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AIM-PIbd-32-Kurbanova-A-A/aimenv/Lib/site-packages/scipy/optimize/tests/test_chandrupatla.py

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lab 1 is done
2024-10-02 22:15:59 +04:00
import pytest
import numpy as np
from numpy.testing import assert_allclose, assert_equal, assert_array_less
from scipy import stats, special
import scipy._lib._elementwise_iterative_method as eim
from scipy.conftest import array_api_compatible
from scipy._lib._array_api import (array_namespace, xp_assert_close, xp_assert_equal,
xp_assert_less, xp_minimum, is_numpy, is_cupy)
from scipy.optimize._chandrupatla import (_chandrupatla_minimize,
_chandrupatla as _chandrupatla_root)
from scipy.optimize._tstutils import _CHANDRUPATLA_TESTS
from itertools import permutations
from .test_zeros import TestScalarRootFinders
def f1(x):
return 100*(1 - x**3.)**2 + (1-x**2.) + 2*(1-x)**2.
def f2(x):
return 5 + (x - 2.)**6
def f3(x):
return np.exp(x) - 5*x
def f4(x):
return x**5. - 5*x**3. - 20.*x + 5.
def f5(x):
return 8*x**3 - 2*x**2 - 7*x + 3
def _bracket_minimum(func, x1, x2):
phi = 1.61803398875
maxiter = 100
f1 = func(x1)
f2 = func(x2)
step = x2 - x1
x1, x2, f1, f2, step = ((x2, x1, f2, f1, -step) if f2 > f1
else (x1, x2, f1, f2, step))
for i in range(maxiter):
step *= phi
x3 = x2 + step
f3 = func(x3)
if f3 < f2:
x1, x2, f1, f2 = x2, x3, f2, f3
else:
break
return x1, x2, x3, f1, f2, f3
cases = [
(f1, -1, 11),
(f1, -2, 13),
(f1, -4, 13),
(f1, -8, 15),
(f1, -16, 16),
(f1, -32, 19),
(f1, -64, 20),
(f1, -128, 21),
(f1, -256, 21),
(f1, -512, 19),
(f1, -1024, 24),
(f2, -1, 8),
(f2, -2, 6),
(f2, -4, 6),
(f2, -8, 7),
(f2, -16, 8),
(f2, -32, 8),
(f2, -64, 9),
(f2, -128, 11),
(f2, -256, 13),
(f2, -512, 12),
(f2, -1024, 13),
(f3, -1, 11),
(f3, -2, 11),
(f3, -4, 11),
(f3, -8, 10),
(f3, -16, 14),
(f3, -32, 12),
(f3, -64, 15),
(f3, -128, 18),
(f3, -256, 18),
(f3, -512, 19),
(f3, -1024, 19),
(f4, -0.05, 9),
(f4, -0.10, 11),
(f4, -0.15, 11),
(f4, -0.20, 11),
(f4, -0.25, 11),
(f4, -0.30, 9),
(f4, -0.35, 9),
(f4, -0.40, 9),
(f4, -0.45, 10),
(f4, -0.50, 10),
(f4, -0.55, 10),
(f5, -0.05, 6),
(f5, -0.10, 7),
(f5, -0.15, 8),
(f5, -0.20, 10),
(f5, -0.25, 9),
(f5, -0.30, 8),
(f5, -0.35, 7),
(f5, -0.40, 7),
(f5, -0.45, 9),
(f5, -0.50, 9),
(f5, -0.55, 8)
]
class TestChandrupatlaMinimize:
def f(self, x, loc):
dist = stats.norm()
return -dist.pdf(x - loc)
@pytest.mark.parametrize('loc', [0.6, np.linspace(-1.05, 1.05, 10)])
def test_basic(self, loc):
# Find mode of normal distribution. Compare mode against location
# parameter and value of pdf at mode against expected pdf.
res = _chandrupatla_minimize(self.f, -5, 0, 5, args=(loc,))
ref = loc
np.testing.assert_allclose(res.x, ref, rtol=1e-6)
np.testing.assert_allclose(res.fun, -stats.norm.pdf(0), atol=0, rtol=0)
assert res.x.shape == np.shape(ref)
@pytest.mark.parametrize('shape', [tuple(), (12,), (3, 4), (3, 2, 2)])
def test_vectorization(self, shape):
# Test for correct functionality, output shapes, and dtypes for various
# input shapes.
loc = np.linspace(-0.05, 1.05, 12).reshape(shape) if shape else 0.6
args = (loc,)
@np.vectorize
def chandrupatla_single(loc_single):
return _chandrupatla_minimize(self.f, -5, 0, 5, args=(loc_single,))
def f(*args, **kwargs):
f.f_evals += 1
return self.f(*args, **kwargs)
f.f_evals = 0
res = _chandrupatla_minimize(f, -5, 0, 5, args=args)
refs = chandrupatla_single(loc).ravel()
ref_x = [ref.x for ref in refs]
assert_allclose(res.x.ravel(), ref_x)
assert_equal(res.x.shape, shape)
ref_fun = [ref.fun for ref in refs]
assert_allclose(res.fun.ravel(), ref_fun)
assert_equal(res.fun.shape, shape)
assert_equal(res.fun, self.f(res.x, *args))
ref_success = [ref.success for ref in refs]
assert_equal(res.success.ravel(), ref_success)
assert_equal(res.success.shape, shape)
assert np.issubdtype(res.success.dtype, np.bool_)
ref_flag = [ref.status for ref in refs]
assert_equal(res.status.ravel(), ref_flag)
assert_equal(res.status.shape, shape)
assert np.issubdtype(res.status.dtype, np.integer)
ref_nfev = [ref.nfev for ref in refs]
assert_equal(res.nfev.ravel(), ref_nfev)
assert_equal(np.max(res.nfev), f.f_evals)
assert_equal(res.nfev.shape, res.fun.shape)
assert np.issubdtype(res.nfev.dtype, np.integer)
ref_nit = [ref.nit for ref in refs]
assert_equal(res.nit.ravel(), ref_nit)
assert_equal(np.max(res.nit), f.f_evals-3)
assert_equal(res.nit.shape, res.fun.shape)
assert np.issubdtype(res.nit.dtype, np.integer)
ref_xl = [ref.xl for ref in refs]
assert_allclose(res.xl.ravel(), ref_xl)
assert_equal(res.xl.shape, shape)
ref_xm = [ref.xm for ref in refs]
assert_allclose(res.xm.ravel(), ref_xm)
assert_equal(res.xm.shape, shape)
ref_xr = [ref.xr for ref in refs]
assert_allclose(res.xr.ravel(), ref_xr)
assert_equal(res.xr.shape, shape)
ref_fl = [ref.fl for ref in refs]
assert_allclose(res.fl.ravel(), ref_fl)
assert_equal(res.fl.shape, shape)
assert_allclose(res.fl, self.f(res.xl, *args))
ref_fm = [ref.fm for ref in refs]
assert_allclose(res.fm.ravel(), ref_fm)
assert_equal(res.fm.shape, shape)
assert_allclose(res.fm, self.f(res.xm, *args))
ref_fr = [ref.fr for ref in refs]
assert_allclose(res.fr.ravel(), ref_fr)
assert_equal(res.fr.shape, shape)
assert_allclose(res.fr, self.f(res.xr, *args))
def test_flags(self):
# Test cases that should produce different status flags; show that all
# can be produced simultaneously.
def f(xs, js):
funcs = [lambda x: (x - 2.5) ** 2,
lambda x: x - 10,
lambda x: (x - 2.5) ** 4,
lambda x: np.nan]
return [funcs[j](x) for x, j in zip(xs, js)]
args = (np.arange(4, dtype=np.int64),)
res = _chandrupatla_minimize(f, [0]*4, [2]*4, [np.pi]*4, args=args,
maxiter=10)
ref_flags = np.array([eim._ECONVERGED,
eim._ESIGNERR,
eim._ECONVERR,
eim._EVALUEERR])
assert_equal(res.status, ref_flags)
def test_convergence(self):
# Test that the convergence tolerances behave as expected
rng = np.random.default_rng(2585255913088665241)
p = rng.random(size=3)
bracket = (-5, 0, 5)
args = (p,)
kwargs0 = dict(args=args, xatol=0, xrtol=0, fatol=0, frtol=0)
kwargs = kwargs0.copy()
kwargs['xatol'] = 1e-3
res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
j1 = abs(res1.xr - res1.xl)
assert_array_less(j1, 4*kwargs['xatol'])
kwargs['xatol'] = 1e-6
res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
j2 = abs(res2.xr - res2.xl)
assert_array_less(j2, 4*kwargs['xatol'])
assert_array_less(j2, j1)
kwargs = kwargs0.copy()
kwargs['xrtol'] = 1e-3
res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
j1 = abs(res1.xr - res1.xl)
assert_array_less(j1, 4*kwargs['xrtol']*abs(res1.x))
kwargs['xrtol'] = 1e-6
res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
j2 = abs(res2.xr - res2.xl)
assert_array_less(j2, 4*kwargs['xrtol']*abs(res2.x))
assert_array_less(j2, j1)
kwargs = kwargs0.copy()
kwargs['fatol'] = 1e-3
res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
h1 = abs(res1.fl - 2 * res1.fm + res1.fr)
assert_array_less(h1, 2*kwargs['fatol'])
kwargs['fatol'] = 1e-6
res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
h2 = abs(res2.fl - 2 * res2.fm + res2.fr)
assert_array_less(h2, 2*kwargs['fatol'])
assert_array_less(h2, h1)
kwargs = kwargs0.copy()
kwargs['frtol'] = 1e-3
res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
h1 = abs(res1.fl - 2 * res1.fm + res1.fr)
assert_array_less(h1, 2*kwargs['frtol']*abs(res1.fun))
kwargs['frtol'] = 1e-6
res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
h2 = abs(res2.fl - 2 * res2.fm + res2.fr)
assert_array_less(h2, 2*kwargs['frtol']*abs(res2.fun))
assert_array_less(h2, h1)
def test_maxiter_callback(self):
# Test behavior of `maxiter` parameter and `callback` interface
loc = 0.612814
bracket = (-5, 0, 5)
maxiter = 5
res = _chandrupatla_minimize(self.f, *bracket, args=(loc,),
maxiter=maxiter)
assert not np.any(res.success)
assert np.all(res.nfev == maxiter+3)
assert np.all(res.nit == maxiter)
def callback(res):
callback.iter += 1
callback.res = res
assert hasattr(res, 'x')
if callback.iter == 0:
# callback is called once with initial bracket
assert (res.xl, res.xm, res.xr) == bracket
else:
changed_xr = (res.xl == callback.xl) & (res.xr != callback.xr)
changed_xl = (res.xl != callback.xl) & (res.xr == callback.xr)
assert np.all(changed_xr | changed_xl)
callback.xl = res.xl
callback.xr = res.xr
assert res.status == eim._EINPROGRESS
assert_equal(self.f(res.xl, loc), res.fl)
assert_equal(self.f(res.xm, loc), res.fm)
assert_equal(self.f(res.xr, loc), res.fr)
assert_equal(self.f(res.x, loc), res.fun)
if callback.iter == maxiter:
raise StopIteration
callback.xl = np.nan
callback.xr = np.nan
callback.iter = -1 # callback called once before first iteration
callback.res = None
res2 = _chandrupatla_minimize(self.f, *bracket, args=(loc,),
callback=callback)
# terminating with callback is identical to terminating due to maxiter
# (except for `status`)
for key in res.keys():
if key == 'status':
assert res[key] == eim._ECONVERR
assert callback.res[key] == eim._EINPROGRESS
assert res2[key] == eim._ECALLBACK
else:
assert res2[key] == callback.res[key] == res[key]
@pytest.mark.parametrize('case', cases)
def test_nit_expected(self, case):
# Test that `_chandrupatla` implements Chandrupatla's algorithm:
# in all 55 test cases, the number of iterations performed
# matches the number reported in the original paper.
func, x1, nit = case
# Find bracket using the algorithm in the paper
step = 0.2
x2 = x1 + step
x1, x2, x3, f1, f2, f3 = _bracket_minimum(func, x1, x2)
# Use tolerances from original paper
xatol = 0.0001
fatol = 0.000001
xrtol = 1e-16
frtol = 1e-16
res = _chandrupatla_minimize(func, x1, x2, x3, xatol=xatol,
fatol=fatol, xrtol=xrtol, frtol=frtol)
assert_equal(res.nit, nit)
@pytest.mark.parametrize("loc", (0.65, [0.65, 0.7]))
@pytest.mark.parametrize("dtype", (np.float16, np.float32, np.float64))
def test_dtype(self, loc, dtype):
# Test that dtypes are preserved
loc = dtype(loc)
def f(x, loc):
assert x.dtype == dtype
return ((x - loc) ** 2).astype(dtype)
res = _chandrupatla_minimize(f, dtype(-3), dtype(1), dtype(5),
args=(loc,))
assert res.x.dtype == dtype
assert_allclose(res.x, loc, rtol=np.sqrt(np.finfo(dtype).eps))
def test_input_validation(self):
# Test input validation for appropriate error messages
message = '`func` must be callable.'
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(None, -4, 0, 4)
message = 'Abscissae and function output must be real numbers.'
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4+1j, 0, 4)
message = "shape mismatch: objects cannot be broadcast"
# raised by `np.broadcast, but the traceback is readable IMO
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, [-2, -3], [0, 0], [3, 4, 5])
message = "The shape of the array returned by `func` must be the same"
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: [x[0], x[1], x[1]], [-3, -3],
[0, 0], [5, 5])
message = 'Tolerances must be non-negative scalars.'
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, xatol=-1)
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, xrtol=np.nan)
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, fatol='ekki')
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, frtol=np.nan)
message = '`maxiter` must be a non-negative integer.'
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, maxiter=1.5)
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, maxiter=-1)
message = '`callback` must be callable.'
with pytest.raises(ValueError, match=message):
_chandrupatla_minimize(lambda x: x, -4, 0, 4, callback='shrubbery')
def test_bracket_order(self):
# Confirm that order of points in bracket doesn't matter
loc = np.linspace(-1, 1, 6)[:, np.newaxis]
brackets = np.array(list(permutations([-5, 0, 5]))).T
res = _chandrupatla_minimize(self.f, *brackets, args=(loc,))
assert np.all(np.isclose(res.x, loc) | (res.fun == self.f(loc, loc)))
ref = res.x[:, 0] # all columns should be the same
assert_allclose(*np.broadcast_arrays(res.x.T, ref), rtol=1e-15)
def test_special_cases(self):
# Test edge cases and other special cases
# Test that integers are not passed to `f`
# (otherwise this would overflow)
def f(x):
assert np.issubdtype(x.dtype, np.floating)
return (x-1) ** 100
with np.errstate(invalid='ignore'):
res = _chandrupatla_minimize(f, -7, 0, 8, fatol=0, frtol=0)
assert res.success
assert_allclose(res.x, 1, rtol=1e-3)
assert_equal(res.fun, 0)
# Test that if all elements of bracket equal minimizer, algorithm
# reports convergence
def f(x):
return (x-1)**2
res = _chandrupatla_minimize(f, 1, 1, 1)
assert res.success
assert_equal(res.x, 1)
# Test maxiter = 0. Should do nothing to bracket.
def f(x):
return (x-1)**2
bracket = (-3, 1.1, 5)
res = _chandrupatla_minimize(f, *bracket, maxiter=0)
assert res.xl, res.xr == bracket
assert res.nit == 0
assert res.nfev == 3
assert res.status == -2
assert res.x == 1.1 # best so far
# Test scalar `args` (not in tuple)
def f(x, c):
return (x-c)**2 - 1
res = _chandrupatla_minimize(f, -1, 0, 1, args=1/3)
assert_allclose(res.x, 1/3)
# Test zero tolerances
# TODO: fatol/frtol = 0?
def f(x):
return -np.sin(x)
res = _chandrupatla_minimize(f, 0, 1, np.pi, xatol=0, xrtol=0,
fatol=0, frtol=0)
assert res.success
# found a minimum exactly (according to floating point arithmetic)
assert res.xl < res.xm < res.xr
assert f(res.xl) == f(res.xm) == f(res.xr)
@array_api_compatible
@pytest.mark.usefixtures("skip_xp_backends")
@pytest.mark.skip_xp_backends('array_api_strict', 'jax.numpy',
reasons=['Currently uses fancy indexing assignment.',
'JAX arrays do not support item assignment.'])
class TestChandrupatla(TestScalarRootFinders):
def f(self, q, p):
return special.ndtr(q) - p
@pytest.mark.parametrize('p', [0.6, np.linspace(-0.05, 1.05, 10)])
def test_basic(self, p, xp):
# Invert distribution CDF and compare against distrtibution `ppf`
a, b = xp.asarray(-5.), xp.asarray(5.)
res = _chandrupatla_root(self.f, a, b, args=(xp.asarray(p),))
ref = xp.asarray(stats.norm().ppf(p), dtype=xp.asarray(p).dtype)
xp_assert_close(res.x, ref)
@pytest.mark.parametrize('shape', [tuple(), (12,), (3, 4), (3, 2, 2)])
def test_vectorization(self, shape, xp):
# Test for correct functionality, output shapes, and dtypes for various
# input shapes.
p = (np.linspace(-0.05, 1.05, 12).reshape(shape) if shape
else np.float64(0.6))
p_xp = xp.asarray(p)
args_xp = (p_xp,)
dtype = p_xp.dtype
xp_test = array_namespace(p_xp) # need xp.bool
@np.vectorize
def chandrupatla_single(p):
return _chandrupatla_root(self.f, -5, 5, args=(p,))
def f(*args, **kwargs):
f.f_evals += 1
return self.f(*args, **kwargs)
f.f_evals = 0
res = _chandrupatla_root(f, xp.asarray(-5.), xp.asarray(5.), args=args_xp)
refs = chandrupatla_single(p).ravel()
ref_x = [ref.x for ref in refs]
ref_x = xp.reshape(xp.asarray(ref_x, dtype=dtype), shape)
xp_assert_close(res.x, ref_x)
ref_fun = [ref.fun for ref in refs]
ref_fun = xp.reshape(xp.asarray(ref_fun, dtype=dtype), shape)
xp_assert_close(res.fun, ref_fun, atol=1e-15)
xp_assert_equal(res.fun, self.f(res.x, *args_xp))
ref_success = [bool(ref.success) for ref in refs]
ref_success = xp.reshape(xp.asarray(ref_success, dtype=xp_test.bool), shape)
xp_assert_equal(res.success, ref_success)
ref_flag = [ref.status for ref in refs]
ref_flag = xp.reshape(xp.asarray(ref_flag, dtype=xp.int32), shape)
xp_assert_equal(res.status, ref_flag)
ref_nfev = [ref.nfev for ref in refs]
ref_nfev = xp.reshape(xp.asarray(ref_nfev, dtype=xp.int32), shape)
if is_numpy(xp):
xp_assert_equal(res.nfev, ref_nfev)
assert xp.max(res.nfev) == f.f_evals
else: # different backend may lead to different nfev
assert res.nfev.shape == shape
assert res.nfev.dtype == xp.int32
ref_nit = [ref.nit for ref in refs]
ref_nit = xp.reshape(xp.asarray(ref_nit, dtype=xp.int32), shape)
if is_numpy(xp):
xp_assert_equal(res.nit, ref_nit)
assert xp.max(res.nit) == f.f_evals-2
else:
assert res.nit.shape == shape
assert res.nit.dtype == xp.int32
ref_xl = [ref.xl for ref in refs]
ref_xl = xp.reshape(xp.asarray(ref_xl, dtype=dtype), shape)
xp_assert_close(res.xl, ref_xl)
ref_xr = [ref.xr for ref in refs]
ref_xr = xp.reshape(xp.asarray(ref_xr, dtype=dtype), shape)
xp_assert_close(res.xr, ref_xr)
xp_assert_less(res.xl, res.xr)
finite = xp.isfinite(res.x)
assert xp.all((res.x[finite] == res.xl[finite])
| (res.x[finite] == res.xr[finite]))
# PyTorch and CuPy don't solve to the same accuracy as NumPy - that's OK.
atol = 1e-15 if is_numpy(xp) else 1e-9
ref_fl = [ref.fl for ref in refs]
ref_fl = xp.reshape(xp.asarray(ref_fl, dtype=dtype), shape)
xp_assert_close(res.fl, ref_fl, atol=atol)
xp_assert_equal(res.fl, self.f(res.xl, *args_xp))
ref_fr = [ref.fr for ref in refs]
ref_fr = xp.reshape(xp.asarray(ref_fr, dtype=dtype), shape)
xp_assert_close(res.fr, ref_fr, atol=atol)
xp_assert_equal(res.fr, self.f(res.xr, *args_xp))
assert xp.all(xp.abs(res.fun[finite]) ==
xp_minimum(xp.abs(res.fl[finite]),
xp.abs(res.fr[finite])))
def test_flags(self, xp):
# Test cases that should produce different status flags; show that all
# can be produced simultaneously.
def f(xs, js):
# Note that full_like and int(j) shouldn't really be required. CuPy
# is just really picky here, so I'm making it a special case to
# make sure the other backends work when the user is less careful.
assert js.dtype == xp.int64
if is_cupy(xp):
funcs = [lambda x: x - 2.5,
lambda x: x - 10,
lambda x: (x - 0.1)**3,
lambda x: xp.full_like(x, xp.nan)]
return [funcs[int(j)](x) for x, j in zip(xs, js)]
funcs = [lambda x: x - 2.5,
lambda x: x - 10,
lambda x: (x - 0.1) ** 3,
lambda x: xp.nan]
return [funcs[j](x) for x, j in zip(xs, js)]
args = (xp.arange(4, dtype=xp.int64),)
a, b = xp.asarray([0.]*4), xp.asarray([xp.pi]*4)
res = _chandrupatla_root(f, a, b, args=args, maxiter=2)
ref_flags = xp.asarray([eim._ECONVERGED,
eim._ESIGNERR,
eim._ECONVERR,
eim._EVALUEERR], dtype=xp.int32)
xp_assert_equal(res.status, ref_flags)
def test_convergence(self, xp):
# Test that the convergence tolerances behave as expected
rng = np.random.default_rng(2585255913088665241)
p = xp.asarray(rng.random(size=3))
bracket = (-xp.asarray(5.), xp.asarray(5.))
args = (p,)
kwargs0 = dict(args=args, xatol=0, xrtol=0, fatol=0, frtol=0)
kwargs = kwargs0.copy()
kwargs['xatol'] = 1e-3
res1 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(res1.xr - res1.xl, xp.full_like(p, 1e-3))
kwargs['xatol'] = 1e-6
res2 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(res2.xr - res2.xl, xp.full_like(p, 1e-6))
xp_assert_less(res2.xr - res2.xl, res1.xr - res1.xl)
kwargs = kwargs0.copy()
kwargs['xrtol'] = 1e-3
res1 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(res1.xr - res1.xl, 1e-3 * xp.abs(res1.x))
kwargs['xrtol'] = 1e-6
res2 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(res2.xr - res2.xl, 1e-6 * xp.abs(res2.x))
xp_assert_less(res2.xr - res2.xl, res1.xr - res1.xl)
kwargs = kwargs0.copy()
kwargs['fatol'] = 1e-3
res1 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(xp.abs(res1.fun), xp.full_like(p, 1e-3))
kwargs['fatol'] = 1e-6
res2 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(xp.abs(res2.fun), xp.full_like(p, 1e-6))
xp_assert_less(xp.abs(res2.fun), xp.abs(res1.fun))
kwargs = kwargs0.copy()
kwargs['frtol'] = 1e-3
x1, x2 = bracket
f0 = xp_minimum(xp.abs(self.f(x1, *args)), xp.abs(self.f(x2, *args)))
res1 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(xp.abs(res1.fun), 1e-3*f0)
kwargs['frtol'] = 1e-6
res2 = _chandrupatla_root(self.f, *bracket, **kwargs)
xp_assert_less(xp.abs(res2.fun), 1e-6*f0)
xp_assert_less(xp.abs(res2.fun), xp.abs(res1.fun))
def test_maxiter_callback(self, xp):
# Test behavior of `maxiter` parameter and `callback` interface
p = xp.asarray(0.612814)
bracket = (xp.asarray(-5.), xp.asarray(5.))
maxiter = 5
def f(q, p):
res = special.ndtr(q) - p
f.x = q
f.fun = res
return res
f.x = None
f.fun = None
res = _chandrupatla_root(f, *bracket, args=(p,), maxiter=maxiter)
assert not xp.any(res.success)
assert xp.all(res.nfev == maxiter+2)
assert xp.all(res.nit == maxiter)
def callback(res):
callback.iter += 1
callback.res = res
assert hasattr(res, 'x')
if callback.iter == 0:
# callback is called once with initial bracket
assert (res.xl, res.xr) == bracket
else:
changed = (((res.xl == callback.xl) & (res.xr != callback.xr))
| ((res.xl != callback.xl) & (res.xr == callback.xr)))
assert xp.all(changed)
callback.xl = res.xl
callback.xr = res.xr
assert res.status == eim._EINPROGRESS
xp_assert_equal(self.f(res.xl, p), res.fl)
xp_assert_equal(self.f(res.xr, p), res.fr)
xp_assert_equal(self.f(res.x, p), res.fun)
if callback.iter == maxiter:
raise StopIteration
callback.iter = -1 # callback called once before first iteration
callback.res = None
callback.xl = None
callback.xr = None
res2 = _chandrupatla_root(f, *bracket, args=(p,), callback=callback)
# terminating with callback is identical to terminating due to maxiter
# (except for `status`)
for key in res.keys():
if key == 'status':
xp_assert_equal(res[key], xp.asarray(eim._ECONVERR, dtype=xp.int32))
xp_assert_equal(res2[key], xp.asarray(eim._ECALLBACK, dtype=xp.int32))
elif key.startswith('_'):
continue
else:
xp_assert_equal(res2[key], res[key])
@pytest.mark.parametrize('case', _CHANDRUPATLA_TESTS)
def test_nit_expected(self, case, xp):
# Test that `_chandrupatla` implements Chandrupatla's algorithm:
# in all 40 test cases, the number of iterations performed
# matches the number reported in the original paper.
f, bracket, root, nfeval, id = case
# Chandrupatla's criterion is equivalent to
# abs(x2-x1) < 4*abs(xmin)*xrtol + xatol, but we use the more standard
# abs(x2-x1) < abs(xmin)*xrtol + xatol. Therefore, set xrtol to 4x
# that used by Chandrupatla in tests.
bracket = (xp.asarray(bracket[0], dtype=xp.float64),
xp.asarray(bracket[1], dtype=xp.float64))
root = xp.asarray(root, dtype=xp.float64)
res = _chandrupatla_root(f, *bracket, xrtol=4e-10, xatol=1e-5)
xp_assert_close(res.fun, xp.asarray(f(root), dtype=xp.float64),
rtol=1e-8, atol=2e-3)
xp_assert_equal(res.nfev, xp.asarray(nfeval, dtype=xp.int32))
@pytest.mark.parametrize("root", (0.622, [0.622, 0.623]))
@pytest.mark.parametrize("dtype", ('float16', 'float32', 'float64'))
def test_dtype(self, root, dtype, xp):
# Test that dtypes are preserved
not_numpy = not is_numpy(xp)
if not_numpy and dtype == 'float16':
pytest.skip("`float16` dtype only supported for NumPy arrays.")
dtype = getattr(xp, dtype, None)
if dtype is None:
pytest.skip(f"{xp} does not support {dtype}")
def f(x, root):
res = (x - root) ** 3.
if is_numpy(xp): # NumPy does not preserve dtype
return xp.asarray(res, dtype=dtype)
return res
a, b = xp.asarray(-3, dtype=dtype), xp.asarray(3, dtype=dtype)
root = xp.asarray(root, dtype=dtype)
res = _chandrupatla_root(f, a, b, args=(root,), xatol=1e-3)
try:
xp_assert_close(res.x, root, atol=1e-3)
except AssertionError:
assert res.x.dtype == dtype
xp.all(res.fun == 0)
def test_input_validation(self, xp):
# Test input validation for appropriate error messages
def func(x):
return x
message = '`func` must be callable.'
with pytest.raises(ValueError, match=message):
bracket = xp.asarray(-4), xp.asarray(4)
_chandrupatla_root(None, *bracket)
message = 'Abscissae and function output must be real numbers.'
with pytest.raises(ValueError, match=message):
bracket = xp.asarray(-4+1j), xp.asarray(4)
_chandrupatla_root(func, *bracket)
# raised by `np.broadcast, but the traceback is readable IMO
message = "...not be broadcast..." # all messages include this part
with pytest.raises((ValueError, RuntimeError), match=message):
bracket = xp.asarray([-2, -3]), xp.asarray([3, 4, 5])
_chandrupatla_root(func, *bracket)
message = "The shape of the array returned by `func`..."
with pytest.raises(ValueError, match=message):
bracket = xp.asarray([-3, -3]), xp.asarray([5, 5])
_chandrupatla_root(lambda x: [x[0], x[1], x[1]], *bracket)
message = 'Tolerances must be non-negative scalars.'
bracket = xp.asarray(-4), xp.asarray(4)
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, xatol=-1)
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, xrtol=xp.nan)
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, fatol='ekki')
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, frtol=xp.nan)
message = '`maxiter` must be a non-negative integer.'
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, maxiter=1.5)
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, maxiter=-1)
message = '`callback` must be callable.'
with pytest.raises(ValueError, match=message):
_chandrupatla_root(func, *bracket, callback='shrubbery')
def test_special_cases(self, xp):
# Test edge cases and other special cases
# Test infinite function values
def f(x):
return 1 / x + 1 - 1 / (-x + 1)
a, b = xp.asarray([0.1, 0., 0., 0.1]), xp.asarray([0.9, 1.0, 0.9, 1.0])
with np.errstate(divide='ignore', invalid='ignore'):
res = _chandrupatla_root(f, a, b)
assert xp.all(res.success)
xp_assert_close(res.x[1:], xp.full((3,), res.x[0]))
# Test that integers are not passed to `f`
# (otherwise this would overflow)
xp_test = array_namespace(a) # need isdtype
def f(x):
assert xp_test.isdtype(x.dtype, "real floating")
# this would overflow if x were an xp integer dtype
return x ** 31 - 1
# note that all inputs are integer type; result is automatically default float
res = _chandrupatla_root(f, xp.asarray(-7), xp.asarray(5))
assert res.success
xp_assert_close(res.x, xp.asarray(1.))
# Test that if both ends of bracket equal root, algorithm reports
# convergence.
def f(x, root):
return x**2 - root
root = xp.asarray([0, 1])
res = _chandrupatla_root(f, xp.asarray(1), xp.asarray(1), args=(root,))
xp_assert_equal(res.success, xp.asarray([False, True]))
xp_assert_equal(res.x, xp.asarray([np.nan, 1.]))
def f(x):
return 1/x
with np.errstate(invalid='ignore'):
inf = xp.asarray(xp.inf)
res = _chandrupatla_root(f, inf, inf)
assert res.success
xp_assert_equal(res.x, xp.asarray(np.inf))
# Test maxiter = 0. Should do nothing to bracket.
def f(x):
return x**3 - 1
a, b = xp.asarray(-3.), xp.asarray(5.)
res = _chandrupatla_root(f, a, b, maxiter=0)
xp_assert_equal(res.success, xp.asarray(False))
xp_assert_equal(res.status, xp.asarray(-2, dtype=xp.int32))
xp_assert_equal(res.nit, xp.asarray(0, dtype=xp.int32))
xp_assert_equal(res.nfev, xp.asarray(2, dtype=xp.int32))
xp_assert_equal(res.xl, a)
xp_assert_equal(res.xr, b)
# The `x` attribute is the one with the smaller function value
xp_assert_equal(res.x, a)
# Reverse bracket; check that this is still true
res = _chandrupatla_root(f, -b, -a, maxiter=0)
xp_assert_equal(res.x, -a)
# Test maxiter = 1
res = _chandrupatla_root(f, a, b, maxiter=1)
xp_assert_equal(res.success, xp.asarray(True))
xp_assert_equal(res.status, xp.asarray(0, dtype=xp.int32))
xp_assert_equal(res.nit, xp.asarray(1, dtype=xp.int32))
xp_assert_equal(res.nfev, xp.asarray(3, dtype=xp.int32))
xp_assert_close(res.x, xp.asarray(1.))
# Test scalar `args` (not in tuple)
def f(x, c):
return c*x - 1
res = _chandrupatla_root(f, xp.asarray(-1), xp.asarray(1), args=xp.asarray(3))
xp_assert_close(res.x, xp.asarray(1/3))
# # TODO: Test zero tolerance
# # ~~What's going on here - why are iterations repeated?~~
# # tl goes to zero when xatol=xrtol=0. When function is nearly linear,
# # this causes convergence issues.
# def f(x):
# return np.cos(x)
#
# res = _chandrupatla_root(f, 0, np.pi, xatol=0, xrtol=0)
# assert res.nit < 100
# xp = np.nextafter(res.x, np.inf)
# xm = np.nextafter(res.x, -np.inf)
# assert np.abs(res.fun) < np.abs(f(xp))
# assert np.abs(res.fun) < np.abs(f(xm))
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