def test_FISTA_cvx(self):
if not cvx_not_installable:
# 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)
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = Norm2sq(A, b, c=0.5, memopt=True)
g0 = ZeroFun()
# Initial guess
x_init = DataContainer(np.zeros((n, 1)))
f.grad(x_init)
# Run FISTA for least squares plus zero function.
x_fista0, it0, timing0, criter0 = FISTA(x_init, f, g0, opt=opt)
# Print solution and final objective/criterion value for comparison
print(
"FISTA least squares plus zero function solution and objective value:"
)
print(x_fista0.array)
print(criter0[-1])
# 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)
else:
self.assertTrue(cvx_not_installable)
def test_FBPD_Norm1_cvx(self):
if not cvx_not_installable:
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.
b = DataContainer(bmat)
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = Norm2sq(A, b, c=0.5, memopt=True)
g0 = ZeroFun()
# Initial guess
x_init = DataContainer(np.zeros((n, 1)))
# Create 1-norm object instance
g1 = Norm1(lam)
# 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)
# Now try another algorithm FBPD for same problem:
x_fbpd1, itfbpd1, timingfbpd1, criterfbpd1 = FBPD(
x_init, Identity(), None, f, g1)
print(x_fbpd1)
print(criterfbpd1[-1])
self.assertNumpyArrayAlmostEqual(numpy.squeeze(x_fbpd1.array),
x1.value, 6)
else:
self.assertTrue(cvx_not_installable)
# conda install -c cvxgrp cvxpy libgcc
# Whether to use or omit CVXPY
use_cvxpy = True
if use_cvxpy:
from cvxpy import *
import numpy as np
import matplotlib.pyplot as plt
# 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)
# Regularization parameter
lam = 10
opt = {'memopt':True}
# Create object instances with the test data A and b.
f = Norm2sq(A,b,c=0.5, memopt=True)
g0 = ZeroFun()
def test_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.
b = DataContainer(bmat)
# Regularization parameter
lam = 10
opt = {'memopt': True}
# Create object instances with the test data A and b.
f = Norm2sq(A, b, c=0.5, memopt=True)
g0 = ZeroFun()
# Initial guess
x_init = DataContainer(np.zeros((n, 1)))
# Create 1-norm object instance
g1 = Norm1(lam)
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)
# Print for comparison
print(
"FISTA least squares plus 1-norm solution and objective value:"
)
print(x_fista1.as_array().squeeze())
print(criter1[-1])
# 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)