=0.1)

Soft thresholding of a vector X with threshold T. If \(X_i < T\), then \(\mathrm{soft}(X_i) = 0\), otherwise \(\mathrm{soft}(X_i) = X_i-T\).

Parameters

  • X – vector of values to threshold

  • T (float) – threshold. Can be a vector of same size as X

Returns

thresholded vector

utils.suppress_stdout()

Suppresses stdout from some healpy functions :meta private:

utils.chebyshev1(X, order)

Calculates the Chebyshev polynomial of the first kind of the given order at point X. Uses the recurrence relation

\(T_{k+1}(X) = 2XT_{k}(X) - T_{k-1}(X)\)

\(T_{1}(X) = X\)

\(T_{0}(X) = 1\)

Parameters

  • X – point at which to calulate \(T_{k+1}\)

  • order (int) – polynomial order

Returns

value of Chebyshev polynomial of the first kind of the given order

utils.chebyshev2(X, order)

Calculates the Chebyshev polynomial of the second kind of the given order at point X. Uses the recurrence relation

\(U_{k+1}(X) = 2XU_{k}(X) - U_{k-1}(X)\)

\(U_{1}(X) = 2X\)

\(U_{0}(X) = 1\)

Parameters

  • X – point at which to calulate \(U_{k+1}\)

  • order (int) – polynomial order

Returns

value of Chebyshev polynomial of the second kind of the given order

utils.cheb1der(X, order)

Evaluates the derivative of the Chebyshev polynomial of the first kind of the given order at point X. Uses the relation

\(dT_{n}/dx = nU_{n-1}\)

Parameters

  • X – point at which to calulate \(dT_{n}/dx\)

  • order (int) – polynomial order

Returns

derivative of Chebyshev polynomial of the second kind of the given order

utils.pixel_area(r, theta1, theta2, phi1, phi2)

Calculates area of a spherical rectangle. Angles must be given in radians.

Params float r

radius

Params float theta1

starting colatitude

Params float theta2

ending colatitude

Params float phi1

starting longitude

Params float phi2

ending longitude

Returns

area of rectangle in squared radians

utils.polar_cap_area(r, theta)

Calculates the area of a polar cap.

Params float r

radius

Params float theta

colatitude in radians of bottom of cap

Returns

area of polar cap in squared radians

utils.calc_pixel_areas(L, r=1)

Calculates the areas of all the pixels in MW <https://arxiv.org/abs/1110.6298> sampling.

Parameters

  • L (int) – bandlimit

  • r (float) – radius

Returns

array of pixel areas with shape \((L, 2L-1)\)

utils.mw_map_weights(L)

Calculates exact quadrature weights for MW <https://arxiv.org/abs/1110.6298> sampling.

Parameters

L (int) – bandlimit

Returns

1D array of quadrature weights with shape \((L(2L-1),)\)

utils.s2_integrate(f, L)

Integrates a spherical image over the whole sphere

Parameters

  • f (array) – spherical image as 1D array of shape \((L(2L-1),)\)

  • L (int) – bandlimit

Returns

integral of f over the sphere

Todo

Infer L from shape of f

utils.snr(signal, noise)

Calculates the signal to noise ratio

\(\mathrm{SNR} = 20\log_{10}\left(\frac{\|\mathrm{signal}\|_2}{\|\mathrm{noise}\|_2}\right)\)

Parameters

  • signal – signal array

  • noise – noise array

Returns

signal-to-noise ratio in decibels

utils.build_mask(L, size=20)

” Builds a mask for the galactic plane and ecliptic 0 at positions to be masked i.e. to apply mask do map * mask

size is the width of each mask in degrees

Mask in MW format