`iczt(X)` is numerical unstable and return nan when `len(X)` is too big (arround > 5000), fix suggestion included
Opened this issue · 1 comments
mammalwong commented
version of czt: 0.0.7, issue was found when using google colab.
To reproduce the issue:
import numpy as np
import czt as czt
for n in [1000,10000]:
x = np.linspace(-4,4,n)
y = np.exp(-x**2)
yhat = czt.czt(y,simple=False)
yphi = czt.iczt(yhat,simple=False)
print(np.any(np.isnan(yhat)),np.any(np.isnan(yphi)))
outputs:
False False
False True
expected result:
False False
False False
mammalwong commented
suggested fix (tested in google colab locally)
The np.cumprod
call in the below lines of the source of iczt
caused this numerical instability issue, it makes many tailing entries in p
become 0:
p = np.r_[1, (W ** k[1:] - 1).cumprod()]
u = (-1) ** k * W ** (k * (k - n + 0.5) + (n / 2 - 0.5) * n) / p
# equivalent to:
# u = (-1) ** k * W ** ((2 * k ** 2 - (2 * n - 1) * k + n * (n - 1)) / 2) / p
u /= p[::-1]
it can be solved by modifying the above few lines like this:
u = (-1) ** k * W ** (k * (k - n + 0.5) + (n / 2 - 0.5) * n) # /p is removed from here (1)
p = np.r_[1, W ** k[1:] - 1]
lp = np.abs(p) # lp stand for ln(p)
lp = np.cumsum(np.log(lp)) + np.angle(np.cumprod(p/lp))*1j
# above seperate the magnitude and angle of the entries in p
# it cumsum magnitude in log domain to replace the unstable cumprod of the magnitude
# and cumprod only the normalized angle to ensure the angle is also stable when X is long
u /= np.exp(lp+lp[::-1]) # /p from (1) is moved to here as +lp in exp()