Are we done with this bug report?  Okay to close?

@Markus: Sorry, I think I misled you.  The 3-output argument syntax is valid for dense matrices as long as there is just a single matrix A.  This is what polyfit.m is relying on and, as I said, it is valid.  The extra argument '0' in

[q,r,p] = qr (a, 0);

is not a matrix B, but a flag asking for an "economy"-sized return value.

So, I think the input validation needs to look like

if (have_b && nargout > 2)
  error (...)

@Markus: Those tests can be removed when the input validation is made tighter.  It will be very obvious because those tests will fail during 'make check' immediately.

There are currently several BISTs like the following ones in qr.cc where `a` is dense:

%! [q,r,p] = qr (a, 0);  t(j++) = __testqr (q, r, a, p);
%! [q,r,p] = qr (a',0);  t(j++) = __testqr (q, r, a', p);
-vebatim-

So is this an un-documented extension in Octave? Or should we also remove these tests?

Ah. Thank you. I misunderstood (and didn't find that explained in the help text).

>> A = sparse(rand(3,2));
>> B = sparse(rand(3,1));
>> [C, R, E] = qr (A, B);
>> X = E*(R\C)
X =

  -0.1954
   0.4075

>> A\B
ans =

Compressed Column Sparse (rows = 2, cols = 1, nnz = 2 [100%])

  (1, 1) -> -0.1954
  (2, 1) -> 0.4075

That looks good to me.

Should we close this as fixed? Or keep it open to document that we now support this syntax for `qr`?

What about the syntax with two full matrices as input and three output arguments (which is also undocumented)? What does it return? Should that be rejected?

I tried the following with Octave at hg id 512591ccb174 (i.e., after the changes for bug #57033 ):

>> A = rand(3,2);
>> B = rand(3,1);
>> [C, R, E] = qr (sparse(A), sparse(B));
>> X = E*(R\C);
>> A*X
ans =

   0.1617
   0.2306
   0.2725

>> B
B =

   0.802331
   0.021141
   0.069525

It looks like the identity described in comment #2 doesn't hold with our current implementation.

Is that a problem?

This may not be implemented in Octave.  Looking at the documentation, the calling forms are:

 -- [Q, R] = qr (A)
 -- [Q, R, P] = qr (A) # non-sparse A
 -- X = qr (A) # non-sparse A
 -- R = qr (A) # sparse A
 -- [C, R] = qr (A, B)
 -- [...] = qr (..., 0)
 -- [...] = qr (..., "vector")
 -- [...] = qr (..., "matrix")

There is a three-output form for a single input matrix A, but there is no listing for a three-output form with 2 inputs.  In the main body of the documentation there is also no discussion of a form such as

[C, R, P] = qr (A, B)

It gets weirder.  Matlab won't accept

[z,r,p] = qr (a,b);

and complains that the matrices must be sparse.  If I do that with

[z,r,p] = qr (sparse(a),sparse(b));

then it works and returns a 3x1 vector.

However, Octave goes the other way.  it will accept full matrices with a permutation output, but not sparse ones:

[z,r,p] = qr(sparse(a),sparse(b));
error: qr: Permutation output is not supported for sparse input

I think we need to decide what should happen and then go implement that.  Should the [z,r,p] form be allowed with full matrices?  Should the [z,r,p] = qr (a,b) form work with sparse matrices?