def test_apply_finite_diff():
x, h = symbols('x h')
f = Function('f')
assert (apply_finite_diff(1, [x-h, x+h], [f(x-h), f(x+h)], x) -
(f(x+h)-f(x-h))/(2*h)).simplify() == 0
assert (apply_finite_diff(1, [5, 6, 7], [f(5), f(6), f(7)], 5) -
(-S(3)/2*f(5) + 2*f(6) - S(1)/2*f(7))).simplify() == 0
def test_apply_finite_diff():
x, h = symbols('x h')
f = Function('f')
assert (apply_finite_diff(1, [x - h, x + h], [f(x - h), f(x + h)], x) -
(f(x + h) - f(x - h)) / (2 * h)).simplify() == 0
assert (apply_finite_diff(1, [5, 6, 7], [f(5), f(6), f(7)], 5) -
(-S(3) / 2 * f(5) + 2 * f(6) - S(1) / 2 * f(7))).simplify() == 0
def test_apply_finite_diff():
x, h = symbols('x h')
f = Function('f')
assert (apply_finite_diff(1, [x-h, x+h], [f(x-h), f(x+h)], x) -
(f(x+h)-f(x-h))/(2*h)).simplify() == 0
assert (apply_finite_diff(1, [5, 6, 7], [f(5), f(6), f(7)], 5) -
(Rational(-3, 2)*f(5) + 2*f(6) - S.Half*f(7))).simplify() == 0
raises(ValueError, lambda: apply_finite_diff(1, [x, h], [f(x)]))