partial_sum.py

# Calculate Partial Sums
# Hezekiah Branch
# Feb 16, 2022

class PartialSum:
    # Object initialization
    def __init__(self, fx=None, lower=0, upper=0, auto=False):
        self.fx = fx
        self.lower = lower
        self.upper = upper
        self.test = None
        self.result = None
        self.tail = None
        self.zero_tail = None
        self.auto = auto
        
        # Run partial sum on auto-mode if user specifies
        # else, user will call each function manually
        if auto:
            self.driver()
       
    # Custom define print function
    def __str__(self):
        return "{}".format(self.result)

    # Validate function inputted correctly
    def validate_function(self):
        try:
            str(type(self.fx)) == "<class 'function'>"
        except TypeError:
           print('First parameter must be a function.')
           
    # Validate bound inputs are numberic
    def validate_bounds(self):
        try:
            str(self.lower).isnumeric() and str(self.upper).isnumeric()
        except TypeError:
           print('Upper and lower bounds must be numbers.')
           
    # Chain input validation
    def validate(self):
        try:
            self.validate_function() and self.validate_bounds()
        except TypeError:
            print("Use syntax {VAR_NAME} = PartialSum(function, lower, upper, auto=True).")
        
    # Calculate the terms of the partial sum
    def initialize(self):
        self.test = [self.fx(x) for x in range(self.lower, self.upper)]
    
    # Calculate partial sum using contiguous values
    def partial_sum(self):
        sum = lambda test : [self.test[0]] + [self.test[i] + self.test[i-1] for i in range(1, len(self.test))]
        self.result = sum(self.test)
        self.tail = self.result[-1]
        if abs(0 - self.tail) < 1e-7:
            self.zero_tail = True
    
    # Driver function for the class
    def driver(self):
        # Validate input
        self.validate()
        # Begin analysis
        self.initialize()
        # Calculate summation
        self.partial_sum()
        # Output location of result
        print("Final result available at .result or by calling 'print()' on PartialSum object.")
        print("To view the output of f(x) for each n as n approaches infinity, use .test to view the entire list.")
        print("To view the nth partial sum (i.e. the limit if input is a convergent infinite series), use .tail to view output.")
        print("To observe if tail approaches zero, use .zero_tail (checks margin of 1e-7).")