[Octave-bug-tracker] [bug #60273] Wrong result in GSVD

[Rik]

Follow-up Comment #4, bug #60273 (project octave):

Octave is definitely taking the matrix Q from LAPACK and returning it as the
matrix X from gsvd which is incorrect.  Documentation on the routine that
Octave calls is at
https://www.math.utah.edu/software/lapack/lapack-d/dggsvd.html.

The variable naming in gsvd.cc shows that the original coder knew that 'q' was
being returned.  Maybe there wasn't a realization that Matlab was not exactly
mapping the outputs of LAPACK to the outputs of the Matlab function.

In any case, there is a 6th undocumented output from Octave's gsvd function
which is the matrix R from LAPACK.  The documentation should really read


[U, V, Q, C, S, R] = gsvd (A, B)


If you do this then the results conform to the LAPACK documentation and


A = U * C * R * Q'
B = V * C * R * Q'


To recover Matlab's behavior


X = Q*R'




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