Refactor into src/libdsdp.jl

[odow]

No description provided.

[odow]

@blegat here's an example:

julia> using DSDP

julia> import MathOptInterface as MOI

julia> src = MOI.Utilities.Model{Float64}()
MOIU.Model{Float64}
├ ObjectiveSense: FEASIBILITY_SENSE
├ ObjectiveFunctionType: MOI.ScalarAffineFunction{Float64}
├ NumberOfVariables: 0
└ NumberOfConstraints: 0

julia> x, _ = MOI.add_constrained_variables(src, MOI.Nonnegatives(2))
(MathOptInterface.VariableIndex[MOI.VariableIndex(1), MOI.VariableIndex(2)], MathOptInterface.ConstraintIndex{MathOptInterface.VectorOfVariables, MathOptInterface.Nonnegatives}(1))

julia> c = MOI.add_constraint(src, 1.0 * x[1] + 1.0 * x[2], MOI.EqualTo(-1.0))
MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}(1)

julia> model = DSDP.Optimizer()
DSDP.Optimizer
├ ObjectiveSense: unknown
├ ObjectiveFunctionType: unknown
├ NumberOfVariables: unknown
└ NumberOfConstraints: unknown

julia> MOI.copy_to(model, src)
MathOptInterface.Utilities.IndexMap with 4 entries:
  MOI.VariableIndex(1)                                                => MOI.VariableIndex(1)
  MOI.VariableIndex(2)                                                => MOI.VariableIndex(2)
  ConstraintIndex{VectorOfVariables, Nonnegatives}(1)                 => ConstraintIndex{VectorOfVariables, Nonnegatives}(1)
  ConstraintIndex{ScalarAffineFunction{Float64}, EqualTo{Float64}}(1) => ConstraintIndex{ScalarAffineFunction{Float64}, EqualTo{Float64}}(1)

julia> MOI.optimize!(model)
Iter   PP Objective      DD Objective    PInfeas   DInfeas     Nu     StepLength   Pnrm
---------------------------------------------------------------------------------------
0     0.00000000e+00   -4.00000000e+09   2.0e+00   4.0e+01   4.0e+09  0.00  0.00   0.00 
1     0.00000000e+00   -4.90006449e+01   2.0e+00   0.0e+00   7.0e+08  0.97  0.21   4.92 
2     0.00000000e+00   -1.74099834e+02   2.0e+00   0.0e+00   7.9e+07  0.97  1.00   0.44 
3     0.00000000e+00   -6.18578860e+02   2.0e+00   0.0e+00   9.9e+07  0.97  1.00   0.44 
4     0.00000000e+00   -2.19782145e+03   2.0e+00   0.0e+00   9.9e+07  0.97  1.00   0.44 
5     0.00000000e+00   -7.80893633e+03   2.0e+00   0.0e+00   9.9e+07  0.97  1.00   0.44 
6     0.00000000e+00   -2.77458734e+04   2.0e+00   0.0e+00   9.9e+07  0.97  1.00   0.44 
7     0.00000000e+00   -9.85877134e+04   2.0e+00   0.0e+00   9.9e+07  0.97  1.00   0.44 
8     0.00000000e+00   -3.50284061e+05   2.0e+00   0.0e+00   9.9e+07  0.97  1.00   0.44 
9     0.00000000e+00   -1.24933346e+06   1.4e+00   0.0e+00   1.4e+07  1.00  1.00   0.45 
10    0.00000000e+00   -5.05548050e+06   1.4e+00   0.0e+00   2.0e+06  0.96  1.00   0.74 
11    0.00000000e+00   -9.26680646e+06   1.4e+00   0.0e+00   1.2e+06  0.79  1.00   0.89 
12    0.00000000e+00   -9.99193632e+06   1.3e+00   0.0e+00   6.1e+03  1.00  1.00  40.09 
13    0.00000000e+00   -9.99991359e+06   1.0e+00   0.0e+00   6.5e+01  1.00  1.00  41.51 
14    0.00000000e+00   -9.99999907e+06   1.0e+00   0.0e+00   6.9e-01  1.00  1.00  41.53 
15    0.00000000e+00   -9.99999995e+06   1.0e+00   0.0e+00   1.5e-01  1.00  0.18   5.16 
16    0.00000000e+00   -9.99999997e+06   1.0e+00   0.0e+00   2.5e-02  1.00  0.30   0.86 

julia> stop = Ref{DSDP.DSDPTerminationReason}()
Base.RefValue{DSDP.DSDPTerminationReason}(DSDP.UnknownMember)

julia> DSDP.DSDPStopReason(model, stop)
0

julia> sol = Ref{DSDP.DSDPSolutionType}()
Base.RefValue{DSDP.DSDPSolutionType}(DSDP.UnknownMember)

julia> DSDP.DSDPGetSolutionType(model, sol)
0

julia> stop
Base.RefValue{DSDP.DSDPTerminationReason}(DSDP.DSDP_CONVERGED)

julia> sol
Base.RefValue{DSDP.DSDPSolutionType}(DSDP.DSDP_PDFEASIBLE)

julia> DSDP.DSDPView(model)
Terminate DSDP after 500 iterations.
Terminate DSDP if dual objective is greater than 1.0000e+20
Terminate DSDP if the relative duality gap is less than 1.0000e-07
Terminate DSDP if step length in D less than 5.0000e-02
Terminate DSDP only if Pnorm less than 1.0000e+30
Max Trust Radius is 1.0000e+10
Reapply Hessian of Barrier up to 4 times per iteration.
The norms of C: 0.0000e+00, A: 1.4142e+00, and b: 1.0000e+00
There are 1 y variables:  largest is 1.0000e+07, bounded below by -1.0000e+07 and above by 1.0000e+07. 
The X variables have a trace of 3.0065e-08 bounded by penalty parameter: 1.0000e+08
Current Barrier Parameter: 2.4863e-02
Potential Parameter: 5.0000e+00 ( times dimension) 
The value of the potential function is -6.3825e+01
(D) Feasible only if R < 1.0000e-06
(P) Feasible only if Pinfeas < 1.0000e-04
 DSDP Solutions are both feasible and bounded
The errors: 5.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 1.0000e+00, 3.0065e-08
0

julia> err = zeros(6)
6-element Vector{Float64}:
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0

julia> DSDP.DSDPGetFinalErrors(model, err)
0

julia> err
6-element Vector{Float64}:
 0.5000000150322539
 0.0
 0.0
 0.0
 0.9999999000000097
 3.006450467196997e-8

This just looks like an upstream bug. Logging shows that it didn't converge and it is not PD feasible...

[blegat]

Yes, I was interested by the rank-1 feature but I got a bit demotivated by all these bugs. You also have all the ComputeX, etc... and if you don't call these in the right order, you also get wrong input. I never really understand what's the right way, the current implementation was obtained by trial and error.