If I issue:
spparms('spumoni',1);
A\b;
Then I can see the decision made by mldivide on how to solve against A. In my case it chooses MA57:
sp\: bandwidth = 26633+1+26633.
sp\: is A diagonal? no.
sp\: is band density (0.00299541) > bandden (0.5) to try banded solver? no.
sp\: is A triangular? no.
sp\: is A morally triangular? no.
sp\: is A a candidate for Cholesky (symmetric, real positive or negative diagonal)? no.
sp\: But A is real symmetric; try MA57.
I would like to cache the decomposition (to conduct more solves against the same matrix later). If I call:
I see
D =
decomposition with properties:
MatrixSize: [27045 27045]
Type: 'ldl'
Sifting through the documentation I can match up ldl to MA57, so I thought this meant I'm using the same decomposition as above.
However a few things hint otherwise:
tic;A\b;toc
tic;D = decomposition(A);toc
tic;D = decomposition(A,'ldl');toc
on my MacPro with 1.5TB memory and 28 cores produces:
Elapsed time is 1.226560 seconds.
Elapsed time is 2.343294 seconds.
Elapsed time is 2.440572 seconds.
- solving with the decomposition gives me a warning that \ doesn't:
alerts me:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 8.766761e-23.
> In decomposition/warnIfIllConditioned (line 714)
In \ (line 404)
Questions:
- Do decomposition and \ make the same decisions on the choice of decomposition to use?
- If not, is there way to get at whatever decomposition \ is actually using? (in my case this "faster" MA57 decomposition)
I'm imagining/wish for something like:
where D would contain the reusable decomposition created and used during \.
