mdp.utils.VartimeCovarianceMatrix

This class stores an empirical covariance matrix that can be updated incrementally. A call to the 'fix' method returns the current state of the covariance matrix, the average and the number of observations, and resets the internal data.

As compared to the CovarianceMatrix class, this class accepts sampled input in conjunction with a non-constant time increment between samples. The covariance matrix is then computed as a (centered) scalar product between functions, that is sampled unevenly, using the trapezoid rule.

fix(self, center=True)

Returns a triple containing the generalized covariance matrix, the average and length of the sequence (in time/summed increments).

The covariance matrix is then reset to a zero-state.

of sequence (in time/summed increments). :rtype: Tuple[np.ndarray, np.ndarray, np.ndarray]

Parameters:

center (bool) - If center is false, the returned matrix is the matrix of the second moments, i.e. the covariance matrix of the data without subtracting the mean.

Returns:

Generalized covariance matrix, average and length

Overrides: CovarianceMatrix.fix

update(self, x, dt=None, time_dep=True)

Update internal structures.

Note that no consistency checks are performed on the data (this is typically done in the enclosing node).

Parameters:

x (numpy.ndarray) - Timed sequence of vectors, with samples along the rows and random variables along the columns.
dt (numpy.ndarray or numeric) - Sequence of time increments between vectors.

Usage with only single chunk of data:

dt should be of length x.shape[0]-1 or a constant. When constant, the time increments are assumed to be constant. If dt is not supplied, a constant time increment of one is assumed. If a time sequence of length x.shape[0] is supplied the first element is disregarded and a warning is presented.

Usage with multiple chunks of data with intended time dependence:

dt should have length x.shape[0]-1 in the first call and be of length x.shape[0] starting with the second call. Starting with the second call, the first element in each chunk will be considered the time difference between the last element of x in the previous chunk and the first element of x of the current chunk. The time_dep argument being True indicates this mode.

Usage with multiple chunks without time dependence:

The moments are computed as a weighted average of the moments of separate chunks, if dt continues to have length x.shape[0]-1 after the first call. Time dependence between chunks is thus omitted and all algorithmic components regard only the time structure within chunks. The time_dep argument being False indicates this mode. As in the single chunk case it is possible to set dt to be a constant or omit it completely for constant or unit time increments within chunks respectively.
time_dep (bool) - Indicates whether time dependence between chunks can be considered. The argument is only relevant if multiple chunks of data are used. Time dependence between chunks is disregarded when data collection has been done time-independently and thus no reasonable time increment between the end of a chunk and beginning of the next can be specified.

Overrides: CovarianceMatrix.update

Class VartimeCovarianceMatrix

init(self, dtype=None)
(Constructor)

fix(self, center=True)

update(self, x, dt=None, time_dep=True)

Class VartimeCovarianceMatrix

__init__(self, dtype=None) (Constructor)

fix(self, center=True)

update(self, x, dt=None, time_dep=True)

init(self, dtype=None)
(Constructor)