animation of left Riemann sums

animatedriemannsum

import matplotlib.pyplot as plt
import numpy
import matplotlib.animation as pltani


# GENERAL FORMAT
# Here, f stands for function, a stands for the beginning of the interval, b stands for the end, and n stands for the number of subdivisions you want to do.

# LEFT RIEMANN PLOT
def plotleftriemannsum(f, a, b, n):
    # plot the function
    x = numpy.linspace(a, b)
    plt.plot(x, f(x).astype(numpy.float))
    # plot the boxes
    delta = (b - a) / n
    x = numpy.arange(a, b, delta)
    y = f(x)
    plt.bar(x, y, width=delta, alpha=0.5, facecolor='orange')
    # show
    plt.show()


# RIGHT RIEMANN PLOT
def plotrightriemannsum(f, a, b, n):
    # plot the function
    x = numpy.linspace(a, b)
    plt.plot(x, f(x).astype(numpy.float))
    # plot the boxes
    delta = (b - a) / n
    x = numpy.arange(a + delta, b + delta, delta)
    y = f(x)
    x = numpy.arange(a, b, delta)
    plt.bar(x, y, width=delta, alpha=0.5, facecolor='red')
    # show
    plt.show()


def riemannsum(f, a, b, n):
    # LEFT RIEMANN
    def leftriemannsum(f, a, b, n):
        return sum([f(a + ((b - a) / n) * i) * ((b - a) / n) for i in range(n)])

    # RIGHT RIEMANN
    def rightriemannsum(f, a, b, n):
        return sum([f(a + ((b - a) / n) * i) * ((b - a) / n) for i in range(1, n + 1)])

    def midriemannsum(f,a,b,n):
        return sum([f((a + ((b - a) / n) * i + (a + ((b-a)/n) * (i-1)))/2) * ((b - a) / n) for i in range(1, n + 1)])

    # BOTH
    def plotboth(f, a, b, n):
        # plot the function
        x = numpy.linspace(a, b)
        plt.plot(x, f(x).astype(numpy.float))
        # plot the left riemann sum
        delta = (b - a) / n
        x = numpy.arange(a, b, delta)
        y = f(x)
        plt.bar(x, y, width=delta, alpha=0.5, align='edge', facecolor='red')

        # plot the right riemann sum
        x1 = numpy.arange(a + delta, b + delta, delta)
        y = f(x1)
        plt.bar(x, y, width=delta, alpha=0.5, align='edge', facecolor='orange')
        # show

        # plot the mid riemann sum
        x2 = (x + x1)/2
        y = f(x2)
        plt.bar(x, y, width=delta, alpha=0.5, align='edge', facecolor='blue')

        plt.show()

    print('LEFT RIEMANN SUM:')
    print(leftriemannsum(f, a, b, n))
    print('RIGHT RIEMANN SUM:')
    print(rightriemannsum(f, a, b, n))
    print('MID RIEMANN SUM:')
    print(midriemannsum(f,a,b,n))

    plotboth(f, a, b, n)

def f(x):
    return x**2

# leftpoint animation

a = 0
b = 1
n = 4
fig, ax = plt.subplots()
xdata = numpy.arange(a, b, 1 / n)
ydata = f(xdata)


x = numpy.linspace(a, b)
ax.set_xlim(0, 1)
ax.set_ylim(-1, 1)
plt.plot(x, f(x).astype(numpy.float))

def animate(n):
    plt.clf()
    x = numpy.linspace(a, b)
    plt.plot(x, f(x).astype(numpy.float))
    n+=1
    delta = (b - a) / n
    x = numpy.arange(a, b, delta)
    y = f(x)
    plt.bar(x, y, width=delta, alpha=0.5, align='edge', facecolor='red')

ani = pltani.FuncAnimation(fig, animate, frames = 100, interval=100, repeat=True)
# save animation
# ani.save(PATH,writer='imagemagick', fps=10)

plt.show()