Resistance network calculator

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

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")

Go

Translation of: Python

<lang go>package main

import (

   "fmt"
   "math/big"
   "strconv"
   "strings"

)

func gauss(a [][]*big.Rat, b []*big.Rat) []*big.Rat {

   n := len(a)
   t := new(big.Rat)
   u := new(big.Rat)
   for i := 0; i < n; i++ {
       t.Abs(a[i][i])
       k := i
       for j := i + 1; j < n; j++ {
           if u.Abs(a[j][i]).Cmp(t) == 1 {
               t.Abs(a[j][i])
               k = j
           }
       }
       if k != i {
           for j := i; j < n; j++ {
               u.Set(a[i][j])
               a[i][j].Set(a[k][j])
               a[k][j].Set(u)
           }
           u.Set(b[i])
           b[i].Set(b[k])
           b[k].Set(u)
       }
       t.Set(u.Inv(a[i][i]))
       for j := i + 1; j < n; j++ {
           a[i][j].Mul(a[i][j], t)
       }
       b[i].Mul(b[i], t)
       for j := i + 1; j < n; j++ {
           t.Set(a[j][i])
           for k := i + 1; k < n; k++ {
               u.Mul(t, a[i][k])
               a[j][k].Sub(a[j][k], u)
           }
           u.Mul(t, b[i])
           b[j].Sub(b[j], u)
       }
   }
   for i := n - 1; i >= 0; i-- {
       for j := 0; j < i; j++ {
           u.Mul(a[j][i], b[i])
           b[j].Sub(b[j], u)
       }
   }
   return b

}

func network(n, k0, k1 int, s string) *big.Rat {

   a := make([][]*big.Rat, n)
   for i := 0; i < n; i++ {
       a[i] = make([]*big.Rat, n)
       for j := 0; j < n; j++ {
           a[i][j] = new(big.Rat)
       }
   }
   arr := strings.Split(s, "|")
   for _, resistor := range arr {
       rarr := strings.Fields(resistor)
       n1, _ := strconv.Atoi(rarr[0])
       n2, _ := strconv.Atoi(rarr[1])
       ri, _ := strconv.Atoi(rarr[2])
       r := new(big.Rat).SetFrac64(1, int64(ri))
       a[n1][n1].Add(a[n1][n1], r)
       a[n2][n2].Add(a[n2][n2], r)
       if n1 > 0 {
           a[n1][n2].Sub(a[n1][n2], r)
       }
       if n2 > 0 {
           a[n2][n1].Sub(a[n2][n1], r)
       }
   }
   a[k0][k0].SetInt64(1)
   b := make([]*big.Rat, n)
   for i := 0; i < n; i++ {
       b[i] = new(big.Rat)
   }
   b[k1].SetInt64(1)
   return gauss(a, b)[k1]

}

func main() {

   var ra [4]*big.Rat
   ra[0] = 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")
   ra[1] = 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")
   ra[2] = 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")
   ra[3] = network(4, 0, 3, "0 1 150|0 2 50|1 3 300|2 3 250")
   for _, r := range ra {
       s := r.String()
       if strings.HasSuffix(s, "/1") {
           fmt.Println(s[0 : len(s)-2])
       } else {
           fmt.Println(s)
       }
   }

}</lang>

Output:

Python

<lang python>from fractions import Fraction

def argmax(m,i): col = [abs(row[i]) for row in m] return col.index(max(col))

def gauss(m): n, p = len(m), len(m[0]) for i in range(n): k = i + argmax(m[i:n],i) m[i], m[k] = m[k], m[i] t = 1 / m[i][i] for j in range(i + 1, p): m[i][j] *= t for j in range(i + 1, n): t = m[j][i] for k in range(i + 1, p): m[j][k] -= t * m[i][k] for i in range(n - 1, -1, -1): for j in range(i): m[j][-1] -= m[j][i] * m[i][-1] return [row[-1] for row in m]

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

zkl

Output: