# 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

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

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

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
`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)    }}`
Output:
```10
1.5
1.85714
180
```

## 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|9 131|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(@\$_);} `
Output:
```    10.000
1.500
1.857
180.000```

## Perl 6

Translation of: Python
`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;`

## 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")`

## zkl

Library: GSL
GNU Scientific Library

This a tweak of Resistor_mesh#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];}`
`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();`
Output:
```10
1.5
1.85714
180
```