#This example uses the banded function provided by the author to solve systems of equations involving a sparse matrix

#with a multidiagonal band.

import numpy as np

import banded as b

import pylab as py

bands=5

#specify number of unknowns, the amount of Voltage nodes we are calculating

N=6

A=np.zeros((bands,N))

v=np.zeros(N)

v[0]=5

v[1]=5

A[0,:]=-1

A[1,:]=-1

A[2,:]=4

A[2,0]=3

A[2,N-1]=3

A[3,:]=-1

A[4,:]=-1

V=np.round(b.banded(A,v,2,2),decimals=3);

i=np.linspace(1,6,6)

print('Voltage at each successive node starting from the first: ',V)

py.scatter(i,V)

py.title('Voltage at each node')

py.show()

#same solution using Gaussian Elimination and backsubsitution to Check

#Example 6.1

import numpy as np

A=np.array([[3,-1,-1,0,0,0],

[0,0,0,-1,-1,3]],float)

v=np.array([5,5,0,0,0,0],float)

N=len(v)

for m in range(N):

div=A[m,m]

A[m,:]/=div

v[m]/=div

for i in range(m+1,N):

mult=A[i,m]

A[i,:]-=mult*A[m,:]

v[i] -= mult*v[m]

x=np.empty(N,float)

for m in range(N-1,-1,-1):

x[m]=v[m]

for i in range(m+1,N):

x[m] -=A[m,i]*x[i]

print(x)

##Now run for N=10,000 Voltage Nodes

bands=5

#specify number of unknowns, the amount of Voltage nodes we are calculating

N=10000

A=np.zeros((bands,N))

v=np.zeros(N)

v[0]=5

v[1]=5

A[0,:]=-1

A[1,:]=-1

A[2,:]=4

A[2,0]=3

A[2,N-1]=3

A[3,:]=-1

A[4,:]=-1

V=np.round(b.banded(A,v,2,2),decimals=3)

i=np.linspace(1,10000,10000)

py.scatter(i,V)

py.title('Voltage at each node')

py.show()