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Add doctest to trapezoidal_rule #11274

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Add doctest to trapezoidal_rule #11274

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9f2d6f7
Add doctest to trapezoidal_rule
kyrtsouv Feb 5, 2024
a951561
Add doctests to trapezoidal_rule
kyrtsouv Feb 5, 2024
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59 changes: 50 additions & 9 deletions maths/trapezoidal_rule.py
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Expand Up @@ -9,7 +9,7 @@
"""


def method_1(boundary, steps):
def method_1(func, boundary, steps):
# "extended trapezoidal rule"
# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
h = (boundary[1] - boundary[0]) / steps
Expand All @@ -20,29 +20,70 @@ def method_1(boundary, steps):
y += (h / 2.0) * f(a)
for i in x_i:
# print(i)
y += h * f(i)
y += h * f(func, i)
y += (h / 2.0) * f(b)
return y


def make_points(a, b, h):
x = a + h
while x < (b - h):
"""
Yields equally spaced points between a and b
>>> x_i = make_points(0, 0.4, 0.1)
>>> next(x_i)
0.1
>>> next(x_i)
0.2
>>> next(x_i)
0.3
>>> next(x_i)
Traceback (most recent call last):
...
StopIteration

>>> x_i = make_points(0, 1, -0.2)
>>> next(x_i)
Traceback (most recent call last):
...
ValueError: h must be positive

>>> x_i = make_points(1,0,0.2)
>>> next(x_i)
Traceback (most recent call last):
...
ValueError: a must be less than b
"""
if h <= 0:
raise ValueError("h must be positive")
if a >= b:
raise ValueError("a must be less than b")

x = round(a + h, 10)
while x <= (b - h):
yield x
x = x + h
x = round(x + h, 10)


def f(x): # enter your function here
y = (x - 0) * (x - 0)
return y
def f(y, x): # enter your function here
"""
Returns the value of a lambda functiοn y at x
>>> f(lambda x: x**2,2)
4
>>> f(lambda x: x**2,-1)
1
>>> f(lambda x: (x+1)/2,5)
3.0
>>> f(lambda x: (x+1)/2,0)
0.5
"""
return y(x)


def main():
a = 0.0 # Lower bound of integration
b = 1.0 # Upper bound of integration
steps = 10.0 # define number of steps or resolution
boundary = [a, b] # define boundary of integration
y = method_1(boundary, steps)
y = method_1(lambda x: x**2, boundary, steps)
print(f"y = {y}")


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