[Octave-bug-tracker] [bug #48807] new gsvd function is incompatible w/Matlab

[Nir Krakauer]

Follow-up Comment #4, bug #48807 (project octave):

It looks like there are differences between Matlab and LAPACK in how GSVD is
defined. This is alluded to vaguely in both Matlab's [1] and Octave's [2]
documentation.

An interface to LAPACK's GSVD routines is good to have available, regardless
of what Matlab is doing.

As far as recovering Matlab's form, we can do that (up to the ordering of
singular values and vectors, which seems to be consistently the opposite) for
at least their Examples 1 and 2 with


[U, V, C, S, X, R] = gsvd (A, B);
X = (R / X)';
[m, n] = size(A);
if m > n
  C = [C; zeros(m-n, n)];
elseif m < n
  C = [C zeros(m, n-m)];
  S0 = S; S = eye(n); S(1:m, 1:m) = S0;
endif



[1] cf.
https://groups.google.com/forum/#!topic/comp.soft-sys.matlab/aBgSZNTBcxU
[2] "Other authors, like S. Van Huffel, define this transformation as the
simulatenous diagonalisation of the input matrices, this can be achieved by
multiplying x by the inverse of [I 0; 0 r]."

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