for i in range(m):
a = np.random.randn(n)
a = a / np.linalg.norm(a)
bi = 1 + np.random.rand(1)
A[i, :] = a
b[i] = bi
q = QCML()
q.parse('''
dimensions m n
variables x(n) r
parameters A(m,n) b(m)
maximize r
A*x + r <= b
''')
q.canonicalize()
q.dims = {'m': m, 'n': n}
q.codegen("python")
socp_data = q.prob2socp(locals())
# stuffed variable size
n = socp_data['G'].shape[1]
ecos_sol = ecos.solve(**socp_data)
socp_sol = ecos_sol['x']
prob_sol_x = q.socp2prob(ecos_sol['x'])['x']
prob_sol_r = q.socp2prob(ecos_sol['x'])['r']
# norm(x,y) applies norm across rows of the matrix [x y]
norm(u,v) <= radii*c
# rctheta is going to be a diagonal matrix
# rctheta[i]*c[i] <= u[i] implemented with rctheta a diag matrix
rctheta*c <= u
""")
# More natural formulation would be:
# minimize 1/(sqrt(2)*noisesigma) * (data - (dictc*c + dictu(u + dictv*v)) + lambda'*c)
# subject to
# sqrt(u.^2 + v.^2) <= radii.*c
# radii.*cos(theta) <= u
raw_input("press ENTER to canonicalize....")
p.canonicalize()
raw_input("press ENTER to generate code....")
if m and n: p.dims = {'m': m, 'n': n}
p.codegen(args.codegen)
raw_input("press ENTER for raw code....")
p.printsource()
#socp_data = p.prob2socp(params=locals())
#import ecos
#sol = ecos.ecos(**socp_data)
#my_vars = p.socp2prob(sol['x'])
#pr.disable()
#ps = pstats.Stats(pr)
#ps.sort_stats('cumulative').print_stats(.5)
objective = []
for i in xrange(T):
objective += ["square(norm(Q*x%i)) + square(norm(R*u%i))" % (i,i)]
#objective += ["square(norm(Q*x%i))" % T]
problem += ["minimize (1/2)*(" + ' + '.join(objective) + ")"]
s = '\n'.join(map(lambda x:' ' + x, problem))
print s
raw_input("press ENTER to parse....")
p = QCML(debug=True)
p.parse(s)
raw_input("press ENTER to canonicalize....")
p.canonicalize()
raw_input("press ENTER to generate code....")
p.dims = {'n': n, 'm': m}
p.codegen("python")
raw_input("press ENTER to solve with ECOS....")
socp_data = p.prob2socp(params=locals())
import ecos
sol = ecos.solve(**socp_data)
