import math
import numpy as np


def left_riemann_sum(f, a, b, num_rects):
    interval_length = float(b - a)
    dx = interval_length / num_rects
    riemann_sum = 0

    for i in range(0, num_rects):
        riemann_sum += f(a + i * dx) * dx

    return riemann_sum

print(round(left_riemann_sum(math.sin, 0, 2*math.pi, 100), 5))
print(round(left_riemann_sum(lambda x: 1, 0, 1, 100), 5))
print(round(left_riemann_sum(math.exp, 1, 2, 100), 5))
print("\n\n")

def joe_riemann_sum_lb(f, a, b, n):
    deltax = float(b-a)/n
    area = 0

    for i in range(0, n):
        area += f(a + i*deltax) * deltax

    return area


print(round(joe_riemann_sum_lb(math.sin, 0, 2*math.pi, 100), 5))
print(round(joe_riemann_sum_lb(lambda x: 1, 0, 1, 100), 5))
print(round(joe_riemann_sum_lb(np.exp, 1, 2, 100), 5))
print("\n")


def joe_riemann_sum_ub(f, a, b, n):
    deltax = float(b-a)/n
    area = 0
    a = a + deltax

    for i in range(0, n):
        area += f(a + i*deltax) * deltax

    return area

print(round(joe_riemann_sum_ub(np.exp, 1, 2, 100), 5))
print("\n")

def joe_riemann_sum_mp(f, a, b, n):
    deltax = float(b-a)/n
    area = 0

    mp = (a + deltax/2.0)

    for i in range(0, n):
        area += f(mp + i*deltax) * deltax

    return area

print(round(joe_riemann_sum_mp(np.sin, 0, 2*np.pi, 100), 5))
print(round(joe_riemann_sum_mp(lambda x: np.ones_like(x), 0, 1, 100), 5))
print(round(joe_riemann_sum_mp(np.exp, 1, 2, 100), 5))
print("\n")


def joe_riemann_sum_mp_numpy(f, a, b, n):
    x = np.linspace(a, b, n)
    deltax = float(b-a)/n
    area = 0
    aplus1 = a + deltax

    mp = (a + deltax/2.0)

    #or funct = lambda i : f(mp + i*deltax) * deltax
    # y = funct(x)
    # np.sum(y)
    #2.77321

    for i in np.nditer(x):
        area += f(mp + i*deltax) * deltax

    return area
print(round(joe_riemann_sum_mp_numpy(np.exp, 1, 2, 100), 5))