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")

Go

Translation of: Python

<lang go>package main

import (

   "fmt"
   "math"
   "strconv"
   "strings"

)

func argmax(m [][]float64, i int) int {

   col := make([]float64, len(m))
   max, maxx := -1.0, -1
   for x := 0; x < len(m); x++ {
       col[x] = math.Abs(m[x][i])
       if col[x] > max {
           max = col[x]
           maxx = x
       }
   }
   return maxx

}

func gauss(m [][]float64) []float64 {

   n, p := len(m), len(m[0])
   for i := 0; i < n; i++ {
       k := i + argmax(m[i:n], i)
       m[i], m[k] = m[k], m[i]
       t := 1 / m[i][i]
       for j := i + 1; j < p; j++ {
           m[i][j] *= t
       }
       for j := i + 1; j < n; j++ {
           t = m[j][i]
           for l := i + 1; l < p; l++ {
               m[j][l] -= t * m[i][l]
           }
       }
   }
   for i := n - 1; i >= 0; i-- {
       for j := 0; j < i; j++ {
           m[j][p-1] -= m[j][i] * m[i][p-1]
       }
   }
   col := make([]float64, len(m))
   for x := 0; x < len(m); x++ {
       col[x] = m[x][p-1]
   }
   return col

}

func network(n, k0, k1 int, s string) float64 {

   m := make([][]float64, n)
   for i := 0; i < n; i++ {
       m[i] = make([]float64, n+1)
   }
   for _, resistor := range strings.Split(s, "|") {
       rarr := strings.Fields(resistor)
       a, _ := strconv.Atoi(rarr[0])
       b, _ := strconv.Atoi(rarr[1])
       ri, _ := strconv.Atoi(rarr[2])
       r := 1.0 / float64(ri)
       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] = 1
   m[k1][n] = 1
   return gauss(m)[k1]

}

func main() {

   var fa [4]float64
   fa[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")
   fa[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")
   fa[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")
   fa[3] = network(4, 0, 3, "0 1 150|0 2 50|1 3 300|2 3 250")
   for _, f := range fa {
       fmt.Printf("%.6g\n", f)
   }

}</lang>

Output:

10
1.5
1.85714
180

Perl

<lang perl>use strict; use warnings;

sub gauss {

 our @m; local *m = shift;
 my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
 foreach my $r (0 .. $rows - 1) {
    $lead < $cols or return;
     my $i = $r;
     until ($m[$i][$lead])
        {++$i == $rows or next;
         $i = $r;
         ++$lead == $cols and return;}
     @m[$i, $r] = @m[$r, $i];
     my $lv = $m[$r][$lead];
     $_ /= $lv foreach @{ $m[$r] };
     my @mr = @{ $m[$r] };
     foreach my $i (0 .. $rows - 1)
        {$i == $r and next;
         ($lv, my $n) = ($m[$i][$lead], -1);
         $_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
     ++$lead;}

}

sub network {

   my($n,$k0,$k1,$grid) = @_;
   my @m;
   push @m, [(0)x($n+1)] for 1..$n;

   for my $resistor (split '\|', $grid) {
       my ($a,$b,$r_inv) = split /\s+/, $resistor;
       my $r = 1 / $r_inv;
       $m[$a][$a] += $r;
       $m[$b][$b] += $r;
       $m[$a][$b] -= $r if $a > 0;
       $m[$b][$a] -= $r if $b > 0;
   }
   $m[$k0][$k0] = 1;
   $m[$k1][ -1] = 1;
   gauss(\@m);
   return $m[$k1][-1];

}

for (

   [   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' ],
   [ 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' ],
   [ 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' ],

   [   4, 0,     3, '0 1 150|0 2 50|1 3 300|2 3 250' ],

) {

   printf "%10.3f\n", network(@$_);

} </lang>

Output:

    10.000
     1.500
     1.857
   180.000

Perl 6

Translation of: Python

<lang perl6>sub gauss ( @m is copy ) {

   for @m.keys -> \i {
       my \k = max |(i .. @m.end), :by({ @m[$_][i].abs });

       @m[i, k] .= reverse if \k != i;

       .[i ^.. *] »/=» .[i] given @m[i];

       for i ^.. @m.end -> \j {
           @m[j][i ^.. *] »-=« ( @m[j][i] «*« @m[i][i ^.. *] );
       }
   }
   for @m.keys.reverse -> \i {
       @m[^i]».[*-1] »-=« ( @m[^i]».[i] »*» @m[i][*-1] );
   }
   return @m».[*-1];

} sub network ( Int \n, Int \k0, Int \k1, Str \grid ) {

   my @m = [0 xx n+1] xx n;

   for grid.split('|') -> \resistor {
       my ( \a, \b, \r_inv ) = resistor.split(/\s+/, :skip-empty);
       my \r = 1 / r_inv;

       @m[a][a] += r;
       @m[b][b] += r;
       @m[a][b] -= r if a > 0;
       @m[b][a] -= r if b > 0;
   }
   @m[k0][k0]  = 1;
   @m[k1][*-1] = 1;

   return gauss(@m)[k1];

} use Test; my @tests =

   (   10,   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' ),
   (  3/2, 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' ),
   ( 13/7, 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' ),
   (  180,   4, 0,     3, '0 1 150|0 2 50|1 3 300|2 3 250' ),

plan +@tests; is .[0], network( |.[1..4] ), .[4].substr(0,10)~'…' for @tests;</lang>

Phix

Translation of: Go

<lang Phix>function argmax(sequence m, integer i)

   sequence col := sq_abs(vslice(m,i))
   return largest(col,return_index:=true)

end function

function gauss(sequence m)

   integer n = length(m), 
           p = length(m[1])
   for i=1 to n do
       integer k := i + argmax(m[i..n],i)-1
       {m[i], m[k]} = {m[k], m[i]}
       atom t := 1/m[i][i]
       for j=i+1 to p do m[i][j] *= t end for
       for j=i+1 to n do
           t = m[j][i]
           for l=i+1 to p do m[j][l] -= t * m[i][l] end for
       end for
   end for
   for i=n to 1 by -1 do
       atom mip = m[i][p]
       for j=1 to i-1 do m[j][p] -= m[j][i] * mip end for
   end for
   return vslice(m,p)

end function

function network(integer n, k0, k1, sequence s)

   sequence m := repeat(repeat(0,n+1), n)
   s = split(s,'|')
   for i=1 to length(s) do
       integer Template:A,b,ri = sq_add(scanf(s[i],"%d %d %d"),Template:1,1,0)
       atom r = 1/ri
       m[a][a] += r
       m[b][b] += r
       if a > 1 then m[a][b] -= r end if
       if b > 1 then m[b][a] -= r end if
   end for
   k0 += 1;  m[k0][k0] = 1
   k1 += 1;  m[k1][n+1] = 1
   return gauss(m)[k1]

end function

printf(1,"%.6g\n",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")) printf(1,"%.6g\n",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")) printf(1,"%.6g\n",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"))

printf(1,"%.6g\n",network(4, 0, 3, "0 1 150|0 2 50|1 3 300|2 3 250"))</lang>

Output:

10
1.5
1.85714
180

Python

<lang python>from fractions import Fraction

def gauss(m): n, p = len(m), len(m[0]) for i in range(n): k = max(range(i, n), key = lambda x: abs(m[x][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

Library: GSL

GNU Scientific Library

This a tweak of Resistor_mesh#zkl <lang zkl>var [const] GSL=Import.lib("zklGSL"); // libGSL (GNU Scientific Library)

fcn network(n,k0,k1,mesh){

  A:=GSL.Matrix(n,n);  // zero filled
  foreach resistor in (mesh.split("|")){
     a,b,r := resistor.split().apply("toInt");
     r=1.0/r;
     A[a,a]=A[a,a] + r;
     A[b,b]=A[b,b] + r;
     if(a>0) A[a,b]=A[a,b] - r;
     if(b>0) A[b,a]=A[b,a] - r;
  }
  A[k0,k0]=1;
  b:=GSL.Vector(n);  // zero filled
  b[k1]=1;
  A.AxEQb(b)[k1];

}</lang> <lang zkl>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") .println();

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") .println();

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") .println();

network(4,0,3,"0 1 150|0 2 50|1 3 300|2 3 250") .println();</lang>

Output:

10
1.5
1.85714
180