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_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)