[英]Efficiently rotate a set of points with a rotation matrix in numpy
I have a list of 3D points stored in numpy array A
with shape (N,3)
and a rotation matrix R
with shape (3,3)
.我有一个存储在形状为
(N,3)
numpy 数组A
中的 3D 点列表和形状为(3,3)
的旋转矩阵R
。 I'd like to compute the dot product of Rx
for each point x
in A
in-place.我想就地计算
A
中每个点x
的Rx
点积。 Naively I can do this:我天真地可以这样做:
for n in xrange(N):
A[n,:] = dot(R, A[n,:])
Is there a way to vectorize this with a native numpy call?有没有办法用原生的 numpy 调用将其矢量化? If it matters, N is on order of a couple thousand.
如果重要的话,N 大约是几千。
您可以将 A 与旋转矩阵的转置相乘:
A = dot(A, R.T)
There's a couple of minor updates/points of clarification to add to Aapo Kyrola's (correct) answer.有几个小的更新/澄清点要添加到 Aapo Kyrola 的(正确)答案中。 First, the syntax of the matrix multiplication can be slightly simplified using the recently added matrix multiplication operator
@
:首先,可以使用最近添加的矩阵乘法运算符
@
稍微简化矩阵乘法的语法:
A = A @ R.T
Also, you can arrange the transformation in the standard form (rotation matrix first) by taking the transpose of A
prior to the multiplication, then transposing the result:此外,您可以通过在乘法之前对
A
进行转置,然后对结果进行转置,以标准形式(先旋转矩阵)排列变换:
A = (R @ A.T).T
You can check that both forms of the transformation produce the same results via the following assertion:您可以通过以下断言检查两种形式的转换是否产生相同的结果:
np.testing.assert_array_equal((R @ A.T).T, A @ R.T)
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