human
1. Write programs for people, not computers
example: meaningful variables, self-contained designs, and documentation"
Please write code following the instructions in jupyter notebook style.
 ... What is a code to 1?
assistant
#Here is code to 1.

import numpy as np
def auto_corr_func(trace,k):
    """ calculates the correlation of a trace of scalars and 
    a shifted copy of itself by k value """
    
    mu  = np.mean(trace)       # mean
    sig = np.std(trace,ddof=1) # standard deviation 
    
    nval = len(trace)-k   # number of overlap values
    
    # find correlation between current and shifted traces
    ac = 0.0 # accumulate correlation
    for i in range(len(trace)-k):
        ac += (trace[i]-mu)*(trace[i+k]-mu)
    # end for i
    ac /= (nval*sig**2.)
    
    return ac
# end def auto_corr_func

def auto_corr_time(trace):
    """ calculates the auto-correlation time of a trace of scalars """
    
    corr_term = 0.0
    #  shift trace by k, and accumulate correlation until it vanishes
    for k in range(1,len(trace)):
        ac = auto_corr_func(trace,k)
        if ac>0:
            corr_term += ac
        else:
            break
        # end if
    # end for k
    
    corr_time = 1.0 + 2*corr_term
    return corr_time
# end def auto_corr_time

data = np.array([-9.  , -8.82, -8.66, -8.55, -8.44, -8.3 , -8.31, -8.18, -8.05,
       -7.93, -8.01, -8.  , -7.87, -7.88, -7.87, -7.95, -7.91, -7.86,
       -7.87, -7.82, -7.87, -7.83, -7.73, -7.8 , -7.8 , -7.78, -7.75,
       -7.75, -7.77, -7.84, -7.87, -7.84, -7.84, -7.78, -7.79, -7.75,
       -7.77, -7.73, -7.76, -7.76, -7.76, -7.85, -7.83, -7.79, -7.77,
       -7.8 , -7.72, -7.61, -7.63, -7.6 ])
auto_corr_time(data)