def test_differentiate_finite():
x, y = symbols('x y')
f = Function('f')
res0 = differentiate_finite(f(x, y) + exp(42), x, y)
xm, xp, ym, yp = [v + sign*S(1)/2 for v, sign in product([x, y], [-1, 1])]
ref0 = f(xm, ym) + f(xp, yp) - f(xm, yp) - f(xp, ym)
assert (res0 - ref0).simplify() == 0
g = Function('g')
res1 = differentiate_finite(f(x)*g(x) + 42, x)
ref1 = (-f(x - S(1)/2) + f(x + S(1)/2))*g(x) + \
(-g(x - S(1)/2) + g(x + S(1)/2))*f(x)
assert (res1 - ref1).simplify() == 0
res2 = differentiate_finite(f(x) + x**3 + 42, x, points=[x-1, x+1],
evaluate=False)
ref2 = (f(x + 1) + (x + 1)**3 - f(x - 1) - (x - 1)**3)/2
assert (res2 - ref2).simplify() == 0
def test_differentiate_finite():
x, y = symbols('x y')
f = Function('f')
res0 = differentiate_finite(f(x, y) + exp(42), x, y, evaluate=True)
xm, xp, ym, yp = [v + sign*S.Half for v, sign in product([x, y], [-1, 1])]
ref0 = f(xm, ym) + f(xp, yp) - f(xm, yp) - f(xp, ym)
assert (res0 - ref0).simplify() == 0
g = Function('g')
res1 = differentiate_finite(f(x)*g(x) + 42, x, evaluate=True)
ref1 = (-f(x - S.Half) + f(x + S.Half))*g(x) + \
(-g(x - S.Half) + g(x + S.Half))*f(x)
assert (res1 - ref1).simplify() == 0
res2 = differentiate_finite(f(x) + x**3 + 42, x, points=[x-1, x+1])
ref2 = (f(x + 1) + (x + 1)**3 - f(x - 1) - (x - 1)**3)/2
assert (res2 - ref2).simplify() == 0
raises(ValueError, lambda: differentiate_finite(f(x)*g(x), x,
pints=[x-1, x+1]))
def test_differentiate_finite():
x, y = symbols('x y')
f = Function('f')
res0 = differentiate_finite(f(x, y) + exp(42), x, y)
xm, xp, ym, yp = [
v + sign * S(1) / 2 for v, sign in product([x, y], [-1, 1])
]
ref0 = f(xm, ym) + f(xp, yp) - f(xm, yp) - f(xp, ym)
assert (res0 - ref0).simplify() == 0
g = Function('g')
res1 = differentiate_finite(f(x) * g(x) + 42, x)
ref1 = (-f(x - S(1)/2) + f(x + S(1)/2))*g(x) + \
(-g(x - S(1)/2) + g(x + S(1)/2))*f(x)
assert (res1 - ref1).simplify() == 0
res2 = differentiate_finite(f(x) + x**3 + 42,
x,
points=[x - 1, x + 1],
evaluate=False)
ref2 = (f(x + 1) + (x + 1)**3 - f(x - 1) - (x - 1)**3) / 2
assert (res2 - ref2).simplify() == 0
def test_differentiate_finite():
x, y, h = symbols('x y h')
f = Function('f')
with ignore_warnings(SymPyDeprecationWarning):
res0 = differentiate_finite(f(x, y) + exp(42), x, y, evaluate=True)
xm, xp, ym, yp = [
v + sign * S.Half for v, sign in product([x, y], [-1, 1])
]
ref0 = f(xm, ym) + f(xp, yp) - f(xm, yp) - f(xp, ym)
assert (res0 - ref0).simplify() == 0
g = Function('g')
with ignore_warnings(SymPyDeprecationWarning):
res1 = differentiate_finite(f(x) * g(x) + 42, x, evaluate=True)
ref1 = (-f(x - S.Half) + f(x + S.Half))*g(x) + \
(-g(x - S.Half) + g(x + S.Half))*f(x)
assert (res1 - ref1).simplify() == 0
res2 = differentiate_finite(f(x) + x**3 + 42, x, points=[x - 1, x + 1])
ref2 = (f(x + 1) + (x + 1)**3 - f(x - 1) - (x - 1)**3) / 2
assert (res2 - ref2).simplify() == 0
raises(TypeError,
lambda: differentiate_finite(f(x) * g(x), x, pints=[x - 1, x + 1]))
res3 = differentiate_finite(f(x) * g(x).diff(x), x)
ref3 = (-g(x) + g(x + 1)) * f(x + S.Half) - (g(x) - g(x - 1)) * f(x -
S.Half)
assert res3 == ref3
res4 = differentiate_finite(f(x) * g(x).diff(x).diff(x), x)
ref4 = -((g(x - Rational(3, 2)) - 2*g(x - S.Half) + g(x + S.Half))*f(x - S.Half)) \
+ (g(x - S.Half) - 2*g(x + S.Half) + g(x + Rational(3, 2)))*f(x + S.Half)
assert res4 == ref4
res5_expr = f(x).diff(x) * g(x).diff(x)
res5 = differentiate_finite(res5_expr, points=[x - h, x, x + h])
ref5 = (-2*f(x)/h + f(-h + x)/(2*h) + 3*f(h + x)/(2*h))*(-2*g(x)/h + g(-h + x)/(2*h) \
+ 3*g(h + x)/(2*h))/(2*h) - (2*f(x)/h - 3*f(-h + x)/(2*h) - \
f(h + x)/(2*h))*(2*g(x)/h - 3*g(-h + x)/(2*h) - g(h + x)/(2*h))/(2*h)
assert res5 == ref5
res6 = res5.limit(h, 0).doit()
ref6 = diff(res5_expr, x)
assert res6 == ref6
