# ----- DRILL -----
# The csv file temperatures.csv consists of two columns [year, temperature] 
# corresponding to the change in global temperatures (C) relative to a baseline 
# from 1880 to 2016. Read this csv file creating two lists consisting of the 
# year and temperature. Plot the change in temperature as a function of year 
# and label the axis accordingly. [NOTE: data will be read in as a string]

import csv
import matplotlib.pyplot as plt

with open( 'temperatures.csv' ) as csvfile:
    csvdata = csv.reader(csvfile)
    next(csvdata, None)  # skip the header
    T = []
    Y = []
    for row in csvdata:
        Y.append( int(row[0]) )
        T.append( float(row[1]) )

plt.plot(Y,T)
plt.xlabel('year')
plt.ylabel('temperature difference (C)')
plt.show()


# extrapolate changes in temperature
import csv
import numpy as np
from numpy.linalg import inv
import matplotlib.pyplot as plt

# ----- load year/temperature data -----
with open( 'temperatures.csv' ) as csvfile:
    reader = csv.reader(csvfile)
    next(reader, None)  # skip the header
    T = []
    Y = []
    for row in reader:
        Y.append( int(row[0]) )
        T.append( float(row[1]) )
        
# ----- fit second-order polynomial -----
# build matrix of years [Y^2 Y 1]
a1 = np.matrix(Y)
a0 = np.matrix( np.ones(len(Y)) )
a2 = np.power(a1,2)
A  = np.concatenate( (a2,a1,a0), axis=0 )
A  = A.transpose()

# build vector of temperatures [T]
b  = np.transpose( np.matrix(T) )

# least-squares estimate of temperature as a function of year
m = inv(A.transpose()*A) * A.transpose() * b

# evaluate and plot model estimates
for y in range(1880,2100,10):
    t = m[0]*y*y + m[1]*y + m[2] # evaluate second-order model
    plt.plot(y,t,'r.')

# plot original data
plt.plot(Y,T)
plt.xlabel('year')
plt.ylabel('temperature difference (C)')
plt.show()