def main():
"""Simple demo"""
logging.info(
"Try out some sample polynomials, bounds, step sizes, and algorithms.")
trapezoid = auc.get_algorithm("trapezoid")
midpoint = auc.get_algorithm("midpoint")
simpson = auc.get_algorithm("simpson")
bounds_simple_1 = auc.Bounds(0, 10, .1)
bounds_simple_2 = auc.Bounds(0, 10, 1)
bounds_symmetric_1 = auc.Bounds(-5, 5, .1)
polynomial_simple_cubic = auc.Polynomial({3: 1})
polynomial_simple_fractional = auc.Polynomial({.5: 1})
LOGGER.info("-Demo 1")
LOGGER.info(
f"Area={auc.area_under_curve(polynomial_simple_cubic, bounds_simple_1, midpoint)}"
)
LOGGER.info("\n-Demo 2 -- larger step size, lower accuracy")
LOGGER.info(
f"Area={auc.area_under_curve(polynomial_simple_cubic, bounds_simple_2, midpoint)}"
)
LOGGER.info(
"\n-Demo 3 -- symmetric bounds and a symmetric function (net area close to zero)"
)
LOGGER.info(
f"Area={auc.area_under_curve(polynomial_simple_cubic, bounds_symmetric_1, simpson)}"
)
LOGGER.info("\n-Demo 4 -- fractional exponents")
# integral of f(x)=x^.5 is (x^1.5)1.5 + sc, or (10*sqrt(10))/1.5 with these bounds
LOGGER.info(
f"Area={auc.area_under_curve(polynomial_simple_fractional, bounds_simple_1, trapezoid)}"
)
def test_bounds_ok3(self):
"""Check that large step sizes don't cause roundoff error problems"""
bounds_ok = auc.Bounds(0, 5, 1)
assert bounds_ok.lower_bound == 0
assert bounds_ok.upper_bound == 5
assert bounds_ok.step_size == 1
assert len(bounds_ok.full_range) == 6 #[0,1,2,3,4,5]
def test_simple_area_5(self):
"""area test 5"""
bounds = auc.Bounds(-5, 5, .01)
polynomial = auc.Polynomial({3: 1}) # f(x) = x^3
algorithm = auc.get_algorithm("midpoint")
area = auc.area_under_curve(polynomial, bounds, algorithm)
self.assertAlmostEqual(area, 0)
def test_simple_area_2(self):
"""area test 2"""
bounds = auc.Bounds(0, 10, .1)
polynomial = auc.Polynomial({2: 1}) # f(x) = x^2
algorithm = auc.get_algorithm("simpson")
area = auc.area_under_curve(polynomial, bounds, algorithm)
self.assertAlmostEqual(area, 1000.0 / 3.0)
def test_simple_area_1(self):
"""area test 1"""
bounds = auc.Bounds(0, 10, .1)
polynomial = auc.Polynomial({1: 1}) # f(x) = x
algorithm = auc.get_algorithm("trapezoid")
area = auc.area_under_curve(polynomial, bounds, algorithm)
self.assertAlmostEqual(area, 50)
def test_bounds_ok2(self):
"""basic bounds check"""
bounds_ok = auc.Bounds(0, 100, .01)
assert bounds_ok.lower_bound == 0
assert bounds_ok.upper_bound == 100
assert bounds_ok.step_size == .01
assert len(bounds_ok.full_range) == 10001
def test_bounds_ok(self):
"""basic bounds check"""
bounds_ok = auc.Bounds(2, 4, .1)
assert bounds_ok.lower_bound == 2
assert bounds_ok.upper_bound == 4
assert bounds_ok.step_size == .1
assert len(bounds_ok.full_range) == 21
def test_bounds_string_rep(self):
"""test string representation of bounds"""
bounds = auc.Bounds(-2, 2.5, .1)
bounds_str = str(bounds)
assert bounds_str == "Bounds: [-2 - 2.5], step_size: 0.1"
def test_bad_bounds_2(self):
"""reject if lower bound <= upper bound"""
with self.assertRaises(ValueError):
auc.Bounds(2, 1, 1)
def test_bad_step_size_2(self):
"""reject invalid step size"""
with self.assertRaises(ValueError):
auc.Bounds(2, 4, -.1)