blastrampoline on julia-1.10

[kalmarek]

Since SCS libraries link with openblas32 it makes sense to link them against blastrampoline in julia-1.10 (after it is announced the new lts); How should we proceed with switching to libblastrampoline?

Options:

1. Dropping support for julia <1.10 and going fully through lbt
2. splitting our codepaths for julia [1.6-1.10) and [1.10 - ).

In both cases running with lbt requires manually forwarding LP64 blas:

(SCS) pkg> st
Project SCS v2.0.1
Status `~/.julia/dev/SCS/Project.toml`
  [b8f27783] MathOptInterface v1.31.1
  [ae029012] Requires v1.3.0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
  [f4f2fc5b] SCS_jll v3.2.7+0 `~/.julia/dev/SCS_jll`
  [2f01184e] SparseArrays v1.10.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

julia> using SCS

julia> using Test

julia> include("test/test_problems.jl")
test_options (generic function with 1 method)

julia> using LinearAlgebra

julia> LinearAlgebra.BLAS.lbt_get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries: 
└ [ILP64] libopenblas64_.so

julia> test_options(SCS.DirectSolver)
------------------------------------------------------------------
	       SCS v3.2.7 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 5, constraints m: 8
cones: 	  l: linear vars: 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:  sparse-direct-amd-qdldl
	  nnz(A): 12, nnz(P): 0
Error: no BLAS/LAPACK library loaded!
[...]
Error: no BLAS/LAPACK library loaded!
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
Error: no BLAS/LAPACK library loaded!
[...]
Error: no BLAS/LAPACK library loaded!
     0|1.94e-318 2.76e-313 1.25e-309  0.00e+00  1.00e-01  6.70e-04 
Error: no BLAS/LAPACK library loaded!
Error: no BLAS/LAPACK library loaded!
Error: no BLAS/LAPACK library loaded!
WARNING - large complementary slackness residual: 0.000000
Error: no BLAS/LAPACK library loaded!
Error: no BLAS/LAPACK library loaded!
Error: no BLAS/LAPACK library loaded!
------------------------------------------------------------------
status:  solved
timings: total: 6.79e-04s = setup: 4.40e-04s + solve: 2.38e-04s
	 lin-sys: 3.39e-06s, cones: 1.68e-06s, accel: 4.00e-08s
------------------------------------------------------------------
objective = 0.000000
------------------------------------------------------------------
Test Failed at /home/kalmar/.julia/dev/SCS/test/test_problems.jl:757
  Expression: isapprox((solution.x)' * args.c, -99.0; rtol = 0.0001)
   Evaluated: isapprox(0.0, -99.0; rtol = 0.0001)

ERROR: There was an error during testing

however after

julia> using OpenBLAS32_jll

julia> LinearAlgebra.BLAS.lbt_forward(OpenBLAS32_jll.libopenblas)
4864

things run as they are expected:

julia> LinearAlgebra.BLAS.lbt_get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries: 
├ [ILP64] libopenblas64_.so
└ [ LP64] libopenblas.so

julia> test_options(SCS.DirectSolver)
------------------------------------------------------------------
	       SCS v3.2.7 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 5, constraints m: 8
cones: 	  l: linear vars: 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:  sparse-direct-amd-qdldl
	  nnz(A): 12, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
     0| 1.26e+02  3.95e+00  1.22e+03 -6.94e+02  1.00e-01  1.91e-04 
   125| 7.47e-05  4.88e-06  3.10e-04 -9.90e+01  1.00e-01  6.02e-04 
------------------------------------------------------------------
status:  solved
timings: total: 6.08e-04s = setup: 1.20e-04s + solve: 4.88e-04s
	 lin-sys: 4.49e-05s, cones: 1.49e-05s, accel: 2.59e-04s
------------------------------------------------------------------
objective = -98.999835
------------------------------------------------------------------

[...]

What is nice is that things run equally well with MKL:

julia> using MKL

julia> MKL.lbt_forward_to_mkl()

julia> LinearAlgebra.BLAS.lbt_get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries: 
├ [ILP64] libmkl_rt.so
└ [ LP64] libmkl_rt.so

julia> test_options(SCS.DirectSolver)
------------------------------------------------------------------
	       SCS v3.2.7 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 5, constraints m: 8
cones: 	  l: linear vars: 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:  sparse-direct-amd-qdldl
	  nnz(A): 12, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
     0| 1.26e+02  3.95e+00  1.22e+03 -6.94e+02  1.00e-01  2.83e-04 
   125| 7.47e-05  4.88e-06  3.10e-04 -9.90e+01  1.00e-01  7.04e-03 
------------------------------------------------------------------
status:  solved
timings: total: 7.05e-03s = setup: 1.94e-04s + solve: 6.86e-03s
	 lin-sys: 2.92e-05s, cones: 7.87e-06s, accel: 6.68e-03s
------------------------------------------------------------------
objective = -98.999835
------------------------------------------------------------------

[...]

[odow]

We can just do what we do for Ipopt:
https://github.com/jump-dev/Ipopt.jl/blob/4c156461ef1fda3c9f015520197afda4e8ca3e26/src/Ipopt.jl#L13-L19