def test_admm_extra_param(self): ''' With parameters for px.sum_squares ''' X = px.Variable((10, 5)) B = np.reshape(np.arange(50), (10, 5)) * 1. prox_fns = [px.norm1(X)] quad_funcs = [px.sum_squares(X, b=B, alpha=0.1, beta=2., gamma=1, c=B)] sltn = admm.solve(prox_fns, quad_funcs, 1.0, eps_rel=1e-5, eps_abs=1e-5) cvx_X = cvx.Variable((10, 5)) cost = 0.1 * cvx.sum_squares(2 * cvx_X - B) + cvx.sum_squares(cvx_X) + \ cvx.norm(cvx_X, 1) + cvx.trace(B.T @ cvx_X) prob = cvx.Problem(cvx.Minimize(cost)) prob.solve() self.assertItemsAlmostEqual(X.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(sltn, prob.value, eps=1e-3) prox_fns = [px.norm1(X)] quad_funcs = [px.sum_squares(X - B, alpha=0.1, beta=2., gamma=1, c=B)] quad_funcs[0] = absorb_offset(quad_funcs[0]) sltn = admm.solve(prox_fns, quad_funcs, 1.0, eps_rel=1e-5, eps_abs=1e-5) self.assertItemsAlmostEqual(X.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(sltn, prob.value, eps=1e-3) prox_fns = [px.norm1(X)] cvx_X = cvx.Variable((10, 5)) # With linear operators. kernel = np.array([1, 2, 3]) x = px.Variable(3) b = np.array([-41, 413, 2]) prox_fns = [px.nonneg(x), px.sum_squares(px.conv(kernel, x), b=b)] sltn = admm.solve(prox_fns, [], 1.0, eps_abs=1e-5, eps_rel=1e-5) kernel_mat = np.matrix("2 1 3; 3 2 1; 1 3 2") cvx_X = cvx.Variable(3) cost = cvx.norm(kernel_mat * cvx_X - b) prob = cvx.Problem(cvx.Minimize(cost), [cvx_X >= 0]) prob.solve() self.assertItemsAlmostEqual(x.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(np.sqrt(sltn), prob.value, eps=2e-2) prox_fns = [px.nonneg(x)] quad_funcs = [px.sum_squares(px.conv(kernel, x), b=b)] sltn = admm.solve(prox_fns, quad_funcs, 1.0, eps_abs=1e-5, eps_rel=1e-5) self.assertItemsAlmostEqual(x.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(np.sqrt(sltn), prob.value, eps=2e-2)
def test_lin_admm_two_prox_fn(self): X = px.Variable((10, 5)) B = np.reshape(np.arange(50), (10, 5)) prox_fns = [px.norm1(X), px.sum_squares(X, b=B)] sltn = ladmm.solve(prox_fns, [], 0.1, max_iters=500, eps_rel=1e-5, eps_abs=1e-5) cvx_X = cvx.Variable((10, 5)) cost = cvx.sum_squares(cvx_X - B) + cvx.norm(cvx_X, 1) prob = cvx.Problem(cvx.Minimize(cost)) prob.solve() self.assertItemsAlmostEqual(X.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(sltn, prob.value) psi_fns, omega_fns = ladmm.partition(prox_fns) sltn = ladmm.solve(psi_fns, omega_fns, 0.1, max_iters=500, eps_rel=1e-5, eps_abs=1e-5) self.assertItemsAlmostEqual(X.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(sltn, prob.value) # With linear operators. kernel = np.array([1, 2, 3]) kernel_mat = np.matrix("2 1 3; 3 2 1; 1 3 2") x = px.Variable(3) b = np.array([-41, 413, 2]) prox_fns = [px.nonneg(x), px.sum_squares(px.conv(kernel, x), b=b)] sltn = ladmm.solve(prox_fns, [], 0.1, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5) cvx_X = cvx.Variable(3) cost = cvx.norm(kernel_mat * cvx_X - b) prob = cvx.Problem(cvx.Minimize(cost), [cvx_X >= 0]) prob.solve() self.assertItemsAlmostEqual(x.value, cvx_X.value, eps=2e-2) psi_fns, omega_fns = ladmm.partition(prox_fns) sltn = ladmm.solve(psi_fns, omega_fns, 0.1, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5) self.assertItemsAlmostEqual(x.value, cvx_X.value, eps=2e-2)
# Create sinogram of forward projected phantom with noise phantom = odl.phantom.shepp_logan(reco_space, modified=True) phantom.show('phantom') data = ray_trafo(phantom) data += odl.phantom.white_noise(ray_trafo.range) * np.mean(data) * 0.1 data.show('noisy data') # Convert to array for ProxImaL rhs_arr = data.asarray() # Set up optimization problem # Note that proximal is not aware of the underlying space and only works with # matrices. Hence the norm in proximal does not match the norm in the ODL space # exactly. x = proximal.Variable(reco_space.shape) funcs = [ proximal.sum_squares(proximal_lang_ray_trafo(x) - rhs_arr), 0.2 * proximal.norm1(proximal.grad(x)), proximal.nonneg(x), proximal.nonneg(1 - x) ] # Solve the problem using ProxImaL prob = proximal.Problem(funcs) prob.solve(verbose=True) # Convert back to odl and display result result_odl = reco_space.element(x.value) result_odl.show('ProxImaL result', force_show=True)
def test_half_quadratic_splitting(self): """Test half quadratic splitting. """ X = px.Variable((10, 5)) B = np.reshape(np.arange(50), (10, 5)) prox_fns = [px.sum_squares(X, b=B)] sltn = hqs.solve(prox_fns, [], eps_rel=1e-4, max_iters=100, max_inner_iters=50) self.assertItemsAlmostEqual(X.value, B, places=2) self.assertAlmostEqual(sltn, 0) prox_fns = [px.norm1(X, b=B, beta=2)] sltn = hqs.solve(prox_fns, [], eps_rel=1e-4, max_iters=100, max_inner_iters=50) self.assertItemsAlmostEqual(X.value, B / 2., places=2) self.assertAlmostEqual(sltn, 0) prox_fns = [px.norm1(X), px.sum_squares(X, b=B)] sltn = hqs.solve(prox_fns, [], eps_rel=1e-7, rho_0=1.0, rho_scale=np.sqrt(2.0) * 2.0, rho_max=2**16, max_iters=20, max_inner_iters=500) cvx_X = cvx.Variable(10, 5) cost = cvx.sum_squares(cvx_X - B) + cvx.norm(cvx_X, 1) prob = cvx.Problem(cvx.Minimize(cost)) prob.solve() self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2) self.assertAlmostEqual(sltn, prob.value, places=3) psi_fns, omega_fns = hqs.partition(prox_fns) sltn = hqs.solve(psi_fns, omega_fns, eps_rel=1e-7, rho_0=1.0, rho_scale=np.sqrt(2.0) * 2.0, rho_max=2**16, max_iters=20, max_inner_iters=500) self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2) self.assertAlmostEqual(sltn, prob.value, places=3) # With linear operators. kernel = np.array([1, 2, 3]) kernel_mat = np.matrix("2 1 3; 3 2 1; 1 3 2") x = px.Variable(3) b = np.array([-41, 413, 2]) prox_fns = [px.nonneg(x), px.sum_squares(px.conv(kernel, x), b=b)] hqs.solve(prox_fns, [], eps_rel=1e-9, rho_0=4, rho_scale=np.sqrt(2.0) * 1.0, rho_max=2**16, max_iters=30, max_inner_iters=500) cvx_X = cvx.Variable(3) cost = cvx.norm(kernel_mat * cvx_X - b) prob = cvx.Problem(cvx.Minimize(cost), [cvx_X >= 0]) prob.solve() self.assertItemsAlmostEqual(x.value, cvx_X.value, places=0) psi_fns, omega_fns = hqs.partition(prox_fns) hqs.solve(psi_fns, omega_fns, eps_rel=1e-9, rho_0=4, rho_scale=np.sqrt(2.0) * 1.0, rho_max=2**16, max_iters=30, max_inner_iters=500) self.assertItemsAlmostEqual(x.value, cvx_X.value, places=0)
def test_pock_chambolle(self): """Test pock chambolle algorithm. """ X = px.Variable((10, 5)) B = np.reshape(np.arange(50), (10, 5)) prox_fns = [px.sum_squares(X, b=B)] sltn = pc.solve(prox_fns, [], 1.0, 1.0, 1.0, eps_rel=1e-5, eps_abs=1e-5) self.assertItemsAlmostEqual(X.value, B, places=2) self.assertAlmostEqual(sltn, 0) prox_fns = [px.norm1(X, b=B, beta=2)] sltn = pc.solve(prox_fns, [], 1.0, 1.0, 1.0, eps_rel=1e-5, eps_abs=1e-5) self.assertItemsAlmostEqual(X.value, B / 2., places=2) self.assertAlmostEqual(sltn, 0, places=2) prox_fns = [px.norm1(X), px.sum_squares(X, b=B)] sltn = pc.solve(prox_fns, [], 0.5, 1.0, 1.0, eps_rel=1e-5, eps_abs=1e-5) cvx_X = cvx.Variable(10, 5) cost = cvx.sum_squares(cvx_X - B) + cvx.norm(cvx_X, 1) prob = cvx.Problem(cvx.Minimize(cost)) prob.solve() self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2) self.assertAlmostEqual(sltn, prob.value) psi_fns, omega_fns = pc.partition(prox_fns) sltn = pc.solve(psi_fns, omega_fns, 0.5, 1.0, 1.0, eps_abs=1e-5, eps_rel=1e-5) self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2) self.assertAlmostEqual(sltn, prob.value) # With linear operators. kernel = np.array([1, 2, 3]) kernel_mat = np.matrix("2 1 3; 3 2 1; 1 3 2") x = px.Variable(3) b = np.array([-41, 413, 2]) prox_fns = [px.nonneg(x), px.sum_squares(px.conv(kernel, x), b=b)] sltn = pc.solve(prox_fns, [], 0.1, 0.1, 1.0, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5) cvx_X = cvx.Variable(3) cost = cvx.norm(kernel_mat * cvx_X - b) prob = cvx.Problem(cvx.Minimize(cost), [cvx_X >= 0]) prob.solve() self.assertItemsAlmostEqual(x.value, cvx_X.value, places=2) psi_fns, omega_fns = pc.partition(prox_fns) sltn = pc.solve(psi_fns, omega_fns, 0.1, 0.1, 1.0, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5) self.assertItemsAlmostEqual(x.value, cvx_X.value, places=2)
def _test_pock_chambolle(self, impl): """Test pock chambolle algorithm. """ #print() #print("----------------------",impl,"-------------------------") if impl == 'pycuda': kw = {'adapter': PyCudaAdapter()} else: kw = {} X = px.Variable((10, 5)) B = np.reshape(np.arange(50), (10, 5)) prox_fns = [px.sum_squares(X, b=B)] sltn = pc.solve(prox_fns, [], 1.0, 1.0, 1.0, eps_rel=1e-5, eps_abs=1e-5, **kw) self.assertItemsAlmostEqual(X.value, B, eps=2e-2) self.assertAlmostEqual(sltn, 0) prox_fns = [px.norm1(X, b=B, beta=2)] sltn = pc.solve(prox_fns, [], 1.0, 1.0, 1.0, eps_rel=1e-5, eps_abs=1e-5, **kw) self.assertItemsAlmostEqual(X.value, B / 2., eps=2e-2) self.assertAlmostEqual(sltn, 0, eps=2e-2) prox_fns = [px.norm1(X), px.sum_squares(X, b=B)] #print("----------------------------------------------------") #print("----------------------------------------------------") sltn = pc.solve(prox_fns, [], 0.5, 1.0, 1.0, eps_rel=1e-5, eps_abs=1e-5, conv_check=1, **kw) cvx_X = cvx.Variable((10, 5)) cost = cvx.sum_squares(cvx_X - B) + cvx.norm(cvx_X, 1) prob = cvx.Problem(cvx.Minimize(cost)) prob.solve() self.assertItemsAlmostEqual(X.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(sltn, prob.value) psi_fns, omega_fns = pc.partition(prox_fns) sltn = pc.solve(psi_fns, omega_fns, 0.5, 1.0, 1.0, eps_abs=1e-5, eps_rel=1e-5, **kw) self.assertItemsAlmostEqual(X.value, cvx_X.value, eps=2e-2) self.assertAlmostEqual(sltn, prob.value) # With linear operators. kernel = np.array([1, 2, 3]) kernel_mat = np.matrix("2 1 3; 3 2 1; 1 3 2") x = px.Variable(3) b = np.array([-41, 413, 2]) prox_fns = [px.nonneg(x), px.sum_squares(px.conv(kernel, x), b=b)] sltn = pc.solve(prox_fns, [], 0.1, 0.1, 1.0, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5, **kw) cvx_X = cvx.Variable(3) cost = cvx.norm(kernel_mat * cvx_X - b) prob = cvx.Problem(cvx.Minimize(cost), [cvx_X >= 0]) prob.solve() self.assertItemsAlmostEqual(x.value, cvx_X.value, eps=2e-2) psi_fns, omega_fns = pc.partition(prox_fns) sltn = pc.solve(psi_fns, omega_fns, 0.1, 0.1, 1.0, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5, **kw) self.assertItemsAlmostEqual(x.value, cvx_X.value, eps=2e-2) # TODO # Multiple variables. x = px.Variable(1) y = px.Variable(1) prox_fns = [ px.nonneg(x), px.sum_squares(vstack([x, y]), b=np.arange(2)) ] sltn = pc.solve(prox_fns, [prox_fns[-1]], 0.1, 0.1, 1.0, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5, try_diagonalize=False) self.assertItemsAlmostEqual(x.value, [0]) self.assertItemsAlmostEqual(y.value, [1]) sltn = pc.solve(prox_fns, [prox_fns[-1]], 0.1, 0.1, 1.0, max_iters=3000, eps_abs=1e-5, eps_rel=1e-5, try_diagonalize=True) self.assertItemsAlmostEqual(x.value, [0]) self.assertItemsAlmostEqual(y.value, [1])
# Convert ray transform to proximal language operator proximal_lang_ray_trafo = odl.as_proximal_lang_operator(ray_trafo) # Create sinogram of forward projected phantom with noise phantom = odl.phantom.shepp_logan(reco_space, modified=True) phantom.show('phantom') data = ray_trafo(phantom) data += odl.phantom.white_noise(ray_trafo.range) * np.mean(data) * 0.1 data.show('noisy data') # Convert to array for ProxImaL rhs_arr = data.asarray() # Set up optimization problem # Note that proximal is not aware of the underlying space and only works with # matrices. Hence the norm in proximal does not match the norm in the ODL space # exactly. x = proximal.Variable(reco_space.shape) funcs = [proximal.sum_squares(proximal_lang_ray_trafo(x) - rhs_arr), 0.2 * proximal.norm1(proximal.grad(x)), proximal.nonneg(x), proximal.nonneg(1 - x)] # Solve the problem using ProxImaL prob = proximal.Problem(funcs) prob.solve(verbose=True) # Convert back to odl and display result result_odl = reco_space.element(x.value) result_odl.show('ProxImaL result')