Resistance network calculator

Resistance network calculator is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Introduction

Calculate the resistance of any resistor network.

• The network is stated with a string.
• The resistors are separated by a vertical dash.
• Each resistor has
  • a starting node
  • an ending node
  • a resistance

Background

Arbitrary Resistor Grid

Regular 3x3 mesh, using twelve one ohm resistors

0 - 1 - 2
|   |   | 
3 - 4 - 5
|   |   |
6 - 7 - 8 

Battery connection nodes: 0 and 8

assert 3/2 == network(9,0,8,"0 1 1|1 2 1|3 4 1|4 5 1|6 7 1|7 8 1|0 3 1|3 6 1|1 4 1|4 7 1|2 5 1|5 8 1")

Regular 4x4 mesh, using 24 one ohm resistors

 0 - 1 - 2 - 3
 |   |   |   |   
 4 - 5 - 6 - 7
 |   |   |   |
 8 - 9 -10 -11
 |   |   |   |
12 -13 -14 -15

Battery connection nodes: 0 and 15

assert 13/7 == network(16,0,15,"0 1 1|1 2 1|2 3 1|4 5 1|5 6 1|6 7 1|8 9 1|9 10 1|10 11 1|12 13 1|13 14 1|14 15 1|0 4 1|4 8 1|8 12 1|1 5 1|5 9 1|9 13 1|2 6 1|6 10 1|10 14 1|3 7 1|7 11 1|11 15 1")

Ten resistor network

Picture

Battery connection nodes: 0 and 1

assert 10 == network(7,0,1,"0 2 6|2 3 4|3 4 10|4 5 2|5 6 8|6 1 4|3 5 6|3 6 6|3 1 8|2 1 8")

Wheatstone network

Picture

This network is not possible to solve using the previous Resistance Calculator as there is no natural starting point.

assert 180 == network(4,0,3,"0 1 150|0 2 50|1 3 300|2 3 250")

Python

<lang python>import copy from fractions import Fraction

def gauss(a, b): n, p = len(a), len(a[0]) for i in range(n): t = abs(a[i][i]) k = i for j in range(i + 1, n): if abs(a[j][i]) > t: t = abs(a[j][i]) k = j if k != i: for j in range(i, n): a[i][j], a[k][j] = a[k][j], a[i][j] b[i], b[k] = b[k], b[i] t = 1 / a[i][i] for j in range(i + 1, n): a[i][j] *= t b[i] *= t for j in range(i + 1, n): t = a[j][i] for k in range(i + 1, n): a[j][k] -= t * a[i][k] b[j] -= t * b[i] for i in range(n - 1, -1, -1): for j in range(i): b[j] -= a[j][i] * b[i] return b

def network(n,k0,k1,s): I = Fraction(1, 1) v = [0*I] * n a = [copy.copy(v) for i in range(n)] arr = s.split('|') for resistor in arr: n1,n2,r = resistor.split(' ') n1 = int(n1) n2 = int(n2) r = Fraction(1,int(r)) a[n1][n1] += r a[n2][n2] += r if n1>0: a[n1][n2] += -r if n2>0: a[n2][n1] += -r a[k0][k0] = I b = [0*I] * n b[k1] = I return gauss(a,b)[k1]

assert 10 == network(7,0,1,"0 2 6|2 3 4|3 4 10|4 5 2|5 6 8|6 1 4|3 5 6|3 6 6|3 1 8|2 1 8") assert 3/2 == network(3*3,0,3*3-1,"0 1 1|1 2 1|3 4 1|4 5 1|6 7 1|7 8 1|0 3 1|3 6 1|1 4 1|4 7 1|2 5 1|5 8 1") assert Fraction(13,7) == network(4*4,0,4*4-1,"0 1 1|1 2 1|2 3 1|4 5 1|5 6 1|6 7 1|8 9 1|9 10 1|10 11 1|12 13 1|13 14 1|14 15 1|0 4 1|4 8 1|8 12 1|1 5 1|5 9 1|9 13 1|2 6 1|6 10 1|10 14 1|3 7 1|7 11 1|11 15 1") assert 180 == network(4,0,3,"0 1 150|0 2 50|1 3 300|2 3 250")</lang>