[英]Vectorize computation on mesh in Python
我有矩阵: f = np.zeros((M, N))
充满了一些浮点数。 我想用其邻居的平均值替换每个内部点f[i, j]
: f_new[i,j] = (f[i-1, j] + f[i+1, j] + f[i, j+1] + f[i, j-1])/4
。 有一个显而易见的方法:
f_new = f.copy()
for i in range(1, M-1):
for j in range(1, N-1):
f_new[i,j] = (f[i-1, j] + f[i+1, j] + f[i, j+1] + f[i, j-1])/4
f = f_new
在Python中是否有更优雅的(矢量化)方法? 谢谢。
只需使用卷积即可 。 有多种开源实现,但是scipy的作品:
import numpy as np
import scipy.signal as signal
import time
f = np.random.random((1000, 1000))
# -------- For loop
start = time.perf_counter()
f_pad = np.pad(f, ((1, 1), (1, 1)), 'constant', constant_values=0) # pad the array
f_new = f_pad.copy()
for i in range(1, f.shape[0]+1):
for j in range(1, f.shape[1]+1):
f_new[i,j] = (f_pad[i-1, j] + f_pad[i+1, j] + f_pad[i, j+1] + f_pad[i, j-1])/4.
f_new = f_new[1:-1, 1:-1]
print("For loop time:", str(time.perf_counter() - start))
# -------- Convolution
start = time.perf_counter()
f_newer = signal.convolve2d(f,
np.array([[0, 0.25, 0],
[0.25, 0, 0.25],
[0, 0.25, 0]]),
mode='same',
boundary='fill',
fillvalue=0)
print("Convolution time:", str(time.perf_counter() - start))
# >> For loop time: 1.4474979060469195
# >> Convolution time: 0.0972418460296467
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