def test_floor():
x = Symbol("x")
y = Symbol("y")
assert floor(nan) == nan
assert floor(oo) == oo
assert floor(-oo) == -oo
assert floor(0) == 0
assert floor(1) == 1
assert floor(-1) == -1
assert floor(E) == 2
assert floor(pi) == 3
assert floor(Rational(1, 2)) == 0
assert floor(-Rational(1, 2)) == -1
assert floor(Rational(7, 3)) == 2
assert floor(-Rational(7, 3)) == -3
assert floor(Float(17.0)) == 17
assert floor(-Float(17.0)) == -17
assert floor(Float(7.69)) == 7
assert floor(-Float(7.69)) == -8
assert floor(I) == I
assert floor(-I) == -I
assert floor(2 * I) == 2 * I
assert floor(-2 * I) == -2 * I
assert floor(E + pi) == floor(E + pi)
assert floor(I + pi) == floor(I + pi)
assert floor(floor(pi)) == 3
assert floor(floor(y)) == floor(y)
assert floor(floor(x)) == floor(floor(x))
assert floor(x) == floor(x)
assert floor(2 * x) == floor(2 * x)
def test_ceiling():
x = Symbol("x")
y = Symbol("y")
assert ceiling(nan) == nan
assert ceiling(oo) == oo
assert ceiling(-oo) == -oo
assert ceiling(0) == 0
assert ceiling(1) == 1
assert ceiling(-1) == -1
assert ceiling(E) == 3
assert ceiling(pi) == 4
assert ceiling(Rational(1, 2)) == 1
assert ceiling(-Rational(1, 2)) == 0
assert ceiling(Rational(7, 3)) == 3
assert ceiling(-Rational(7, 3)) == -2
assert ceiling(Float(17.0)) == 17
assert ceiling(-Float(17.0)) == -17
assert ceiling(Float(7.69)) == 8
assert ceiling(-Float(7.69)) == -7
assert ceiling(I) == I
assert ceiling(-I) == -I
assert ceiling(2 * I) == 2 * I
assert ceiling(-2 * I) == -2 * I
assert ceiling(E + pi) == ceiling(E + pi)
assert ceiling(I + pi) == ceiling(I + pi)
assert ceiling(ceiling(pi)) == 4
assert ceiling(ceiling(y)) == ceiling(y)
assert ceiling(ceiling(x)) == ceiling(ceiling(x))
assert ceiling(x) == ceiling(x)
assert ceiling(2 * x) == ceiling(2 * x)
def test_polygamma():
assert polygamma(0, -9) == zoo
assert polygamma(0, -9) == zoo
assert polygamma(0, -1) == zoo
assert polygamma(0, 0) == zoo
assert polygamma(0, 1) == -EulerGamma
assert polygamma(0, 7) == Rational(49, 20) - EulerGamma
assert polygamma(1, 1) == pi**2 / 6
assert polygamma(1, 2) == pi**2 / 6 - 1
assert polygamma(1, 3) == pi**2 / 6 - Rational(5, 4)
assert polygamma(3, 1) == pi**4 / 15
assert polygamma(3, 5) == 6 * (Rational(-22369, 20736) + pi**4 / 90)
assert polygamma(5, 1) == 8 * pi**6 / 63
def test_as_numer_denom():
x, y = Rational(17, 26).as_numer_denom()
assert x == Integer(17)
assert y == Integer(26)
x, y = Integer(-5).as_numer_denom()
assert x == Integer(-5)
assert y == Integer(1)
def test_Pow_base_exp():
x = Symbol("x")
y = Symbol("y")
e = Pow(x + y, 2)
assert isinstance(e, Pow)
assert e.exp == 2
assert e.base == x + y
assert sqrt(x - 1).as_base_exp() == (x - 1, Rational(1, 2))
def test_S():
assert S(0) == Integer(0)
assert S(1) == Integer(1)
assert S(-1) == Integer(-1)
assert S(1) / 2 == Rational(1, 2)
assert S.One is S(1)
assert S.Zero is S(0)
assert S.NegativeOne is S(-1)
assert S.Half is S(1) / 2
assert S.Pi is pi
assert S.NaN is S(0) / 0
assert S.Infinity is -oo * -10
assert S.NegativeInfinity is oo * (-3)
assert S.ComplexInfinity is zoo
assert S.Exp1 is (E + 1 - 1)
assert S.ImaginaryUnit is sqrt(-1)
assert S.GoldenRatio * 2 / 2 is GoldenRatio
assert S.Catalan * 1 is Catalan
assert S.EulerGamma is polygamma(0, 1) * -1
assert S.true is Eq(2, 2)
assert S.false is Eq(2, 3)
assert S(1) / 0 is zoo
assert S.Pi * 1 is pi
assert type(S.One) == One
def test_dirichlet_eta():
assert dirichlet_eta(0) == Rational(1, 2)
assert dirichlet_eta(-1) == Rational(1, 4)
assert dirichlet_eta(1) == log(2)
assert dirichlet_eta(2) == pi**2 / 12
assert dirichlet_eta(4) == pi**4 * Rational(7, 720)
def test_zeta():
x = Symbol("x")
assert zeta(1) == zoo
assert zeta(1, x) == zoo
assert zeta(0) == Rational(-1, 2)
assert zeta(0, x) == Rational(1, 2) - x
assert zeta(1, 2) == zoo
assert zeta(1, -7) == zoo
assert zeta(2, 1) == pi**2 / 6
assert zeta(2) == pi**2 / 6
assert zeta(4) == pi**4 / 90
assert zeta(6) == pi**6 / 945
assert zeta(2, 2) == pi**2 / 6 - 1
assert zeta(4, 3) == pi**4 / 90 - Rational(17, 16)
assert zeta(6, 4) == pi**6 / 945 - Rational(47449, 46656)
assert zeta(-1) == -Rational(1, 12)
assert zeta(-2) == 0
assert zeta(-3) == Rational(1, 120)
assert zeta(-4) == 0
assert zeta(-5) == -Rational(1, 252)
assert zeta(-1, 3) == -Rational(37, 12)
assert zeta(-1, 7) == -Rational(253, 12)
assert zeta(-1, -4) == Rational(119, 12)
assert zeta(-1, -9) == Rational(539, 12)
assert zeta(-4, 3) == -17
assert zeta(-4, -8) == 8772
assert zeta(0, 1) == -Rational(1, 2)
assert zeta(0, -1) == Rational(3, 2)
assert zeta(0, 2) == -Rational(3, 2)
assert zeta(0, -2) == Rational(5, 2)
def test_special_constants():
assert Zero() == Integer(0)
assert One() == Integer(1)
assert NegativeOne() == Integer(-1)
assert Half() == Rational(1, 2)
def test_is_real():
assert Rational(1, 2).is_real
assert Symbol('x').is_real is None
def test_is_nonnegative():
assert Rational(1, 2).is_nonnegative
assert not Rational(-2, 3).is_nonnegative
assert Symbol('x').is_nonnegative is None
def test_special_constants():
assert S.Zero == Integer(0)
assert S.One == Integer(1)
assert S.NegativeOne == Integer(-1)
assert S.Half == Rational(1, 2)
import numpy as np from numpy.testing.utils import assert_allclose from jitcsde import jitcsde_jump, y, UnsuccessfulIntegration import platform from symengine import symbols, exp, Rational import unittest if platform.system() == "Windows": compile_args = None else: from jitcxde_common import DEFAULT_COMPILE_ARGS compile_args = DEFAULT_COMPILE_ARGS+["-g","-UNDEBUG"] f = [-y(0)**3 + 4*y(0) + y(0)**2] g = [5*exp(-y(0)**2+y(0)-Rational(3,2)) + 3] λ = 1000 initial_value = np.array([1.0]) # Normal noise result = None class CompareResults(unittest.TestCase): def compare_with_result(self,new_result): global result if result is None: result = new_result else: assert_allclose( result-initial_value,
from numpy.testing.utils import assert_allclose
from jitcsde import jitcsde, y, UnsuccessfulIntegration, test
import platform
from symengine import symbols, exp, Rational, Function
import unittest
if platform.system() == "Windows":
compile_args = None
else:
from jitcxde_common import DEFAULT_COMPILE_ARGS
compile_args = DEFAULT_COMPILE_ARGS + ["-g", "-UNDEBUG"]
# Ensures that all kinds of formatting the input actually work and produce the same result. The correctness of this result itself is checked in validation_test.py.
f = [-y(0)**3 + 4 * y(0) + y(0)**2]
g = [5 * exp(-y(0)**2 + y(0) - Rational(3, 2)) + 3]
initial_value = np.array([1.0])
# Normal noise
result = None
class CompareResults(unittest.TestCase):
def compare_with_result(self, new_result):
global result
if result is None:
result = new_result
else:
assert_allclose(result - initial_value,
new_result - initial_value,
from numpy.testing.utils import assert_allclose
from jitcsde import jitcsde, y, UnsuccessfulIntegration, test
import platform
from symengine import symbols, exp, Rational
import unittest
if platform.system() == "Windows":
compile_args = None
else:
from jitcxde_common import DEFAULT_COMPILE_ARGS
compile_args = DEFAULT_COMPILE_ARGS + ["-g", "-UNDEBUG"]
# Ensures that all kinds of formatting the input actually work and produce the same result. The correctness of this result itself is checked in validation_test.py.
f = [-y(0)**3 + 4 * y(0) + y(0)**2]
g = [5 * exp(-y(0)**2 + y(0) - Rational(3, 2)) + 3]
initial_value = np.array([1.0])
# Normal noise
result = None
class CompareResults(unittest.TestCase):
def compare_with_result(self, new_result):
global result
if result is None:
result = new_result
else:
assert_allclose(result - initial_value,
new_result - initial_value,