# -*- coding: utf-8 -*-
"""
@author: neil
"""
# program to plot a sine curve and its derivative (cosine)
# the cosine is calculated simply as the slope of the sine curve by
# taking (sine(x+dx)-sine(x))/((x+dx)-x)  as dy/dx

# the main reason for this program is to illustrate simple python coding, introduce 'numpy'
# and show a standard way of plotting on the screen using 'matplotlib'

import numpy as np
import matplotlib.pyplot as plt

# start of program, note that comments are GOOD!, also note that numbers are hard coded in this program which
# is poor programing, all numbers should be defined at the beginning of a program in a header section so they can be changed
 
x = np.linspace(0,7,30)               #np.linspace(start,stop,number) is a very useful generator, look it up! (google 'numpy linspace')
w = np.sin(x)                         # create a list of x points and the matching sin(x) points, in w, note np.sin() works on entire array

fig = plt.figure()                    #create a place to plot. plt.figure() is a standard method of matplotlib to make a blank plotting canvas
ax  = fig.add_subplot(111)            #create 1 axes.  you can create multiple plots on the same figure with subplot(2,3,1) example
ax.plot(x,w,'r-o')                    #simple 'xy' plot, with sine 'w' ploted against radians 'x', you can add LOTS of options
                                      # very common is a string like 'r-o' for a red 'r', line '-', with markers 'o'
ax.set_title("Sine and Derivative")
ax.set_xlabel("This is an x label, Radians")
ax.set_ylabel("Blue is the numpy cosine, black is ours")

diff = np.zeros(len(w)-1)             # many ways to make an array, using np.zeros(shape and size) makes a zero filled array
for i in np.arange(0,len(w)-1):       # 'for' loop, remember it always has a ':' to denote the following is part of the loop
    diff[i] = w[i+1] - w[i]           # calc the difference between all the adjacent values of the sine curve
	
diff = diff/(x[1]-x[0])               # divide the difference by 'dx' and we have an estimate of 'dy/dx'

ax.plot(x[:-1],diff,'k-+')            # note the x positions are not correct, they should be in the middle of the steps
                                      # also the x[:-1]; is pythonic 'slicing' for 'part of array x, starting at 0 excluding the last
ax.plot(x,np.cos(x),'b')              # might as well plot the cosine, or the analytic derivative									  
plt.show()                            # Spyder will let you skip this line, but it is required for a standalone program