def test_single_func(self):
"""Test problems with only a single function to minimize.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8), (4, 2)) * 1.
prox_fns = [sum_squares(X - B)]
prob = Problem(prox_fns[0])
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, B, places=2)
def test_single_func(self):
"""Test problems with only a single function to minimize.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8), (4, 2)) * 1.
prox_fns = [sum_squares(X - B)]
prob = Problem(prox_fns[0])
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, B, places=2)
def test_multiple_vars(self):
"""Test problems with multiple variables."""
x = Variable(3)
y = Variable(6)
rhs = np.array([1, 2, 3])
prob = Problem([sum_squares(x - rhs),
sum_squares(subsample(y, [2]) - x)])
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(x.value, [1, 2, 3], places=3)
self.assertItemsAlmostEqual(y.value, [1, 0, 2, 0, 3, 0], places=3)
def test_multiple_vars(self):
"""Test problems with multiple variables."""
x = Variable(3)
y = Variable(6)
rhs = np.array([1, 2, 3])
prob = Problem(
[sum_squares(x - rhs),
sum_squares(subsample(y, [2]) - x)])
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(x.value, [1, 2, 3], places=3)
self.assertItemsAlmostEqual(y.value, [1, 0, 2, 0, 3, 0], places=3)
def test_problem(self):
"""Test problem object.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8), (4, 2)) * 1.
prox_fns = [norm1(X), sum_squares(X, b=B)]
prob = Problem(prox_fns)
# prob.partition(quad_funcs = [prox_fns[0], prox_fns[1]])
prob.set_automatic_frequency_split(False)
prob.set_absorb(False)
prob.set_implementation(Impl['halide'])
prob.set_solver('admm')
prob.solve()
true_X = norm1(X).prox(2, B.copy())
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="pc")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs", eps_rel=1e-6,
rho_0=1.0, rho_scale=np.sqrt(2.0) * 2.0, rho_max=2**16,
max_iters=20, max_inner_iters=500, verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# CG
prob = Problem(prox_fns)
prob.set_lin_solver("cg")
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs", eps_rel=1e-6,
rho_0=1.0, rho_scale=np.sqrt(2.0) * 2.0, rho_max=2**16,
max_iters=20, max_inner_iters=500, verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Quad funcs.
prob = Problem(prox_fns)
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Absorbing lin ops.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X, b=B)]
prob = Problem(prox_fns)
prob.set_absorb(True)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
cvx_X = cvx.Variable(4, 2)
cost = cvx.sum_squares(-2 * cvx_X - B) + cvx.norm(5 * cvx.mul_elemwise(B, cvx_X), 1)
cvx_prob = cvx.Problem(cvx.Minimize(cost))
cvx_prob.solve(solver=cvx.SCS)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
prob.set_absorb(False)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
# Constant offsets.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X - B)]
prob = Problem(prox_fns)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
def test_problem_absorb(self):
"""Test problem object with absorption.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8, dtype=np.float32), (4, 2), order='F')
# Absorbing lin ops.
prox_fns = sum_squares(-2 * X, b=B) + norm1(5 * mul_elemwise(B, X))
prob = Problem(prox_fns)
prob.set_absorb(True)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
cvx_X = cvx.Variable((4, 2))
cost = cvx.sum_squares(-2 * cvx_X - B) + cvx.norm(
5 * cvx.multiply(B, cvx_X), 1)
cvx_prob = cvx.Problem(cvx.Minimize(cost))
cvx_prob.solve(solver=cvx.SCS)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
prob.set_absorb(False)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
# Constant offsets.
prox_fns = sum_squares(-2 * X - B) + norm1(5 * mul_elemwise(B, X))
prob = Problem(prox_fns)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
def test_problem_no_absorb(self):
"""Test problem object without absorption.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8, dtype=np.float32), (4, 2), order='F')
prox_fns = [norm1(X), sum_squares(X, b=B)]
prob = Problem(prox_fns)
# prob.partition(quad_funcs = [prox_fns[0], prox_fns[1]])
prob.set_automatic_frequency_split(False)
prob.set_absorb(False)
prob.set_solver('admm')
prob.solve()
cvx_X = cvx.Variable((4, 2))
cost = cvx.sum_squares(cvx_X - B) + cvx.norm(cvx_X, 1)
cvx_prob = cvx.Problem(cvx.Minimize(cost))
cvx_prob.solve(solver=cvx.SCS)
true_X = cvx_X.value
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="pc")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs",
eps_rel=1e-6,
rho_0=1.0,
rho_scale=np.sqrt(2.0) * 2.0,
rho_max=2**16,
max_iters=20,
max_inner_iters=500,
verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# CG
prob = Problem(prox_fns)
prob.set_lin_solver("cg")
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs",
eps_rel=1e-6,
rho_0=1.0,
rho_scale=np.sqrt(2.0) * 2.0,
rho_max=2**16,
max_iters=20,
max_inner_iters=500,
verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Quad funcs.
prob = Problem(prox_fns)
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
def test_problem(self):
"""Test problem object.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8), (4, 2)) * 1.
prox_fns = [norm1(X), sum_squares(X, b=B)]
prob = Problem(prox_fns)
# prob.partition(quad_funcs = [prox_fns[0], prox_fns[1]])
prob.set_automatic_frequency_split(False)
prob.set_absorb(False)
prob.set_implementation(Impl['halide'])
prob.set_solver('admm')
prob.solve()
true_X = norm1(X).prox(2, B.copy())
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="pc")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs",
eps_rel=1e-6,
rho_0=1.0,
rho_scale=np.sqrt(2.0) * 2.0,
rho_max=2**16,
max_iters=20,
max_inner_iters=500,
verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# CG
prob = Problem(prox_fns)
prob.set_lin_solver("cg")
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs",
eps_rel=1e-6,
rho_0=1.0,
rho_scale=np.sqrt(2.0) * 2.0,
rho_max=2**16,
max_iters=20,
max_inner_iters=500,
verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Quad funcs.
prob = Problem(prox_fns)
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Absorbing lin ops.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X, b=B)]
prob = Problem(prox_fns)
prob.set_absorb(True)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
cvx_X = cvx.Variable(4, 2)
cost = cvx.sum_squares(-2 * cvx_X - B) + cvx.norm(
5 * cvx.mul_elemwise(B, cvx_X), 1)
cvx_prob = cvx.Problem(cvx.Minimize(cost))
cvx_prob.solve(solver=cvx.SCS)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
prob.set_absorb(False)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
# Constant offsets.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X - B)]
prob = Problem(prox_fns)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)