;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 [https://physics.stackexchange.com/questions/19295/how-calculate-resistance-between-two-points-for-arbitrary-resistor-grid 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
[https://photos.google.com/photo/AF1QipPfPkOrrBpJq-KFwWR-BVlfzM5VKklKWnP31nC_ 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
[https://photos.google.com/photo/AF1QipP7yjK4gA5_xKMTo4IiO6-taHNEzelGtAIkGgE0 Picture]
This network is not possible to solve using the previous [http://www.rosettacode.org/wiki/Resistance_Calculator 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
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)
}
}
10
1.5
1.85714
180
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"))
No assertion errors.
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(@$_);
}
10.000
1.500
1.857
180.000
Perl 6
sub gauss ( @m is copy ) {
for @m.keys -> \i {
my \k = max |(i .. @m.end), :by({ @m[$_][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;
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 {{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"))
10
1.5
1.85714
180
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
{{libheader|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();
10
1.5
1.85714
180