英文:
Is there any method to generate a piecewise function for tensors in pytorch?
问题
我想要在PyTorch中为张量创建一个分段函数，类似这样。但我不知道如何定义它。我使用了一种非常愚蠢的方法来实现它，但似乎在我的代码中不起作用。
def trapezoid(self, X):
Y = torch.zeros(X.shape)
Y[X % (2 * pi) < (0.5 * pi)] = (X[X % (2 * pi) < (0.5 * pi)] % (2 * pi)) * 2 / pi
Y[(X % (2 * pi) >= (0.5 * pi)) & (X % (2 * pi) < 1.5 * pi)] = 1.0
Y[X % (2 * pi) >= (1.5 * pi)] = (X[X % (2 * pi) >= (1.5 * pi)] % (2 * pi)) * (-2 / pi) + 4
return Y
你能帮我找出如何设计函数trapezoid，以便对于张量X，我可以直接使用trapezoid(X) 来获得结果吗？
英文:
I want to get a piecewise function like this for tensors in pytorch. But I don't know how to define it. I use a very stupid method to do it, but it seems not to work in my code.
def trapezoid(self, X):
Y = torch.zeros(X.shape)
Y[X % (2 * pi) < (0.5 * pi)] = (X[X % (2 * pi) < (0.5 * pi)] % (2 * pi)) * 2 / pi
Y[(X % (2 * pi) >= (0.5 * pi)) & (X % (2 * pi) < 1.5 * pi)] = 1.0
Y[X % (2 * pi) >= (1.5 * pi)] = (X[X % (2 * pi) >= (1.5 * pi)] % (2 * pi)) * (-2 / pi) + 4
return Y
could do you help me find out how to design the function trapezoid, so that for tensor X, I can get the result directly using trapezoid(X)?
答案1
得分: 1
由于您的函数具有2π的周期，我们可以关注[0,2π]。由于它是分段线性的，可以将其表示为在[0,2π]上的小型ReLU网络，如下所示：
trapezoid(x) = 1 - relu(x-1.5π)/0.5π - relu(0.5π-x)/0.5π
因此，我们可以像这样在Pytorch中编写整个函数：
import torch
import torch.nn.functional as F
from torch import tensor
from math import pi
def trapezoid(X):
# 左角位置、右角位置、高度
a, b, h = tensor(0.5*pi), tensor(1.5*pi), tensor(1.0)
# 对2*pi取余以实现周期性
X = torch.remainder(X,2*pi)
return h - F.relu(X-b)/a - F.relu(a-X)/a
绘图以进行双重检查并生成正确的图像：
import matplotlib.pyplot as plt
X = torch.linspace(-10,10,1000)
Y = trapezoid(X)
plt.plot(X,Y)
plt.title('Pytorch Trapezoid Function')
英文:
Since your function has period 2π we can focus on [0,2π]. Since it's piecewise linear, it's possible to express it as a mini ReLU network on [0,2π] given by:
trapezoid(x) = 1 - relu(x-1.5π)/0.5π - relu(0.5π-x)/0.5π
Thus, we can code the whole function in Pytorch like so:
import torch
import torch.nn.functional as F
from torch import tensor
from math import pi
def trapezoid(X):
# Left corner position, right corner position, height
a, b, h = tensor(0.5*pi), tensor(1.5*pi), tensor(1.0)
# Take remainder mod 2*pi for periodicity
X = torch.remainder(X,2*pi)
return h - F.relu(X-b)/a - F.relu(a-X)/a
Plotting to double check produces the correct picture:
import matplotlib.pyplot as plt
X = torch.linspace(-10,10,1000)
Y = trapezoid(X)
plt.plot(X,Y)
plt.title('Pytorch Trapezoid Function')
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