import clarabel
import numpy as np
from scipy import sparse
n = 3
nvec = int(n*(n+1)/2)
P = sparse.csc_matrix((nvec,nvec))
P = P.tocsc()
q = np.array([1.,0.,1.,0.,0.,1.])
sqrt2 = np.sqrt(2.)
A = sparse.csc_matrix( \
[[-1., 0., 0., 0., 0., 0.],
[0., -sqrt2, 0., 0., 0., 0.],
[0., 0., -1., 0., 0., 0.],
[0., 0., 0., -sqrt2, 0., 0.],
[0., 0., 0., 0., -sqrt2, 0.],
[0., 0., 0., 0., 0., -1.],
[1., 4., 3., 8., 10., 6.],]);
b = np.append(np.zeros(nvec),1.)
cones = [clarabel.PSDTriangleConeT(n),
clarabel.ZeroConeT(1)]
settings = clarabel.DefaultSettings()
solver = clarabel.DefaultSolver(P,q,A,b,cones,settings)
solver.solve()