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)
def test_fraction_reject(self):
"""reject negative input with fractional exponents"""
with self.assertRaises(ValueError):
polynomial_reject_fraction = auc.Polynomial({2.5: 1})
polynomial_reject_fraction.evaluate(-2)
def test_frac_ok(self):
"""correctly evaluate valid polynomial with fraction"""
polynomial_ok = auc.Polynomial({1.5: 1})
assert polynomial_ok.evaluate(0) == 0
assert polynomial_ok.evaluate(2) == 2 * math.sqrt(2)
def test_constant_ok(self):
"""correctly evaluate valid polynomial f(x)=c"""
polynomial_ok = auc.Polynomial({0: 5})
assert polynomial_ok.evaluate(3) == 5
assert str(polynomial_ok) == "f(x)=5"
def test_string_rep_ok_2(self):
"""test string reprentation of polynomial"""
polynomial_1 = auc.Polynomial({0: 5})
assert str(polynomial_1) == "f(x)=5"
def test_zero_ok(self):
"""correctly evaluate valid polynomial f(x)=0"""
polynomial_ok = auc.Polynomial({0: 0})
assert polynomial_ok.evaluate(5) == 0
assert str(polynomial_ok) == "f(x)=0"
def test_string_rep_ok_1(self):
"""test string reprentation of polynomial"""
polynomial_1 = auc.Polynomial({0: -2.5, 1: 1.5, 3: 2, 4: 1})
assert str(polynomial_1) == "f(x)=x^4 + 2x^3 + 1.5x + -2.5"
def test_int_ok(self):
"""correctly evaluate valid polynomial"""
polynomial_ok = auc.Polynomial({2: 3, 1: 4, 0: 5})
assert polynomial_ok.evaluate(-2) == 9
assert polynomial_ok.evaluate(0) == 5
assert polynomial_ok.evaluate(2) == 25
def test_negative_exp_frac_reject(self):
"""reject negative fractional exponents"""
with self.assertRaises(ValueError):
auc.Polynomial({-2.5: 1})
def test_negative_exp_reject(self):
"""reject negative exponents"""
with self.assertRaises(ValueError):
auc.Polynomial({-2: 1})