def _compute_nfp_real(l, u, counts, sizes):
    """Computes the expected number of false positives caused by using
    u to approximate set sizes in the interval [l, u], using the real
    set size distribution.

    Args:
        l: the lower bound on set sizes.
        u: the upper bound on set sizes.
        counts: the complete distribution of set sizes.
        sizes: the complete domain of set sizes.

    Return (float): the expected number of false positives.
    """
    if l > u:
        raise ValueError("l must be less or equal to u")
    return np.sum((float(sizes[u])-sizes[l:u+1])/float(sizes[u])*counts[l:u+1])
def _compute_nfp_real(l, u, counts, sizes):
    """Computes the expected number of false positives caused by using
    u to approximate set sizes in the interval [l, u], using the real
    set size distribution.

    Args:
        l: the lower bound on set sizes.
        u: the upper bound on set sizes.
        counts: the complete distribution of set sizes.
        sizes: the complete domain of set sizes.

    Return (float): the expected number of false positives.
    """
    if l > u:
        raise ValueError("l must be less or equal to u")
    return np.sum((float(sizes[u])-sizes[l:u+1])/float(sizes[u])*counts[l:u+1])
def _compute_nfp_real ( l , u , counts , sizes ) : if l > u : raise ValueError ( "l must be less or equal to u" ) return np . sum ( ( float ( sizes [ u ] ) - sizes [ l : u + 1 ] ) / float ( sizes [ u ] ) * counts [ l : u + 1 ] )
Computes the expected number of false positives caused by using
    u to approximate set sizes in the interval [l, u], using the real
    set size distribution.

    Args:
        l: the lower bound on set sizes.
        u: the upper bound on set sizes.
        counts: the complete distribution of set sizes.
        sizes: the complete domain of set sizes.

    Return (float): the expected number of false positives.
Computes the expected number of false positives caused by using u to approximate set sizes in the interval [ l u ] using the real set size distribution .