Need to figure out how to remove the cold section from the samples.

Currently, the program does not run in macOS due to some compilation errors.

Previously, Rhat is supposed to use for one chain. Now the program is sampling multiple chain. So, the Rhat function need to be updated.

Should update Documentation. Both input and output changed quite a lot.

For dense matrices, our linear solver is pretty slow. So, make sure the program can select the right solver and the program runs efficiently using JL.

(Example: ME_matrix_GlcAer_WT)

`Warning: The following error was caught while executing 'MexSolver' class destructor:
Invalid MEX-file
'C:\Users\santo\OneDrive\Documents\GitHub\PolytopeSamplerMatlab\code\solver\CSolver_dd.mexw64':
Missing dependent shared libraries:
'VCRUNTIME140_1.dll' required by
'C:\Users\santo\OneDrive\Documents\GitHub\PolytopeSamplerMatlab\code\solver\CSolver_dd.mexw64'.

Error in MexSolver/delete (line 31)
o.func('delete', o.uid);

Error in MexSolver (line 16)
function o = MexSolver(A, precision)

Error in Solver (line 22)
o = MexSolver(A, precision);

Error in Polytope/remove_dependent_rows (line 368)
solver = Solver(o.A, 'doubledouble');

Error in Polytope/simplify (line 243)
o.remove_dependent_rows();

Error in Polytope (line 195)
o.simplify();

Error in sample (line 42)
polytope = Polytope(problem, opts);

Error in demo (line 9)
o = sample(P, 100); % Number of samples = 100

In MexSolver (line 16)
In Solver (line 22)
In Polytope/remove_dependent_rows (line 368)
In Polytope/simplify (line 243)
In Polytope (line 195)
In sample (line 42)
In demo (line 9)
Invalid MEX-file
'C:\Users\santo\OneDrive\Documents\GitHub\PolytopeSamplerMatlab\code\solver\CSolver_dd.mexw64':
Missing dependent shared libraries:
'VCRUNTIME140_1.dll' required by
'C:\Users\santo\OneDrive\Documents\GitHub\PolytopeSamplerMatlab\code\solver\CSolver_dd.mexw64'.

Error in MexSolver (line 27)
o.uid = o.func('init', uint64(randi(2^32-1,'uint32')), A);

Error in Solver (line 22)
o = MexSolver(A, precision);

Error in Polytope/remove_dependent_rows (line 368)
solver = Solver(o.A, 'doubledouble');

Error in Polytope/simplify (line 243)
o.remove_dependent_rows();

Error in Polytope (line 195)
o.simplify();

Error in sample (line 42)
polytope = Polytope(problem, opts);

Error in demo (line 9)
o = sample(P, 100); % Number of samples = 100`

The program converges to take step size 0.

There are two things need to be done

1. run both col and leverage score row by row instead of col by col
2. Reorder the loop so that it is more cache friendly

Implement Rhat and a similar summer function as other solver

Make DebugLogger really log the algorithm.

Currently, there is the use of warnings scatter throughout the program.
Maybe move all to the log function.
Make the default logging involves printing out the warning.

Currently, the output of our program is not understandable.

@ruoqishen, what are the output of other sampling packages?
Can you give me some examples? Then we can decide what we output.

• Make sure the code is updated with the current module system
• Run all available coverage tests by one script.
• I can choose how long is the test.
• I can choose to run one of the item.
• When the coverage test fails, save the output object for easier debugging. (Probably only save say the first 10 fails.)

Before further development, we need an automatic way to do a coverage test. I am lazy and won't make a unit test for everything. Instead, we will only have three tests

• Small tests just for making sure the program works for different
• Tests for checking the presolve is correct.
• Tests for sampling.

Some small todo:

• Remove the recenter in demo and move it to load problem. It probably will only confuse user.

The distribution is incorrect due to weightedBarrier

This is a temp fix for polytope.m

        tau = solver.leverageScoreComplement();
        w = sqrt((max(tau,eps))./hess)+eps;

need example of loading instance from a .m or .mat file in demo.m

We didn't verify Ax=b in the sampler and the coverage test.

Note that
tv_ball2 has slow mixing time
tv_ball has fast mixing time.

In general, seems many polytope is small due to the uniform weight of log barrier.
Probably it is better to switch to log barrier

• Check for macOS
• Check for linux
• Check for Windows

Maybe we can prove the convergence of hypercube formally. Then we can use it to tune the algorithm?
(I fixed the warm start issue..)

@santoshv

@ruoqishen

I have changed many things for the C part. So, you should test if it runs now (for the branch newsolver)

If I thin the sample according to ess, seems the output is not exactly independent.

initSampler
p_hist = zeros(1000,1);
parfor i = 1:1000
P = struct; dim = 100;
P.Aeq = ones(1, dim);
P.beq = 1;
P.lb = zeros(dim, 1);

o = sample(P, 200); % Number of samples = 100
[pVal] = uniformtest(o, struct('toPlot', true));
p_hist(i) = pVal;
i
end

• Make a smallest example
• Add this to coverage test

https://github.com/qacwnfq/bigg-model-downloader

Allow user to avoid calling presolve twice

The documentation is a bit repetitive and not simple enough.
Ideally, each test should be just a few lines.
Everything needs to be understandable for the general audience