def test_class():
"""
runs several class methods on generic instance
"""
n, p = 100, 20
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y)
pen = rr.l1norm(p, lagrange=1.0)
problem = rr.simple_problem(loss, pen)
problem.latexify()
for debug, coef_stop, max_its in product([True, False], [True, False], [5, 100]):
rr.gengrad(problem, rr.power_L(X) ** 2, max_its=max_its, debug=debug, coef_stop=coef_stop)
def test_simple_problem_nonsmooth(self):
tests = []
atom, q = self.atom, self.q
loss = self.loss
p2 = copy(atom)
p2.quadratic = atom.quadratic + q
problem = rr.simple_problem.nonsmooth(p2)
solver = rr.FISTA(problem)
solver.fit(tol=1.0e-14,
FISTA=self.FISTA,
coef_stop=self.coef_stop,
min_its=100)
gg = rr.gengrad(
problem,
2.) # this lipschitz constant is based on knowing our loss...
tests.append((atom.proximal(q), gg,
'solving prox with gengrad\n %s ' % str(self)))
tests.append((atom.proximal(q), atom.solve(q),
'solving prox with solve method\n %s ' % str(self)))
tests.append((
atom.proximal(q), solver.composite.coefs,
'solving prox with simple_problem.nonsmooth with monotonicity\n %s '
% str(self)))
# use the solve method
p3 = copy(atom)
p3.quadratic = atom.quadratic + q
soln = p3.solve(tol=1.e-14, min_its=10)
tests.append((atom.proximal(q), soln,
'solving prox with solve method\n %s ' % str(self)))
p4 = copy(atom)
p4.quadratic = atom.quadratic + q
problem = rr.simple_problem.nonsmooth(p4)
solver = rr.FISTA(problem)
solver.fit(tol=1.0e-14,
monotonicity_restart=False,
coef_stop=self.coef_stop,
FISTA=self.FISTA,
min_its=100)
tests.append((
atom.proximal(q), solver.composite.coefs,
'solving prox with simple_problem.nonsmooth with no monotonocity\n %s '
% str(self)))
if not self.interactive:
for test in tests:
yield (all_close, ) + test + (self, )
else:
for test in tests:
yield all_close(*((test + (self, ))))
def test_class():
'''
runs several class methods on generic instance
'''
n, p = 100, 20
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y)
pen = rr.l1norm(p, lagrange=1.)
problem = rr.simple_problem(loss, pen)
problem.latexify()
for debug, coef_stop, max_its in product([True, False], [True, False],
[5, 100]):
rr.gengrad(problem,
rr.power_L(X)**2,
max_its=max_its,
debug=debug,
coef_stop=coef_stop)
def test_gengrad():
Z = np.random.standard_normal(100) * 4
p = rr.l1norm(100, lagrange=0.13)
L = 0.14
loss = rr.quadratic_loss.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
prox_coef = p.proximal(rr.identity_quadratic(L, Z, 0, 0))
p2 = rr.l1norm(100, lagrange=0.13)
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.l1norm(100, lagrange=0.13)
p.quadratic = rr.identity_quadratic(L, Z, 0, 0)
problem = rr.simple_problem.nonsmooth(p)
simple_nonsmooth_gengrad = rr.gengrad(problem, L, tol=1.0e-10)
p = rr.l1norm(100, 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
loss2 = rr.quadratic_loss.shift(Z, coef=0.6 * L)
loss2.quadratic = rr.identity_quadratic(0.4 * L, Z, 0, 0)
p.coefs *= 0
problem2 = rr.simple_problem(loss2, p)
loss2_coefs = problem2.solve(coef_stop=True)
solver2 = rr.FISTA(problem2)
solver2.fit(tol=1.0e-10, debug=True, coef_stop=True)
yield all_close, prox_coef, simple_nonsmooth_gengrad, 'prox to nonsmooth gengrad', None
yield all_close, prox_coef, separable_coef, 'prox to separable', None
yield all_close, prox_coef, simple_nonsmooth_coef, 'prox to simple_nonsmooth', None
yield all_close, prox_coef, simple_coef, 'prox to simple', None
yield all_close, prox_coef, loss2_coefs, 'simple where loss has quadratic 1', None
yield all_close, prox_coef, solver2.composite.coefs, 'simple where loss has quadratic 2', None
def test_gengrad():
Z = np.random.standard_normal(100) * 4
p = rr.l1norm(100, lagrange=0.13)
L = 0.14
loss = rr.quadratic_loss.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
prox_coef = p.proximal(rr.identity_quadratic(L, Z, 0, 0))
p2 = rr.l1norm(100, lagrange=0.13)
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.l1norm(100, lagrange=0.13)
p.quadratic = rr.identity_quadratic(L, Z, 0, 0)
problem = rr.simple_problem.nonsmooth(p)
simple_nonsmooth_gengrad = rr.gengrad(problem, L, tol=1.0e-10)
p = rr.l1norm(100, 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
loss2 = rr.quadratic_loss.shift(Z, coef=0.6 * L)
loss2.quadratic = rr.identity_quadratic(0.4 * L, Z, 0, 0)
p.coefs *= 0
problem2 = rr.simple_problem(loss2, p)
loss2_coefs = problem2.solve(coef_stop=True)
solver2 = rr.FISTA(problem2)
solver2.fit(tol=1.0e-10, debug=True, coef_stop=True)
yield all_close, prox_coef, simple_nonsmooth_gengrad, "prox to nonsmooth gengrad", None
yield all_close, prox_coef, separable_coef, "prox to separable", None
yield all_close, prox_coef, simple_nonsmooth_coef, "prox to simple_nonsmooth", None
yield all_close, prox_coef, simple_coef, "prox to simple", None
yield all_close, prox_coef, loss2_coefs, "simple where loss has quadratic 1", None
yield all_close, prox_coef, solver2.composite.coefs, "simple where loss has quadratic 2", None
def test_simple_problem_nonsmooth(self):
tests = []
atom, q = self.atom, self.q
loss = self.loss
p2 = copy(atom)
p2.quadratic = atom.quadratic + q
problem = rr.simple_problem.nonsmooth(p2)
solver = rr.FISTA(problem)
solver.fit(tol=1.0e-14, FISTA=self.FISTA, coef_stop=self.coef_stop, min_its=100)
gg = rr.gengrad(problem, 2.) # this lipschitz constant is based on knowing our loss...
tests.append((atom.proximal(q), gg, 'solving prox with gengrad\n %s ' % str(self)))
tests.append((atom.proximal(q), atom.solve(q), 'solving prox with solve method\n %s ' % str(self)))
tests.append((atom.proximal(q), solver.composite.coefs, 'solving prox with simple_problem.nonsmooth with monotonicity\n %s ' % str(self)))
# use the solve method
p3 = copy(atom)
p3.quadratic = atom.quadratic + q
soln = p3.solve(tol=1.e-14, min_its=10)
tests.append((atom.proximal(q), soln, 'solving prox with solve method\n %s ' % str(self)))
p4 = copy(atom)
p4.quadratic = atom.quadratic + q
problem = rr.simple_problem.nonsmooth(p4)
solver = rr.FISTA(problem)
solver.fit(tol=1.0e-14, monotonicity_restart=False, coef_stop=self.coef_stop,
FISTA=self.FISTA,
min_its=100)
tests.append((atom.proximal(q), solver.composite.coefs, 'solving prox with simple_problem.nonsmooth with no monotonocity\n %s ' % str(self)))
if not self.interactive:
for test in tests:
yield (all_close,) + test + (self,)
else:
for test in tests:
yield all_close(*((test + (self,))))
def test_gengrad_blocknorms():
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_loss.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 = rr.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
yield (all_close, prox_coef, simple_coef, 'prox to simple', None)
yield (all_close, prox_coef, simple_nonsmooth_gengrad,
'prox to nonsmooth gengrad', None)
yield (all_close, prox_coef, separable_coef, 'prox to separable', None)
yield (all_close, prox_coef, simple_nonsmooth_coef,
'prox to simple_nonsmooth', None)
def test_gengrad_blocknorms():
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_loss.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 = rr.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
yield (all_close, prox_coef, simple_coef, "prox to simple", None)
yield (all_close, prox_coef, simple_nonsmooth_gengrad, "prox to nonsmooth gengrad", None)
yield (all_close, prox_coef, separable_coef, "prox to separable", None)
yield (all_close, prox_coef, simple_nonsmooth_coef, "prox to simple_nonsmooth", None)
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 all_close, loss2.objective(ww), loss.objective(
ww), 'checking objective', None
yield all_close, lq.objective(ww, 'func'), loss.nonsmooth_objective(
ww), 'checking nonsmooth objective', None
yield all_close, loss2.smooth_objective(
ww, 'func'), 0.5 / 0.3 * loss.smooth_objective(
ww, 'func'), 'checking smooth objective func', None
yield all_close, loss2.smooth_objective(
ww, 'grad'), 0.5 / 0.3 * loss.smooth_objective(
ww, 'grad'), 'checking smooth objective grad', None
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(problem, 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)
yield all_close, problem.objective(
ww), atom.nonsmooth_objective(ww) + q.objective(ww, 'func'), '', None
atom = rr.l1norm(40, quadratic=atomq, lagrange=0.12)
aq = atom.solve(q)
for p, msg in zip([
solver3.composite.coefs, gg_soln, solver2.composite.coefs, dsoln2,
solver.composite.coefs, solver4.composite.coefs
], [
'simple_problem with loss having no quadratic', 'gen grad',
'container with loss having no quadratic',
'dual problem with loss having a quadratic',
'container with loss having a quadratic',
'simple_problem having a quadratic'
]):
yield all_close, aq, p, msg, None
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_loss.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_loss.shift(Z, coef=L)
yield all_close, loss2.objective(ww), loss.objective(ww), 'checking objective', None
yield all_close, lq.objective(ww, 'func'), loss.nonsmooth_objective(ww), 'checking nonsmooth objective', None
yield all_close, loss2.smooth_objective(ww, 'func'), 0.5 / 0.3 * loss.smooth_objective(ww, 'func'), 'checking smooth objective func', None
yield all_close, loss2.smooth_objective(ww, 'grad'), 0.5 / 0.3 * loss.smooth_objective(ww, 'grad'), 'checking smooth objective grad', None
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_loss.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(problem, L)
loss6 = rr.quadratic_loss.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)
yield all_close, problem.objective(ww), atom.nonsmooth_objective(ww) + q.objective(ww,'func'), '', None
atom = rr.l1norm(40, quadratic=atomq, lagrange=0.12)
aq = atom.solve(q)
for p, msg in zip([solver3.composite.coefs,
gg_soln,
solver2.composite.coefs,
dsoln2,
solver.composite.coefs,
solver4.composite.coefs],
['simple_problem with loss having no quadratic',
'gen grad',
'container with loss having no quadratic',
'dual problem with loss having a quadratic',
'container with loss having a quadratic',
'simple_problem having a quadratic']):
yield all_close, aq, p, msg, None
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.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