def test_FISTA_cvx(self):
if False:
if not cvx_not_installable:
try:
# Problem data.
m = 30
n = 20
np.random.seed(1)
Amat = np.random.randn(m, n)
A = LinearOperatorMatrix(Amat)
bmat = np.random.randn(m)
bmat.shape = (bmat.shape[0], 1)
# A = Identity()
# Change n to equal to m.
#b = DataContainer(bmat)
vg = VectorGeometry(m)
b = vg.allocate('random')
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = LeastSquares(A, b, c=0.5)
g0 = ZeroFunction()
# Initial guess
#x_init = DataContainer(np.zeros((n, 1)))
x_init = vg.allocate()
f.gradient(x_init, out = x_init)
# Run FISTA for least squares plus zero function.
#x_fista0, it0, timing0, criter0 = FISTA(x_init, f, g0, opt=opt)
fa = FISTA(x_init=x_init, f=f, g=g0)
fa.max_iteration = 10
fa.run(10)
# Print solution and final objective/criterion value for comparison
print("FISTA least squares plus zero function solution and objective value:")
print(fa.get_output())
print(fa.get_last_objective())
# Compare to CVXPY
# Construct the problem.
x0 = Variable(n)
objective0 = Minimize(0.5*sum_squares(Amat*x0 - bmat.T[0]))
prob0 = Problem(objective0)
# The optimal objective is returned by prob.solve().
result0 = prob0.solve(verbose=False, solver=SCS, eps=1e-9)
# The optimal solution for x is stored in x.value and optimal objective value
# is in result as well as in objective.value
print("CVXPY least squares plus zero function solution and objective value:")
print(x0.value)
print(objective0.value)
self.assertNumpyArrayAlmostEqual(
numpy.squeeze(x_fista0.array), x0.value, 6)
except SolverError as se:
print (str(se))
self.assertTrue(True)
else:
self.assertTrue(cvx_not_installable)
def stest_FISTA_Norm1_cvx(self):
if not cvx_not_installable:
try:
opt = {'memopt': True}
# Problem data.
m = 30
n = 20
np.random.seed(1)
Amat = np.random.randn(m, n)
A = LinearOperatorMatrix(Amat)
bmat = np.random.randn(m)
#bmat.shape = (bmat.shape[0], 1)
# A = Identity()
# Change n to equal to m.
vgb = VectorGeometry(m)
vgx = VectorGeometry(n)
b = vgb.allocate()
b.fill(bmat)
#b = DataContainer(bmat)
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = LeastSquares(A, b, c=0.5)
g0 = ZeroFunction()
# Initial guess
#x_init = DataContainer(np.zeros((n, 1)))
x_init = vgx.allocate()
# Create 1-norm object instance
g1 = lam * L1Norm()
g1(x_init)
g1.prox(x_init, 0.02)
# Combine with least squares and solve using generic FISTA implementation
#x_fista1, it1, timing1, criter1 = FISTA(x_init, f, g1, opt=opt)
fa = FISTA(x_init=x_init, f=f, g=g1)
fa.max_iteration = 10
fa.run(10)
# Print for comparison
print("FISTA least squares plus 1-norm solution and objective value:")
print(fa.get_output())
print(fa.get_last_objective())
# Compare to CVXPY
# Construct the problem.
x1 = Variable(n)
objective1 = Minimize(
0.5*sum_squares(Amat*x1 - bmat.T[0]) + lam*norm(x1, 1))
prob1 = Problem(objective1)
# The optimal objective is returned by prob.solve().
result1 = prob1.solve(verbose=False, solver=SCS, eps=1e-9)
# The optimal solution for x is stored in x.value and optimal objective value
# is in result as well as in objective.value
print("CVXPY least squares plus 1-norm solution and objective value:")
print(x1.value)
print(objective1.value)
self.assertNumpyArrayAlmostEqual(
numpy.squeeze(x_fista1.array), x1.value, 6)
except SolverError as se:
print (str(se))
self.assertTrue(True)
else:
self.assertTrue(cvx_not_installable)