Task: Resistor mesh







Python: DIFF_THRESHOLD = 1e-40

class Fixed:
    FREE = 0
    A = 1
    B = 2

class Node:
    __slots__ = ["voltage", "fixed"]
    def __init__(self, v=0.0, f=Fixed.FREE):
        self.voltage = v
        self.fixed = f

def set_boundary(m):
    m[1][1] = Node( 1.0, Fixed.A)
    m[6][7] = Node(-1.0, Fixed.B)

def calc_difference(m, d):
    h = len(m)
    w = len(m[0])
    total = 0.0

    for i in xrange(h):
        for j in xrange(w):
            v = 0.0
            n = 0
            if i != 0:  v += m[i-1][j].voltage; n += 1
            if j != 0:  v += m[i][j-1].voltage; n += 1
            if i < h-1: v += m[i+1][j].voltage; n += 1
            if j < w-1: v += m[i][j+1].voltage; n += 1
            v = m[i][j].voltage - v / n

            d[i][j].voltage = v
            if m[i][j].fixed == Fixed.FREE:
                total += v ** 2
    return total

def iter(m):
    h = len(m)
    w = len(m[0])
    difference = [[Node() for j in xrange(w)] for i in xrange(h)]

    while True:
        set_boundary(m) 
        if calc_difference(m, difference) < DIFF_THRESHOLD:
            break
        for i, di in enumerate(difference):
            for j, dij in enumerate(di):
                m[i][j].voltage -= dij.voltage

    cur = [0.0] * 3
    for i, di in enumerate(difference):
        for j, dij in enumerate(di):
            cur[m[i][j].fixed] += (dij.voltage *
                (bool(i) + bool(j) + (i < h-1) + (j < w-1)))

    return (cur[Fixed.A] - cur[Fixed.B]) / 2.0

def main():
    w = h = 10
    mesh = [[Node() for j in xrange(w)] for i in xrange(h)]
    print "R = %.16f" % (2 / iter(mesh))

main()





Ada: with Ada.Text_IO; use Ada.Text_IO;
procedure ResistMesh is
   H, W : constant Positive := 10;
   rowA, colA : constant Positive := 2; 
   rowB : constant Positive := 7;
   colB : constant Positive := 8;

   type Ntype is (A, B, Free);
   type Vtype is digits 15;
   type Node is record
      volt : Vtype := 0.0;
      name : Ntype := Free;
   end record;
   type NodeMesh is array (Positive range <>, Positive range <>) of Node;
   package IIO is new Ada.Text_IO.Float_IO (Vtype);
   mesh, dmesh : NodeMesh (1 .. H, 1 .. W);
   curA, curB, diff : Vtype;

   procedure set_AB (mesh : in out NodeMesh) is begin
      mesh (rowA, colA).volt :=  1.0;  mesh (rowA, colA).name := A;
      mesh (rowB, colB).volt := -1.0;  mesh (rowB, colB).name := B;
   end set_AB;

   function sides (i : Positive; j : Positive) return Vtype is
      s : Integer := 0;
   begin
      if i /= 1 and i /= H then s := s + 2; else s := s + 1; end if;
      if j /= 1 and j /= W then s := s + 2; else s := s + 1; end if;
      return Vtype (s);
   end sides;

   procedure calc_diff (mesh : NodeMesh; dmesh : out NodeMesh;
      total : out Vtype)  is
      n : Natural;
      v : Vtype := 0.0;
   begin
      total := 0.0;
      for i in Positive range 1 .. H loop
         for j in Positive range 1 .. W loop
            n := 0;    v := 0.0;
            if  i /= 1 then v := v + mesh (i - 1, j).volt; n := n + 1; end if;
            if j /= 1 then  v := v + mesh (i, j - 1).volt; n := n + 1; end if;
            if i < H then v := v + mesh (i + 1, j).volt; n := n + 1; end if;
            if j < W then v := v + mesh (i, j + 1).volt; n := n + 1; end if;
            v := mesh (i, j).volt - v / Vtype (n);
            dmesh (i, j).volt := v;
            if mesh (i, j).name = Free then total := total + v ** 2; end if;
         end loop;
      end loop;
   end calc_diff;

begin

   loop
      set_AB (mesh);
      calc_diff (mesh, dmesh, diff);
      exit when diff < 1.0e-40;
      for i in Positive range 1 .. H loop
         for j in Positive range 1 .. W loop
            mesh (i, j).volt := mesh (i, j).volt - dmesh (i, j).volt;
         end loop;
      end loop;
   end loop;

   curA := dmesh (rowA, colA).volt * sides (rowA, colA);
   curB := dmesh (rowB, colB).volt * sides (rowB, colB);
   diff := 4.0 / (curA - curB);
   IIO.Put (diff, Exp => 0); New_Line;
end ResistMesh;