pyssaBSS.utils

Functions

ball_kernel_local_sample_covariance(data, ...)	Computes the local covariance using a ball kernel.
gaussian_kernel_local_sample_covariance(...)	Computes the local covariance using a ring kernel.
generate_random_invertible_matrix(p)	Generate a random invertible matrix of size p x p
generate_random_orthogonal_matrix(n)	Generate a random orthogonal matrix of size n x n
ring_kernel_local_sample_covariance(data, ...)	Computes the local covariance using a ring kernel.
sample_autocovariance(data, lag[, segment, ...])	Sample autocovariance matrix at a given lag.
sample_covariance(data[, segment, seg_mean])	Compute the covariance of the data points.
sample_mean(data[, segment])	Compute the mean of the data points.
scaled_local_sample_covariance(data, coords, ...)	Computes the scaled local covariance using a ball kernel.
standardize_data(data)	Standardize the data.

pyssaBSS.utils.ball_kernel_local_sample_covariance(data, coords, radius, segment=None, seg_mean=None)

Computes the local covariance using a ball kernel.

Parameters:

• data (ndarray of shape (p, n))

• coords (ndarray of shape (n, 2))

• radius (float) – radius of the ball kernel

• segment (ndarray, optional) – indicates a subset of indices over which the local covariance is computed

• seg_mean (ndarray of shape (p, 1), optional) – A precomputed mean of the segment. If None, it is computed

Returns:

l_cov – local (spatial) covariance matrix

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.gaussian_kernel_local_sample_covariance(data, coords, radius, segment=None, seg_mean=None)

Computes the local covariance using a ring kernel.

Parameters:

• data (ndarray of shape (p, n))

• coords (ndarray of shape (n, 2))

• radius (float) – radius of the gaussian kernel

• segment (ndarray, optional) – indicates a subset of indices over which the local covariance is computed

• seg_mean (ndarray of shape (p, 1), optional) – A precomputed mean of the segment. If None, it is computed

Returns:

l_cov – local (spatial) covariance matrix

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.generate_random_invertible_matrix(p)

Generate a random invertible matrix of size p x p

Parameters:

p (int) – Number of rows and columns

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.generate_random_orthogonal_matrix(n)

Generate a random orthogonal matrix of size n x n

Parameters:

n (int) – Number of rows and columns

Return type:

ndarray of shape (n, n)

pyssaBSS.utils.ring_kernel_local_sample_covariance(data, coords, inner_radius, outer_radius, segment=None, seg_mean=None)

Computes the local covariance using a ring kernel.

Parameters:

• data (ndarray of shape (p, n))

• coords (ndarray of shape (n, 2))

• inner_radius (float) – inner radius of the ring kernel

• outer_radius (float) – outer radius of the ring kernel

• segment (ndarray, optional) – indicates a subset of indices over which the local covariance is computed

• seg_mean (ndarray of shape (p, 1), optional) – A precomputed mean of the segment. If None, it is computed

Returns:

l_cov – local (spatial) covariance matrix

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.sample_autocovariance(data, lag, segment=None, seg_mean=None)

Sample autocovariance matrix at a given lag.

Parameters:

• data (ndarray of shape (p, n))

• lag (int) – Lag at which to compute autocovariance. Must be >= 0.

• segment (ndarray of int indices, optional)

• seg_mean (ndarray of shape (p,) or (p, 1), optional) – If None, computed from the segment.

Returns:

acov – Not necessarily symmetric (acov(lag) != acov(lag).T for lag > 0).

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.sample_covariance(data, segment=None, seg_mean=None)

Compute the covariance of the data points.

Parameters:

• data (ndarray of shape (p, n))

• segment (ndarray, optional) – if provided, compute the covariance over the given indices

• seg_mean (ndarray, optional) – if provided, the mean is not recomputed

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.sample_mean(data, segment=None)

Compute the mean of the data points.

Parameters:

• data (ndarray of shape (p, n)) – if provided, compute the covariance over the given indi

• segment (ndarray, optional)

Return type:

ndarray of shape (p,)

pyssaBSS.utils.scaled_local_sample_covariance(data, coords, radius, segment=None, seg_mean=None)

Computes the scaled local covariance using a ball kernel.

Parameters:

• data (ndarray of shape (p, n))

• coords (ndarray of shape (n, 2))

• radius (float) – radius of the ball kernel

• segment (ndarray, optional) – indicates a subset of indices over which the local covariance is computed

• seg_mean (ndarray of shape (p, 1), optional) – A precomputed mean of the segment. If None, it is computed

Returns:

l_cov – local (spatial) covariance matrix

Return type:

ndarray of shape (p, p)

pyssaBSS.utils.standardize_data(data)

Standardize the data.

Afterwards, data has mean 0 and covariance I.

Parameters:

data (ndarray of shape (p, n))

Returns:

• white_data (ndarray of shape (p, n)) – data after standardization

• whitener (ndarray of shape (p, p)) – inverse square root of the covariance