On Thu, Oct 26, 2017 at 12:11 PM, Daniele Nicolodi <dani...@grinta.net> wrote:
> Hello, > > is there a better way to write the dot product between a stack of > matrices? In my case I need to compute > > y = A.T @ inv(B) @ A > > with A a 3x1 matrix and B a 3x3 matrix, N times, with N in the few > hundred thousands range. I thus "vectorize" the thing using stack of > matrices, so that A is a Nx3x1 matrix and B is Nx3x3 and I can write: > > y = np.matmul(np.transpose(A, (0, 2, 1)), np.matmul(inv(B), A)) > > which I guess could be also written (in Python 3.6 and later): > > y = np.transpose(A, (0, 2, 1)) @ inv(B) @ A > > and I obtain a Nx1x1 y matrix which I can collapse to the vector I need > with np.squeeze(). > > However, the need for the second argument of np.transpose() seems odd to > me, because all other functions handle transparently the matrix stacking. > > Am I missing something? Is there a more natural matrix arrangement that > I could use to obtain the same results more naturally? There has been discussion of adding a operator for transposing the matrices in a stack, but no resolution at this point. However, if you have a stack of vectors (not matrices) you can turn then into transposed matrices like `A[..., None, :]`, so `A[..., None, :] @ inv(B) @ A[..., None]` and then squeeze. Another option is to use einsum. Chuck
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