function covars¶

deeptime.covariance.covars(X, Y, remove_mean=False, modify_data=False, symmetrize=False, weights=None, sparse_mode='auto', sparse_tol=0.0)¶

Computes the covariance and cross-covariance matrix of X and Y.

If symmetrize is False, computes

\[\begin{aligned} C_{XX} &= X^{\top} X \\ C_{XY} &= X^{\top} Y \end{aligned}\]

If symmetrize is True, computes

\[\begin{aligned} C_{XX} &= \frac{1}{2} (X^{\top} X + Y^{\top} Y)\\ C_{XY} &= \frac{1}{2} (X^{\top} Y + Y^{\top} X) \end{aligned}\]

while exploiting zero or constant columns in the data matrix. WARNING: Directly use moments_XXXY() if you can. The covars function does an additional constant-matrix multiplication and does not return the mean.

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.
symmetrize (bool) – Computes symmetrized means and moments (see above)
weights (None or ndarray(T, )) – weights assigned to each trajectory point of X. If None, all data points have weight one. If ndarray, each data point is assigned a separate weight.
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.

Returns:

C_XX (ndarray (M, M)) – Covariance matrix of X
C_XY (ndarray (M, N)) – Covariance matrix of XY