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_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_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_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_smith_sq():
""" Smith Form of Minimize(square(v0)) """
v0 = Variable(name='v0')
v1 = Variable(name='v1')
p0 = Parameter(name='p0')
p1 = Parameter(name='p1')
obj = square(v0)
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='smith')
assert (len(c.constraints) == 1)
assert (c.objective is not obj)
assert ('sym0' == c.objective.name)
assert (hasattr(c.constraints[0].expr.args[0], 'name'))
assert (c.constraints[0].expr.args[0].name == 'sym0')
assert (hasattr(c.constraints[0].expr.args[1], 'args'))
assert (hasattr(c.constraints[0].expr.args[1].args[0], 'value'))
assert (c.constraints[0].expr.args[1].args[0].value == -1.0)
assert (hasattr(c.constraints[0].expr.args[1].args[1], 'name'))
assert (c.constraints[0].expr.args[1].args[1].name == 'square')
reset_symbols()
def test_matrix_sq():
""" Matrix Form of Minimize(square(v0)) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(v0)
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True)
assert(c.c == [0, 0, 1])
assert(c.A is None)
assert(c.b is None)
assert_G = {
'row':[0, 1, 2],
'col':[2, 2, 0],
'val':[Constant(-1.0), Constant(-1.0), Constant(2.0)]
}
assert_h = [Constant(1.0), Constant(-1.0), Constant(0.0)]
assert_G = COO_to_CS(assert_G, (len(assert_h), len(c.c)), 'col')
assert(c.G == assert_G)
assert(all([c.h[n].value == t.value for n, t in enumerate(assert_h)]))
assert(c.dims == {'q': [3], 'l': 0})
reset_symbols()
def test_relax_sq2norm_constr():
""" Relaxed Form of Minimize(square(norm(v0))) with v0 >= p0"""
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0))
con = [v0 >= p0] # should become -v0 + p0 <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='relax')
assert( type(c.constraints[-1]) is le)
assert( type(c.constraints[-1].expr) is sums.sum)
assert( type(c.constraints[-1].expr.args[0]) is muls.smul)
assert( type(c.constraints[-1].expr.args[1]) is muls.smul)
assert( c.objective is not obj )
assert( 'sym0' == c.objective.name )
string_equals = [
"""((-1.0 * sym1) + (1.0 * norm2(v0))) <= 0""",
"""((-1.0 * sym0) + (1.0 * square(sym1))) <= 0""",
"""((-1.0 * v0) + (p0 * 1.0)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n],'==',string,'?')
assert(str(c.constraints[n]) == string)
print('SUCCESS!')
reset_symbols()
def test_relax_sq2norm():
""" Relaxed Form of Minimize(square(norm(v0))) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0))
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='relax')
assert( c.objective is not obj )
assert( 'sym0' == c.objective.name )
# Let up on the testing rigor a bit, now that we checked core fundamentals
string_equals = [
"""((-1.0 * sym1) + (1.0 * norm2(v0))) <= 0""",
"""((-1.0 * sym0) + (1.0 * square(sym1))) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n],'==',string,'?')
assert(str(c.constraints[n]) == string)
print('SUCCESS!')
reset_symbols()
def test_relax_sq():
""" Relaxed Form of Minimize(square(v0)) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(v0)
con = []
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='relax')
assert( len(c.constraints) == 1 )
assert( c.objective is not obj )
assert( 'sym0' == c.objective.name )
assert(type(c.constraints[0]) is le)
assert(c.constraints[0].expr.args[0].curvature == 0)
assert(c.constraints[0].expr.args[1].curvature == +1)
assert(c.constraints[0].expr.args[1].symbol_groups()[0][0].value == 1.0)
assert(c.constraints[0].expr.args[1].symbol_groups()[2][0].name == 'square')
reset_symbols()
def test_relax_least_squares_constr():
""" Relaxed Form : Minimize(square(norm(F*x - g))) with x >= p0 """
x = Variable ((3,1),name='x')
F = Parameter((3,3),name='F')
g = Parameter((3,1),name='g')
objective = square(norm( F*x - g ))
objective = Minimize(objective)
problem = Problem(objective, [x >= 0])
c = Canonicalize(problem, verbose=True, only='relax')
string_equals = [
"""(sym2 + (-1.0 * matmul(F, x))) == 0""",
"""(sym3 + (-1.0 * sym2) + (g * 1.0)) == 0""",
"""((-1.0 * sym1) + (1.0 * norm2(sym3))) <= 0""",
"""((-1.0 * sym0) + (1.0 * square(sym1))) <= 0""",
"""((-1.0 * x)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n],' ???? ',string, end=' ')
assert(str(c.constraints[n]) == string)
print('... SUCCESS!')
reset_symbols()
def test_norm_inf():
x = Variable((3, 1), name='x')
objective = norm(x, kind='inf') # returns max(abs(x))
objective = Minimize(objective)
problem = Problem(objective, [])
c = Canonicalize(problem, verbose=True, only='smith')
assert (len(c.constraints) == 4)
string_equals = [
"""(sym1[0][0] + (-1.0 * abs(x[0][0]))) == 0""",
"""(sym1[1][0] + (-1.0 * abs(x[1][0]))) == 0""",
"""(sym1[2][0] + (-1.0 * abs(x[2][0]))) == 0""",
"""(sym0 + (-1.0 * max(sym1))) == 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n], ' ???? ', string, end=' ')
assert (str(c.constraints[n]) == string)
print('... SUCCESS!')
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_matrix_sq2norm_sqcon():
""" Relaxed Form : Minimize(square(norm(v0))) with v0 >= square(v1) """
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0 + v1))
con = [v0 >= square(v1)] # should become -v0 + square(v1) <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True)
sym3 = [v for vn, v in c.vars.items() if vn == 'sym3'][0]
assert_A = {'row': [0, 0, 0],
'col': [0, 1, 4],
'val': [Constant(-1.0), Constant(-1.0), Constant(1.0)]}
assert_b = [Constant(0.0)]
#assert_G = {'row': [0, 0, 1, 2, 3, 4, 5, 6, 7, 8],
# 'col': [0, 5, 3, 4, 2, 2, 3, 5, 5, 1],
# 'val': [Constant(-1.0), Constant(0.0), Constant(-1.0), Constant(1.0),
# Constant(-1.0), Constant(-1.0), Constant(2.0), Constant(-1.0),
# Constant(-1.0), Constant(2.0)]}
assert_G = {'row': [0, 0, 1, 2, 3, 4, 5, 6, 7, 8],
'col': [0, 5, 3, 4, 2, 2, 3, 5, 5, 1],
'val': [Constant(-1.0), Constant(1.0), Constant(-1.0), Constant(1.0),
Constant(-1.0), Constant(-1.0), Constant(2.0), Constant(-1.0),
Constant(-1.0), Constant(2.0)]}
assert_h = [ (-1.0 * sym3), Constant(0.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0)]
assert_h = [Constant(0.0), Constant(0.0), Constant(0.0), Constant(1.0),
Constant(-1.0), Constant(0.0), Constant(1.0), Constant(-1.0),
Constant(0.0)]
assert_dims = {'q': [2, 3, 3], 'l': 1}
assert_A = COO_to_CS(assert_A, (len(assert_b), len(c.c)), 'col')
assert_G = COO_to_CS(assert_G, (len(assert_h), len(c.c)), 'col')
assert_c = [0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
assert(c.c == assert_c)
assert(c.A == assert_A)
assert(c.b == assert_b)
assert(c.G == assert_G)
assert(all([c.h[n].value == t.value for n, t in enumerate(assert_h)]))
assert(c.dims == assert_dims)
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 test_matrix_least_squares_constr():
""" Minimize(square(norm(F*x - g))) with x >= p0 """
x = Variable ((3,1),name='x')
F = Parameter((3,3),name='F')
g = Parameter((3,1),name='g')
objective = square(norm( F*x - g ))
objective = Minimize(objective)
problem = Problem(objective, [x >= 1])
c = Canonicalize(problem, verbose=True)
# Test for errors, not asserts, and for solution outcome (via ecos_solution)
reset_symbols()
def __init__(self, problem, name = 'embedded', folder = None,
lang = 'c', verbose = False,
temp = 'main_set'):
lang = lang.lower()
self.problem = problem
self.name = name
if not folder:
self.location = pathlib.Path(self.name)
else:
self.location = pathlib.Path(folder) / self.name
self.set = temp # which set of templates to use?
self.canonical = Canonicalize(self.problem, verbose = verbose)
if lang not in ['c']: # Catch unimplemented languages
raise(NotImplemented('Only C99 Code Generation Supported'))
self.write(lang)
def test_matrix_sq2norm_constr():
""" Matrix Form of Minimize(square(norm(v0))) with v0 >= p0"""
v0 = Variable(name = 'v0')
v1 = Variable(name = 'v1')
p0 = Parameter(name = 'p0')
p1 = Parameter(name = 'p1')
obj = square(norm(v0))
con = [v0 >= p0] # should become -v0 + p0 <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True)
assert_c = [0.0, 0.0, 1.0, 0.0]
assert_A = COO_to_CS({'row':[],'col':[],'val':[]}, (0,4), 'col')
assert_G = {'row': [0, 1, 2, 3, 4, 5], 'col': [0, 3, 0, 2, 2, 3],
'val': [Constant(-1.0), Constant(-1.0), Constant(1.0),
Constant(-1.0), Constant(-1.0), Constant(2.0)]}
assert_h = [(-1.0 * p0), Constant(0.0), Constant(0.0),
Constant(1.0), Constant(-1.0), Constant(0.0)]
assert_G = COO_to_CS(assert_G, (len(assert_h), len(c.c)), 'col')
assert(c.c == assert_c)
assert(c.A is None)
assert(c.b is None)
assert(c.G == assert_G)
assert(all([c.h[n].value == t.value for n, t in enumerate(assert_h)]))
assert(c.dims == {'q': [2, 3], 'l': 1})
reset_symbols()
def test_smith_sq2norm_sqcon():
""" Smith Form : Minimize(square(norm(v0))) with v0 >= square(v1) """
v0 = Variable(name='v0')
v1 = Variable(name='v1')
p0 = Parameter(name='p0')
p1 = Parameter(name='p1')
obj = square(norm(v0 + v1))
con = [v0 >= square(v1)] # should become -v0 + square(v1) <= 0
p = Problem(Minimize(obj), con)
c = Canonicalize(p, verbose=True, only='smith')
assert (type(c.constraints[-1]) is le)
assert (type(c.constraints[-1].expr) is sums.sum)
assert (type(c.constraints[-1].expr.args[0]) is muls.smul)
assert (type(c.constraints[-1].expr.args[1]) is muls.smul)
assert (c.objective is not obj)
assert ('sym0' == c.objective.name)
string_equals = [
"""(sym2 + (-1.0 * v0) + (-1.0 * v1)) == 0""",
"""(sym1 + (-1.0 * norm2(sym2))) == 0""",
"""(sym0 + (-1.0 * square(sym1))) == 0""",
"""(sym3 + (-1.0 * square(v1))) == 0""",
"""((-1.0 * v0) + (1.0 * sym3)) <= 0""",
]
for n, string in enumerate(string_equals):
print(c.constraints[n], ' ???? ', string, end=' ')
assert (str(c.constraints[n]) == string)
print('... SUCCESS!')
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()