def auto_correlation(seq, start=0, end=None):
avg = Analysis.avg(seq, start=start, end=end)
var = Analysis.var(seq, start=start, end=end)
res = OrderedDict()
y = seq.y
if not end:
end = len(seq._seq)
for shift in range(start, end):
res[shift - start] = sum([(y[x] - avg) * (y[x + shift] - avg)
for x in range(0, end - shift)]) / var
return Sequence.from_dict(
OrderedDict(zip(seq.x[start:end], res.values())))
def cross_correlation(first, second):
if (len(first) != len(second)):
raise ValueError("Sequences are not the same size")
first_avg = Analysis.avg(first)
second_avg = Analysis.avg(second)
div = math.sqrt(Analysis.var(first) + Analysis.var(second))
res = []
f_y = first.y
s_y = second.y
for shift in range(len(first)):
res.append(
sum([(f_y[k] - first_avg) * (s_y[k + shift] - second_avg)
for k in range(len(first) - shift)]) / div)
return Sequence.from_dict(OrderedDict(zip(first.x, res)))
def dtf(seq):
n = len(seq)
y_tmp = seq.y
res = []
for k in range(n):
Re = 0
Im = 0
for t in range(n):
angle = 2 * math.pi * t * k / n
Re += y_tmp[t] * math.cos(angle)
Im += y_tmp[t] * math.sin(angle)
res.append(math.sqrt((Re / n)**2 + (Im / n)**2))
return Sequence.from_dict(
OrderedDict(zip(seq.x[:n // 2:], res[:n // 2])))
def dtf(seq):
n = len(seq)
y_tmp = seq.y
x_tmp = seq.x
res = []
for k in range(n):
Re = 0
Im = 0
for t in range(n):
angle = 2 * math.pi * t * k / n
Re += y_tmp[t] * math.cos(angle)
Im += y_tmp[t] * math.sin(angle)
res.append(math.sqrt((Re / n)**2 + (Im / n)**2))
freq_top = 1 / (2 * (x_tmp[1] - x_tmp[0]))
freq_delta = 2 * freq_top / n
x_tmp = [freq_delta * x for x in range(len(seq.x[:n // 2]))]
return Sequence.from_dict(OrderedDict(zip(x_tmp, res[:n // 2])))
def untrend(seq, window_size=5):
res = OrderedDict()
for idx, x in enumerate(seq.x):
res[x] = Analysis.avg(seq, max(0, idx - window_size),
min(len(seq) - 1, idx + window_size))
return seq - Sequence.from_dict(res)