Initial data commit

Task/Resistor-mesh/JavaScript/resistor-mesh.js

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+// Vector addition, scalar multiplication & dot product:
+const add = (u, v) => {let i = u.length; while(i--) u[i] += v[i]; return u;};
+const sub = (u, v) => {let i = u.length; while(i--) u[i] -= v[i]; return u;};
+const mul = (a, u) => {let i = u.length; while(i--) u[i] *= a; return u;};
+const dot = (u, v) => {let s = 0, i = u.length; while(i--) s += u[i]*v[i]; return s;};
+
+const W = 10, H = 10, A = 11, B = 67;
+
+function getAdjacent(node){ // Adjacency lists for square grid
+  let list = [], x = node % W, y = Math.floor(node / W);
+  if (x > 0)     list.push(node - 1);
+  if (y > 0)     list.push(node - W);
+  if (x < W - 1) list.push(node + 1);
+  if (y < H - 1) list.push(node + W);
+  return list;
+}
+
+function linOp(u){ // LHS of the linear equation
+  let v = new Float64Array(W * H);
+  for(let i = 0; i < v.length; i++){
+    if ( i === A || i === B ) {
+      v[i] = u[i];
+      continue;
+    }
+    // For each node other then A, B calculate the net current flow:
+    for(let j of getAdjacent(i)){
+      v[i] += (j === A || j === B) ? u[i] : u[i] - u[j];
+    }
+  }
+  return v;
+}
+
+function getRHS(phiA = 1, phiB = 0){ // RHS of the linear equation
+  let b = new Float64Array(W * H);
+  // Setting boundary conditions (electric potential at A and B):
+  b[A] = phiA;
+  b[B] = phiB;
+  for(let j of getAdjacent(A)) b[j] = phiA;
+  for(let j of getAdjacent(B)) b[j] = phiB;
+  return b;
+}
+
+function init(phiA = 1, phiB = 0){ // initialize unknown vector
+  let u = new Float64Array(W * H);
+  u[A] = phiA;
+  u[B] = phiB;
+  return u;
+}
+
+function solveLinearSystem(err = 1e-20){ // conjugate gradient solver
+
+  let b = getRHS();
+  let u = init();
+  let r = sub(linOp(u), b);
+  let p = r;
+  let e = dot(r,r);
+
+  while(true){
+    let Ap    = linOp(p);
+    let alpha = e / dot(p, Ap);
+    u = sub(u, mul(alpha, p.slice()));
+    r = sub(linOp(u), b);
+    let e_new = dot(r,r);
+    let beta  = e_new / e;
+
+    if(e_new < err) return u;
+
+    e = e_new;
+    p = add(r, mul(beta, p));
+  }
+}
+
+function getResistance(u){
+  let curr = 0;
+  for(let j of getAdjacent(A)) curr += u[A] - u[j];
+  return 1 / curr;
+}
+
+let phi = solveLinearSystem();
+let res = getResistance(phi);
+console.log(`R = ${res} Ohm`);