def test_simple(): Z = np.random.standard_normal((10,10)) * 4 p = rr.l1_l2((10,10), lagrange=0.13) dual = p.conjugate L = 0.23 loss = rr.quadratic.shift(-Z, coef=L) problem = rr.simple_problem(loss, p) solver = rr.FISTA(problem) solver.fit(tol=1.0e-10, debug=True) simple_coef = solver.composite.coefs q = rr.identity_quadratic(L, Z, 0, 0) prox_coef = p.proximal(q) p2 = copy(p) p2.quadratic = rr.identity_quadratic(L, Z, 0, 0) problem = rr.simple_problem.nonsmooth(p2) solver = rr.FISTA(problem) solver.fit(tol=1.0e-14, debug=True) simple_nonsmooth_coef = solver.composite.coefs p = rr.l1_l2((10,10), lagrange=0.13) p.quadratic = rr.identity_quadratic(L, Z, 0, 0) problem = rr.simple_problem.nonsmooth(p) simple_nonsmooth_gengrad = gengrad(problem, L, tol=1.0e-10) p = rr.l1_l2((10,10), lagrange=0.13) problem = rr.separable_problem.singleton(p, loss) solver = rr.FISTA(problem) solver.fit(tol=1.0e-10) separable_coef = solver.composite.coefs ac(prox_coef, Z-simple_coef, 'prox to simple') ac(prox_coef, simple_nonsmooth_gengrad, 'prox to nonsmooth gengrad') ac(prox_coef, separable_coef, 'prox to separable') ac(prox_coef, simple_nonsmooth_coef, 'prox to simple_nonsmooth')
def test_simple(): Z = np.random.standard_normal((10, 10)) * 4 p = rr.l1_l2((10, 10), lagrange=0.13) dual = p.conjugate L = 0.23 loss = rr.quadratic.shift(-Z, coef=L) problem = rr.simple_problem(loss, p) solver = rr.FISTA(problem) solver.fit(tol=1.0e-10, debug=True) simple_coef = solver.composite.coefs q = rr.identity_quadratic(L, Z, 0, 0) prox_coef = p.proximal(q) p2 = copy(p) p2.quadratic = rr.identity_quadratic(L, Z, 0, 0) problem = rr.simple_problem.nonsmooth(p2) solver = rr.FISTA(problem) solver.fit(tol=1.0e-14, debug=True) simple_nonsmooth_coef = solver.composite.coefs p = rr.l1_l2((10, 10), lagrange=0.13) p.quadratic = rr.identity_quadratic(L, Z, 0, 0) problem = rr.simple_problem.nonsmooth(p) simple_nonsmooth_gengrad = gengrad(problem, L, tol=1.0e-10) p = rr.l1_l2((10, 10), lagrange=0.13) problem = rr.separable_problem.singleton(p, loss) solver = rr.FISTA(problem) solver.fit(tol=1.0e-10) separable_coef = solver.composite.coefs ac(prox_coef, Z - simple_coef, 'prox to simple') ac(prox_coef, simple_nonsmooth_gengrad, 'prox to nonsmooth gengrad') ac(prox_coef, separable_coef, 'prox to separable') ac(prox_coef, simple_nonsmooth_coef, 'prox to simple_nonsmooth')
def test_quadratic_for_smooth(): """ this test is a check to ensure that the quadratic part of the smooth functions are being used in the proximal step """ L = 0.45 W = np.random.standard_normal(40) Z = np.random.standard_normal(40) U = np.random.standard_normal(40) atomq = rr.identity_quadratic(0.4, U, W, 0) atom = rr.l1norm(40, quadratic=atomq, lagrange=0.12) # specifying in this way should be the same as if we put 0.5*L below loss = rr.quadratic.shift(-Z, coef=0.6 * L) lq = rr.identity_quadratic(0.4 * L, Z, 0, 0) loss.quadratic = lq ww = np.random.standard_normal(40) # specifying in this way should be the same as if we put 0.5*L below loss2 = rr.quadratic.shift(-Z, coef=L) yield ac, loss2.objective(ww), loss.objective(ww), "checking objective" yield ac, lq.objective(ww, "func"), loss.nonsmooth_objective(ww), "checking nonsmooth objective" yield ac, loss2.smooth_objective(ww, "func"), 0.5 / 0.3 * loss.smooth_objective( ww, "func" ), "checking smooth objective func" yield ac, loss2.smooth_objective(ww, "grad"), 0.5 / 0.3 * loss.smooth_objective( ww, "grad" ), "checking smooth objective grad" problem = rr.container(loss, atom) solver = rr.FISTA(problem) solver.fit(tol=1.0e-12) problem3 = rr.simple_problem(loss, atom) solver3 = rr.FISTA(problem3) solver3.fit(tol=1.0e-12, coef_stop=True) loss4 = rr.quadratic.shift(-Z, coef=0.6 * L) problem4 = rr.simple_problem(loss4, atom) problem4.quadratic = lq solver4 = rr.FISTA(problem4) solver4.fit(tol=1.0e-12) gg_soln = rr.gengrad(problem4, L) loss6 = rr.quadratic.shift(-Z, coef=0.6 * L) loss6.quadratic = lq + atom.quadratic atomcp = copy(atom) atomcp.quadratic = rr.identity_quadratic(0, 0, 0, 0) problem6 = rr.dual_problem(loss6.conjugate, rr.identity(loss6.primal_shape), atomcp.conjugate) problem6.lipschitz = L + atom.quadratic.coef dsoln2 = problem6.solve(coef_stop=True, tol=1.0e-10, max_its=100) problem2 = rr.container(loss2, atom) solver2 = rr.FISTA(problem2) solver2.fit(tol=1.0e-12, coef_stop=True) q = rr.identity_quadratic(L, Z, 0, 0) ac(problem.objective(ww), atom.nonsmooth_objective(ww) + q.objective(ww, "func")) aq = atom.solve(q) for p, msg in zip( [ solver3.composite.coefs, gg_soln, solver2.composite.coefs, solver4.composite.coefs, dsoln2, solver.composite.coefs, ], [ "simple_problem with loss having no quadratic", "gen grad", "container with loss having no quadratic", "simple_problem container with quadratic", "dual problem with loss having a quadratic", "container with loss having a quadratic", ], ): yield ac, aq, p, msg
def test_quadratic_for_smooth(): ''' this test is a check to ensure that the quadratic part of the smooth functions are being used in the proximal step ''' L = 0.45 W = np.random.standard_normal(40) Z = np.random.standard_normal(40) U = np.random.standard_normal(40) atomq = rr.identity_quadratic(0.4, U, W, 0) atom = rr.l1norm(40, quadratic=atomq, lagrange=0.12) # specifying in this way should be the same as if we put 0.5*L below loss = rr.quadratic.shift(-Z, coef=0.6*L) lq = rr.identity_quadratic(0.4*L, Z, 0, 0) loss.quadratic = lq ww = np.random.standard_normal(40) # specifying in this way should be the same as if we put 0.5*L below loss2 = rr.quadratic.shift(-Z, coef=L) yield ac, loss2.objective(ww), loss.objective(ww), 'checking objective' yield ac, lq.objective(ww, 'func'), loss.nonsmooth_objective(ww), 'checking nonsmooth objective' yield ac, loss2.smooth_objective(ww, 'func'), 0.5 / 0.3 * loss.smooth_objective(ww, 'func'), 'checking smooth objective func' yield ac, loss2.smooth_objective(ww, 'grad'), 0.5 / 0.3 * loss.smooth_objective(ww, 'grad'), 'checking smooth objective grad' problem = rr.container(loss, atom) solver = rr.FISTA(problem) solver.fit(tol=1.0e-12) problem3 = rr.simple_problem(loss, atom) solver3 = rr.FISTA(problem3) solver3.fit(tol=1.0e-12, coef_stop=True) loss4 = rr.quadratic.shift(-Z, coef=0.6*L) problem4 = rr.simple_problem(loss4, atom) problem4.quadratic = lq solver4 = rr.FISTA(problem4) solver4.fit(tol=1.0e-12) gg_soln = rr.gengrad(problem4, L) loss6 = rr.quadratic.shift(-Z, coef=0.6*L) loss6.quadratic = lq + atom.quadratic atomcp = copy(atom) atomcp.quadratic = rr.identity_quadratic(0,0,0,0) problem6 = rr.dual_problem(loss6.conjugate, rr.identity(loss6.shape), atomcp.conjugate) problem6.lipschitz = L + atom.quadratic.coef dsoln2 = problem6.solve(coef_stop=True, tol=1.e-10, max_its=100) problem2 = rr.container(loss2, atom) solver2 = rr.FISTA(problem2) solver2.fit(tol=1.0e-12, coef_stop=True) q = rr.identity_quadratic(L, Z, 0, 0) ac(problem.objective(ww), atom.nonsmooth_objective(ww) + q.objective(ww,'func')) aq = atom.solve(q) for p, msg in zip([solver3.composite.coefs, gg_soln, solver2.composite.coefs, solver4.composite.coefs, dsoln2, solver.composite.coefs], ['simple_problem with loss having no quadratic', 'gen grad', 'container with loss having no quadratic', 'simple_problem container with quadratic', 'dual problem with loss having a quadratic', 'container with loss having a quadratic']): yield ac, aq, p, msg
def test_quadratic_for_smooth2(): ''' this test is a check to ensure that the quadratic part of the smooth functions are being used in the proximal step ''' L = 2 W = np.arange(5) Z = 0.5 * np.arange(5)[::-1] U = 1.5 * np.arange(5) atomq = rr.identity_quadratic(0.4, U, W, 0) atom = rr.l1norm(5, quadratic=atomq, lagrange=0.1) # specifying in this way should be the same as if we put 0.5*L below loss = rr.quadratic.shift(-Z, coef=0.6*L) lq = rr.identity_quadratic(0.4*L, Z, 0, 0) loss.quadratic = lq ww = np.ones(5) # specifying in this way should be the same as if we put 0.5*L below loss2 = rr.quadratic.shift(-Z, coef=L) np.testing.assert_allclose(loss2.objective(ww), loss.objective(ww)) np.testing.assert_allclose(lq.objective(ww, 'func'), loss.nonsmooth_objective(ww)) np.testing.assert_allclose(loss2.smooth_objective(ww, 'func'), 0.5 / 0.3 * loss.smooth_objective(ww, 'func')) np.testing.assert_allclose(loss2.smooth_objective(ww, 'grad'), 0.5 / 0.3 * loss.smooth_objective(ww, 'grad')) problem = rr.container(loss, atom) solver = rr.FISTA(problem) solver.fit(tol=1.0e-12) problem3 = rr.simple_problem(loss, atom) solver3 = rr.FISTA(problem3) solver3.fit(tol=1.0e-12, coef_stop=True) loss4 = rr.quadratic.shift(-Z, coef=0.6*L) problem4 = rr.simple_problem(loss4, atom) problem4.quadratic = lq solver4 = rr.FISTA(problem4) solver4.fit(tol=1.0e-12) gg_soln = rr.gengrad(problem4, L) loss6 = rr.quadratic.shift(-Z, coef=0.6*L) loss6.quadratic = lq + atom.quadratic atomcp = copy(atom) atomcp.quadratic = rr.identity_quadratic(0,0,0,0) problem6 = rr.dual_problem(loss6.conjugate, rr.identity(loss6.shape), atomcp.conjugate) problem6.lipschitz = L + atom.quadratic.coef dsoln2 = problem6.solve(coef_stop=True, tol=1.e-10, max_its=100) problem2 = rr.container(loss2, atom) solver2 = rr.FISTA(problem2) solver2.fit(tol=1.0e-12, coef_stop=True) q = rr.identity_quadratic(L, Z, 0, 0) ac(problem.objective(ww), atom.nonsmooth_objective(ww) + q.objective(ww,'func')) aq = atom.solve(q) for p, msg in zip([solver3.composite.coefs, gg_soln, solver2.composite.coefs, solver4.composite.coefs, dsoln2, solver.composite.coefs], ['simple_problem with loss having no quadratic', 'gen grad', 'container with loss having no quadratic', 'simple_problem container with quadratic', 'dual problem with loss having a quadratic', 'container with loss having a quadratic']): yield ac, aq, p, msg