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

# # Homework 19

# In[2]:


import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')
from scipy.integrate import quad
from scipy.interpolate import interp1d
from scipy.optimize import curve_fit


# ### Problem 1
# 
# * In a previous assignment we used thermo data for heat capacities of species. 
# * It is annoying that we have two temperature ranges for each species. 
# * For the given array of temperatures (K) below, the corresponding cp/Rg array is given for CH4. This is computed using the equations and the coefficients for the two temperature ranges given in previous assignments.
# 
# Fit a single 4th order polynomial to the whole range of temperature data.
# 
# Report the average and maximum relative errors that occurs over the list of temperatures. That is, at each T, you have the old and new values of cp/Rg, so you can compute the relative error. Treat the old fit as "exact." Then report the maximum and average values.
# 
# Plot the two versions to visually compare the original data and your polynomial fit.

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# THE FOLLOWING CODE PROVIDES ARRAYS T AND cpRg, which you can treat as the "given" data

T = np.linspace(300.,3000.,100)

a_lo = np.array([ 5.149876130,-1.367097880E-02,4.918005990E-05,-4.847430260E-08,1.666939560E-11])
a_hi = np.array([7.485149500E-02,1.339094670E-02,-5.732858090E-06,1.222925350E-09,-1.018152300E-13])
cpRg = np.zeros(len(T))
for k in range(5): cpRg[np.logical_and(T>=300,T<1000)]   += a_lo[k]*T[np.logical_and(T>=300,T<1000)]**k
for k in range(5): cpRg[np.logical_and(T>=1000,T<=3000)] += a_hi[k]*T[np.logical_and(T>=1000,T<=3000)]**k
    
#------------------ 


# ### Problem 2
# The following kinetic data for ```r``` versus ```T``` were collected. We want to fit this to the following model function: $r = kT^me^{-E_a/T}$. Here, $k$, $m$, and $E_a$, are adjustable parameters that we want to find so that our model best fits the data. 
# 
# Find the best parameters and plot the data and the model function together on the same graph.
# 

# In[6]:


T = np.linspace(500.,1000.,8)
r = [105.598, 89.700, 70.768, 66.996, 60.711, 58.992, 55.8328, 53.420]



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