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
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")
11l
<lang 11l>F gauss(&m)
V (n, p) = (m.len, m[0].len) L(i) 0 .< n V k = max(i .< n, key' x -> abs(@m[x][@i])) swap(&m[i], &m[k]) V t = 1 / m[i][i] L(j) i + 1 .< p m[i][j] *= t L(j) i + 1 .< n t = m[j][i] L(k) i + 1 .< p m[j][k] -= t * m[i][k] L(i) (n - 1 .< -1).step(-1) L(j) 0 .< i m[j].last -= m[j][i] * m[i].last R m.map(row -> row.last)
F network(n, k0, k1, s)
V m = [[0.0] * (n+1)] * n V resistors = s.split(‘|’) L(resistor) resistors V (aa, bb, rr) = resistor.split(‘ ’) V (a, b, r) = (Int(aa), Int(bb), (1 / Int(rr))) m[a][a] += r m[b][b] += r I a > 0 m[a][b] -= r I b > 0 m[b][a] -= r m[k0][k0] = 1 m[k1].last = 1 R gauss(&m)[k1]
F is_equal(a, b)
R abs(a - b) < 1e-6
assert(is_equal(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(is_equal(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(is_equal(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(is_equal(180 , network(4, 0, 3, ‘0 1 150|0 2 50|1 3 300|2 3 250’))) print(‘OK’)</lang>
Go
<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
Julia
<lang julia>function gauss(m)
n, p = length(m), length(m[1]) for i in 1:n _, k = findmax(map(x -> abs(m[x][i]), i:n)) .+ (i - 1) m[i], m[k] = m[k], m[i] t = 1 // m[i][i] for j in i+1:p m[i][j] *= t end for j in i+1:n t = m[j][i] for k in i+1:p m[j][k] -= t * m[i][k] end end end for i in n:-1:1, j in 1:i-1; m[j][end] -= m[j][i] * m[i][end]; end return [row[end] for row in m]
end
function network(n, k0, k1, s)
m = [[0//1 for i in 1:n + 1] for j in 1:n] resistors = split(s, "|") for resistor in resistors astr, bstr, rstr = split(resistor, " ") a, b, r = parse(Int, astr), parse(Int, bstr), 1 // parse(Int, rstr) m[a + 1][a + 1] += r m[b + 1][b + 1] += r if a > 0; m[a + 1][b + 1] -= r end if b > 0; m[b + 1][a + 1] -= r end end m[k0+1][k0+1] = m[k1+1][end] = 1 // 1 return gauss(m)[k1+1]
end
@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(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> No assertion errors.
Nim
<lang Nim>import rationals, sequtils, strscans, strutils, sugar
type Fraction = Rational[int]
func argmax(m: seq[seq[Fraction]]; i: int): int =
var max = -1 // 1 for x in i..m.high: let val = abs(m[x][i]) if val > max: max = val result = x
func gauss(m: var seq[seq[Fraction]]): seq[Fraction] =
let n = m.len let p = m[0].len
for i in 0..<n: let k = m.argmax(i) swap m[i], m[k] let t = 1 / m[i][i] for j in (i + 1)..<p: m[i][j] *= t for j in (i + 1)..<n: let t = m[j][i] for k in (i + 1)..<p: m[j][k] -= t * m[i][k]
for i in countdown(n - 1, 0): for j in 0..<i: m[j][^1] -= m[j][i] * m[i][^1]
result = collect(newSeq, for row in m: row[^1])
func network(n, k0, k1: int; s: string): Fraction =
var m = newSeqWith(n, repeat(0 // 1, n + 1)) let resistors = s.split('|') for resistor in resistors: var a, b, c: int if not resistor.scanf("$i $i $i", a, b, c): raise newException(ValueError, "Wrong resistor: " & resistor) let r: Fraction = 1 // c m[a][a] += r m[b][b] += r if a > 0: m[a][b] -= r if b > 0: m[b][a] -= r m[k0][k0] = 1 // 1 m[k1][^1] = 1 // 1 result = gauss(m)[k1]
assert 10 // 1 == network(7, 0, 1, "0 2 6|2 3 4|3 4 10|4 5 2|5 6 8|6 1 4|3 5 6|3 6 6|3 1 8|2 1 8")
assert 3 // 2 == network(3*3, 0, 3*3-1, "0 1 1|1 2 1|3 4 1|4 5 1|6 7 1|7 8 1|0 3 1|3 6 1|1 4 1|4 7 1|2 5 1|5 8 1")
assert 13 // 7 == network(4*4, 0, 4*4-1, "0 1 1|1 2 1|2 3 1|4 5 1|5 6 1|6 7 1|8 9 1|9 10 1|10 11 1|12 13 1|13 14 1|14 15 1|0 4 1|4 8 1|8 12 1|1 5 1|5 9 1|9 13 1|2 6 1|6 10 1|10 14 1|3 7 1|7 11 1|11 15 1")
assert 180 // 1 == network(4, 0, 3, "0 1 150|0 2 50|1 3 300|2 3 250")</lang>
- Output:
No assertion failed.
Perl
<lang perl>use strict; use warnings;
sub gauss {
our @m; local *m = shift; my ($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
Phix
with javascript_semantics 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) m = deep_copy(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 {{a,b,ri}} = sq_add(scanf(s[i],"%d %d %d"),{{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"))
- 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>
Raku
(formerly Perl 6)
<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>
Wren
<lang ecmascript>import "/fmt" for Fmt
var argmax = Fn.new { |m, i|
var lm = m.count var col = List.filled(lm, 0) var max = -1 var maxx = -1 for (x in 0...lm) { col[x] = m[x][i].abs if (col[x] > max ) { max = col[x] maxx = x } } return maxx
}
var gauss = Fn.new { |m|
var n = m.count var p = m[0].count for (i in 0...n) { var k = i + argmax.call(m[i...n], i) var t = m[i] m[i] = m[k] m[k] = t t = 1 / m[i][i] var j = i + 1 while (j < p) { m[i][j] = m[i][j] * t j = j + 1 } j = i + 1 while (j < n) { t = m[j][i] var l = i + 1 while (l < p) { m[j][l] = m[j][l] - t*m[i][l] l = l + 1 } j = j + 1 } } for (i in n-1..0) { for (j in 0...i) { m[j][p-1] = m[j][p-1] - m[j][i]*m[i][p-1] } } var col = List.filled(n, 0) for (x in 0...n) col[x] = m[x][p-1] return col
}
var network = Fn.new { |n, k0, k1, s|
var m = List.filled(n, null) for (i in 0...n) m[i] = List.filled(n+1, 0) for (resistor in s.split("|")) { var rarr = resistor.split(" ") var a = Num.fromString(rarr[0]) var b = Num.fromString(rarr[1]) var ri = Num.fromString(rarr[2]) var r = 1/ri m[a][a] = m[a][a] + r m[b][b] = m[b][b] + r if (a > 0) m[a][b] = m[a][b] - r if (b > 0) m[b][a] = m[b][a] - r } m[k0][k0] = 1 m[k1][n] = 1 return gauss.call(m)[k1]
}
var fa = [
network.call(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"), network.call(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"), network.call(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"), network.call(4, 0, 3, "0 1 150|0 2 50|1 3 300|2 3 250")
] for (f in fa) Fmt.print("$.5g", f)</lang>
- Output:
10.0 1.5 1.85714 180.0
zkl
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