#!/usr/bin/env python
# coding: utf-8

# ### $ y=2x+ \cos x$ 와 역함수의 그래프

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
import numpy as np
import matplotlib.pyplot as plt
import seaborn


# In[2]:


x=np.linspace(0,4,100)
y=2*x+np.cos(x)


# In[3]:


fig, ax =plt.subplots()
ax.plot(x,2*x+np.cos(x),color="red")
ax.plot(y,x,color="blue")
ax.set_aspect(1)
ax.grid(True,which='both')
ax.axhline(y=0,color='k')
ax.axvline(x=0,color='k')


# In[4]:


# fig, ax =plt.subplots()
# ax.plot(x,2*x+np.cos(x),color="red")
# ax.plot(y,x,color="blue")
# ax.set_aspect(0.5)
# ax.grid(True,which='both')
# ax.axhline(y=0,color='k')
# ax.axvline(x=0,color='k')
# ax.hist(x,y, histtype='stepfilled', facecolor='g')


# ### $\ln 10$ 값의 리만합 근사

# In[5]:


import math


# In[6]:


math.log(10)


# In[7]:


xlist=np.linspace(1,10,11)


# In[8]:


xlist


# In[9]:


def stf(x):
    return 1/x


# In[10]:


import matplotlib
def reimann(a, b, n, l, f):
    numRange = np.arange(a, b, .02)
    y = f(numRange)
    w = float(b - a)/n
    x = 0.0
    d = {"l": 0, "r": 1, "m": 0.5}
    offset = d[l[0]]
    for i in range(n):
        x += f(a + (i+offset)*w)
        plt.gca().add_patch(matplotlib.patches.Rectangle((i*w + a,0),w,f(a + (i+offset)*w)))
    plt.plot(numRange, y, color=(1.0, 0.00, 0.00), zorder=5)
    s = w * x
    #print('\n', s, '\n')

# def main():
#     functionString = input("\nEnter a function: ")
#     a = int(input("Enter the start point: "))
#     b = int(input("Enter the end point: "))
#     n = int(input("Enter the number of rectangles: "))
#     l = input("Type right, left, or middle: ")
#     reimann(a, b, n, l, lambda x: eval(functionString))
#     plt.show()


# In[11]:


def app(n):
    risum=0
    ylist=[]
    xlist=np.linspace(1,10,n+1)
    dx= 9/n
    for i in range(n):
        risum=risum+stf(xlist[i])*dx
        ylist.append(stf(xlist[i]))
#     print(ylist)
    fig, ax =plt.subplots()
    ax.scatter(xlist[:n],ylist, color='g')
    ax.set_aspect(4)
    ax.grid(True,which='both')
    ax.axhline(y=0,color='k')
    ax.axvline(x=0,color='k')
    reimann(xlist[0], xlist[-1], n, 'middle',stf)
    return risum
        
    
    


# In[12]:


app(10)


# In[13]:


app(100)


# In[15]:


app(1000)


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