GWForge.fisher.inner_product

Functions

inner_product(aa, bb, interferometer)

Noise-weighted inner product of two frequency-domain series.

optimal_snr_squared(signal, interferometer)

\(\langle h \mid h \rangle\) for a signal in one detector.

inner_product_matrix(left, right, interferometer)

Gram matrix of inner products between two stacks of series.

Module Contents

GWForge.fisher.inner_product.inner_product(aa, bb, interferometer)[source]

Noise-weighted inner product of two frequency-domain series.

Wraps bilby.gw.utils.noise_weighted_inner_product() – the same routine bilby uses for its own SNRs, so a Fisher SNR and an injection SNR are guaranteed to agree – and takes the real part, which is what the Fisher matrix is built from.

Only bins inside the interferometer’s frequency_mask contribute. Outside it bilby leaves the PSD at an arbitrary sentinel value, so including those bins would silently corrupt the integral.

Parameters:

  • aa (array_like) – Frequency-domain series on the interferometer’s frequency grid. aa is the one that gets conjugated. Either may be complex.

  • bb (array_like) – Frequency-domain series on the interferometer’s frequency grid. aa is the one that gets conjugated. Either may be complex.

  • interferometer (bilby.gw.detector.Interferometer) – Supplies the PSD, the frequency mask and the segment duration.

Returns:

The real inner product.

Return type:

float

GWForge.fisher.inner_product.optimal_snr_squared(signal, interferometer)[source]

\(\langle h \mid h \rangle\) for a signal in one detector.

Parameters:

  • signal (array_like) – Frequency-domain detector response.

  • interferometer (bilby.gw.detector.Interferometer) – Detector whose PSD is used.

Return type:

float

GWForge.fisher.inner_product.inner_product_matrix(left, right, interferometer)[source]

Gram matrix of inner products between two stacks of series.

Building the Fisher matrix means taking len(left) * len(right) inner products that all share the same PSD weighting, so the weighting is applied once and the rest is a single matrix product. For an 11-parameter Fisher over a 65537-bin grid this is roughly two orders of magnitude faster than looping over inner_product().

Parameters:

  • left (array_like) – Arrays of shape (n_left, n_frequencies) and (n_right, n_frequencies). left is conjugated.

  • right (array_like) – Arrays of shape (n_left, n_frequencies) and (n_right, n_frequencies). left is conjugated.

  • interferometer (bilby.gw.detector.Interferometer) – Supplies the PSD, the frequency mask and the segment duration.

Returns:

Real array of shape (n_left, n_right).

Return type:

numpy.ndarray