linsys solver using hipsparse

[kalmarek]

This is just a proof of concept of how far can I push the idea of "instruct chatGPT to write software for me", hip-edition ;) Made only possible by the amazing design and the documentation of scs. Thanks @bodono!

At the moment this

• compiles with make DLONG=0 USE_OPENMP=1 hip, after the adjustments of necessary paths in scs.mk,
• unfortunately it still doesn't run as expected:

./out/demo_socp_hip 100      
seed : 1728819068

A is 400 by 100, with 10 nonzeros per column.
A has 1000 nonzeros (2.500000% dense).
Nonzeros of A take 0.000007 GB of storage.
Row idxs of A take 0.000004 GB of storage.
Col ptrs of A take 0.000000 GB of storage.

ScsCone information:
Zero cone rows: 40
LP cone rows: 120
Number of second-order cones: 8, covering 240 rows, with sizes
[20, 34, 14, 51, 22, 31, 1, 67, ]
Number of rows covered is 400 out of 400.

true pri opt = 0.816196
true dua opt = 0.816196
------------------------------------------------------------------
               SCS v3.2.7 - Splitting Conic Solver
        (c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 100, constraints m: 400
cones:    z: primal zero / dual free vars: 40
          l: linear vars: 120
          q: soc vars: 240, qsize: 8
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
          alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
          max_iters: 100000, normalize: 1, rho_x: 1.00e-06
          acceleration_lookback: 10, acceleration_interval: 10
          compiled with openmp parallelization enabled
lin-sys:  hipsparse-direct
          nnz(A): 1000, nnz(P): 0
Error in init -- bufferSize: 10.
Error in init -- analysis: 10.
Error in init -- numeric fact: 10.
Error in factorisation: 10.
ERROR: init_lin_sys_work failure
Failure:could not initialize work
true pri opt = 0.816196
true dua opt = 0.816196
scs pri obj=  nan
scs dua obj = -nan

since hipsparseDcsrsv2_bufferSize refuses to compute the buffer size with HIPSPARSE_STATUS_NOT_SUPPORTED(10), which most probably is related to kkt matrix being symmetric. I've asked about this here:
ROCm/hipSPARSE#541

[bodono]

Oh cool! Thanks for looking into this, it would be great to get this in. Happy to take a look once you have it ready.

[kalmarek]

it seems that rocsparse doesn't support symmetric matrices at the moment.

[bodono]

That's a shame, I presume it's because we only store the lower triangular part? If so we could always fill in the upper triangular part, but we would lose some efficiency.

[kalmarek]

but also they lack the integration of pivoting etc. I think this is a bit premature, but I'll try something else, given my motivation recently ;)