Merge pull request #1 from hacquees/agrange_interpolation

Create lagrange_interpolation.py

Author: hacquees

maths/numerical_analysis/lagrange_interpolation.py

@@ -0,0 +1,58 @@
+import math
+from typing import List
+
+def lagrange_interpolation(x: List[float], y: List[float], value: float) -> float:
+    """
+    Calculate the Lagrange interpolation of a function based on provided data points.
+
+    Parameters:
+        x (List[float]): List of x-values (independent variable).
+        y (List[float]): List of corresponding y-values (dependent variable).
+        value (float): The value at which to interpolate the function.
+
+    Returns:
+        float: The interpolated value of the function at the specified 'value'.
+
+    for eg.:
+        
+        >>> x = [5, 6, 9, 11]
+        >>> y = [12, 13, 14, 16]
+        >>> lagrange_interpolation(x, y, 10)
+        14.666666666666666
+
+    """
+    ans = 0
+    n = len(x)
+
+    for i in range(n):  
+        term = y[i]
+        for j in range(n):
+            if i != j:
+                term *= (value - x[j]) / (x[i] - x[j])
+        ans += term
+
+    return ans
+
+def main():
+    """
+    Main function for performing Lagrange interpolation.
+    Takes user input for data points and the value to interpolate, then displays the interpolated result.
+    """
+    n = int(input("Enter the number of values: "))
+    x = []
+    y = []
+
+    print("Enter the values of x in a list: ")
+    x = list(map(float, input().split()))
+
+    print("Enter the values of corresponding y: ")
+    y = list(map(float, input().split()))
+
+    value_to_interpolate = float(input("Enter the value to interpolate:"))
+
+    interpolated_value = lagrange_interpolation(x, y, value_to_interpolate)
+
+    print(f"The interpolated value at {value_to_interpolate} is {interpolated_value}")
+
+if __name__ == "__main__":
+    main()