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_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_sum_entries(self):
"""Sum of entries of lin op.
"""
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = sum_entries(tmp)
x = fn.prox(1.0, v.copy())
self.assertItemsAlmostEqual(x, v - 1)
def test_sum_entries(self):
"""Sum of entries of lin op.
"""
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = sum_entries(tmp)
x = fn.prox(1.0, v.copy())
self.assertItemsAlmostEqual(x, v - 1)
def test_merge_all(self):
"""Test function to merge all prox operators possible.
"""
# merge all
x = Variable(10)
lin_op = grad(x)
fns = [sum_squares(lin_op), sum_entries(lin_op), nonneg(lin_op)]
merged = merge_all(fns)
assert len(merged) == 1
v = np.reshape(np.arange(10) * 1.0 - 5.0, (10, 1))
prox_val1 = merged[0].prox(1.0, v.copy())
tmp = nonneg(lin_op, c=np.ones((10, 1)), gamma=1.0)
prox_val2 = tmp.prox(1.0, v.copy())
self.assertItemsAlmostEqual(prox_val1, prox_val2)
def test_merge_all(self):
"""Test function to merge all prox operators possible.
"""
# merge all
x = Variable(10)
lin_op = grad(x)
fns = [sum_squares(lin_op), sum_entries(lin_op), nonneg(lin_op)]
merged = merge_all(fns)
assert len(merged) == 1
v = np.reshape(np.arange(10) * 1.0 - 5.0, (10, 1))
prox_val1 = merged[0].prox(1.0, v.copy())
tmp = nonneg(lin_op, c=np.ones((10, 1)), gamma=1.0)
prox_val2 = tmp.prox(1.0, v.copy())
self.assertItemsAlmostEqual(prox_val1, prox_val2)
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)
