""" Helpers for randomized testing """
from __future__ import print_function, division
from random import uniform
import random
from sympy.core.numbers import I
from sympy.simplify.simplify import nsimplify
from sympy.core.containers import Tuple
from sympy.core.numbers import comp
from sympy.core.symbol import Symbol
from sympy.core.compatibility import is_sequence, as_int
[docs]def random_complex_number(a=2, b=-1, c=3, d=1, rational=False):
"""
Return a random complex number.
To reduce chance of hitting branch cuts or anything, we guarantee
b <= Im z <= d, a <= Re z <= c
"""
A, B = uniform(a, c), uniform(b, d)
if not rational:
return A + I*B
return nsimplify(A, rational=True) + I*nsimplify(B, rational=True)
[docs]def verify_numerically(f, g, z=None, tol=1.0e-6, a=2, b=-1, c=3, d=1):
"""
Test numerically that f and g agree when evaluated in the argument z.
If z is None, all symbols will be tested. This routine does not test
whether there are Floats present with precision higher than 15 digits
so if there are, your results may not be what you expect due to round-
off errors.
Examples
========
>>> from sympy import sin, cos
>>> from sympy.abc import x
>>> from sympy.utilities.randtest import verify_numerically as tn
>>> tn(sin(x)**2 + cos(x)**2, 1, x)
True
"""
f, g, z = Tuple(f, g, z)
z = [z] if isinstance(z, Symbol) else (f.free_symbols | g.free_symbols)
reps = list(zip(z, [random_complex_number(a, b, c, d) for zi in z]))
z1 = f.subs(reps).n()
z2 = g.subs(reps).n()
return comp(z1, z2, tol)
[docs]def test_derivative_numerically(f, z, tol=1.0e-6, a=2, b=-1, c=3, d=1):
"""
Test numerically that the symbolically computed derivative of f
with respect to z is correct.
This routine does not test whether there are Floats present with
precision higher than 15 digits so if there are, your results may
not be what you expect due to round-off errors.
Examples
========
>>> from sympy import sin
>>> from sympy.abc import x
>>> from sympy.utilities.randtest import test_derivative_numerically as td
>>> td(sin(x), x)
True
"""
from sympy.core.function import Derivative
z0 = random_complex_number(a, b, c, d)
f1 = f.diff(z).subs(z, z0)
f2 = Derivative(f, z).doit_numerically(z0)
return comp(f1.n(), f2.n(), tol)
def _randrange(seed=None):
"""Return a randrange generator. ``seed`` can be
o None - return randomly seeded generator
o int - return a generator seeded with the int
o list - the values to be returned will be taken from the list
in the order given; the provided list is not modified.
Examples
========
>>> from sympy.utilities.randtest import _randrange
>>> rr = _randrange()
>>> rr(1000) # doctest: +SKIP
999
>>> rr = _randrange(3)
>>> rr(1000) # doctest: +SKIP
238
>>> rr = _randrange([0, 5, 1, 3, 4])
>>> rr(3), rr(3)
(0, 1)
"""
if seed is None:
return random.randrange
elif isinstance(seed, int):
return random.Random(seed).randrange
elif is_sequence(seed):
seed = list(seed) # make a copy
seed.reverse()
def give(a, b=None, seq=seed):
if b is None:
a, b = 0, a
a, b = as_int(a), as_int(b)
w = b - a
if w < 1:
raise ValueError('_randrange got empty range')
try:
x = seq.pop()
except AttributeError:
raise ValueError('_randrange expects a list-like sequence')
except IndexError:
raise ValueError('_randrange sequence was too short')
if a <= x < b:
return x
else:
return give(a, b, seq)
return give
else:
raise ValueError('_randrange got an unexpected seed')
def _randint(seed=None):
"""Return a randint generator. ``seed`` can be
o None - return randomly seeded generator
o int - return a generator seeded with the int
o list - the values to be returned will be taken from the list
in the order given; the provided list is not modified.
Examples
========
>>> from sympy.utilities.randtest import _randint
>>> ri = _randint()
>>> ri(1, 1000) # doctest: +SKIP
999
>>> ri = _randint(3)
>>> ri(1, 1000) # doctest: +SKIP
238
>>> ri = _randint([0, 5, 1, 2, 4])
>>> ri(1, 3), ri(1, 3)
(1, 2)
"""
if seed is None:
return random.randint
elif isinstance(seed, int):
return random.Random(seed).randint
elif is_sequence(seed):
seed = list(seed) # make a copy
seed.reverse()
def give(a, b, seq=seed):
a, b = as_int(a), as_int(b)
w = b - a
if w < 0:
raise ValueError('_randint got empty range')
try:
x = seq.pop()
except AttributeError:
raise ValueError('_randint expects a list-like sequence')
except IndexError:
raise ValueError('_randint sequence was too short')
if a <= x <= b:
return x
else:
return give(a, b, seq)
return give
else:
raise ValueError('_randint got an unexpected seed')
