code: OCD

code/lib/gdp.py

@@ -28,6 +28,7 @@ MISS  = 0   # Number of additions to the cache.
 TOTAL = 0   # Number of cache accesses.
 
 
+def load_data(path):
   '''
     Read data from a file.
 
@@ -36,7 +37,6 @@ TOTAL = 0   # Number of cache accesses.
     Returns:
       data - A list of tuples [uid, timestamp, lng, lat, loc].
   '''
-def load_data(path):
   print('Loading data from', os.path.abspath(path), '... ', end='')
   data = []
   try:
@@ -50,6 +50,7 @@ def load_data(path):
     exit()
 
 
+def save_output(path, t, e, a_b, a_f, a):
   '''
     Save output to a file.
 
@@ -63,7 +64,6 @@ def load_data(path):
     Returns:
       Nothing.
   '''
-def save_output(path, t, e, a_b, a_f, a):
   # timestamp = time.strftime('%Y%m%d%H%M%S')
   print('Saving output to %s... ' %(path), end='', flush=True)
   os.makedirs(os.path.dirname(path), exist_ok=True)
@@ -74,6 +74,7 @@ def save_output(path, t, e, a_b, a_f, a):
   print('OK.', flush=True)
 
 
+def get_timestamps(data):
   '''
     Get all the timestamps from the input data.
 
@@ -82,7 +83,6 @@ def save_output(path, t, e, a_b, a_f, a):
     Returns:
       timestamps - An ndarray of all of the timestamps from the input data.
   '''
-def get_timestamps(data):
   print('Getting a list of all timestamps... ', end='', flush=True)
   timestamps = np.sort(np.unique(np.array(data)[:, 1]))
   if not len(timestamps):
@@ -103,6 +103,7 @@ def get_timestamps(data):
   return timestamps
 
 
+def get_locs(data):
   '''
     Get all the unique locations from the input data.
 
@@ -111,7 +112,6 @@ def get_timestamps(data):
     Returns:
       locs - A sorted ndarray of all the unique locations int the input data.
   '''
-def get_locs(data):
   print('Getting a list of all locations... ', end='', flush=True)
   locs = np.sort(np.unique(np.array(data)[:, 4].astype(np.int)))
   if not len(locs):
@@ -123,6 +123,7 @@ def get_locs(data):
   return list(map(str, locs))
 
 
+def get_cnts(data, t):
   '''
     Get the counts at every location for a specific timestamp.
 
@@ -132,7 +133,6 @@ def get_locs(data):
     Returns:
       cnts - A dict {loc:cnt} with the counts at every location for a specific timestamp.
   '''
-def get_cnts(data, t):
   print('Getting all counts at %s... ' %(t), end='', flush=True)
   locs = get_locs(data)
   cnts = dict.fromkeys(locs, 0)
@@ -145,6 +145,7 @@ def get_cnts(data, t):
   return cnts
 
 
+def get_all_cnts(data):
   '''
     Get the counts at every location for every timestamp.
 
@@ -153,7 +154,6 @@ def get_cnts(data, t):
     Returns:
       cnts - A dict {timestamp:loc} with all the counts at every location for every timestamp.
   '''
-def get_all_cnts(data):
   cnts = {}
   for d in data:
     key = d[1] + '@' + d[4]
@@ -163,6 +163,7 @@ def get_all_cnts(data):
   return cnts
 
 
+def get_usrs(data):
   '''
     Get a list of unique users in the input data set.
 
@@ -171,7 +172,6 @@ def get_all_cnts(data):
     Returns:
       users - An ndarray of all unique users.
   '''
-def get_usrs(data):
   users = np.sort(np.unique(np.array(data)[:, 0].astype(np.int)))
   if not len(users):
     print('No users found.')
@@ -181,6 +181,7 @@ def get_usrs(data):
   return users
 
 
+def get_usr_data(data, id):
   '''
     Get the data of a particular user from a data set.
 
@@ -190,7 +191,6 @@ def get_usrs(data):
     Returns:
       output - A list of the data of the targeted user.
   '''
-def get_usr_data(data, id):
   output = []
   for d in data:
     if (d[0] == str(id)):
@@ -200,6 +200,7 @@ def get_usr_data(data, id):
   return output
 
 
+def get_usrs_data(data):
   '''
     Get the data of every user in a data set.
 
@@ -208,13 +209,13 @@ def get_usr_data(data, id):
     Returns:
       output - A dict {usr, [usr_data]} with the data of each user.
   '''
-def get_usrs_data(data):
   output = {}
   for d in data:
     output[d[0]] = output.get(d[0], []) + [d]
   return output
 
 
+def get_usr_traj(data):
   '''
     Get the trajectory of a user from her data.
 
@@ -223,7 +224,6 @@ def get_usrs_data(data):
     Returns:
       traj - A list [(timestamp, loc)] with the locations and corresponding timestamps that the user was at.
   '''
-def get_usr_traj(data):
   traj = []
   for d in data:
     traj.append((d[1], d[4]))
@@ -232,6 +232,7 @@ def get_usr_traj(data):
   return traj
 
 
+def get_poss_trans(data):
   '''
     Get all the possible transitions.
 
@@ -240,7 +241,6 @@ def get_usr_traj(data):
     Returns:
       trans - A set with all the possible forward transitions in the input.
   '''
-def get_poss_trans(data):
   print('Getting possible transitions... ', end='', flush=True)
   trans = set()
   for u, u_data in data.items():
@@ -253,6 +253,7 @@ def get_poss_trans(data):
   return trans
 
 
+def get_bwd_trans(data):
   '''
     Get all backward transitions in a data set.
 
@@ -262,7 +263,6 @@ def get_poss_trans(data):
       trans - A dict {(t, t-1):[transitions]} with all the backward transitions
               at every sequential timestamp pair in the input data set.
   '''
-def get_bwd_trans(data):
   print('Getting all backward transitions... ', end='', flush=True)
   trans = {}
   for u, u_data in data.items():
@@ -276,6 +276,7 @@ def get_bwd_trans(data):
   return trans
 
 
+def get_fwd_trans(data):
   '''
     Get all forward transitions in a data set.
 
@@ -285,7 +286,6 @@ def get_bwd_trans(data):
       trans - A dict {(t-1, t):[transitions]} with all the forward transitions
               at every sequential timestamp pair in the input data set.
   '''
-def get_fwd_trans(data):
   print('Getting all forward transitions... ', end='', flush=True)
   trans = {}
   for u, u_data in data.items():
@@ -299,6 +299,7 @@ def get_fwd_trans(data):
   return trans
 
 
+def safe_div(a, b):
   '''
     Divide two numbers. If the divisor is 0 return inf.
 
@@ -308,12 +309,12 @@ def get_fwd_trans(data):
     Returns:
       The float result of the division.
   '''
-def safe_div(a, b):
   if b == 0:
     return math.inf
   return float(a/b)
 
 
+def max_val(q, d, a):
   '''
     Calculate the maximum value of the objective function.
 
@@ -325,12 +326,12 @@ def safe_div(a, b):
     Returns:
       The maximum value of the objective function.
   '''
-def max_val(q, d, a):
   if a == math.inf:
     return math.nan
   return (q*(math.exp(a) - 1) + 1)/(d*(math.exp(a) - 1) + 1)
 
 
+def find_qd(p, a):
   '''
     Find two different rows (q and d) of a transition matrix (p)
     that maximize the product of the objective function and return
@@ -345,7 +346,6 @@ def max_val(q, d, a):
       sum_q - The sum of the elements of q.
       sum_d - The sum of the elements of d.
   '''
-def find_qd(p, a):
   res = 0.0
   sum_q, sum_d = 0.0, 0.0
   for q in p:  # A row from the transition matrix.
@@ -374,6 +374,7 @@ def find_qd(p, a):
   return sum_q, sum_d
 
 
+def gen_data(usrs, timestamps, locs):
   '''
     Generate data.
 
@@ -384,7 +385,6 @@ def find_qd(p, a):
     Returns:
       data - The generated data.
   '''
-def gen_data(usrs, timestamps, locs):
   print('Generating data... ', end='', flush=True)
   # Generate timestamps.
   ts = []
@@ -412,6 +412,7 @@ def gen_data(usrs, timestamps, locs):
   return data
 
 
+def gen_trans_mt(n, s):
   '''
     Generate a transition matrix.
 
@@ -423,7 +424,6 @@ def gen_data(usrs, timestamps, locs):
     Returns:
       p_ - The transition matrix.
   '''
-def gen_trans_mt(n, s):
   if DEBUG:
     print('Generating transition matrix %dx%d with s = %.4f... ' %(n, n, s), end='', flush=True)
   p = np.zeros((n, n), float)
@@ -439,6 +439,7 @@ def gen_trans_mt(n, s):
   return p_
 
 
+def get_trans_mt(locs, trans):
   '''
     Get the transition matrix
 
@@ -449,7 +450,6 @@ def gen_trans_mt(n, s):
       p - A 2d dict {{locs}{locs}} containing the
           corresponding location transition probabilities.
   '''
-def get_trans_mt(locs, trans):
   if DEBUG:
     print('Generating the transition matrix... ', end='', flush=True)
   # Initialize the transition matrix.
@@ -476,6 +476,7 @@ def get_trans_mt(locs, trans):
   return p
 
 
+def get_entropy(mt):
   '''
     Calculate the measure-theoretic (Kolmogorov-Sinai) entropy
     of a transition matrix.
@@ -485,7 +486,6 @@ def get_trans_mt(locs, trans):
     Returns:
       h - The Kolmogorov-Sinai entropy of the matrix.
   '''
-def get_entropy(mt):
   if DEBUG:
     print('Calculating the measure-theoretic entropy... ', end='', flush=True)
   h = 0.0
@@ -523,6 +523,7 @@ def get_entropy(mt):
   return h
 
 
+def get_2darray(mt):
   '''
     Convert a 2d dict to a 2d array.
 
@@ -531,7 +532,6 @@ def get_entropy(mt):
     Returns:
       p - The 2d numpy array.
   '''
-def get_2darray(mt):
   if type(mt) == type(np.array([])):
     return mt
   p = np.zeros((len(mt), len(mt)), float)
@@ -540,6 +540,7 @@ def get_2darray(mt):
   return p
 
 
+def get_laplace_pd(ts, t, sc):
   '''
     Get a Laplace probability distribution.
 
@@ -550,12 +551,12 @@ def get_2darray(mt):
     Returns:
       The probability distribution.
   '''
-def get_laplace_pd(ts, t, sc):
   x = np.arange(0, len(ts), 1)
   loc = np.where(ts == t)
   return laplace.pdf(x, loc=loc, scale=sc)[0]
 
 
+def get_norm_pd(ts, t, sc):
   '''
     Get a Gaussian probability distribution.
 
@@ -566,12 +567,12 @@ def get_laplace_pd(ts, t, sc):
     Returns:
       The probability distribution.
   '''
-def get_norm_pd(ts, t, sc):
   x = np.arange(0, len(ts), 1)
   loc = np.where(ts == t)
   return norm.pdf(x, loc=loc, scale=sc)[0]
 
 
+def get_sample(ts, t, pct, pd):
   '''
     Get a sample from the time series.
 
@@ -584,7 +585,6 @@ def get_norm_pd(ts, t, sc):
     Returns:
       spl - An ndarray of the sampled timestamps.
   '''
-def get_sample(ts, t, pct, pd):
   if DEBUG:
     print('Sampling %.2f%% of %s at %s... ' %(pct*100, ts, t), end='', flush=True)
   # Check that it is a valid timestamp.
@@ -604,6 +604,7 @@ def get_sample(ts, t, pct, pd):
   return spl
 
 
+def priv_l(p, a, e):
   '''
     Calculate the backward/forward privacy loss at the current
     timestamp.
@@ -617,11 +618,11 @@ def get_sample(ts, t, pct, pd):
       The backward/forward privacy loss at the current
       timestamp.
   '''
-def priv_l(p, a, e):
   sum_q, sum_d = find_qd(p, a)
   return math.log(max_val(sum_q, sum_d, a)) + e
 
 
+def priv_l_m(p, a, e):
   '''
     Calculate the backward/forward privacy loss at the current
     timestamp using memoization.
@@ -635,7 +636,6 @@ def priv_l(p, a, e):
       The backward/forward privacy loss at the current
       timestamp.
   '''
-def priv_l_m(p, a, e):
   key = xxhash.xxh64(p).hexdigest() + str(a) + str(e)
   global MEM, TOTAL, MISS
   TOTAL += 1
@@ -648,6 +648,7 @@ def priv_l_m(p, a, e):
   return result
 
 
+def bpl(p, a, e, t):
   '''
     Calculate the total backward privacy loss at every timestamp.
 
@@ -661,13 +662,13 @@ def priv_l_m(p, a, e):
       a - The backward privacy loss at every timestamp
           due to the previous data releases.
   '''
-def bpl(p, a, e, t):
   a[0] = e[0]
   for i in range(1, t):
     a[i] = priv_l(p, a[i - 1], e[i])
   return a
 
 
+def bpl_m(p, a, e, t):
   '''
     Calculate the total backward privacy loss at the current
     timestamp with memoization.
@@ -683,12 +684,12 @@ def bpl(p, a, e, t):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_m(p, a, e, t):
   a[0] = e[0]
   for i in range(1, t):
     a[i] = priv_l_m(p, a[i - 1], e[i])
   return a
 
+
 def bpl_lmdk_mem(p, a, e, t, lmdk):
   # t is (near) the landmark
   if lmdk == t - 1 or t == lmdk:
@@ -702,6 +703,7 @@ def bpl_lmdk_mem(p, a, e, t, lmdk):
   return a
 
 
+def bpl_s(p, e, i, w):
   '''
     Calculate the total backward privacy loss at the current
     timestamp using the static model, i.e., previous releases
@@ -717,7 +719,6 @@ def bpl_lmdk_mem(p, a, e, t, lmdk):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_s(p, e, i, w):
   if i - w > 1:
     # print('bpl_s: %d - %d [%d]' %(i, i - w, w))
     return priv_l(np.linalg.matrix_power(p, w), bpl_s(p, e, i - w, w), e[i - 1])
@@ -729,6 +730,7 @@ def bpl_s(p, e, i, w):
     return e[0]
 
 
+def bpl_s_m(p, e, i, w):
   '''
     Calculate the total backward privacy loss at the current
     timestamp using the static model, i.e., previous releases
@@ -744,7 +746,6 @@ def bpl_s(p, e, i, w):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_s_m(p, e, i, w):
   if i - w > 1:
     return priv_l_m(np.linalg.matrix_power(p, w), bpl_s_m(p, e, i - w, w), e[i - 1])
   elif i - w <= 1:
@@ -753,6 +754,7 @@ def bpl_s_m(p, e, i, w):
     return e[0]
 
 
+def bpl_l(p, e, i, w, l):
   '''
     Calculate the total backward privacy loss at the current
     timestamp using the linear model, i.e., previous releases
@@ -770,7 +772,6 @@ def bpl_s_m(p, e, i, w):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_l(p, e, i, w, l):
   if i - w*l > 1:
     # print('bpl_l: %d - %d [%d]' %(i, i - w*l, w*l))
     return priv_l(np.linalg.matrix_power(p, w*l), bpl_l(p, e, i - w*l, w, l + 1), e[i - 1])
@@ -782,6 +783,7 @@ def bpl_l(p, e, i, w, l):
     return e[0]
 
 
+def bpl_l_m(p, e, i, w, l):
   '''
     Calculate the total backward privacy loss at the current
     timestamp using the linear model, i.e., previous releases
@@ -800,7 +802,6 @@ def bpl_l(p, e, i, w, l):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_l_m(p, e, i, w, l):
   if i - w*l > 1:
     return priv_l_m(np.linalg.matrix_power(p, w*l), bpl_l_m(p, e, i - w*l, w, l + 1), e[i - 1])
   elif i - w*l <= 1:
@@ -809,6 +810,7 @@ def bpl_l_m(p, e, i, w, l):
     return e[0]
 
 
+def bpl_e(p, e, i, w, h):
   '''
     Calculate the total backward privacy loss at the current
     timestamp using the exponential model, i.e., previous releases
@@ -826,7 +828,6 @@ def bpl_l_m(p, e, i, w, l):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_e(p, e, i, w, h):
   if i - w**h > 1:
     # print('bpl_e: %d - %d [%d]' %(i, i - w**h, w**h))
     return priv_l(np.linalg.matrix_power(p, w**h), bpl_e(p, e, i - w**h, w, h + 1), e[i - 1])
@@ -838,6 +839,7 @@ def bpl_e(p, e, i, w, h):
     return e[0]
 
 
+def bpl_e_m(p, e, i, w, h):
   '''
     Calculate the total backward privacy loss at the current
     timestamp using the exponential model, i.e., previous releases
@@ -856,7 +858,6 @@ def bpl_e(p, e, i, w, h):
       a - The backward privacy loss at the current timestamp
           due to the previous data releases.
   '''
-def bpl_e_m(p, e, i, w, h):
   if i - w**h > 1:
     return priv_l_m(np.linalg.matrix_power(p, w**h), bpl_e_m(p, e, i - w**h, w, h + 1), e[i - 1])
   elif i - w**h <= 1:
@@ -865,6 +866,7 @@ def bpl_e_m(p, e, i, w, h):
     return e[0]
 
 
+def fpl(p, a, e, t):
   '''
     Calculate the total forward privacy loss at the current
     timestamp.
@@ -880,13 +882,13 @@ def bpl_e_m(p, e, i, w, h):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl(p, a, e, t):
   a[t - 1] = e[t - 1]
   for i in range(t - 2, -1, -1):
     a[i] = priv_l(p, a[i + 1], e[i])
   return a
 
 
+def fpl_m(p, a, e, t):
   '''
     Calculate the total forward privacy loss at the current
     timestamp, using memoization.
@@ -902,7 +904,6 @@ def fpl(p, a, e, t):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_m(p, a, e, t):
   a[t - 1] = e[t - 1]
   for i in range(t - 2, -1, -1):
     a[i] = priv_l_m(p, a[i + 1], e[i])
@@ -921,6 +922,7 @@ def fpl_lmdk_mem(p, a, e, t, lmdk):
   return a
 
 
+def fpl_s(p, e, i, t, w):
   '''
     Calculate the total forward privacy loss at the current
     timestamp using the static model, i.e., next releases
@@ -936,7 +938,6 @@ def fpl_lmdk_mem(p, a, e, t, lmdk):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_s(p, e, i, t, w):
   if i + w < t:
     # print('fpl_s: %d - %d [%d]' %(i, i + w, w))
     return priv_l(np.linalg.matrix_power(p, w), fpl_s(p, e, i + w, t, w), e[i - 1])
@@ -948,6 +949,7 @@ def fpl_s(p, e, i, t, w):
     return e[t - 1]
 
 
+def fpl_s_m(p, e, i, t, w):
   '''
     Calculate the total forward privacy loss at the current
     timestamp using the static model, i.e., next releases
@@ -963,7 +965,6 @@ def fpl_s(p, e, i, t, w):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_s_m(p, e, i, t, w):
   if i + w < t:
     return priv_l_m(np.linalg.matrix_power(p, w), fpl_s_m(p, e, i + w, t, w), e[i - 1])
   elif i + w >= t:
@@ -972,6 +973,7 @@ def fpl_s_m(p, e, i, t, w):
     return e[t - 1]
 
 
+def fpl_l(p, e, i, t, w, l):
   '''
     Calculate the total forward privacy loss at the current
     timestamp using the linear model, i.e., next releases
@@ -989,7 +991,6 @@ def fpl_s_m(p, e, i, t, w):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_l(p, e, i, t, w, l):
   if i + w*l < t:
     # print('fpl_l: %d - %d [%d]' %(i, i + w*l, w*l))
     return priv_l(np.linalg.matrix_power(p, w*l), fpl_l(p, e, i + w*l, t, w, l + 1), e[i - 1])
@@ -1001,6 +1002,7 @@ def fpl_l(p, e, i, t, w, l):
     return e[t - 1]
 
 
+def fpl_l_m(p, e, i, t, w, l):
   '''
     Calculate the total forward privacy loss at the current
     timestamp using the linear model, i.e., next releases
@@ -1019,7 +1021,6 @@ def fpl_l(p, e, i, t, w, l):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_l_m(p, e, i, t, w, l):
   if i + w*l < t:
     return priv_l_m(np.linalg.matrix_power(p, w*l), fpl_l_m(p, e, i + w*l, t, w, l + 1), e[i - 1])
   elif i + w*l >= t:
@@ -1028,6 +1029,7 @@ def fpl_l_m(p, e, i, t, w, l):
     return e[t - 1]
 
 
+def fpl_e(p, e, i, t, w, h):
   '''
     Calculate the total forward privacy loss at the current
     timestamp using the exponential model, i.e., next releases
@@ -1045,7 +1047,6 @@ def fpl_l_m(p, e, i, t, w, l):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_e(p, e, i, t, w, h):
   if i + w**h < t:
     # print('fpl_e: %d - %d [%d]' %(i, i + w**h, w**h))
     return priv_l(np.linalg.matrix_power(p, w**h), fpl_e(p, e, i + w**h, t, w, h + 1), e[i - 1])
@@ -1057,6 +1058,7 @@ def fpl_e(p, e, i, t, w, h):
     return e[t - 1]
 
 
+def fpl_e_m(p, e, i, t, w, h):
   '''
     Calculate the total forward privacy loss at the current
     timestamp using the exponential model, i.e., next releases
@@ -1075,7 +1077,6 @@ def fpl_e(p, e, i, t, w, h):
       a - The forward privacy loss at the current timestamp
           due to the next data releases.
   '''
-def fpl_e_m(p, e, i, t, w, h):
   if i + w**h < t:
     return priv_l_m(np.linalg.matrix_power(p, w**h), fpl_e_m(p, e, i + w**h, t, w, h + 1), e[i - 1])
   elif i + w**h >= t:
@@ -1084,6 +1085,7 @@ def fpl_e_m(p, e, i, t, w, h):
     return e[t - 1]
 
 
+def tpl(bpl, fpl, e):
   '''
     Calculate the total privacy loss at every timestamp.
 
@@ -1094,10 +1096,10 @@ def fpl_e_m(p, e, i, t, w, h):
     Returns:
       The list of total privacy loss at every timestamp.
   '''
-def tpl(bpl, fpl, e):
   return [x + y - z for (x, y, z) in zip(bpl, fpl, e)]
 
 
+def tpl_lmdk_mem(e, p_b, p_f, seq, lmdks):
   '''
     Calculate the temporal privacy loss at every timestamp
     taking into account landmarks.
@@ -1118,7 +1120,6 @@ def tpl(bpl, fpl, e):
       a   - The total privacy loss at every timestamp
             taking into account landmarks.
   '''
-def tpl_lmdk_mem(e, p_b, p_f, seq, lmdks):
   a_b = np.zeros(len(seq))
   a_f = np.zeros(len(seq))
   a = np.zeros(len(seq))
@@ -1135,6 +1136,7 @@ def tpl_lmdk_mem(e, p_b, p_f, seq, lmdks):
   return a_b, a_f, a
 
 
+def get_limits(t, seq, lmdks):
   '''
     Get the limits for the calculation of temporal privacy loss.
 
@@ -1146,7 +1148,6 @@ def tpl_lmdk_mem(e, p_b, p_f, seq, lmdks):
       t_prv - The previous landmark.
       t_nxt - The next landmark.
   '''
-def get_limits(t, seq, lmdks):
   # Add landmark limits.
   seq_lmdks = np.copy(lmdks)
   # if seq[0] not in seq_lmdks:
@@ -1174,6 +1175,7 @@ def get_limits(t, seq, lmdks):
   return t_prv, t_nxt
 
 
+def plot_loss(title, e, a_b, a_f, a):
   '''
     Plots the privacy loss of the time series.
 
@@ -1186,7 +1188,6 @@ def get_limits(t, seq, lmdks):
     Returns:
       Nothing.
   '''
-def plot_loss(title, e, a_b, a_f, a):
   plt.rc('font', family='serif')
   plt.rc('font', size=10)
   plt.rc('text', usetex=True)
@@ -1221,6 +1222,7 @@ def plot_loss(title, e, a_b, a_f, a):
   plt.show()
 
 
+def cmp_loss(title, a, a_s, a_e, a_l):
   '''
     Plots a comparison of the privacy loss of all models.
 
@@ -1233,7 +1235,6 @@ def plot_loss(title, e, a_b, a_f, a):
     Returns:
       Nothing.
   '''
-def cmp_loss(title, a, a_s, a_e, a_l):
   plt.rc('font', family='serif')
   plt.rc('font', size=10)
   plt.rc('text', usetex=True)
@@ -1268,6 +1269,7 @@ def cmp_loss(title, a, a_s, a_e, a_l):
   plt.show()
 
 
+def parse_args():
   '''
     Parse arguments.
 
@@ -1284,7 +1286,6 @@ def cmp_loss(title, a, a_s, a_e, a_l):
       -t, --time,         The time limit.
       -w, --window,       The size of the event protection window.
   '''
-def parse_args():
   # Create argument parser.
   parser = argparse.ArgumentParser()