def test_ecos_trivial_invpos():
x = cvx.Variable( (2), name='x')
constraints = [x[0] >= 0]
constraints += [x[1] >= x[0]]
constraints += [x[1] >= cvx.inv_pos(x[0])]
objective = x[1]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
canon.assign_values({})
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'][0:2])
assert( np.allclose(solution['x'][0:2], [1.0, 1.0]) )
reset_symbols()
def test_ecos_trivial_geomean():
x = cvx.Variable( (2), name='x')
constraints = [x[0] >= 0]
constraints += [x[1] <= cvx.geo_mean(x[0], 5)]
constraints += [x[1] >= 5]
objective = x[0] + x[1] # farthest down and left
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
canon.assign_values({})
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'][0:2])
assert( np.allclose(solution['x'][0:2], [5.0, 5.0]) )
reset_symbols()
def test_ecos_leastsquares():
x = cvx.Variable (name='x')
F = cvx.Parameter(name='F')
g = cvx.Parameter(name='g')
objective = cvx.square(cvx.norm( F*x - g ))
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, [])
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'F' : 42,
'g' : 42,
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'][0])
assert( np.isclose(solution['x'][0], 1.0) )
reset_symbols()
def test_ecos_polyhedradist():
import cvx_sym as cvx
n = 2 # number of dimensions
m = 3 # number of lines defining polyhedron 1
p = 3 # number of lines defining polyhedron 2
x1 = cvx.Variable ((n,1),name='x1')
x2 = cvx.Variable ((n,1),name='x2')
A1 = cvx.Parameter((m,n),name='A1')
A2 = cvx.Parameter((p,n),name='A2')
B1 = cvx.Parameter((m,1),name='B1')
B2 = cvx.Parameter((p,1),name='B2')
objective = cvx.square(cvx.norm(x1 - x2))
constraints = [ A1[i,:].T * x1 <= B1[i] for i in range(m) ]
constraints += [ A2[i,:].T * x2 <= B2[i] for i in range(p) ]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'A1' : np.array([[-1,1],[1,1],[0,-1]]),
'B1' : np.array([[3],[3],[0]]),
'A2' : np.array([[.5,-1],[0,1],[+1,0]]),
'B2' : np.array([[-3],[3],[5]]),
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
# Solution is found at intersection of polyhedra
assert( np.allclose(x_solution, [0,3, 0,3], atol=1e-4) )
# So therefore the objective should be near zero
assert( np.allclose(solution['info']['pcost'], 0.0 ) )
reset_symbols()
def test_ecos_robustlp():
import cvx_sym as cvx
n = 2 # number of dimensions
m = 3 # number of elementwise elements
x = cvx.Variable ((n,1),name='x')
A = cvx.Parameter((m,n),name='A')
B = cvx.Parameter((m,1),name='B')
C = cvx.Parameter((n,1),name='C')
P = cvx.Parameter((m,n),name='P')
objective = C.T * x
constraints = [A[i].T * x + cvx.norm(P[i].T * x) <= B[i] for i in range(m)]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'A' : np.array([[1,1],[1,1],[1,1]]),
'B' : np.array([[3],[3],[3]]),
'C' : np.array([[.1],[.2]]),
'P' : np.array([[1,2],[3,4],[5,6]])
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.allclose(x_solution, [3,-3] ) )
reset_symbols()
def test_ecos_chebyshevcenter():
import cvx_sym as cvx
n = 2
m = 3
r = cvx.Variable((1,1),name='r')
x = cvx.Variable((n,1),name='x')
A = cvx.Parameter((m,n),name='A')
B = cvx.Parameter((m,1),name='B')
objective = -r
constraints = [A[i,:].T * x + r * cvx.norm(A[i,:]) <= B[i] for i in range(m)]
constraints += [r >= 0]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'A' : np.array([[-1,1],[1,1],[0,-1]]),
'B' : np.array([[3],[3],[0]]),
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.allclose(x_solution, [0, 1.242641] ) )
reset_symbols()
def test_ecos_leastsquares_constr():
x = cvx.Variable ((3,1),name='x')
F = cvx.Parameter((3,3),name='F')
g = cvx.Parameter((3,1),name='g')
U = cvx.Parameter((3,1),name='U')
L = cvx.Parameter((3,1),name='L')
constraints = []
objective = cvx.square(cvx.norm( F*x - g ))
constraints += [ x <= U ]
constraints += [ L <= x ]
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
# Set values of parameters
parameters = {
'F' : np.array([[1,2,3],[4,5,6],[7,8,9]]),
'g' : np.array([[1],[2],[3]]),
'U' : np.array([[42],[42],[42]]),
'L' : np.array([[1],[2],[3]])
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.allclose(x_solution, [1,2,3] ) )
reset_symbols()
def test_ecos_trivial_norm1():
x = cvx.Variable((3,1),name='x')
constraints = [x >= -1]
constraints += [x <= +1]
objective = cvx.norm(x, kind=1)
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose=True)
canon.assign_values({})
solution = cvx.solve(canon, verbose = True)
if solution:
print('Solution obj:', solution['info']['pcost'])
print('Solution x:', solution['x'])
assert( np.allclose(solution['x'][0:3], [0.0, 0.0, 0.0]) )
reset_symbols()
def full_scale_ecos_control():
""" Takes a long time to canonicalize, so don't run as routine test """
import cvx_sym as cvx
n = 8
m = 2
T = 50
x = cvx.Variable((n, T+1), name='x')
u = cvx.Variable((m, T), name='u')
x_0 = cvx.Parameter((n,1), name='x_0')
A = cvx.Parameter((n,n), name='A')
B = cvx.Parameter((n,m), name='B')
states = []
constraints = [ x[:,T] == 0 ]
constraints += [ x[:,0] == x_0[:,0] ]
for t in range(T):
constraints += [ x[:,t+1] == A*x[:,t] + B*u[:,t] ]
constraints += [ cvx.norm(u[:,t], kind = 'inf') <= 1 ]
cost = cvx.sum_squares(x[:,t+1]) + cvx.sum_squares(u[:,t])
states.append( cost )
# sums problem objectives and concatenates constraints.
objective = cvx.sum(states)
objective = cvx.Minimize(objective)
problem = cvx.Problem(objective, constraints)
canon = Canonicalize(problem, verbose = 1 )
np.random.seed(1)
alpha = 0.2
beta = 5
A_set = np.eye(n) + alpha*np.random.randn(n,n)
B_set = np.random.randn(n,m)
x_0_set = beta*np.random.randn(n,1)
# Set values of parameters
parameters = {
'A' : A_set,
'B' : B_set,
'x_0' : x_0_set,
}
canon.assign_values(parameters)
solution = cvx.solve(canon, verbose = True)
if solution:
obj = solution['info']['pcost']
# Gather the OG solution variables
v_indices = [n for n, vn in enumerate(canon.vars.keys()) if 'x' in vn]
x_solution = [solution['x'][i] for i in v_indices]
print('Solution obj:', obj)
print('Solution x:', x_solution)
print('Solution vec:', solution['x'])
assert( np.isclose(obj, 64470.59019495451) )
reset_symbols()
