英文:
Tensorproduct of multiple vectors in an array
问题
我需要计算存储在两个数组中的多对向量的张量积。我将给您一个示例：
a = np.array([[3, 5, 1], [6, 5, 4]])
b = np.array([[8, 2, 3], [7, 8, 9]])
我想要计算的是：
np.array([tensorproduct(a[0], b[0]), tensorproduct(a[1], b[1])])
我找不到使用numpy函数完成这个任务的好方法，而且我不想将数组拆分为其各个向量，因为这太耗时了（我需要在递归模拟中使用这个，所以我可以节省的每一点时间都非常宝贵）。我希望有人可以帮助我。
英文:
I need to compute the tensor product of several pairs of vectors, that are stored in two arrays. I'll give you an example:
a=np.array([[3,5,1],[6,5,4]])
b=np.array([[8,2,3],[7,8,9]])
what I want to compute is:
np.array([tensorproduct(a[0],b[0]),tensorproduct(a[1],b[1])])
I couldn't find a good way to do this with numpy functions and I don't want to do it by splitting the arrays up into their individual vectors, because this takes way to long (I need this for a recursive simulation, so every bit of time I can save is gold). I hope there is a quick way to do this, can anyone help me?
答案1
得分: 1
如果您指的是张量积仅仅是矩阵乘法/点积，我认为您想要类似这样的东西：
z = a * b
z = np.sum(z, axis=1)
编辑：
根据您的评论，我认为您想要（可以做）的是使用广播将维度添加，以便可以进行简单的乘法。
z = x[:, :, None, None] * y[None, None, :, :]
英文:
If by tensorproduct you just mean a matmul/dot product, I think you want something like this:
z = a * b
z = np.sum(z, axis=1)
Edit:
Based on your comment what I think you want (can do) is use broadcasting to add dimensions so that you can do a simple multiplication.
z = x[:, :, None, None] * y[None, None, :, :]
答案2
得分: 0
如果你想要计算(a[0]*b[0]).sum()和(a[1]*b[1]).sum()
你可以使用numpy.einsum来进行计算：
np.einsum('ij,ij->i', a, b)
输出：array([ 37, 118])
英文:
If you want (a[0]*b[0]).sum() and (a[1]*b[1]).sum(),
You can use numpy.einsum with:
np.einsum('ij,ij->i', a, b)
Output: array([ 37, 118])
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