function moments_block

deeptime.covariance.moments_block(X, Y, remove_mean=False, modify_data=False, sparse_mode='auto', sparse_tol=0.0, column_selection=None, diag_only=False)

Computes the first two unnormalized moments of X and Y forward and backward.

Computes

\[\begin{aligned} s_x &= \sum_t x_t\\ s_y &= \sum_t y_t\\ C_{XX} &= X^\top X\\ C_{XY} &= X^\top Y\\ C_{YX} &= Y^\top X\\ C_{YY} &= Y^\top Y \end{aligned}\]

while exploiting zero or constant columns in the data matrix.

Parameters:

• X (ndarray (T, M)) – Data matrix

• Y (ndarray (T, N)) – Second data matrix

• remove_mean (bool) – True: remove column mean from the data, False: don’t remove mean.

• modify_data (bool) – If remove_mean=True, the mean will be removed in the data matrix X, without creating an independent copy. This option is faster but might lead to surprises because your input array is changed.

• sparse_mode (str) –

  one of:

  • ’dense’ : always use dense mode

  • ’sparse’ : always use sparse mode if possible

  • ’auto’ : automatic

• sparse_tol (float) – Threshold for considering column to be zero in order to save computing effort when the data is sparse or almost sparse. If max(abs(X[:, i])) < sparse_tol, then row i (and also column i if Y is not given) of the covariance matrix will be set to zero. If Y is given and max(abs(Y[:, i])) < sparse_tol, then column i of the covariance matrix will be set to zero.

• column_selection (ndarray(k, dtype=int) or None) – Indices of those columns that are to be computed. If None, all columns are computed.

• diag_only (bool) – If True, the computation is restricted to the diagonal entries (autocorrelations) only.

Returns:

• w (float) – statistical weight of this estimation

• s ([ndarray (M), ndarray (M)]) – list of two elements with s[0]=sx and s[1]=sy

• C ([[ndarray(M,M), ndarray(M,N)], [ndarray(N,M),ndarray(N,N)]]) – list of two lists with two elements. C[0,0] = Cxx, C[0,1] = Cxy, C[1,0] = Cyx, C[1,1] = Cyy