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
