On Wed, Jan 24, 2024 at 11:02 PM Marten van Kerkwijk <[email protected]>
wrote:
> Stack of matrices in this context is a an ndarray in which the last two
> dimensions are interpreted as columns and rows of matrices (in that
> order), stack of vectors as an ndarray in which the last dimension is
> interpreted as column vectors. (Well, axes in all these functions can
> be chosen arbitrarily, but those are the defaults.)
>
> So a simple example for matvec would be a rotation matrix that I'd like
> to apply to a large number of vectors (say to points in space); this is
> currently not easy. Complex vectors might be Fourier components. (Note
> that I was rather sloppy in calling it multiplication rather than using
> the term vector-matrix product, etc.; it is definitely not element-wise!).
>
> The vector-matrix product comes up a bit less, but as mentioned by
> Evgeni in physics there is, e.g., the bra-ket stuff with Hamiltonians
> (<\psi | \hat H | \psi>), and in linear least squares one often gets
> terms which for real data are written as Xᵀ Z, but for complex would be
> Xᴴ Z [1]
>
> Hope this clarifies things!
>
>
Thanks, but I'm still confused about the need.
Perhaps the following illustrates why.
With respect to the example you offered, what am I missing?
Alan Isaac
import numpy as np
rng = np.random.default_rng()
rot = np.array([[0,-1],[1,0]]) #a rotation matrix
print("first type of stack of vectors:")
vecs1 = rng.random((2,10))
print(vecs1.shape==(2,10))
result1 = rot.dot(vecs1)
print("second type of stack of vectors:")
rng = np.random.default_rng(314)
vecs2 = vecs1.T
result2 = rot.dot(vecs2.T)
print(f"same result2? {(result1==result2).all()}")
print("third type of stack of vectors:")
vecs3 = np.reshape(vecs2,(10,2,1))
result3 = rot.dot(vecs3.squeeze().T)
print(f"same result3? {(result1==result3).all()}")
print("fourth type of stack of vectors:")
vecs4 = np.reshape(vecs2,(10,1,2))
result4 = rot.dot(vecs4.squeeze().T)
print(f"same result4? {(result1==result4).all()}")
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