41CL Quiz: Determinant of 30x30 anti-Identity matrix

[Ángel Martin]

Yes, I'm listening :-D

in fact I've been busy fixing a few glitches in the MCODE as a result of the beta testing, which this test case has also contributed to...

Thanks for the example, it is indeed an interesting one (but of course it *had* to be given its source ;-). First off, there's a few remarks to be made:

• The execution times are pretty much independent from the actual element values, as there's no provision in the MCODE for special cases (such as 1 or 0) in the calculations. Therefore the D30 example takes about 11 seconds, same as the 30x30 anti-identity matrix took in the previous example.
  

• The accuracy is the same as using the Advantage module. Remember: I didn't write new code - only patched it to allow for CL Y-registers as well as the standard RAM registers or X-Mem registers allowed by the Advantage.
  

With those two remarks made, here's how I did it.

First, the program used to create the matrices and calculate the determinant:

01 LBL "DDN" - expects n in X-Reg
02 RCL X
03 E3
04 /
05 +
06 "Y" - matrix will use the Y-Registers, starting at Y_001
07 MATDIM
08 1
09 MCON - in the SandMatrix
10 CLX
11 MSIJA
12 2
13 LBL 00
14 1
15 +
16 MSC+
17 SF 25
18 J+
19 FS?C 25
20 GTO 00
21 MDET
22 END

And these are the results:

D(11) = 1,486,442,880.0 - in 1.8 seconds
D(13) = 2.834656472 E11 - in 2.01 seconds
D(30) = 3.311538747 E34 - in about 11 seconds

Not bad again, in fact surprisingly good. Using Gerson's values as the reference, these results are practically as accurate as those obtained using the equivalent formula D(n) = (n+1)!*H(n+1). - which can be easily programmed using the Harmonic function in the SandMath (step #4 in the trivial program below):

01 LBL "DN" - n is expected in X
02 1
03 +
04 HARM
05 LASTX
06 FACT
07 *
08 END

which returns respectively (in just a few milliseconds this time):

D(11) = 1,486,442,880.0
D(13) = 2.834656474 E11
D(30) = 3.311538746 E34

Thanks for the case study, it's helped with the beta testing and adds another interesting problem to the list.

Saludos,
Á.