# -*- coding: utf-8 -*-
"""
Created on Tue Apr 27 16:15:13 2021

@author: neil
"""

#xi are the nodal locations, the A matrix contains the integrals of the 'phi'
# functions (the lengths of the elements), while C is the forcing vector
# the integral of f(x), the first line in A and C needs to set a0 to f(xi[0])

b = np.diff(xi)/2                  # produce a list of element lengths/2
for i in range(1,len(xi)):         # do each element in sequence

    # integral of 'f(x)' from x1 to x2, (integral done in class)
    x1 = xi[i-1]
    x2 = xi[i]
    If = -np.cos(x2)+np.cos(x1)+0.05*(x2*x2-x1*x1)+2*(x2-x1)
    
    A[i,i]   = b[i-1]              # the A matrix is integrals of phi
    A[i,i-1] = b[i-1]
    C[i] = If                      # the C matrix is integrals of f(x)