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import warnings
import numpy as np
import pytest
from scipy.optimize import fmin_ncg
from sklearn.exceptions import ConvergenceWarning
from sklearn.utils._bunch import Bunch
from sklearn.utils._testing import assert_allclose
from sklearn.utils.optimize import _check_optimize_result, _newton_cg
def test_newton_cg(global_random_seed):
# Test that newton_cg gives same result as scipy's fmin_ncg
rng = np.random.RandomState(global_random_seed)
A = rng.normal(size=(10, 10))
x0 = np.ones(10)
def func(x):
Ax = A.dot(x)
return 0.5 * (Ax).dot(Ax)
def grad(x):
return A.T.dot(A.dot(x))
def hess(x, p):
return p.dot(A.T.dot(A.dot(x.all())))
def grad_hess(x):
return grad(x), lambda x: A.T.dot(A.dot(x))
# func is a definite positive quadratic form, so the minimum is at x = 0
# hence the use of absolute tolerance.
assert np.all(np.abs(_newton_cg(grad_hess, func, grad, x0, tol=1e-10)[0]) <= 1e-7)
assert_allclose(
_newton_cg(grad_hess, func, grad, x0, tol=1e-7)[0],
fmin_ncg(f=func, x0=x0, fprime=grad, fhess_p=hess),
atol=1e-5,
)
@pytest.mark.parametrize("verbose", [0, 1, 2])
def test_newton_cg_verbosity(capsys, verbose):
"""Test the std output of verbose newton_cg solver."""
A = np.eye(2)
b = np.array([1, 2], dtype=float)
_newton_cg(
grad_hess=lambda x: (A @ x - b, lambda z: A @ z),
func=lambda x: 0.5 * x @ A @ x - b @ x,
grad=lambda x: A @ x - b,
x0=np.zeros(A.shape[0]),
verbose=verbose,
) # returns array([1., 2])
captured = capsys.readouterr()
if verbose == 0:
assert captured.out == ""
else:
msg = [
"Newton-CG iter = 1",
"Check Convergence",
"max |gradient|",
"Solver did converge at loss = ",
]
for m in msg:
assert m in captured.out
if verbose >= 2:
msg = [
"Inner CG solver iteration 1 stopped with",
"sum(|residuals|) <= tol",
"Line Search",
"try line search wolfe1",
"wolfe1 line search was successful",
]
for m in msg:
assert m in captured.out
if verbose >= 2:
# Set up a badly scaled singular Hessian with a completely wrong starting
# position. This should trigger 2nd line search check
A = np.array([[1.0, 2], [2, 4]]) * 1e30 # collinear columns
b = np.array([1.0, 2.0])
# Note that scipy.optimize._linesearch LineSearchWarning inherits from
# RuntimeWarning, but we do not want to import from non public APIs.
with pytest.warns(RuntimeWarning):
_newton_cg(
grad_hess=lambda x: (A @ x - b, lambda z: A @ z),
func=lambda x: 0.5 * x @ A @ x - b @ x,
grad=lambda x: A @ x - b,
x0=np.array([-2.0, 1]), # null space of hessian
verbose=verbose,
)
captured = capsys.readouterr()
msg = [
"wolfe1 line search was not successful",
"check loss |improvement| <= eps * |loss_old|:",
"check sum(|gradient|) < sum(|gradient_old|):",
"last resort: try line search wolfe2",
]
for m in msg:
assert m in captured.out
# Set up a badly conditioned Hessian that leads to tiny curvature.
# X.T @ X have singular values array([1.00000400e+01, 1.00008192e-11])
A = np.array([[1.0, 2], [1, 2 + 1e-15]])
b = np.array([-2.0, 1])
with pytest.warns(ConvergenceWarning):
_newton_cg(
grad_hess=lambda x: (A @ x - b, lambda z: A @ z),
func=lambda x: 0.5 * x @ A @ x - b @ x,
grad=lambda x: A @ x - b,
x0=b,
verbose=verbose,
maxiter=2,
)
captured = capsys.readouterr()
msg = [
"tiny_|p| = eps * ||p||^2",
]
for m in msg:
assert m in captured.out
# Test for a case with negative Hessian.
# We do not trigger "Inner CG solver iteration {i} stopped with negative
# curvature", but that is very hard to trigger.
A = np.eye(2)
b = np.array([-2.0, 1])
with pytest.warns(RuntimeWarning):
_newton_cg(
# Note the wrong sign in the hessian product.
grad_hess=lambda x: (A @ x - b, lambda z: -A @ z),
func=lambda x: 0.5 * x @ A @ x - b @ x,
grad=lambda x: A @ x - b,
x0=np.array([1.0, 1.0]),
verbose=verbose,
maxiter=3,
)
captured = capsys.readouterr()
msg = [
"Inner CG solver iteration 0 fell back to steepest descent",
]
for m in msg:
assert m in captured.out
A = np.diag([1e-3, 1, 1e3])
b = np.array([-2.0, 1, 2.0])
with pytest.warns(ConvergenceWarning):
_newton_cg(
grad_hess=lambda x: (A @ x - b, lambda z: A @ z),
func=lambda x: 0.5 * x @ A @ x - b @ x,
grad=lambda x: A @ x - b,
x0=np.ones_like(b),
verbose=verbose,
maxiter=2,
maxinner=1,
)
captured = capsys.readouterr()
msg = [
"Inner CG solver stopped reaching maxiter=1",
]
for m in msg:
assert m in captured.out
def test_check_optimize():
# Mock some lbfgs output using a Bunch instance:
result = Bunch()
# First case: no warnings
result.nit = 1
result.status = 0
result.message = "OK"
with warnings.catch_warnings():
warnings.simplefilter("error")
_check_optimize_result("lbfgs", result)
# Second case: warning about implicit `max_iter`: do not recommend the user
# to increase `max_iter` this is not a user settable parameter.
result.status = 1
result.message = "STOP: TOTAL NO. OF ITERATIONS REACHED LIMIT"
with pytest.warns(ConvergenceWarning) as record:
_check_optimize_result("lbfgs", result)
assert len(record) == 1
warn_msg = record[0].message.args[0]
assert "lbfgs failed to converge after 1 iteration(s)" in warn_msg
assert result.message in warn_msg
assert "Increase the number of iterations" not in warn_msg
assert "scale the data" in warn_msg
# Third case: warning about explicit `max_iter`: recommend user to increase
# `max_iter`.
with pytest.warns(ConvergenceWarning) as record:
_check_optimize_result("lbfgs", result, max_iter=1)
assert len(record) == 1
warn_msg = record[0].message.args[0]
assert "lbfgs failed to converge after 1 iteration(s)" in warn_msg
assert result.message in warn_msg
assert "Increase the number of iterations" in warn_msg
assert "scale the data" in warn_msg
# Fourth case: other convergence problem before reaching `max_iter`: do not
# recommend increasing `max_iter`.
result.nit = 2
result.status = 2
result.message = "ABNORMAL"
with pytest.warns(ConvergenceWarning) as record:
_check_optimize_result("lbfgs", result, max_iter=10)
assert len(record) == 1
warn_msg = record[0].message.args[0]
assert "lbfgs failed to converge after 2 iteration(s)" in warn_msg
assert result.message in warn_msg
assert "Increase the number of iterations" not in warn_msg
assert "scale the data" in warn_msg
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