Work on removing FIND-DIAGONALIZER-IN-E-BASIS #845
Closed
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
stylewarning
force-pushed
the
diag-to-schur
branch
from
6fbb3c1
to
2bb9a97
Compare
|
I think the original Python implementation from #841 fell prey to the note from
Specifically, in the comment # Generalized Schur decomposition writes
# Re[U] = L D_r R^T, Im[U] = L D_i R^TI think it should be In [1]: from scipy.linalg import norm, qz
In [2]: from scipy.stats import unitary_group
In [3]: rng = unitary_group(dim=2, seed=1729)
In [4]: print(u := rng.rvs())
[[-0.29585687+0.47303725j -0.76750556+0.31565756j]
[ 0.71123856-0.42760284j -0.55613711-0.04479994j]]
In [5]: diag_r, diag_i, left, right = qz(u.real, u.imag)
In [6]: v = (left.T @ diag_r @ right) + 1j * (left.T @ diag_i @ right)
In [7]: norm(u - v)
Out[7]: 3.0436364816617974e-16 |
|
I take back my earlier comment; for unitary (defun gen-gaussian (n)
(magicl:from-list
(loop :for i :from 0 :below (* n n) :collect (alexandria:gaussian-random))
(list n n)))
(defun gen-unitary (n)
(let* ((m (magicl:.complex (gen-gaussian n) (gen-gaussian n)))
(z (magicl:./ m (sqrt 2))))
(multiple-value-bind (q r) (magicl:qr z)
(let* ((d (magicl:diag r))
(normalized-d
(magicl:from-list
(loop :for x :in d :collect (/ x (abs x)))
(list n 1)))
(matrix-d (magicl:hstack (loop :for _ :from 0 :below n :collect normalized-d))))
(magicl:.* q matrix-d)))))and setting * (loop :for _ :from 0 :below 100 :do (orthogonal-decomposition-of-uu^t (gen-unitary 100)))
NILAs such, I'm not sure what's up with the CI failures. |
|
FWIW there's a pretty serious flaw in my pitch to use gges for this. I detailed a bit more in #841 |
|
going to close this since it needs re-thinking |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
This is an attempt to replace
F-D-I-E-Bwith @kilimanjaro's idea of using a Schur decomposition.This aims to fix #841
CC @genos