A class for playing with numerical integrals and derivatives.

Cfunction.py

class Cfunction:
    """
    A class for numeric calculus experiments
    """
    def __init__(self, fcn, eps=0.001):
        self.fcn = fcn
        self.__eps = eps
        self.integral = lambda x: self.integrate(0, x)  # Indefinite integral
        self.derivative = self._derivative()  # f'(x)

    def __call__(self, x):
        return self.fcn(x)

    def _integral(self):
        """
        Indefinite integral.  Calculated using midpoint.
        """
        return lambda x: self.__eps * (self.fcn(x) + self.fcn(x + self.__eps)) / 2.

    def _derivative(self):
        """
        Numeric derivative, calculated using rightward step.
        """
        return lambda x: (self.fcn(x + self.__eps) - self.fcn(x)) / self.__eps

    def integrate(self, lower, upper):
        """
        Definite integral
        """
        steps = int((upper - lower) / self.__eps)
        return sum(self._integral()(lower + self.__eps * x) for x in range(steps))


def example():
    """
    How to use the above code
    """
    f = Cfunction(lambda x: x * x)
    print(f.integral(2))  # f.integral should be (x^3)/3, so ~8/3 is good
    print(f.derivative(2))  # f.derivative should be 2x, so ~4 is good
    print(f.integrate(-1, 1))  # (1/3) - (-1/3) = 2/3