September 2017 Update
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Ingy döt Net
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14570 changed files with 153136 additions and 63871 deletions
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@ -2,7 +2,7 @@
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;Task:
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Given <big> 10×10 </big> grid nodes (as shown in the image) interconnected by <big> 1Ω </big> resistors as shown,
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<br>find the resistance between point '''A''' and '''B'''.
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<br>find the resistance between points '''A''' and '''B'''.
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;See also:
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62
Task/Resistor-mesh/Kotlin/resistor-mesh.kotlin
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62
Task/Resistor-mesh/Kotlin/resistor-mesh.kotlin
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// version 1.1.4-3
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typealias List2D<T> = List<List<T>>
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const val S = 10
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class Node(var v: Double, var fixed: Int)
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fun setBoundary(m: List2D<Node>) {
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m[1][1].v = 1.0; m[1][1].fixed = 1
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m[6][7].v = -1.0; m[6][7].fixed = -1
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}
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fun calcDiff(m: List2D<Node>, d: List2D<Node>, w: Int, h: Int): Double {
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var total = 0.0
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for (i in 0 until h) {
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for (j in 0 until w) {
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var v = 0.0
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var n = 0
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if (i > 0) { v += m[i - 1][j].v; n++ }
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if (j > 0) { v += m[i][j - 1].v; n++ }
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if (i + 1 < h) { v += m[i + 1][j].v; n++ }
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if (j + 1 < w) { v += m[i][j + 1].v; n++ }
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v = m[i][j].v - v / n
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d[i][j].v = v
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if (m[i][j].fixed == 0) total += v * v
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}
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}
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return total
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}
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fun iter(m: List2D<Node>, w: Int, h: Int): Double {
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val d = List(h) { List(w) { Node(0.0, 0) } }
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val cur = DoubleArray(3)
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var diff = 1e10
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while (diff > 1e-24) {
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setBoundary(m)
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diff = calcDiff(m, d, w, h)
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for (i in 0 until h) {
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for (j in 0 until w) m[i][j].v -= d[i][j].v
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}
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}
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for (i in 0 until h) {
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for (j in 0 until w) {
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var k = 0
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if (i != 0) k++
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if (j != 0) k++
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if (i < h - 1) k++
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if (j < w - 1) k++
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cur[m[i][j].fixed + 1] += d[i][j].v * k
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}
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}
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return (cur[2] - cur[0]) / 2.0
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}
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fun main(args: Array<String>) {
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val mesh = List(S) { List(S) { Node(0.0, 0) } }
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val r = 2.0 / iter(mesh, S, S)
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println("R = $r")
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}
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@ -1,46 +1,45 @@
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/*REXX program calculates the resistance between any two points on a resister grid.*/
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numeric digits 20 /*use moderate decimal digs (precision)*/
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minVal = (1'e-' || (digits()*2)) / 1 /*calculate the threshold minimul value*/
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if 1=='f1'x then ohms = 'ohms' /*EBCDIC machine? Then use 'ohms'. */
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else ohms = 'ea'x /* ASCII " " " Greek Ω.*/
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parse arg high wide Arow Acol Brow Bcol . /*obtain optional arguments from the CL*/
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if 2=='f2'x then ohms = "ohms" /*EBCDIC machine? Then use 'ohms'. */
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else ohms = "Ω" /* ASCII " " " Greek Ω.*/
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parse arg high wide Arow Acol Brow Bcol digs . /*obtain optional arguments from the CL*/
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if high=='' | high=="," then high=10 /*Not specified? Then use the default.*/
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if wide=='' | wide=="," then wide=10 /* " " " " " " */
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if Arow=='' | Arow=="," then Arow= 2 /* " " " " " " */
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if Acol=='' | Acol=="," then Acol= 2 /* " " " " " " */
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if Brow=='' | Brow=="," then Brow= 7 /* " " " " " " */
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if Bcol=='' | Bcol=="," then Bcol= 8 /* " " " " " " */
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say ' minimum value = ' translate(format(minVal, , , , 0), "e", 'E'); say
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say ' resistor mesh is of size: ' wide "wide, " high 'high' ; say
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if digs=='' | digs=="," then digs=20 /* " " " " " " */
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numeric digits digs /*use moderate decimal digs (precision)*/
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minVal = 1'e-' || (digs*2) /*calculate the threshold minimul value*/
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say ' minimum value is ' format(minVal,,,,0) " using " digs ' decimal digits'; say
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say ' resistor mesh size is: ' wide "wide, " high 'high' ; say
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say ' point A is at (row,col): ' Arow"," Acol
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say ' point B is at (row,col): ' Brow"," Bcol
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@.=0; cell.=1
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do until $ <= minVal; v = 0
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@.Arow.Acol = +1 ; cell.Arow.Acol = 0
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@.Brow.Bcol = -1 ; cell.Brow.Bcol = 0
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$=0
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do i=1 for high; im=i - 1; ip=i + 1
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do j=1 for wide; jm=j - 1; jp=j + 1; n=0; v=0
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if i\==1 then do; v=v + @.im.j; n=n + 1; end
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if j\==1 then do; v=v + @.i.jm; n=n + 1; end
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if i<high then do; v=v + @.ip.j; n=n + 1; end
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if j<wide then do; v=v + @.i.jp; n=n + 1; end
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v=@.i.j - v/n; #.i.j=v; if cell.i.j then $=$ + v*v
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end /*j*/
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end /*i*/
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do r=1 for High
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do c=1 for Wide; @.r.c = @.r.c - #.r.c
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end /*c*/
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end /*r*/
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end /*until*/
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@.=0; cell.=1
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do until $<=minVal; v=0
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@.Arow.Acol= 1 ; cell.Arow.Acol=0
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@.Brow.Bcol= '-1' ; cell.Brow.Bcol=0
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$=0
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do i=1 for high; im=i-1; ip=i+1
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do j=1 for wide; n=0; v=0
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if i\==1 then do; v=v + @.im.j; n=n+1; end
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if j\==1 then do; jm=j-1; v=v + @.i.jm; n=n+1; end
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if i<high then do; v=v + @.ip.j; n=n+1; end
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if j<wide then do; jp=j+1; v=v + @.i.jp; n=n+1; end
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v=@.i.j - v/n; #.i.j=v; if cell.i.j then $=$ + v*v
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end /*j*/
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end /*i*/
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do r=1 for High
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do c=1 for Wide; @.r.c= @.r.c - #.r.c
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end /*c*/
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end /*r*/
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end /*until*/
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say
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Acur = #.Arow.Acol * sides(Arow,Acol)
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Bcur = #.Brow.Bcol * sides(Brow,Bcol)
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say ' resistance between point A and point B is: ' 4/(Acur-Bcur) ohms
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Acur= #.Arow.Acol * sides(Arow, Acol)
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Bcur= #.Brow.Bcol * sides(Brow, Bcol)
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say ' resistance between point A and point B is: ' 4 / (Acur - Bcur) ohms
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sides: parse arg row,col; z=0; if row\==1 & row\==high then z=z + 2
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else z=z + 1
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if col\==1 & col\==wide then z=z + 2
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else z=z + 1
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sides: parse arg row,col; z=0; if row\==1 & row\==high then z=z+2; else z=z+1
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if col\==1 & col\==wide then z=z+2; else z=z+1
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return z
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@ -23,10 +23,8 @@ func set_boundary {
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func calc_diff {
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var total_diff = 0
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for i,j in (^h ~X ^w) {
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var p = n[i][j]
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var w = 0
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p.each { |a| w += v.dig(a...) }
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d[i][j] = (w = (v[i][j] - w/p.len))
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var w = n[i][j].map { |a| v.dig(a...) }.sum
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d[i][j] = (w = (v[i][j] - w/n[i][j].len))
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f[i][j] || (total_diff += w*w)
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}
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total_diff
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20
Task/Resistor-mesh/Zkl/resistor-mesh-1.zkl
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Task/Resistor-mesh/Zkl/resistor-mesh-1.zkl
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var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
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fcn onGrid(i,j,p,q){ ((0<=i<p) and (0<=j<q)) }
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fcn gridResistor(p,q, ai,aj, bi,bj){
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n,A := p*q, GSL.Matrix(n,n); // zero filled
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foreach i,j in (p,q){
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k:=i*q + j;
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if(i==ai and j==aj) A[k,k]=1;
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else{
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c:=0;
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if(onGrid(i+1,j, p,q)){ c+=1; A[k, k+q]=-1 }
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if(onGrid(i-1,j, p,q)){ c+=1; A[k, k-q]=-1 }
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if(onGrid(i, j+1, p,q)){ c+=1; A[k, k+1]=-1 }
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if(onGrid(i, j-1, p,q)){ c+=1; A[k, k-1]=-1 }
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A[k,k]=c;
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}
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}
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b:=GSL.Vector(n); // zero filled
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b[k:=bi*q + bj]=1;
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A.AxEQb(b)[k];
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}
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1
Task/Resistor-mesh/Zkl/resistor-mesh-2.zkl
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1
Task/Resistor-mesh/Zkl/resistor-mesh-2.zkl
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@ -0,0 +1 @@
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gridResistor(10,10, 1,1, 7,6).println();
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