## for numpy see:
## https://numpy.org/doc/stable/user/index.html
## for basic info on numpy random number generation see:
## https://numpy.org/doc/stable/reference/random/index.html#module-numpy.random


## Data Science Handbook, 2nd Ed, page 52
# For many types of operations, NumPy provides a convenient interface into just this kind of
# statically typed, compiled routine.  This is know as a *vectorized* operation.
# For simple operations vectorization is a simple as using Python arithmetic operators directly on the array object.
# This vectorized approach is designed to push the loop into the compiled layer that underlies NumPy,
# leading to much faster execution. 

## page 53
# Any time you see such a loop in a NumPy script, you should consider whether it can be replaced
# with a vectorized expression.

## This example is taken from Data Science Handbook, 2nd Ed, page 60
## We just sum a big array different ways and see how long they take

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numpy.random import default_rng
from time import time

## write a function which sums by looping
def mysum(x):
   '''sum x with  loop'''
   temp = 0.0
   for v in x:
      temp += v
   return temp

## big array that we will sum
n = 1000000 #size of array
rng = default_rng(34)
barray = rng.random(n) ## iid U(0,1)
print(pd.Series(barray).describe())

## plot
nplt = 100 #number draws to plot
plt.scatter(np.arange(nplt),barray[:nplt])
plt.xlabel("draw number"); plt.ylabel("draw")
plt.title("iid U(0,1)")
plt.show()

## check the same answer from different approaches to computing the sum
s0 = sum(barray)
s1 = mysum(barray)
s2 = barray.sum()
s3 = np.sum(barray)
print(f'\n** the four are {s0}, {s1}, {s2}, and {s3}')

## time
t1 = time()
temp = mysum(barray)
t2 = time()
print(f'the time for mysum is {t2-t1}')
t1 = time()
temp = barray.sum()
t2 = time()
print(f'the time for the sum method is {t2-t1}')

## time the different approaches
print("python sum function")
%timeit sum(barray)
print("numpy sum function")
%timeit np.sum(barray)
print("ndarray sum method")
%timeit barray.sum()
print("mysum function with loop")
%timeit mysum(barray)

#mus: microsecond, one millionth of a second
#ns: nanosecond, one billionth of a second 
#ms: millisecond, one thousandth of a second