On Tue, Jun 25, 2019 at 4:29 AM Cameron Blocker <cameronjblocker@gmail.com> wrote:
In my opinion, the matrix transpose operator and the conjugate transpose operator should be one and the same. Something nice about both Julia and MATLAB is that it takes more keystrokes to do a regular transpose instead of a conjugate transpose. Then people who work exclusively with real numbers can just forget that it's a conjugate transpose, and for relatively simple algorithms, their code will just work with complex numbers with little modification.
I'd argue that MATLAB's feature of `'` meaning adjoint (conjugate transpose etc.) and `.'` meaning regular transpose causes a lot of confusion and probably a lot of subtle bugs. Most people are unaware that `'` does a conjugate transpose and use it habitually, and when for once they have a complex array they don't understand why the values are off (assuming they even notice). Even the MATLAB docs conflate the two operations occasionally, which doesn't help at all. Transpose should _not_ incur conjugation automatically. I'm already a bit wary of special-casing matrix dynamics this much, when ndarrays are naturally multidimensional objects. Making transposes be more than transposes would be a huge mistake in my opinion, already for matrices (2d arrays) and especially for everything else. András
Ideally, I'd like to see a .H that was the defacto Matrix/Linear Algebra/Conjugate transpose that for 2 or more dimensions, conjugate transposes the last two dimensions and for 1 dimension just conjugates (if necessary). And then .T can stay the Array/Tensor transpose for general axis manipulation. I'd be okay with .T raising an error/warning on 1D arrays if .H did not. I commonly write things like u.conj().T@v even if I know both u and v are 1D just so it looks more like an inner product.
-Cameron
On Mon, Jun 24, 2019 at 6:43 PM Ilhan Polat <ilhanpolat@gmail.com> wrote:
I think enumerating the cases along the way makes it a bit more tangible for the discussion
import numpy as np z = 1+1j z.conjugate() # 1-1j
zz = np.array(z) zz # array(1+1j) zz.T # array(1+1j) # OK expected. zz.conj() # 1-1j ?? what happened; no arrays? zz.conjugate() # 1-1j ?? same
zz1d = np.array([z]*3) zz1d.T # no change so this is not the regular 2D array zz1d.conj() # array([1.-1.j, 1.-1.j, 1.-1.j]) zz1d.conj().T # array([1.-1.j, 1.-1.j, 1.-1.j]) zz1d.T.conj() # array([1.-1.j, 1.-1.j, 1.-1.j]) zz1d[:, None].conj() # 2D column vector - no surprises if [:, None] is known
zz2d = zz1d[:, None] # 2D column vector - no surprises if [:, None] is known zz2d.conj() # 2D col vec conjugated zz2d.conj().T # 2D col vec conjugated transposed
zz3d = np.arange(24.).reshape(2,3,4).view(complex) zz3d.conj() # no surprises, conjugated zz3d.conj().T # ?? Why not the last two dims swapped like other stacked ops
# For scalar arrays conjugation strips the number # For 1D arrays transpose is a no-op but conjugation works # For 2D arrays conjugate it is the matlab's elementwise conjugation op .' # and transpose is acting like expected # For 3D arrays conjugate it is the matlab's elementwise conjugation op .' # but transpose is the reversing all dims just like matlab's permute() # with static dimorder.
and so on. Maybe we can try to identify all the use cases and the quirks before we can make design the solution. Because these are a bit more involved and I don't even know if this is exhaustive.
On Mon, Jun 24, 2019 at 8:21 PM Marten van Kerkwijk <m.h.vankerkwijk@gmail.com> wrote:
Hi Stephan,
Yes, the complex conjugate dtype would make things a lot faster, but I don't quite see why we would wait for that with introducing the `.H` property.
I do agree that `.H` is the correct name, giving most immediate clarity (i.e., people who know what conjugate transpose is, will recognize it, while likely having to look up `.CT`, while people who do not know will have to look up regardless). But at the same time agree that the docstring and other documentation should start with "Conjugate tranpose" - good to try to avoid using names of people where you have to be in the "in crowd" to know what it means.
The above said, if we were going with the initial suggestion of `.MT` for matrix transpose, then I'd prefer `.CT` over `.HT` as its conjugate version.
But it seems there is little interest in that suggestion, although sadly a clear path forward has not yet emerged either.
All the best,
Marten
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