def test_merge(self):
"""Test merging functions.
"""
# sum_entries
x = Variable(10)
fn1 = sum_entries(x, gamma=1.0)
fn2 = norm1(x)
assert can_merge(fn1, fn2)
merged = merge_fns(fn1, fn2)
v = np.arange(10) * 1.0 - 5.0
prox_val1 = merged.prox(1.0, v.copy())
tmp = norm1(x, c=np.ones(10), gamma=1.0)
prox_val2 = tmp.prox(1.0, v.copy())
self.assertItemsAlmostEqual(prox_val1, prox_val2)
# sum_squares
x = Variable(10)
val = np.arange(10)
fn1 = sum_squares(x, gamma=1.0, beta=2.0, alpha=3.0, b=val)
fn2 = norm1(x)
assert can_merge(fn1, fn2)
merged = merge_fns(fn1, fn2)
v = np.arange(10) * 1.0 - 5.0
prox_val1 = merged.prox(1.0, v.copy())
tmp = norm1(x, c=-12 * val, gamma=1.0 + 12, d=val.dot(val))
prox_val2 = tmp.prox(1.0, v.copy())
self.assertItemsAlmostEqual(prox_val1, prox_val2)
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_merge(self):
"""Test merging functions.
"""
# sum_entries
x = Variable(10)
fn1 = sum_entries(x, gamma=1.0)
fn2 = norm1(x)
assert can_merge(fn1, fn2)
merged = merge_fns(fn1, fn2)
v = np.arange(10) * 1.0 - 5.0
prox_val1 = merged.prox(1.0, v.copy())
tmp = norm1(x, c=np.ones(10), gamma=1.0)
prox_val2 = tmp.prox(1.0, v.copy())
self.assertItemsAlmostEqual(prox_val1, prox_val2)
# sum_squares
x = Variable(10)
val = np.arange(10)
fn1 = sum_squares(x, gamma=1.0, beta=2.0, alpha=3.0, b=val)
fn2 = norm1(x)
assert can_merge(fn1, fn2)
merged = merge_fns(fn1, fn2)
v = np.arange(10) * 1.0 - 5.0
prox_val1 = merged.prox(1.0, v.copy())
tmp = norm1(x, c=-12 * val, gamma=1.0 + 12, d=val.dot(val))
prox_val2 = tmp.prox(1.0, v.copy())
self.assertItemsAlmostEqual(prox_val1, prox_val2)
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_norm1(self):
"""Test L1 norm prox fn.
"""
# No modifiers.
tmp = Variable(10)
fn = norm1(tmp)
rho = 1
v = np.arange(10) * 1.0 - 5.0
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - 1.0 / rho, 0))
rho = 2
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - 1.0 / rho, 0))
# With modifiers.
mod_fn = norm1(tmp,
alpha=0.1,
beta=5,
c=np.ones(10) * 1.0,
b=np.ones(10) * -1.0,
gamma=4)
rho = 2
v = np.arange(10) * 1.0
x = mod_fn.prox(rho, v.copy())
# vhat = mod_fn.beta*(v - mod_fn.c/rho)*rho/(rho+2*mod_fn.gamma) - mod_fn.b
# rho_hat = rho/(mod_fn.alpha*mod_fn.beta**2)
# xhat = fn.prox(rho_hat, vhat)
x_var = cvx.Variable(10)
cost = 0.1 * cvx.norm1(5 * x_var + np.ones(10)) + np.ones(10).T * x_var + \
4 * cvx.sum_squares(x_var) + (rho / 2) * cvx.sum_squares(x_var - v)
prob = cvx.Problem(cvx.Minimize(cost))
prob.solve()
self.assertItemsAlmostEqual(x, x_var.value, places=3)
# With weights.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = weighted_norm1(tmp, -v + 1)
rho = 2
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - np.abs(-v + 1) / rho, 0))
def test_overloading(self):
"""Test operator overloading.
"""
x = Variable(1)
fn = sum_squares(x, b=1)
val = fn.prox(2.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn = 2 * sum_squares(x, b=1)
val = fn.prox(4.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn = sum_squares(x, b=1) * 2
val = fn.prox(4.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn = sum_squares(x, b=1) / 2
val = fn.prox(1.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn1 = sum_squares(x, b=1)
fn2 = norm1(x)
arr = fn1 + fn2
self.assertEqual(type(arr), list)
self.assertEqual(len(arr), 2)
arr = arr + fn2
self.assertEqual(type(arr), list)
self.assertEqual(len(arr), 3)
def test_overloading(self):
"""Test operator overloading.
"""
x = Variable(1)
fn = sum_squares(x, b=1)
val = fn.prox(2.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn = 2 * sum_squares(x, b=1)
val = fn.prox(4.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn = sum_squares(x, b=1) * 2
val = fn.prox(4.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn = sum_squares(x, b=1) / 2
val = fn.prox(1.0, 0)
self.assertItemsAlmostEqual([val], [0.5])
fn1 = sum_squares(x, b=1)
fn2 = norm1(x)
arr = fn1 + fn2
self.assertEqual(type(arr), list)
self.assertEqual(len(arr), 2)
arr = arr + fn2
self.assertEqual(type(arr), list)
self.assertEqual(len(arr), 3)
def test_norm1(self):
"""Test L1 norm prox fn.
"""
# No modifiers.
tmp = Variable(10)
fn = norm1(tmp)
rho = 1
v = np.arange(10) * 1.0 - 5.0
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 1.0 / rho, 0))
rho = 2
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 1.0 / rho, 0))
# With modifiers.
mod_fn = norm1(tmp, alpha=0.1, beta=5,
c=np.ones(10) * 1.0, b=np.ones(10) * -1.0, gamma=4)
rho = 2
v = np.arange(10) * 1.0
x = mod_fn.prox(rho, v.copy())
# vhat = mod_fn.beta*(v - mod_fn.c/rho)*rho/(rho+2*mod_fn.gamma) - mod_fn.b
# rho_hat = rho/(mod_fn.alpha*mod_fn.beta**2)
# xhat = fn.prox(rho_hat, vhat)
x_var = cvx.Variable(10)
cost = 0.1 * cvx.norm1(5 * x_var + np.ones(10)) + np.ones(10).T * x_var + \
4 * cvx.sum_squares(x_var) + (rho / 2) * cvx.sum_squares(x_var - v)
prob = cvx.Problem(cvx.Minimize(cost))
prob.solve()
self.assertItemsAlmostEqual(x, x_var.value, places=3)
# With weights.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = weighted_norm1(tmp, -v + 1)
rho = 2
x = fn.prox(rho, v)
self.assertItemsAlmostEqual(x, np.sign(v) *
np.maximum(np.abs(v) - np.abs(-v + 1) / rho, 0))
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)
def test_absorb_lin_op(self):
"""Test absorb lin op operator.
"""
# norm1.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = norm1(mul_elemwise(-v, tmp), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 5. *
np.abs(v) / rho, 0))
fn = norm1(mul_elemwise(-v, mul_elemwise(2 * v, tmp)), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 5. *
np.abs(v) / rho, 0))
new_prox = absorb_lin_op(new_prox)[0]
x = new_prox.prox(rho, v.copy())
new_v = 2 * v * v
self.assertItemsAlmostEqual(x, np.sign(new_v) *
np.maximum(np.abs(new_v) - 5. * np.abs(new_v) / rho, 0))
# nonneg.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = nonneg(mul_elemwise(-v, tmp), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, fn.prox(rho, -np.abs(v)))
# sum_squares.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
alpha = 5.
val = np.arange(10)
fn = sum_squares(mul_elemwise(-v, tmp), alpha=alpha, c=val)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) * (rho / 2) +
5 * cvx.sum_squares(cvx.mul_elemwise(-v,
cvx_x)) + (val * -v).T * cvx_x
))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=3)
# Test scale.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = norm1(10 * tmp)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x, 1)))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=3)
val = np.arange(10)
fn = norm1(10 * tmp, c=val, b=val, gamma=0.01)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) +
cvx.norm(10 * cvx_x - val, 1) + 10 * val.T * \
cvx_x + cvx.sum_squares(cvx_x)
))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=2)
# sum_entries
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = sum_entries(sum([10 * tmp, mul_elemwise(v, tmp)]))
funcs = absorb.absorb_all_lin_ops([fn])
c = __builtins__['sum']([func.c for func in funcs])
self.assertItemsAlmostEqual(c, v + 10, places=3)
def test_absorb_lin_op(self):
"""Test absorb lin op operator.
"""
# norm1.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = norm1(mul_elemwise(-v, tmp), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0))
fn = norm1(mul_elemwise(-v, mul_elemwise(2 * v, tmp)), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0))
new_prox = absorb_lin_op(new_prox)[0]
x = new_prox.prox(rho, v.copy())
new_v = 2 * v * v
self.assertItemsAlmostEqual(
x,
np.sign(new_v) *
np.maximum(np.abs(new_v) - 5. * np.abs(new_v) / rho, 0))
# nonneg.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = nonneg(mul_elemwise(-v, tmp), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, fn.prox(rho, -np.abs(v)))
# sum_squares.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
alpha = 5.
val = np.arange(10)
fn = sum_squares(mul_elemwise(-v, tmp), alpha=alpha, c=val)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(
cvx.Minimize(
cvx.sum_squares(cvx_x - v) * (rho / 2) +
5 * cvx.sum_squares(cvx.mul_elemwise(-v, cvx_x)) +
(val * -v).T * cvx_x))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=3)
# Test scale.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = norm1(10 * tmp)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(
cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x, 1)))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=3)
val = np.arange(10)
fn = norm1(10 * tmp, c=val, b=val, gamma=0.01)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) +
cvx.norm(10 * cvx_x - val, 1) + 10 * val.T * \
cvx_x + cvx.sum_squares(cvx_x)
))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=2)
# sum_entries
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = sum_entries(sum([10 * tmp, mul_elemwise(v, tmp)]))
funcs = absorb.absorb_all_lin_ops([fn])
c = __builtins__['sum']([func.c for func in funcs])
self.assertItemsAlmostEqual(c, v + 10, places=3)