using Clarabel, SparseArrays

P = spzeros(3,3)

q = [-1.,0.,0.]

A = sparse([
-1.  0.  0.;
0. -1.  0.;
0.  0. -1.;
0.  1.  0.;
0.  0.  1.]);

b = [0.,0.,0.,1.,exp(5.)];

cones  = [Clarabel.ExponentialConeT(), Clarabel.ZeroConeT(2)]

solver = Clarabel.Solver()

settings = Clarabel.Settings()

Clarabel.setup!(solver, P, q, A, b, cones, settings)

result = Clarabel.solve!(solver)
-------------------------------------------------------------
Clarabel.jl v0.5.1  -  Clever Acronym
(c) Paul Goulart
University of Oxford, 2022
-------------------------------------------------------------

problem:
variables     = 3
constraints   = 5
nnz(P)        = 0
nnz(A)        = 5
cones (total) = 2
: Zero        = 1,  numel = 2
: Exponential = 1,  numel = 3

settings:
linear algebra: direct / qdldl, precision: Float64
max iter = 200, time limit = Inf,  max step = 0.990
tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
max iter = 10, stop ratio = 5.0
equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
max iter = 10

iter    pcost        dcost       gap       pres      dres      k/t        μ       step
---------------------------------------------------------------------------------------------
0   0.0000e+00  -0.0000e+00  0.00e+00  9.89e-01  5.04e-01  1.00e+00  1.00e+00   ------
1   3.1741e+00   6.5571e+00  1.07e+00  9.18e-01  9.36e-02  4.36e+00  2.23e-01  7.84e-01
2   1.4884e+01   3.0958e+01  1.08e+00  6.79e-01  1.93e-02  1.70e+01  4.97e-02  7.84e-01
3   2.4751e+01   5.2175e+01  1.11e+00  2.61e-01  5.58e-03  2.79e+01  1.27e-02  7.84e-01
4   8.0481e+00   1.5052e+01  8.70e-01  6.52e-02  1.77e-03  7.18e+00  3.92e-03  7.84e-01
5  -1.6416e+00  -4.3466e-02  1.60e+00  1.38e-02  3.71e-04  1.64e+00  8.74e-04  7.84e-01
6  -4.1601e+00  -3.7998e+00  9.48e-02  3.04e-03  8.12e-05  3.69e-01  1.95e-04  7.84e-01
7  -4.9775e+00  -4.9667e+00  2.18e-03  8.70e-05  2.32e-06  1.11e-02  5.60e-06  9.80e-01
8  -4.9997e+00  -4.9993e+00  6.43e-05  2.50e-06  6.65e-08  3.29e-04  1.61e-07  9.80e-01
9  -5.0000e+00  -5.0000e+00  1.88e-06  7.17e-08  1.91e-09  9.63e-06  4.62e-09  9.80e-01
10  -5.0000e+00  -5.0000e+00  5.48e-08  2.06e-09  5.49e-11  2.80e-07  1.33e-10  9.80e-01
11  -5.0000e+00  -5.0000e+00  1.59e-09  5.92e-11  1.58e-12  8.12e-09  3.81e-12  9.80e-01
---------------------------------------------------------------------------------------------
Terminated with status = solved
solve time = 77.6ms
>>> Clarabel - Results
Status: SOLVED
Iterations: 11
Objective: -5.000
Solve time: 77.6ms

result.x
3-element Vector{Float64}:
4.999999989153166
0.9999999998246705
148.41315907622325