def test_dr_virtual_zero():
# Virtual 0-prox
prox_f = lambda u, la: 0 * 0
prox_g = lambda u, la: u * 0
# observations of size (5,1)
y = np.zeros((5, 1))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
# observations of size (5,2)
y = np.zeros((5, 2))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
def test_dr_zero():
# Prox of F, G = 0
prox_f = lambda u, la: u
prox_g = lambda u, la: u
# observations of size (5,1)
y = np.zeros((5, 1))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
# observations of size (5,2)
y = np.zeros((5, 2))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
def test_dr_virtual_zero():
# Virtual 0-prox
prox_f = lambda u, la: 0 * 0
prox_g = lambda u, la: u * 0
# observations of size (5,1)
y = np.zeros((5, 1))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
# observations of size (5,2)
y = np.zeros((5, 2))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
def test_dr_zero():
# Prox of F, G = 0
prox_f = lambda u, la: u
prox_g = lambda u, la: u
# observations of size (5,1)
y = np.zeros((5, 1))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
# observations of size (5,2)
y = np.zeros((5, 2))
x_rec = douglas_rachford(prox_f, prox_g, y)
assert_array_almost_equal(y, x_rec)
def _ic_minimization(DJ, Omega_x0, maxiter):
"""
Returns the solution of the problem
min_{w \in Ker(D_J)} ||Omega sign(D_I^* x_0) - w||_\infty
"""
proj = np.dot(np.dot(DJ.T,scipy.linalg.pinv(np.dot(DJ,DJ.T))), DJ)
prox_indic = lambda w, la: w - np.dot(proj, w)
proxinf = dual_prox(l1ball_projection)
prox_obj = lambda x, la: -proxinf(Omega_x0 - x, la) + Omega_x0
w = douglas_rachford(prox_indic, prox_obj, np.zeros((np.size(DJ,1),1)),
maxiter=maxiter)
return np.max(np.abs(Omega_x0 - w))
def test_dr_l1_cs():
# Dimension of the problem
n = 200
p = n // 4
# Matrix and observations
A = np.random.randn(p, n)
# Use a very sparse vector for the test
x = np.zeros((n, 1))
x[1, :] = 1
y = np.dot(A, x)
# operator callbacks
prox_f = soft_thresholding
prox_g = lambda x, tau: x + np.dot(
A.T, lin.solve(np.dot(A, A.T), y - np.dot(A, x)))
x_rec = douglas_rachford(prox_f, prox_g, np.zeros((n, 1)))
assert_array_almost_equal(x, x_rec)
def test_dr_l1_cs():
# Dimension of the problem
n = 200
p = n // 4
# Matrix and observations
A = np.random.randn(p, n)
# Use a very sparse vector for the test
x = np.zeros((n, 1))
x[1, :] = 1
y = np.dot(A, x)
# operator callbacks
prox_f = soft_thresholding
prox_g = lambda x, tau: x + np.dot(A.T, lin.solve(np.dot(A, A.T),
y - np.dot(A, x)))
x_rec = douglas_rachford(prox_f, prox_g, np.zeros((n, 1)))
assert_array_almost_equal(x, x_rec)
def test_dr_l1_cs():
# Dimension of the problem
n = 200
p = n//4
# Matrix and observations
A = np.random.randn(p,n)
# Use a very sparse vector for the test
x = np.zeros((n,1))
x[1,:] = 1
y = np.dot(A,x)
# operator callbacks
ProxF = soft_thresholding
ProxG = lambda x,tau: x + np.dot(A.T, np.linalg.solve(np.dot(A,A.T),
y - np.dot(A,x)))
xRec = douglas_rachford(ProxF, ProxG, np.zeros((n,1)), maxiter=1000)
assert_array_almost_equal(x, xRec)
