#Makenzie Mayfield
#PHSX216N-section 2
#Lab 3: Projectile Motion
#09/25/16
#%matplotlib inline


import numpy as np
import matplotlib.pyplot as plt

#--------------------------#
#When you make your iPython notebook,
#add the following line at the top of your code
#after your comments:
# %matplotlib inline
#--------------------------#


#Create arrays for your data
theta = np.array([35.5, 38.5, 41.5, 44.5, 47.5])


#Create and array for your y-axis uncertainties
ymean = np.array([0.6442, 0.6994, 0.7238, 0.6862, 0.6396])
yerr= np.array([0.01086, 0.004833, 0.02357, 0.020745, 0.005653])

#Reassign variables
x = theta
y = ymean
dy = yerr

#size the plot
plt.figure(figsize=(15,10))

#create scatter plot
plt.scatter(x, y, color='blue', marker='o')

#create labels
plt.xlabel('$\\theta$ (degrees)')
plt.ylabel('$y_{mean}$ (m)')
plt.title('Height on wall vs Launcher Angle')

#fitting to a 2nd degree polynomial
c,b,a=np.polynomial.polynomial.polyfit(x,y,2,w=dy)

#Annotate with values of A, B, C from best fit polynomial
plt.annotate('A = {value:.{digits}E}'.format(value=a, digits=3),
             (0.05, 0.9), xycoords='axes fraction')

plt.annotate('B = {value:.{digits}E}'.format(value=b, digits=3),
             (0.05, 0.85), xycoords='axes fraction')

plt.annotate('C = {value:.{digits}E}'.format(value=c, digits=3),
             (0.05, 0.8), xycoords='axes fraction')
#Create fit line
xnew = np.linspace(x.min(), x.max(), 300)
fit = a*xnew**2 + b*xnew +c

plt.scatter(xnew, fit, color='red')
plt.show()

print "C = ",c , "B = ",b, "A = ",a