ucorrelate.py

@numba.jit
def ucorrelate(t, u, maxlag=None):
    """Compute correlation of two signals defined at uniformly-spaced points.
    The correlation is defined only for positive lags (including zero).
    The input arrays represent signals defined at uniformily-spaced
    points. This function is equivalent to :func:`numpy.correlate`, but can
    efficiently compute correlations on a limited number of lags.
    Note that binning point-processes with uniform bins, provides
    signals that can be passed as argument to this function.
    Arguments:
        tx (array): first signal to be correlated
        ux (array): second signal to be correlated
        maxlag (int): number of lags where correlation is computed.
            If None, computes all the lags where signals overlap
            `min(tx.size, tu.size) - 1`.
    Returns:
        Array contained the correlation at different lags.
        The size of this array is equal to the input argument `maxlag`
        (if defined) or to `min(tx.size, tu.size) - 1`, and its `dtype`
        is the same as argument `t`'s.
    Example:
        Correlation of two signals `t` and `u`::
            >>> t = np.array([1, 2, 0, 0])
            >>> u = np.array([0, 1, 1])
            >>> pycorrelate.ucorrelate(t, u)
            array([2, 3, 0])
        The same result can be obtained with numpy swapping `t` and `u` and
        restricting the results only to positive lags::
            >>> np.correlate(u, t, mode='full')[t.size - 1:]
            array([2, 3, 0])
        Also works with other types:
            >>> t = np.array([1.2, 2.4, 0.5, 0.6])
            >>> u = np.array([0, 1.2, 1.3])
            >>> pycorrelate.ucorrelate(t, u)
            array([3.53, 4.56, 1.56])
    """
    if maxlag is None:
        maxlag = u.size
    maxlag = int(min(u.size, maxlag))
    C = np.empty(maxlag, dtype=t.dtype)
    for lag in range(C.size):
        tmax = min(u.size - lag, t.size)
        umax = min(u.size, t.size + lag)
        C[lag] = (t[:tmax] * u[lag:umax]).sum()
    return C