<< I received the attachment! How?? --rwg >> Apparently small ones can on occasion be smuggled under the wire. That program has now been substantially improved --- eg. I eventually figured out how to truncate those infernal Maple 16-digit hardware fl. pt. numbers for printing, and cleaned up the rather dodgy random orthonormal matrix generator. Source/results posted on request. On 5/19/16, Warren D Smith <warren.wds@gmail.com> wrote:
... --ok, I immediately see from that last URL that you did it wrong. A0 to A1 looks reasonable. A1 to A2 is already wrong because note row #2 was left unaltered (should have changed) but row #1 changed (should have been unaltered).
(1) Steps A0 to A2 operate on rows 3 and 4, not 1 and 2 . (2) My program executes the sequence you specified as follows --- 7 4 8 2 5 9 1 3 6 ... I did previously point out this elementary malfunction, which is the responsibility of the designer rather than the programmer. Once an A_ij to be cleared is specified, Givens' R_ij alters rows & cols i,j , intentionally or otherwise! (3) I did however summon the initiative to investigate alternative scanning sequences: NW instead of SE along diagonals, and inwards rather than outwards. Unsurprisingly, they fail as well. [In fact, I still find it rather surprising that scanning columns does work --- as you point out elsewhere, both N-ward and S-ward versions.]
Remember we are doing adjacent Givens's as per request so it would have been only rows 2 & 3 being affected during the transition from A1 to A2 zeroing first entry in row #3.
(4) Please explain how a struggling mortal is expected to a clear A_ij utilising a _single_ adjacent Givens' R_{i,i+1}(t) , unless j = i+1 . Otherwise, once away from the main sub-diagonal, we are obliged to resort to general Givens' R_ij , are we not?
Look, I really do not want to debug your code for you line by line.
A prospect which would, I expect, horrify us both equally ...
But you ought to perform the most trivial inspection of your output before telling me I'm a horse.
Nay, I look forward to others inspecting it as carefully as I have. Fred Lunnon