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physics.py
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'''
Copyright by Artem Vorontsov, Kaspersky Lab US, 2021
email: artem7vorontsov@gmail.com
'''
import numpy as np
from sklearn.preprocessing import StandardScaler
np_DTYPE = np.float32
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def init(L, N, al, be):
x = np.linspace(-L/2, L/2, N)
y = np.linspace(-L/2, L/2, N)
X, Y = np.meshgrid(x, y)
hat = np.exp(-al*(X**2 + Y**2))
J0 = np.sum(hat*np.exp(-be*(X**2 + Y**2)))
return hat, J0, X, Y
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def sim(u, tr, be, X, Y, hat, J0, t, frame_noise_pow=0.0):
xt, yt = tr[0], tr[1]
z = np.random.randn(hat.shape[0], hat.shape[1])
x, y = interp(xt, t), interp(yt, t)
frame = np.exp(-be*((X - (x - u[0]))**2 + (Y - (y - u[1]))**2)) + frame_noise_pow*z
J = metric(frame, hat, J0)
return J, frame, [x, y]
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def metric(frame, hat, J0):
M = frame*hat
J = 1.0 - np.sum(M)/J0
return J
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def interp(xt, t):
if t == np.floor(t):
x = xt[int(t)]
else:
ind0 = int(np.floor(t))
ind1 = int(min(np.ceil(t), len(xt)))
x = ((ind1 - t)*xt[ind0] + (t - ind0)*xt[ind1])
return x
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def gen_traj(type, len, ker_type='exp', ker_size=2000, power=1, vel=500):
if type == 'rnd':
tr = gen_random_traj((len, 2), ker_type=ker_type, ker_size=ker_size, power=power)
else:
tr = [np.sin(np.asarray(range(len))/vel), np.cos(np.asarray(range(len))/vel)]
return tr
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def gen_random_traj(shape, ker_type, ker_size, power):
(L, n_vars) = shape
if L < ker_size:
w = np.random.randn(ker_size, n_vars).astype(np_DTYPE)
else:
w = np.random.randn(L, n_vars).astype(np_DTYPE)
if ker_type == 'exp/2':
x = np.linspace(-3.0, 0.0, ker_size, dtype=np_DTYPE)
ker = np.exp(-x**2)
elif ker_type == 'exp':
x = np.linspace(-3.0, 3.0, ker_size, dtype=np_DTYPE)
ker = np.exp(-x**2)
elif ker_type == 'haar':
ker = np.ones((ker_size,), dtype=np_DTYPE)
else:
ker = np.ones((1,), dtype=np_DTYPE)
res = convolve(w, ker, 'periodic')
scaler = StandardScaler()
tr = power*scaler.fit_transform(res)
if L < ker_size:
tr = tr[:L, :]
return list(tr.T)
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def convolve(w, ker, mode):
L, n_vars = w.shape
n_ker = len(ker)
res = []
if mode == 'periodic':
ker_ = np.zeros((L,), dtype=np_DTYPE)
# Inverse order of ker for using fft(ker_) instead of ifft(ker_)
ker_[:n_ker] = ker[n_ker - 1 - np.asarray(range(n_ker))]
tmp1 = ker_/np.sum(ker)
tmp2 = np.fft.fft(tmp1)
tmp2 = np.stack([tmp2]*n_vars, axis=1)
tmp3 = np.fft.fft(w, axis=0)
tmp4 = np.fft.ifft(np.multiply(tmp2, tmp3), axis=0)
res = np.real(tmp4)
elif mode == 'smooth':
w_ = np.zeros((L + 2*n_ker, n_vars), dtype=np_DTYPE)
w_[n_ker : L + n_ker, :] = w
ker_ = np.zeros((L + 2*n_ker,), dtype=np_DTYPE)
ker_[:n_ker] = ker[n_ker - 1 - np.asarray(range(n_ker))]
tmp1 = ker_/np.sum(ker)
tmp2 = np.fft.fft(tmp1)
tmp2 = np.stack([tmp2] * n_vars, axis=1)
tmp3 = np.fft.fft(w_, axis=0)
tmp4 = np.fft.ifft(np.multiply(tmp2, tmp3), axis=0)
res = np.real(tmp4)
res = res[n_ker : L + n_ker, :]
else:
print('Please, specify the convolution mode!')
return res