drift.core.kltransform

Functions

collect_m_array(mlist, func, shape, dtype)

collect_m_arrays(mlist, func, shapes, dtype)

eigh_gen(A, B[, message])

Solve the generalised eigenvalue problem.

inv_gen(A)

Find the inverse of A.

Classes

KLTransform(bt[, subdir])

Perform KL transform.
class drift.core.kltransform.KLTransform(bt, subdir=None)

Bases: Reader

Perform KL transform.

subset

If True, throw away modes below a S/N threshold.

Type:

boolean

threshold

S/N threshold to cut modes at.

Type:

scalar

inverse

If True construct and cache inverse transformation.

Type:

boolean

use_thermal, use_foregrounds

Whether to use instrumental noise/foregrounds (default: both True)

Type:

boolean

_foreground_regulariser

The regularisation constant for the foregrounds. Adds in a diagonal of size reg * cf.max(). Default is 2e-15

Type:

scalar

evals_all()

Collects the full eigenvalue spectrum for all m-modes.

Reads in from files on disk.

Returns:

evarray – The full set of eigenvalues across all m-modes.

Return type:

np.ndarray

evals_m(mi, threshold=None)

Fetch the KL-modes for a particular m.

This attempts to read in the results from disk, if available and if not will create them.

Also, it will cache the previous m-mode in memory, so as to avoid disk access in many cases. However this is not sensitive to changes in the threshold, be careful.

Parameters:

  • mi (integer) – m to fetch KL-modes for.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

evals – KL-modes with S/N greater than some threshold. Both evals and evecs are potentially None, if there are no modes either in the file, or satisfying S/N > threshold.

Return type:

np.ndarray

foreground()

Compute the foreground covariance matrix (on the sky).

Returns:

cv_fg

Return type:

np.ndarray[pol2, pol1, l, freq1, freq2]

generate(regen=False)

Perform the KL-transform for all m-modes and save the result.

Uses MPI to distribute the work (if available).

Parameters:

mlist (array_like, optional) – Set of m’s to calculate KL-modes for By default do all m-modes.

invmodes_m(mi, threshold=None)

Get the inverse modes.

If the true inverse has been cached, return the modes for the current threshold. Otherwise generate the Moore-Penrose pseudo-inverse.

Parameters:

  • mi (integer) – m-mode to generate for.

  • threshold (scalar) – S/N threshold to use.

Returns:

invmodes

Return type:

np.ndarray

modes_m(mi, threshold=None)

Fetch the KL-modes for a particular m.

This attempts to read in the results from disk, if available and if not will create them.

Also, it will cache the previous m-mode in memory, so as to avoid disk access in many cases. However this is not sensitive to changes in the threshold, be careful.

Parameters:

  • mi (integer) – m to fetch KL-modes for.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

evals, evecs – KL-modes with S/N greater than some threshold. Both evals and evecs are potentially None, if there are no modes either in the file, or satisfying S/N > threshold.

Return type:

np.ndarray

project_matrix_sky_to_kl(mi, mat, threshold=None)

Project a covariance matrix from the sky into the eigenbasis.

Parameters:

  • mi (integer) – Mode index to fetch for.

  • mat (np.ndarray) – Sky matrix to project.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

projmatrix – The matrix projected into the eigenbasis.

Return type:

np.ndarray

project_matrix_svd_to_kl(mi, mat, threshold=None)

Project a matrix from the telescope basis into the eigenbasis.

Parameters:

  • mi (integer) – Mode index to fetch for.

  • mat (np.ndarray) – Telescope matrix to project.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

projmatrix – The matrix projected into the eigenbasis.

Return type:

np.ndarray

project_vector_kl_to_svd(mi, vec, threshold=None)

Project a vector in the Eigenbasis back into the telescope space.

Parameters:

  • mi (integer) – Mode index to fetch for.

  • vec (np.ndarray) – Eigenbasis data vector.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

projvector – The vector projected into the eigenbasis.

Return type:

np.ndarray

project_vector_sky_to_kl(mi, vec, threshold=None)

Project an m-vector from the sky into the eigenbasis.

Parameters:

  • mi (integer) – Mode index to fetch for.

  • vec (np.ndarray) – Sky data vector packed as [freq, pol, l]

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

projvector – The vector projected into the eigenbasis.

Return type:

np.ndarray

project_vector_svd_to_kl(mi, vec, threshold=None)

Project a telescope data vector into the eigenbasis.

Parameters:

  • mi (integer) – Mode index to fetch for.

  • vec (np.ndarray) – Telescope data vector.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

projvector – The vector projected into the eigenbasis.

Return type:

np.ndarray

signal()

Compute the signal covariance matrix (on the sky).

Returns:

cv_fg

Return type:

np.ndarray[pol2, pol1, l, freq1, freq2]

skymodes_m(mi, threshold=None)

Find the representation of the KL-modes on the sky.

Use the beamtransfers to rotate the SN-modes onto the sky. This routine is based on modes_m, as such the same caching and caveats apply.

Parameters:

  • mi (integer) – Mode index to fetch for.

  • threshold (real scalar, optional) – Returns only KL-modes with S/N greater than threshold. By default return all modes saved in the file (this maybe be a subset already, see transform_save).

Returns:

skymodes – The modes as found in \(a_{lm}(\nu)\) space. Note this routine does not return the evals.

Return type:

np.ndarray

See also

modes_m()

sn_covariance(mi)

Compute the signal and noise covariances (on the telescope).

The signal is formed from the 21cm signal, whereas the noise includes both foregrounds and instrumental noise. This is for a single m-mode.

Parameters:

mi (integer) – The m-mode to calculate at.

Returns:

s, n – Signal and noice covariance matrices.

Return type:

np.ndarray[nfreq, ntel, nfreq, ntel]

transform_save(mi)

Save the KL-modes for a given m.

Perform the transform and cache the results for later use.

Parameters:

  • mi (integer) – m-mode to calculate.

  • Results

  • -------

  • evals (np.ndarray) – See transfom_m for details.

  • evecs (np.ndarray) – See transfom_m for details.

drift.core.kltransform.eigh_gen(A, B, message='')

Solve the generalised eigenvalue problem. \(\mathbf{A} \mathbf{v} = \lambda \mathbf{B} \mathbf{v}\)

This routine will attempt to correct for when B is not positive definite (usually due to numerical precision), by adding a constant diagonal to make all of its eigenvalues positive.

Parameters:

  • A (np.ndarray) – Matrices to operate on.

  • B (np.ndarray) – Matrices to operate on.

  • message (string, optional) – Optional string to print if an exception is thrown. Default: “”.

Returns:

  • evals (np.ndarray) – Eigenvalues of the problem.

  • evecs (np.ndarray) – 2D array of eigenvectors (packed column by column).

  • add_const (scalar) – The constant added on the diagonal to regularise.

drift.core.kltransform.inv_gen(A)

Find the inverse of A.

If a standard matrix inverse has issues try using the pseudo-inverse.

Parameters:

A (np.ndarray) – Matrix to invert.

Returns:

inv

Return type:

np.ndarray