228 lines
6.5 KiB
Python
228 lines
6.5 KiB
Python
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"""
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When you need to use random numbers in SymPy library code, import from here
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so there is only one generator working for SymPy. Imports from here should
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behave the same as if they were being imported from Python's random module.
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But only the routines currently used in SymPy are included here. To use others
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import ``rng`` and access the method directly. For example, to capture the
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current state of the generator use ``rng.getstate()``.
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There is intentionally no Random to import from here. If you want
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to control the state of the generator, import ``seed`` and call it
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with or without an argument to set the state.
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Examples
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========
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>>> from sympy.core.random import random, seed
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>>> assert random() < 1
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>>> seed(1); a = random()
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>>> b = random()
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>>> seed(1); c = random()
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>>> assert a == c
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>>> assert a != b # remote possibility this will fail
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"""
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from sympy.utilities.iterables import is_sequence
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from sympy.utilities.misc import as_int
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import random as _random
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rng = _random.Random()
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choice = rng.choice
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random = rng.random
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randint = rng.randint
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randrange = rng.randrange
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sample = rng.sample
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# seed = rng.seed
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shuffle = rng.shuffle
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uniform = rng.uniform
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_assumptions_rng = _random.Random()
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_assumptions_shuffle = _assumptions_rng.shuffle
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def seed(a=None, version=2):
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rng.seed(a=a, version=version)
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_assumptions_rng.seed(a=a, version=version)
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def random_complex_number(a=2, b=-1, c=3, d=1, rational=False, tolerance=None):
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"""
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Return a random complex number.
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To reduce chance of hitting branch cuts or anything, we guarantee
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b <= Im z <= d, a <= Re z <= c
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When rational is True, a rational approximation to a random number
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is obtained within specified tolerance, if any.
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"""
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from sympy.core.numbers import I
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from sympy.simplify.simplify import nsimplify
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A, B = uniform(a, c), uniform(b, d)
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if not rational:
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return A + I*B
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return (nsimplify(A, rational=True, tolerance=tolerance) +
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I*nsimplify(B, rational=True, tolerance=tolerance))
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def verify_numerically(f, g, z=None, tol=1.0e-6, a=2, b=-1, c=3, d=1):
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"""
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Test numerically that f and g agree when evaluated in the argument z.
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If z is None, all symbols will be tested. This routine does not test
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whether there are Floats present with precision higher than 15 digits
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so if there are, your results may not be what you expect due to round-
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off errors.
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Examples
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========
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>>> from sympy import sin, cos
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>>> from sympy.abc import x
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>>> from sympy.core.random import verify_numerically as tn
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>>> tn(sin(x)**2 + cos(x)**2, 1, x)
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True
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"""
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from sympy.core.symbol import Symbol
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from sympy.core.sympify import sympify
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from sympy.core.numbers import comp
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f, g = (sympify(i) for i in (f, g))
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if z is None:
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z = f.free_symbols | g.free_symbols
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elif isinstance(z, Symbol):
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z = [z]
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reps = list(zip(z, [random_complex_number(a, b, c, d) for _ in z]))
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z1 = f.subs(reps).n()
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z2 = g.subs(reps).n()
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return comp(z1, z2, tol)
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def test_derivative_numerically(f, z, tol=1.0e-6, a=2, b=-1, c=3, d=1):
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"""
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Test numerically that the symbolically computed derivative of f
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with respect to z is correct.
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This routine does not test whether there are Floats present with
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precision higher than 15 digits so if there are, your results may
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not be what you expect due to round-off errors.
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Examples
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========
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>>> from sympy import sin
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>>> from sympy.abc import x
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>>> from sympy.core.random import test_derivative_numerically as td
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>>> td(sin(x), x)
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True
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"""
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from sympy.core.numbers import comp
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from sympy.core.function import Derivative
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z0 = random_complex_number(a, b, c, d)
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f1 = f.diff(z).subs(z, z0)
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f2 = Derivative(f, z).doit_numerically(z0)
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return comp(f1.n(), f2.n(), tol)
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def _randrange(seed=None):
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"""Return a randrange generator.
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``seed`` can be
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* None - return randomly seeded generator
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* int - return a generator seeded with the int
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* list - the values to be returned will be taken from the list
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in the order given; the provided list is not modified.
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Examples
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========
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>>> from sympy.core.random import _randrange
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>>> rr = _randrange()
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>>> rr(1000) # doctest: +SKIP
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999
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>>> rr = _randrange(3)
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>>> rr(1000) # doctest: +SKIP
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238
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>>> rr = _randrange([0, 5, 1, 3, 4])
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>>> rr(3), rr(3)
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(0, 1)
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"""
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if seed is None:
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return randrange
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elif isinstance(seed, int):
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rng.seed(seed)
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return randrange
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elif is_sequence(seed):
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seed = list(seed) # make a copy
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seed.reverse()
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def give(a, b=None, seq=seed):
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if b is None:
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a, b = 0, a
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a, b = as_int(a), as_int(b)
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w = b - a
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if w < 1:
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raise ValueError('_randrange got empty range')
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try:
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x = seq.pop()
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except IndexError:
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raise ValueError('_randrange sequence was too short')
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if a <= x < b:
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return x
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else:
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return give(a, b, seq)
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return give
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else:
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raise ValueError('_randrange got an unexpected seed')
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def _randint(seed=None):
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"""Return a randint generator.
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``seed`` can be
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* None - return randomly seeded generator
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* int - return a generator seeded with the int
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* list - the values to be returned will be taken from the list
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in the order given; the provided list is not modified.
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Examples
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========
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>>> from sympy.core.random import _randint
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>>> ri = _randint()
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>>> ri(1, 1000) # doctest: +SKIP
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999
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>>> ri = _randint(3)
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>>> ri(1, 1000) # doctest: +SKIP
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238
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>>> ri = _randint([0, 5, 1, 2, 4])
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>>> ri(1, 3), ri(1, 3)
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(1, 2)
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"""
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if seed is None:
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return randint
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elif isinstance(seed, int):
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rng.seed(seed)
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return randint
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elif is_sequence(seed):
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seed = list(seed) # make a copy
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seed.reverse()
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def give(a, b, seq=seed):
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a, b = as_int(a), as_int(b)
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w = b - a
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if w < 0:
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raise ValueError('_randint got empty range')
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try:
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x = seq.pop()
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except IndexError:
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raise ValueError('_randint sequence was too short')
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if a <= x <= b:
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return x
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else:
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return give(a, b, seq)
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return give
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else:
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raise ValueError('_randint got an unexpected seed')
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