def test(self):
np.random.seed(0)
cvx_problem = problem_gen()
problem = TestTensorProblem(TensorProblem(cvx_problem))
data = cvx_problem.get_problem_data(cvx.SCS)
# Compare with manually implemented SCS iterations
m, n = data["A"].shape
u0 = np.zeros((m + n + 1, 1))
v0 = np.zeros((m + n + 1, 1))
u0[-1] = 1
v0[-1] = 1
# variables
u, v = scs_tf.create_variables(problem)
cache = scs_tf.create_cache(problem)
counters = scs_tf.create_counters()
# ops
init_op = tf.initialize_all_variables()
init_cache_op = scs_tf.init_cache(problem, cache)
iterate_op = scs_tf.iterate(problem, u, v, cache, counters)
residuals = scs_tf.compute_residuals(problem, u, v)
# Run two iterations
u_vec = vstack([u.x, u.y, u.tau])
v_vec = vstack([v.r, v.s, v.kappa])
with self.test_session():
init_op.run()
init_cache_op.run()
tf.logging.info("initialization")
assert_allclose(u0, u_vec.eval())
assert_allclose(v0, v_vec.eval())
tf.logging.info("first iteration")
iterate_op.run()
u_tilde0 = expected_subspace_projection(data, u0 + v0)
u0 = expected_cone_projection(data, u_tilde0 - v0)
v0 = v0 - u_tilde0 + u0
assert_allclose(u0, u_vec.eval(), rtol=0, atol=1e-4)
assert_allclose(v0, v_vec.eval(), rtol=0, atol=1e-4)
u0 = u_vec.eval()
v0 = v_vec.eval()
tf.logging.info("second iteration")
iterate_op.run()
u_tilde0 = expected_subspace_projection(data, u0 + v0)
u0 = expected_cone_projection(data, u_tilde0 - v0)
v0 = v0 - u_tilde0 + u0
assert_allclose(u0, u_vec.eval(), rtol=0, atol=1e-2)
assert_allclose(v0, v_vec.eval(), rtol=0, atol=1e-2)
def test(self):
np.random.seed(0)
cvx_problem = problem_gen()
problem = TestTensorProblem(TensorProblem(cvx_problem))
data = cvx_problem.get_problem_data(cvx.SCS)
# Compare with manually implemented SCS iterations
m, n = data["A"].shape
u0 = np.zeros((m+n+1,1))
v0 = np.zeros((m+n+1,1))
u0[-1] = 1
v0[-1] = 1
# variables
u, v = scs_tf.create_variables(problem)
cache = scs_tf.create_cache(problem)
counters = scs_tf.create_counters()
# ops
init_op = tf.initialize_all_variables()
init_cache_op = scs_tf.init_cache(problem, cache)
iterate_op = scs_tf.iterate(problem, u, v, cache, counters)
residuals = scs_tf.compute_residuals(problem, u, v)
# Run two iterations
u_vec = vstack([u.x, u.y, u.tau])
v_vec = vstack([v.r, v.s, v.kappa])
with self.test_session():
init_op.run()
init_cache_op.run()
tf.logging.info("initialization")
assert_allclose(u0, u_vec.eval())
assert_allclose(v0, v_vec.eval())
tf.logging.info("first iteration")
iterate_op.run()
u_tilde0 = expected_subspace_projection(data, u0 + v0)
u0 = expected_cone_projection(data, u_tilde0 - v0)
v0 = v0 - u_tilde0 + u0
assert_allclose(u0, u_vec.eval(), rtol=0, atol=1e-4)
assert_allclose(v0, v_vec.eval(), rtol=0, atol=1e-4)
u0 = u_vec.eval()
v0 = v_vec.eval()
tf.logging.info("second iteration")
iterate_op.run()
u_tilde0 = expected_subspace_projection(data, u0 + v0)
u0 = expected_cone_projection(data, u_tilde0 - v0)
v0 = v0 - u_tilde0 + u0
assert_allclose(u0, u_vec.eval(), rtol=0, atol=1e-2)
assert_allclose(v0, v_vec.eval(), rtol=0, atol=1e-2)
def A(self, x):
xs = {}
for var_id, var_size in self.sym_data.var_sizes.items():
var_offset = self.sym_data.var_offsets[var_id]
idx = slice(var_offset, var_offset+var_size[0]*var_size[1])
xs[var_id] = mat(x[idx,:], var_size)
return vstack([vec(cvxpy_expr.tensor(Ai, xs)) for Ai in self.A_exprs])
def get_constraint_tensors(constraints):
"""Get expression for Ax + b."""
A_exprs = [constr.expr for constr in tree_mat.prune_constants(constraints)]
b = vstack(
[vec(tf.constant(-tree_mat.mul(constr.expr, {}), dtype=tf.float32))
for constr in constraints])
return A_exprs, b
def A(self, x):
xs = {}
for var_id, var_size in self.sym_data.var_sizes.items():
var_offset = self.sym_data.var_offsets[var_id]
idx = slice(var_offset, var_offset + var_size[0] * var_size[1])
xs[var_id] = mat(x[idx, :], var_size)
return vstack([vec(cvxpy_expr.tensor(Ai, xs)) for Ai in self.A_exprs])
def get_constraint_tensors(constraints):
"""Get expression for Ax + b."""
A_exprs = [constr.expr for constr in tree_mat.prune_constants(constraints)]
b = vstack([
vec(tf.constant(-tree_mat.mul(constr.expr, {}), dtype=tf.float32))
for constr in constraints
])
return A_exprs, b
def proj_cone(cone_slices, x, dual=False):
ys = []
prefix = "proj_dual_" if dual else "proj_"
for cone, idx in cone_slices:
proj = globals()[prefix + cone]
ys.append(proj(x[idx,:]))
return vstack(ys)
def proj_second_order(x):
s, v = x[:1,:], x[1:,:]
norm_v = norm(v)
s = tf.squeeze(s)
return tf.case(
((norm_v <= -s, lambda: tf.zeros_like(x)),
(norm_v <= s, lambda: x)),
lambda: 0.5*(1 + s/norm_v)*vstack([tf.reshape(norm_v, (1,1)), v]))
def AT(self, y):
ys = []
offset = 0
for constr in self.constraints:
idx = slice(offset, offset+constr.size[0]*constr.size[1])
ys.append(mat(y[idx,:], constr.size))
offset += constr.size[0]*constr.size[1]
x_map = sum_dicts(cvxpy_expr.adjoint_tensor(Ai, ys[i])
for i, Ai in enumerate(self.A_exprs))
return vstack([vec(x_map[var_id]) for var_id in self.var_ids])
def AT(self, y):
ys = []
offset = 0
for constr in self.constraints:
idx = slice(offset, offset + constr.size[0] * constr.size[1])
ys.append(mat(y[idx, :], constr.size))
offset += constr.size[0] * constr.size[1]
x_map = sum_dicts(
cvxpy_expr.adjoint_tensor(Ai, ys[i])
for i, Ai in enumerate(self.A_exprs))
return vstack([vec(x_map[var_id]) for var_id in self.var_ids])
def get_objective_tensor(var_ids, sym_data):
"""Get objective tensor via gradient of c'x."""
xs = [tf.Variable(tf.zeros(sym_data.var_sizes[var_id], dtype=tf.float32))
for var_id in var_ids]
xs_map = dict(zip((var_id for var_id in var_ids), xs))
obj_t = cvxpy_expr.tensor(sym_data.objective, xs_map)
# get gradient, handling None values
return vstack([
vec(ci) if ci is not None
else vec(tf.zeros(sym_data.var_sizes[var_ids[i]], dtype=tf.float32))
for i, ci in enumerate(tf.gradients(obj_t, xs))])
def get_objective_tensor(var_ids, sym_data):
"""Get objective tensor via gradient of c'x."""
xs = [
tf.Variable(tf.zeros(sym_data.var_sizes[var_id], dtype=tf.float32))
for var_id in var_ids
]
xs_map = dict(zip((var_id for var_id in var_ids), xs))
obj_t = cvxpy_expr.tensor(sym_data.objective, xs_map)
# get gradient, handling None values
return vstack([
vec(ci) if ci is not None else vec(
tf.zeros(sym_data.var_sizes[var_ids[i]], dtype=tf.float32))
for i, ci in enumerate(tf.gradients(obj_t, xs))
])