Just another update
This commit is contained in:
Ingy döt Net
parent
a25938f123
commit
00a190b0a6
6591 changed files with 94363 additions and 23227 deletions
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@ -1,5 +1,6 @@
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[[image:resistor-mesh.svg]]
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Given 10 × 10 grid nodes interconnected by 1Ω resistors as shown, find the resistance between point A and B.
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Given 10 × 10 grid nodes interconnected by 1Ω resistors as shown,
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find the resistance between point A and B.
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See also [[http://xkcd.com/356/]]
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3
Task/Resistor-mesh/00META.yaml
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3
Task/Resistor-mesh/00META.yaml
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@ -0,0 +1,3 @@
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---
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category:
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- Electronics
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@ -3,42 +3,44 @@ import std.stdio, std.traits;
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enum Node.FP differenceThreshold = 1e-40;
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struct Node {
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alias real FP;
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alias FP = real;
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enum Kind : size_t { free, A, B }
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FP voltage = 0.0;
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private Kind kind = Kind.free;
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@property Kind fixed() const pure nothrow { return kind; }
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/*const*/ private Kind kind = Kind.free;
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// Remove kindGet once kind is const.
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@property Kind kindGet() const pure nothrow @nogc {return kind; }
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}
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Node.FP iter(size_t w, size_t h)(ref Node[w][h] m) pure nothrow {
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Node.FP iter(size_t w, size_t h)(ref Node[w][h] m) pure nothrow @nogc {
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static void enforceBoundaryConditions(ref Node[w][h] m)
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pure nothrow {
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pure nothrow @nogc {
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m[1][1].voltage = 1.0;
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m[6][7].voltage = -1.0;
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}
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static Node.FP calcDifference(in ref Node[w][h] m,
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ref Node[w][h] d) pure nothrow {
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ref Node[w][h] d) pure nothrow @nogc {
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Node.FP total = 0.0;
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foreach (i; 0 .. h)
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foreach (j; 0 .. w) {
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foreach (immutable i; 0 .. h) {
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foreach (immutable j; 0 .. w) {
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Node.FP v = 0.0;
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{
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size_t n = 0;
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if (i != 0) { v += m[i - 1][j].voltage; n++; }
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if (j != 0) { v += m[i][j - 1].voltage; n++; }
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if (i < h-1) { v += m[i + 1][j].voltage; n++; }
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if (j < w-1) { v += m[i][j + 1].voltage; n++; }
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if (i != 0) { v += m[i - 1][j].voltage; n++; }
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if (j != 0) { v += m[i][j - 1].voltage; n++; }
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if (i < h - 1) { v += m[i + 1][j].voltage; n++; }
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if (j < w - 1) { v += m[i][j + 1].voltage; n++; }
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v = m[i][j].voltage - v / n;
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}
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d[i][j].voltage = v;
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if (m[i][j].fixed == Node.Kind.free)
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if (m[i][j].kindGet == Node.Kind.free)
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total += v ^^ 2;
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}
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}
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return total;
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}
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@ -49,16 +51,16 @@ Node.FP iter(size_t w, size_t h)(ref Node[w][h] m) pure nothrow {
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enforceBoundaryConditions(m);
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if (calcDifference(m, difference) < differenceThreshold)
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break;
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foreach (i, const(Node[]) di; difference)
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foreach (j, ref const(Node) dij; di)
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foreach (immutable i, const di; difference)
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foreach (immutable j, const ref dij; di)
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m[i][j].voltage -= dij.voltage;
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}
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Node.FP[EnumMembers!(Node.Kind).length] cur = 0.0;
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foreach (i, const(Node[]) di; difference)
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foreach (j, ref const(Node) dij; di)
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cur[m[i][j].fixed] += dij.voltage *
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(!!i + !!j + (i < h-1) + (j < w-1));
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foreach (immutable i, const di; difference)
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foreach (immutable j, const ref dij; di)
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cur[m[i][j].kindGet] += dij.voltage *
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(!!i + !!j + (i < h-1) + (j < w-1));
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return (cur[Node.Kind.A] - cur[Node.Kind.B]) / 2.0;
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}
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@ -72,5 +74,5 @@ void main() {
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mesh[1][1] = Node( 1.0, Node.Kind.A);
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mesh[6][7] = Node(-1.0, Node.Kind.B);
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writefln("R = %.19f", 2 / iter(mesh));
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writefln("R = %.19f", 2 / mesh.iter);
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}
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40
Task/Resistor-mesh/Octave/resistor-mesh.octave
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40
Task/Resistor-mesh/Octave/resistor-mesh.octave
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@ -0,0 +1,40 @@
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N = 10;
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NN = N*N;
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G = sparse(NN, NN);
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node = 0;
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for row=1:N;
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for col=1:N;
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node++;
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if row > 1
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G(node, node)++;
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G(node, node - N) = -1;
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end
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if row < N;
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G(node, node)++;
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G(node, node + N) = -1;
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end
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if col > 1
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G(node, node)++;
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G(node, node - 1) = -1;
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end
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if col < N;
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G(node, node)++;
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G(node, node + 1) = -1;
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end
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end
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end
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current = sparse(NN, 1);
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Ar = 2; Ac = 2; A = Ac + N*( Ar - 1 );
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Br = 7; Bc = 8; B = Bc + N*( Br - 1 );
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current( A ) = -1;
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current( B ) = +1;
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voltage = G \ current;
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VA = voltage( A );
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VB = voltage( B );
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full( abs( VA - VB ) )
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71
Task/Resistor-mesh/Python/resistor-mesh-2.py
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71
Task/Resistor-mesh/Python/resistor-mesh-2.py
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@ -0,0 +1,71 @@
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import sys, copy
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from fractions import Fraction
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def gauss(a, b):
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n, p = len(a), len(a[0])
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for i in range(n):
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t = abs(a[i][i])
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k = i
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for j in range(i + 1, n):
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if abs(a[j][i]) > t:
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t = abs(a[j][i])
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k = j
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if k != i:
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for j in range(i, n):
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a[i][j], a[k][j] = a[k][j], a[i][j]
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b[i], b[k] = b[k], b[i]
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t = 1/a[i][i]
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for j in range(i + 1, n):
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a[i][j] *= t
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b[i] *= t
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for j in range(i + 1, n):
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t = a[j][i]
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for k in range(i + 1, n):
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a[j][k] -= t*a[i][k]
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b[j] -= t * b[i]
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for i in range(n - 1, -1, -1):
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for j in range(i):
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b[j] -= a[j][i]*b[i]
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return b
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def resistor_grid(p, q, ai, aj, bi, bj):
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n = p*q
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I = Fraction(1, 1)
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v = [0*I]*n
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a = [copy.copy(v) for i in range(n)]
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for i in range(p):
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for j in range(q):
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k = i*q + j
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if i == ai and j == aj:
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a[k][k] = I
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else:
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c = 0
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if i + 1 < p:
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c += 1
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a[k][k + q] = -1
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if i >= 1:
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c += 1
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a[k][k - q] = -1
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if j + 1 < q:
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c += 1
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a[k][k + 1] = -1
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if j >= 1:
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c += 1
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a[k][k - 1] = -1
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a[k][k] = c*I
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b = [0*I]*n
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k = bi*q + bj
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b[k] = 1
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return gauss(a, b)[k]
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def main(arg):
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r = resistor_grid(int(arg[0]), int(arg[1]), int(arg[2]), int(arg[3]), int(arg[4]), int(arg[5]))
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print(r)
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print(float(r))
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main(sys.argv[1:])
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# Output:
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# python grid.py 10 10 1 1 7 6
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# 455859137025721/283319837425200
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# 1.6089912417307297
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@ -1,36 +1,36 @@
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/*REXX pgm calculates resistance between any 2 points on a resister grid*/
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numeric digits 20 /*use moderate digits (precision)*/
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minVal=(1'e-'||(digits()*2)) / 1 /*calculate the threshold min val*/
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minVal = (1'e-' || (digits()*2)) / 1 /*calculate the threshold min val*/
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if 1=='f1'x then ohms = 'ohms' /*EBCDIC machine? Use 'ohms'. */
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else ohms = 'ea'x /* ASCII machine? Use Greek Ω.*/
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parse arg wide high Arow Acol Brow Bcol .
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say 'minVal = ' format(minVal,,,,0) ; say
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say 'resistor mesh is of size: ' wide "wide, " high 'high.' ; say
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parse arg high wide Arow Acol Brow Bcol .
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say 'minVal = ' format(minVal,,,,0) ; say
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say 'resistor mesh is of size: ' 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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@.=0; cell.=1
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do until $ <= minVal; $=0; 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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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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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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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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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 done.*/
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/*──────────────────────────────────sides subroutine────────────────────*/
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sides: parse arg i,j; !=0; if i\==1 & i\==high then !=!+2
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70
Task/Resistor-mesh/Racket/resistor-mesh.rkt
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70
Task/Resistor-mesh/Racket/resistor-mesh.rkt
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@ -0,0 +1,70 @@
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#lang racket
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(require racket/flonum)
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(define-syntax-rule (fi c t f) (if c f t))
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(define (neighbours w h)
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(define h-1 (sub1 h))
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(define w-1 (sub1 w))
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(lambda (i j)
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(+ (fi (zero? i) 1 0)
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(fi (zero? j) 1 0)
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(if (< i h-1) 1 0)
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(if (< j w-1) 1 0))))
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(define (mesh-R probes w h)
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(define h-1 (sub1 h))
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(define w-1 (sub1 w))
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(define-syntax-rule (v2ref v r c) ; 2D vector ref
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(flvector-ref v (+ (* r w) c)))
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(define w*h (* w h))
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(define (alloc2 (v 0.))
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(make-flvector w*h v))
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(define nghbrs (neighbours w h))
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(match-define `((,fix+r ,fix+c) (,fix-r ,fix-c)) probes)
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(define fix+idx (+ fix+c (* fix+r w)))
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(define fix-idx (+ fix-c (* fix-r w)))
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(define fix-val
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(match-lambda**
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[((== fix+idx) _) 1.]
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[((== fix-idx) _) -1.]
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[(_ v) v]))
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(define (calc-diff m)
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(define d
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(for*/flvector #:length w*h ((i (in-range h)) (j (in-range w)))
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(define v
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(+ (fi (zero? i) (v2ref m (- i 1) j) 0)
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(fi (zero? j) (v2ref m i (- j 1)) 0)
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(if (< i h-1) (v2ref m (+ i 1) j) 0)
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(if (< j w-1) (v2ref m i (+ j 1)) 0)))
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(- (v2ref m i j) (/ v (nghbrs i j)))))
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(define Δ
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(for/sum ((i (in-naturals)) (d.v (in-flvector d)) #:when (= (fix-val i 0.) 0.))
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(sqr d.v)))
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(values d Δ))
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(define final-d
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(let loop ((m (alloc2)) (d (alloc2)))
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(define m+ ; do this first will get the boundaries on
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(for/flvector #:length w*h ((j (in-naturals)) (m.v (in-flvector m)) (d.v (in-flvector d)))
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(fix-val j (- m.v d.v))))
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(define-values (d- Δ) (calc-diff m+))
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(if (< Δ 1e-24) d (loop m+ d-))))
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(/ 2
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(/ (- (* (v2ref final-d fix+r fix+c) (nghbrs fix+r fix+c))
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(* (v2ref final-d fix-r fix-c) (nghbrs fix-r fix-c)))
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2)))
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(module+ main
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(printf "R = ~a~%" (mesh-R '((1 1) (6 7)) 10 10)))
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@ -1,7 +1,7 @@
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package require Tcl 8.6; # Or 8.5 with the TclOO package
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# This code is structured as a class with a little trivial DSL parser so it is
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# easy to change what problem is being worked on.
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# This code is structured as a class with a little trivial DSL parser
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# so it is easy to change what problem is being worked on.
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oo::class create ResistorMesh {
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variable forcePoints V fixed w h
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