用标度平方法代替欧拉法的积分

我试图在python中实现moler和van loan,2003;arsigny等人,2006b,a.中描述的用于集成的缩放和平方方法。该方法基本上说明,如果时间步数是2的幂,那么可以通过缩放和平方方法来确定解。有关该方法的说明,见附文第3页。 https://ufile.io/8xdx7 是的。

附言:不是家庭作业什么的。我只是想优化我已经使用euler方法但速度慢的函数代码。

shape = image.shape
dx = np.random.normal(0, 10, shape)
dy = np.random.normal(0, 1, shape)

dx = gaussian_filter(dx, 10)
dy = gaussian_filter(dy, 10)
# dx = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
# dy = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
han_window_1 = np.hanning(shape[0])
han_window_2 = np.hanning(shape[1])

for i in range(0, shape[1]):
dy[:,i] = dy[:,i] * han_window_1
for i in range(0, shape[0]):
dx[i,:] = dx[i,:] * han_window_2

# here I want to integrate dx and dy using the aforementioned method instead of Euler's method.