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

# # Charge on a plate
# Slightly more advanced method of moments where we try to calculate the electrostatic charge on a plate.
# 
# ## Notes
# Still interested in the calculation of the positional information. I am guessing that the X_m, y_m are the integer numbers since the dx is already involved? Perhaps then the charge on a line is meant to be integers. 

# In[60]:


import numpy as np
from scipy.sparse.linalg import cg as conjgradsolve
import matplotlib.pyplot as plt

def charge_on_a_plate():
    
    def build_matrix(n,dx,a=0):
        output = []
        #output.append(0)
        j = 0
        diag = (2*a/np.pi)*np.log(1+np.sqrt(2))
        out_matrix = []
        mid = n/2
        for i in range(n+1):
            row = []
            for i in range(n+1):
                if i == j:
                    row.append(diag)
                else:
                    znm = dx/(np.sqrt((j-mid)**2)+(i-mid)**2) #
                    row.append(znm)
            j += 1
            out_matrix.append(row)
            print(row)
            
        out_matrix = np.array(out_matrix)
        return out_matrix
        
        
    bm = 1 #4*np.pi#*8.854e-12 # normalise
    n = 225 
    dx = 1/(n+1)
    
    a_matrix = build_matrix(n,dx)
    b_matrix = [bm for x in a_matrix] # no description of how bm should be formed. Odd that it wouldnt chnage. 
    
    #b_matrix[-1] = 0 # boundary conditions zero field on ends
    #b_matrix[0] = 0 # perhaps these are artificial and the issue is in the matirx
    solution = conjgradsolve(a_matrix,b_matrix, tol=1e-9)
    
    plt.plot(abs(solution[0]*8.854e-12*4*np.pi))
    plt.show()


# In[62]:


charge_on_a_plate()


# Not quite sure why this appears as it does. Looks a little like a point source. 
# 
# Attempted to flip the input matrix but this had no effect. Guess that makes sence because the electrical field is constant.