Measurements

Measurement operators operate on some image X to predict observations Y. Adjoints operate on measurements to return some image.

Note

We use the terms image and pixels in this documentation because the code was originally written for 2D imaging problems. In general, pixels should be taken to mean parameters in the space in which the measurement operator gets applied.

class measurements.Measurement(ndata, npix)

Base class.

Parameters

• ndata (int) – number of observed data points

• npix (int) – number of pixels in image

forward(X)

Forward modelling from image to observations. Implemented by user in custom child class.

Parameters

X – image

Returns

observations

adjoint(Y)

Adjoint modelling from observations to image. Not necessarily the inverse of self.forward(). Implemented by user in custom child class.

Parameters

Y – observations

Returns

image

class measurements.Identity(ndata, npix)

Identity measurement operator i.e. what goes in comes out.

class measurements.PathIntegral(path_matrix)

Path integration using a matrix that describes a set of paths.

Todo

Since this is just a matrix multiplication, can be renamed to something more generic.

Parameters

path_matrix – \(N_{\mathrm{paths}}\times N_{\mathrm{pix}}\) matrix describing a set of paths.

class measurements.WeakLensingHarmonic(L, mask=None, ngal=None)

Weak Gravitational Lensing spherical Forward model in spherical harmonic space

forward(klm)

Spherical weak lensing measurement operator

Args:

klm (complex array): Convergence signal in harmonic space

adjoint(glm)

Spherical weak lensing adjoint measurement operator

Args:

glm (complex array): Shear Observations in harmonic space

sks_estimate(glm)

Computes spherical Kaiser-Squires estimator (for first estimate)

Args:

glm (complex array): Shear Observations in harmonic space

compute_harmonic_kernel()

Compuptes harmonic space kernel mapping.

harmonic_mapping(flm)

Applys harmonic space mapping.

Args:

flm (complex array): harmonic coefficients.

harmonic_inverse_mapping(flm)

Applys harmonic space inverse mapping.

Args:

flm (complex array): harmonic coefficients.

class measurements.WeakLensing(L, mask=None, ngal=None)

Weak Gravitational Lensing spherical Forward model in pixel space

forward(kappa)

Spherical weak lensing measurement operator

Args:

kappa (complex array): Convergence signal

adjoint(gamma)

Spherical weak lensing adjoint measurement operator

Args:

glm (complex array): Shear Observations in harmonic space

mask_forward(f)

Applies given mask to a field.

Args:

f (complex array): Realspace Signal

Raises:

ValueError: Raised if signal is nan ValueError: Raised if signal is of incorrect shape.

mask_adjoint(x)

Applies given mask adjoint to observations

Args:

x (complex array): Set of observations.

Raises:

ValueError: Raised if signal is nan

ngal_to_inv_cov(ngal)

Converts galaxy number density map to data covariance.

Assumes no correlation between pixels.

Args:

ngal (real array): pixel space map of number of observations per pixel.

cov_weight(x)

Applies covariance weighting to observations.

Assumes no correlation between pixels.

Args:

x (array): pixel space map to be inverse covariance weighted.