numpy 3D 点积

Question

我有两个 3dim numpy 矩阵，我想根据一个轴做点积而不使用循环：

a=[ [[ 0, 0, 1, 1, 0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
    [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [ [ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [ [ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]],
 [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0.]],
 [[ 0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
  [ 1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
  [ 0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
  [ 0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  1,  0,  0]]]

b=[[[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]],
 [[ 0,  0,  1,  0,  0.],
  [ 1,  0,  0,  0,  0.],
  [ 0,  0,  0,  0,  0.],
  [ 0,  1,  0,  0,  0.]]]
dt = np.dtype(np.float32)
a=np.asarray(a,dtype=dt)
b=np.asarray(b,dtype=dt)
print(a.shape)
print(b.shape)

a 的形状为 (7, 4, 15)，b 的形状为 (7, 4, 5)。我希望 c=np.dot(a,b) 的大小为 (7,5,15)，如下所示：

c = np.zeros((7,15,5))
for i in range(7):
   c[i,:,:] = np.dot(a[i,:,:].T , b[i,:,:])

但我正在寻找没有 for 循环的解决方案。类似于：

c = np.tensordot(a.reshape(4,7,5),b.reshape(7,4,15),axes=([1,0],[0,1]))

但是这个没有按预期工作。

我也试过这个：

newaxes_a=[2,0,1]
newaxes_b=[1,0,2]

newshape_a=(-1,28)
newshape_b=(28,-1)
a_t = a.transpose(newaxes_a).reshape(newshape_a)
b_t = b.transpose(newaxes_b).reshape(newshape_b)
c = np.dot(a_t, b_t)

没有按预期工作。

有什么想法吗？

Answer 1

你可以使用np.einsum-

#to match the given example
c2 = np.einsum('ijk,ijl->ikl',a,b)
print np.allclose(c, c2)

另一个使用 broadcasting -

c = (a[:,:,None,:]*b[...,None]).sum(1)

numpy 3D 点积

numpy 3D dot product

python

numpy

vectorization

dot-product

array-broadcasting