Initial data commit

Task/Resistor-mesh/Python/resistor-mesh-1.py

@@ -0,0 +1,64 @@
+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) # Enforce boundary conditions.
+        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()

Task/Resistor-mesh/Python/resistor-mesh-2.py

@@ -0,0 +1,71 @@
+import sys, copy
+from fractions import Fraction
+
+def gauss(a, b):
+    n, p = len(a), len(a[0])
+    for i in range(n):
+        t = abs(a[i][i])
+        k = i
+        for j in range(i + 1, n):
+            if abs(a[j][i]) > t:
+                t = abs(a[j][i])
+                k = j
+        if k != i:
+            for j in range(i, n):
+                a[i][j], a[k][j] = a[k][j], a[i][j]
+            b[i], b[k] = b[k], b[i]
+        t = 1/a[i][i]
+        for j in range(i + 1, n):
+            a[i][j] *= t
+        b[i] *= t
+        for j in range(i + 1, n):
+            t = a[j][i]
+            for k in range(i + 1, n):
+                a[j][k] -= t*a[i][k]
+            b[j] -= t * b[i]
+    for i in range(n - 1, -1, -1):
+        for j in range(i):
+            b[j] -= a[j][i]*b[i]
+    return b
+
+def resistor_grid(p, q, ai, aj, bi, bj):
+    n = p*q
+    I = Fraction(1, 1)
+    v = [0*I]*n
+    a = [copy.copy(v) for i in range(n)]
+    for i in range(p):
+        for j in range(q):
+            k = i*q + j
+            if i == ai and j == aj:
+                a[k][k] = I
+            else:
+                c = 0
+                if i + 1 < p:
+                    c += 1
+                    a[k][k + q] = -1
+                if i >= 1:
+                    c += 1
+                    a[k][k - q] = -1
+                if j + 1 < q:
+                    c += 1
+                    a[k][k + 1] = -1
+                if j >= 1:
+                    c += 1
+                    a[k][k - 1] = -1
+                a[k][k] = c*I
+    b = [0*I]*n
+    k = bi*q + bj
+    b[k] = 1
+    return gauss(a, b)[k]
+
+def main(arg):
+    r = resistor_grid(int(arg[0]), int(arg[1]), int(arg[2]), int(arg[3]), int(arg[4]), int(arg[5]))
+    print(r)
+    print(float(r))
+
+main(sys.argv[1:])
+
+# Output:
+# python grid.py 10 10 1 1 7 6
+# 455859137025721/283319837425200
+# 1.6089912417307297