Added 'limit' calculus

Author: cfgnunes

README.md

@@ -39,6 +39,10 @@ python3 main.py
 
 ## Implementations
 
+### Limits
+
+- Epsilon-delta method
+
 ### Solutions of equations
 
 - Bisection method

limits.py

@@ -0,0 +1,40 @@
+"""Methods for compute limits."""
+
+import math
+
+
+def limit_epsilon_delta(f, x, toler, iter_max):
+    """Calculate a limit using the epsilon-delta definition.
+
+    Args:
+        f (function): equation f(x).
+        x (float): the value the independent variable is approaching.
+        toler (float): tolerance (stopping criterion).
+        iter_max (int): maximum number of iterations (stopping criterion).
+
+    Returns:
+        limit (float): the limit value.
+    """
+    delta = 0.5
+    limit_low_prev = -math.inf
+    limit_up_prev = math.inf
+
+    converged = False
+    for i in range(0, iter_max + 1):
+        delta /= (i + 1)
+        limit_low = f(x - delta)
+        limit_up = f(x + delta)
+
+        if math.fabs(limit_low_prev - limit_low) <= toler \
+           and math.fabs(limit_up_prev - limit_up) <= toler \
+           and math.fabs(limit_up_prev - limit_low_prev) <= toler:
+            converged = True
+            break
+
+        limit_up_prev = limit_up
+        limit_low_prev = limit_low
+
+    if limit_low * limit_up < 0 or math.fabs(limit_up - limit_low) > toler:
+        raise ValueError("Two sided limit does not exist.")
+
+    return limit_low, i, converged

main.py

@@ -13,6 +13,7 @@
 import differentiation
 import integration
 import interpolation
+import limits
 import linear_systems
 import linear_systems_iterative
 import ode
@@ -30,6 +31,30 @@ def wrapper(*args, **kwargs):
     return wrapper
 
 
+@print_docstring
+def example_limit_epsilon_delta():
+    """Run an example 'Limits: epsilon-delta definition'."""
+    def f(x):
+        return math.sin(x) / x
+
+    x = 0
+    toler = 10 ** -5
+    iter_max = 100
+
+    print("Inputs:")
+    print(f"x = {x}")
+    print(f"toler = {toler}")
+    print(f"iter_max = {iter_max}")
+
+    print("Execution:")
+    limit, i, converged = limits.limit_epsilon_delta(f, x, toler, iter_max)
+
+    print("Output:")
+    print(f"limit = {limit:.5f}")
+    print(f"i = {i}")
+    print(f"converged = {converged}")
+
+
 @print_docstring
 def example_solution_bisection():
     """Run an example 'Solutions: Bisection'."""
@@ -732,6 +757,9 @@ def main():
     """Run the main function."""
     # Execute all examples
 
+    # Limits
+    example_limit_epsilon_delta()
+
     # Solutions of equations
     example_solution_bisection()
     example_solution_secant()