def test_solver_comparison(self):
"""
Test that all solvers return the same and correct solution.
"""
# Convex functions.
y = [1, 0, 0.1, 8, -6.5, 0.2, 0.004, 0.01]
sol = [0.75, 0, 0, 7.75, -6.25, 0, 0, 0]
w1, w2 = .8, .4
f1 = functions.norm_l2(y=y, lambda_=w1 / 2.) # Smooth.
f2 = functions.norm_l1(lambda_=w2 / 2.) # Non-smooth.
# Solvers.
L = w1 # Lipschitz continuous gradient.
step = 1. / L
lambda_ = 0.5
params = {'step': step, 'lambda_': lambda_}
slvs = []
slvs.append(
solvers.forward_backward(accel=acceleration.dummy(), step=step))
slvs.append(solvers.douglas_rachford(**params))
slvs.append(solvers.generalized_forward_backward(**params))
# Compare solutions.
params = {'rtol': 1e-14, 'verbosity': 'NONE', 'maxit': 1e4}
niters = [2, 61, 26]
for solver, niter in zip(slvs, niters):
x0 = np.zeros(len(y))
ret = solvers.solve([f1, f2], x0, solver, **params)
nptest.assert_allclose(ret['sol'], sol)
self.assertEqual(ret['niter'], niter)
self.assertIs(ret['sol'], x0) # The initial value was modified.
def test_acceleration_comparison(self):
"""
Test that all solvers return the same and correct solution.
"""
# Convex functions.
y = [1, 0, 0.1, 8, -6.5, 0.2, 0.004, 0.01]
sol = [0.75, 0, 0, 7.75, -6.25, 0, 0, 0]
w1, w2 = .8, .4
f1 = functions.norm_l2(y=y, lambda_=w1 / 2.) # Smooth.
f2 = functions.norm_l1(lambda_=w2 / 2.) # Non-smooth.
# Solvers.
L = w1 # Lipschitz continuous gradient.
step = 1. / L
slvs = []
slvs.append(solvers.forward_backward(accel=acceleration.dummy(),
step=step))
slvs.append(solvers.forward_backward(accel=acceleration.fista(),
step=step))
slvs.append(solvers.forward_backward(
accel=acceleration.fista_backtracking(eta=.999), step=step))
# Compare solutions.
params = {'rtol': 1e-14, 'verbosity': 'NONE', 'maxit': 1e4}
niters = [2, 2, 6]
for solver, niter in zip(slvs, niters):
x0 = np.zeros(len(y))
ret = solvers.solve([f1, f2], x0, solver, **params)
nptest.assert_allclose(ret['sol'], sol)
self.assertEqual(ret['niter'], niter)
def test_forward_backward(self):
"""
Test forward-backward splitting algorithm without acceleration, and
with L1-norm, L2-norm, and dummy functions.
"""
y = [4., 5., 6., 7.]
solver = solvers.forward_backward(accel=acceleration.dummy())
param = {'solver': solver, 'rtol': 1e-6, 'verbosity': 'NONE'}
# L2-norm prox and dummy gradient.
f1 = functions.norm_l2(y=y)
f2 = functions.dummy()
ret = solvers.solve([f1, f2], np.zeros(len(y)), **param)
nptest.assert_allclose(ret['sol'], y)
self.assertEqual(ret['crit'], 'RTOL')
self.assertEqual(ret['niter'], 35)
# L1-norm prox and L2-norm gradient.
f1 = functions.norm_l1(y=y, lambda_=1.0)
f2 = functions.norm_l2(y=y, lambda_=0.8)
ret = solvers.solve([f1, f2], np.zeros(len(y)), **param)
nptest.assert_allclose(ret['sol'], y)
self.assertEqual(ret['crit'], 'RTOL')
self.assertEqual(ret['niter'], 4)
# Sanity check
f3 = functions.dummy()
x0 = np.zeros((4, ))
self.assertRaises(ValueError, solver.pre, [f1, f2, f3], x0)
def test_acceleration_comparison(self):
"""
Test that all solvers return the same and correct solution.
"""
# Convex functions.
y = [1, 0, 0.1, 8, -6.5, 0.2, 0.004, 0.01]
sol = [0.75, 0, 0, 7.75, -6.25, 0, 0, 0]
w1, w2 = .8, .4
f1 = functions.norm_l2(y=y, lambda_=w1 / 2.) # Smooth.
f2 = functions.norm_l1(lambda_=w2 / 2.) # Non-smooth.
# Solvers.
L = w1 # Lipschitz continuous gradient.
step = 1. / L
slvs = []
slvs.append(
solvers.forward_backward(accel=acceleration.dummy(), step=step))
slvs.append(
solvers.forward_backward(accel=acceleration.fista(), step=step))
slvs.append(
solvers.forward_backward(
accel=acceleration.fista_backtracking(eta=.999), step=step))
# Compare solutions.
params = {'rtol': 1e-14, 'verbosity': 'NONE', 'maxit': 1e4}
niters = [2, 2, 6]
for solver, niter in zip(slvs, niters):
x0 = np.zeros(len(y))
ret = solvers.solve([f1, f2], x0, solver, **params)
nptest.assert_allclose(ret['sol'], sol)
self.assertEqual(ret['niter'], niter)
def test_solver_comparison(self):
"""
Test that all solvers return the same and correct solution.
"""
# Convex functions.
y = [1, 0, 0.1, 8, -6.5, 0.2, 0.004, 0.01]
sol = [0.75, 0, 0, 7.75, -6.25, 0, 0, 0]
w1, w2 = .8, .4
f1 = functions.norm_l2(y=y, lambda_=w1 / 2.) # Smooth.
f2 = functions.norm_l1(lambda_=w2 / 2.) # Non-smooth.
# Solvers.
L = w1 # Lipschitz continuous gradient.
step = 1. / L
lambda_ = 0.5
params = {'step': step, 'lambda_': lambda_}
slvs = []
slvs.append(solvers.forward_backward(accel=acceleration.dummy(),
step=step))
slvs.append(solvers.douglas_rachford(**params))
slvs.append(solvers.generalized_forward_backward(**params))
# Compare solutions.
params = {'rtol': 1e-14, 'verbosity': 'NONE', 'maxit': 1e4}
niters = [2, 61, 26]
for solver, niter in zip(slvs, niters):
x0 = np.zeros(len(y))
ret = solvers.solve([f1, f2], x0, solver, **params)
nptest.assert_allclose(ret['sol'], sol)
self.assertEqual(ret['niter'], niter)
self.assertIs(ret['sol'], x0) # The initial value was modified.
def test_forward_backward(self):
"""
Test forward-backward splitting algorithm without acceleration, and
with L1-norm, L2-norm, and dummy functions.
"""
y = [4., 5., 6., 7.]
solver = solvers.forward_backward(accel=acceleration.dummy())
param = {'solver': solver, 'rtol': 1e-6, 'verbosity': 'NONE'}
# L2-norm prox and dummy gradient.
f1 = functions.norm_l2(y=y)
f2 = functions.dummy()
ret = solvers.solve([f1, f2], np.zeros(len(y)), **param)
nptest.assert_allclose(ret['sol'], y)
self.assertEqual(ret['crit'], 'RTOL')
self.assertEqual(ret['niter'], 35)
# L1-norm prox and L2-norm gradient.
f1 = functions.norm_l1(y=y, lambda_=1.0)
f2 = functions.norm_l2(y=y, lambda_=0.8)
ret = solvers.solve([f1, f2], np.zeros(len(y)), **param)
nptest.assert_allclose(ret['sol'], y)
self.assertEqual(ret['crit'], 'RTOL')
self.assertEqual(ret['niter'], 4)
# Sanity check
f3 = functions.dummy()
x0 = np.zeros((4,))
self.assertRaises(ValueError, solver.pre, [f1, f2, f3], x0)
def __init__(self, step=1., accel=None):
if step < 0:
raise ValueError('Step should be a positive number.')
self.step = step
self.accel = acceleration.dummy() if accel is None else accel
def __init__(self, step=1., accel=None):
if step < 0:
raise ValueError('Step should be a positive number.')
self.step = step
self.accel = acceleration.dummy() if accel is None else accel