import pytest
import numpy as np
from numpy.testing import assert_array_less, assert_allclose, assert_equal
from scipy.optimize._bracket import _bracket_root, _bracket_minimum, _ELIMITS
import scipy._lib._elementwise_iterative_method as eim
from scipy import stats
class TestBracketRoot:
@pytest.mark.parametrize("seed", (615655101, 3141866013, 238075752))
@pytest.mark.parametrize("use_xmin", (False, True))
@pytest.mark.parametrize("other_side", (False, True))
@pytest.mark.parametrize("fix_one_side", (False, True))
def test_nfev_expected(self, seed, use_xmin, other_side, fix_one_side):
# Property-based test to confirm that _bracket_root is behaving as
# expected. The basic case is when root < a < b.
# The number of times bracket expands (per side) can be found by
# setting the expression for the left endpoint of the bracket to the
# root of f (x=0), solving for i, and rounding up. The corresponding
# lower and upper ends of the bracket are found by plugging this back
# into the expression for the ends of the bracket.
# `other_side=True` is the case that a < b < root
# Special cases like a < root < b are tested separately
rng = np.random.default_rng(seed)
xl0, d, factor = rng.random(size=3) * [1e5, 10, 5]
factor = 1 + factor # factor must be greater than 1
xr0 = xl0 + d # xr0 must be greater than a in basic case
def f(x):
f.count += 1
return x # root is 0
if use_xmin:
xmin = -rng.random()
n = np.ceil(np.log(-(xl0 - xmin) / xmin) / np.log(factor))
l, u = xmin + (xl0 - xmin)*factor**-n, xmin + (xl0 - xmin)*factor**-(n - 1)
kwargs = dict(xl0=xl0, xr0=xr0, factor=factor, xmin=xmin)
else:
n = np.ceil(np.log(xr0/d) / np.log(factor))
l, u = xr0 - d*factor**n, xr0 - d*factor**(n-1)
kwargs = dict(xl0=xl0, xr0=xr0, factor=factor)
if other_side:
kwargs['xl0'], kwargs['xr0'] = -kwargs['xr0'], -kwargs['xl0']
l, u = -u, -l
if 'xmin' in kwargs:
kwargs['xmax'] = -kwargs.pop('xmin')
if fix_one_side:
if other_side:
kwargs['xmin'] = -xr0
else:
kwargs['xmax'] = xr0
f.count = 0
res = _bracket_root(f, **kwargs)
# Compare reported number of function evaluations `nfev` against
# reported `nit`, actual function call count `f.count`, and theoretical
# number of expansions `n`.
# When both sides are free, these get multiplied by 2 because function
# is evaluated on the left and the right each iteration.
# When one side is fixed, however, we add one: on the right side, the
# function gets evaluated once at b.
# Add 1 to `n` and `res.nit` because function evaluations occur at
# iterations *0*, 1, ..., `n`. Subtract 1 from `f.count` because
# function is called separately for left and right in iteration 0.
if not fix_one_side:
assert res.nfev == 2*(res.nit+1) == 2*(f.count-1) == 2*(n + 1)
else:
assert res.nfev == (res.nit+1)+1 == (f.count-1)+1 == (n+1)+1
# Compare reported bracket to theoretical bracket and reported function
# values to function evaluated at bracket.
bracket = np.asarray([res.xl, res.xr])
assert_allclose(bracket, (l, u))
f_bracket = np.asarray([res.fl, res.fr])
assert_allclose(f_bracket, f(bracket))
# Check that bracket is valid and that status and success are correct
assert res.xr > res.xl
signs = np.sign(f_bracket)
assert signs[0] == -signs[1]
assert res.status == 0
assert res.success
def f(self, q, p):
return stats.norm.cdf(q) - p
@pytest.mark.parametrize('p', [0.6, np.linspace(0.05, 0.95, 10)])
@pytest.mark.parametrize('xmin', [-5, None])
@pytest.mark.parametrize('xmax', [5, None])
@pytest.mark.parametrize('factor', [1.2, 2])
def test_basic(self, p, xmin, xmax, factor):
# Test basic functionality to bracket root (distribution PPF)
res = _bracket_root(self.f, -0.01, 0.01, xmin=xmin, xmax=xmax,
factor=factor, args=(p,))
assert_equal(-np.sign(res.fl), np.sign(res.fr))
@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.
p = np.linspace(-0.05, 1.05, 12).reshape(shape) if shape else 0.6
args = (p,)
maxiter = 10
@np.vectorize
def bracket_root_single(xl0, xr0, xmin, xmax, factor, p):
return _bracket_root(self.f, xl0, xr0, xmin=xmin, xmax=xmax,
factor=factor, args=(p,),
maxiter=maxiter)
def f(*args, **kwargs):
f.f_evals += 1
return self.f(*args, **kwargs)
f.f_evals = 0
rng = np.random.default_rng(2348234)
xl0 = -rng.random(size=shape)
xr0 = rng.random(size=shape)
xmin, xmax = 1e3*xl0, 1e3*xr0
if shape: # make some elements un
i = rng.random(size=shape) > 0.5
xmin[i], xmax[i] = -np.inf, np.inf
factor = rng.random(size=shape) + 1.5
res = _bracket_root(f, xl0, xr0, xmin=xmin, xmax=xmax, factor=factor,
args=args, maxiter=maxiter)
refs = bracket_root_single(xl0, xr0, xmin, xmax, factor, p).ravel()
attrs = ['xl', 'xr', 'fl', 'fr', 'success', 'nfev', 'nit']
for attr in attrs:
ref_attr = [getattr(ref, attr) for ref in refs]
res_attr = getattr(res, attr)
assert_allclose(res_attr.ravel(), ref_attr)
assert_equal(res_attr.shape, shape)
assert np.issubdtype(res.success.dtype, np.bool_)
if shape:
assert np.all(res.success[1:-1])
assert np.issubdtype(res.status.dtype, np.integer)
assert np.issubdtype(res.nfev.dtype, np.integer)
assert np.issubdtype(res.nit.dtype, np.integer)
assert_equal(np.max(res.nit), f.f_evals - 2)
assert_array_less(res.xl, res.xr)
assert_allclose(res.fl, self.f(res.xl, *args))
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 - 1.5,
lambda x: x - 1000,
lambda x: x - 1000,
lambda x: np.nan]
return [funcs[j](x) for x, j in zip(xs, js)]
args = (np.arange(4, dtype=np.int64),)
res = _bracket_root(f, xl0=[-1, -1, -1, -1], xr0=[1, 1, 1, 1],
xmin=[-np.inf, -1, -np.inf, -np.inf],
xmax=[np.inf, 1, np.inf, np.inf],
args=args, maxiter=3)
ref_flags = np.array([eim._ECONVERGED,
_ELIMITS,
eim._ECONVERR,
eim._EVALUEERR])
assert_equal(res.status, ref_flags)
@pytest.mark.parametrize("root", (0.622, [0.622, 0.623]))
@pytest.mark.parametrize('xmin', [-5, None])
@pytest.mark.parametrize('xmax', [5, None])
@pytest.mark.parametrize("dtype", (np.float16, np.float32, np.float64))
def test_dtype(self, root, xmin, xmax, dtype):
# Test that dtypes are preserved
xmin = xmin if xmin is None else dtype(xmin)
xmax = xmax if xmax is None else dtype(xmax)
root = dtype(root)
def f(x, root):
return ((x - root) ** 3).astype(dtype)
bracket = np.asarray([-0.01, 0.01], dtype=dtype)
res = _bracket_root(f, *bracket, xmin=xmin, xmax=xmax, args=(root,))
assert np.all(res.success)
assert res.xl.dtype == res.xr.dtype == dtype
assert res.fl.dtype == res.fr.dtype == dtype
def test_input_validation(self):
# Test input validation for appropriate error messages
message = '`func` must be callable.'
with pytest.raises(ValueError, match=message):
_bracket_root(None, -4, 4)
message = '...must be numeric and real.'
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4+1j, 4)
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 'hello')
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, xmin=np)
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, xmax=object())
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, factor=sum)
message = "All elements of `factor` must be greater than 1."
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, factor=0.5)
message = '`xmin <= xl0 < xr0 <= xmax` must be True'
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, 4, -4)
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, xmax=np.nan)
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, xmin=10)
message = "shape mismatch: objects cannot be broadcast"
# raised by `np.broadcast, but the traceback is readable IMO
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, [-2, -3], [3, 4, 5])
# Consider making this give a more readable error message
# with pytest.raises(ValueError, match=message):
# _bracket_root(lambda x: [x[0], x[1], x[1]], [-3, -3], [5, 5])
message = '`maxiter` must be a non-negative integer.'
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, maxiter=1.5)
with pytest.raises(ValueError, match=message):
_bracket_root(lambda x: x, -4, 4, maxiter=-1)
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 ** 99 - 1
res = _bracket_root(f, -7, 5)
assert res.success
# Test maxiter = 0. Should do nothing to bracket.
def f(x):
return x - 10
bracket = (-3, 5)
res = _bracket_root(f, *bracket, maxiter=0)
assert res.xl, res.xr == bracket
assert res.nit == 0
assert res.nfev == 2
assert res.status == -2
# Test scalar `args` (not in tuple)
def f(x, c):
return c*x - 1
res = _bracket_root(f, -1, 1, args=3)
assert res.success
assert_allclose(res.fl, f(res.xl, 3))
# Test other edge cases
def f(x):
f.count += 1
return x
# 1. root lies within guess of bracket
f.count = 0
_bracket_root(f, -10, 20)
assert_equal(f.count, 2)
# 2. bracket endpoint hits root exactly
f.count = 0
res = _bracket_root(f, 5, 10, factor=2)
bracket = (res.xl, res.xr)
assert_equal(res.nfev, 4)
assert_allclose(bracket, (0, 5), atol=1e-15)
# 3. bracket limit hits root exactly
with np.errstate(over='ignore'):
res = _bracket_root(f, 5, 10, xmin=0)
bracket = (res.xl, res.xr)
assert_allclose(bracket[0], 0, atol=1e-15)
with np.errstate(over='ignore'):
res = _bracket_root(f, -10, -5, xmax=0)
bracket = (res.xl, res.xr)
assert_allclose(bracket[1], 0, atol=1e-15)
# 4. bracket not within min, max
with np.errstate(over='ignore'):
res = _bracket_root(f, 5, 10, xmin=1)
assert not res.success
class TestBracketMinimum:
def init_f(self):
def f(x, a, b):
f.count += 1
return (x - a)**2 + b
f.count = 0
return f
def assert_valid_bracket(self, result):
assert np.all(
(result.xl < result.xm) & (result.xm < result.xr)
)
assert np.all(
(result.fl >= result.fm) & (result.fr > result.fm)
| (result.fl > result.fm) & (result.fr > result.fm)
)
def get_kwargs(
self, *, xl0=None, xr0=None, factor=None, xmin=None, xmax=None, args=()
):
names = ("xl0", "xr0", "xmin", "xmax", "factor", "args")
return {
name: val for name, val in zip(names, (xl0, xr0, xmin, xmax, factor, args))
if isinstance(val, np.ndarray) or np.isscalar(val)
or val not in [None, ()]
}
@pytest.mark.parametrize(
"seed",
(
307448016549685229886351382450158984917,
11650702770735516532954347931959000479,
113767103358505514764278732330028568336,
)
)
@pytest.mark.parametrize("use_xmin", (False, True))
@pytest.mark.parametrize("other_side", (False, True))
def test_nfev_expected(self, seed, use_xmin, other_side):
rng = np.random.default_rng(seed)
args = (0, 0) # f(x) = x^2 with minimum at 0
# xl0, xm0, xr0 are chosen such that the initial bracket is to
# the right of the minimum, and the bracket will expand
# downhill towards zero.
xl0, d1, d2, factor = rng.random(size=4) * [1e5, 10, 10, 5]
xm0 = xl0 + d1
xr0 = xm0 + d2
# Factor should be greater than one.
factor += 1
if use_xmin:
xmin = -rng.random() * 5
n = int(np.ceil(np.log(-(xl0 - xmin) / xmin) / np.log(factor)))
lower = xmin + (xl0 - xmin)*factor**-n
middle = xmin + (xl0 - xmin)*factor**-(n-1)
upper = xmin + (xl0 - xmin)*factor**-(n-2) if n > 1 else xm0
# It may be the case the lower is below the minimum, but we still
# don't have a valid bracket.
if middle**2 > lower**2:
n += 1
lower, middle, upper = (
xmin + (xl0 - xmin)*factor**-n, lower, middle
)
else:
xmin = None
n = int(np.ceil(np.log(xl0 / d1) / np.log(factor)))
lower = xl0 - d1*factor**n
middle = xl0 - d1*factor**(n-1) if n > 1 else xl0
upper = xl0 - d1*factor**(n-2) if n > 1 else xm0
# It may be the case the lower is below the minimum, but we still
# don't have a valid bracket.
if middle**2 > lower**2:
n += 1
lower, middle, upper = (
xl0 - d1*factor**n, lower, middle
)
f = self.init_f()
xmax = None
if other_side:
xl0, xm0, xr0 = -xr0, -xm0, -xl0
xmin, xmax = None, -xmin if xmin is not None else None
lower, middle, upper = -upper, -middle, -lower
kwargs = self.get_kwargs(
xl0=xl0, xr0=xr0, xmin=xmin, xmax=xmax, factor=factor, args=args
)
result = _bracket_minimum(f, xm0, **kwargs)
# Check that `nfev` and `nit` have the correct relationship
assert result.nfev == result.nit + 3
# Check that `nfev` reports the correct number of function evaluations.
assert result.nfev == f.count
# Check that the number of iterations matches the theoretical value.
assert result.nit == n
# Compare reported bracket to theoretical bracket and reported function
# values to function evaluated at bracket.
bracket = np.asarray([result.xl, result.xm, result.xr])
assert_allclose(bracket, (lower, middle, upper))
f_bracket = np.asarray([result.fl, result.fm, result.fr])
assert_allclose(f_bracket, f(bracket, *args))
self.assert_valid_bracket(result)
assert result.status == 0
assert result.success
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 - 1.5)**2,
lambda x: x,
lambda x: x,
lambda x: np.nan]
return [funcs[j](x) for x, j in zip(xs, js)]
args = (np.arange(4, dtype=np.int64),)
xl0, xm0, xr0 = np.full(4, -1.0), np.full(4, 0.0), np.full(4, 1.0)
result = _bracket_minimum(f, xm0, xl0=xl0, xr0=xr0,
xmin=[-np.inf, -1.0, -np.inf, -np.inf],
args=args, maxiter=3)
reference_flags = np.array([eim._ECONVERGED, _ELIMITS,
eim._ECONVERR, eim._EVALUEERR])
assert_equal(result.status, reference_flags)
@pytest.mark.parametrize("minimum", (0.622, [0.622, 0.623]))
@pytest.mark.parametrize("dtype", (np.float16, np.float32, np.float64))
@pytest.mark.parametrize("xmin", [-5, None])
@pytest.mark.parametrize("xmax", [5, None])
def test_dtypes(self, minimum, xmin, xmax, dtype):
xmin = xmin if xmin is None else dtype(xmin)
xmax = xmax if xmax is None else dtype(xmax)
minimum = dtype(minimum)
def f(x, minimum):
return ((x - minimum)**2).astype(dtype)
xl0, xm0, xr0 = np.array([-0.01, 0.0, 0.01], dtype=dtype)
result = _bracket_minimum(
f, xm0, xl0=xl0, xr0=xr0, xmin=xmin, xmax=xmax, args=(minimum, )
)
assert np.all(result.success)
assert result.xl.dtype == result.xm.dtype == result.xr.dtype == dtype
assert result.fl.dtype == result.fm.dtype == result.fr.dtype == dtype
def test_input_validation(self):
# Test input validation for appropriate error messages
message = '`func` must be callable.'
with pytest.raises(ValueError, match=message):
_bracket_minimum(None, -4, xl0=4)
message = '...must be numeric and real.'
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, 4+1j)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xl0='hello')
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xmin=np)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xmax=object())
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, factor=sum)
message = "All elements of `factor` must be greater than 1."
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x, -4, factor=0.5)
message = '`xmin <= xl0 < xm0 < xr0 <= xmax` must be True'
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, 4, xl0=6)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xr0=-6)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xl0=-3, xr0=-2)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xl0=-6, xr0=-5)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xl0=-np.nan)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xr0=np.nan)
message = "shape mismatch: objects cannot be broadcast"
# raised by `np.broadcast, but the traceback is readable IMO
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, [-2, -3], xl0=[-3, -4, -5])
message = '`maxiter` must be a non-negative integer.'
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xr0=4, maxiter=1.5)
with pytest.raises(ValueError, match=message):
_bracket_minimum(lambda x: x**2, -4, xr0=4, maxiter=-1)
@pytest.mark.parametrize("xl0", [0.0, None])
@pytest.mark.parametrize("xm0", (0.05, 0.1, 0.15))
@pytest.mark.parametrize("xr0", (0.2, 0.4, 0.6, None))
# Minimum is ``a`` for each tuple ``(a, b)`` below. Tests cases where minimum
# is within, or at varying disances to the left or right of the initial
# bracket.
@pytest.mark.parametrize(
"args",
(
(1.2, 0), (-0.5, 0), (0.1, 0), (0.2, 0), (3.6, 0), (21.4, 0),
(121.6, 0), (5764.1, 0), (-6.4, 0), (-12.9, 0), (-146.2, 0)
)
)
def test_scalar_no_limits(self, xl0, xm0, xr0, args):
f = self.init_f()
kwargs = self.get_kwargs(xl0=xl0, xr0=xr0, args=args)
result = _bracket_minimum(f, xm0, **kwargs)
self.assert_valid_bracket(result)
assert result.status == 0
assert result.success
assert result.nfev == f.count
@pytest.mark.parametrize(
# xmin is set at 0.0 in all cases.
"xl0,xm0,xr0,xmin",
(
# Initial bracket at varying distances from the xmin.
(0.5, 0.75, 1.0, 0.0),
(1.0, 2.5, 4.0, 0.0),
(2.0, 4.0, 6.0, 0.0),
(12.0, 16.0, 20.0, 0.0),
# Test default initial left endpoint selection. It should not
# be below xmin.
(None, 0.75, 1.0, 0.0),
(None, 2.5, 4.0, 0.0),
(None, 4.0, 6.0, 0.0),
(None, 16.0, 20.0, 0.0),
)
)
@pytest.mark.parametrize(
"args", (
(0.0, 0.0), # Minimum is directly at xmin.
(1e-300, 0.0), # Minimum is extremely close to xmin.
(1e-20, 0.0), # Minimum is very close to xmin.
# Minimum at varying distances from xmin.
(0.1, 0.0),
(0.2, 0.0),
(0.4, 0.0)
)
)
def test_scalar_with_limit_left(self, xl0, xm0, xr0, xmin, args):
f = self.init_f()
kwargs = self.get_kwargs(xl0=xl0, xr0=xr0, xmin=xmin, args=args)
result = _bracket_minimum(f, xm0, **kwargs)
self.assert_valid_bracket(result)
assert result.status == 0
assert result.success
assert result.nfev == f.count
@pytest.mark.parametrize(
#xmax is set to 1.0 in all cases.
"xl0,xm0,xr0,xmax",
(
# Bracket at varying distances from xmax.
(0.2, 0.3, 0.4, 1.0),
(0.05, 0.075, 0.1, 1.0),
(-0.2, -0.1, 0.0, 1.0),
(-21.2, -17.7, -14.2, 1.0),
# Test default right endpoint selection. It should not exceed xmax.
(0.2, 0.3, None, 1.0),
(0.05, 0.075, None, 1.0),
(-0.2, -0.1, None, 1.0),
(-21.2, -17.7, None, 1.0),
)
)
@pytest.mark.parametrize(
"args", (
(0.9999999999999999, 0.0), # Minimum very close to xmax.
# Minimum at varying distances from xmax.
(0.9, 0.0),
(0.7, 0.0),
(0.5, 0.0)
)
)
def test_scalar_with_limit_right(self, xl0, xm0, xr0, xmax, args):
f = self.init_f()
kwargs = self.get_kwargs(xl0=xl0, xr0=xr0, xmax=xmax, args=args)
result = _bracket_minimum(f, xm0, **kwargs)
self.assert_valid_bracket(result)
assert result.status == 0
assert result.success
assert result.nfev == f.count
@pytest.mark.parametrize(
"xl0,xm0,xr0,xmin,xmax,args",
(
( # Case 1:
# Initial bracket.
0.2,
0.3,
0.4,
# Function slopes down to the right from the bracket to a minimum
# at 1.0. xmax is also at 1.0
None,
1.0,
(1.0, 0.0)
),
( # Case 2:
# Initial bracket.
1.4,
1.95,
2.5,
# Function slopes down to the left from the bracket to a minimum at
# 0.3 with xmin set to 0.3.
0.3,
None,
(0.3, 0.0)
),
(
# Case 3:
# Initial bracket.
2.6,
3.25,
3.9,
# Function slopes down and to the right to a minimum at 99.4 with xmax
# at 99.4. Tests case where minimum is at xmax relatively further from
# the bracket.
None,
99.4,
(99.4, 0)
),
(
# Case 4:
# Initial bracket.
4,
4.5,
5,
# Function slopes down and to the left away from the bracket with a
# minimum at -26.3 with xmin set to -26.3. Tests case where minimum is
# at xmin relatively far from the bracket.
-26.3,
None,
(-26.3, 0)
),
(
# Case 5:
# Similar to Case 1 above, but tests default values of xl0 and xr0.
None,
0.3,
None,
None,
1.0,
(1.0, 0.0)
),
( # Case 6:
# Similar to Case 2 above, but tests default values of xl0 and xr0.
None,
1.95,
None,
0.3,
None,
(0.3, 0.0)
),
(
# Case 7:
# Similar to Case 3 above, but tests default values of xl0 and xr0.
None,
3.25,
None,
None,
99.4,
(99.4, 0)
),
(
# Case 8:
# Similar to Case 4 above, but tests default values of xl0 and xr0.
None,
4.5,
None,
-26.3,
None,
(-26.3, 0)
),
)
)
def test_minimum_at_boundary_point(self, xl0, xm0, xr0, xmin, xmax, args):
f = self.init_f()
kwargs = self.get_kwargs(xr0=xr0, xmin=xmin, xmax=xmax, args=args)
result = _bracket_minimum(f, xm0, **kwargs)
assert result.status == -1
assert args[0] in (result.xl, result.xr)
assert result.nfev == f.count
@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.
a = np.linspace(-0.05, 1.05, 12).reshape(shape) if shape else 0.6
args = (a, 0.0)
maxiter = 10
@np.vectorize
def bracket_minimum_single(xm0, xl0, xr0, xmin, xmax, factor, a):
return _bracket_minimum(self.init_f(), xm0, xl0=xl0, xr0=xr0, xmin=xmin,
xmax=xmax, factor=factor, maxiter=maxiter,
args=(a, 0.0))
f = self.init_f()
rng = np.random.default_rng(2348234)
xl0 = -rng.random(size=shape)
xr0 = rng.random(size=shape)
xm0 = xl0 + rng.random(size=shape) * (xr0 - xl0)
xmin, xmax = 1e3*xl0, 1e3*xr0
if shape: # make some elements un
i = rng.random(size=shape) > 0.5
xmin[i], xmax[i] = -np.inf, np.inf
factor = rng.random(size=shape) + 1.5
res = _bracket_minimum(f, xm0, xl0=xl0, xr0=xr0, xmin=xmin, xmax=xmax,
factor=factor, args=args, maxiter=maxiter)
refs = bracket_minimum_single(xm0, xl0, xr0, xmin, xmax, factor, a).ravel()
attrs = ['xl', 'xm', 'xr', 'fl', 'fm', 'fr', 'success', 'nfev', 'nit']
for attr in attrs:
ref_attr = [getattr(ref, attr) for ref in refs]
res_attr = getattr(res, attr)
assert_allclose(res_attr.ravel(), ref_attr)
assert_equal(res_attr.shape, shape)
assert np.issubdtype(res.success.dtype, np.bool_)
if shape:
assert np.all(res.success[1:-1])
assert np.issubdtype(res.status.dtype, np.integer)
assert np.issubdtype(res.nfev.dtype, np.integer)
assert np.issubdtype(res.nit.dtype, np.integer)
assert_equal(np.max(res.nit), f.count - 3)
self.assert_valid_bracket(res)
assert_allclose(res.fl, f(res.xl, *args))
assert_allclose(res.fm, f(res.xm, *args))
assert_allclose(res.fr, f(res.xr, *args))
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 ** 98 - 1
result = _bracket_minimum(f, -7, xr0=5)
assert result.success
# Test maxiter = 0. Should do nothing to bracket.
def f(x):
return x**2 - 10
xl0, xm0, xr0 = -3, -1, 2
result = _bracket_minimum(f, xm0, xl0=xl0, xr0=xr0, maxiter=0)
assert_equal([result.xl, result.xm, result.xr], [xl0, xm0, xr0])
# Test scalar `args` (not in tuple)
def f(x, c):
return c*x**2 - 1
result = _bracket_minimum(f, -1, args=3)
assert result.success
assert_allclose(result.fl, f(result.xl, 3))
# Initial bracket is valid.
f = self.init_f()
xl0, xm0, xr0 = [-1.0, -0.2, 1.0]
args = (0, 0)
result = _bracket_minimum(f, xm0, xl0=xl0, xr0=xr0, args=args)
assert f.count == 3
assert_equal(
[result.xl, result.xm, result.xr],
[xl0, xm0, xr0],
)
assert_equal(
[result.fl, result.fm, result.fr],
[f(xl0, *args), f(xm0, *args), f(xr0, *args)],
)