cholmod_solve2(CHOLMOD_L) with a subset of rows of B

[dkogan]

Hi. I'm using cholmod_solve2() to solve PLx = b (not Ax = b) many times with different vectors b. Each b is mostly 0, with a small number of non-zero entries. I have working code that specifies b as full, dense matrices, but this is very slow (I'm caling cholmod_solve2() many times). Can I somehow specify a sparse b and have this become fast? There's cholmod_spsolve(), but that reconstructs the full dense b. And cholmod_solve2() takes a Bset argument, but I think this applies to the output x, not the input b; right?

I want to say the permutation P makes this difficult; is that right? Would this be any easier if I was asking about Ax = b?

Thank you

[dkogan]

I worked on this a bit more, and made a bit of progress. I was misinterpreting the documentation: Bset does apply to the input b, as expected. I'm running a test solving Ax = b (to keep things simple) with a sparse b and with/without Bset. The resulting x should be the same in both cases, but it is not. The "right" x is not sparse at all (non-zero in all entries; verified with a dense solve). And the solve without Bset does return this correct x. Using Bset I observe cholmod_solve2() report a sparse output structure in the Xset variable. The values in this sparse x are indeed correct (they match the dense solve and the no-Bset solve). However, the values of x outside Xset are wrong. This isn't unexpected given the sparse Xset, but in this case Xset should be "all the elements", and it isn't. Am I doing this wrong? I can create a simple reproducer if that's useful, although I'm pretty sure I'm just doing something incorrectly.

Thanks.

[dkogan]

Sorry to keep replying to my own question. The problem (overly sparse Xset) is easily observable in the cholmod demos. I'm looking here:

SuiteSparse/CHOLMOD/Demo/cholmod_dl_demo.c

Line 457 in 8ac3f51

cholmod_l_solve2 (CHOLMOD_A, L, B2, NULL, &X, NULL,

. We're creating a B2 vector that contains exactly one non-zero value. And we then solve with and without Bset. We compare the results here:

SuiteSparse/CHOLMOD/Demo/cholmod_dl_demo.c

Line 501 in 8ac3f51

resid [3] = MAX (resid [3], err) ;

. The comparisons are good. But the comparison code only looks at the values referenced by Xset. Outside Xset, the values of X1x should be 0, but they're not, and this is not checked.

I'm observing this with suitesparse 7.8.3 on Debian:

cd /tmp

apt source suitesparse
# version 7.8.3 downloaded

gcc -O0 -ggdb3 -I/usr/include/suitesparse -o /tmp/demo /tmp/suitesparse-7.8.3+dfsg/CHOLMOD/Demo/cholmod_dl_demo.c  -lcholmod -lamd -lcolamd -lcamd -lccolamd -lsuitesparseconfig

< /tmp/suitesparse-7.8.3+dfsg/CHOLMOD/Demo/Matrix/bcsstk01.tri /tmp/demo